Operational Flexibility in Electric Power Systems

DISS. ETH NO. 21882

A thesis submitted to attain the degree of

DOCTOR OF SCIENCES of ETH ZURICH (Dr. sc. ETH Zurich)

presented by

ANDREAS ULBIG

Dipl.-Ing. (Technische Kybernetik), Universität Stuttgart Diplôme de Master recherche, Supélec

born on 16 September 1981 in Halle (Saale), Germany citizen of Germany

accepted on the recommendation of

Prof. Dr. G¨oran Andersson, examiner Prof. Dr. David J. Hill, co-examiner Prof. Dr. Martin Greiner, co-examiner

2014 © Andreas Ulbig, Zurich, Switzerland, 2014

ETH Zurich¨ EEH – Power Systems Laboratory Physikstrasse 3 8092 Zurich Switzerland www.eeh.ee.ethz.ch/psl

DOI: 10.3929/ethz-a-010337152 Fur¨ meine Familie. Pour ma famille. For my family.

Preface

This doctoral thesis was written during my time as a PhD student at the Power Systems Laboratory of ETH Zurich¨ from October 2008 to March 2014. First, I would like to express my sincere gratitude to Professor Göran Andersson for giving me the opportunity to pursue my PhD studies at the Power Systems Laboratory. Through his support, guidance and, certainly, the granted freedom, he enabled me to follow my own ideas and interests in my research work. I appreciate his generally positive spirit and open-minded attitude towards new research ideas, collabora- tion efforts, and projects throughout the duration of my PhD studies. I would like to sincerely thank Professor David J. Hill from Hong Kong University and Professor Martin Greiner from Aarhus University, Den- mark for their kind willingness to co-examine this doctoral thesis and for the inspiring discussions that we had at various occasions before, certainly during, and finally after my PhD defense. Their long lasting passion for the power & control field, respectively the power & energy field of research is an inspiration. I would like to thank Professor Ning Lu and Dr. Yuri Makarov for hosting my at the Advanced Power & Energy Systems Group at Pacific Northwest National Laboratory (PNNL) in the spring of 2012 and for giving me the opportunity to share my experience of the European TSOs and how they cope with variable Renewable Energy Sources with a North-American TSO community. I would like to thank Professor Duncan Callaway for the opportunity to visit him and his group at University of California, Berkeley in the summer of 2012. I really appreciated the inspiring coffee discussions with him and his attitude to always aspire to push out existing research boundaries. My gratitude also goes to all the people I met in Berkeley and the fun time we spent on-campus as well as outside the campus.

v vi Preface

Several master students completed their semester thesis or master thesis under my supervision. I would like to acknowledge their motivation, hard work, and often enough also novel research results and insights, part of which contributed to the research presented in this thesis. There are numerous, almost countless, colleagues and friends that I worked with during my time at ETH Zurich¨ at large and at the Power Systems Laboratory in particular. Together we worked, sometimes we struggled but most often we succeeded in our endeavors – we certainly spend together an important and deﬁning time period for all of us. I would like to thank the entire group for the nice, friendly atmosphere and the great fun we had inside and outside the ETL building. Last but not least I am deeply grateful to my family for their tremendous amount of support and compassion throughout these years.

Andreas Ulbig Zurich, March 2014 Abstract

This doctoral thesis deals with operational flexibility in power system operation and analyzes its role for mitigating operation disturbances and improving the grid integration of Renewable Energy Sources (RES). The topic of this thesis is motivated by the increasing challenges for power system operation, mainly due to rising energy shares from variable RES but also caused by impacts of power market liberalization, notably higher grid utilization. Operational flexibility is an important property of electric power systems, especially for the transition of existing power systems, many of them based on fossil fuels, to power systems effectively accommodating high shares of variable RES. Availability of sufficient operational flexibility is a necessary precondition for the grid integration of large energy shares from variable RES, notably wind turbines and Photovoltaic (PV) units. The provision of operational flexibility can be enabled and improved by introducing more sensing, i.e. sensor elements, computation, e.g. in the form of operation optimization schemes, as well as control, i.e. actuators, into power system operation. Improving controllability & observability of power system processes will help to improve power system operation and management, i.e. allowing a more secure, efficient and stable operation. The role of operational flexibility for power system operation is discussed and analyzed from different angles, ranging from power system modeling approaches to analytic approaches inspired by well-known control theory concepts to qualitative and quantitative simulation-based assessments. A supplementary idea that is discussed is the concept of control-based grid adaptation as an alternative to conventional hardware-based grid adaptation for the operational challenges related to large-scale RES deployment. This allows a cost-saving trade-off between costs for computation and communication versus conventional grid investment.

vii viii Abstract

The doctoral thesis is structured in three parts, each part addressing separate topic streams.

Part I – New Challenges & Opportunities in Power Systems An overview of paradigm change in power system operation is given. Some of the important new challenges to power system operation and control, mainly related to the large-scale deployment of variable RES units but also to increasing power market activity and rising electricity demand in conjunction with only limited grid reinforcement at the same time, are illustrated. A discussion of opportunities for mitigating these operational challenges concludes this part.

Part II – Modeling Frameworks for Power & Energy Systems An overview of established modeling frameworks for power & energy systems is given. Notably, the Network-Preserving Model Framework and the Energy Hub Concept are presented and the motivation for complementary modeling frameworks is discussed. The Power Nodes Modeling Framework is presented. New contributions and insights to this modeling approach conclude this part.

Part III – Modeling & Analysis of Operational Flexibility A discussion of operational flexibility in power systems, necessary flexibility metrics and modeling approaches, both for individual units as well as for aggregations (pools) of diverse power system units introduces the topic. Then an analysis of operational flexibility in power systems is presented. First, a purely qualitative analysis of the flexibility of individual power system units and small pools is conducted. Second, a more quantitative analysis of the operational flexibility of the German, Swiss and interconnected European power system is conducted. Kurzfassung

Diese Dissertation befasst sich mit der Thematik der operativen Fle- xibilität im Betrieb elektrischer Energiesysteme und analysiert deren Rolle fur¨ die Dämpfung von Betriebsstörungen und die Verbesserung der Netzintegration von fluktuierend-einspeisenden Erneuerbaren Ener- gien (EE). Das Doktoratsthema wird mit der Zunahme an Herausfor- derungen im Stromnetzbetrieb begrundet.¨ Diese werden hauptsächlich durch den steigenden EE-Anteil im Strommix aber auch durch die Aus- wirkungen der Liberalisierung des Stromsektors, vor allem der höheren Netzauslastung, verursacht.

Operative Flexibilität ist eine wichtige Eigenschaft elektrischer Ener- giesysteme, insbesondere fur¨ die Transition der existierenden Energie- systeme, meist basierend auf fossilen Brennstoffen, zu Energiesystemen die hohe Anteile fluktuierender EE effektiv aufnehmen können. Die Verfugbarkeit¨ ausreichender operativer Flexibilität ist eine notwendige Voraussetzung fur¨ die Netzintegration grosser Leistungsanteile von fluktuierenden EE, insbesondere von Windturbinen und Photovoltaik- Anlagen. Die Bereitstellung operativer Flexibilität kann durch die Ein- fuhrung¨ von mehr Sensorik, sprich Sensorelementen, Rechenleistung, z.B. in Form betrieblicher Optimierungsmethoden, sowie Regelungs- eingriffen, durch entsprechende Aktuatoren, im Netzbetrieb ermöglicht und/oder verbessert werden. Eine grössere Steuerbarkeit und Beobacht- barkeit von Stromnetzprozessen wird dazu beitragen, Netzbetrieb und -management zu verbessern, damit dieses immer sicher, effizient und stabil betrieben werden kann. Die Rolle operativer Flexibilität fur¨ den Netzbetrieb wird von verschiedenen Blickwinkeln aus diskutiert und analysiert. Diese reichen von Modellierungsansätzen fur¨ Energiesysteme zu regelungstheorie-inspirierten analytischen Ansätzen hin zu simulati- onsbasierten qualitativen und quantitativen Analysen.

ix x Kurzfassung

Eine in der Arbeit diskutierte Idee ist das Konzept einer kybernetischen, sprich regelungstechnik-basierten, Stromnetzanpassung als Alternative zur herk¨ommlichen physikalisch-basierten Stromnetzanpassung fur¨ die operativen Herausforderungen des EE-Ausbaus. Dies erlaubt einen kos- tensparenden Kompromiss zwischen den Kosten fur¨ ben¨otigte Rechen- leistung & Kommunikation und denen fur¨ konventionellen Netzausbau. Die Dissertation ist in drei Teile strukturiert, die sich mit unterschied- lichen Themenfeldern befassen.

Teil I – Neue Denkansätze fur¨ Elektrische Energiesysteme Eine Ubersicht¨ zum Paradigmenwechsel im Netzbetrieb wird vorgestellt. Einige der wichtigsten neuen Herausforderungen an Netzbe- trieb & -regelung, verursacht hauptsächlich durch den umfangreichen EE-Ausbau aber auch durch zunehmende Strommarktaktivität und steigenden Stromverbrauch bei gleichzeitig begrenzten Netzausbau, werden dargestellt. Eine Diskussion zu Lösungsmöglichkeiten fur¨ diese betrieblichen Herausforderungen beendet diesen Teil.

Teil II – Modellierungskonzepte fur¨ Strom- & Energiesysteme Eine Ubersicht¨ uber¨ etablierte Modellierungsmethoden fur¨ Strom & Energiesysteme wird vorgestellt. Insbesondere das sogenannte strukturerhaltende Modell eines elektrischen Energiesystems (Network Preserving Model) als auch das Energy Hub Modellierungskon- zept werden vorgestellt. Die Motivation fur¨ hierzu komplement¨are Modellierungsmethoden wird diskutiert. Das Power Nodes Modellie- rungskonzept wird vorgestellt. Die Diskussion neuer konzeptioneller Beitr¨age and Erkenntnisse hierzu beenden diesen Teil.

Teil III – Modellierung & Analyse Operativer Flexibilität Das Konzept operativer Flexibilität in Energiesystemen als auch dafur¨ notwendige Flexibilitätsmetriken und Modellierungsansätze, sowohl fur¨ einzelne Kraftwerks-, Speicher- oder Lasteinheiten als auch fur¨ Aggrega- tionen (Pools) aus verschiedenen Einheiten werden vorgestellt. Darauf folgt eine Analyse der operativen Flexibilität in elektrischen Energiesys- temen. Zuerst wird eine rein qualitative Analyse der operativen Flexibi- lität einzelner Stromsystemeinheiten und kleiner Pools durchgefuhrt.¨ Es folgt eine quantitative Flexibiltiätsanalyse des deutschen und schweize- rischen Stromnetzes als auch des europäischen Verbundstromnetzes. Contents

Abstract ...... vii Kurzfassung ...... ix List of Acronyms ...... xix List of Figures ...... xxiv List of Tables ...... xxv

1 Introduction1 1.1 Background and Motivation ...... 1 1.2 Contributions ...... 2 1.3 Outline of the Thesis ...... 3 1.4 List of Publications ...... 4

I Paradigm Change, New Challenges & Oppor- tunities in Power Systems9

2 Paradigm Change in Power System Operation 11 2.1 Introduction ...... 11 2.2 Power System Control, Operation and Planning over Time 14 2.2.1 Frequency Control and Power Dispatch ...... 16 2.2.2 Modeling Inertial Response ...... 20 2.2.3 Aggregated Swing Equation Model ...... 21 2.3 Trends in Energy and Power Systems ...... 22 2.3.1 Technological Trends ...... 22 2.3.2 Economic Trends ...... 27 2.4 Trends in Information and Communication Technology ... 31 2.4.1 Technological Trends ...... 31 2.4.2 Economic Trends ...... 32 2.5 Paradigm Change ...... 34 2.5.1 Changes in the German Power System ...... 38

xi xii CONTENTS

3 New Challenges in Power Systems Operation 43 3.1 Classical Challenges ...... 43 3.2 New Technical Challenges...... 46 3.2.1 RES Integration ...... 46 3.2.2 Demand Response & Aggregators ...... 55 3.2.3 Power Market Activity & Liberalization ...... 58 3.3 New Economic Challenges ...... 61 3.3.1 RES Integration ...... 61 3.3.2 Demand Response & Aggregators ...... 61 3.3.3 Power Market Activity & Liberalization ...... 62 3.4 Situation in Germany ...... 64 3.4.1 Technical Challenges...... 64 3.4.2 Economic Challenges ...... 70 3.5 Need for Operational Flexibility in Power Systems ...... 73

4 Opportunities in Power Systems Operation 75 4.1 Introduction ...... 75 4.2 Operational Flexibility in Power Systems ...... 78 4.2.1 Role of Operational Flexibility ...... 78 4.2.2 Sources of Operational Flexibility ...... 79 4.2.3 Classiﬁcation of Operational Flexibility ...... 80 4.3 Controllability & Observability in Power Systems ...... 84 4.3.1 Traditional Controllability & Observability in Power Systems ...... 84 4.3.2 Emerging Controllability & Observability in Power Systems ...... 84 4.3.3 Actuators & Sensors in Power Systems ...... 89 4.4 Hardware-based versus Control-based Grid Adaptation ... 93

II Modeling Frameworks for Power & Energy Systems 95

5 Modeling Frameworks for Power & Energy Systems 97 5.1 Motivation for Modeling and Simulation of Power & En- ergy Systems ...... 97 5.2 Modeling of Electric Power Systems ...... 98 5.2.1 Review of Modeling Frameworks for Generation, Storage and Load Units ...... 98 5.2.2 Power System Modeling along Time-Scales ...... 102 CONTENTS xiii

5.2.3 Limitations of Classical Power System Modeling ..... 102 5.3 Modeling of Energy Systems ...... 104 5.3.1 Energy Hub Modeling Framework ...... 104 5.4 Motivation for new Power & Energy Modeling Frameworks108 5.4.1 Modeling of Background Processes ...... 108 5.4.2 Control-based Categorization of Power System Units ...... 109

6 Power Nodes Modeling Framework 113 6.1 Introduction ...... 113 6.2 Deﬁnition of Power Nodes Modeling Framework ...... 115 6.2.1 Domain Models ...... 115 6.2.2 Model of a Single Power Node...... 117 6.2.3 Mapping from Power Nodes to Grid Domain ...... 120 6.2.4 DC Grid Model with Power Nodes ...... 121 6.2.5 Characterization of Unit Properties...... 122 6.2.6 Unit Properties ...... 122 6.2.7 Performance Evaluation via System-Level Power & Energy Balances ...... 124 6.3 Power Nodes Modeling Examples ...... 127 6.3.1 Combustible-fueled Thermal Generation Units ...... 127 6.3.2 Variably Producing Generation Units ...... 128 6.3.3 Hydro-based Generation Units ...... 129 6.3.4 Load Demand Units ...... 135 6.3.5 Power Systems Units with Schedule Flexibility ...... 137 6.4 Functional Model Representation ...... 139 6.4.1 Comparison of Functionality of Diverse Power System Unit Types...... 141 6.5 Power Nodes Modeling Extensions...... 143 6.5.1 Modeling of Non-linear Aspects ...... 143 6.5.2 Power Nodes as Descriptor Systems ...... 144 6.6 Modeling Controllability & Observability Properties of Power System Units ...... 145 6.6.1 Decomposition into Controllable & Observable Power Flows and Energy States...... 145 6.6.2 Classiﬁcation of Power System Controllability ..... 147 6.6.3 Role of Storage Functionality for Controllability ..... 153 6.7 Connections between Energy Hub and Power Nodes Modeling Frameworks ...... 154 xiv CONTENTS

6.7.1 Transformation between Energy Hub and Power Node Models...... 154 6.7.2 Power Nodes Framework as a Generalization of Energy Hubs...... 156 6.8 Connections between Power Nodes and Network Preserv- ing Model (NPM) Frameworks...... 157

III Modeling & Analysis of Operational Flexi- bility in Electric Power Systems 159

7 Operational Flexibility in Electric Power Systems 161 7.1 Introduction ...... 161 7.2 Sources of Operational Flexibility ...... 162 7.3 Deﬁnitions of Operational Flexibility...... 164 7.3.1 Metrics for Operational Flexibility ...... 164 7.4 Modeling of Operational Flexibility ...... 168 7.4.1 Quantiﬁcation of Operational Flexibility ...... 168

8 Qualitative Simulation Studies 171 8.1 Introduction ...... 171 8.2 Qualitative Analysis of Operational Flexibility ...... 172 8.2.1 Needed Operational Flexibility...... 172 8.2.2 Available Operational Flexibility ...... 174 8.2.3 Needed Flexibility versus Available Flexibility ..... 177 8.2.4 Aggregation of Operational Flexibility ...... 178 8.3 Analyzing Operational Flexibility ...... 179 8.3.1 Quantiﬁcation of Operational Flexibility ...... 179 8.3.2 Visualization of Operational Flexibility ...... 181 8.3.3 Aggregation of Operational Flexibility ...... 185 8.3.4 Available Operational Flexibility versus Needed Operational Flexibility ...... 187 8.4 Applications of Flexibility Analysis Methods...... 190

9 Quantitative Simulation Studies 193 9.1 Introduction ...... 193 9.2 Power Nodes Simulator Platform...... 194 9.3 Power Dispatch Problem ...... 195 9.3.1 Introduction ...... 195 9.3.2 Predictive Power Dispatch Scheme ...... 196 CONTENTS xv

9.4 Simulation Studies of Various Power System Cases ...... 206 9.4.1 Germany...... 206 9.4.2 Switzerland ...... 214 9.4.3 Interconnected European Power System ...... 219 9.5 Obtaining Operational Flexibility from Dynamic Line Rating ...... 224 9.5.1 Motivation for Dynamic Line Rating ...... 224 9.5.2 Dynamic Line Rating Modeling ...... 224

10 Summary & Conclusion 231

Bibliography 232

Curriculum Vitae 253

List of Acronyms

AC Alternating Current AMI Automatic Metering Infrastructure AMS Asset Management System AS Ancillary Services ASE Aggregated Swing Equation BESS Battery Energy Storage System BMS Business Management System CAES Compressed Air Energy Storage CCGT Combined Cycle Gas Turbine CCS Carbon, Capture and Storage CE Continental European CHP Combined Heat and Power Plant CIGRE´ Conseil International des Grands Reseaux Electriques´ COI Center Of Inertia CSP Concentrating Solar Power DAE Diﬀerential Algebraic Equations DC Direct Current DG Distributed Generation DLR Dynamic Line Rating DMS Distribution Management System DR Demand Response DSM Demand-Side Management

xvii xviii List of Acronyms

DSO Distribution System Operator DSP Demand-Side Participation DSS Descriptor State Space ED Economic Dispatch EEG Erneuerbare-Energien-Gesetz EEX European Energy Exchange EMS Energy Management System ENTSO-E European Network of Transmission System Operators for Electricity EPEX European Power Exchange EV Electric Vehicle FACTS Flexible AC Transmission System FERC Federal Energy Regulatory Commission FIT Feed-In Tariﬀ HP Heat Pump HSL Hydro Storage Lake HV High Voltage HVAC Heating, Ventilation, and Air Conditioning ICE Internal Combustion Engine ICT Information & Communication Technology IEA International Energy Agency IED Intelligent Electronic Device IEEE Institute of Electrical and Electronics Engineers LMI Linear Matrix Inequalities LTI Linear Time-Invariant MPC Model Predictive Control NIS Network Information System NLR Nominal Line Rating NPM Network-Preserving Model NREAP National Renewable Energy Action Plan NTC Net Transfer Capacities List of Acronyms xix

PHEV Plug-in Hybrid Electric Vehicles PHS Pumped Hydro Storage PJM Pennsylvania–New Jersey–Maryland Interconnection PMU Phasor Measurement Unit PSHP Pumped Storage Hydro Plant PST Phase-Shifting Transformer PURPA Public Utility Regulatory Policies Act PV Photovoltaic PWA Piece-wise Affine RD Royal Decree REE Red Eléctrica España RES Renewable Energy Sources ROR Run-Of-River Hydro RMS Root Mean Square RPS Renewable Portfolio Standards RTE Réseau de Transport d’Electricité´ SATW Schweizerische Akademie der Technischen Wissenschaften SCADA Supervisory Control And Data Acquisition SOC State-of-Charge T&D Transmission and Distribution TSO Transmission System Operator VPP Virtual Power Plants WAMPAC Wide-Area Monitoring, Protection And Control List of Figures

2.1 Relevant Time-Scales of Electric Power Systems ...... 12 2.2 Geographical Scope of Synchronous ENTSO-E CE Grid .. 12 2.3 Diagram of an Electric Power System...... 13 2.4 Grid Operation Hierarchy ...... 14 2.5 ENTSO-E Nested Frequency Control Loops...... 18 2.6 ENTSO-E Frequency Control Categories...... 19 2.7 Wind Power Deployment Worldwide ...... 24 2.8 PV Power Deployment Worldwide ...... 25 2.9 Battery Energy Densities...... 26 2.10 Cross-Border Power Flows in Europe ...... 27 2.11 Industrial Energy Prices ...... 28 2.12 European Power Capital Cost Index ...... 29 2.13 Cost Curves of Wind Turbines & PV ...... 30 2.14 EV Battery Cost Estimates...... 30 2.15 Exponential Laws in ICT – Moore’s Law ...... 32 2.16 Exponential Cost Trends for ICT ...... 33 2.17 Traditional Categorization of Power System Processes..... 34 2.18 Contemporary Categorization of Power System Processes 36 2.19 Evolution of RES Deployment in Germany 1990–2017..... 39 2.20 Evolution of Day-Ahead Power Market Shares...... 42

3.1 A Classiﬁcation of Power System Instabilities...... 44 3.2 Range of Relevant Time-Scales for Renewable Energy Sources (RES) Power Feed-In ...... 46 3.3 Range of Relevant Time-Scales for Real-Time Operation of Electric Power Systems...... 47 3.4 Renewable Energy Sources (RES) Integration Challenges on Diﬀerent Time-Scales ...... 49 3.5 Evolution of Forecast Error of RES Power Feed-In ...... 50 3.6 Improvement of Wind Forecast Error Grid ...... 51

xx LIST OF FIGURES xxi

3.7 Dynamic Response of ENTSO-E CE Power System to Fault Events...... 53 3.8 Concept of Price-based Demand Response ...... 56 3.9 Price-based Demand Response in France ...... 57 3.10 Deterministic Frequency Disturbances Related to Power Market Activity ...... 59 3.11 Time-Evolution of RES Forecast Error and Gate-Closure Time ...... 63 3.12 Histogram of RES Volume versus European Power Ex- change (EPEX) Day-Ahead Spot Volume ...... 64 3.13 Examples of Wind & PV Forecast Errors in the German Power System...... 65 3.14 Brut Load Demand versus Residual Load Demand...... 66 3.15 Power Dispatch Situation in German Power System...... 68 3.16 Rotational Inertia Situation in German Power System..... 69 3.17 Impact of PV Feed-In on Spot Prices ...... 71 3.18 Curtailment of RES Power Feed-In ...... 72

4.1 Sources of Operational Flexibility ...... 80 4.2 Classiﬁcation of Operational Flexibility Resources & Re- serves...... 81 4.3 Plug-in Hybrid Electric Vehicles (PHEV) Ancillary Ser- vices Availability for One Day ...... 82 4.4 Sources of Operational Flexibility in the Swiss Power Sys- tem ...... 83 4.5 Dynamic Response of ENTSO-E CE Power System to Fault Events...... 87 4.6 Communication Structure of Ancillary Service Manager .. 89 4.7 Robust Control Framework ...... 89 4.8 Minimum-Energy Control Analysis ...... 92

5.1 Illustration of Power Network Devices as Circuit Elements100 5.2 Illustration of IEEE 37 Micro-Grid ...... 101 5.3 Interaction between Power System Units and Grid in Network Preserving Modeling ...... 103 5.4 Transformation of Energy Carriers in Energy Hubs ...... 104 5.5 Transformation of Energy Carriers in Energy Hubs ...... 105 5.6 Storage Elements in Energy Hubs...... 105 5.7 Interconnected Energy Hubs ...... 107 5.8 Background Processes in Power System Operation ...... 108 xxii LIST OF FIGURES

5.9 Kalman Decomposition of State-Space Model...... 111

6.1 Illustration of the Power Nodes Three-Domain Concept... 116 6.2 Notation for a Single Power Node...... 118 6.3 Functional Representation of Generic Hydro Storage Basin131 6.4 Functional Representation of Hydro Storage Cascade ...... 133 6.5 Functional Representation of Load with Schedule Flexi- bility ...... 137 6.6 Functional Representation of Generator with Schedule Flexibility ...... 138 6.7 Functional Representation Using Power Nodes Notation .. 140 6.8 Functional Equivalence of Power System Units ...... 142 6.9 PWA-based Modeling of Non-linear Gas Turbine ...... 144 6.10 Functional Power Node Representation of Non- Controllable Load and Generator ...... 148 6.11 Functional Power Node Representation of Sheddable Load and Curtailable Generator...... 149 6.12 Functional Power Node Representation of Controllable Load and Generator ...... 149 6.13 Fully Controllable Generation Unit ...... 150 6.14 Curtailable RES Generation Unit ...... 151 6.15 Sheddable Demand Response (DR) Load Unit...... 152 6.16 Transformation between Power Node and Energy Hub (Generator) ...... 155 6.17 Transformation between Power Node and Energy Hub (Load Demand)...... 155 6.18 Storage Modeling Options for Power Node Unit Types .... 156 6.19 Connections between Power Nodes and Network Preserv- ing Model Frameworks ...... 157

7.1 Sources of Power System Flexibility ...... 163 7.2 Flexibility Metrics in Power Systems Operation ...... 165 7.3 Inter-Temporal Linking of Flexibility Metrics ...... 167 7.4 Operational Flexibility Cube ...... 170

8.1 Needed Operational Flexibility ...... 172 8.2 Brut Load Demand and Residual Load Proﬁles in Ger- many (2012) ...... 173 8.3 Needed Operational Flexibility in Germany (2012) ...... 174 8.4 Frequency-dependent Categorization of Flexibility Sources176 LIST OF FIGURES xxiii

8.5 Needed Operational Flexibility versus Available Opera- tional Flexibility...... 177 8.6 Necessary Condition for Suﬃcient Operational Flexibil- ity in a Power System ...... 178 8.7 Aggregation of Operational Flexibility ...... 179 8.8 Operational Flexibility Cube ...... 181 8.9 Time-Evolution of Available Operational Flexibility (Simpliﬁed Analysis) ...... 182 8.10 Time-Evolution of Available Operational Flexibility (Reach Analysis) ...... 184 8.11 Reached Flexibility Volume...... 185 8.12 Aggregation of Maximum Operational Flexibility of In- dividual Power System Units ...... 188 8.13 Needed versus Available Operational Flexibility...... 189

9.1 Power Nodes Simulator Platform...... 195 9.2 Operation Principle of Model Predictive Control...... 199 9.3 Comparison of Power Dispatch Performance ...... 205 9.4 Simulation Example for the German Power System ...... 207 9.5 Predictive Power Dispatch (20% wind & 10% PV Share) . 210 9.6 Predictive Power Dispatch (50% wind & 50% PV Share) . 211 9.7 Curtailed RES Power Feed-In (Status Quo) ...... 212 9.8 Curtailed RES Power Feed-In (High Energy Storage)...... 212 9.9 Storage Expansion Strategy (German Power System)...... 213 9.10 Load Demand and RES Generation Proﬁles of Swiss Power System...... 215 9.11 Exemplary Power Dispatch Result for Swiss Power System217 9.12 ETH Scenario 2050 Storage Expansion Scenarios ...... 218 9.13 Interconnected European Power System ...... 220 9.14 EU-29 Dispatch Simulations – Power Flow Patterns ...... 222 9.15 RES Curtailment as a Function of RES Energy Share ..... 223 9.16 Current Rating of Overhead Line as a Function of Am- bient Conditions...... 225 9.17 Reconstruction of Ambient Conditions for DLR ...... 226 9.18 Illustration of Germany-based Six-Node Benchmark Model227 9.19 Line Loading from Zone A (BREMEN) to Zone B (COLOGNE)...... 228 9.20 Transmission Corridor of Zone A (BREMEN) to Zone B (COLOGNE) ...... 229 xxiv LIST OF FIGURES

9.21 Predictive Dispatch and Curtailment of Feed-In/Out Curtailments for Zone A (BREMEN)...... 230 List of Tables

2.1 Speciﬁcations of German Power System (2011) ...... 41

6.1 Unit Properties Deﬁned by Power Node Constraints ...... 124

8.1 Classiﬁcation of Flexibility Sources ...... 175

xxv xxvi LIST OF TABLES Chapter 1

Introduction

This ﬁrst chapter describes the motivation for the developed methods and states the main contributions of this doctoral thesis. In addition, the thesis outline is given and the published papers are listed.

1.1 Background and Motivation

This doctoral thesis analyzes the role of operational flexibility in power systems. Operational flexibility is an important property of electric power systems. The term flexibility is widely used in the context of power systems although at times without a proper definition. The topic of this thesis is motivated by the increasing challenges for power system operation, mainly due to the rising energy shares from variable Renewable Energy Sources (RES), notably wind & PV units as well as the impacts of power market liberalization, notably the increasing grid utilization levels. The role of operational flexibility for the transition of existing power systems, many of them based on fossil fuels, to power systems effectively accommodating high shares of variable RES is widely recognized. Avail- ability of sufficient operational flexibility is a necessary precondition for the grid integration of large shares of power feed-in from variable RES, for example wind power and PV.

1 2 Chapter 1. Introduction

1.2 Contributions

The main contributions of this doctoral thesis are:

1. Presentation of technological and economic trends in the power systems and ICT sectors that are re-shaping power systems infrastructure and are effectively creating a paradigm change in power system operation. 2. Analysis of new challenges to power system operation and their causes as well as opportunities for mitigating these challenges, namely by increasing operational flexibility. 3. Necessary modeling frameworks for modeling the complex interactions of power system units and in turn allowing the quantification of operational flexibility of individual units as well as aggregations thereof, i.e. pools, are presented. The functional modeling of all power system units is accomplished using the Power Nodes Mod- eling Framework. 4. Extensions to the Power Nodes Modeling Framework and its link- age to other well-know power & energy modeling frameworks such as the well-known Network-Preserving Model (NPM) and the En- ergy Hub Concept are presented. 5. Necessary flexibility metrics for categorizing different types of operational flexibility are discussed and a new methodology that allows to quantify and visualize the technically available operational flexibility of individual power system units and power system pools are presented. 6. Qualitative analysis insights regarding operational flexibility are derived, notably regarding the limits of RES integration for a given power system with its specific flexibility properties. 7. Quantitative analysis insights are derived by means of extensive simulation studies of single as well as interconnected power systems, assessing the role that operational flexibility has for the mitigation of operational challenges, namely forced curtailment, arising from high shares of variable RES power feed-in, which cannot be grid-integrated at all times. 1.3. Outline of the Thesis 3

1.3 Outline of the Thesis

The thesis is structured in three separate parts and contains altogether ten chapters. Each part is addressing a separate topic stream, namely Power System Operation and Operational Challenges, Modeling Frame- works for Power & Energy Systems as well as Modeling and Analysis of Operational Flexibility in Power Systems. Part I – Paradigm Change, New Challenges & Opportunities in Power System Operation • Chapter 2 – Presents an overview of power system operation and technological & economical trends in power systems and ICT. Ex- plains why these trends lead to paradigm change in power systems. • Chapter 3 – Gives a brief review of old challenges and a detailed analysis of new challenges, i.e. RES, in power systems operation. • Chapter 4 – Discusses a range of opportunities in power systems operation for mitigating challenges stemming from variable RES.

Part II – Modeling Frameworks for Power & Energy Systems • Chapter 5 – Presents an overview of modeling frameworks for power & energy systems, i.e. NPMs and Energy Hubs and discusses the motivation for new ones. • Chapter 6 – Introduces the Power Nodes Modeling Framework and presents several new contributions to the framework. • Chapter 7 – Gives a deﬁnition of operational ﬂexibility and explains its importance in the context of power system operation.

Part III – Modeling & Analysis of Operational Flexibility in Electric Power Systems • Chapter 8 – Presents two qualitative approaches for assessing the operational ﬂexibility of individual units and aggregations (pools). • Chapter 9 – Presents quantitative simulation studies for large power systems, i.e. Germany, Switzerland and the European power system. Assesses RES grid integration capability and the crucial role that operational ﬂexibility has for system performance.

Chapter 10 – Concludes the thesis with a summary of discussed topics and contributions and outlines suggestions for future research work. 4 Chapter 1. Introduction

1.4 List of Publications

The following papers have been published over the course of the research work leading to this doctoral thesis. They are mostly peer-reviewed, published conference or journal contributions.

Most of these publications relate, directly or indirectly, to the main topic of this thesis, i.e. the role of Operational Flexibility in Electric Power Systems.

Peer-Reviewed Journals

1. Andreas Ulbig and G¨oran Andersson, Analyzing Operational Flexibility of Power Systems, PSCC 2014 Best Paper Selection, submitted for special issue of International Journal of Electrical Power & Energy Systems.

2. Marcus Hildmann, Andreas Ulbig and G¨oran Andersson, Revis- iting the Merit-Order Eﬀect of Renewable Energy Sources, invited submission for IEEE Transactions on Power Systems (submitted in Feb. 2014, 2nd review).

3. Michael Koller, Theodor S. Borsche, Andreas Ulbig and G¨oran Andersson, Review of Grid Applications with the Zurich 1 MW Battery Energy Storage System, invited submission to Electric Power Systems Research (EPSR), published Dec. 2014.

4. Kai Heussen, Stephan Koch, Andreas Ulbig and G¨oran An- dersson, Uniﬁed System-Level Modeling of Intermittent Renewable Energy Sources and Energy Storage for Power System Operation, IEEE Systems Journal, March 2012.

Book Chapter

1. Andreas Ulbig and G¨oran Andersson, Role of Power System Flexibility, Renewable Energy Integration: Practical Manage- ment of Variability, Uncertainty and Flexibility in Power Grids, Lawrence E. Jones (Ed.), Elsevier, 2014. ISBN 978-0-12-407910-6. 1.4. List of Publications 5

Peer-Reviewed Conference Papers

1. Philipp Fortenbacher, Andreas Ulbig, Stephan Koch and G¨oran Andersson, Grid-Constrained Optimal Predictive Power Dispatch in Large Multi-Level Power Systems with Renewable Energy Sources, EEE PES Innovative Smart Grid Technologies (ISGT) Europe 2014, Istanbul, Turkey, October 2014.

2. Andreas Ulbig, Theodor S. Borsche and G¨oran Andersson, Im- pact of Low Rotational Inertia on Power System Stability and Op- eration, IFAC World Congress 2014, Capetown, South Africa.

3. Theodor S. Borsche, Andreas Ulbig and G¨oran Andersson, Impact of Frequency Control Reserve Provision by Storage Sys- tems on Power System Operation, IFAC World Congress 2014, Capetown, South Africa.

4. Bolun Xu, Alexandre Oudalov, Jan Poland, Andreas Ulbig and G¨oran Andersson, Battery Energy Storage System (BESS) Con- trol Strategies for Participating in Grid Frequency Regulation, IFAC World Congress 2014, Capetown, South Africa.

5. Andreas Ulbig and G¨oran Andersson, Analyzing Operational Flexibility of Power Systems, 18th Power Systems Computa- tion Conference (PSCC 2014), Wroclaw, Poland, August 2014. (Best Paper Selection)

6. Theodor S. Borsche, Andreas Ulbig and G¨oran Andersson, A New Frequency Control Reserve Framework based on Energy- Constrained Units, 18th Power Systems Computation Conference (PSCC 2014), Wroclaw, Poland, August 2014.

7. Andreas Ulbig, Tobias Rinke, Spyros Chatzivasileiadis and G¨oran Andersson, Predictive Control for Real-Time Frequency Regulation and Rotational Inertia Provision in Power Systems, IEEE Conference on Decision and Control (CDC), Florence, Italy, December 2013.

8. Farid Comaty, Andreas Ulbig and G¨oran Andersson, The Value of Flexibility in a European Power System with High Shares of Re- newable Energies, International Renewable Energy Storage Con- ference (IRES), Berlin, November 2013. 6 Chapter 1. Introduction

9. Bolun Xu, Andreas Ulbig and G¨oran Andersson, Impacts of Dynamic Line Rating on Power Dispatch Performance and Grid Integration of Renewable Energy Sources, 4th IEEE Innovative Smart Grid Technologies Europe (ISGT 2013 Europe), Copen- hagen, October 2013. (Best Poster Award)

10. Theodor Borsche, Andreas Ulbig, Michael Koller and G¨oran Andersson, Power and Energy Capacity Requirements of Stor- ages Providing Frequency Control Reserves, IEEE Power & En- ergy Society General Meeting, Vancouver, Canada, July 2013. (Best of the Best Conference Paper Award)

11. Kilian Dallmer-Zerbe, Matthias A. Bucher, Andreas Ulbig and G¨oran Andersson, Assessment of Capacity Factor and Dispatch Flexibility of Concentrated Solar Power Units, IEEE Powertech Conference, Grenoble, France, June 2013.

12. Michael Koller, Theodor Borsche, Andreas Ulbig and Göran Andersson, Defining a Degradation Cost Function for Optimal Control of a Battery Energy Storage System, IEEE Powertech Conference, Grenoble, France, June 2013. (Best Paper Selec- tion [Top 5], High Quality Paper Certificate)

13. Vasco Lenzi, Andreas Ulbig and G¨oran Andersson, Impacts of Forecast Accuracy on Grid Integration of Renewable En- ergy Sources, IEEE Powertech Conference, Grenoble, France, June 2013.

14. Farzaneh Abbaspourtorbati, Marc Scherer, Andreas Ulbig, and G¨oran Andersson, Towards an Optimal Activation Pattern of Ter- tiary Control Reserves in the Power System of Switzerland, Amer- ican Control Conference (ACC), Montr´eal, Canada, June 2012.

15. Andreas Ulbig, Stephan Koch, and G¨oran Andersson, The Power Nodes Modeling Framework – Modeling and Assessing the Operational Flexibility of Hydro Power Units, XII SEPOPE, Rio de Janeiro, Brazil, May 2012.

16. Andreas Ulbig and G¨oran Andersson, On Operational Flexi- bility in Power Systems, IEEE Power & Energy Society General Meeting, San Diego, USA, July 2012. 1.4. List of Publications 7

17. Frauke Oldewurtel, Andreas Ulbig, Manfred Morari and Göran Andersson, Building Control and Storage Management with Dy- namic Tariffs for Shaping Demand Response, IEEE PES Con- ference on Innovative Smart Grid Technologies (ISGT) Europe, Manchester, UK, December 2011. 18. Andreas Ulbig, Michèle Arnold, Spyros Chatzivasileiadis, Göran Andersson, Framework for Multiple Time-Scale Cascaded MPC Application in Power Systems, 18th IFAC World Congress, Milan, Italy, August/Sept. 2011. 19. Fernando De Samaniego Steta, Andreas Ulbig, Stephan Koch, Göran Andersson, A model-based optimal operation strategy for compressed air energy storage (CAES) plants, 17th Power Sys- tems Computation Conference (PSCC 2011), Stockholm, Sweden, August 2011. 20. Marcus Hildmann, Andreas Ulbig and Göran Andersson, Elec- tricity Grid Feed-In from Renewable Sources: A Risk for Pumped- Storage Hydro Plants?, European Energy Market (EEM) 2011, Zagreb, Croatia, May 2011. 21. Frauke Oldewurtel, Andreas Ulbig, Alessandra Parisio, Göran Andersson and Manfred Morari, Reducing Peak Electricity De- mand in Building Climate Control using Real-Time Pricing and Model Predictive Control, 49th IEEE Conference on Decision and Control (CDC), Atlanta, Georgia, USA, December 2010. 22. Kai Heussen, Stephan Koch, Andreas Ulbig and Göran An- dersson, Energy Storage in Power System Operation: The Power Nodes Modeling Framework, Conference on Innovative Smart Grid Technologies (ISGT) Europe, Gothenburg, Sweden, October 2010. 23. Andreas Ulbig, Matthias D. Galus, Spyros Chatzivasileiadis and Göran Andersson, General Frequency Control with Aggregated Control Reserve Capacity from Time-Varying Sources: The Case of PHEVs, 2010 IREP Symposium – Bulk Power System Dynam- ics and Control – VIII (IREP), Búzios, RJ, Brazil, August 2010. 24. Andreas Ulbig and Göran Andersson, Towards Variable End- Consumer Electricity Tariffs Reflecting Marginal Costs: A Bench- mark Tariff, European Energy Market (EEM) 2010, Madrid, Spain, June 2010. 8 Chapter 1. Introduction

Non Peer-Reviewed Publications

1. Farid Comaty, Andreas Ulbig und G¨oran Andersson, Ist das geplante Stromsystem der Schweiz fur¨ die Umsetzung der En- ergiestrategie 2050 aus technischer Sicht geeignet? (Langfassung) – Swiss Energy Strategy 2050 and the Consequences for Electricity Grid Operation (Full Report), July 2014.

2. Andreas Ulbig, Speichertechnologien fur¨ das Stromnetz, TEC21, Jhg. 138, Nr. 38, September 2012.

3.G ¨oran Andersson, Konstantinos Boulouchos und Lucas Bretschger, Mit Beitr¨agen von: Robert Boes, Fabian Brutsch,¨ Massimo Filippini, Hansjurg¨ Leibundgut, Marco Mazzotti, Fabrizio Noembrini, Roger Ramer und Andreas Ulbig, Energiezukunft Schweiz, ETH Zurich,¨ November 2011. Part I

Paradigm Change, New Challenges & Opportuni- ties in Power Systems

Chapter 2

Paradigm Change in Power System Operation

2.1 Introduction

Power systems are inherently large-scale dynamical systems with a high degree of complexity along several dimensions, i.e. spatio-temporal and hierarchical. Many power system processes happen in parallel, sometimes independent from each other but often interacting. They extend along several time-scales, spatial distribution is high and multiple grid hierarchies exist. An illustrative, physics-oriented introductory description of power systems and their complexity can be found in [1,2]. Power system operation, and for that matter also optimization, is faced with this tremendous complexity of the power systems infrastructure. Complexity exists along several dimensions, notably

• Temporal scale, as illustrated by Fig. 2.1: – (milli-)seconds, e.g. protection device switching, rotational inertia, primary/secondary frequency and voltage control, – minutes, e.g. secondary/tertiary frequency and voltage control, intra-day spot market-based unit scheduling, – hours & days, e.g. spot market-based scheduling,

11 12 Chapter 2. Paradigm Change in Power System Operation

– weeks & months, e.g. seasonal storage usage as well as typical seasonal variations of load demand and production from hydro Photovoltaic (PV) and wind turbine units, – years & decaded, e.g. grid and power plant infrastructure planning and energy policy goals.

Figure 2.1: Relevant Time-Scales of Electric Power Systems (source [2]).

• Spatial scale, as illustrated by Fig. 2.2: – geographical scope, e.g. the interconnected Continental European (CE) grid spanning over 1,000s of kilometers (Portugal–Ukraine: 3,600 km, Denmark–Tunisia: 3,500 km), – total line length, e.g. the electricity grid of the German power system (1,500,000 km).

Figure 2.2: Geographical Scope of Synchronous ENTSO-ECE Grid. Turkey’s grid became synchronized to the Central European grid starting in 2010. 2.1. Introduction 13

• Grid Topological Hierarchy, as illustrated by Fig. 2.3:

– distribution grid, e.g. 120/230/400 V (1,070,000 km), – sub-transmission grid, e.g. 10/20/110 kV (75,000 km), – HV transmission grid, e.g. 220/380 kV (36,000 km). All line length information is given for the German power system.

Figure 2.3: Diagram of an Electric Power System (source: FERC).

• Grid Operation Hierarchy, as illustrated by Fig. 2.4:

– high-level operation, i.e. Business Management System (BMS) that are, for example, interfacing with power market trading and other business-relevant platforms, – medium-level operation, i.e. Energy Management Sys- tem (EMS), Asset Management System (AMS), Distribution Management System (DMS) and Demand-Side Management (DSM) / Demand-Side Participation (DSP) – low-level operation, i.e. plant automation, substation automation, distribution automation and demand-side automation using measurement, e.g., Automatic Metering In- frastructure (AMI), Phasor Measurement Unit (PMU), and control, e.g., Intelligent Electronic Device (IED) and Virtual Power Plants (VPP). The information exchange and interaction between medium- and low- level operation entities is accomplished by means of often dedicated communication channels, for example, Supervisory Control And Data Acquisition (SCADA), Wide-Area Monitoring, Protection And Control (WAMPAC) and Network Information System (NIS). 14 Chapter 2. Paradigm Change in Power System Operation

Figure 2.4: Hierarchy in Grid Operation (source: IEA ISGAN, [3]).

In addition to the just presented spatio-temporal and hierarchical complexity of power systems, there are the non-linear dynamics of grid frequency and voltage that always need to be considered and dealt with in power system control and operation [4,5].

2.2 Power System Control, Operation and Planning over Time

Power system control and optimization is accomplished on diﬀerent time-scales ranging from seconds to minutes in the case of voltage and frequency control, from minutes to hours in the case of intra-day and day-ahead power dispatch, from days to weeks to months for pump- storage optimization and from months to several years in the case of capacity planning for electricity transmission, storage and generation. Traditionally, power system control and operational tasks are treated separately and, often for simplicity, also independent from one another. For example, frequency control and power dispatch are treated as separate topics, having diﬀering objectives, i.e.

• Frequency control: keeping grid frequency f at nominal level f0, • Power dispatch: reducing overall cost of electricity production via an Economic Dispatch (ED), 2.2. Power System Control, Operation & Planning 15 and diﬀerent constraints, i.e.

• Frequency control: on available power and energy reserves and

• Power dispatch: on transmission line and power plant capacity as well as on energy reserves of storage units.

Nevertheless, important interactions occur between both tasks. Tran- sient mismatches in power production, caused by dispatch operations with generators having differing generator ramp rates, are a common event and can create severe grid frequency deviations [6]. However, there is no automated feedback loop from the frequency regulation entity, the Transmission System Operator (TSO), to the entity performing the generation scheduling as defined by an economic power dispatch, i.e. by the electric utilities. Another example is grid expansion planning. Here, investment decisions are driven by long-term trends such as load demand evolution and generation unit placement. On the one hand, power transmission and generation usage patterns within a grid depend mainly on the outcome of the power dispatch. If the dispatch results shift considerably due to changing power system economics, e.g. changes in fuel costs, introduction of a carbon price or a RES Feed-In Tariff (FIT), transmission and generation usage patterns will as well. Eventually, this will also change the need for transmission and generation infrastructure. On the other hand, building new transmission and generation capacity also alters the output of an economic dispatch optimization. Further- more, operation problems such as frequent line congestion or seasonally recurring events like rolling black-outs during extreme weather conditions may also trigger the decision to build new infrastructure. Such information on grid operation performance should be passed onto grid planning tools. Several inter-dependencies exist between control loops and optimization processes that are acting simultaneously in power systems. They should only be perceived as decoupled processes, and hence neglected, under the assumption of steady-state grid operation. Furthermore, power system control structures for regulating a given system variable, for example voltage levels or frequency, are usually realized via a number of nested control loops. 16 Chapter 2. Paradigm Change in Power System Operation

An illustration of the four nested control-loops for grid frequency regulation as well as their activation pattern, i.e. primary, secondary, tertiary frequency control and time control, is given later on by Figures 2.5–2.6. In a power dispatch optimization, in which energy is dispatched in time blocks of individual hours [7], there is no consideration of the underlying voltage and frequency control loops since their dynamics are happening on a considerably faster time-scale. However, other considerations such as transmission line constraints are taken into account. In the optimization of pump-storage unit operation, daily eﬀects, e.g. pumping at night-time and generating at day-time, as well as seasonal eﬀects, e.g. dry and rainy seasons, may need to be considered. For the optimal planning of new transmission, generation and storage capacities, expected future load demand and expected future electricity prices are the key factors for making investment decisions.

2.2.1 Frequency Control and Power Dispatch

One main characteristic of power systems is that frequency stability, and hence stable operation, depends on the active power balance, meaning that the total power feed-in minus the total consumption, including systems losses, is kept close to zero. Small local disturbances can evolve into consequences inﬂuencing the whole power system, in the worst case ending in cascading faults and black-outs. Regarding active power balance, the key system state to observe and control is the grid frequency f . In multi-area power systems, which have several grid control zones, also tie-line power exchanges between these grid zones are of relevance for proper frequency regulation. The grid frequency f is directly coupled to the rotational speed of a synchronous generator via the factor 2π, i.e. ω = 2π f . Deviations from its nominal value, f0, should be kept small, as damaging vibrations in synchronous machines and load shedding occur in case of large deviations, i.e. less than or equal to 1.5 − 2.5Hz [8]. Maintaining the grid frequency within an acceptable range is thus a necessary requirement for the stable operation of power systems. In normal operation small variations occur spontaneously. Large frequency deviations are caused by errors in load demand or RES forecasts and the loss of loads, generators or lines. 2.2. Power System Control, Operation & Planning 17

Stable power system operation is provided by traditional frequency control, which in the ENTSO-E Continental European grid [9] has four categories (Fig. 2.5):

1. Primary frequency control is provided within a few seconds after the occurrence of a frequency deviation. It provides power output proportional to the deviation (P control), stabilizing the system frequency but not restoring it to f0. Primary frequency control is accomplished by responsible generation and storage units in all grid control zones of the inter-connected transmission system. 2. Secondary frequency control on the other hand is provided only by units within the grid control zone in which the fault occurred. The responsible units in the grid control zone of the imbalance start to take over from primary frequency control after approximately 30s. As secondary control has an integral control part (PI control), it restores both the grid frequency from its residual deviation and the corresponding tie-line power exchanges with other control zones to the set-point values. 3. Tertiary frequency control manually adapts the power generation set-points and coordinates the power production operation beyond the initial 15-minute time-frame after a fault occurrence. For call- ing up tertiary frequency control, the topology and the congestion status of the transmission grid within the respective grid control zone needs to be taken into account. 4. Time control corrects global time deviations of the synchronous time and is activated once daily.

Additionally, generator rescheduling is manually activated according to the expected residual power fault in order to relieve tertiary frequency control by cheaper sources at a later stage, i.e. after 45-75 minutes [9–11]. This economic power (re-) dispatch (ED) is then often determined via intra-day auctions on power markets. This traditional categorization is missing an important contributor to frequency stability: the inertial response, a stabilizing quality of a power system to counteract sudden imposed changes to the grid frequency. The contribution of rotational inertia is an inherent feature of rotating synchronous generators. Due to electro-mechanical coupling, kinetic energy stored in a generator’s rotating mass is provided to the grid in case of a frequency 18 Chapter 2. Paradigm Change in Power System Operation

Figure 2.5: Nested Frequency Control Loops (source: ENTSO-E[9]).

R deviation. The amount of kinetic energy, Einertia = Pinertia dt, provided is proportional to the rate of change of frequency ∆ f˙. Inertia damping reacts instantaneously in all control zones. It is a purely physically- motivated eﬀect and cannot be considered as an active control measure – at least not in the case of synchronous generators. The mathematical representation of these four frequency control categories can be formulated as follows:

Pinertia = Kinertia ∆ f˙ Pprimary = Kprimary ∆ f P = −y + dT · P (2.1) secondary, j primary CZ j primary Ptertiary, j = −ysecondary, j ∀ j = 1,..., n , where Pinertia is the immediate power feed-in from the kinetic energy stored in the rotating mass of the generators in case of a frequency drop. Pprimary is the power feed-in from primary frequency control. Psecondary, j corresponds to the power feed-in from secondary frequency control. It alleviates the control eﬀort of primary control reserves, i.e. yprimary, coming from generators of all n control zones of the grid by control reserve power Pprimary coming only from the control zone j (CZ j), where a power fault occurred. Ptertiary, j corresponds to the power feed-in from tertiary frequency control and is aimed at alleviating the eﬀort of secondary control reserves, i.e. ysecondary, j. 2.2. Power System Control, Operation & Planning 19

It is conceivable that in the future the traditional distinction between primary, secondary and tertiary control reserve power may eventually be modified due to changing general conditions of power system structures. With increasing feed-in of fluctuating energy sources and therefore changing requirements on control reserve’s reaction times and procurable power & energy amounts as well as increasingly available computational power, the emergence of new grid control schemes is fore- seeable. One possibility would be to merge the overlapping control tasks of the separated control schemes, acting on different time-scales, into one unified grid control scheme. This could be done via the implementation of an Ancillary Services manager (confer Section 4.3.2). The activation patterns of the nested frequency and power control schemes after the occurrence of a fault event is illustrated here in Fig. 2.6. Since the time-scales for activation and duration of primary to tertiary frequency control, and also time control, range from seconds to hours and even days, these four control loops are practically de-coupled from each other, but called to action in a cascaded fashion depending on the duration of a frequency deviation and the location of the fault within the transmission grid. This is also true for other power system controls, e.g. voltage regulation, resulting in numerous de-coupled control loops operating in parallel on different time-scales in a power system.

Figure 2.6: ENTSO-E Frequency Control Categories [9–11] (own illustration taken from [12,13]). 20 Chapter 2. Paradigm Change in Power System Operation

Please note that power system definitions may vary from country to country. This thesis refers exclusively to the power system conventions and grid code specifications of the ENTSO-E Continental European grid as defined by [9], one of the world’s largest synchronous power systems ( f0 = 50Hz). Classifications of other power systems, e.g. the three North American grids, will differ.

2.2.2 Modeling Inertial Response

Following a frequency deviation, kinetic energy stored in the rotating masses of generators is released, rendering frequency dynamics slower and, hence, more benign to regulate. The rotational energy is given as 1 E = J(2π f )2 , (2.2) kin 2 m with J as the moment of inertia of the synchronous machine and fm the machine’s rotating frequency. The inertia constant H is deﬁned by E J(2π f )2 H = kin = m , (2.3) SB 2SB with SB as the rated power of the generator and H denoting the time duration during which the machine can supply its rated power with stored kinetic energy. Typical values for H are 2–10 s [14, Table 3.2]. The classical swing equation, a well-known model representation for synchronous generators, describes the inertial response of the synchronous generator as the change in rotational speed ωm (or rotational frequency ωm fm = 2π ) of the synchronous generator following a power imbalance as

2 2HSB E˙kin = J(2π) fm · f˙m = · f˙m = (Pm − Pe) , (2.4) fm with Pm as the mechanical power supplied by the generator and Pe as the electric power demand. Noting that frequency excursions are usually small deviations around the reference value, fm can be replaced by f0, and the classical swing equation is completed by adding frequency- dependent load damping, a self-stabilizing property of power systems,

f0 f0 f˙m = − fm + (Pm, 0 − Pe) . (2.5) 2HSBDload 2HSB

Here f0 is the reference frequency and Dload denotes the frequency- dependent load damping constant. Pm, 0 is the nominally scheduled 2.2. Power System Control, Operation & Planning 21 mechanical generator power. Note that a concurrent and also often used deﬁnition of load damping is the inverse term k = 1 . The high Dload share of conventional generators is translated into a large rotational inertia of the here presented interconnected power system. The higher the inertia constant H of the system, the slower are grid frequency dynamics, i.e. the smaller are frequency deviations fm and its derivative ∆ f˙m during identical power imbalance faults.

2.2.3 Aggregated Swing Equation Model

Modeling interconnected power systems, i.e. diﬀerent generator and load nodes that are interconnected via tie-lines, can be realized in a similar fashion as modeling individual generators. Reformulating the swing equation (Eq. 2.5) for a power system with n generators, j loads and l lines, leads to an Aggregated Swing Equation (ASE)[14], i.e.

f0 f0 f˙ = − f + (Pm − Pload − Ploss) , (2.6) 2HSBDload 2HSB with n n n ∑i=1 HiSB,i fi ∑i=1 HiSB,i f = n , SB = ∑ SB,i , H = , ∑i=1 HiSB,i i=1 SB n j l Pm = ∑ Pm,i , Pload = ∑ Pload,i , Ploss = ∑ Ploss,i . i=1 i=1 i=1 Here f is the Center Of Inertia (COI) grid frequency, H the aggregated inertia constant of the n generators, SB the total rated power of the generators, Pm the total mechanical power of the generators, Pload the total system load of the grid, Ploss the total transmission losses of the l lines making up the grid topology and f0 = 50 Hz. Frequency damping Dload is assumed constant and uniform throughout the grid topology. The ASE model (Eq. 2.6) is valid for a highly meshed grid, in which all units can be assumed to be connected to the same grid bus, representing the center of inertia of the given grid. Since load-frequency disturbances are normally relatively small, linearized swing equations with ∆ fi = fi − f0 can be used. Considering the system change (∆) before and after a disturbance, the ASE’s relative formulation, assuming ∆Ploss = 0, is f0 f0 ∆ f˙ = − ∆ f + (∆Pm − ∆Pload) . (2.7) 2HSBDload 2HSB 22 Chapter 2. Paradigm Change in Power System Operation

2.3 Trends in Energy and Power Systems

2.3.1 Technological Trends

Power systems are made up of generation and load units, with storage units seen as a hybrid unit of the former two unit types, and of course the grid infrastructure itself.

Generation-Side Th rise of Distributed Generation (DG) has clearly been the strongest change agent in power systems in recent decades. The term Dis- tributed Generation is generally not used in a consistent form by different sources. However, one thorough definition is given in [15]. Ac- cording to Ackermann et al., Distributed Generation plants can both be fossil-fueled or driven by Renewable Energy Sources [15, Def. E1]. What is more important is the power system unit’s connection to the distribution grid [15, Def. B1] and its power rating, i.e. from 1 W to about 300 MW [15, Def. C1]. Distributed Generation technologies thus comprise the full range of easily-scalable generation units, from Combined Cycle Gas Turbines (CCGTs), Combined Heat and Power Plants (CHPs) and Internal Combustion Engines (ICEs) to all types of RES-sources such as wind turbines and biomass units, small hydro, geothermal, solar thermal andPV units [15, Tab. 1]. This definition would also include energy storage units, which is debatable since one can argue that even ideal energy storage units, i.e. having both a generation and load side as well as no efficiency losses, are not actual net energy producers.

The world’s first DG power plant was the famous Pearl Street Generat- ing Station (6×100kW, 220 V DC) built in 1882 [16], which served the electric lighting needs in a part of Lower Manhattan, NYC. In the following decades, electricity generation became more and more centralized and the electricity infrastructure, i.e. power plants and electricity grids, increasingly monopolized. By the 1970s, the diminishing economies of scale of centralized electricity systems using large-scale generation plants became apparent. It was also recognized that the increasing electricity and in general also energy demand would require more and more infrastructure, and infrastructure investment, for producing and transporting the needed electricity. This motivated the discussion and proposal of 2.3. Trends in Energy & Power Systems 23 new energy policy approaches and, not surprisingly, also heated de- bate. Rather telling in this respect are the energy studies A Time to Choose by the Ford Foundation from 1974 [17], i.e. promoting renewable energies as well as energy efficiency, and No Time to Confuse by the Institute for Contemporary Studies, an industry think-tank, from 1975 [18], i.e. promoting fossil and nuclear energy sources. Numerous studies for such alternative approaches to energy policy date back to Amory Lovins seminal work Energy Strategy: The Road Not Taken? (1976 [19]) and his analysis of Hard Paths, i.e. the investment into a centralized, capital-intensive and increasingly inefficient energy infrastructure, versus Soft Paths, i.e. the investment into a decentralized, less capital-intensive and more efficient energy infrastructure, in energy policy for the case of the US from 1977 [20]. This was followed in the same year by the first 100% Renewable Energy Scenario studies, notably the Solar Sweden study looking ahead to the year 2015 ( [21]). A little later, Florentin Krause et al. conceived the related and, in retro- spect, also seminal study Energiewende – Growth and Prosperity without Oil and Uranium for the situation in West-Germany in 1980 [22]. The study exhibits a strong collaborative link to the one by Lovins, not surprisingly so and thanks to the support and coordination at the time by the Friends of the Earth Foundation. In the process, the term En- ergiewende (engl. Energy Transition) was coined, meaning the transition from a centralized, capital- and carbon-intensive energy infrastructure with large-scale power plants to a decentralized and more efficient energy infrastructure, having distributed, smaller-scale fossil-fueled and RES-based power plants, with a lower resource and carbon footprint. The last three decades have seen, first the (re-) emergence of DGs in the 1980s, often promoted by new legislation, e.g. PURPA in the USA [23] and EEG in Germany [24, 25], then the spreading of both fossil-fueled and RES-fueled DG notably in Denmark and Germany in the 1990s and finally the large-scale deployment of notably RES-based DG worldwide since the 2000s. RES capacity comprised about 25% of total global power generation capacity (GW) and produced an estimated 20.3% of global electric energy demand (TWh) by year-end 2011. Although most RES electricity is still provided by hydro-power (15% of global electricity demand) other renewables (5.3%) are on the rise. Of world total generation capacity estimated at 5360 GWel, wind power made up 238 GWel (4.4%), so- 24 Chapter 2. Paradigm Change in Power System Operation lar Photovoltaic (PV) 70 GWel (1.3%) and concentrating solar thermal power (CSP) 1.8 GWel (0.03%). In addition to its scale, wind &PV deployment is also happening fast: by year-end 2012 there was already about 100 GW ofPV capacity and close to 300 GW of wind turbine capacity installed worldwide. The time-evolution, and increasing rapid- ness, of RES-based DG deployment is illustrated below for the two most prominent technologies, wind turbines (Fig. 2.7) and PV units (Fig. 2.8).

Figure 2.7: Wind Power Deployment Worldwide (source: REN21 [26]).

Within the European Union (EU-27), with its total generation capacity estimated at about 890 GWel, wind power made up 106 GWel (11.9%), PV 69 GWel (7.8%) and Concentrating Solar Power (CSP) 2 GWel (0.2%) by year-end 2012. Comparing the European RES deployment with other major countries: China had a wind andPV power capacity of 75 GWel and 7 GWel, respectively, whereas the US had a wind and PV power capacity of 60 GWel and 7.2 GWel by year- end 2012 (REN21 [26]). Since both the US and China have a higher electricity consumption and installed capacity than the European Union (EU-27) [27], the EU-27 is for the time being the political entity with the highest absolute as well as relative share of wind & PV generation in its power systems. RES deployment is, globally speaking, not limited by any practical boundaries. The worldwide RES physical potential has been estimated by Nitsch et al. to be around 2000–3000 times and the technical potential around 5–6 times the world’s primary energy consumption [28, Tab. 1]– [29, Fig. 1], with wind and solar energy being the largest con- tributors. Also in a regional context, for example for the region Europe 2.3. Trends in Energy & Power Systems 25 and North-Africa, the technical available energy potential is vast [30,31] and concrete proposals for exploitation are readily available, i.e. DE- SERTEC and TRANS-CSP [32]. Another important factor is the continuous improvement of conventional large-scale power plants. Better high-temperature materials for turbines, boilers, tubing and the like in combination with more sophisticated plant control schemes allow increasing plant eﬃciency while at the same time also improving plant ﬂexibility, e.g. it’s ability to modulate power output over time (see also Chapter7 and Def.2).

Figure 2.8: PV Power Deployment Worldwide (source: REN21 [26]).

Load-Side First, the rising share of controllable loads, notably larger thermal loads in the industrial, i.e. electric furnaces, as well as the commercial sector, i.e. Heating, Ventilation, and Air Conditioning (HVAC) systems in oﬃce buildings, but also thermal loads in the residential sector, i.e. hot-water boilers and Heat Pump (HP) [33], add an important degree of freedom to power system operation. Their electric load demand curve can, at least partially, be modulated if need be. Second, the on-going deployment of so-called smart meters is another important trend on the load-side. Smart meters allow a ﬁne-grained measurement of electricity consumption on the scale of seconds to minutes. This measurement data is, depending on the Distribution System Operator (DSO) setup, either available in real-time or ex post. In both cases, the smart metering measurement data potentially allows an improved calibration of existing load models in distribution grids. 26 Chapter 2. Paradigm Change in Power System Operation

Furthermore, controllable loads in conjunction with smart metering gives rise to sophisticated electricity pricing models with hourly or even sub-hourly tariffs that can translate the volatile supply/demand situation of electricity spot markets that are clearly driven by wind & PV feed-in in regions with significant RES shares into straight-forward economic incentives on the side of commercial and residential end- consumers to adjust load demand, i.e. shifting flexible loads away from expensive to cheap hours. Third, the starting deployment of storage units, in particular modern BESSs with higher power & energy densities (Fig. 2.9) and continuously decreasing installation costs gives rise to interesting applications such as (local) voltage and frequency control, peak shifting as well as energy arbitrage.

Figure 2.9: Energy Densities of Various Battery Technologies (source: Nexergy).

Grid-Side The recent decades have seen the advent of new sensors and actuators that in principal allow improved power system control and operation. The deployment of new sensor types, notably PMUs that allow highly accurate measurements of voltage, frequency and current as well as so- called Power Donots that in addition to PMUs also provide measurements of conductor temperature and inclination [34], allows a better 2.3. Trends in Energy & Power Systems 27 real-time awareness of the power system. This is in particular true for transient grid dynamics with a previously in-achievable spatio-temporal resolution in the case of PMUs and Dynamic Line Rating (DLR) in the case of Power Donots. The deployment of new actuator types, notably power-ﬂow actuators like Flexible AC Transmission Systems (FACTSs) and to a lesser degree also Phase-Shifting Transformers (PSTs) give rise to power ﬂow control that was previously unattainable, when the only actuator were voltage tap changers a the MV/HV level and basic line switching operations.

2.3.2 Economic Trends

With the on-set of power market liberalization in the early 1990s, ﬁrst in Chile, then in the US and Europe, and the establishment of national and regional spot power markets, e.g. Nordpool in Scandinavia [35] and the EPEX in Central Europe [7], the electricity volumes traded on power market platforms and, in particular, the cross-border electricity trade have dramatically risen. In Europe, physical cross-border power ﬂows amounted to about 380 TWh in 2010, which constitutes both more than 10% of overall European generation as well as an eight-fold increase compared to 1975 (Fig. 2.10).

Figure 2.10: Cross-Border Power Flows (ENTSO-E, 1975–2010).

With the increasing de-bundling of power generation, transmission and 28 Chapter 2. Paradigm Change in Power System Operation distribution, required by legislation for instance in Europe [36], true- cost pricing as well as general cost efficiency have become a priority in power system operation. Nevertheless, the cost of electricity has stayed at the same level, in the US, or has even significantly risen, in the EU, since the year 2000 (Fig. 2.11). Arguably, European electricity rates have risen in line with higher natural gas prices, whereas in the US electricity rates have stayed at the same level despite falling natural gas prices. Note that gas-fueled generation units, both in the US and in Europe, have a strong influence on spot market prices for electricity as they constitute often enough the last accepted supply price bid of the merit-order curve; thus setting the spot price. Also arguably is that in the latter case, the short-stopped market liberalization of the US energy sector is a key cause.

Figure 2.11: Industrial Energy Prices 2000–12 (in e¢/kWh, [37]). Investment needs and hence investment costs of electricity infrastructure are, in principal, driven by the peak power feed-in (generation) or feed- out (demand) expected for the near- or mid-term planning horizon. The assessment of future investments into electricity infrastructure, and energy systems in general, has always involved immense sums, in the 1970s and 80s (see again [19, 22]) as today. The International Energy Agency (IEA) and it’s lead publication World Energy Outlook is currently assessing the cumulative investment need in the power sector at $17.0 trillion over the period 2013–2035 [38, p.191–192]. Investment in generation capacity amounts to 58% or about $10 trillion, of which about two-thirds or $6 trillion are for RES. The remainder, 42% or about $7 trillion are for Transmission and Distribution (T&D) networks. What has indeed changed in recent years are the specific investment costs for different types of generation units. The installation costs 2.3. Trends in Energy & Power Systems 29 of conventional generation units has increased by 70%–91% in Eu- rope (Fig. 2.12), and more than 100% in North America, since the year 2000. At the same time the installation costs of prominent RES technologies has fallen significantly over the last decades, especially for PV modules (Fig. 2.13). The significant cost reduction of RES technologies was achieved to a large part thanks to the economies of scale of wide-spread RES deployment. This was made possible by generous government support schemes for RES, be it FITs in Europe or Renewable Portfolio Standards (RPS) in the US. Such schemes have in many countries created a favorable investment environment for RES. Investment into wind turbines, biomass-fired, hydro and geothermal power generation units as well asPV units has thrived.

Figure 2.12: European Power Capital Cost Index (IHS CERA, [39]).

In addition to this, energy storage units such as Battery Energy Stor- age System (BESS) units are becoming cheaper and investment costs are expected to decrease at least by half until 2020 [40, Fig. 16], as is illustrated by Fig. 2.14. 30 Chapter 2. Paradigm Change in Power System Operation

Figure 2.13: Cost Curves of Wind Turbines & PV Modules (IPCC [41]).

Figure 2.14: Estimates of Electric Vehicle Battery Costs 2012–2020, (source: MIT Technology Review [42]). 2.4. Trends in Information & Communication Technology 31

2.4 Trends in Information and Communi- cation Technology

Compared to the traditionally decade(s)-long investment cycles and, admittedly, also similarly long innovation cycles in the energy and power sector, technological and economic change in the Information & Com- munication Technology (ICT) sector has been extremely fast over the past decades.

These ICT advances do now also constitute a driving force for change in power system operation and control as is pointed out here.

2.4.1 Technological Trends

Moore’s exponential law for computation power, i.e. a doubling of the number of transistors per chip every 18–24 months [43] as illustrated in Fig. 2.15, and similar exponential laws for communication and storage technology have dramatically impacted the technological potential of computation, communication and data storage.

These ICT trends bring numerous power system applications in reach such as the long-dreamed-oﬀ Demand Response and Demand-Side Par- ticipation, advocated by visionaries like Schweppe et al. as early as in the year 1980 [33].

Real-time communication with and online operational optimization of even the smallest generation, load and storage units in distribution grids has, from a technological point-of-view, clearly become feasible.

In addition to this, vast amounts of operational data like load demand and production, voltage and frequency measurements can now be stored with very high temporal and spatial resolution. 32 Chapter 2. Paradigm Change in Power System Operation

Figure 2.15: Exponential Laws in ICT – Moore’s Law 1971–2011 [43].

2.4.2 Economic Trends

Comparably dramatic to the advancing computing power has been the exponential cost reduction for computing power, communication band- width and data storage as is qualitatively illustrated by Fig. 2.16. Also, the size of networks that can still be operated and managed has increased exponentially. This trend in cost reduction per unit of ICT capacity is certainly interesting when compared to the roughly steady or even rising energy and electricity costs (Fig. 2.11). ICT costs and the related eﬀort for realizing practical DR or DSP schemes, or more generally aggregator-driven load, generation or energy storage schemes, have signiﬁcantly fallen year by year, whereas electricity costs have not. 2.4. Trends in Information & Communication Technology 33

Figure 2.16: Exponential Cost Trends for ICT (source: O’Reilly [44]).

This makes many coordination and optimization schemes for the power sector, be it direct load or generation control or price-driven schemes, more and more economically viable with each passing year. Clearly, advances in technological capabilities and cost reduction of In- formation & Communication Technology do not by themselves auto- matically lead to purpose- and meaningful power system applications let alone business cases. Nevertheless, numerous concepts notably in the area of real-time generation & load control (or management), and connected to this also real-time power markets are becoming at least technologically feasible. 34 Chapter 2. Paradigm Change in Power System Operation

2.5 Paradigm Change

Traditionally, power system operation is conducted with a precise idea of the underlying processes in mind: Electricity generation, mainly in the form of large power plants, reliably fueled with natural gas, coal or uranium, is considered to be ﬁrm, i.e. fully dispatchable or controllable. Electricity demand is considered to be non-dispatchable, i.e. non- controllable, but fortunately relatively well predictable, Fig. 2.17.

Fully controllable power generation thus simply has to follow the non- controllable load demand. Storage units are used mainly for techno- economic optimization, allowing large base-load power plants such as nuclear or coal-fired power plants to operate at a constant, full-load operation point despite the fluctuating pattern of load demand, driven by short-term cycles (day/night), mid-term cycles (weekday/weekend) and long-term cycles (seasonal, summer/winter). The remaining variations between scheduled generation and actual real-time load demand, caused by stochastic effects on both generation- and demand-side, are balanced via reserve capacities. These are put at the disposal of the grid operator in the form of automated, i.e. primary and secondary frequency control, or manual, i.e. tertiary frequency control power reserves. The same control reserves are necessary for unplanned outages of plants and power lines.

Figure 2.17: Traditional Categorization of Power System Processes – Fully Dispatchable Conventional Generation, Non-Controllable Load Demand and Large-Scale Hydro-Based Storage (own illustration [45]). 2.5. Paradigm Change 35

This somewhat idealistic perception of power system operation largely matched the reality in power system operation for many years. This is changing in recent years due to:

1. The wide-spread deployment of variable Renewable Energy Sources (RES) in many countries has led to significant relative and absolute shares of power generation with a stochastic compo- nent. This significantly increases the part of non-controlled power feed-in into power systems. Well-known operational issues caused by this are non-deterministic power imbalances and power flow changes on all grid levels.

2. The growing power market activity on the increasingly integrated national and transnational power markets has led to operational concerns of its own. These are, besides others, rapid deterministic frequency deviations caused by transient power imbalances, due to more frequent changes in the now market-driven operation set- point schedules of power plants [6].

3. The emergence of a smart grid notion or vision as a driver for change in power system operation (cf also to Def.1). This includes the deployment of smart metering, i.e. allowing accurate load demand sensing on the household-level via a capable communication infrastructure, and the establishment of controllability over distributed power system units. These distributed units include generation, ranging from well-controllable, e.g. CHP units to partially controllable units, e.g. wind and PV, whose power output can be curtailed as well as more and diﬀerent storage units, e.g. stationary battery systems as well as non-stationary battery capacity of electric vehicles (PHEV/EV ﬂeets) [46, 47] and loads, e.g. DSP of thermal residential loads [48, 49].

Notably the envisioned massive deployment of smart meters as one of the key features of national energy policies in many countries worldwide [50] will create the necessary infrastructure for sophisticated load management schemes. This includes both DR schemes steered by dynamic electricity tariﬀs [51], which allow to establish a mild load controllability or steerability, i.e. peak load reduction as well as load valley ﬁlling, and DSP schemes that are driven directly by control signals, which allows a more stringent load controllability. 36 Chapter 2. Paradigm Change in Power System Operation

In eﬀect, a part of the overall load demand will be rendered controllable. Today, load control is often restricted to shedding load processes, which in practice often means large industrial load demand.

Altogether, these developments constitute a major paradigm shift in the management of generation and load portfolios, as illustrated in Fig. 2.18. In the future, an increasingly better controllable load demand will have to follow more and more the increasingly fluctuating power generation profiles in the power system. More storage capacities, based on different technologies, will be decisive in buffering the spatio-temporal mismatch of electricity generation and load demand.

This paradigm change is going beyond the mere aspects of controllability, and as dual concept also observability, of power system processes:

The key question to raise is rather which generators as well as storage and loads units can provide needed operational ﬂexibility, i.e. the technical ability to modulate power feed-in or feed-out. Eventually, this paradigm shift will have to be reﬂected in power system operation procedures.

Figure 2.18: Contemporary Categorization of Power System Processes – Signiﬁcant Shares of Variable RES Generation, Controllable Load Demand and more Storage Capacity (own illustration [45]). 2.5. Paradigm Change 37

In order to make the outlined paradigm change technically feasible, future power system operation will necessitate:

1. Enhanced control & management schemes in power system operation that are able, for example, to explicitly employ predictions of future power feed-in/out processes, i.e. wind & PV production and load demand forecast time-series, as well as 2. Better modeling & analysis frameworks allowing the detailed description of power system processes, i.e. the controllability, observability and ﬂexibility properties of generation, load demand and storage units. This also included knowledge of background processes, i.e. primary fuel supply, end-use demand and energy storage levels (SOC). 3. Power system modeling will need to address in greater detail the aspects of controllability and observability of power system processes. What is the degree of control that a system operator has for intervening in undesirable or critical situations? And what information of the power system state is available, i.e. can be observed by the operator? 4. Improving the operator’s awareness of power system processes will be a crucial and decisive challenge for power system operation.

Definition 1 – Smart Grid Using the reference framework of control theory, the term smart grid can be understood as the sum of all efforts that improve observability and controllability over individual power system processes, i.e. power feed-in to the grid and power feed-out from the grid as well as power flows on the demand and supply side, happening on all electricity grid levels. An improved observability and controllability of individual power system units leads also to an improved observability and controllability of the entire power system and the processes happening therein. Well-known concepts from control theory such as the Kalman decomposition allow to categorize power system processes with respect to controllability and observability and, eventually, lead to a better understanding. 38 Chapter 2. Paradigm Change in Power System Operation

2.5.1 Changes in the German Power System

In order to illustrate the technological and economic trends acting on power systems with a concrete case study, in the following a comparison is made between the status of the German Power System in the year 1990 and the year 2013. The focus is especially on the change in share of fully dispatchable, i.e. controllable, versus non-dispatchable, i.e. non- controllable, power generation and load demand.

Power Generation

Around the same time as the liberalization of many European Elec- tricity markets in the early 1990s, government support schemes with the specific goal of promoting large-scale deployment of renewable energy sources (RES) were introduced. The German Renewable Energy Act, Erneuerbare-Energien-Gesetz (EEG) [25], a well-known support scheme, provides a favorable FIT for a variety of RES since the year 2000 and builds on the good experience with its predecessor, the Stromein- speisungsgesetz from 1990 [24]. In Germany, a fixed FIT is granted for 20 years. Furthermore, a guaranteed grid connection and feed-in priority is granted for FIT-subsidized RES units over power feed-in from conventional power plants, i.e., fossil- and nuclear-fueled thermal and old, often large hydro-based power plants. This favorable investment case has generated installed capacities of more than 30 GW each for wind and PV units by year-end 2012. The evolution of installed variable RES capacities and annual energy production in Germany from 1990 to 2013 [52], including an outlook till 2017 [53], are shown in Fig. 2.19. The original goal of the FIT, i.e., large-scale RES deployment (Fig. 2.19a) and significant RES energy shares (Fig. 2.19b) is achieved. With a combined installed capacity of wind &PV units of around 65 GW by year-end 2012, roughly the same as the average load demand in Germany (63–68 GW dependent on load demand measure), variable RES units clearly cannot be treated anymore as marginal let alone negligible electricity sources anymore. A further increase of RES capacity, notably of PV, is expected in the near future. For year-end 2016, installed capacities of 42 GW in wind turbines and 44 GW in PV units are estimated [54]. The cumulative variable RES generation capacity would amount to 86 GW, roughly equivalent to the total capacity of firm conventional generation units by year-end 2011 [55]. 2.5. Paradigm Change 39

(a) Installed Capacities [GWel]

(b) Annual Energy Production [TWhel]

Figure 2.19: Evolution of RES Deployment in Germany 1990–2017, (own analyis [56], year 2013–2017 values are best estimates). 40 Chapter 2. Paradigm Change in Power System Operation

Whereas almost all of the total generation capacity in Germany was considered fully dispatchable, i.e. about 99%, in the year 1990, about half of the generation capacity, i.e. about 45% or 70 GW, and a sizable share of electricity production, i.e. about 14% or 78 TWh, was made up of wind &PV units by year-end 2013 [53]. They can only be considered time-varying dispatchable, as their output can only be controlled, i.e. curtailed, within the bounds of available primary wind or solar energy.

Load Demand

In the year 1990 most of the overall yearly load demand in Germany, approximately 505 TWh [27, Electrical Energy Supplied], was considered non-controllable. Fortunately, load demand is well observable in real-time and comparatively well predictable. Furthermore some controllability over interruptible loads by either manual or schedule-based control means already existed. This included notably large industrial loads that could be shedded manually or residential hot water boilers that were controllable via existing ripple control schemes, a simple form of power-line communication. In 2013 most of the overall yearly load demand, 561 TWh [27, Elec- trical Energy Supplied (estimated)] with a winter peak load demand of about 86 GW, could still be considered non-controllable. However, more and more aggregator concepts are being implemented, mostly for large industrial or commercial loads often in conjunction with back-up generation units.

Storage

In 1990, only hydro-based bulk storage units were available. By 2013 some new hydro storage units had been realized, bringing the total storage capacity to about 7 GW power rating with 42 GWh energy rating, and plans for more units exist. There is also a slow deployment of stationary BESS, i.e. industrial-size systems in the low MW/MWh-range, as well as non-stationary BESS, i.e. PHEV/EV ﬂeets. 2.5. Paradigm Change 41

Table 2.1: Speciﬁcations of German Power System (by year-end 2011): Overview of Generation and Storage Capacities as well as Load Demand (Percentage Values with Respect to Peak Load Demand) [27].

Power System Power π Energy ε Ramping ρ Unit Types GW [GW] [%] [GWh] [ 15min. ] [GW/h] Conv. Generation 85 98.8 504,600 ±3.0 ±12.0 Pumped Hydro 7 8.1 42 (Cap.) ±7.0 ±7.0 Load Demand 86.0, 100, +3.0, +12.6, 561,300 (max/min) 37.7 43.9 −2.3 −8.4 +3.7, +3.6, Wind Turbines 29.0 33.7 48,900 −3.7 −3.9 +1.2, +4.3, Solar PV 24.8 28.9 19,300 −1.4 −3.8

Power Market

A country-wide spot market for electricity in Germany, the European Energy Exchange (EEX) is in place since 2002 [57]. Since 2009, Ger- many’s electricity spot market is part of the EPEX, a multi-national continental European electricity spot market split into three different market zones, i.e. France, Germany & Austria and Switzerland [7]. By the stipulations of the EEG, all of Germany’s subsidized renewable electricity production has to be completely inserted into the EPEX combined German-Austrian spot market by each German TSO. This is accomplished by bidding the renewable electricity into the spot market’s merit-order curve using low price bids; as low as the minimum price bid, which is currently at -3000 e/MWh [58]. The power market volume has increased from 31.5 TWh, or 5.3% of combined German-Austrian load demand in 2002 to 245 TWh or 39.2% of estimated load demand in 2013. This is in principal a good development as higher power market trading volumes improves RES grid integration [56]. However, whereas still only around two-fifth (≈ 39% in 2013) of the yearly load demand in the German–Austrian grid zone is traded on the in EPEX day-ahead market, more than four-fifth (≈ 85% in 2013) of the load demand of the neighboring Nord Pool countries (except Estonia) is traded on the day-ahead market. This means there 42 Chapter 2. Paradigm Change in Power System Operation is still considerable room for improvement in Germany and Central Eu- rope when compared to the Nordic countries. The evolution of the EPEX day-ahead, which was the EEX spot until 2009, and the Nord Pool day-ahead market shares of the yearly load demand in their respective market zones is illustrated in Figure 2.20. All references and more detailed analysis on spot markets, and the impact of FIT-subsidized RES power feed-in on them, can be found in [56].

Figure 2.20: Evolution of Day-Ahead Power Market Shares in the EPEX German–Austrian Market Zone Compared to Nord Pool Spot (own analysis [56]). Chapter 3

New Challenges in Power Systems Operation

This chapter is titled new challenges since there are, of course, also old, i.e. classical, challenges in power system operation and control that are well-known, analyzed and understood. Operational challenges, in the best case, are causing a mere nuisance to grid operators. In the worst case, however, power system disturbances may lead to diﬀerent types of power system instabilities. After giving ﬁrst an overview of traditional power system challenges, the focus in the remainder of this chapter is on the qualitatively new technical and economic challenges of RES power generation, aggregator schemes and the activity of power markets.

3.1 Classical Challenges

A good overview of power system operation and control challenges & issues is given by Wood & Wollenberg in [59] and Kundur in [14]. A definition and classification of the different types of power system (in-) stability, i.e. rotor angle, frequency and voltage stability, as well as an explanation of classical causes is given by the authors of [60, IEEE/CIGRE Joint Task Force on Stability Terms and Definitions]. An illustration is given in Fig. 3.1. A review regarding specifically the challenges of DG integration is given with [61].

43 44 Chapter 3. New Challenges in Power Systems Operation

Classical challenges in power system operation and control are disturbances of voltage, frequency and rotor angles as caused by events related to typical infrastructure failures such as power plant outages, which were the triggering event causing the large blackout in Southern Swe- den & Eastern Denmark in 2003 [62], and line outages, which were the initial event causing the large blackouts in Italy and the US, also in 2003 [63,64]. Other challenges are shortcomings in transmission grid management which may just as well lead to wide-spread outages as wit- nessed in the ENTSO-E Continental European grid in 2006 (Box1). In- terestingly, load forecast errors, i.e. mismatches between predicted and actual load demand, have been much less a concern for grid operation.

Figure 3.1: A Classiﬁcation of Power System Instabilities. [60].

Wrapping-up this excursion, it has to be noted that analysis of past blackout occurrences shows that there is often a complex chain or cascade of individual failure events that in the end may (or may not) lead to a blackout [65, IEEE Task Force on Understanding, Prediction, Mitiga- tion and Restoration of Cascading Failures]. Lacking situational awareness of the full system state and inadequate understanding of the system that subsequently lead to aggravating decisions by system operators are often more to blame than the initial fault triggering event, as pointed out in [63]. 3.1. Classical Challenges 45

Info-Box 1 – European System Disturbance (4 Nov. 2006)

This infamous large system disturbance event is a prime example of the difficulties that TSOs face when a significant part of RES power generation cannot be controlled by grid operators and counteract grid restoration efforts. Shortly after 10 pm on Saturday, 4 November 2006, the ENTSO-E Continental European grid split into three non-synchronous grid zones. In total, 15 million European households had to be load- shedded by various TSOs for up to two hours. Grid regions from Poland to Spain, and even Morocco were concerned. The grid situation just previous to this event was characterized by low load demand and significant east-west power flows due to power market trading and comparably high wind power feed-in throughout Europe. The immediate actions taken by the TSOs prevented the disturbance to turn into a severe Europe-wide blackout. Surprisingly, the root-cause of this disturbance was a planned routine disconnection of a power line crossing over the river Ems in Northwest Germany in order to allow a large ship to pass beneath the overhead lines. Due to insufficient communication between German and French TSOs this lead to a mismatch in power flow schedules in the different dispatching centers in turn causing the grid split. The official ENTSO-E report stated that uncontrolled on/off switching of wind turbine units, approx. 5,400 MW located in Northern Germany and 800 MW in Austria, and lacking operational flexibility of larger thermal generation units to counterbalance this, notably in the German 50HERTZ grid zone, led to infeasible power flow situations within theCE grid region [66, p. 30–36] and made grid restoration much more difficult.

ENTSO-E CE grid split into three areas [66]. 46 Chapter 3. New Challenges in Power Systems Operation

3.2 New Technical Challenges

In the following sections the discussion will focus on qualitatively new disturbance phenomena and challenges, most of them related directly or indirectly to ﬂuctuations in power feed-in of variable RES units such as wind & PV units or increased power market activity.

3.2.1 RES Integration

Although the challenges of the grid integration of RES power feed-in are manifold, the main concern are power feed-in ﬂuctuations. Many RES- based generation technologies exhibit some variability of power feed-in, ranging from short time-scales, i.e. minutes or less, to very long time- scales, i.e. seasons or even years. A categorization of relevant time-scales for diﬀerent RES technologies is given by Fig. 3.2.

Figure 3.2: Range of Relevant Time-Scales for RES Power Feed-In (source: IEA [67]).

Power Feed-In Fluctuations – A Question of Time-Scales

However, out of the different RES-based generation technologies only those unit types with comparatively fast (un-controlled) fluctuating power feed-in profiles, i.e. so-called variable RES-based generation such as wind & PV units, are a genuine source of operational challenges. This is due to the fact that only the time-scales of their output variability, 3.2. New Technical Challenges 47 i.e. seconds to hours, coincides with the time-scales of generator dynamics as well as frequency and power control, as is illustrated by Fig. 3.3. Please note that the power feed-in fluctuations are by themselves merely a symptom of the reduced controllability that system operators have over these variable RES-based unit types and, foremost, their primary fuel provision, i.e. mechanical wind power and solar insolation.

Figure 3.3: Range of Relevant Time-Scales for Real-Time Operation of Electric Power Systems [2].

Diﬀerent operational aspects are relevant on diﬀerent time-scales:

• Frequency Inertia (seconds) A loss of frequency inertia is caused by increasing inverter-based RES power generation, which is displacing conventional generators and with it the rotating mass of generators and turbines.

• Frequency Regulation and Stability (seconds to minutes) Problems are caused by ﬂuctuations of RES feed-in and load feed- out. Concerned are primary and secondary frequency control.

• Voltage Regulation and Stability (seconds to hours) Problems are created by either large power feed-in or feed-out as well as reverse power ﬂows in (radial) distribution grids.

• Power Flow Management (minutes to hours) Is mostly a question of the mismatch in geographic location and timing of RES units power feed-in and load units power consumption. Geographic mismatch between generation and load units has always been an issue in power system planning, notably in power systems with large centralized generation units. Timing mismatch 48 Chapter 3. New Challenges in Power Systems Operation

between RES generation and load units, mainly a problem of non- controllability and non-observability of generation units, and to a lesser degree also load units, is a new phenomenon.

• Energy Regulation & Management (minutes to years) – Time-scale of 15 min.–hours: Real-time to short-term forecast errors of RES feed-in (to smaller extent also load feed- out), short-term storage management. – Time-scale of hours–1 day: Short-term storage management (mostly deterministic daily load and RES generation fluctuations, i.e. (PV)). – Time-scale of 1 week–1 month: Mid-term storage management (fluctuations in hydro feed-in, influence of outdoor temperature on load demand) . – Time-scale of 1 month–1 year or even years: Long-term storage management. Seasonal effects: fluctuations in seasonal hydro, wind and PV power feed-in.

An illustration of the ﬂuctuations of RES power feed-in as well as load demand feed-out on diﬀerent time-scales is shown here for the case of the German Power System. As can be seen here, the challenges for the electric power system as a whole to maintain the active power balance on all time-scales vary from absorbing fast power peaks, Fig. 3.4 (a)–(b), to dealing with seasonal changes in energy demand, Fig. 3.4(c).

Power Feed-In Fluctuation – A Question of Forecast Accuracy

Forecast accuracy of RES with stochastic power feed-in, e.g., wind turbines &PV, receives attention due to the impact that stochastic electricity generation proﬁles can have on power system stability. The rapid deployment of variable RES units worldwide raises the problem that currently existing power systems are often ill-equipped for accommodating their variability and limited predictability. Forecast accuracy generally degrades over the length of the time- horizon. This degradation, however, must not necessarily happen either uniformly or symmetrically. The evolution of the average RES forecast errors over the prediction horizon illustrates the forecast characteristics for all wind andPV feed-in in the four German TSO zones (Fig. 3.5). 3.2. New Technical Challenges 49

(a) Intra-day challenge (8760 hours) [TWhel]

(b) Intra-week challenge (365 days) [TWhel]

(c) Intra-year challenge (12 months) [TWhel] Figure 3.4: RES Integration Challenges on Diﬀerent Time-Scales – Situation in the German Power System, Year 2010 (own analysis [68]). 50 Chapter 3. New Challenges in Power Systems Operation

Noteworthy is that RES forecast accuracy has significantly improved over the past years as is illustrated for the case of the grid zone of Red Eléctrica España (REE), the Spanish TSO, in Fig. 3.6. This is in part due to better forecast tools, i.e. incorporating better weather models and algorithms as well as more measurement data and computation, but in part also to the positive aggregation effect of the growing wind & PV capacity base. Interestingly, the short-term forecast error is comparatively small but does not necessarily converge to zero. The average aggregated short-term wind forecast error was around 4% with respect to the mean production (1h-ahead) in 2010.

Figure 3.5: Evolution of Wind & PV Production Forecast Errors over the Time Horizon for the Four German TSO Zones (own analysis [69]). 3.2. New Technical Challenges 51

Figure 3.6: Improvement of Wind Power Forecast Error in REE Grid.

Impacts of Forecast Accuracy on Power System Operation

Forecast errors, both of power feed-in of variable RES generators as well as power feed-out of load demand, need to be balanced in real-time by control reserves. These control reserves will be dispatched according to error the absolute forecast error Pabsolute, which is the product of the relative forecast error εrelative and the RES capacity that is online at a given time instant PRES, as given by

εabsolute [GW] = εrelative [%] × PRES [GW]. (3.1)

The question then arises what the future requirements for control reserve capacity will be. If the installed RES capacity of wind &PV units continues to rise and forecast accuracy does not improve, i.e. the relative forecast error εrel. stays the same, the absolute forecast error and hence the required control reserve capacity will have to increase.

An elegant mitigation of this issue is then clearly to further improve forecast accuracy of wind,PV, but also load demand in order to reduce the need for (more) control reserves. 52 Chapter 3. New Challenges in Power Systems Operation

Inertia Reduction due to Inverter-connected RES

Other known challenges to RES integration are related to the fact that most modern wind &PV units are inverter-connected to the grid. These inverters are often lacking fault-ride through capabilities and do not a priori provide rotational inertia to the grid. The increasing share of inverter-based power generation and the associated displacement of usually large-scale synchronous generation units and their rotational masses has the following consequences:

1. The rotational inertia of power systems becomes highly time- variant and is reduced, often non-uniformly within the grid topology as wind & PV shares are ﬂuctuating heavily over time. This is notably a concern for small power networks, e.g. island or micro grids, with a high share of generation capacity not con- tributing any inertia as was discussed, for example, in [70]. 2. The inertia reduction or inertia loss from conventional synchronous generators can potentially lead to new frequency insta- bility phenomena in interconnected power systems, as discussed by this author in [71].

In general, faster frequency dynamics due to lower levels of rotational inertia raise the question whether fast frequency control, e.g the primary frequency control scheme in the continental European grid area of ENTSO-E, will remain sufficiently fast for mitigating fault events before a critical frequency drop has occurred. Clearly, frequency control becomes more difficult and appropriate adaptations of grid codes are needed in the near-term future. An interesting side-effect is that in interconnected power systems in particular, faster frequency dynamics also mean that the swing dynamics of the individual grid areas with each other will likely be amplified. This would lead to significantly amplified transient power exchanges over the power lines, which in turn could trigger automatic protection relays [71]. To better illustrate these, at first, rather theoretical statements on power system stability, a realistic case-study of low rotational inertia impacts on daily operational practices in the power systems domain is presented; analyzing the dynamic response of the ENTSO-E Continental European power system to fault events. 3.2. New Technical Challenges 53

An Aggregated Swing Equation (ASE), Eq. 2.6, is considered. Realis- tic system parameters as identiﬁed from actual measurements [6] were used. A typical summer load demand situation is assumed, e.g. 230GW (15 August 2012, 8–9am MEST), and diﬀerent values of the inertia constant H are considered. Then the design worst-case fault event, i.e. an abrupt loss of ∆P = 3000MW is applied, while nominal primary and secondary frequency control schemes are active, i.e. primary frequency control reacts with a maximum delay of 5s and achieving full activation after 30s. These are the control reserve requirements of ENTSO-E[72]. As shown in Fig. 3.7, the design worst-case power fault event that the Continental European power system should still be able to sustain, can be absorbed as foreseen during a high inertia situation (Hagg = 6s, shown in black). However, the same fault event becomes critical during a low inertia situation (Hagg = 3s, shown in red) as the system frequency drops lower than 49.5 Hz before the nominal primary control fully kicks in fully, i.e. 30s after the fault. The automatic shedding of a combined wind &PV capacity well above 10 GW is, in the current power system setup (year 2013), not merely a theoretical but rather a likely possibility. Further details as well as extensions to this analysis can be found in [71].

Figure 3.7: Dynamic Response of ENTSO-E Continental European Power System to Fault Events (own analysis [71]). Black: high inertia (H = 6s), i.e. no wind & PV power feed-in share, nominal frequency control reserve. Red: low inertia (H = 3s), i.e. 50% wind &PV power feed-in share, nominal frequency control reserve. 54 Chapter 3. New Challenges in Power Systems Operation

Changes in Power Flow Patterns

Large-scale changes in the placement patterns of generation units, i.e. deployment of RES units and phasing out of conventional units, will also have an impact on power flow patterns. This in turn will have repercussions both on daily power system operation and planning. The power system may become more stressed due to changes and increases in regional and cross-border power flow patterns. Also, envisioned grid re- inforcements focusing on today’s grid bottlenecks, as caused by today’s power flow patterns, may become irrelevant for substantially different future power flow patterns. A detailed simulation-based analysis of how power system flows will change in the ENTSO-E Continental European over the next decades will be presented in Section 9.4.3.

Displacement of Must-Run Generation

Another effect that the increasing share of inverter-based power generation and, in turn, the displacement of usually large-scale and fully controllable generation units has is that the pool of suitable conventional power plants for providing traditional control reserve power is significantly diminished. In the past this has not been a critical issue, since conventional power plants provided Ancillary Services (AS) simply as a by-product of power generation. In the daily operation of power systems with high RES energy shares, power market dispatch will regularly lead to displacement of fully dispatchable, i.e. fully controllable, conventional plants by RES units, which are often only partially dispatchable or controllable. This is driven by the fact that notably variable RES generation, i.e. wind & PV units, has no or only comparatively low marginal operation costs [56], whereas conventional, i.e. fossil-fuel based units have substantial marginal operation costs due to their fuel demand. This is also true for hydro-based units; certainly for Hydro Storage Lake (HSL) and Pumped Hydro Storage (PHS) units because there is always the consideration of the so-called water value, i.e. the economic value of the potential energy stored in the water reservoirs corresponding to the run-cost of the conventional, fossil-fueled units it displaces [73]. But also for Run-Of-River Hydro (ROR) plants, since there often exist 3.2. New Technical Challenges 55 marginal operation costs, i.e. fees for water usage as well as the wear and tear of the machinery [56]. The necessity to provideAS, i.e. active reserve power for mitigating frequency & power imbalances as well as reactive control reserve power for mitigating voltage deviations, most of it in the form of spinning reserve, means that some fully dispatchable generation units, i.e. usually large conventional or hydro units, have to be kept online as so-called must-run generation. A situation can thus arise in which system operators will have to keep conventional, fossil- fueled power plants online and spinning in order to provideAS even though their energy production is momentarily not needed. This would be the case for times of high wind &PV production in power systems with high RES shares, e.g. in Spain, Denmark or Germany. The above described operational must-run constraint can thus lead to an economically sub-optimal power dispatch, potentially resulting in high opportunity costs in power system operation.Due to this Ancillary Services could become significantly more costly than today in power systems with high RES shares.

3.2.2 Demand Response & Aggregators

An increasing fraction of the total load demand is becoming to a degree controllable by means of Demand Response or Demand-Side Participa- tion schemes. Such schemes may also be used as an integral part of aggregator schemes, coordinating the dispatch of all distributed unit types, i.e. generation, load and storage units. Examples of such aggregator schemes were discussed, besides others, in [74]. The potential problem with load response and aggregator schemes that are proactively controlled by a third-party is that they may not act as expected by T&D system operators. They rely on load forecasts and expected line flows, often based on the assumption that loads are uncontrolled and follow some random distribution in their load behavior. Especially the active control of sizable EV/PHEV fleets may lead to unexpected and erratic load behavior from the perspective of the system operator, i.e. unintentionally creating large peak load events. This has been discussed for the case of the City of Zurich, Switzerland in [75]. This problem field is not entirely new as there have been long-standing efforts to establish some degree of controllability over parts of the load 56 Chapter 3. New Challenges in Power Systems Operation demand, notably thermal loads such as water and space heaters, e.g. water boilers andHPs.

Two options for this had been available in the past. First, establishing direct load control (DSP) via dedicated communication channels, for example via so-called ripple control, a basic form of power-line communication, allowing to turn on and oﬀ the electricity supply to thermal loads. Second, establishing an indirect control mechanism via electricity price signals as an economic incentive for end-consumers. Variable electricity tariﬀs for steering price-responsive loads can be seen as a rather crude form of feed-forward control as is illustrated by (Fig. 3.8).

Figure 3.8: Concept of Price-based Demand Response (DR).

Regarding the later, simple high/low tariffs, also labeled peak/off-peak and day/night tariffs, have existed for many years in numerous Eu- ropean countries, e.g. France, Germany and Switzerland [51]. Many variable tariff schemes that are in place at present have in common that electricity prices during the low price period are only about half that of prices during the high price period. Although these variable tariff schemes are simple in nature, they are nevertheless creating a strong economic incentive to shift certain dispatchable loads, especially thermal heat storage, i.e. electric water or space heating, from the traditionally more expensive day hours to the cheaper night time.

It has to be mentioned, however, that there are already today examples of how a good intention, i.e. the wish to induce load valley filling and reduced peak demand, may in some circumstances also backfire. A telling example of what can happen to the aggregated load demand due to price-based DR is illustrated below for the grid zone of the French TSO Réseau de Transport d’Electricité(´ RTE). Figure 3.9 shows how the existing high/low tariffs scheme unintentionally, but rather effectively, can accidentally cause both the steepest power ramp as well as the highest consumption peak of the day shortly after the switching instance between the expensive day tariff to the cheaper night tariff at 10 pm. 3.2. New Technical Challenges 57

Figure 3.9: Price-based Demand Response in France (source: RTE[76]). A power ramp of more than 5 GW/h is induced at 10 pm (30 June 2013). 58 Chapter 3. New Challenges in Power Systems Operation

3.2.3 Power Market Activity & Liberalization

The hypothesis, right or wrong, that market liberalization is to blame for the more stressed grid situation, namely parallel flows and reduced security margins and in general the increasing usage levels of power system infrastructure has been voiced by many, and discussed in greater detail by Bialek in [77], [78]. Matter of fact is that the increasing power market activity that was already discussed in Section 2.3.2 is in a significant part due to the rapidly increasing RES power feed-in that needs to be integrated, i.e. sold, in the short-term. This happens for the most part via day-ahead and intra-day power markets, in Europe for example via EPEX[7] or Nord- pool [35] trading platforms. An increasing power market activity driven by economic considerations, i.e. the goal of a least-cost power dispatch, and in addition the superimposed impacts of volatile power feed-in patterns of variable RES units inevitably lead to more frequent changes of market-based power plant schedules and, hence, to more fluctuations and changes in power flow patterns. Set-point changes of power plants are increasing both in frequency, i.e. number of events per day, as well as in magnitude, i.e. the change in power output ∆P per event. In turn this means that more and larger ramping maneuvers of power plants are necessary in order to fulfill the more fluctuating power plant schedules. Due to the highly synchronous set-point changes of many power plants, e.g. at the quarter-hour and hour change, significant power imbalance due to imperfect power plant set-point trajectory maneuvers may occur. In fact, transient mismatches in power production, caused by dispatch operations with generators having differing generator ramp rates, are nowadays a common event and can create severe grid frequency deviations. This has been discussed and analyzed, besides others, in the work of Weissbach and Welfonder [6,79]. A nice illustration of this phenomenon is given by grid frequency measurements of the Swiss TSO swissgrid (Fig. 3.10). Although the power imbalances are transient in nature and deterministic, e.g. always happening at the hourly change, they trigger the use of frequency regulation reserves. This actually constitutes a false activation of primary and secondary frequency control reserves happens because there is no automated feedback loop from the frequency regulation entity, i.e. the TSO, to the entity performing the scheduling as defined by an Economic Dispatch (ED), i.e. the power utilities. 3.2. New Technical Challenges 59

Figure 3.10: Deterministic Frequency Disturbances Related to Power Market-induced Schedule Change (Courtesy of W. Sattinger, swissgrid).

Altogether, this phenomenon has become a considerable nuisance for grid operation. However, it may under unfortunate circumstance also become an actual threat. For instance if a large transient power imbalance at the hour change coincides with a real power outage, which then overwhelms already saturated primary and secondary frequency controllers. Such a situation may lead to a critical frequency excursion that in turn triggers automated generator or load tripping. The root-cause of this phenomenon is the inability or economically driven unwillingness to perform power plant set-point changes and ramping maneuvers according to the standing grid codes, which may cause more wear and tear on machinery. Coming back to the hypothesis that market liberalization is to blame for the increasing diﬃculties with grid operation, for instance the described transient power & frequency imbalances, one can state the following:

• As was pointed out above, it is true that power markets have lead to higher utilization levels of the power systems infrastructure.

• It is also true that higher grid utilization, notably in conjunction with lacking investments, makes old-fashioned operation of power 60 Chapter 3. New Challenges in Power Systems Operation

systems, i.e. half-blind due to lacking power system state awareness and half-deaf due to lacking inter-TSO coordination, more diﬃcult if not impossible in the long-term.

• However, as was pointed out by Bialek that to ”run the interconnected system very conservatively, maintaining large security margin at a high cost to everyone” [77] cannot be an option.

• Signiﬁcant improvements in both system awareness and system operation coordination are thus direly needed.

This doctoral thesis proposes some new ideas in this respect regarding the topic of Operational Flexibility in Chapters7–9. 3.3. New Economic Challenges 61

3.3 New Economic Challenges

3.3.1 RES Integration

In power systems with high shares of variable RES, it is becoming more and more difficult to integrate all of the available renewable electricity generation. In fact, an increasing share of RES energy production cannot be integrated and has thus to be curtailed. Operational inflexibility in keeping the power balance, i.e. must-run generation constraints, and grid bottlenecks, notably on the distribution grid, are the dominating factors for this. Forced curtailment effects so far predominantly wind power feed-in and varies from one power system to another and from year to year. Re- cent data suggests that wind energy curtailment in the Spanish power system was about 0.8% of available yearly wind energy in 2010 and about 0.2% in 2011 (source: REE). The figures are in the same range for Germany, i.e. about 0.6–1.1% in 2011 (source: Ecofys). The forced curtailment and hence loss of this available electricity production is becoming an economic concern both for owners of affected RES units and grid operators. It constitutes a welfare loss in the range of millions of eu- ros. On the other hand, the complete grid integration of variable wind & PV production may require significant technical efforts, i.e. higher operational flexibility, and with it economic costs that may not be jus- tifiable in the long-run. A more detailed analysis of this aspect follows in Section 3.4.2.

3.3.2 Demand Response & Aggregators

The crucial question for many proposed DR and DSP schemes confer to [80] for a substantial review, is whether or not they are economically viable today or will become so in the future. Although there may be a clear economic beneﬁt of using DR in grid operation, say in the form of reduced peak load events, which would eventually lead to investment deferral, due to existing regulatory frameworks as well as power andAS market structures this beneﬁt may not be passed on to aggregators thus making their business case nonviable. However, due to the previously illustrated exponential cost reduction trend for computation and communication capability (Section 2.4), while at the 62 Chapter 3. New Challenges in Power Systems Operation same time energy prices and costs for grid infrastructure are – at least on a decade-long average – not falling, some of the proposed ideas in the area of Demand Response may not make economic sense today but may very well do so in the near future after further reductions in ICT costs.

3.3.3 Power Market Activity & Liberalization

Merit-Order Eﬀect

Increasing RES production has, in some countries, already today significant effects on power markets, notably in the form of the so-called merit-order effect. Especially the decoupling of spot market prices and RES feed-in due to FIT regulations, results in lower average spot price levels and in some instances also negative spot prices. One effect of this is that flexible but expensive power plants such as gas-fired units are threatened in their profitability because peak spot prices are too often below these units’ marginal operation costs. All market participants, e.g. large producers, traders and public utilities, are to some degree affected by the impact that renewable electricity feed-in has on electricity spot prices. This impact is visible notably as increased spot market volatility. The stochastic character of feed-in from variable RES units, e.g. wind and PV units, and the resulting impacts of RES power feed-in on the spot market’s merit-order curve and prices are widely being discussed. The focus thus far has mostly been on RES feed-in from wind turbines [81]. A recent paper also eludes on the effects ofPV power feed-in, which is even more pronounced and leads to significantly lower or even negative spot prices and decreased mid- day load peaks. Due to the decreasing spread of peak/base spot prices, energy storage facilities, i.e. Pumped Storage Hydro Plants (PSHPs), are also at risk of not being profitably anymore [82]. Recent events such as the occurrences of forced curtailment of power market activities as well as highly negative spot market prices, for instance in Germany throughout the year 2009 [83], have shown that high shares of fluctuating RES power can drive power systems into undesirable situations. This is particularly the case if not all technically available flexibility measures, i.e. generation rescheduling and RES curtailment, are used. Such situations can be alleviated by increasing the operational flexibility as is discussed at the end of this chapter. 3.3. New Economic Challenges 63

Inﬂexible Power Market Structures

Today’s power andAS market frameworks are not yet providing an ideal structure for accommodating either large shares of RES power feed-in or demand response and aggregators. Due to the structuring of power and AS products, i.e. procurement length, delays in the market processes and market sampling times, some ineﬃciency losses are inevitable. Of notable importance are here process delays, i.e. the so-called gate-closure time which is the time-delay between the end of a market auction and the begin of the actual power orAS delivery. The role of gate-closure delays is illustrated in the following for the time-evolution of RES forecast errors (Fig. 3.11). The shorter the gate-closure time is, the more precise will be the forecasts of RES energy production.

Figure 3.11: Time-Evolution of RES Forecast Error and Gate-Closure Time (own illustration). 64 Chapter 3. New Challenges in Power Systems Operation

3.4 Situation in Germany

3.4.1 Technical Challenges

RES Forecast Errors

The day-to-day power dispatch of the EPEX German–Austrian Spot Market zone, and hence in the German power system, is driven largely by the high relative shares of RES power feed-in. This is illustrated in the following by the histogram of the RES production’s relative share at the EPEX spot for the full-year 2011 (Fig. 3.12). When comparing this to the RES production’s relative share with the actual load demand in Germany, as provided by ENTSO-E, it becomes clear that RES production is in fact over-represented at the EPEX spot.

Figure 3.12: Histogram of Subsidized RES Feed-In Volume versus EPEX Day-Ahead Spot Volume in 2011 (own analysis [56]).

Both generation types do, at times, provide ﬂuctuating power feed-in in the double-digit gigawatt range. In turn, absolute RES forecast errors can thus become substantial as well – at times up to several gigawatts. 3.4. Situation in Germany 65

As is illustrated in Fig. 3.13, the characteristics of forecast errors can change dramatically from one exemplary day to another.

Figure 3.13: Examples of Wind & PV Forecast Errors in the German Power System (own analysis, using time-series from EEX[84]). The behavior of the RES forecast error can range from exhibiting

1. Almost no forecast error, i.e. PV power feed-in on 30/5/2011, to 2. Constant oﬀsets, i.e. wind power feed-in on 24/5/2011, to 3. Sudden changes in RES forecast accuracy for certain hours, i.e.PV power feed-in on 31/5/2011, and ﬁnally 4. Gravely inaccurate RES forecasts with a varying power mismatch of ±1–2 GW or more, i.e. wind power feed-in on 31/5/2011.

In order to mitigate the power mismatch between the day-ahead dispatch planning and the actual situation in the last case, signiﬁcant power up/down ramping of dispatchable generation in the gigawatt range is required several times per day. This illustrates how reliant eﬀective power system operation is on having accurate RES forecasts. 66 Chapter 3. New Challenges in Power Systems Operation

Increased Flexibility Need due to Fluctuating RES Production

Another operational issue related to the ﬂuctuating RES electricity production is the behavior of the so-called residual load demand in the German power system. The residual load demand is the net load demand that remains after accounting for all variable RES power feed-in, i.e.

residual brut variable RES Pload demand = Pload demand − Pgen . (3.2)

The residual load demand needs to be provided by the remaining fully dispatchable generators and energy storage units. As can be seen in Fig. 3.14, the residual load demand looks qualitatively similar to the brut load demand curve, i.e. having pronounced day/night load changes. However, the residual load curve does also exhibit a significantly more erratic behavior over time than the brut load curve. This can be clearly seen for this exemplary time-series, the first week of January 2012, for the period following time-step 100: Here, the maximum power ramp (in GW/h) is about 35% higher for the residual load curve than for the brut load demand. In turn this means that the dispatchable generators covering the residual load demand have to ramp up/down more often. Accomplishing this requires a sufficient capacity of flexible power plants and energy storage that can modulate their power output sufficiently fast, i.e. with the required ramp-rates.

Figure 3.14: Brut Load Demand versus Residual Load Demand (own analysis using time-series from EEX[84]). 3.4. Situation in Germany 67

Inertia Loss due to Inverter-based RES Production

Due to the rising RES shares also the number of hours per year in which RES feed-in makes up a large part or the majority of power production in a grid region is increasing. For the case of Germany, this eﬀect is already very pronounced as is shown in Fig. 3.15. Here, the power dispatch situation of wind &PV units as well as conventional generation in the German power system is illustrated for the time-period of December 2012 (31 days). Also, the histogram of the total inverter-connected RES feed-in, i.e. wind &PV, as a share of the total load demand in Germany is given for the full year 2012. Over the course of that year the share of inverter-connected RES units often reaches signiﬁcant levels: a share of 30% or more is reached for 495 hours a year (5.6%), 40% or more for 221 hours (2.5%) and a record 50% for 0.75 hours (0.009%), respectively. In 2013, the share of inverter-connected RES units was more than 60% for some hours (Section 3.4.1). In frequency stability analysis often the assumption is used that the (aggregated) inertia constant H is constant, and the same, for all grid zones of a multi-area power system. This assumption was valid in the past but is nowadays increasingly tested by reality as is illustrated in Fig. 3.16.

It shows that the aggregated inertia Hagg of the German power system, as calculated using Eq. 2.6, has become highly time-variant, fluctuating between its nominal value of 6 seconds, i.e. at times when only conventional generators are dispatched, and significantly lower levels of 3–4 seconds, i.e. at times when significant shares of wind &PV generation units are active. Note that the lowest level of rotational inertia of this year was reached during the Christmas vacation in which demand levels were at their lowest while notably wind power feed-in was un- usually high. The histogram for the full-year 2012 reveals that inertia levels drop to lower levels for a significant part of the time: Hagg was below 4 seconds for 293 hours (3.3%) and below 3.5 seconds for 57 hours (0.65%) of the time. The qualitative results of this example are valid also for the inertia situation in other countries with high RES shares. 68 Chapter 3. New Challenges in Power Systems Operation

(a) Power Dispatch Situation (December 2012)

(b) Histogram of Inverter-Connected Power Feed-In Shares (full-year 2012)

Figure 3.15: Power Dispatch Situation in German Power System (own analysis [71]). 3.4. Situation in Germany 69

(a) Time-Variant Aggregated Rotational Inertia Hagg (December 2012)

(b) Histogram of Aggregated Rotational Inertia (full-year 2012)

Figure 3.16: Rotational Inertia Situation in German Power System (own analysis [71]). 70 Chapter 3. New Challenges in Power Systems Operation

Recent RES Power Feed-In Records

Although the yearly power feed-in shares of wind &PV units may still seem minor, the contributions were around 10% in the case of wind power production and around 5% in the case ofPV production compared to the overall annual load demand in Germany by year-end 2013, rather extreme feed-in situations do happen from time to time. Two recent records were days in which more than half of the instant load demand in the German power system was covered by wind &PV:

• 61% of instant load demand covered by wind (9.3 GW) & PV (20.3 GW) power production on 16 June 2013, and

• 59.1% of instant load demand covered by wind (13.9 GW) & PV (20.1 GW) power production on 3 October 2013.

Please note that both events happened on low-load days, a sunday and a national holiday, respectively.

3.4.2 Economic Challenges

Merit-Order Eﬀect of RES Power Feed-In

In the following, a short assessment of the correlation of RES power feed-in with electricity spot prices is presented. The impacts of RES power feed-in on EPEX spot price profiles regarding the intra-day profiles are analyzed. As was explained before, the significant power feed-in of FIT-subsidized RES units, which is given to power markets at zero cost, has a noticeable impact on spot market price levels via the merit-order effect [81,85]. This spot price impact can usually be observed in the form of lower than fundamentally expected or even negative spot prices and, in the case of PV feed-in, significantly decreased mid-day load peaks. As can be studied in Fig. 3.17, the normalized hourly spot price has become substantially depressed over mid-day, i.e. noon hours, over the course of recent years (2006–2010). This coincided with rapidly rising PV feed-in over the same time-period. The available empirical data suggests a strong causal link for the EPEX 3.4. Situation in Germany 71 spot market and can be explained via the mechanism of the merit-order effect. For this analysis publicly available data from the German TSOs and EPEX have been used. The complete study results can be found in [82].

Figure 3.17: Impact ofPV Feed-In on Spot Prices (own analysis [82]).

RES Curtailment

Due to the continuing RES deployment, forced curtailment of RES power feed-in in Germany due to grid congestion or grid stability problems is also on a steep rise – from virtually zero in the year 2004 to about 200–400 GWh in the year 2011. For the time being mostly wind power feed-in and distribution grid companies in Northern Germany are concerned. Some DSOs in northern Germany had to curtail wind power feed-in every 1–2 days in the year 2011, impacting 3–42% of the installed wind turbine capacity in their respective grid regions. In total, about 0.6–1.1% of the overall yearly wind energy produced in 2011 could not be integrated into the electricity grid. Grid operators that are unable to integrate RES electricity currently have to pay a penalty fee as stip- 72 Chapter 3. New Challenges in Power Systems Operation ulated by the German Feed-In Tariﬀ law EEG[25]. It is estimated that about EUR 30–40 million had to be paid in the year 2011. Since 2013 also PV units are obliged to take part in curtailment schemes in order to reduce the grid contingencies that are already surfacing. It is expected that this new regulation will lead to signiﬁcant PV curtailment. However, thus far there are no quantitative studies of how much energy from PV units is being curtailed. The evolution of forced wind feed-in curtailment over the years is illustrated by Fig. 3.18.

Figure 3.18: Curtailment of RES Power Feed-In (source: ecofys). 3.5. Need for Operational Flexibility in Power Systems 73

3.5 Need for Operational Flexibility in Power Systems

This chapter has illustrated some of the new challenges that power system operation is facing, notably – but not only – due to rising RES energy shares but also due to increasing power market activity. Many but not all of the here high-lighted challenges relate to a need for more power system flexibility, e.g. for counterbalancing power mismatches and unplanned power flows throughout the grid. Flexibility as such is, admittedly, a rather vague term. This doctoral thesis thus exclusively refers to technical operational flexibility, i.e. meaning the technical ability of a grid operator to modulate – if need be – the power in-/outflow on a global scale, i.e. for achieving the power balance, and within a grid topology, i.e. to control power flows at specific grid nodes. Confer also to Def.2 and Sec. 7.3.1 for more details. Clearly, the grid integration of large shares of variable RES requires operational flexibility for absorbing the steep and abrupt power ramps of it’s power feed-in profiles. Operational flexibility can be obtained as ’energy products’ via power markets, i.e. day-ahead and intra-day spot markets, as well as ’control reserve products’, i.e. primary/secondary/tertiary frequency control, from Ancillary Services markets. The issue is that the need for more operational flexibility will inevitably lead to more costs for fully dispatchable/controllable back-up power capacities. In addition, keeping these back-up capacities spinning may lead to sub-optimal Economic Dispatch results caused by stringent must-run generation constraints that have to be respected in the optimization. Faced with the mid-term prospect of rising challenges for grid operation on both the demand side due to growing electricity consumption caused by the likely electrification of the heating sector, i.e. via Heat Pump, and the transport sector, i.e. via PHEV/EV fleets, and the generation side, i.e. potentially very large shares of variable RES due to ambitious energy policy goals of achieving an 80% carbon-free electricity generation by the year 2050, the need for more operational flexibility resources and the urge to acquire them by all possible means is apparent. The following chapter will outline some of the options for obtaining these (re-) sources of operational flexibility for power system operation.

Chapter 4

Opportunities in Power Systems Operation

4.1 Introduction

The previous chapter has presented some long-known operational challenges as well as some new challenges for power system operation, mainly due to RES generation. One of the main issues related to this discussion is the perceived lack of operational ﬂexibility for power system operation, needed to absorb steep and abrupt power ramps in RES electricity generation. In general it can be stated that the need for Ancillary Ser- vices (AS), i.e. active as well as reactive control reserves, is increasing with rising shares of non-controllable power feed-in. Possible mitigation options are to deploy more ﬂexible conventional generation units, to introduce controllability over a fraction of load demand viaDR schemes, to make RES power feed-in curtailable and to increase energy storage capacities. However, DR schemes are still a niche solution and the expansion of available bulk energy storage technologies faces various limitations, for instance geographic limits, as is clearly the case for hydro-based storage and Compressed Air Energy Storage (CAES) units, or economic limits in the case of batteries since they are still expensive. Therefore, grid operators still rely predominately on fast-responding

75 76 Chapter 4. Opportunities in Power Systems Operation dispatchable power plants, and as a last resort measure the curtailment of RES power feed-in, in order to mitigate sudden and unexpected power imbalances. Additional control reserve capacity offers the possibility to increase the transmission grid’s stability reserve margins, meaning its capability to robustly respond to occurring fault events. Larger control reserve capacities can facilitate the integration of increasing amounts of fluctuating electric power feed-in from fluctuating renewable sources. A widely popularized idea for providing additional control reserve capacity is the utilization of battery storage capacity of PHEV/EV fleets and the capability to modulate the aggregated load profile from DSP schemes as well as the curtailment of fluctuating electricity feed-in from renewable sources to offer additionally control reserve capacity. This is seen as beneficial especially in regions with a large share of fluctuating electricity feed-in from renewable energy sources. However, the potentially useful control reserve capacity coming from either PHEV/EV batteries, DSP schemes or RES power feed-in has a highly fluctuating availability – depending on week day, time of the day and prevailing electricity consumption patterns. For wind turbines or PV installations the availability depends on wind or solar insolation forecasts. Having reliable predictions of the future availability of control reserve power over time is thus crucial. However, the questions arise from which sources, conventional and unconventional, necessary control reserves can be procured in principal, and whether or not existingAS frameworks have to be adapted in order to allow the provision of additional control reserves also in practice. The ultimate usefulness of supplementary control reserve capacity from time-varying sources thus depends on two questions:

1. Can supplementary control reserve capacity from time-varying sources be integrated into existing ancillary service frameworks? 2. Can the existing ancillary service frameworks be adopted and made more ﬂexible such that the integration of certain sources for supplementary control reserve capacity is facilitated?

Most existing allocation frameworks for ancillary services, i.e. primary and secondary control reserve with their influence on power quality as well as tertiary control reserve with its influence on power flows, have unfortunately rather rigid structures [8]. 4.1. Introduction 77

Despite these concerns and practical implementation problems, several benefits of providing supplementary control reserve capacity can be envisioned. Two of those are discussed here in more detail. First of all, increasing the available quantity of control reserves increases the (transmission) grid’s stability reserve margin in critical situations. This means that the grid’s flexibility or robustness when reacting to fault events increases. Combining control reserve capacities from conventional sources as well as from time-variant sources, while explicitly taking into account any constraints that are implied by this time- variability, enables the full utilization of potentially available control reserve power from all connected sources, i.e. controllable generators and loads. This results in a larger available reserve capacity that can be called upon in an emergency situation. Second, aggregating control reserve power from time-varying renewable energy sources like onshore and offshore wind turbines as well asPV arrays, adds the notion of controllability over the power feed-in of these energy sources. The formerly uncontrolled fluctuating electric power feed- in from these sources is then at least partially controllable via measures such as partial generation curtailment or delta operation mode [86]. In power systems with substantial RES shares, the fluctuating electricity feed-in should not any longer be understood simply as a disturbance on the grid and as an inherently uncontrollable phenomenon. Controlling the fluctuating RES power feed-in is possible. Achieving this goal will need updated and possibly new grid management schemes. One of the possible solutions could be an ancillary service manager that is able to allocate and dispatch supplementary control reserve from time-variant, only partially controllable, sources. Not using the described additional control reserve power to the fullest extent deprives the grid and the existing grid control schemes of potentially available control actuator. Crucial for the effective RES grid integration is to improve the availability, controllability, observability and predictability of RES units:

• Availability: Issues in real-time and very short-term time- scale (min./hours, i.e. wind andPV) to long-term time- scale(weeks/months, i.e. hydro).

• Controllability: Issues on real-time (min.) to short-term (hours) time-scale, e.g. a system operator’s ability to limit wind & PV power feed-in. 78 Chapter 4. Opportunities in Power Systems Operation

• Observability & Predictability: Issues on real-time (min.) to short-term (hours/days) time-scale, i.e. a system operator’s ability to measure and predict wind &PV feed-in and to have a clear understanding of on-going power feed-in and feed-out processes.

A complimentary approach to increasing the operational ﬂexibility of a power system, i.e. increasing available control reserves, is to improve forecast accuracy of variable RES generation as this reduces the need for control reserve capacities that merely serve as back-up for RES feed-in uncertainties. Analyzing the impact that RES forecast accuracy has on the dimensioning of needed control reserve capacities is thus a highly relevant task, certainly for power systems that already have or are expected to have high variable RES feed-in shares.

4.2 Operational Flexibility in Power Sys- tems

4.2.1 Role of Operational Flexibility

The term Operational Flexibility in power systems is often not properly defined. In a power systems context, the term flexibility may refer to very different things ranging from the quick response times of generation units, e.g. gas turbines, to the degree of efficiency or robustness of a given power market setup. The topic is receiving wide attention [45,87–91].

In the remainder of this doctoral thesis the focus is solely on the technical aspects of operational ﬂexibility. Operational ﬂexibility of a power system refers to the existing slack in system operation that an operator can use to mitigate disturbances. It is the ability to modulate the electrical power feed-in/out over time in order to absorb power imbalances as stated in Def.2. 4.2. Operational Flexibility in Power Systems 79

Definition 2 – Operational Flexibility in Power Systems Operational flexibility is the technical ability of a power system unit to modulate electrical power feed-in to the grid and/or power feed-out from the grid over time. This means the technical ability of a grid operator to modulate the power in-/outflow on a global scale, i.e. for achieving power balance, and within a grid topology, i.e. to control power flows via the modulation of power injections and outtakes at specific grid nodes.

4.2.2 Sources of Operational Flexibility

Several sources of operational ﬂexibility in power systems exist as is illustrated by Fig. 4.1:

• Conventional generation, i.e. in the form of dynamically fast responding conventional power plants, e.g. gas turbines.

• Storage, i.e. in the form of stationary storage capacities, i.e. hydro- based bulk energy storage, or time-variant storage capacities, i.e. from the batteries of PHEV/EV ﬂeets.

• Load demand, i.e. by means of adapting the load demand curve via DSP schemes for thermal loads in the residential sector or sizable industrial loads to partially absorb ﬂuctuating RES power.

• RES units, i.e. by directly curtailing a part of the ﬂuctuating power feed-in from wind & PV units.

Operation flexibility in power system operation and dispatch planning is of importance and has a significant commercial value. Ancillary service markets facilitate system operators the cost-effective procurement of needed control reserve products. In the case of frequency control, in essence a set of flexibility services provided to system operators for achieving active power regulation on different time-scales [9], the overall remuneration for providing control power and energy on ancillary service markets is usually higher than for energy from spot markets. 80 Chapter 4. Opportunities in Power Systems Operation

Figure 4.1: Sources of Operational Flexibility (own illustration [68]).

4.2.3 Classiﬁcation of Operational Flexibility

In the following a classification of operational flexibility in resources and reserves is presented. It is inspired by the established classification systems for natural resources, e.g. crude oil or natural gas [92]. The categories for classifying available operational flexibility are:

• Potential Flexibility Resources, i.e the ﬂexibility resources exist physically and could be used. The necessary controllability over the respective power system units is however lacking.

• Actual Flexibility Resources, i.e. the part of the Potential Flexibility Resources that can in fact be used because controllability over the respective power system units exists.

• Flexibility Reserves, i.e. the part of the Actual Flexibility Re- sources that can be used economically.

• Market-Available Flexibility Reserves, i.e. the part of the Flexibility Reserves that can be sold and, vice versa, also procured from power or Ancillary Services markets. This steems from the fact that additional constraints due toAS product structuring may limit the amount of the Flexibility Reserves that can be procured in practice. 4.2. Operational Flexibility in Power Systems 81

The procurement of the Market-Available Flexibility Reserves is, in a liberalized setting, accomplished via the market auctioning of

• Flexibility products, i.e. Ancillary Services, or

• Power market products, i.e. via the scheduling mechanism of spot intra-day and day-ahead power markets.

Figure 4.2: Classification of Operational Flexibility Resources and Re- serves (own illustration). Making existingAS procurement more flexible would add an important degree of freedom for the integration of time-variant flexibility (re- ) sources, such as PHEV/EV fleets [93]. However, control reserve capacity for primary and secondary control is even today usually still procured by TSOs as fixed power capacity for longer time periods, e.g. one week to one month, for instance “Provide 10 MW (positive and/or negative) secondary control reserve capacity, available at all times, for the whole month of January 2014” [94]. Unfortunately, this rather rigid structuring ofAS products severely limits the ability of providing control reserves by time-variant flexibility (re-) sources. As a simple example, only 38.2% (0.0%) of aggregated battery capacity from a PHEV fleet of several thousand cars may be available for providing fixed positive (negative) control reserve power at all times during a given time period, here one day (24 h), see Fig. 4.3. If instead positive (negative) control reserve power could be allocated on an hourly basis, which would be reasonable for the case of a PHEV fleet with a well predictable availability profile, most of the additional control reserve power, i.e. 95.3% (76.0%), could be allocated in a reliable manner. In practice, only the above stated sub-optimal, i.e. fixed, allocation of the theoretical available reserve capacity from such time-variant flexibility (re-) sources is possible. 82 Chapter 4. Opportunities in Power Systems Operation

Another constraining factor in today’s ancillary service allocation frameworks is the traditional distinction between primary, secondary and tertiary control reserve power, which derives from the existing grid control structures. It can be concluded that existing frameworks for procuring ancillary services are not as flexible as would be needed for the full integration of supplementary control reserve power from time-variant sources. In practice, only a sub-optimal allocation of the theoretical available reserve capacity from such sources is possible. It has to be noted as well that first steps towards making the procurement of ancillary services more flexible have been accomplished recently. Some European TSOs, for instance the Swiss TSO swissgrid, have recently changed control reserve capacity auctions for primary and secondary control reserve from monthly to weekly periods, due to the observed lack of liquidity in the capacity auctions [95]. Shorter allocation periods for ancillary services, allow a more flexible procurement of control reserve capacity also from conventional generation. It is conceivable to organize ancillary service auctions on even shorter time horizons, for example on the basis of one- or two-day-ahead auctions, since weather predictions on such short time horizons are relatively accurate [96]. This would enable a more efficient and robust utilization of control reserve power from wind & PV installations.

Figure 4.3: PHEV Ancillary Services Availability for One Day (24 h) (own illustration [12]). 4.2. Operational Flexibility in Power Systems 83

A quantification of potential resources of operational flexibility is illustrated in the following for the Swiss power system (Fig. 4.4). For the case of the existing Swiss power system, the amount of operational flexibility in the form of power & energy capacity from hydro- based storage units, i.e. Pumped Hydro Storage and Hydro Stor- age Lake, greatly outsizes all other resources such as time-variant PHEV/EV fleets and DSP schemes. Hydro-based storage units provide vast amounts of bulk energy storage capacity, both in terms of power rating, i.e. hydro pumps for storage charging and hydro turbines for storage discharging. In the Swiss case, these units are all located in remote alpine areas and, thus, connected to the high voltage transmission grid. Potential grid bottlenecks due to the discussed energy transition are more likely to occur, however, in the low and medium voltage distribution grids. Smaller distributed energy storage and DR units would provide here a better leverage than traditional bulk energy storage units.

Figure 4.4: Sources of Operational Flexibility in the Swiss Power Sys- tem (own illustration, adapted from [97]). 84 Chapter 4. Opportunities in Power Systems Operation

4.3 Controllability & Observability in Power Systems

4.3.1 Traditional Controllability & Observability in Power Systems

In traditional power system setups, all generation and bulk energy storage units are considered to be both controllable as well as observable over time. Load demand on the other hand is not considered to be controllable. The assumption is, however, that load demand is suﬃciently well observable, usually in the form of aggregated load demand at a substation, where measurement equipment exists, as well as suﬃciently well predictable over the relevant time-horizon, i.e. for the following hours to days. DG units, especially variable RES units are not considered to be controllable nor directly observable. They are, however, indirectly observable in the form of a lower than expected load demand, i.e. the residual load.

4.3.2 Emerging Controllability & Observability in Power Systems

Controllability of Variable RES

In times of rising installed DG generation capacities and energy shares, notably in the form of wind & PV, an obvious approach for system operators is to improve both controllability and observability of variable RES units. Fluctuating power feed-in from wind turbines andPV arrays is predictable to a certain extent [98]. Nowadays, information on the fore- casted future power feed-in is included in the power plant day-ahead dispatch in areas with significant RES penetration. Forecast errors are balanced via intra-day power trading and conventional control reserves, not by the intermittent generators themselves. Curtailment of intermittent power feed-in is typically only employed as an abnormal measure. The utilization of on-line control measures for intermittent generation units, such as partial generation curtailment [99,100], has been included 4.3. Controllability & Observability in Power Systems 85 in the grid code of many countries with significant wind & PV power penetration, for instance in Denmark, Spain and Germany. This kind of controllability, however, remains limited by the availability of the primary energy carrier, e.g. the wind force. The challenge of systematically integrating such methods into power system operation and control constitutes another motivation for the present work. As an illustrative example, the efforts of the Spanish TSO REE for achieving controllability & observability over RES units in their grid are presented:

• REE can control and observe most of the variable generation power feed-in in Spain directly from it’s National Renewables Dispatch Center (CECRE). It aggregates information from 30 regional Renewable Energy Control Centers (RESCCs), i.e. an example of the aggregator concept.

• All RES units with a power rating greater 10 MWp have to be connected to a RESCC by Royal Decree (RD) 1565/2010.

• A quantitative analysis of RES controllability & observability in the REE grid gives the following results (mid-year 2012):

1. Controllability (an obligation for all RES units ≥ 10 MWp) – 95% of total wind power capacity, – ≈100% of total CSP power capacity, and, – 10.6% of total PV power capacity (experimental). 2. Observability (an obligation for all RES units & aggregations ≥ 1 MWp) – 100% of total wind power capacity, – 100% of total CSP power capacity, and, – 68% of total PV power capacity (only 3% prior to RD 1565/2010).

Similiar trends and TSO-side eﬀorts exist in other countries with high variable RES shares, e.g. in Denmark in Germany. For the German TSOs, one argument for improving RES controllability & observability was also the experience of the 2006 European Blackout and the role that non-controlled wind power plants had played as an additional disturbance during the power system restoration phase (Info-Box1). 86 Chapter 4. Opportunities in Power Systems Operation

Controllable Energy Storage for Power Systems

All forms of energy storage entail energy conversion processes based on a wide range of technologies [101]. In addition to reversible energy storage in the form of pumped hydro, batteries, flywheels etc., a very important form is heat storage. Methods to improve the controllability of loads with inherent storage are emerging, such as control strategies for household appliances with thermal inertia and for prospectively large numbers of electric vehicles connected to the grid [102, 103]. Ubiquitous controllable energy storage is likely to have positive effects on system operation, ranging from security-relevant power reserves to loss reduction on the distribution system level [104–106]. Especially in power systems dominated by fluctuating and/or inflexible generation capacity, flexibility is valuable [107] and energy storage units are well-suited for providing it. However, current grid operation frameworks do not directly support the specific properties of energy storage. For instance, storage reserves are not conceptually considered in the traditional procurement of control reserves: only power reserves are considered by system operators, whereas the regulation energy required for performing control actions is usually not visible to the operator and is settled only in post-operation. Due to energy storage dynamics and slow reacting power plants, their associated inter-temporal dependencies, i.e. energy and power ramp-rate constraints, as well as other controllability limitations are particularly relevant for power dispatch problems. Here, the optimization methodology of Model Predictive Control has proven itself to be especially suitable [108–110]. Reconsidering the issue of grid inertia loss and faster grid frequency dynamics as presented previously in Section 3.2.1: The challenge of faster frequency excursions could be mitigated, if energy storage units would be available for providingAS products, notably, faster primary control reserves, e.g. fully activated within 5 s after a fault. This approach would in fact by highly effective, as shown in Fig. 4.5 (shown in green). Notably modern BESS are well-suited for providing a fast power response as was shown in [111], [112], [113] and [114]. Another viable option is the provision of temporary primary frequency control from (variable speed) wind turbines [115]. 4.3. Controllability & Observability in Power Systems 87

Further details as well as extensions to this analysis can be found in [71].

Figure 4.5: Dynamic Response of ENTSO-E Continental European Power System to Fault Events (own analysis [71]). Black: high inertia (H = 6s), i.e. no wind & PV power feed-in share, nominal frequency control reserve. Red: low inertia (H = 3s), i.e. 50% wind &PV power feed-in share, nominal frequency control reserve. Green: low inertia (H = 3s), fast control reserves.

Novel Control Structures

The additional degrees of freedom that energy storage and increased controllability over RES feed-in and loads provide, can only be utilized if a suitable control architecture is established.

Several novel control structures, often utilizing aggregation principles, have been proposed in this context, including: Virtual Power Plants [116], Cells [117], or MicroGrids [118]. The performance assessment of diﬀerent operation and control approaches constitutes a challenge in itself [119]. 88 Chapter 4. Opportunities in Power Systems Operation

Aggregators

The concept of aggregators has been proposed for the aggregation of small distributed, but controllable, generators, storage and load units in order to perform various services such as frequency regulation for power systems [120]. The idea of using battery capacities of PHEV/EV fleets and curtailable RES generators to perform ancillary services is popular [86,121]. How- ever, comparably small and distributed energy generation and storage units cannot contribute easily to procuring the services, as their individual power and/or storage ratings are small. Many distributed power system units have a time-variant availability, e.g. wind turbines can only be curtailed when it’s windy and PHEV/EV fleet batteries can only balance fluctuations when connected to the grid. An illustration of an Ancillary Service Manager is shown in Fig. 4.6. It can aggregate control reserve capacity from both fully-dispatchable sources, e.g. conventional generators, as well as from time-variant and only partially controllable sources, e.g. PHEV/EV fleets, DSP schemes, curtailable wind generators and PV installations. The blocks shown on the grid domain symbolize conventional generators and storage (larger blocks), wind farms (medium-sized blocks) and PHEVs/EVs as well as DSP-controlled consumers (small/medium-sized blocks). The ancillary service manager communicates directly with conventional generation, storage units, and indirectly via aggregator entities with distributed, smaller generation, storage and load units. TheAS manager sends out control signals and receives information on unit availability and technical constraints, which is then used for updates of the optimization setup. For the effectiveness of this Ancillary Service Manager, both its communication structure with underlying aggregating entities and the employed optimization setup are key factors. The communication links between the Ancillary Service Manager and the aggregators on the one hand as well as the aggregators and the individual small to large power system units on the other hand are qualitatively indicated as black lines. Communication from the aggregators to the individual units is accomplished via various communication channels, e.g. internet, GPRS or PowerLine (ripple control). More details are given in [113]. 4.3. Controllability & Observability in Power Systems 89

Figure 4.6: Communication Structure of Ancillary Service Manager to Lower Level Controllers (communication links indicated as black lines). (own illustration [113]).

4.3.3 Actuators & Sensors in Power Systems

A useful framework for illustrating the beneﬁts of increasing controllability & observability is discussed in the following. In a power systems context, controllability is denoted by the available control knobs or actuators u and observability is denoted by the available sensors y for power system operation as is illustrated by the well-known Robust Control Framework shown by Fig. 4.7[122].

Figure 4.7: Robust Control Framework (own illustration). 90 Chapter 4. Opportunities in Power Systems Operation

The relevant system variables and models in robust control [122] are:

• Plant G, i.e. the system to be controlled, in this analysis a power system or a model thereof,

• Disturbance w, i.e. all exogenous system variables and set-points that are not controllable by the system operator and hence act as a disturbance to power system operation,

• Plant output z, e.g. power generation, load demand or storage states,

• Measured/estimated system state y, i.e. exogenous system processes and storage states,

• Control input u, i.e. all endogenous system variables such as load, generator and curtailment set-points, and,

• Controller (Optimizer) K, i.e. the entity that governs power system operation. In a power system context this would be the system operator.

Qualitatively, it can be said that if a system operation entity K has more information about the given power system G, i.e. via measurements or estimation of y and/or has more control actuators u at its disposal, the (optimal) control policy u (or u∗) should improve, i.e. the plant output z is improved with respect to a given performance metric.

Please note that in robust control, an optimal control policy is often calculated as u∗ = −Ky, where K is derived from LQR/LQG theory. The control policy can improve if additional input information y or additional actuators u become available. 4.3. Controllability & Observability in Power Systems 91

Quantifying Controllability & Observability

The notion of minimum-energy control [123, p. 65] Z 2 T −1 −1 u = u u dt = f (WR ) or f (WC ) , (4.1) i.e. the control eﬀort needed to transfer the system from system state x0 to x1, i.e. x0 → x1 (reachability), or vice versa from system state x1 to x0 , i.e. x1 → x0 (controllability), where

Z t −t 1 0 At 0 A0t WR(t0,t1) = e BB e dt , (4.2) 0 Z t −t 1 0 −At 0 −A0t WC(t0,t1) = e BB e dt , (4.3) 0 is also a useful analysis tool in a power systems context. Qualitatively, it can be stated that the more control a system operation entity has over its power system, i.e. the larger the matrix entries of B are or the closer the actuator u is to the disturbance d, the less control eﬀort u2 will be needed to mitigate this disturbance. Obviously, the analysis will be diﬀerent between copper-plate & line-constrained power systems, e.g. more complex in the later case. Benchmark Example In a power system, an operator has controllable inputs u and non- controllable inputs, i.e. disturbances d. Increasing the entries of the matrix Bu makes system control easier & faster. Decreasing the entries of the matrix Bd reduces impacts of disturbances, i.e. both the system excursion distance and speed. In the following, a double-integrator system is used for a purely qualitative analysis and illustration of the here expressed thoughts. As will be shown later on, double-integrators are a very relevant system type in a power systems context (in Chapter8).

x˙ = Ax + Bu u + Bd d

As is shown by the simulation plots in Fig. 4.8, the control task as measured by the term u2 becomes easier, or faster, if the matrix entries of Bu increase. 92 Chapter 4. Opportunities in Power Systems Operation

Figure 4.8: Minimum-Energy Control Analysis (own analysis). Left Plot: 1 · Bu, Right Plot: 2 · Bu.

In this analysis setup, the controllability (and observability) of power systems can quantitatively be compared. System I (right) is better (easier, faster) controllable as System II (left). The influence of non-controlled inputs, i.e. disturbances, on the sys- 2 tem states can be assessed via Wc and u . It can be shown that it’s a good choice to reduce the influence of non-controlled inputs d, i.e. reducing the matrix entries of Bd, and increase the influence of controlled inputs u, i.e. increasing the matrix entries of u. 4.4. Hardware- versus Control-based Grid Adaptation 93

4.4 Hardware-based versus Control-based Grid Adaptation

After having outlined the arising challenges ahead for power system operation due to high shares of RES generation, and having explained the crucial role that operational flexibility plays for RES grid integration, the question remains what are effective means for grid adaptation. This thesis proposes that such grid adaptation measures should be divided into two categories, i.e. into traditional hardware-based grid adaptation, i.e. investing into copper and steel, and control-based grid adaptation, i.e. investing into efforts that allow more controllability and observability of the power system. A detailed specification of what is meant by the terms hardware-based and control-based grid adaptation is given by Def.3 and Def.4. Since grid planning is traditionally based on the existing or assumed future power peak, either the maximum load demand or maximum generation peak, a hardware-based grid expansion for power systems with, for example, high PV energy share would yield a significantly over-sized electricity grid, requiring both high investment as well as high maintenance efforts. Contrary to this, in control-based grid adaptation, one can take advantage of the trade-off between employing more computation & communication, which is cheap and generally getting cheaper versus employing physical grid infrastructure, for which investments are expensive.

Deﬁnition 3 – Hardware-based Grid Adaptation Hardware-based grid adaptation includes the addition or increased power & energy rating of all grid hardware that is pas- sive, i.e. Transmission and Distribution (T&D) grid infrastructure such as line additions or replacements, e.g. high-temperature overhead conductors, as well as transformer additions or replacements, e.g. allowing higher voltage levels. The challenges of RES power feed-in, higher load demand and increasing power market activity are hence mitigated simply by higher line and transformer power ratings. This is accomplished, for instance, by adding transmission grid layers with higher voltage levels. 94 Chapter 4. Opportunities in Power Systems Operation

Definition 4 – Control-based Grid Adaptation Control-based grid adaptation includes all active elements in the grid infrastructure such as the deployment of FACTS devices, the addition of new, preferably distributed generation and storage units or the flexibilization of existing conventional generators as back-up reserves and large-scale hydro-based storage as buffer, as well as all smart means, i.e. adding ICT infrastructure in order to create new or improved, e.g. faster or more accurate, control loops around existing hardware elements, for enhancing the utilization level of existing physical grid infrastructure. Such measures include Demand Response (DR) schemes on the industrial (large demand), commercial (medium demand) and residential (small demand) scale, controlling the active and reactive power feed-in of RES generators as well as operating and coordinating distributed storage units for both local control tasks, i.e. peak shaving, voltage & reactive power regulation and global control tasks, i.e.frequency & power regulation. Also included are all improvements in the fields of grid state- estimation, for example Dynamic Line Rating (DLR), load demand and feed-in prediction and optimization of power system operation , i.e. power dispatch and storage management, optimal power flow and control reserves procurement. Further- more, flexibilization measures for existing conventional generation, i.e. higher power ramp-rate capabilities, reduction of activation as well as start/stop times, and storage units, i.e. flexible pumps and turbines, higher power & energy rating, are included. Part II

Modeling Frameworks for Power & Energy Systems

Chapter 5

Modeling Frameworks for Power & Energy Systems

5.1 Motivation for Modeling and Simula- tion of Power & Energy Systems

The internal workings of power & energy processes are in reality complex. In addition to this, new technological & economical trends lead to change in the complex dynamics of power feed-in and feed-out processes, as pointed out in earlier chapters increasing RES power feed-in as well as more frequent power set-point changes both of generators and loads, i.e. DR, make grid operation more complex than in the past. When diﬀerent energy systems, i.e. electricity, natural gas and heat grids, are coupled with each other, the interactions between them become especially complex. The prerequisite for increased operational eﬃciency is a better qualitative and quantitative understanding of the underlying processes, namely of primary fuel supply for producing electricity in the case of variable RES units, i.e. wind &PV, and of end-use power & energy demand of electricity, i.e. of load units. This is the motivation for novel modeling frameworks that allow for more modeling detail of underlying processes in power & energy systems.

97 98 Chapter 5. Modeling of Power & Energy Systems

5.2 Modeling of Electric Power Systems

5.2.1 Review of Modeling Frameworks for Genera- tion, Storage and Load Units

A Structure Preserving Model framework for power system stability analysis was introduced by Hill and Bergen in [124]. This modeling framework, later on also coined Network-Preserving Model (NPM) allows the modeling and analysis of frequency-dependent loads (ν1) and synchronous generators (ν2). A recent modeling extension to this takes into account the rising share of inverter-connected Direct Current (DC) generation units, i.e.PV units, as well as many modern wind turbines that are grid-connected, but also electro-mechanically decoupled from frequency dynamics and rotational inertia, via AC-DC-AC converters. In [125] a model is proposed for DC inverters (ν3) that are droop-controlled. A complete power system model is given by the union set ν of loads, synchronous and inverter- connected generators: ν = ν1 ∪ ν2 ∪ ν3. In the following, the model description of a power system with respect to the dynamic real power balance is presented. For consistency of the different contributions, the following equations are given in a notation similar to the one used by Dörfler and Bullo in [126]. Frequency-Dependent Loads ˙ Diθi + Pload,i = − ∑ ai j sin(θi − θ j), i ∈ ν1 , (5.1) j∈Ci

Synchronous Generators ¨ ˙ Miθi + Diθi = Pmech,i − ∑ ai j sin(θi − θ j), i ∈ ν2 , (5.2) j∈Ci

Inverter-connected Generators ˙ Diθi = Pgen,i − ∑ ai j sin(θi − θ j), i ∈ ν3 , (5.3) j∈Ci ˙ where θi ∈ S and θi ∈ R are the generator rotor angle and frequency, respectively. The power terms Pload,i ≤ 0, Pmech,i ≤ 0 and Pgen,i ≤ 0 describe the load unit’s electric power feed-out (load demand), the synchronous generator unit’s mechanical power feed-In and an inverter- connected generator unit’s electric power feed-in, respectively. 5.2. Modeling of Electric Power Systems 99

The terms Mi > 0 and Di > 0 are the rotational inertia and frequency damping coeﬃcients of the corresponding units. For brevity, the term ai j is used as a shorthand of the complete formulation ai j = |Vi| · |Vj| · bi j, where Vi and Vj are the voltages, given with Root Mean Square (RMS) values, and bi j is the susceptance or imaginary part of the line admittance yi j between nodes i and j. The set Ci is the set of all nodes j that are adjacent to node i. This modeling approach can be extended to also include the active and reactive power balance at each (load) node (confer also [127]): Active Power Balance at Node i

Pi(Vi) = ∑ ai jsin(θi − θ j) , (5.4) j∈Ci

Reactive Power Balance at Node i

Qi(Vi) = − ∑ ai jcos(θi − θ j) , (5.5) j∈Ci where Pi and Qi are the real and reactive power injections (input or output) at a given node. For load units, both terms can have a voltage- dependence according to the load’s characteristics. Equations 5.4–5.5 correspond to the classical Alternating Current (AC) power ﬂow equations for a loss-less network, i.e. typical of high-voltage AC transmission networks, where only the imaginary part of the line admittance yi j = gi j +ibi j between nodes i and j, the susceptance bi j, is considered, whereas the real part, the conductance gi j, is neglected. The modeling equations (Eq. 5.1–5.5) can be grouped into a higher- dimensional set of Diﬀerential Algebraic Equations (DAE), also known as Descriptor State Space (DSS) models, of the form

x˙ = f (x, y) , (5.6) y = g(x, y) , (5.7) where the dynamic state vector x includes for each generator two associated state variables, i.e. voltage angle θi and frequency ωi = θ˙i and, if they are included in the modeling process, also higher-order generator and/or load dynamics. The algebraic variable vector y includes all load bus voltages Vi. As pointed out in [127], if loads are modeled as being 100 Chapter 5. Modeling of Power & Energy Systems dynamic, then there will be additional dynamic state variables that correspond to internal behavior of these loads, e.g. motor slips, that makes them voltage-dependent. An illustration of individual power system elements, i.e loads, lines and generators, is given in Fig. 5.1.

(a) Load Element (b) Generator Element

Figure 5.1: Illustration of Power Network Devices as Circuit Ele- ments (source: D¨orﬂer et al. [126]).

Possible modeling extensions of NPMs, notably employing energy functions for better modeling loads and lines, are numerous. An extensive yet concise overview of such methods can be found in the book by Pai [128]. In practice, such nonlinear dynamic load models have to be derived by model identification means using actual grid measurement data. Well-documented studies on voltage-dependent loads have been conducted, for example, for the Swedish power system [129, 130]. Links to graph theory and coupled oscillators are rather straightforward as pointed out by Dörfler et al. in [126]: Under some assumptions, i.e. with exception of the inertial terms Mi, rotor angles θi and the, in practice, probably non-unit coefficients Di, the above stated model of power network dynamics is an electrical analogous model of the the well-known Kuramoto Model of an originally chemical coupled oscilla- ¨ n tor [131, p. 164], namely θi = ωi − ai j ∑ j=1 sin(θi − θ j) with the nodal 5.2. Modeling of Electric Power Systems 101 parameters ωi ∈ {−Pload,i, Pmech,i, Pgen.,i} and, respectively, the inter- connecting chemical or electrical network with weights ai j. Already before that, Chen and Hill [127, Section 3] had pointed out the connections of power systems to graph theory, coupled oscillators as well as network synchronization theory and synchronization conditions. An IEEE benchmark micro-grid populated with individual power system elements is shown in Fig. 5.2.

Figure 5.2: Illustration of IEEE 37 Micro-Grid with Individual Power System Elements: Synchronous Generators (red), Load Buses (blue) and Inverter-connected Generators (yellow) (source: Dörfler et al. [126]). Please note that the original NPM framework from 1981 [124], as well as recent extensions to it notably by [125,126] but also others like [132] and [133], were all introduced for theoretical studies such as synchronization in power systems. Although some underlying assumptions in the NPM equations in the latter research work are suitable for mathematical analysis and make proofs easier, they are often crude oversim- plifications of the more complex, generally non-linear, power systems reality. This is arguably the case for instance for angle stability criteria [133] as well as for the assumption of small inertia to damping ratios M ( D )[134] that cannot be applied in transmission grids which are naturally underdamped, whereas it is workable for micro grids as was shown by [132]. Also the assumption of fixed voltage levels can be too simplistic: Con- sider a three bus linear network with generators on each end and a load bus in the middle, the power flow at the load bus in the middle would have a decisive affect on the synchronization behavior of the two generators at the edges. These rather difficile effects was the motivation at 102 Chapter 5. Modeling of Power & Energy Systems the time to move to more complete DAE models, which allowed more general load characteristics; confer for instance to [135–139].

5.2.2 Power System Modeling along Time-Scales

The above introduced Network-Preserving Model (NPM) Framework for power systems is of interest for the analysis on short time-scales, where fast dynamical processes such as generator swing dynamics and transient voltage dynamics are relevant. On longer time-scales, however, all fast frequency and voltage dynamics, i.e. the transient dynamics, will disappear. The NPM’s swing equation and droop dynamics (Eq. 5.1–5.3) thus simplify to the active power balance equation at every grid node (Eq. 5.4), since in (quasi) steady- state operation the transient system states converge to zero, i.e. θï = θ˙i = 0, and with it the effects of rotational inertia, Mi, and frequency- dependent load damping as well as frequency-droop control, Di, vanish from the modeling equations. When also considering the reactive power balance (Eq. 5.5), the classical AC power flow model is recovered. From a physical perspective this finding makes perfect sense: The rotational inertia, M, describes an energy storage element, i.e. the rotating masses of a generator’s/load’s machinery that stores rotational kinetic energy. This energy storage is very small and depleted after a few seconds (= value of inertia constant H) at nominal power rating (P0). Frequency-dependent load damping and frequency droop-control, both described by the term D, are also dynamically fast processes that disappear on longer time-scales1.

5.2.3 Limitations of Classical Power System Modeling

A clear limitation or shortcoming of the NPM framework, Eq. 5.1–5.3, is that it only describes active and reactive power injections at the respective grid node (Fig. 5.3). The background processes that are behind the individual power system units and the corresponding power in-ﬂows and out-ﬂows, i.e. primary

1 Please note that the transient states {θ˙i, θi} = {∆ωi, ∆θi} are defined here as ˙ 0 0 0 0 deviations around a steady-state operation point {θi , θi } = {ωi , θi }. They thus vanish as soon as this nominal operation point has been recovered in steady-state. 5.2. Modeling of Electric Power Systems 103 fuel provision, end-use demand and storage functionality, are not modeled and, thus, remain hidden. The pure power flow interactions can therefore only give an opaque picture of what happens behind power system units. Comparatively slow dynamics, i.e. bulk energy storage processes and fluctuating primary power availability notably from variable RES units, are neither considered nor modeled here. There is thus a strong motivation for developing complimentary modeling frameworks that allow to capture this missing model information.

Figure 5.3: Interaction between Power System Units and Electricity Grid in Network-Preserving Model representation (own illustration). 104 Chapter 5. Modeling of Power & Energy Systems

5.3 Modeling of Energy Systems

5.3.1 Energy Hub Modeling Framework

The well-known Energy Hub concept [140] focuses on multi-carrier energy networks. It allows the study of synergies that the combination of electricity, natural gas, and heat network infrastructures may provide for energy dispatch [141], infrastructure reliability [142], and investment decisions under uncertainty [143]. Energy storage is one element of the concept, but is not necessarily considered since the focus of Energy Hubs is primarily on the transformation of energy carriers between different network infrastructures (Fig. 5.4). The Energy Hub concept facilitates the unified modeling of energy networks and resulting synergies of electricity networks, i.e. electric power R Pe and energy Ee = Pe dt, natural gas networks, i.e. gas flow (or power) R Pg = m˙ g and energy Eg = Pg dt = mg, as well as district heat networks, R i.e. thermal power Ph and energy Eh = Ph dt. This allows the analysis as well as the operational and structural optimization of multi-carrier energy systems [144]. Furthermore, studies of optimal investment strategies in multi-carrier energy systems are largely facilitated by using Energy Hubs [145]. Finally, Energy Hubs are naturally suited for usage in conjunction with model-based, predictive optimization schemes for multi-carrier energy systems [146]. This allows the optimal operation of generation, load and, especially, storage units as a function of available load demand and RES generation forecast time-series.

Figure 5.4: Transformation of Energy Carriers in Energy Hubs (source: [147]). 5.3. Modeling of Energy Systems 105

The Energy Hub modeling concept is based on the relationship

L + M = C · [P − Q] , (5.8) where L corresponds to the vector of output-side load flows, M to the vector of output-side storage flows, P to the vector of input-side power flows and Q to the vector of input-side storage flows. The term C denotes the so-called coupling matrix, which contains as entries the individual efficiencies ηα,β of the transformation between a given input-side energy carrier flow Pα , e.g. natural gas, and a given output-side energy carrier flow Lβ , e.g. electricity (Fig. 5.5).

Figure 5.5: Transformation of Energy Carrier Flows in the Energy Hubs Modeling Framework (source: [148]).

Storage elements can also be represented within the Energy Hub Con- cept, both on the input-side as well as on the output-side, as presented in the PhD thesis of M. Geidl [148] and illustrated here by Fig. 5.6.

Figure 5.6: Storage Elements in Energy Hubs (source: [148]). 106 Chapter 5. Modeling of Power & Energy Systems

Motivation

Due to the wide-spread deployment of Distributed Generation (DG) technologies, such as Photovoltaic (PV) units, wind turbines, Combined Heat and Power Plant (CHP), biomass-fired plants and others, energy production is transformed from a paradigm of a few centralized units to numerous and technically diverse distributed units, located at lower voltage levels [149], i.e. in the electric distribution grid. Moreover, the fluctuating power feed-in of variable RES as well as the uncertainties in their predicted available power output, create the need for storage solutions and appropriate operation strategies. An- other changing aspect within the current power system structure is that strong(er) couplings between electricity networks on the one hand and natural gas as well as heat networks on the other hand arise. This coupling is created, notably via CHP units that produce simultaneously electricity and heat by consuming natural gas as a primary fuel. Additional couplings could arise in the future with the possible advent of commercial electrolysis and methanization units, popularized under the label power-to-gas technologies [150], that allow to convert surplus electricity production into chemical energy carriers, i.e. hydrogen (H2) and synthetic methane (CH4), as a means of seasonal storage. Also, due to the availability of various energy carriers for end-use, consumers are more flexible in their purchasing choice, which allows them to make decisions depending on criteria such as costs, reliability and energy system emissions, i.e. CO2. For investigating all of these aspects, the Energy Hub Concept comes as a natural choice. Energy systems are considered to consist of a number of interconnected energy hubs, which represent the interface between consumers and the power supply of the different energy systems.

Energy Hub Networks

In the following, an exemplary Energy Hub network is presented, consisting of three energy hubs interconnected by an electricity (solid) and natural gas (dashed) network, as illustrated by Fig. 5.7. Each hub represents a prosumer, e.g. an aggregation of both loads and DG units.

Each of the hubs has its own local electrical energy production Gi, with G electric power production Pe,i, for i ∈ {1,2,3}. Hubs H1 and H2 have 5.3. Modeling of Energy Systems 107 access to adjacent natural gas networks N1, N2. Each hub consumes H H electric power Pe,i and gas Pg,i, and supplies energy to its electric load Le,i and its heat load Lh,i. For energy conversion, the hubs contain a CHP CHP CHP with its respective conversion eﬃciencies, i.e. ηge,i and ηgh,i , as well F as a furnace with eﬃciency ηgh,i. The dispatch factor νg,i (0 ≤ νg,i ≤ 1) determines how the gas is divided between the CHP and the furnace.

For each hub Hi, the outputs Li +Mi and inputs Pi correlate as follows: CHP H Le,i + Me,i 1 νg,iηge,i Pe,i = CHP F H . (5.10) Lh,i + Mh,i 0 νg,iηgh,i + (1 − νg,i)ηgh,i Pg,i | {z } | {z }| {z } Li+Mi Ci Pi Each hub contains both an electrical and heat storage unit. The storage devices are modeled as an ideal storage in combination with a storage interface (ee/h,i). The power exchange Me/h,i(k) at time step k is deﬁned as the diﬀerence between the actually stored energy Ee/h,i(k) at two ˙ stb consecutive time steps, plus some stand-by energy losses Ee/h,i E (k) − E (k − 1) 1 e/h,i e/h,i ˙ stb Me/h,i(k) = + Ee/h,i . (5.11) ee/h,i ∆t More detailed information on hub modeling is given in [148, 151].

Figure 5.7: System Setup of Three Interconnected Energy Hubs (source: [152]). 108 Chapter 5. Modeling of Power & Energy Systems

5.4 Motivation for new Power & Energy Modeling Frameworks

5.4.1 Modeling of Background Processes

As was pointed out before, the mere consideration of power inputs and outputs neglects all system processes happening behind a given power system unit. This includes notably storage functionality, primary fuel provision as well as end-use energy demand; and with it also information on energy conversion efficiencies (η). Relevant operation and planning questions, i.e. which of the considered power system units are storage units, and are thus energy-constrained, or generators that provide fluctuating power feed-in or, as a dual problem, loads with fluctuating power feed-out (load demand) are left an- swered (Fig. 5.8). In this respect, the Energy Hub Concept thus represents a significant step forward as it allows to explicitly include modeling information of these background processes, e.g. end-use energy demand or availability of RES production. However, for a complete functional modeling, some information of specific characteristics of a given power system unit and it’s background processes, namely their controllability & observability, are still missing. Especially in the case of time-variant RES generation, the question of what controllability and observability (full/partial/none) a system operator has over the fluctuating generation profiles is highly relevant. An analogous question arises in the case of Demand Response (DR) units and their end-use demand profiles.

Figure 5.8: Relevant Background Processes in Power System Operation (own illustration). 5.4. Motivation for new Power&Energy Model Frameworks109

Due to the deployment of more and more ﬂuctuating power feed-ining from RES units and also more DR schemes for load units and, in general more storage capabilities in power system, a more detailed functional modeling of power system units is beneﬁcial for system operation, if not even necessary. Whether or not load demand or RES generation can be curtailed has become an important aspect of power system modeling and control. The original Energy Hub Modeling Framework is, however, too rigid and does as such not enable the consideration of load shedding and generation curtailment.

Thus complementary modeling frameworks are required that, due to their more versatile modeling capability, can provide a higher degree of system awareness especially of time-variant processes such as time- variant power feed-in, i.e. RES units, and feed-out, i.e. load demand, as well as time-variantly available energy storage SOC and storage capacity, i.e. EV ﬂeets.

5.4.2 Control-based Categorization of Power Sys- tem Units

In the following a control-based categorization of power system units, inspired by the well-know Kalman Decomposition [153, 154] from control theory, is proposed. Following it’s line of thought, all the various types of power system units would thus be categorized into being either dispatchable/controllable or non-dispatchable/non-controllable and, in a dual perspective, being either observable or non-observable. As a brief recapitulation: via the Kalman Decomposition an arbitrary state-space system, given by the tuple (A, B, C, D), and deﬁned as

x˙ = Ax + Bu y = Cx + Du , (5.12) where x is the state vector, y the system output vector, u the control input, A the system state matrix, B the control input matrix, C the system output matrix and D the system feed-forward matrix, is transformed into a new tuple (Aˆ , Bˆ , Cˆ , Dˆ ). 110 Chapter 5. Modeling of Power & Energy Systems

This new state-space tuple (Aˆ , Bˆ , Cˆ , Dˆ ) is deﬁned as

xˆ˙ = Aˆ xˆ + Buˆ ,      AR,O¯ A12 A13 A14 xˆ1 BR,O¯  0 AR,O 0 A24 xˆ2 BR,O xˆ˙ =   + u , (5.13)  0 0 AR¯,O¯ A34 xˆ3  0  0 0 0 AR¯,O xˆ4 0 | {z }| {z } | {z } A¯ xˆ B¯ y˙ = Cˆ xˆ + Duˆ ,   xˆ1 xˆ y˙ = 0 C 0 C  2+Duˆ , (5.14) R,O R¯,O xˆ  | {z } 3 Cˆ xˆ4 | {z } xˆ where Aˆ = T−1AT, Bˆ = T−1B, Cˆ = CT, Dˆ = D and x = T−1xˆ with T = [TR,O¯ TR,O TR¯,O¯ TR¯,O] as the appropriate transformation matrix employed for the decomposition. This resulting tuple (Aˆ , Bˆ , Cˆ , Dˆ ) can then easily be split into its four sub-systems, i.e. (non-) reachable/controllable and (non-) observable sub-systems, as is illustrated qualitatively by Fig. 5.9. As a result one obtains a clear separation of the full system input vector into controllable inputs Bu u, i.e. system control inputs, and non-controllable inputs Bd d,i.e. system disturbances. For the case of uncontrollable processes, a separation in observable/estimable and, over the time-horizon predictable, disturbances Bd,O dO, and non- observable and, over the time-horizon thus non-predictable, disturbances Bd,O¯ dO¯ can be made. Likewise, a separation in observable/estimable states xO, i.e. measurable/estimable and predictable and non-observable system states xO¯ can be obtained. In the context of power system analysis, this approach yields a classiﬁ- cation of typical power system units into the four categories as follows:

• Conventional Generation Unit Power feed-in is considered both observable & controllable, i.e. fully dispatchable.

• Aggregated Load Demand Power feed-out is well observable/predictable, at least for suﬃ- ciently large aggregations, but not controllable. 5.4. Motivation for new Power&Energy Model Frameworks111

• Demand Response (DR) Load Unit Power feed-out is controllable – at least in aggregation – but establishing observability, notably of storage states, i.e. the temperature of the heat storage of thermal load units, is often a key problem for making DR schemes viable.

• Hydro-based Bulk Energy Storage Unit Power feed-in & feed-out is both observable & controllable.

• Variable RES unit Power feed-in from variable RES, i.e. wind &PV, can range from being non-observable & non-controllable to being observable & controllable, i.e. curtailable within the range of available primary power.

Please note that in this way only a binary decision regarding controllability and observability can be made. Using in addition approaches based on the Gramian matrices, WR, WC and WO, allows for a quantitative assessment of how well controllable & observable a given power system unit is at a given point in time (see also Chapter8). This is needed as most power system processes are inherently time-variant.

Figure 5.9: Kalman Decomposition of State-Space Model (own illustration).

Chapter 6

Power Nodes Modeling Framework

The Power Nodes Modeling Framework was first proposed in a conference article by Kai Heussen, Stephan Koch, Andreas Ulbig and Göran Andersson in 2010 [155]. An extended journal version was later on published by the same authors in 2012 [156]. Please note that some of the following sections are derived directly or indirectly from this collabo- ration effort (Sections 6.1–6.2). The remaining parts, Sections 6.3–6.8, are the original contributions of the author of this doctoral thesis. The focus in the following is on power systems and electric power processes. However, other energy carriers such as thermal and chemical energy flows, i.e. heat and natural gas, can also be considered with appropriate adaptations regarding the modeling of the grid infrastructure.

6.1 Introduction

The Power Nodes modeling framework is a uniﬁed framework for the functional modeling of power system units, such as:

• diverse storage units, e.g. batteries, pumped hydro, CAES[157],

113 114 Chapter 6. Power Nodes Modeling Framework

• diverse generation units, e.g. fully dispatchable conventional generators, variably producing power units, and

• diverse load units, e.g. conventional (non-controllable), interruptible or thermal (both partially controllable), including their respective operational constraints as well as relevant information of underlying power supply and demand processes. Operation constraints such as min/max power ramp rates, min/max power operation ranges and energy storage operation ranges, i.e. energy storage capacity and State-of-Charge (SOC), can be modeled explicitly. Power Nodes modeling is based on the accurate modeling of three system domains, namely the power demand & supply domain, the energy storage & conversion domain and the power transport & distribution domain, i.e. the electricity grid, and their respective energy interactions. Like the Energy Hub concept, the Power Nodes framework has been developed for the study of hypothetical future energy scenarios and is aimed specifically at the analysis of future power system operation, which requires a multi-stage simulation environment [158]. Prior studies evaluating power system operation with increased RES and energy storage, e.g. [159], utilized multi-stage simulation environments which were founded on existing tools and operation concepts. For future power systems, however, operation and control principles and market structure are subject to re-design. A structured simulation environment can provide the context necessary for experimental development and systematic assessment of new operation strategies that are tailored for future scenarios by including a reasonable market dispatch to generate reference data, as well as a framework for evaluating their control performance. The Power Nodes framework facilitates the consideration of energy storage, fluctuating generation and other types of non-conventional energy resources by providing a conceptual model for energy storage as well as for different levels of controllability over power system units [160]. Modeling information of controllability of underlying power system processes, be they fully controllable, curtailable/sheddable or non-controllable, can also be included. The same is true for the dual modeling information on observability and predictability as obtained by either actual state measurements and/or state-estimation and prediction of these underlying power system processes, be they fully or only partially observable/estimable or predictable system states and control inputs. 6.2. Definition of Power Nodes Modeling Framework 115

6.2 Deﬁnition of Power Nodes Modeling Framework

The basic premise of the Power Nodes approach is that any power source or sink connected to the electric power system requires the conversion of some form of energy into electric power, or vice versa. These forms may be termed “supply-” or “use-forms” of energy, respectively. The degrees of freedom available for fulfilling the power balance in the grid arise from the freedom that the supply- and use-forms of energy flows provide, either by being controllable or by offering inherent storage capacity. Abstracting from the physical properties and the internal composition of a supply- or use-process including the associated energy conversion processes, we represent it from a grid-perspective as a single lumped unit with characteristic parameters, a “Power Node”.

6.2.1 Domain Models

The introduction of a generic energy storage perspective adds a modeling layer to the classical modeling of power systems, illustrated in Fig. 6.1. In the resulting enhanced model, the electro-mechanical domain of the electric grid is interfaced with the pre-grid Power Node domain, which represents conversion processes and an associated energy storage functionality. A third, external, domain accounts for the demand/supply processes consuming energy from and feeding energy into the Power Node domain. As shown in Fig. 6.1, these processes may be thought of as externally driven, e.g. intermittent renewable energy supply, or fully controllable, e.g. fuel supply for dispatchable generators. Here, the Power Node- and Grid domains are model-internal domains, both are considered integral parts of the electric energy system. The domain of Demand/Supply processes is considered external, indicated by the dashed frame. The arrows represent energy flows that are accounted for. Empty arrowheads indicate energy flows, i.e. power, that are exchanged with the environment, while black arrowheads indicate energy flows into or across the modeled domains. For ensuring model consistency, it is important to define unambiguous domain interfaces. Generally, these are exchanges of energy flows in continuous time. For instance, the exchange between the Power Node 116 Chapter 6. Power Nodes Modeling Framework

Figure 6.1: Illustration of the Power Nodes Three-Domain Con- cept [156]. domain and the Grid domain is defined as the active power fed into or consumed from the grid. In the case of a dynamical grid model, the inertia of synchronous machines is part of the Grid domain, and thus the active power interface is equivalent to the mechanical power exerted by the prime mover of a synchronous generator. Grid losses are modeled inside the electro-mechanical Grid domain, while pre-grid losses, such as storage and conversion losses, are accounted for in the Power Nodes domain. This clear separation allows the Power Nodes framework to integrate with a number of different physical network representations common in power systems modeling (cf. Section 6.2.3). All supply and demand processes are connected via a power node to the electricity grid. Consequently, the total energy provided to or demanded from the grid may differ from the actual energy served or utilized by external processes. All considered modes of energy flow are illustrated by arrows in Fig. 6.1 and Fig. 6.2. This mathematically redundant choice of energy flow modes establishes a formalized interpretation (cf. Sec- tion 6.2.5) of real-world effects that cause supplied energy to be lost, or demanded energy to remain unserved. For example, energy conversion implies conversion losses, power feed-in from wind turbines may be curtailed, and a load may get disconnected from the grid. In order to evaluate the overall system performance, it is necessary to account for these losses and the energy value associated with them. For this 6.2. Definition of Power Nodes Modeling Framework 117 purpose, balance terms as presented in Section 6.2.7 can be utilized.

6.2.2 Model of a Single Power Node

Consider the structure of a single power node consisting of the elements illustrated in Fig. 6.2. In comparison with Fig. 6.1, the provided and demanded energies are lumped into an external process termed ξ, with ξ < 0 denoting use and ξ > 0 supply. The term ugen ≥ 0 describes a conversion corresponding to a power generation with efficiency ηgen, while uload ≥ 0 describes a conversion corresponding to a consumption with efficiency ηload. The energy storage level (SOC) is normalized to 0 ≤ x ≤ 1 with energy storage capacity being C ≥ 0. Figure 6.2 illustrates how the storage serves as a buffer between the external process ξ and the two grid- related exchanges ugen and uload. Internal energy losses associated with energy storage, e.g. physical, state-dependent losses, are modeled by the term v ≥ 0, while enforced energy losses, e.g. curtailment/shedding of a supply/demand process, are denoted by the waste term w, where w > 0 denotes a loss of provided energy and w < 0 an unserved demand process. This labeling for the power node equation provides a generic embedding of energy conversion and storage processes.

Generic Model

The dynamics of a generic Power Node i ∈ N = {1,...,N}, which may exhibit nonlinear eﬀects in the general case, are described as:

−1 Ci x˙i = ηload,i uload,i − ηgen,i ugen,i + ξi − wi − vi, (6.1) s.t. (a) 0 ≤ xi ≤ 1 , min max (b) 0 ≤ ugen,i ≤ ugen,i ≤ ugen,i , min max (c) 0 ≤ uload,i ≤ uload,i ≤ uload,i , (d) 0 ≤ ξi · wi ,

(e) 0 ≤ |ξi| − |wi| ,

(f) 0 ≤ vi ∀i = 1,...,N .

In the above given model equation for a generic Power Node, the term 118 Chapter 6. Power Nodes Modeling Framework

• 0 ≤ xi ≤ 1 describes the storage level (SOC), whereas the corresponding Ci quantiﬁes the storage capacity, • ξ > 0 describes an external energy supply, • ξ < 0 describes and external energy consumption,

• ugen,min < 0, umax > 0 and C > 0 describes a reversible energy storage,

max • Stochastic power feed-in (uncontrollable): ξ(t) = ξstoch(t), max • Stochastic power feed-in (continuously : ξ(t) = [0...ξstoch(t)],

• vi > 0 describes energy loss, and

• wi captures technology-dependent energy curtailment.

The constraints (a)–(f) denote a generic set of requirements on the variables. They are to express that (a) the state of charge is normalized, (b, c) the grid variables are non-negative and bounded, (d) the supply/demand and the curtailment need to have the same sign, (e) the supply/demand curtailment cannot exceed the supply/demand itself, and (f) the storage losses are non-negative.

Figure 6.2: Notation for a Single Power Node Representing a Generic Power System Unit [156]. 6.2. Deﬁnition of Power Nodes Modeling Framework 119

The explicit mathematical form of a power node equation depends on the particular modeling case:

• Depending on the speciﬁc process represented by a power node and the investigated application, each term in the power node equation may in general be controllable or not, observable or not, and driven by an external process or not.

• Internal dependencies, such as a state-dependent energy loss term vi = vi(xi), are feasible and correspond to physical realities, i.e. heat dissipation is a function of temperature diﬀerence.

• Charge/discharge eﬃciencies may be non-constant, e.g. state- dependent: ηload,i = ηload,i(xi), ηgen,i = ηgen,i(xi). This can be well-approximated via Piece-wise Aﬃne (PWA) models.

• Ramp-rate constraints, especially constraints on the derivatives u˙gen,i and u˙load,i, can be included for power system studies under dynamic operating conditions (cf. Table 6.1). Additional constraints may be imposed, e.g. in order to deﬁne certain standard unit types with characteristic properties (cf. Section 6.2.5).

The Power Nodes notation provides technology-independent categories that can be linked to the evaluation functions given in Section 6.2.7.

Modeling Power Nodes without Storage

Power nodes can also represent processes independent of energy storage, such as ﬂuctuating RES generation or conventional generation and load. A process without storage implies an algebraic coupling between the instantaneous quantities ξi, wi, ugen,i, and uload,i. In this case storage- dependent loss does not exist (vi = 0). Equation (6.1) degenerates to

−1 ξi − wi = ηgen,i ugen,i − ηload,i uload,i , (6.2) which holds for both externally driven processes and controllable power generation. The waste term wi is particularly relevant for external supply and demand processes which are not directly controllable, while there is the option to curtail them. Examples are intermittent power generation proﬁles, i.e. ξdrv,i(t) ≥ 0, and classical load demand, i.e. ξdrv,i(t) ≤ 0. 120 Chapter 6. Power Nodes Modeling Framework

For a fully controllable supply process such as a conventional generator, either the grid-related variables ugen,i, uload,i, or the power exchange with the environment through ξi can be considered controlled variables. The term ξi is then accounting, for example, the primary energy usage.

6.2.3 Mapping from Power Nodes to Grid Domain

All electric load and generation units are represented by power nodes, i.e. no further injections and loads need to be accounted for. Consider a power grid composed of a set M of M buses and a set N of N power nodes in total, representing a number of single or aggregated units. There may be 0 to N power nodes attached to any bus m in the grid model, and a power node has to be connected to exactly one bus. A Power Node connected to a grid bus m can then be formulated as a mapping, i.e. Nm : N → M , with the properties Nm ⊂ N , N j ∩Nk = S /0 for j 6= k , and m∈M Nm = N . The net power injection to a grid node m ∈ M is given in the following. As ugen,i and uload,i are the only power node variables “visible” from the grid perspective, they constitute the load or generation at a bus m:

Pgen,m = ∑ ugen,i , Pload,m = ∑ uload,i . (6.3) i∈Nm i∈Nm Pnetinj,m = Pgen,m − Pload,m (6.4)

Pnetinj,m = ∑ ugen,i − ∑ uload,i . (6.5) i∈Nm i∈Nm

Once a system boundary is established, all electric load and generation units inside are represented by power nodes, i.e. no further injections and loads need to be accounted for. Consider a grid composed of M busses denoted by m,n ∈ M = {1,...,M} and a set of N power nodes i ∈ N = {1,...,N}, representing a number of single or aggregated units. A mapping is formulated by index sets N → M . The power node indices are divided into sets Nm ⊆ N associated with one bus each; having the properties: Nm ∩ Nn = /0 for m 6= n, and S m∈M Nm = N . The net power injection to a grid node m ∈ M is thus:

Pnetinj,m = ∑ ugen,i − ∑ uload,i . (6.6) i∈Nm i∈Nm 6.2. Deﬁnition of Power Nodes Modeling Framework 121

6.2.4 DC Grid Model with Power Nodes

The Power Systems literature offers many options for power system modeling, depending on the relevant study questions. In principle, the Power Nodes domain can be interfaced with many grid model types, such as DC or AC power flow, static or dynamical grid models, due to the clear separation from the electro-mechanical domain1. To illustrate the approach, this section formulates an electric network represented by linear DC power flow equations. The DC network representation is used for example in an active power dispatch of a unit portfolio in a capacity-constrained transmission system. The DC power flow assumes small angle differences, a constant, flat voltage profile, and neglects the resistance of lines. While voltage angles are generally small, the critical assumptions are flat voltage profiles and negligible line resistances [161]. The DC power flow is then governed by the following equations:

Pexch,m = ∑ Bmn(δm − δn) , (6.7) n∈M n6=m M 0 = ∑ (Pnetinj,m − Pexch,m) , (6.8) m=1 where δm is the voltage angle at bus m, and Bmn = 1/Xmn the susceptance, i.e. inverse of the reactance, of the line connecting buses m and n. The line ﬂows may also be subject to capacity constraints:

cap cap − Pmn ≤ Bmn(δm − δn) ≤ Pmn . (6.9) The system frequency can be described by an aggregate inertia model:

M Hω˙ = ∑ Pnetinj,m , (6.10) m=1 where H is the aggregate inertia constant and ω is the angular frequency of the system.

1 In most cases it is appropriate to model the power-exchange ugen/load as a power injection to the respective bus. In case of a dynamical grid model, i.e. used for transient simulations, with the Power Node being a synchronous machine, the proper interface would be the mechanical power exerted on the generator shaft. 122 Chapter 6. Power Nodes Modeling Framework

6.2.5 Characterization of Unit Properties

Obviously, there is only a limited number of Power Node unit types that actually are of practical relevance in power system operation. As discussed in Section 6.2.1, the kinds of energy flows available in the generic power node model allow for a wide range of unit types. A given practical unit type is thus classified by its characteristic subset of the possible modes of energy flows. A “unit” in the power nodes framework is an arbitrary generation, load, or storage device, or a group of devices aggregated to behave as one unit in the given modeling context. The type distinction is established via a set of constraints on the energy-flow variables used in (6.1), i.e. uload,i, ugen,i, Ci, xi, ξi, vi, and wi. These constraints hold in addition to the principal constraints (a)–(f) in (6.1), thus providing a classification of units with different operational properties.

6.2.6 Unit Properties

First, a set of unit properties is established, then a number of possible combinations of these properties are listed, providing a link between the modeling framework and real units found in power systems. Table 6.1 establishes a set of basic properties deﬁning the operational behavior of a unit modeled as a power node. It thus provides a taxonomy of unit types that can be modeled using the Power Nodes framework. The interpretation of constraints is given in the following:

• Energy inﬂow ugen,i and energy outﬂow uload,i The variables ugen,i and uload,i determine whether a power node is injecting power into or consuming power from the grid. A pure generation process implies that uload,i = 0 at all times; a pure load cannot inject power, expressed by ugen,i = 0. In a bi-directional conversion system, both variables can assume non-zero values. A further distinction is whether both conversions can happen at the same time, e.g. in a storage with two separate conversion units such as a pumped hydro plant with independent turbine and pump, or whether one of the variables must always be zero, e.g. in an inverter-connected battery storage.

• Energy storage capacity Ci The storage capacity determines whether a unit is modeled with, i.e. Ci > 0, or without energy storage capabilities, i.e. Ci = 0. 6.2. Deﬁnition of Power Nodes Modeling Framework 123

• External energy ﬂow process ξ i The sign of the external process variable accounts for supply, i.e. ξi > 0, or demand processes, i.e. ξi < 0. For pure electricity storage, i.e. BESS, the equality constraint ξi = 0 holds.

• Curtailment or shedding term wi The term wi determines whether curtailment of a generation process, i.e. w > 0, or shedding of a load demand process, i.e. w < 0, is possible or not, i.e. w = 0.

• Controllability Modeling using ξ i,wi Constraints on ξi and wi indicate the controllability of power exchange via an external process. If ξi is driven by an external signal ξi = ξdrv,i(t), e.g. induced by intermittent supply, it may either be curtailable, i.e. no further constraint on wi, or non-controllable, i.e. no curtailment is possible (wi = 0). If ξi is not externally driven and can thus be controlled, the unit is controllable. In this case, the relationship wi = 0 can be assumed because the curtailment of a directly controllable process would be unnecessary2.

• Storage loss term vi The storage associated with a power node is considered loss-less if vi = 0 and lossy otherwise.

• Ramping constraints u˙load/gen,i The grid variables ugen,i and uload,i may be additional rate- constraints may be applied to the grid variables, which is reﬂected in continuous time by an upper and lower bound on their derivatives. This serves to model physical limitations on the rate of change of a power conversion process, e.g. due to the amount of thermal stress on power plant components.

Based on these properties, all unit types relevant for establishing the energy-balance in a power system can be classified and modeled inside the Power Nodes framework. A basic classification of unit types is included in [160]. Additional constraints may be considered for specific applications.

2Note that more detailed sets of constraints may be established for the power node variables in order to model particular units. In this case, it may be practical to allow for a non-zero wi even in the presence of a (partly) controllable external process ξi. 124 Chapter 6. Power Nodes Modeling Framework

Table 6.1: Unit Properties Deﬁned by Power Node Constraints.

Variable(s) Constraint(s) Implication for Unit Type

ugen,i, ugen,i = 0 Load

uload,i uload,i = 0 Generator

Ci Ci = 0 Non-buﬀered unit

Ci > 0 Buﬀered unit

ξi ξi = 0 No external process

ξi ≥ 0 Supply process

ξi ≤ 0 Demand process

ξi, wi ξi = ξdrv,i(t) ∧ wi = 0 Non-controllable

ξi = ξdrv,i(t) ∧ wi 6= 0 Curtailable ξi controllable ∧ wi = 0 Controllable

vi vi = 0 Lossless storage

vi > 0 Lossy storage min max u˙gen,i u˙gen,i ≤ u˙gen,i ≤ u˙gen,i Ramp-rate constraint (gen.) min max u˙load,i u˙load,i ≤ u˙load,i ≤ u˙load,i Ramp-rate constraint (load)

6.2.7 Performance Evaluation via System-Level Power & Energy Balances

The embedding of all energy units in the Power Nodes notation provides an energy-accounting framework. The performance of operation and control strategies can then be evaluated on the basis of this framework in the form of

• instantaneous quantities, characterizing the current operational state of the system, or

• time-integrals, serving to evaluate the system performance over a certain time span.

Note that the expressions stated here are considered examples, not a complete list of possible balance terms. The list can be extended with respect to the speciﬁed power and energy performance indicators and can also include technology-dependent weighting terms for economic costs, 6.2. Deﬁnition of Power Nodes Modeling Framework 125 e.g. marginal operation costs, or environmental impacts, e.g. CO2 emissions. Examples for power balance terms indicating the current operation state of a given power system, or in a more general sense a given energy system, include the following metrics:

grid • Power supplied to grid: Pgen (t) = ∑ ugen,i(t), i∈N grid • Power consumed from grid: Pload(t) = ∑ uload,i(t), i∈N

• Currently stored energy: Estored(t) = ∑ Cixi(t), i∈N total • Available power supply: ξsupply(t) = ∑ ξi(t), i∈{i|ξi>0}⊂N total • Power demand: ξdemand(t) = ∑ ξi(t), i∈{i|ξi<0}⊂N + • Power supply curtailed: w (t) = ∑ wi , i∈{i|wi>0}⊂N − • Power demand not served: w (t) = ∑ wi , i∈{i|wi<0}⊂N • Power conversion loss:

1 − η (t) P (t) = gen,i u (t)+ 1 − η (t) · u (t). loss ∑ (t) gen,i ∑ load,i load,i i∈N ηgen,i i∈N All of the above quantities can be restricted in order to consider only certain unit types or unit groups by placing restrictions on the index i. For example, the consideration of all non-controllable, non-buﬀered generation units, which is a typical representation for intermittent renewable generation without curtailment capability, would require a summation over the index i ∈ i|Ci = 0 ∧ ξi = ξdrv,i(t) ≥ 0 ∧ wi = 0 ⊂ N . Based on line ﬂows estimated by the DC model and its underlying assumption R X, grid losses may be approximated by:

M−1 M grid Ploss (t) = ∑ ∑ kGmn (δm(t) − δn(t))k , (6.11) m=1 n=m+1 126 Chapter 6. Power Nodes Modeling Framework with Gmn being the (m,n)-th element of the bus conductance matrix. In additions to this energy balance terms can be derived by integration of power balance terms over the time interval [t1, t2], such as

Z t 2 grid • Electric energy supplied to grid: Pgen (t) dt , t1 Z t 2 total • Primary energy supplied: ξsupply(t) dt , t1

Z t2 • Primary energy curtailed: w+(t) dt , t1

Z t2 • Energy conversion losses: Ploss(t) dt . t1

The calculated power and energy quantities can be combined with time- speciﬁc cost, or energy- and fuel- speciﬁc emissions information, for instance when evaluating the performance of hypothetical scenarios of future power & energy systems (see also Chapter9). 6.3. Power Nodes Modeling Examples 127

6.3 Power Nodes Modeling Examples

Always starting with the general Power Node model formulation

−1 Ci x˙i = ηload,i uload,i − ηgen,i ugen,i + ξi − wi − vi , (6.12) one can derive modeling sets for a wide variety of power system units. A non-exhaustive list of practical modeling examples for power system units is presented in the following.

6.3.1 Combustible-fueled Thermal Generation Units

Such generation units use a combustible fuel for producing heat, which is then turned into mechanical power and, ﬁnally, converted into electric power. Since the primary fuel – be it coal, natural gas, uranium or biomass – is easily stockable, the fuel supply can be considered reliable and, at least under normal operating conditions, does not impede power plant dispatch decisions beyond the usual start/stop and ramping constraints. The primary power supply, ξi ≥ 0, is thus known and can be considered to be fully controllable (dispatchable). When considering day-ahead or intra-day power dispatch decisions that usually happen on the time-scale of 5–15 minutes up to 1 hour, fast power plant dynamics and with it the heated steam as an embedded storage source can be neglected. Thus, when using the above mentioned time-scale, this power plant type can be modeled without considering an embedded storage, i.e. the thermal inertia of the water steam and tubing, inside the plant itself, i.e. Ci = 0. The general Power Nodes equation is thus reduced to the algebraic equality constraint

−1 ηgen,i ugen,i = ξi . (6.13)

In case the power generation ugen,i is given exogenously, i.e. as the result of power dispatch planning, the fuel supply ξi has to follow the power generation and becomes an endogenous variable. The unit’s electric output ugen,i is thus controllable or fully dispatchable. Depending on power ramp constraints as well as start-up and shut-down time-constraints, the operational ﬂexibility of these unit types varies between small, e.g. large- scale lignite power plants, and comparatively high, e.g. modern coal and gas-ﬁred units. 128 Chapter 6. Power Nodes Modeling Framework

If the primary fuel supply ξi is given exogenously and is thus non- controllable, which in practice is often the case for biogas or biomass generation units – due to particular energy policies in place, i.e. feed-in priority, but no actual technical constraints – then the electricity generation ugen,i has to follow the volatile external process ξi. The unit’s electric output ugen,i is thus non-controllable.

6.3.2 Variably Producing Generation Units

Typical examples of generation units that are – inherently – producing electricity with a variable production pattern are variable RES units, i.e. wind turbines and PV units. The availability of primary fuels ξi such as mechanical wind power or global solar irradiance is exogeneously given and in addition time-variant in nature. Again no inherent energy storage exists, unless an additional battery storage or similar devices are present, and therefore Ci = 0.

The operational ﬂexibility of these unit types is driven by the availability patterns of the primary fuel ξi, i.e. solar irradiance, daily and seasonal pattern, and wind ﬂow with its seasonal and, depending on location, also daily patterns. Altogether two modeling realizations are possible:

−1 non-controllable unit ηgen,i ugen,i = ξi , (6.14) −1 curtailable unit ηgen,i ugen,i = ξi − wi . (6.15)

In both cases the models are algebraic equality constraints. However, in the first case, Eq. 6.14, the unit’s electric output ugen,i is driven entirely by the non-controllable primary fuel supply ξi and is thus also non- controllable. Whereas in the second case, Eq. 6.15, the unit’s electric output ugen,i is also influenced by the waste term wi, effectively rendering the unit’s electric output ugen,i partially controllable, i.e. curtailable.

This means, if the primary fuel ξi is available, e.g. the wind blows or the sun shines, then the power set-point ugen,i of the generation unit can be decided upon, within the limits of available primary power ξi, by curtailing part of the available power feed-in via wi. 6.3. Power Nodes Modeling Examples 129

6.3.3 Hydro-based Generation Units

The different classical sub-categories of hydro power units, namely run- of-river hydro, storage (or reservoir) hydro and pumped storage hydro, as well as any hybrid units, for example storage hydro lakes that also have pumping capabilities, can readily be modeled in Power Nodes notation. The inherent energy storage capability of these hydro unit types differs significantly and along with it also the operational flexibility that can be provided for power system operation.

Pumped Hydro Storage Units

Pumped Hydro Storage (PHS) units consis of at least two water basins with a significant height difference. Water is pumped or discharged between the basins in order to consume or produce electricity, respectively. When considering a pure PHS plant, there is no – or at least no significant – water influx that would impede power dispatch decisions, i.e. ξi ≈ 0. The water basins are rather small, allowing the storage of potential energy on the scale of a few gigawatt-hours, i.e. Ci = 0.1 ... 50 GWh. The water transport between the basins is accomplished by fully dispatchable turbines, i.e. electric generation ugen,i and pumps, i.e. electric loads uload,i. Altogether, one arrives at the modeling equation −1 Ci x˙i = ηload,i uload,i − ηgen,i ugen,i . (6.16) The operational flexibility is high and independent of seasonal effects.

Reservoir Hydro Units

Reservoir hydro units, also known as storage hydro, consist normally of one or several large water basins, i.e. a hydro dam that retains water in a sizable storage. The storage for potential energy is high compared to PHS units, i.e. on the scale of terawatt-hours, i.e. Ci = 0.1 ... 100 TWh. The basin is replenished by a considerable water inﬂux from rivers, rainfall and/or snow melting, i.e. ξi > 0. There exist fully dispatchable turbines, i.e. electric generation ugen,i, but usually no pump units due to the lack of a sizable lower water basin. An additional waste term wi ≥ 0 can be added to account for a required minimal water ﬂow as enforced by environmental regulation as well as for representing water 130 Chapter 6. Power Nodes Modeling Framework

ﬂow over the barrage, i.e. water and with it also energy spillage, if the storage lake is full. Water leakage or evaporation eﬀects in the storage basin can also be accounted for by using the term vi. Altogether, one arrives at the modeling equation

−1 Ci x˙i = −ηgen,i ugen,i + ξi − wi − vi . (6.17)

The operational flexibility usually exhibits a seasonal pattern. During a rainy season or when snow melting sets in, the water influx into the storage lakes is very high and the in-flowing water has to be generated most of the time. Operational flexibility is thus reduced, provided that spilling shall be avoided as much as possible.

A similar situation occurs during dry seasons as there is not much water that can actually be used for electricity generation as the storage water becomes increasingly scarce and thus valuable.

Run-Of-River Hydro Units

Run-Of-River Hydro (ROR) plants produce electricity by turbinating water inﬂow from a river, ξi > 0, at a location where the river has a sizable height drop.

The power plant is usually using only a part of the available river water flow that is deviated by means of an artificial channel. Depending on whether or not the difference in water-level between upper and lower river courses can be modulated by the ROR plant via turbine flow and lock positioning, as is explained in great detail in [162, p. 45 and p. 63 ff.], time-dependent storage capability exists, i.e. Ci (k) ≥ 0, or not, i.e. Ci = 0.

The size of the storage capability depends on the geography of the upper river course, i.e. water volume and height difference to lower river course. An additional waste term wi can be used to account for spillage effects, i.e. water flow over the barrage at high water levels or any other intentional water diversion. Altogether, one arrives at the modeling equation −1 water inflow Ci x˙i = −ηgen,i ugen,i + ξi − wi . (6.18) 6.3. Power Nodes Modeling Examples 131

Modeling complex hydro cascade power plants

In practice a group of several individual hydro power units can as a whole constitute a complex system of hydro cascades. An example would be a storage hydro lake that inﬂuences run-of-river plants in the lower course of the river that is fed by the water of this storage lake. In order to also allow the modeling of such complex hydro systems, a Power Node equation for a generic water basin stage is introduced as

−1 Ci x˙i = ηload,i uload,i − ηgen,i ugen,i − wi − vi + ∑ξi,k . (6.19) k This water basin has dispatchable turbine and pump units and a constrained storage whose energy content depends on the height difference with the water-level of a lower basin. The water influx may come from an upper basin or from other water inflows ξi,k≥2. A waste term, wi, for energetically unused water discharge into a lower basin as well as a loss term vi can be introduced to account for water evaporation and/or water leakage from the bassin (Fig. 6.3).

Figure 6.3: Functional Representation of Generic Hydro Storage Basin (own illustration [163]).

Having as a ﬁrst step established the equations of one generalized hydro storage stage i, the next step is to model the manifold interactions between two or more hydro cascade stages. In the following, the generalized case of a hydro cascade with n hydro stages, as illustrated in Fig. 6.4, is analyzed. 132 Chapter 6. Power Nodes Modeling Framework

The first and highest hydro stage (1) can be fed by several water inflows. These inflows can be constituted by inflows from an artificial channel ξ1,1 or by natural surface water inflows ξ1,k≥2. Water turbinated in hydro stage (1) will arrive at the next hydro stage (2) below in the form of an artificial water inflow ξ2,1. This relationship between the water outflow of one hydro stage and the water inflow of the next hydro stage holds for all neighboring hydro stages (i) and (i + 1).

The full hydro cascade system can thus be modeled in Power Nodes notation as follows

−1 C1 x˙1 = ηload,1 uload,1 − ηgen,1 ugen,1 − w1 − v1 + ∑ξ1,k , k −1 C2 x˙2 = ηload,2 uload,2 − ηgen,2 ugen,2 − w2 − v2 + ∑ξ2,k , k −1 C3 x˙3 = ηload,3 uload,3 − ηgen,3 ugen,3 − w3 − v3 + ∑ξ3,k , k ... −1 Cn x˙n = ηload,n uload,n − ηgen,n ugen,n − wn − vn + ∑ξn,k , k C(n+1) x˙(n+1) = −w(n+1) + ∑ξ(n+1),k . (6.20) | {z } | {z } k small storage basin final water outflow | {z } sum of all water inflows

Please note that a small hydro basin (n + 1), serving as an equalization basin, is added at the end of the hydro cascade. It collects all the hydro cascade outflows of the hydro basin (n) and eventually discharges (spills) the final outflow water of the hydro cascade into a river. The amount of water that is pumped (uload,1) or generated (ugen,1) between stages (1) and (2), and hence the potential energy ∆Epot,1→2 involved, depends on the relative height difference ∆h1→2 between the water levels of both basins.

Not only the potential energy ∆Epot,1→2 that is transported between the two basins depends on the relative height difference ∆h1→2 with the next basin below. The energy storage content C1 as well as the energetic value of spilled water w1 of the first hydro stage (1) also depends on the relative height difference ∆h1→2. Again, the same qualitative relationship is true for all neighboring hydro basins i and (i + 1) up to the final sizable hydro basin n. 6.3. Power Nodes Modeling Examples 133

Figure 6.4: Functional Representation of Hydro Storage Cascade (own illustration [163]).

The dependencies between energy value, storage content and relative height diﬀerence, which fortunately still remain linear, are

∆Epot(k) = ∆m(k) · ggrav · ∆h(k) . (6.21)

Out of this follows ! ∆hi→(i+1)(k) ⇒ Ci(k) = Ci,0 · g ∆hi→(i+1)(k) = Ci,0 · 0 , ∆hi→(i+1)(k) ! ∆hi→(i+1)(k) ⇒ wi(k) = wi,0 · 0 . (6.22) ∆hi→(i+1)(k)

The energetic value of the water ﬂow between two hydro stages i and (i+ 1) can be established as follows, using the relative height diﬀerences of water levels between basins i ←→ (i + 1) and (i + 1) ←→ (i + 2), i.e. ∆Epot(k) = ∆m(k)·ggrav ·∆h(k) with ηgen,i(k) = ηgen,0 ·l ∆hi→(i+1)(k) . (6.23) Out of this follows

−1 ⇒ ξ(i+1),1(k) = f ηgen,i(k) · ugen,i(k) ◦ g ∆hi→(i+1)(k), ∆h(i+1)→(i+2)(k) ! −1 ∆h(i+1)→(i+2)(k) ⇒ ξ(i+1),1(k) = ηgen,i(k) · ugen,i(k) · . (6.24) ∆hi→(i+1)(k) 134 Chapter 6. Power Nodes Modeling Framework

Please note the concatenation of the functions f (·) and g(·) above and the fact that also the turbine efficiency ηgen,i(k) is a function of the relative height difference of the water levels in the basins, i.e. l ∆hi→(i+1)(k) . If needed, time-delay effects of water flows between two hydro basins that are geographically detached from each other, as would be the case for ROR cascades, can also be implemented.

The modeling possibilities allow

1.) having no water ﬂow time-delay at all, i.e. Tt = 0 and ugen,i(k),

−1 ξ(i+1),1(k) = f ηgen,i(k) · ugen,i(k) ◦ g ∆hi→(i+1)(k), ∆h(i+1)→(i+2)(k) , (6.25)

2.) having a pure water ﬂow time-delay, i.e. Tt > 0 and ugen,i(k − Tt ),

−1 ξ(i+1),1(k) = f ηgen,i(k) · ugen,i(k − Tt ) ◦g ∆hi→(i+1)(k), ∆h(i+1)→(i+2)(k) (6.26)

3.) or even having a PT1-type water ﬂow time-delay as shown by

ξ(i+1),1(k) = !! −1 1 f η (k) · · ugen,i(k) − ξ (k − 1) + ξ (k − 1) ◦ gen,i T + 1 (i+1),1 (i+1),1 TS g ∆hi→(i+1)(k), ∆h(i+1)→(i+2)(k) . (6.27) 6.3. Power Nodes Modeling Examples 135

6.3.4 Load Demand Units

There exist highly diverse types of load demand units, which unfortunately cannot all be presented in this doctoral thesis due to space constraints. However, all load unit types can, in a ﬁrst stage, be grouped into uncontrollable loads that have no embedded storage capability, e.g. lighting, and in principal controllable load units that do have an embedded storage capability, e.g. thermal load units.

Non-controllable Loads

Uncontrollable load units without storage capability can be modeled analogously to uncontrollable generation units as an algebraic equality constraint as 0 = ηload,i uload,i + ξi . (6.28)

The unit’s electric load demand uload,i is here entirely driven by the end- use demand proﬁle ξi, which is assumed to be an exogenous variable.

Controllable Loads

Controllable load units with embedded storage, Ci > 0, that allows for a degree of freedom in decoupling the primary energy demand process, ξi ≤ 0, from the electric load demand process (uload,i). Load shedding, partial or complete, can be implemented via the waste term wi. Any occurring internal storage losses can be expressed in the loss term vi. In the following some more insights into two particular load types that are of practical interest in power system operation. Thermal Loads Residential electric water heaters are an example of a time-dependent dispatchable load. The electric load demand uload,i is used to produce hot water via a heating element. The storage element is a water tank with a rather constrained “storage” capacity i.e. Ci ≈ 10 kWh. The end-use load demand, ξi < 0, is here a hot water proﬁle that follows a well predictable daily pattern. Signiﬁcant internal heat dissipation from the hot water storage exists, i.e. vi > 0. This leads to the following modeling equation

Ci x˙i = ηload,i uload,i + ξi − wi − vi . (6.29) 136 Chapter 6. Power Nodes Modeling Framework

Electric Vehicle Units

Electric mobility in the form of PHEV/EV fleets is a rising trend in power systems. Via their internal battery storage, i.e. Ci ≈ 10−20 kWh, which typically exhibits only very small losses, i.e. vi ≈ 0, electric vehicles represent a time-variant storage unit, which is available when the vehicles are actually grid-connected. When the vehicles are grid- connected, i.e. when they are parked and recharging for the next jour- ney, both the generation & load side of the battery system become, in principal, available for providing Ancillary Services to the grid [74]. The end-use demand profile of electric vehicles is linked to it’s driving profile (ξ < 0). In case of EVs that have no other fuel supply, this link is direct, i.e. w = 0, whereas in the case of PHEVs there is the possibility to substitute electricity demand by the hybrid combustible fuel (w ≥ 0). Two operation modes exist for PHEV/EV battery systems, thus leading to differing Power Nodes representations.

• Smart-Charging-Only Operation

Ci x˙i = ηload,i uload,i + ξi . (6.30)

In this operation mode, only the battery recharging pattern is modulated in a grid-friendly manner, i.e. reducing peak load demand or providing active control reserve. Here, the charging de- min mand uload,i is changed within it’s operational limits, i.e. uload,i ≤ max uload,i ≤ uload,i.

• Full Vehicle-to-Grid (V2G) Operation

−1 Ci x˙i = ηload,i uload,i − ηgen,i ugen,i + ξi − wi , (6.31)

In this operation mode, the battery system can both be charged and discharged in order to provide Ancillary Services to the grid. Here, both charging uload,i and discharging ugen,i can be changed within it’s operational limits. The later operation mode (full V2G) allows to take full advantage of the electric vehicle’s battery power rating, i.e. the combined rating of uload,i and ugen,i, and it’s energy capacity. 6.3. Power Nodes Modeling Examples 137

6.3.5 Power Systems Units with Schedule Flexibility

Load Units with Schedule Flexibility

Considering a load unit that for one reason or another has time- flexibility in its choice, i.e. unit-internal optimization, when to use electricity without that there exists a physical storage element. A prime example of such a load unit would be a production process, which can be shifted in time or whose process time can be stretched or contracted, thus indirectly also modulating the electricity demand away from its nominal load demand profile ξload,fix(k). Such a situation would lead to a change in the modeling of the load demand profile:

ξload,ﬁx(k) → ξload,ﬂex(k) . (6.32)

The time-evolution of the nominal and modulated electricity demand profiles, i.e. ξload,fix(k) and ξload,flex(k) respectively, is shown in Fig. 6.5. This modification in turn results in a change of the Power Node modeling representation, leading to the new model equation Cvirtual x˙SOC(k) = ξload,fix(k) − ξload,flex(k) , (6.33) where there now exists a virtual energy storage term Cvirtual defined as Cvirtual xSOC(k) = Tsample · ξload,fix(k) − ξload,flex(k) , (6.34) with Tsample denoting the sampling time of the discrete model equation. Constraints on ξload,flex, notably on the energy constraint of the storage element Cvirtual over the time-horizon k = 1 ... N, can be stated as N min max Cvirtual xSOC ≤ Tsample · ∑ ξload,fix(k) − ξload,flex(k) ≤ Cvirtual xSOC . k=1 (6.35)

Figure 6.5: Functional Representation of Load with Schedule Flexibility. Energy Content of Virtual Storage Cvirtual xSOC Denoted as Area Filling (own illustration). 138 Chapter 6. Power Nodes Modeling Framework

Generation Units with Schedule Flexibility

Fully dispatchable generation units by definition also have schedule flexibility. A plant operator can freely choose the production plan within the bounds of any existing power ramping constraints etcetera. This schedule flexibility derives from the assumption that the primary fuel supply ξi, e.g. combustible energy carriers like natural gas, coal or biomass, is considered as an endogenous variable, as pointed out previously in Section 6.3.1, and can thus be freely set, i.e. dispatched, in order to directly control the unit’s power output ugen,i as shown by −1 dispatchable dispatchable ηgen,i ugen,i = ξi . (6.36) Somewhat hidden behind this assumption is that the free dispatchabil- dispatchable ity of the fuel supply, ξi > 0, depends on the existence of yet another storage element, the physical fuel storage Cfuel,i. This fuel storage element, e.g. a natural gas storage, is crucial since it acts as a time delivery buffer between a potentially intermittent fuel delivery, ξi > 0, and dispatchable the fuel supply, ξi > 0, e.g. natural gas supplied by pipeline, dispatchable delivery Cfuel,i x˙fuel,i = −ξi + ξi . (6.37)

dispatchable dispatchable In the process both terms, ξi and ugen,i , are rendered fully controllable/dispatchable. The following modeling equation −1 dispatchable delivery Cfuel,i x˙fuel,i = −ηgen,i ugen,i + ξi , (6.38) thus arises with the complete functional representation being illustrated by Fig. 6.6. This illustration also gives rise to a broader discussion of the role of storage functionality for achieving controllability over power & energy system processes, which will be treated later on in Section 6.6.3.

Figure 6.6: Functional Representation of Generator with Schedule Flex- ibility, i.e. Having a Fuel Storage (own illustration). 6.4. Functional Model Representation 139

Please note that this modeling example would look identical for other fuel types, e.g. coal, and a coal heap next to plant as the storage element. Please also note that precedents of fuel supply being too intermittent, i.e. a fuel supply breakdown, leading to widespread blackouts do in fact exist. For example a coal supply freeze in the former East-Germany in the Winter 1978/79 [164].

6.4 Functional Model Representation

The modeling examples and illustrations in the prior section show that the Power Nodes framework allows to go beyond the rather limited and incomplete modeling perspective of only considering power input and output processes of the individual power system units, i.e. generation, load and storage, with the electricity grid as was discussed previously in Section 5.4 in the context of NPM frameworks and is illustrated by Fig. 6.7a. Instead, the Power Nodes Modeling Framework allows to describe the detailed functional modeling of each power system unit, specifically of existing storage functionality and the otherwise hidden but highly relevant background processes, i.e. the exogenous or endogenous power provision and power demand processes ξi, as is illustrated by Fig. 6.7b. Having the combined modeling information of all these unit properties allows to create the functional model of the power system processes in question and facilitates the assessment of the operational flexibility of individual power system units. This functional representation of complex power system interactions using the Power Nodes notation allows a straight-forward assessment of operational flexibility metrics, as will be pointed out later on in Chapter7. 140 Chapter 6. Power Nodes Modeling Framework

(a) High-level Modeling.

(b) Detailed Functional Modeling Representation.

Figure 6.7: Functional Representation Using Power Nodes Notation of Power Generation (incl. Storage and Curtailment), Bulk Energy Stor- age and Load Demand (incl. Storage, Shedding and Consumption De- ferral) (own illustration [68]). 6.4. Functional Model Representation 141

6.4.1 Comparison of Functionality of Diverse Power System Unit Types

In the following a comparison is made of the diﬀerent power system unit types, i.e. load, generation and storage, and their functionality or ability in providing Ancillary Services, e.g. active control reserves for power system operation. Control reserve provision and the actual control reserve activation is equivalent to the activation of power regulation up/down over time, as is illustrated by Fig. 6.8a. All power system units, whose power feed-in or feed-out can be modulated over time, can in principal provide this service – within the bounds of their operational constraints, i.e. on power ramping, power output and energy storage capacity.

1. Generators, both fossil-fueled and curtailable RES-fueled, can provide control reserves by modulating the control signal around their base-line power production, as is illustrated by Fig. 6.8b. 2. Load units, can in a very similar way provide control reserves by modulating the control signal around their base-line electricity consumption, as is illustrated by Fig. 6.8c.

3. Fast energy storage units, i.e. batteries can provide control reserves by simply tracking the control signal by charging/discharging its energy content, as is illustrated by Fig. 6.8d.

Whereas in the ﬁrst and second case the provision of the control reserve power relies on a base-line power in-/output, which may imply yet another inﬂexibility, i.e. must-run constraints, in the third case control reserve provision is completely decoupled from other power processes. Only the energy constraint of the storage unit is of relevance. 142 Chapter 6. Power Nodes Modeling Framework

(a) Required Control Reserve Proﬁle.

(b) Generator Response.

(d) Energy Storage Response.

Figure 6.8: Functional Equivalence of Power System Units (own illustration). 6.5. Power Nodes Modeling Extensions 143

6.5 Power Nodes Modeling Extensions

The Power Nodes Modeling Framework allows to model power system units in the form of general discrete-time Linear Time-Invariant (LTI) systems, which can be described in state-space form as follows

x(k + 1) = Ax(k) + Bu(k) , (6.39) y(k) = C x(k) + Du(k) , (6.40) and subjected to general linear inequality constraints

T T u ∈ U = gx x(k) ≤ 0 , k = 0,..., N , (6.41) T T x ∈ X = gu u(k) ≤ 0 , k = 0,..., N − 1 , (6.42)

n T where x ∈ R is the discrete state vector with x(0) = [x1(0),...,xn(0)] = m x0, u ∈ R the discrete control input vector, y the system output, Tp = N ∗ k the relevant prediction horizon of load demand and power production n×n n×m time-series, A ∈ R and B ∈ R .

The q = qx + qu constraints imposed on the system state x and control m×q m×q input u are deﬁned by the vectors gx ∈ R x and gu ∈ R u respectively.

6.5.1 Modeling of Non-linear Aspects

Some modeling parameters of power system units are in reality nonlinear in nature. This is, for example, the case of conversion efficiencies η between energy carriers. They are often a function of the actual plant operation points, i.e. ηgen = f (ugen) and ηload = f (uload), due to thermodynamic changes in thermal turbine efficiencies and the impact of height difference, i.e. the water head, in the case of hydro turbines.

In order to capture such non-linear modeling aspects, the above system model can be extended with ease to so-called PWA systems. According to E. Sontag in his seminal paper [165], PWA systems represent the most simple extension of linear systems and allow to model nonlinear and non-smooth processes by means of a switch between diﬀerent system dynamics. 144 Chapter 6. Power Nodes Modeling Framework

General PWA systems are defined as follows x(k + 1) = Ai x(k) + Bi u(k) + fi x(k) ∀ ∈ Ωi, (6.43) y(k) = Ci x(k) + Di u(k) + gi u(k) where Ωi are convex polyhedra defined by a finite number of linear n+m inequalities in the input and state space Ω ∈ R with Ωi ⊂ Ω. The n m l variables x(k) ∈ R , u(k) ∈ R and y(k) ∈ R denote the system state, input and output, respectively, at time instant k. An illustration is given below of how typical non-linear gas turbine efficiency curves can be mapped into a piece-wise affine model (Fig. 6.9). Depending on the number of employed PWA sub-systems, there will be more or less model information loss.

Figure 6.9: PWA-based Modeling of Non-linear Gas Turbine Eﬃciency (sources: left [IEA], right [own]). In addition to this also other types of non-linearity arise due to required minimum generation or load set-points as well as minimum up/down times of thermal power plants. Capturing those in the Power Nodes Modeling Framework is part of on-going research work.

6.5.2 Power Nodes as Descriptor Systems

As was discussed before in Section 6.3, there are two types of Power Node models for representing power system units:

1. Power Node equations with storage elements are regular state- T space equations, i.e. Cix˙i = ai xi + bi u. The existing storage functionality, i.e. Cix˙i, allows a degree of ﬂexibility, or slack, for system operation, i.e. managing power input and output. 6.6. Modeling Controllability & Observability Properties 145

2. Power Node equations without storage elements are singular state- T space equations, i.e. algebraic equality constraints 0 = ai xi + bi u, since no storage functionality exists. Therefore no degree of ﬂexi- bility, or slack, exists for system operation.

The form of Power Nodes equations corresponds to the well-known De- scriptor State-Space systems, which are known to be very suitable for representing physical models as is discussed by D. Luenberger in [166].

6.6 Modeling Controllability & Observability Properties of Power System Units

6.6.1 Decomposition into Controllable & Observable Power Flows and Energy States

In the following the idea of using the Kalman Decomposition [153, 154] is brought up again and discussed for a system of diﬀerent power system units modeled by Power Node equations.

Please note that the decomposition scheme is meant in a control context to apply to the categorization of system states x. In a power systems context, however, an interesting question is also which of the power ﬂows u are controllable & observable and which are not. Since it is always possible to add another system state describing a system input, i.e. x˙u = u, this generalization should be permissible.

As was pointed out, the Power Nodes Modeling Framework fulﬁlls the form of Descriptor State-Space systems, i.e. Ex˙ = Ax+Buu+Bdd, where the entries of the descriptor matrix E are either deﬁned as Eii = CSoC,i, in the case of a unit i with some storage functionality, or Eii = 0 ∀i 6= k, in the case of a unit i without any storage functionality. All other matrix entries are zero, i.e. Eik = 0, ∀i 6= k. 146 Chapter 6. Power Nodes Modeling Framework

Considering for illustration a benchmark system with typical power system unit types:

1. Classical Generator, i.e. fully dispatchable via fuel supply ξ1,

−1 CSoC,1 x˙1 ≡ 0 = −ηgen,1 ugen,1 + ξ1 , (6.44)

2. Classical Load, i.e. uncontrollable or curtailable,

CSoC,2 x˙2 ≡ 0 = ηload,2 uload,2 + ξ2 −w2 , (6.45)

3. Generic Energy Storage Unit, i.e. fully controllable (subject to energy constraints on CSoC,3 x˙3),

−1 CSoC,3 x˙3 = ηload,3 uload,3 − ηgen,3 ugen,3 + ξ3 − w3 − v3 ·x3 , (6.46)

4. Variable RES Unit, i.e. uncontrollable or curtailable,

−1 CSoC,4 x˙4 ≡ 0 = −ηgen,4 ugen,4 + ξ4 −w4 . (6.47)

All power flow in- & outputs can now be separated in controllable inputs Bu u, i.e. control inputs and non-controllable inputs Bd d, i.e. disturbances. Here, the controllable power flows u correspond to the set of endogenous input variables that can actively be set by a plant or system operator via load/generation set-point changes and/or curtail- T ment and load shedding, i.e. u = [ugen, uload, wcurtailable, ξcontrollable] . Likewise the non-controllable power flows d correspond to the set of exogenous input variables that are beyond the control of an operator, T i.e. d = [ξnon-controllable] . System states in power system modeling include all energy storage states (xSOC). Depending on the circumstance involved, some of these states may or may not be measurable/estimable or predictable. As before, a separation in observable states xO, i.e. measurable/estimable and predictable and non-observable states xO¯ is possible. All energy flow in- & outputs that are controllable by an operator are assumed to also be observable. Non-controllable energy flows that are of interest include T d = [ξnon-controllable,uref] . 6.6. Modeling Controllability & Observability Properties 147

For all these non-controllable processes, a separation in observable/estimable and, over the time-horizon predictable, disturbances Bd,O dO, and non-observable/non-estimable and, over the time-horizon non-predictable, disturbances Bd,O¯ dO¯ can be accomplished. The modeling formulation of the Power Node benchmark system without the grid topology, including the input separation is then given as

Ex˙ = Ax + Bu u + Bd d , (6.48)

        0 0 0 0 0 0 0 0 x1 0 0 0 0 0 0 0 0 0 0 0 0 0x2 0 1 0 0ξ2  x˙ =   +   0 0 1 0 0 0 −v3 0x3 0 0 1 0ξ3 0 0 0 0 0 0 0 0 x4 0 0 0 1 ξ4 | {z } | {z }| {z } | {z }| {z } E A x Bd d  −1   −ηgen,1 0 0 1 0 0 0 ufull,1  0 0 ηload,2 −10 0 0ufull,2 + −1   .  0 0 −ηgen,3 ηload,3 −1 0 0ufull,3 −1 u 0 0 0 −ηgen,4 0 −10 full,4 | {z } | {z } u Bu

The vector formulation for the set of controllable inputs u is given as  T ugen,1 ugen,2 ugen,3 ugen,4 T u u u u uT uT uT uT =  load,1 load,2 load,3 load,4 . full,1 full,2 full,3 full,4  w w w w  | {z }  1 2 3 4  u ξ1 0 0 0 | {z } u

6.6.2 Classiﬁcation of Power System Controllability

With respect to their power in-/output, i.e. power generation and power demand, all power system units can be categorized as being either controllable or non-controllable. It makes sense to furthermore distinguish controllable power system units into being either fully dispatchable, when the primary fuel supply or end-use demand can be set endoge- nously, or curtailable/sheddable, when the power generation or the load demand can be set within the bounds of the available exogenous primary fuel supply or the required exogenous end-use demand, respectively. 148 Chapter 6. Power Nodes Modeling Framework

1. Non-controllable power system units

a) Non-controllable generator Non-controllable, intermit- non-controllable tent primary fuel supply ξRES without any storage element results in the non-controllable, intermittent electric- non-controllable ity generation uRES, gen (Fig. 6.10a). b) Non-controllable load Non-controllable, intermittent end- non-controllable use power demand ξload without any storage element results in the non-controllable, intermittent electricity non-controllable demand uload (Fig. 6.10b).

(a) Non-Controllable Generator. (b) Non-Controllable Load.

Figure 6.10: Functional Power Node Representation of Non- Controllable Load and Generator (own illustration).

2. Partially controllable power system units

a) Curtailable RES generator Non-controllable, intermit- non-controllable tent primary fuel supply ξRES can be curtailed curtailed (redirected into a waste storage wRES , from which it cannot be recuperated, i.e. zero-efficient cycling (η = 0). This configuration results in the curtailable, i.e. partly control- curtailable lable, electricity generation uRES (Fig. 6.11a). b) Sheddable load Non-controllable end-use power demand non-controllable ξload can be shed, i.e. redirected into a waste stor- shedded age wload , from which it cannot be recuperated, i.e. zero- efficient cycling (η = 0). This configuration results in the sheddable partly controllable electricity demand uload (Fig. 6.11b). 6.6. Modeling Controllability & Observability Properties 149

(a) Curtailable Generator. (b) Sheddable Load.

Figure 6.11: Functional Power Node Representation of Sheddable Load and Curtailable Generator (own illustration).

3. Fully controllable power system units a) Dispatchable generator Controllable primary fuel supply dispatchable ξgen comes from a (large) fuel reservoir, which allows a decoupling or buﬀering of intermittent fuel delivery delivery dispatchable ξfuel and electricity generation ugen (Fig. 6.12a). b) Dispatchable load Controllable end-use demand dispatchable ξload is buﬀered by a (large) storage element, end-use which allows a decoupling of intermittent end-use ξload dispatchable and electricity demand uload (Fig. 6.12b).

(a) Controllable Generator. (b) Controllable Load.

Figure 6.12: Functional Power Node Representation of Controllable Load and Generator (own illustration).

In the following is a mathematical deﬁnition of the set of feasible operation points within which a controllable generator, a curtailable RES generator and a sheddable load unit can adjust their power output ugen, respectively their load demand uload over a time horizon k = 1 ... N. This is discussed both for real-time measurements of primary fuel supply or end-use demand ξ as well as for predictions thereof (ξˆ). 150 Chapter 6. Power Nodes Modeling Framework

Controllable Generator

controllable The power generation ugen is dispatchable, i.e. can be freely chosen, within the bounds of the feasible set of continuous generation set- points. These bounds are given by the operation limits of the generator, min/max i.e. min/max generation set-points ugen .

controllable RES The primary fuel supply ξprimary fuel (k) is an endogenous variable and is set in order to control the power output. An illustration of the feasible set of operation points over time is given by Fig. 6.13.

controllable k = 1 : ξ(k) := ξprimary fuel(k) , controllable ugen (k) = ηgenξ (k) , min controllable max ugen ≤ ugen (k) ≤ ugen . (6.49)

ˆ ˆcontrollable k > 1 : ξ(k) := ξprimary fuel(k) , controllable ˆ uˆgen (k) = ηgenξ (k) , min controllable max ugen ≤ uˆgen (k) ≤ ugen . (6.50)

Figure 6.13: Fully Controllable Generation Unit (own illustration). 6.6. Modeling Controllability & Observability Properties 151

Curtailable RES Generator curtailable The power generation ugen is dispatchable, i.e. can be freely chosen, within the bounds of the feasible set of continuous generation set-points. These bounds are given by the operation limits of min/max the generator, i.e. min/max generation set-points ugen , as well as the availability of the exogenous and time-variant primary fuel sup- non-controllable RES ply ξprimary fuel (k). An illustration of the feasible set of operation points over time is given by Fig. 6.14. non-controllable RES k = 1 : ξ(k) := ξprimary fuel (k) , curtailable ugen (k) = ηgen · (ξ (k) − w(k)) , min if ugen ≤ ηgen · (ξ (k) − w(k)), min curtailable max then ugen ≤ ugen (k) ≤ ηgenξ (k) ≤ ugen , curtailable else ugen (k) = 0 . (6.51)

ˆ ˆnon-controllable RES k > 1 : ξ(k) := ξprimary fuel (k) , curtailable ˆ uˆgen (k) = ηgen · ξ (k) − w(k) , min ˆ if ugen ≤ ηgen · ξ (k) − w(k) , min curtailable ˆ max then ugen ≤ uˆgen (k) ≤ ηgenξ (k) ≤ ugen , curtailable else uˆgen (k) = 0 . (6.52)

Figure 6.14: Curtailable RES Generation Unit (own illustration). 152 Chapter 6. Power Nodes Modeling Framework

Sheddable DR Load Unit sheddable The power demand uload is dispatchable, i.e. can be freely chosen, within the bounds of the feasible set of (continuous) load consumption set-points. These bounds are given by the operation limits of the load min/max unit, i.e. min/max load demand set-points uload , as well as the non-controllable exogenous and time-variant end-use load demand ξload (k). An illustration of the feasible set of operation points over time is given by Fig. 6.15.

non-controllable k = 1 : ξ(k) := ξload (k) , sheddable −1 uload (k) = −ηload · (ξ (k) − w(k)) , min −1 if uload ≤ −ηload · (ξ (k) − w(k)), min sheddable −1 max then uload ≤ uload (k) ≤ −ηloadξ (k) ≤ uload , sheddable else uload (k) = 0 . (6.53)

ˆ ˆnon-controllable k > 1 : ξ(k) := ξload (k) , sheddable −1 ˆ uˆload (k) = −ηload · ξ (k) − w(k) , min −1 ˆ if uload ≤ −ηload · ξ (k) − w(k) , min sheddable −1 ˆ max then uload ≤ uˆload (k) ≤ −ηloadξ (k) ≤ uload , sheddable else uˆload (k) = 0 . (6.54)

Figure 6.15: SheddableDR Load Unit (own illustration). 6.6. Modeling Controllability & Observability Properties 153

6.6.3 Role of Storage Functionality for Controllability

As has become clear in the previous sections, the controllability over the energy in-flows ugen and energy out-flows uload of individual power system units depends on the existence of some storage functionality that allows the modulation of these electric power flows u, and if need be, also the primary fuel supply or end-use demand flows ξ. In this respect the following analytic findings can be made:

1. Dispatchable generation units are dispatchable, i.e. controllable, simply because there is some storage functionality attached to this unit, i.e. in the form of a fuel stockage. From a functional modeling perspective conventional generators are very similar to hydro storage lakes and in their respective Power Node equations, in fact, even identical. This finding seems to be rather obvious in the power systems context but misconceptions are widespread, sometimes leading to tautological statements such as in [167, ...we prove that it is always optimal to place zero storage at generator buses ...]. 2. Dispatchable load units, i.e. Demand Response (DR) loads, whose electricity demand can be modulated over time do in one way or another also have a storage, either a physical one, i.e. thermal loads, or a virtual one, i.e. schedule flexibility. 3. Curtailable RES units, like wind & PV, have a waste storage for dumping unwanted primary power supply, i.e. a zero-efficient energy storage from which energy cannot be recovered. 4. Sheddable load units likewise have a waste storage for dumping unserved end-use demand. 154 Chapter 6. Power Nodes Modeling Framework

6.7 Connections between Energy Hub and Power Nodes Modeling Frameworks

The attentive reader will at least by now have pondered upon the connection between the earlier presented Energy Hub Modeling Framework, see Section 5.3.1, and the Power Nodes Modeling Framework. Although the motivation and circumstances for the respective development of both modeling frameworks were quite diﬀerent – Energy Hubs having been developed for modeling and studying multi-carrier energy networks, and Power Nodes having been developed for modeling curtailable RES units and DR load schemes – the conceptual connections are in fact very close. In the following it will, ﬁrst, be explained how Energy Hub and Power Node models can be transformed into each other. Second, it will be shown that the Power Nodes framework can be seen and understood as a versatile modeling generalization of the original Energy Hub concept.

6.7.1 Transformation between Energy Hub and Power Node Models

In principle, a transformation between Power Nodes and Energy Hub models is possible. This is illustrated in the following for two cases. Conversion Natural Gas → Electricity

In this case, there is not electric load demand, i.e. uload = 0, and no output-side storage element is assumed, i.e. Mβ = 0, which could, however, also be included. The transformation between the Energy Hub and Power Nodes modeling notations is then given by the following equations

gas −1 electricity gas Ci x˙i = −ηgen,i ugen,i + ξin-ﬂow, i , (6.55) electricity gas gas ugen,i = ηgen,i · ξin-ﬂow, i −Ci x˙i , (6.56)

⇔ Lβ = cαβ · (Pα − Qα ) . (6.57)

gas gas where the following terms are equivalent: Qα = Ci x˙i, Eα = Ci xi and gas Pα = ξin-ﬂow, i. The term cαβ denotes the conversion eﬃciency from natural gas to electricity. This is furthermore illustrated by Fig. 6.16. 6.7. Connections between Energy Hub and Power Nodes 155

Figure 6.16: Transformation between Power Node and Energy Hub for a Generation Unit (own illustration). Conversion Electricity → Natural Gas

In this case, there is not electric generation, i.e. ugen = 0, and again no output-side storage element is assumed, i.e. Mβ = 0, which again could, however, also be included. The transformation between the Energy Hub and Power Nodes modeling notations is given by the following equations

gas electricity gas Ci x˙i = ηload,i uload,i − ξout-flow, i , (6.58) gas gas electricity Ci x˙i + ξout-flow, i = ηload,i uload,i , (6.59) ⇔ Pα + Qα = cβα · Lβ . (6.60) gas where, again, the following terms are equivalent: Qα = Ci x˙i, Eα = gas gas Ci xi and Pα = ξin-flow, i. The term cβα denotes the conversion efficiency from electricity to natural gas. This is illustrated in Fig. 6.17.

Figure 6.17: Transformation between Power Node and Energy Hub for Load Demand (own illustration). Please note that a transformation of Power Nodes equations of curtailable/sheddable units, which include the waste term w, into the Energy Hub notation is not possible. This means that there is only a one- way complete compatibility from Energy Hub models to Power Nodes models but not vice versa. 156 Chapter 6. Power Nodes Modeling Framework

6.7.2 Power Nodes Framework as a Generalization of Energy Hubs

Both the Power Nodes and the Energy Hub modeling frameworks allow storage variables that enable the temporary stockage of input and output power flows, termed Qα and Mβ in the scope of Energy Hubs and C x˙ in the scope of Power Nodes. The main functional difference between the Energy Hub and Power Nodes modeling frameworks is, however, the concept of the waste term w, i.e. allowing a waste storage, in the later framework. Thanks to this term both sheddable and curtailable power & energy system units can be modeled and simulated via the Power Nodes framework, which is not possible in the Energy Hubs framework. This is a significant advantage for power & energy system modeling, which allows a more complete functional modeling, simulation and analysis of such systems, notably the analysis of controllability aspects. This is not the case of the Energy Hub framework, where the modeling of multi-energy carriers and not controllability analysis are the clear focus. Furthermore, the Power Nodes framework is not limited to modeling power systems. An application example in which heat, gas and electricity power flows were modeled for the case of a Concentrating Solar Power (CSP) using Power Nodes already exists. Modeling and simulation results were presented by this author in [168].

(a) Power Node Generation Unit. (b) Power Node Load Unit.

Figure 6.18: Storage Modeling Options for Power Node Unit Types (own illustration). 6.8. Connections between Power Nodes and NPM 157

6.8 Connections between Power Nodes and Network Preserving Model (NPM) Frameworks

The Power Nodes modeling framework allows to model the background processes of power & energy system units with high versatility. The modeled energy in-ﬂow and out-ﬂow variables, i.e. ugen and uload, can then be coupled to existing Network-Preserving Model (NPM) models as is illustrated by Fig. 6.19.

Since a grid topology and fast power system dynamics such as the swing dynamics of generators can also be added directly into the Power Nodes modeling framework, a uniﬁed modeling is in principal possible. In this case the fast time-scales of frequency and voltage dynamics would be tied together with the slow(er) dynamics of bulk energy storage processes and the time-variant behavior of RES power feed-in and load demand proﬁles. Such an approach would be useful in particular if power system simulations are accomplished, for example, by using simulations and operational optimization on multiple time-scales as presented by this author for Model Predictive Control (MPC) applications in power systems in [152]. In this context the term predictive power dispatch was coined.

Figure 6.19: Connections between Power Nodes and Network- Preserving Model Frameworks (own illustration). 158 Chapter 6. Power Nodes Modeling Framework

Another, admittedly more powerful approach would be to use heteroge- neous time-sampling over a given simulation horizon, i.e. starting with fine time-steps in the range of seconds. On this time-scale transient frequency & voltage dynamics are relevant but bulk energy storage dynamics, RES power feed-in and load demand appear constant. And then moving to gradually coarser time-steps in the range of minutes, hours, days or even seasons, in which any fast dynamics will have decayed and only active/reactive power balances exist on the grid-side, whereas bulk energy storage dynamics, RES power feed-in and load demand profiles will fluctuate. Part III

Modeling & Analysis of Operational Flexibility in Electric Power Systems

159

Chapter 7

Operational Flexibility in Electric Power Systems

7.1 Introduction

Operational flexibility is an important property of electric power systems and plays a crucial role for the transition of existing power systems, many of them based on fossil fuels, towards power systems that can ef- ficiently accommodate high shares of variable RES. Operational flexibility is essential for mitigating disturbances in a power system such as outages or forecast errors of either power feed-in, i.e. from wind turbines or solar units, or power feed-out, i.e. load demand. The availability of sufficient operational flexibility in a given power system is a necessary precondition for the effective grid integration of large shares of fluctuating power feed-in from variable RES, i.e. wind power and Photovoltaics. In the context of this doctoral thesis the available operational flexibility of a power system means the combined operational flexibility that the ensemble of all the diverse power system units in a geographically confined grid zone can provide in each time-step during the operational planning, given load demand and RES forecast time-series, as well as in real-time in case of a contingency.

161 162 Chapter 7. Operational Flexibility in Power Systems

Section 7.2 briefly discusses what the source of providing operational flexibility are. In Section 7.3 definitions of relevant metrics for operational flexibility are presented. Metrics for assessing the technical operational flexibility of power systems, i.e. power ramp-rate, electric power capacity and energy capacity, have recently been proposed by Makarov et al. in [87] and their meaning further discussed, besides others, by the author of this doctoral thesis in [45]. Section 7.4 explains how the modeling of Operational Flexibility can be accomplished using the Power Nodes modeling framework that was introduced previously in Chapter6. This analysis is continued in the following Chapter8, which illustrates how Operational Flexibility can be quantified and analyzed for individual power system units as well as for unit ensembles.

7.2 Sources of Operational Flexibility

Diﬀerent sources for procuring power system ﬂexibility from a diverse set of power system units exist, as is illustrated in Fig. 7.1.

1. Operational flexibility can be obtained on the generation-side in the form of dynamically fast responding conventional power plants, e.g. gas or oil-fueled turbines or rather flexible modern coal- fired power plants and on the demand-side by means of adapting the load demand curve to partially absorb fluctuating RES power feed-in.

2. In addition to this, RES power feed-in can also be curtailed or, in more general terms, modulated below its given time-variant maximum output level. Furthermore, stationary storage capacities, e.g. hydro storages (PHS, CAES, stationary battery or fly-wheel systems, as well as time-variant storage capacities, e.g. electric vehicle fleets, are well-suited for providing operational flexibility.

3. Further operational flexibility can be obtained from other grid zones via the electricity grid’s tie-lines in case that the available operational flexibility in one’s own grid zone is not sufficient or more expensive than elsewhere.

4. Matter of fact, power import and export, nowadays facilitated by more and more integrated transnational power markets, is used 7.2. Sources of Operational Flexibility 163

in daily power system operation to a certain degree as a slack bus for fulfilling the active power balance and mitigating power flow problems of individual grid zones by tapping into the flexibility potential of other zones. For power system operation, importing needed power in certain situations and exporting undesirable power feed-in in other situations to neighboring grid zones is for the time being probably the most convenient and cheapest measure for increasing operational flexibility. However, power import/export can only be performed within the limits given by the agreed line transfer capacities between the grid zones. In the European context this corresponds to the so-called Net Transfer Capacities (NTC)[9], which are a rather conservative measure of available grid transfer capacity.

Figure 7.1: Sources of Power System Flexibility (own illustration). 164 Chapter 7. Operational Flexibility in Power Systems

7.3 Deﬁnitions of Operational Flexibility

The term Operational Flexibility in power systems, or simply flexibility is often not properly defined and may refer to very different things, ranging from the quick response times of certain generation units, e.g. gas turbines, to the degree of efficiency and robustness of a given power market setup. The topic has received wide attention in recent years [45, 87–89]. In the following the focus is on the basic technical capability of individual power system units to modulate power injection into the grid, respectively power outtake from the grid.

7.3.1 Metrics for Operational Flexibility

For analysis purposes, this technical capability of power modulation needs to be characterized and categorized by appropriate metrics for operational ﬂexibility. A valuable method for assessing the needed operational ﬂexibility of power systems, for example for accommodating high shares of wind power production, has been proposed by Makarov et al. in [87]. There, the following metrics have been characterized:

• Power capacity π [MW] for up/down power regulation,

• Power ramp rate ρ [MW/min.] for up/down power ramping,

• Storage energy ε [MWh], i.e. power mismatches over time and

• Ramp duration δ [min.].

The respective role of these flexibility metrics in modulating the operation point of a unit and with it the relative power flow into the grid (> 0) and out of the grid (< 0) with respect to the nominally planed operation point is illustrated in Fig. 7.2. Here, the deliberate deviation between the nominal power plant output trajectory and the actual power output trajectory constitutes the available operational flexibility of the power system unit in question. Note that for load units the picture would be very similar except that the 7.3. Definitions of Operational Flexibility 165 modulation of power outtake instead of power injection would then be considered. Operational flexibility is thus the set of all possible operation set-points, i.e. the reach set, which are bounded by the maximum flexibility capa- ± ± ± bility, i.e. the three metrics ρmax, πmax and εmax. For the sake of simplicity and clarity we will stick to the same notation as in [87]. An intriguing feature is that the metric terms ρ, π and ε are closely linked via integration and differentiation operations in the time domain. The interactions of the individual metrics clearly exhibit so-called double integrator dynamics: energy is the integral of power, which in turn is the integral of power ramp-rate. Due to their inter-temporal linking, the three metrics constitute a flexibility trinity in power system operation (Eq. 7.1). For the sake of simplicity and clarity we will adhere in the following to the same notation as in [87].

Figure 7.2: Flexibility Metrics in Power Systems Operation: Power Ramp-Rate ρ, Power π and Energy ε (own illustration).

Although the power ramp-rate ρ is the key ﬂexibility metric, it does nevertheless depend on the other two metrics. The causal inter-linking between the three metrics are further on illustrated in Fig. 7.3. As can be seen here, the constraints on metrics π and ε are clearly also constraining ρ, i.e. the choice of feasible values for ρ. The power ramping for absorbing a given disturbance event, measured 166 Chapter 7. Operational Flexibility in Power Systems in MW/min, in a power system may be abundant at a certain time instant. But for a persistent disturbance over time, the maximum regulation power that can be provided by a generator is limited as is the maximum regulation energy that can be provided by storage units, which are inherently energy-constrained. Ramp-Rate Power Energy [MW/min.] [MW] [MWh] R dt R dt ρ π ε (7.1) d d dt dt k k k 1 2 ρ π = (ρ ·t ) ε = ( 2 · ρ ·t )

Using these three flexibility metrics instead of only one, i.e. the power ramping capability ρ as is done in [89], allows a more accurate and complete representation of power system flexibility over a time interval. Since the share of storage units in power systems as well as their importance for the grid integration of RES power feed-in is rising, the inter-temporal links between providing ramping capability and eventually reaching power/energy limits cannot be neglected when assessing the overall available operational flexibility of a power system. Having defined these flexibility metrics as well as the causal inter-linking between them, now allows the assessment of available operational flexibility of an individual power system unit and for whole power systems. Please note that the operational constraints, i.e. min/max ramping (ρ), power (π) and energy constraints (ε), of individual power system units have to be considered when assessing their operational flexibility. 7.3. Definitions of Operational Flexibility 167

Figure 7.3: Inter-Temporal Linking of Flexibility Metrics Including In- ternal Storage Losses, i.e. Dissipation (own illustration). 168 Chapter 7. Operational Flexibility in Power Systems

7.4 Modeling of Operational Flexibility

The analysis and assessment of operational flexibility first of all necessi- tates a modeling framework that allows to explicitly include information on the degree of freedom for shifting operation set-points so as to modulate the power input and output patterns of individual power system units. This includes information on whether or not a unit has a storage and is thus energy-constrained, whether or not a unit provides fluctuating power feed-in, and what type of controllability and observability, including predictability, i.e. full, partial or none, a system operator has over fluctuating generation and demand processes. The combination of all these properties defines a unit’s operational flexibility.

In this thesis, the modeling of operational ﬂexibility relies on the previously introduced Power Nodes modeling framework, which allows a versatile and detailed functional modeling of diverse power system units. More details on the Power Node modeling framework, modeling examples and reasoning can be obtained in Chapter6.

7.4.1 Quantiﬁcation of Operational Flexibility

Section 7.3.1 has introduced generalized ﬂexibility metrics (Eq. 7.1) and Chapter6 has illustrated the Power Nodes modeling framework that enables the explicit modeling of controllability and ﬂexibility features of individual power system units.

With this all the necessary components for assessing the operational flexibility of individual power system units, be it generation, storage or load units, as well as for assessing the operational flexibility of a whole power system consisting of a portfolio of diverse generation, load and storage units, as depicted in Fig. 7.1, have been established. The functional representation of complex power system interactions using the Power Nodes notation, as was illustrated in the previous Chapter by Fig. 6.7, allows a straight-forward assessment of the three metrics of operational flexibility, i.e. power ramping capability ρ, power operation capability π and energy storage capability ε. 7.4. Modeling of Operational Flexibility 169

Taking as an example the operational ﬂexibility of a generation unit i that also has an inherent storage function and the possibility for curtailment, e.g. a hydro storage lake, given the by following Power Node modeling equation

−1 Ci x˙i = −ηgen,i ugen,i + ξi − wi − vi . (7.2)

Calculating the operational ﬂexibility that this power system unit can provide, say for power regulation up/down, is accomplished by calculating the set of all feasible power regulation points {πi(k)}, based on the following equation

n o n feasible o 0 πi(k) = ugen,i (k) − ugen,i(k) (7.3)

n o 0 = ηgen · (ξ − w − vx −Cx˙) − ugen,i(k) k,i min feasible max s.t. 0 ≤ ugen,i(k) ≤ {ugen (k)} ≤ ugen,i(k) . (7.4)

0 Within Eq. 7.3, ugen,i(k) denotes the nominal (actual) set-point of the feasible generation unit and the term ugen,i (k) represents an arbitrary set- point from the set of all feasible operating points {·} to which the unit can be steered to provide operational flexibility; in this case power regulation. Both terms can be chosen to be time-variant. They are given here for time-step k. n o The set of all feasible operation points, i.e. πi(k) , thus depends upon the internal status of the generation unit, as defined by the terms ξi(k), wi(k), vi(xi(k)) and Ci(xi(k)), and is bounded by the unit’s power rating constraints (Eq. 7.4), for reference see also Eq. 6.1 (b–d)). Furthermore, it makes sense to split up the set of all feasible operation n o points, i.e. πi(k) : Let power regulation up/down be denoted by ’+/−’ respectively, then one can define the subset of feasible operation point n + o n o that can provide power up regulation as πi (k) = ∀πi(k)kπi(k) > 0 . n + o The term πi (k) thus represents the positive part of power output flexibility. Equivalently, one can define the subset of feasible op- n − o eration point that can provide power down regulation as πi (k) = n o n − o ∀πi(k)kπi(k) < 0 . The term πi (k) thus represents the negative part of the set of power output flexibility. 170 Chapter 7. Operational Flexibility in Power Systems

This separation of positive and negative flexibility capabilities will be of importance in the next chapter. This flexibility assessment for metric π, i.e. the set of all feasible operation points (Eq. 7.3), can of course be extended to the other two metrics, ρ and ε, via time-differentiation and integration of π, respectively. The three thereby calculated metrics span a so-called flexibility volume, which can be represented in its simplified form as a flexibility cube for a generic power system unit i, where the vertices or extreme points are + − + − + − defined by the set of metric terms {ρmax ,ρmax ,πmax ,πmax ,εmax ,εmax} as is qualitatively shown below (Fig. 7.4).

Figure 7.4: Flexibility Cube of Maximum Available Operational Flexi- bility of a Generic Power System Unit. Chapter 8

Qualitative Simulation Studies

8.1 Introduction

This chapter presents two novel approaches for analyzing and visualizing the operational flexibility of a given power system unit. The flexibility properties of different power system unit types, e.g. load, generation and storage units that are non-controllable, curtailable or fully controllable are qualitatively analyzed and compared to each other. Two methods for visualizing and assessing the operational flexibility of actual power system units are presented. These methods, their differences and the insight they bring are explained using intuitive power system examples. Section 8.2 presents a qualitative analysis of the role of needed and available operational flexibility in power system operation, abstracting from actual power system unit portfolios. Section 8.3, illustrates how operational flexibility can be quantified and analyzed for individual power system units as well as for unit ensembles, i.e. aggregations.

171 172 Chapter 8. Qualitative Simulation Studies

8.2 Qualitative Analysis of Operational Flexibility

There are two sides to operational flexibility in power systems. First, the needed flexibility that system operators require for coping with a wide range of power imbalances. Second, the available flexibility that system operators can obtain from various flexibility sources.

8.2.1 Needed Operational Flexibility

In general, operational flexibility is needed for balancing out schedule deviations and disturbances coming from load demand as well as conventional and renewable generation units, and of course, all kinds of outages that cause power and power flow imbalances. Matter of fact, the original work of Makarov et al. was concerned with quantifying the necessary operational flexibility for mitigating the feed- in uncertainty of high energy shares of wind power [87]. There, the needed operational flexibility in order to allow operators to always re- balance power feed-in disturbances was quantified by using probabilistic worst-case scenarios and capturing their flexibility requirements using the previously established three, respectively four, flexibility metrics (see Chapter7). An illustration of this type of analysis for needed flexibility in power systems is given below by Fig. 8.1.

Figure 8.1: Needed Operational Flexibility (source: taken from Makarov et al. [87]). 8.2. Qualitative Analysis of Operational Flexibility 173

Growing Flexibility Needs in German Power System

As was discussed previously in Section 3.4.1, the amount of needed operational flexibility, notably power ramping (ρ) and power regulation capability (π), is higher in power systems with significant shares of variable RES due to the more erratic behavior of the resulting residual load profile. Eluding again on the situation of the German power system as presented previously by Section 3.4.1). Due to the significant production shares of wind & PV power feed-in, around 10% and 5% of annual energy production share respectively, the resulting residual load profile exhibits larger and steeper power ramps (Fig. 8.2a) than the original brut load demand profile (Fig. 8.2b) did. Balancing out the up/down power swings of the residual load profile requires significantly more operational flexibility in the form of notably faster ramping control reserve units.

(a) Residual Load Demand. (b) Brut Load Demand.

Figure 8.2: Brut Load Demand and Residual Load Profiles in the Ger- man Power System, 1–7 January 2012 (own analysis). An analysis of the load demand and RES power feed-in time-series (15 minute values) for the full full-year 2012 shows that overall flexibility requirements have risen by • ∆ρ+ = +1.5% and ∆ρ- = +20%, • ∆π+ = +24% and ∆π- = +28%, • ∆ε+ = −3.9% and ∆ε- = −3.9%. compared to the base case in which the original brut load demand profile needed to be balanced. 174 Chapter 8. Qualitative Simulation Studies

As can be seen, the requirements for both power regulation up/down (π+/-) as well as for power ramping down (ρ-) are significantly higher. The other flexibility metrics are considerably less impacted. Representing this quantitative information in the form of flexibility cubes leads to the following illustrations (Fig. 8.3).

(a) Residual Load Demand. (b) Brut Load Demand.

Figure 8.3: Needed Operational Flexibility in the German Power Sys- tem, 1–7 January 2012 (own analysis).

Please note, that the furthermore aggravating impact of load or RES forecast errors has not even been considered (see Chapter9 for complementary analysis). The here assessed additionally needed operational ﬂexibility corresponds thus to a best-case, i.e. perfect load demand and RES predictions (no forecast error).

8.2.2 Available Operational Flexibility

Sources of Operational Flexibility

The available operational flexibility that a power system unit can provide depends on this unit’s ability to modulate it’s power output, i.e. for a generation unit, or power input, i.e. for a consumption unit or both for a two-way storage unit. The flexibility type, i.e. ρ, π and/or ε, as well as the actual amount of it that be provided is given by the unit’s 0 0 operation constraints and nominal operating point {ugen,i, uload,i (k) at time-step k. What type of operational flexibility can be provided depends thus on the characteristics of the specific power system unit in question. 8.2. Qualitative Analysis of Operational Flexibility 175

A purely qualitative classiﬁcation of how well-suited a given power system unit type is in providing one of the three ﬂexibility metrics is presented in the following for a non-exhaustive list of generation, load and storage unit types (Table 8.1).

Table 8.1: Classification of Flexibility Sources (own analysis). Power System Unit Ramping ρ Power π Energy ε Pumped Hydro Unit ++ ++ ++ Storage Lake (part load) ++ ++ + + ++ Battery (Li-Ion) + + + + + Super Cap + + + − − − − Coal-fired Plant (part load) − ++ + + + Gas-fired Plant (part load) + ++ + + + Thermal Loads (Heat Pumps) + + / + ++ ++ + Chemical Storage (H2/CH4) − ++ + + +

Valuation of Operational Flexibility

The next question that arises is then how the provision of operational ﬂexibility can be valued, respectively priced. Using the three established ﬂexibility metrics {ρ, π, ε} as a basis for evaluating and analyzing the payment structure of the existing Ancillary Services (AS) products in the ENTSO-E Continental European power system, the following analysis can be made:

1. In general, faster control reserves, i.e. a faster control actuator response, are valued higher than slower control reserves.

2. Faster control reserves are paid predominantly for their provision of ramping capability, whereas slower control reserves are paid predominantly for their energy provision.

3. In the ENTSO-E CE grid the following payment structures exist:

• Primary Frequency Control Service payment per unit power πprimary that can be provided with at least the predeﬁned ramping capability ρprimary, i.e. πprimary (ρ ≥ ρprimary ). 176 Chapter 8. Qualitative Simulation Studies

• Secondary Frequency Control Service payment per unit of secondary control power πsecondary that is provided with the predeﬁned ramping capability ρsecondary, i.e. πsecondary (ρ ≥ ρsecondary ). In addition to this comes a service payment for each unit of actually provided (secondary) regulation energy εsecondary.

• Tertiary Frequency Control Service payment per unit of tertiary control power πtertiary that can be provided with at least the predeﬁned ramping capability ρtertiary, i.e. πtertiary (ρ ≥ ρtertiary ). In addition to this comes a service payment for each unit of actually provided (tertiary) regulation energy εtertiary.

Also inAS markets of other grid regions, a faster control response is valued more than a slower one. In this respect, an interesting payment scheme exists in the PJM grid area: The so-called pay-for-performance regime allows both slow and fast units to provide secondary control reserves. Unlike in ENTSO-E there exists no rigidAS product structuring. Service payments are calculated individually based on the performance of each unit’s control actuation within a continuous frequency band.

The analysis shows that the value of fast control reserves is higher than the one of slow control reserves. Also, fast reserves are essentially providing their high ramping capability whereas slow reserves are providing energy. Looking at a continuous frequency band of control response, the following qualitative picture arises (Fig. 8.4).

Figure 8.4: Frequency-dependent Categorization of Flexibility Sources (own analysis based on Ancillary Services Products in ENTSO-ECE). 8.2. Qualitative Analysis of Operational Flexibility 177

8.2.3 Needed Flexibility versus Available Flexibility

The relationship between needed operational flexibility, as assessed by using deterministic or probabilistic worst-case scenarios, and the available operational flexibility, as given by an assessment of the capabilities and constraints of the available power system unit pool, is rather straight-forward. The operational flexibility that is available to system operators should be at least as large as the operational flexibility they need for mitigating the expected worst-case disturbance. Clearly, this condition needs to be fulfilled individually for every time-step k and not just on average. Figu- ratively this means that the cube of needed operational flexibility needs to fit nicely into the cube of available operational flexibility. In mathematical terms this condition corresponds to the following six conditions for the flexibility metrics:

+ + - - ρneeded ≤ ρavailable , ρneeded ≤ ρavailable , (8.1) + + - - πneeded ≤ πavailable , πneeded ≤ πavailable , (8.2) + + - - εneeded ≤ εavailable , εneeded ≤ εavailable . (8.3)

In case that one of these conditions is violated, this would correspond figuratively to a situation where one of the sides of the (smaller) cube of needed flexibility sticks out of the (larger) cube of available flexibility as is illustrated by Fig. 8.5–8.6.

Figure 8.5: Needed Operational Flexibility versus Available Operational Flexibility (own illustration). 178 Chapter 8. Qualitative Simulation Studies

Figure 8.6: Necessary Condition for Suﬃcient Operational Flexibility in a Power System (own illustration).

8.2.4 Aggregation of Operational Flexibility

The key idea behind an aggregation or pooling of several power system units is that this leads to the addition of individual flexibility metrics (via Minkowski Summation). In turn, potentially existing individual flexibility deficiencies with respect to one or more of the metrics {ρ, π, ε} can be“masked”(Y. Makarov) within an appropriately chosen unit pool. In the following, an introductory example is illustrated:

• A dynamically slow unit, e.g. a thermal/hydro power plant with the qualitative ﬂexibility metrics ρ small, π large, ε only limited by fuel provision, is pooled with

• A dynamically fast but energy-constrained storage unit, e.g. a ﬂy-wheel or battery with the ﬂexibility metrics ρ large, π small, ε limited and small.

• The aggregation of these two units will feature the sum of the individual ﬂexibility capabilities. The energy constraint of the energy storage unit will thus be eﬀectively masked within the resulting unit pool.

A qualitative illustration of the aggregation and masking eﬀect is given for the above example by Fig. 8.7. 8.3. Analyzing Operational Flexibility 179

Figure 8.7: Aggregation of Operational Flexibility (own illustration).

The subsequent sections will present two approaches that allow an assessment of the ﬂexibility aggregation of diverse power system units. Such an assessment is in general rather challenging due to the fact that the dispatch of any power system unit entails decisions on time- and path-dependent energy storage states, i.e. Ci xSOC,i (k) and opera- 0 0 tion points, i.e. {ugen,i, uload,i (k), with inter-temporal constraints. This means that the complexity of assessing the ﬂexibility capabilities of a unit pool rises with the number of involved power system units i.

8.3 Analyzing Operational Flexibility

The functional representation of complex power system interactions using the Power Nodes notation allows a straight-forward analysis of the three metrics of operational ﬂexibility, i.e. power ramping capability ρ, power capability π and energy storage capability ε.

8.3.1 Quantiﬁcation of Operational Flexibility

Quantifying operational flexibility is, from the perspective of power system operation, very close to the question of what the limits of providing operational flexibility are and, for a given grid topology with transmission bottlenecks, at which grid nodes these bottlenecks are located. Taking again the example of the operational flexibility of a generation unit i that also has an inherent storage function and the possibility for curtailment, e.g. a Hydro Storage Lake, given by following Power Node modeling equation −1 Ci x˙i = −ηgen,i ugen,i + ξi − wi − vi . (8.4) 180 Chapter 8. Qualitative Simulation Studies

The maximum available operational ﬂexibility for power regulation up/down is given thus as

+ (k) = max − wmin − v −Cx, umax − u0 (k), (8.5) πmax,i min ηgen ξ x ˙ gen k,i gen,i

− (k) = min − wmax − v −Cx, umin − u0 (k), (8.6) πmin,i max ηgen ξ x ˙ gen k,i gen,i

min max in which wi (k) and wi (k) define the minimum/maximum allowable curtailment for generation unit i at time-step k. In case the primary fuel min max supply is controllable, the terms ξi (k) and ξi (k) define the minimum/maximum allowable primary power provision. Please note that sign of the storage power term Cx˙ is negative when providing positive power, i.e. storage discharging (Cx˙ < 0), and positive when providing negative power, i.e. storage charging (Cx˙ > 0). Also, in the time-discrete case the term Cx˙ becomes Cδx = C (x(k) − x(k − 1)). This flexibility assessment for metric π (Eq. 8.5) can be extended to the other two metrics, ρ and ε, via time-differentiation and integration of π, respectively, as shown by the equations

π+ (k + h) − π+ (k − h) ρ+ (k) = max,i max,i , (8.7) max,i 2h

π+ (k + h) − π+ (k − h) ρ+ (k) = min,i min,i , (8.8) min,i 2h and

k + + εmax,i(k) = ∑ h · πmax,i(l) , (8.9) l=0 k − + εmin,i(k) = ∑ h · πmin,i(l) , (8.10) l=0 where the term h denotes the sampling interval, i.e. h = tk −tk−1. The ﬂexibility assessment for other power system unit types can be accomplished in a similar fashion. 8.3. Analyzing Operational Flexibility 181

8.3.2 Visualization of Operational Flexibility

Analytical Approach

The three flexibility metrics that can be obtained by the just derived analytical approach span a so-called flexibility volume, which can be represented in its simplified form as a flexibility cube for a generic power system unit i, where the vertices or extreme points are defined by the set + − + − + − of metric terms {ρmax ,ρmax ,πmax ,πmax ,εmax ,εmax}, as is illustrated below (Fig. 8.8).

Figure 8.8: Flexibility cube of Maximum Available Operational Flexi- bility of a Generic Power System Unit (own illustration).

This analytical approach allows a simple and fast analysis of the maximum operational flexibility that can be obtained from a given unit 0 over the time-evolution of the power system unit’s set-point ugen,i(k). One clear drawback is, however, that the maximum available flexibility calculated in this way is without any consideration of how long a certain power system unit would need to reach a new operation point that allows this provision of operational flexibility. The approach only answers the question of how large the flexibility, n o i.e. how large the flexibility set πi(k) is.

The evolution over time of the (maximum) available operational flexibility from a generic storage unit with both load and generation terms, 182 Chapter 8. Qualitative Simulation Studies uload(k) and ugen(k), is illustrated in Fig. 8.9. The plots show that the available operational flexibility is highly time-variant due to the actual storage usage over time. In order to illustrate the contributions of the positive and negative part of the three flexibility metrics, + − + − + − i.e. {ρmax ,ρmax ,πmax ,πmax ,εmax ,εmax}, the flexibility volumes of the subsequent plots are cut into eight (= 23) separate sectors.

Figure 8.9: Time-Evolution of Maximum Available Operational Flexi- bility (Simulation time-step k = 1h, 12h, 24h, 36h, 48h, 60h) [169]. 8.3. Analyzing Operational Flexibility 183

Reachability Approach

However, in order to obtain a more realistic picture of how long it takes a power system unit to change it’s operation point sufficiently to provide the required operational flexibility, the internal double-integrator dynamics of the flexibility metrics, as given by Z ZZ ε = π dt = ρ dt , (8.11) have to be taken into account. In order to do this, this thesis proposes the usage of established methods from reachability/verification analysis [170]. Hereby, the information of how long it takes to reach a certain new operation point providing a required set of operational flexibility {ρ, π, ε } is explicitly given. Calculating the available set of operational flexibility that is achievable after a given number of time-steps k is equivalent to a classical reach set calculation. This later approach, although more exact, is significantly more computationally expensive than the simpler analytic approach sketched out by Eq. 8.5–8.9. For the reach-set calculations, the reachability functions of the MPT Toolbox [171] have been used. There a so-called polytope method is employed that involves besides other things the calculation of the Controllability Gramian WC. (See [172, p. 19 ff.] for a general discussion of reachability analysis.) The advantage of the MPT Toolbox is that it explicitly allows the usage of box constraints for inputs and states of dynamical systems. In a power system context, a typical example of a box constraint are the limitations on min/max power min max ramping, e.g. u˙gen. ≤ u˙gen. (k) ≤ u˙gen. , and min/max power output, min max e.g. ugen. ≤ ugen. (k) ≤ ugen. . Other approaches for calculating grami- ans and the corresponding reach-sets include Linear Matrix Inequali- ties (LMI) methods, as explained by Boyd et al. in [173], as well as so-called ellipsoidal methods, which have been implemented for example in the Ellipsoidal Toolbox [174]. Please note that ellipsoidal methods have a potential disadvantage as they only allow ellipsoidal constraints on system input and states. On the other hand they are computationally much less expensive than MPT’s polytope method when it comes to larger system sizes as is nicely illustrated by Kurzhanskiy et al. in [172, p. 63 ff.]. Due to this more accurate but in turn computationally much more expensive approach, the flexibility volume becomes a significantly more 184 Chapter 8. Qualitative Simulation Studies complex polytope object. An illustration of the more realistic polytope volume of operational flexibility is given in Fig. 8.10.

Figure 8.10: Time-Evolution of Available Operational Flexibility from a Storage Unit at Its Planned Operation Point (k = 0). Green: Time-Evolution of Available Flexibility after k Time-Steps with k = 1h, 2h, 3h, 5h, 10h, 15h (Calculated via Reach Sets). Red: Maximum Available Operational Flexibility at k → ∞ (Calculated using the proposed Analytical Approach, i.e. Eq. 8.5–8.9). 8.3. Analyzing Operational Flexibility 185

The set of reachable operation points providing additional flexibility (green) becomes larger when the available time span is longer. The flexibility set or flexibility volume remains, however, always smaller or becomes at most equal to a theoretic maximum flexibility set or volume (red) as defined by the underlying technical constraints of a given power system unit. Note that the theoretical maximum reachability volume calculated by the analytic approach may in fact never be fully reached by the power system unit, when using the reach set approach (Fig. 8.11).This mismatch is due to the employed finite sampling time when performing the reach set calculation in combination with somewhat pathological operation points at some of the flexiblity cube’s vertices. These operation points exist but are only feasible for infinitesimal small time periods and thus not of any practical relevance, e.g. fully discharging an energy storage unit (π−) while at the same time keeping the storage unit at it’s maximum energy storage level (ε+).

Figure 8.11: Reached Flexibility Volume, V(k) = (ρ · π · ε)(k), after k Time-Steps for a Storage Unit at Its Planned Operation Point (k = 0).

8.3.3 Aggregation of Operational Flexibility

An important question in power system analysis is how a group or pool of power system units act together in achieving a given objective, i.e. de- livering a scheduled power trajectory or providing ancillary services by tracking a control signal. Pooling together different power system units to provide a service that they cannot provide individually is thus an active research field. A prime example is to combine a dynamically slow power plant with a dynamically fast, but energy-constrained storage unit, e.g. a battery, to 186 Chapter 8. Qualitative Simulation Studies provide fast frequency regulation that neither of the units could provide individually [175] due to the lack of one flexibility metric, i.e. the missing fast ramping capability ρ of the power plant, or another, i.e. the small energy capability ε of the storage unit. Obtaining the aggregated operational flexibility that a pool of different power system units provides, is equivalent to aggregating the flexibility volumes of the individual units. Since these are given by more or less complex polytope sets, depending on the chosen calculation approach presented in the previous section, a well-known polytope operation, the Minkowski Summation, can be employed for calculating the aggregated flexibility of the pool. In the following, we illustrate the aggregation of a slow-ramping power plant together with a fast-ramping but energy-constrained storage unit in Fig. 8.12. We assume that within the grid zone of a unit pool, grid constraints are minor and not of practical relevance for the quantification of aggregated flexibility. Although this is an important simplifying assumption, i.e. copperplate grid, it is often used for instance in power markets operation. The aggregation of two or more power system units leads to the addition of individual flexibility metrics

{ρ,π,ε}agg = {ρ,π,ε}slow + {ρ,π,ε}fast . (8.12)

The aggregation of the operational ﬂexibility of both units, given individually by their respective polytope objects, is accomplished via Minkowski Summation

+ + − − ρagg = ∑ρi , ρagg = ∑ρi , i i + + − − πagg = ∑πi , πagg = ∑πi , (8.13) i i + + − − εagg = ∑εi , εagg = ∑εi . i i

The slow-ramping unit, e.g. a thermal power plant, with {ρ,π,ε}slow, is assumed to have an unlimited fuel supply, which implies that no energy constraints exist and that the energy provision capability is inﬁnite (εslow → ∞). Also, the potential power output π is large. Dynami- cally slow means in this context that the power ramp-rate ρ is small. The fast-ramping storage unit, e.g. a ﬂy-wheel or battery system, with 8.3. Analyzing Operational Flexibility 187

{ρ,π,ε}fast, has a limited run-time bounded by energy constraints of the storage unit and thus only a limited energy storage capability exists (0 < εfast εslow). As is often the case for storage units, ramp-rate ρ is large whereas power capability π is comparatively small. Depending on storage technology, time-dependent energy storage losses, v(x), can be signiﬁcant. This is notably the case of ﬂy-wheel energy storage systems, where storage losses due to bearing friction become large when going beyond a storage cycle duration of a few minutes.

8.3.4 Available Operational Flexibility versus Needed Operational Flexibility

At last we compare the needed operational flexibility for mitigating a disturbance event with the available operational flexibility that a given power system can offer. The needed flexibility could, for example, be derived from the assumed worst-case succession of the combined wind andPV feed-in forecast errors over a given time interval. Effectively balancing this requires the ability to follow steep power ramps as well as to provide large amounts of regulating power and energy over time. In order for a given power system to successfully accommodate such a disturbance event, the available flexibility volume should always envelope the needed flexibility volume, as shown in Fig. 8.13. If this would not be the case, flexibility capability is lacking along at least one axis of the flexibility metrics, for + instance πagg. <= 0. In this case the disturbance event could not be fully accommodated. Calculating the polytope of the still available operational flexibility that remains while mitigating the expected disturbance boils down to yet another polytope operation, the Pontryagin Difference. 188 Chapter 8. Qualitative Simulation Studies

Figure 8.12: Aggregation of Maximum Operational Flexibility of Indi- vidual Power System Units. Flexibility of Conventional Generation Unit with no Energy Constraint (yellow), Flexibility of Energy-Constrained Storage (blue) and Aggregated Flexibility of Both Units (green). 8.3. Analyzing Operational Flexibility 189

Figure 8.13: Needed versus Available Operational Flexibility. Needed Flexibility Volume for Balancing a Disturbance (red), Avail- able Flexibility Volume (green) and Remaining Flexibility Volume after Subtracting the Needed Flexibility Volume (magenta). 190 Chapter 8. Qualitative Simulation Studies

8.4 Applications of Flexibility Analysis Methods

This chapter presented modeling and analysis techniques for the quantitative assessment and visualization of operational flexibility in electric power systems. These techniques allow in a first phase the modeling and definition of operational flexibility of individual power system units by building up on our previous work on the Power Nodes modeling framework [155, 156] and combining it with the valuable work of others, notably of Makarov et al. in [87]. In a second phase, the analysis and visualization of the operational flexibility of individual power system units is presented for some illustrative examples. The approaches are, however, also applicable for more complex, larger-scale power system setups. For the later, the illustrated method of aggregation of the operational flexibility from several and different individual power system units is useful. It allows the analysis of the combined flexibility properties of unit pools, in which different power system units are aggregated and work together to achieve a common control objective. The calculation of the remaining operational flexibility in a power system after having subtracted the needed from the originally available operational flexibility was shown for an illustrative case study. The outlined methods can help power system operators to evaluate the needed flexibility for coping with system disturbances as well as to assess the available flexibility that the currently dispatched unit portfolio can provide for them. We envision that these techniques will become useful tools for system operators, allowing the aggregation of the available – often too plentiful – power system state information into intuitive visual charts, i.e. 3D images of available and needed operational flexibility cubes, and straight-forward flexibility quantification, i.e. the flexibility metrics {ρ,π,ε}, for the current system state as well as for predicted future system states. This would notably allow the real-time analysis of the overall flexibility properties of unit pools, in which different power system units are aggregated and work together to achieve a common control objective, e.g. frequency and power balance regulation, but also the calculation of the remaining operational flexibility set in a power system after having subtracted the needed flexibility for mitigating a disturbance, e.g. fore- 8.4. Applications of Flexibility Analysis Methods 191 cast error, from the originally available operational flexibility. Thereby operators in control centers could better assess in real-time how close to the limits the power system is currently operated or would be operated in case of a disturbance event and from which sources flexibility could be drawn in such a scenario for system balancing and restoration [176]. The implementation of such flexibility visualization and analysis methods will hopefully lead to a qualitatively and quantitatively improved (power) system awareness, control and operation.

Chapter 9

Quantitative Simulation Studies

9.1 Introduction

In this chapter quantitative simulation results of the operation performance of the German, the Swiss and the interconnected European power system (ENTSO-E) are presented. Power system operation performance is analyzed here mostly with respect to a power system’s ability to integrate stochastic power feed-in from RES units. The curtailment of RES power feed-in from wind & PV units over the course of reference simulation years is quantified for the different power systems. This serves as a proxy for evaluating the effectiveness of RES grid integration. The goal of the quantitative simulation studies presented in the following is to assess the operational behavior and performance of possible future power system setups. In this respect it is analyzed whether more operational flexibility, for instance in the form of more energy storage capacity (π, ε) or better utilized power transfer capacities obtained via Dynamic Line Rating (DLR) methods, improve a power system’s capability to integrate high shares of variable RES grid integration. To this end large-scale and computationally expensive power dispatch optimization of the generation, load and storage unit portfolio in the

193 194 Chapter 9. Quantitative Simulation Studies simulated power systems are performed. It is argued that a predictive dispatch scheme approximates a real-world power dispatch better than simpler methods, such as rule-based dispatch schemes that – in realistically complex setups – would arguably perform sub-optimal in comparison.

9.2 Power Nodes Simulator Platform

In the following the Power Nodes Simulator Platform is presented (Fig. 9.1). This simulator platform allows to perform time-series simulations of generic power systems with a high temporal resolution. In the subsequent simulation case studies, sampling times of 15 minutes or 1 hour have been used. For yearly simulations, this leads to about 35,000 quarter-hourly or 8,760 hourly simulation steps. For each simulation step, the power dispatch of the given power system unit portfolio has to be decided upon. In all the following study cases, a predictive power dispatch scheme is used that minimizes the operation cost of the power system, while explicitly accounting for unit constraints and available forecast information. The Power Nodes simulator platform allows to incorporate various information of a given power system. This includes the generation, storage and load unit modeling information, which is given in the form of Power Node equations, the grid topology, which can be given in the form of an energy transport model as well as in the form of DC or AC grid models, and various time-series profiles of wind &PV power feed-in, load demand and in the case of hydro units also precipitation profiles. All time-series should ideally have the same high temporal resolution. Please note that also power feed-in/out forecasts, be they perfect or imperfect, can be passed on to the simulator and the predictive dispatch scheme. The Power Nodes simulator platform can be parametrized such as to allow the creation of Monte-Carlo-type simulation scenarios, e.g. simu- lating the occurrence of different RES energy shares or larger available storage capacity. Since these scenarios are independent from each other, the parallel simulation runs of 10–1000s scenarios as perfectly parallel tasks is possible. After the simulation runs, the assessment of relevant balance terms, as introduced previously in Section 6.2.7 and subsequent data analysis follows. 9.3. Power Dispatch Problem 195

In its current form the Power Nodes Simulator Platform is based on Matlab [177]. The power dispatch optimization is accomplished in a parallelized fashion using Matlab’s Parallel Computing Tool- box and CPLEX as (mixed-integer) quadratic programming (MIQP/QP) solver of choice [178].

Figure 9.1: Power Nodes Simulator Platform (own illustration).

9.3 Power Dispatch Problem

9.3.1 Introduction

Power Dispatch planning activities are aimed at establishing the best possible use of available resources. This objective can be formulated as minimizing the cost of system operation, while maintaining power system security constraints. In real-time operation, these schedules deﬁne the baseline of expectations for the actual events. Since the primary objective is to maintain a secure operating state of the power system in spite of unexpected variations and events, optimality becomes a merely secondary objective.

Today, the schedules for operation planning are usually an outcome of power market operations, facilitating the coordination of multiple 196 Chapter 9. Quantitative Simulation Studies actors. In the perspective of a system operator, an economic dispatch approximates the outcome of power market operations [179]. An optimal power dispatch would require perfect information about the actual operating conditions, which is in reality not available in ad- vance. In particular, uncertainty in the prediction of load demand or wind &PV production time-series induces a mismatch between previously scheduled and actual energy ﬂow realizations. As predictions become more accurate when they get closer to their realization, it is useful to schedule the diﬀerent power system units day-ahead based on the available predictions and to allow for an additional intra-day update when more accurate predictions become available. Since this schedule will be imperfect as well, the remaining mismatch has to be accounted for by control reserves, i.e. allowing a real-time power balancing.

9.3.2 Predictive Power Dispatch Scheme

Motivation

The motivation behind using a model-based predictive power dispatch optimization scheme is as follows. The time-series simulation of a power system, and hence the analysis of the simulation results, can only be worthwhile if that power system’s operation, i.e. the simulated power dispatch choices that govern every- thing, resembles as close as possible to a real-world power dispatch. In reality, system operation has the goal of minimizing the system operation cost, i.e. dispatching the cheapest available generation units as given by a merit-order curve, while serving all load demand. This is equivalent to upholding the power balance of the power system and accounting for power flow constraints within a grid topology as well as respecting each unit’s operational constraints. This is furthermore complicated as system operation is faced with forecast uncertainty of RES power production and load demand and various inter-temporal constraints, notably those that arise through energy storage operation. In today’s power system operation, the economic dispatch strategy is either decided by an “all-knowing” central entity that performs a potentially large-scale optimization, a prime example of this being the North American power system. The dispatch strategy is the result of a spot-market clearing process, a prime example of this being the EPEX 9.3. Power Dispatch Problem 197 and Nordpool spot markets in the European power system. In the later case, instead of a centralized optimization, each market participant runs a local optimization for his own unit portfolio and the available forecast information and then decides individually on power supply & demand bids. In an ideal world, both power dispatch decision approaches would converge to the same globally optimal power dispatch strategy. Due to the incomplete or inaccurate information, arguably, only sub- optimal power dispatch strategies are obtained in reality independent of the chosen power dispatch approach. Please note that both dispatch approaches can be applied for uniform- and zonal-pricing as well as for locational marginal pricing regimes. The predictive power dispatch scheme proposed here intends to mimic the power dispatch process of a central entity, i.e. solving a large-scale dispatch optimization. The advantage of the proposed optimization procedure is that it structurally allows to explicitly take into account available forecast information of both load demand as well as wind & PV power feed-in over a finite prediction horizon, e.g. up to several days. When seasonal (hydro) storage units are present significantly longer prediction horizons of several weeks and even months are needed.

Unit Commitment & Optimal Power Flow Problem

Economic Dispatch (ED), the so-called unit commitment problem in the case no grid constraints are considered, i.e. the well-known copperplate grid simplification, or a so-called Optimal Power Flow (OPF) problem in the case grid constraints are considered. Both power dispatch approaches are in fact optimization problems that are for realistic setups usually complex and large-scale in nature as pointed out in the seminal articles of J. Carpentier [180, 181]. In both cases the optimization’s goal is to derive the efficient operation and/or planning of power systems as was discussed, for example, by Carpentier and Merlin in [182]. Approximating the power dispatch process of the spot market by a central decision entity is not a trivial task. The economic dispatch optimization of the power system is usually dictated by the operation costs of the generators, i.e. marginal costs, ramping costs as well as start/stop costs. Furthermore, the optimization scheme behind the decision entity should 198 Chapter 9. Quantitative Simulation Studies respect any operational constraints of the generators and storage units, i.e. power ratings and power ramp-rates as well as energy constraints and current State-of-Charge (SOC). Due to the stringent inter-temporal constraints of storage scheduling, i.e. the energy constraints, but also generator scheduling, i.e. power ramp-rate constraints and start/stop times, a multi-period-optimization scheme is imperatively required. Finally, the optimization scheme should be able to explicitly use available forecast information of load demand as well as PV and wind power feed-in over a finite prediction horizon, up to several days, for its dispatch decisions, because forecasts provide valuable information. This is important for a realistic simulation setting, and simulation results, as forecast information of load demand and RES power feed-in are in reality significantly influencing power market bidding strategies and power plant dispatch decisions, notably those of large storage units. Naturally, the forecast accuracy also plays a role for power dispatch performance.

Model Predictive Control

The here proposed optimization scheme has been inspired by optimal control theory, in particular Model Predictive Control theory. MPC combines a receding, finite horizon optimization with a periodic ob- servation of actual state variables of the plant and a subsequent optimization update of the control output. This emulates a closed-loop-like behavior, which enables the central optimization scheme to deal with unanticipated disturbances, i.e. differences between previously predicted and actual power feed-in or feed-/out. MPC offers several advantages for formulating control/optimization problems in a power systems context, e.g.

• Constraints on system states, i.e. power balance , energy storage states as well as voltage levels,

• Constraints on control in-/output, e.g. grid actuators that control either power feed-in/ot, and,

• Control objectives, i.e. a cost function for power dispatch that can then be minimized. Furthermore, MPC theory oﬀers valuable properties such as the optimality of the calculated control strategy with respect to the chosen 9.3. Power Dispatch Problem 199 objective function and, if needed, guaranteed stability via the inclusion of so-called stability constraints. An illustration of MPC’s operation principle is given by Fig. 9.2.

Figure 9.2: Operation Principle of Model Predictive Control (source: [183]).

Power Nodes Optimization Setup

Within the Power Nodes approach, the state of the “plant” is the set of State-of-Charge (SOC) variables xi of the storage units, and external predictions for power feed-ins and loads are considered up to the optimization horizon. Although the nature of the given dispatch problem is stochastic, a deterministic dispatch based on the available predictions is chosen here for simplicity. Since there exists a feedback-loop in an MPC scheme, imperfect forecasts can be accommodated and the introduced error will be bounded over time. The MPC-based power dispatch scheme can be extended in order to better represent the stochasticity of the underlying processes by a

1. Stochastic programming approach, i.e. stochastic MPC, or

2. Monte-Carlo scenario-based optimization. 200 Chapter 9. Quantitative Simulation Studies

If uncertain processes (ξi) act on the storage levels or if a mismatch of plant and model dynamics has to be accounted for, the actual SOC state needs to be observed in order to capture deviations. Due to the possibility of various model-plant mismatches, e.g. introduced by nonlinear storage eﬃciencies (ηi) and losses (vi), it is also useful if no actual stochastic processes (ξi), e.g. RES production or load demand, are simulated.

The main parameters of the predictive power dispatch scheme are the

1. Optimization frequency, e.g. daily, hourly, sub-hourly, ...,

2. Sampling time Tsample,

3. Prediction horizon Tpred. = N · Tsample,

4. Available predictions at the time of carrying out the optimization, e.g. 24-hour ahead wind & PV forecast with 1 hour resolution, and

5. Time-lag between the execution of the optimization, e.g. applying the obtained power plant schedules and the realization, in liberalized settings given by the gate closure time of power markets.

Cost functions

The details of the multi-stage predictive power dispatch optimization are given in the following.

For a compact cost function formulation, we deﬁne the system state and input variable vectors as

T x = [x1,..., xn] , (9.1)

u = [ugen,1,..., ugen,N, uload,1,..., uload,N, ξ1,..., ξN, (9.2) T w1,..., wN] ,

δuk = uk − uk−1 , (9.3) where the terms x, ugen, uload, ξ and w correspond to the previously introduced Power Nodes states and energy ﬂow in-/outputs (Chapter6). 9.3. Power Dispatch Problem 201

The following cost function type for the economic power dispatch is considered in all subsequent simulation cases,

l=k+N ref T ref T ref Jk = ∑ (xl − xl ) Q(xl − xl ) + q (xl − xl ) (9.4) l=k l=k+N ref T ref T ref + ∑ (ul − ul ) R(ul − ul ) + r (ul − ul ) (9.5) l=k l=k+N T + ∑ δul δRδul , (9.6) l=k where the terms xref and uref are reference values for state and input variable vectors.

The individual terms in the cost function have the following meaning:

• The first line (Eq. 9.4) penalizes a deviation of the state from a desired target value. Penalizing state deviation is only meaningful in cases when actual financial costs are incurred by the deviation, or when the state shall be kept in the vicinity of a certain level, e.g. in order to reduce the risk of a storage depletion or overflow under uncertain load and RES forecasts.

• The second line (Eq. 9.5) penalizes all instantaneous quantities except for the physical loss term v. This includes mainly generator cost functions, i.e. linear and/or quadratic terms, for fuel costs as well as operation and maintenance (O&M), and penalties for curtailments of load and generation. The latter is only relevant when actual compensation payments have to be made e.g. for RES curtailments.

• The third line (Eq. 9.6) represents power ramping costs incurred by set-point changes. This is particularly relevant for thermal generation processes where thermal stress is an important factor for unit lifetime.

The complete (economic) predictive power dispatch problem for a power system unit portfolio of dispatchable and non-dispatchable generators, 202 Chapter 9. Quantitative Simulation Studies controllable and non-controllable loads as well as diﬀerent types of storage units, can then be formulated as

min Jk u s.t. (a) xl+1 = A · xl + B · ul , min max (b) 0 ≤ x ≤ xl ≤ x ≤ 1 , min max (c) u ≤ ul ≤ u , min max (d) δu ≤ δuk ≤ δu ,

(e) ubus,l − Gmap ul = 0 ,

(f) ubus,l − Gline Pline,l = 0 ,

(g) pline − B f Θ = 0 , min max (h) Pline,l ≤ Pline,l ≤ Pline,l , (i) Θmin ≤ Θl ≤ Θmax , (9.7)

where the cost function term Jk has been introduced by Eq. 9.4–9.6 for the current time step k.

The term xl represents state variables, i.e. the SOC of storage units and lin ul is the power nodes’ power feed-in/out, for prediction time step l. Ru , quad Ru and δRu represent linear and quadratic marginal as well as power ramping cost terms, respectively.

Equation 9.7(a) represents the (linear) Power Nodes model of the power system, 9.7(b)–(d) denotes operational constraints of the power system units, 9.7(e)–(f) define the grid topology, and 9.7(g)–(i) defines, in this case, a (linear) DC power flow as well as line and voltage angle constraints.

min max Please note that the terms Pline,l and Pline,l are constant in the case of Nominal Line Rating (NLR), whereas they represent time-variant line limit profiles in the case of DLR. Such time-variant DLR profiles are calculated from temperature, wind speed, and solar radiation profiles. 9.3. Power Dispatch Problem 203

Discussion of Predictive Power Dispatch Performance

Due to the significant impact of inter-temporal constraints, which are inevitably for realistic setups, introduced both by power plant ramping constraints as well as energy constraints of storage units, coupled with the forecast information of future load demand and RES power feed-in profiles, a predictive power dispatch optimization scheme based on Model Predictive Control (MPC) is proposed as a central power dispatch entity. The author argues that such a predictive dispatch approximates a real-world power dispatch better than other methods, such as rule-based dispatch schemes that – in realistically complex settings – arguably can only perform sub-optimal in comparison. However, it has been shown that simplified special cases exist in which a simple rule-based power dispatch scheme can be proven to be optimal. Recent research work by D. Heide, M. Greiner et al. presented such simulation studies for a fully renewable European power system, for example in [184]: Here all power generation is based on wind &PV units. A generic energy storage technology with given charging and discharging efficiencies (ηin and ηout) and an energy constraint given by the maximum storage capacity (EH) is used. In such a simplified setup, the only power dispatch decisions that can be made are, first, to discharge the storage unit in case there is not enough RES power generation to fulfill load demand, second, to charge the storage unit in case there is an oversupply of RES power generation or, third, if the storage unit is already full to curtail such an oversupply. In this specific simulation setup, the above presented three-case-rule set that governs the power dispatch [184, Eq. 4] is sufficient and arguably also optimal. Here, inter-temporal constraints and, thus, forecast information are not relevant for deciding the power dispatch strategy. However, this finding is not generalizable to more complex power systems that also include other generation units different, i.e. conventional units with differing marginal costs and ramp-rate constraints as well as different types of storage units, i.e. having different transformation efficiencies and energy storage constraints. The set of possible individual dispatch options, Odispatch, in each time step is inevitably larger. In addition, in such a more complex setup, the inter-temporal constraints induced by power ramping and, certainly, energy storage constraints have a significant impact on power dispatch performance and cannot by ignored. The set of possible dispatch strategies, Sdispatch, i.e. the 204 Chapter 9. Quantitative Simulation Studies set of individual dispatch choices that are causally connected over the given prediction horizon Tpred. = N ·Tsample, will thus simply explode for N sufficiently long horizons, i.e. Sdispatch = Odispatch . In the later case, it is therefore hardly conceivable that rule-based dispatch schemes that provide an optimal performance for a multi-stage power dispatch can be found. A predictive power dispatch optimization is thus necessary for realistically complex simulation setups because there exists a veri- fiable significant impact of the prediction horizon length Tpred. on the performance of the economic power dispatch. A quantification example of the prediction horizon’s impact on power dispatch performance is presented in the following:

• The simulation example uses a simplified German power system with varying wind & PV yearly energy shares. • The simulations are full-year simulations for the reference year 2010. The sampling time Tsample is 15 min, resulting in 35,040 simulation and dispatch steps per simulation year, i.e. ≈ 880,000 simulation steps per prediction horizon setup. • In order to amplify the effect of inter-temporal constraints an artificial pumped hydro storage capacity of 50 times the existing storage capacities (power: 7 GW, energy: 40 GWh) is considered. • Full-year simulations of 25 power system setups with varying wind &PV shares are accomplished for different prediction horizon lengths Tpred. = {1h, 6h, 12h, 24h, 48h, 96h}.

In such a setup, a strong impact of the prediction horizon length Tpred. and with it the explicit consideration of more or less forecast information, is visible for the power dispatch performance. An illustration of this is given by Fig. 9.3, where the dispatch performance, measured as RES integration capability, i.e. avoided RES curtailment, is presented for a simpliﬁed power system model with varying wind &PV energy shares. Please note that the choice of the prediction horizon also has an impact of whether wind or PV power feed-in can be better grid- integrated. For the short prediction horizon Tpred. = 1h, PV power curtailment is much larger than wind power curtailment, whereas for the longer prediction horizon Tpred. = 24h, the situation is inverse. The betterPV integration for longer horizons is due to the daily cycle of PV feed-in, of which the dispatch scheme is fully aware in the later case. 9.3. Power Dispatch Problem 205

(a) Prediction Horizon Tpred. = 1h. (b) Prediction Horizon Tpred. = 6h.

(e) Prediction Horizon Tpred. = 48h. (f) Prediction Horizon Tpred. = 96h.

Figure 9.3: Comparison of Dispatch Performance for Diﬀerent Predic- tion Horizons Tpred. (own illustration). x-axis: [0, 10,..., 50%]PV energy share of yearly load demand, y-axis: [0, 10,..., 50%] wind energy share of yearly load demand, Color coding: RES curtailment (dark blue: ≈ 0%, dark red: ≈ 50%). 206 Chapter 9. Quantitative Simulation Studies

9.4 Simulation Studies of Various Power System Cases

In the following three power system simulation studies are presented. The analysis focus is in each case to assess the capability for RES grid integration of the respective power systems. Of particular interest is to ﬁnd out if and how more operational ﬂexibility, provided in particular by more energy storage capacities {π, ε}, can improve the grid integration of large energy shares of wind &PV units.

9.4.1 Germany

Study Setup

The case study considers the German power system, whose specifications were given already in Chapter2 (Table 2.1). By year-end 2011, the German power system featured significant combined shares of wind andPV power feed-in, both in absolute numbers, i.e. about 54 GW, as well as in relative numbers, i.e. about 63% of yearly peak load demand. Firm, fully dispatchable generation capacities, i.e. fossil- and biofuel- based, nuclear and ROR units, were slightly lower than the peak load demand, i.e. about 85 GW or about 98.8% of peak load demand (86 GW) and are made up of a diverse set of large and small, dynamically slow and fast generation units. In aggregation, these units feature good ramping capabilities. When combining firm generation and PHS units, the positive power capacity π+ and the ramping capacity ρ± can, on the one hand, accommodate the significant fluctuations in load demand and variable RES power feed-in in every time-step. The energy storage capacity ε in the form of traditional PHS units is, on the other hand, rather small, i.e. about 40 GWh [185]. A spinning control reserve of 4.5GW from firm generation units is allocated in order to emulate existing reserve requirements of primary and secondary control. The power dispatch optimization necessary for assessing the operational flexibility of the power system has been performed in parallelized yearly simulation runs with high temporal resolution, i.e. Tsample = 15min.. All simulations have been performed using a predictive power dispatch optimization with a look-ahead, i.e. prediction horizon, of 72 hours, 9.4. Simulation Studies of Various Power System Cases 207 prediction update intervals of 8 hours and a sampling time of 15 min. for the full year 2011. Publicly available hourly load data for Germany as provided by ENTSO- E, i.e. about 490.2 TWh (year 2011) [9], scaled-up to match the realized yearly electrical energy supplied, i.e. about 550 TWh (year 2011) derived from an estimation based on [186,187], as well as realized wind & PV feed-in data from all German grid zones as provided by EEX [188] have been incorporated. For the time being, a simple copperplate grid model was assumed, hence abstracting from all power flow and voltage level constraints. Further- more, the load and RES energy forecasts are assumed for now to provide perfect information, i.e. the forecast error is zero. The here presented simulation results constitute thus a performance benchmark. They are significantly better than any power dispatch optimization under more realistic, i.e. more constrained, operation conditions and imperfect forecast information could ever expected to be. An exemplary simulation run for the German power systems, namely the evolution of power feed-in into and feed-out out of the grid as well as the SOC of the aggregated PHS capacity for the month of May 2010, featuring 30% wind and 50%PV energy share, are illustrated by Fig. 9.4. The calculation time was approximately 1 minute.

Figure 9.4: Simulation Example for the German Power Sys- tem (May 2010) (own illustration). 208 Chapter 9. Quantitative Simulation Studies

RES Curtailment

Now, the RES grid integration capability of the German power system is tested by applying signiﬁcant variable power feed-in from wind & PV units, i.e. with 0–50% yearly energy share, for full-year simulations with high time resolution. Although only a copperplate grid model without any import/export capability to neighboring countries is considered, the simulation results nevertheless provide valuable insights:

• Simulation series using a large-scale parameter screening of 121 (11 × 11) different combinations of yearly RES energy shares, ranging from 0% to 50% of energy feed-in shares from wind &PV generators, have been accomplished. The goal was to evaluate the effectiveness of RES integration in terms of curtailed, i.e. wasted, RES feed-in for the different wind & PV combinations. Two simulation setups of the German power system (Table 2.1) were investigated, i.e. using

1. No storage capability at all (ε0 = 0GWh), and

2. Energy storage capability of PHS units (ε0 = 40GWh). • A parameter variation over two flexibility metrics (π, ε), with ρ set constant, has been assessed: 1. An energy scenario with medium RES shares of 20% wind and 10% PV energy, close to Germany’s energy policy goals for the year 2020 as expressed in the National Renew- able Energy Action Plan (NREAP), i.e. 18.4% wind and 7.3% PV[50, p. 113 ff.], is considered. Doubling the storage units’ power capability π from it’s existing value of 7GW to 14GW reduces RES curtailment by half, i.e. from about 4 % to about 2 %. Doubling the storage units’ energy capability ε from 40GWh (it’s existing value) to 84GWh has almost no effect unless π is further increased. Results are shown in Fig. 9.5(a)–(c). 2. An energy scenario with high RES shares of wind and PV energy, 50% each, is considered. Increasing the storage units’ power capability π ten-fold and the storage units’ energy capability ε twenty-fold reduces RES curtailment to a third, i.e. from about 51 % to only about 17 %. Results are given in Fig. 9.6(a)–(c). 9.4. Simulation Studies of Various Power System Cases 209

• Depending on the chosen energy scenarios, a different flexibility metric is most relevant. In the first scenario (20% wind and 10% PV), the power capability π is most important whereas in the second scenario (50% wind and 50%PV) it is rather the energy capability ε. This, however, may be different in the long-term: For the extreme case of high RES energy shares (50% for wind and PV each) as shown in Fig. 9.6(a)–(b), one can observe that

1. Increasing available power ramping capability ρ or power capability π from its current nominal values (ρ0 := 1, π0 := 1) would hardly improve integration performance. 2. In comparison to this, increasing the available energy storage capacity ε would somewhat improve RES integration as shown in Fig. 9.6 (c): Increasing the current storage capacity ε0 = 40GWh by a factor of ten would reduce RES curtailment from around 43% to around 42%.

• The overall simulation results indicate that the integration of high PV energy shares will, in fact, be more diﬃcult than the integration of high wind energy shares: Forced curtailment of less than 15% of total available RES feed-in in the case of high wind energy shares instead of more than 65% in the case of high PV energy shares. This is illustrated in Fig. 9.7. In case no storage capability is considered, the RES curtailment losses would be higher than 80%. However, whether wind or PV power feed-in can be better grid- integrated depends on several factors, namely the 1. Characteristics of load demand, wind & PV power feed-in time-series and how well these correlate, 2. Characteristics of the power system’s storage capacities, π i.e. the power to energy capacity ratio, ε , as well as 3. Availability and accuracy of forecasts as pointed out earlier. In this respect, the grid integration of PV power production may also be easier than for wind power production when energy storage capacity is greatly enlarged, as is illustrated by Fig. 9.8. 210 Chapter 9. Quantitative Simulation Studies

Figure 9.5: Predictive Power Dispatch (20% wind and 10% PV). (a+b) Optimization Results (Simulation Snapshot of June 2011). (c) RES Curtailment as Function of Available Energy Storage. 9.4. Simulation Studies of Various Power System Cases 211

Figure 9.6: Predictive Power Dispatch (50% wind and 50%PV). (a+b) Optimization Results (Simulation Snapshot of June 2011). (c) RES Curtailment as Function of Available Energy Storage. 212 Chapter 9. Quantitative Simulation Studies

Figure 9.7: Curtailed RES Power Feed-In as Function of RES Deploy- ment for the Existing German Power System (π0 = 7GW, ε0 = 40GWh). Curtailment shown in % of available yearly RES energy. (Red line: RES deployment path for 1990 – 2012.)

Figure 9.8: Curtailed RES Power Feed-In for a Hypothetical German Power System (π0 = 30 × 7GW, ε0 = 20 × 40GWh). Curtailment shown in % of available RES yearly energy. (Red line: RES deployment path for 1990 – 2012.) 9.4. Simulation Studies of Various Power System Cases 213

Storage Expansion Strategies

The previously presented simulation results for the German power system allow the derivation of energy storage expansion strategies in order to better mitigate and integrate high RES shares. For the German power system currently in place it would be very ben- eﬁcial in terms of reduced RES curtailment to increase the power rating (π) of the existing hydro storage units, i.e. the power rating of the installed pumps and turbines. In contrary to this, increasing the energy rating (ε) does not show a relevant improvement of grid integration as is illustrated by Fig. 9.9.

Figure 9.9: Storage Expansion Strategy for German Power System. 214 Chapter 9. Quantitative Simulation Studies

9.4.2 Switzerland

Study Setup

In the following a hypothetical future Swiss power system for the year 2050 is simulated and analyzed. The system specifications are based on ETH Zurich’s Energiezukunft Schweiz study [97], which was an important scientific precursor for the now official Swiss energy policy outlook (BFE Energieperspektiven 2050 [189]). The Swiss power system described in [97, ETH 2050 Scenario] exhibits high variable RES shares, namely 14 TWh fromPV, 3 TWh from wind turbines and 39 TWh from hydro units, i.e. HSL& ROR. The total yearly load consumption is assumed as 78 TWh (medium scenario). All hydro-inflow profiles, ξ hydro(k), follow the typical seasonal characteristics for rain-fall as well as for snow-melting. Conventional backup generation capacity exists in the form of gas-fueled turbines. The marginal operation costs are set comparatively high, thus making them a last resort option. The existing PHS capacities (1.7 GW, 50 GWh) are cor- rectly modeled as well. The time-series data has been obtained from the Swiss TSO swissgrid (load demand), the Swiss Federal Office of En- ergy (BFE) (hydro time-series) and from EEX (wind & PV). For the simulations all available time-series data was re-sampled to match an hourly sampling rate. Again, the power system is modeled without the consideration of a grid topology, i.e. a copperplate grid model for which no import or export with neighboring countries is considered. An illustration of the load demand and RES power feed-in profiles, i.e. wind, PV, ROR and HSL, is illustrated by Fig. 9.10. As can be seen there are, on the basis of daily power averages, only few instances during the summer, where RES power production is larger than load demand (Fig. 9.10a). However, on the basis of hourly power averages, there are many instances throughout the year, especially but not limited to the summer season, where PV power “peaks” are almost twice as high as the load demand (Fig. 9.10b). 9.4. Simulation Studies of Various Power System Cases 215

(a) Daily Proﬁle.

(b) Hourly Proﬁle.

Figure 9.10: Load-Demand and RES Generation Proﬁles of Swiss Power System based on ETH 2050 Scenario [97] (own illustration). 216 Chapter 9. Quantitative Simulation Studies

Paradigm Change in Storage Operation

An interesting effect of the very high RES shares in this hypothetical power system is that the traditional storage operation pattern will, most of the time, become completely reversed. Instead of pumping water into upper basins during nighttime, i.e. the typical off-peak load demand period, and producing electricity by discharging water via the turbines into lower basins during noon-hours, i.e. the typical peak load demand period, the exact opposite will happen on many days. The dominant storage strategy is now to absorb RES power feed-in, notably from PV units during sunny noon-hours, and instead to supply load demand during night-hours, where there is no PV feed-in. This new storage operation paradigm is depicted for a typical summer week by Fig.9.11. Please note that all hydro-based units (ROR, HSL and PHS) do contribute operational flexibility with their respective storage functionality, also ROR units that are assumed to have a small but not negligible storage capacity. Wind &PV units do also contribute flexibility via RES curtailment, in case no other options are available.

Storage Expansion Strategies

Compared to other power systems, the large share of hydro units in the Swiss power system, all providing some albeit differing degrees of operational flexibility as discussed in Section 6.3, allows the effective grid integration of significant shares of variable RES power production. This is shown in the following via the analysis of full-year simulation runs with varying PHS energy and power ratings. The ETH 2050 Sce- nario, with 14 TWh PV and 3 TWh wind energy shares is used here as the base case. As can be seen clearly in Fig. 9.12a, today’s existing PHS storage capacities (1.7 GW, ca. 50 GWh) are largely sufficient as forced curtailment of available wind & PV power feed-in is very low, i.e. less than ≤5%. Thus, no significant energy storage capacity expansion would be necessary. If it is done nevertheless, the aim should be to increase the power rating of the PHS units. Only if RES shares are increased further, say an additional 50% on top of the base case, i.e. 21 TWhPV and 4.5 TWh wind energy, forced curtailment of available wind &PV power feed-in would noticeable increase, i.e. to about 10% (Fig. 9.12c). For a twice as high RES deployment, i.e. 28 TWh PV and 6 TWh wind energy, forced curtail- 9.4. Simulation Studies of Various Power System Cases 217

Figure 9.11: Exemplary Power Dispatch Result for Swiss Power System for a Typical Summer Week (Days 167–175), (own illustration). y-axis: Power Feed-In (positive) / Power Feed-Out (negative) 218 Chapter 9. Quantitative Simulation Studies ment of available wind &PV power feed-in would rise further, i.e. to about 20% (Fig. 9.12d). In these latter two cases, storage expansion via increasing PHS power rating has a higher eﬀect than in the former two cases (Fig. 9.12a–9.12b).

(a) Base Case. (b) Base Case (+25% wind&PV).

Figure 9.12: ETH Scenario 2050 Storage Expansion Scenarios. x-axis: [1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5x] PHS power rating (1.7 GW). y-axis: [1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5x] PHS energy rating (50 GWh). Color Coding: Wind & PV Curtailment (dark blue: 0%, dark red: 20%). 9.4. Simulation Studies of Various Power System Cases 219

9.4.3 Interconnected European Power System

Study Setup

In the following, the complete interconnected European Power System, illustrated by Fig.9.13, is simulated using the Power Nodes Framework. The power system model consists of altogether 29 countries. Each country “node” contains eight different aggregated Power Node unit types, i.e. non-controllable load demand as well as curtailable load DSP, wind &PV, CSP, PHS, fast & slow conventional generation. In total about 230 Power Node units are modeled. The individual characteristics of the aggregated Power Nodes unit types for each country node are specifically modeled, i.e. power and ramp rating (for storage units also energy rating). The country-specific time-series data for the different power system unit types is also passed on to the Power Nodes simulator. Eventually, full-year simulations with an hourly temporal resolution, i.e. 8,760 steps per simulation year, are conducted for five different scenario families [190]. The existing grid topology, i.e. about 50–60 transmission corridors, is approximated by an 29 node energy transfer model, using the official Net Transfer Capacities (NTC) values of the interconnected European power system as published by ENTSO-E. All data of time-series and power system unit ratings was obtained in the process of the EU-Project IRENE-40 [191]. The five IRENE-40 scenario families are given as follows

• IRENE-40 BAU – Business as Usual Scenario

• IRENE-40 CCS – Carbon, Capture and Storage (CCS) Scenario

• IRENE-40 DES – Desertec Scenario

• IRENE-40 EFF – High Eﬃciency Scenario

• IRENE-40 RES – High Renewable Energy Sources (RES) Scenario

All IRENE-40 scenarios include significant grid expansion and bulk storage deployment over the time-frame 2010–2050. Each scenario family consists of power system specifications and time-series for five reference years, i.e. 2010, 2020, 2030, 2040 and 2050. Thus altogether 25 full-year 220 Chapter 9. Quantitative Simulation Studies scenarios are available. All scenarios for the start reference year 2010 are identical but diverge considerably for later reference years.

More details on the IRENE-40 scenario modeling are given in [190,191].

Figure 9.13: Interconnected European Power System including Yearly Power Flow Patterns (source: ENTSO-E[9]).

Changes of Power Flow Patterns

All of the IRENE-40 scenario families assume continuing RES deployment, mostly wind & PV units, throughout the European power system. This has significant impacts on power system operation, as the pattern of where generation units are deployed and at which grid nodes these are feeding-in, will change as well. The change in generation deployment 9.4. Simulation Studies of Various Power System Cases 221 patterns combined with the characteristic variability of RES power feed- in will lead to very different power feed-in patterns in the future and, as a result of this, power flow patterns will change as well. Clearly, the impact will be stronger for scenarios in which RES deployment is high. An illustration of power flow changes in the interconnected European power system is given by Fig. 9.14. Here, the weekly averaged power flow condition for eight important country interconnections is shown over the course of the year. As can be clearly seen, today’s power flow patterns, i.e. the IRENE-40 BAU scenario for the year 2010 (Fig. 9.14a), are very different from the power flow patterns of hypothetical but possible future scenarios, for instance the IRENE-40 RES scenario for the year 2050 (Fig. 9.14b). Changes of regional power flow patterns correspond to a change in the utilization of the grid infrastructure. Such effects have surely to be kept in mind, when considering power system expansion planning. Expansion planning that considers today’s grid utilization patterns and projects these trends often linearly into the future, i.e. considering a business-as-usual outlook scenario, may lead to the derivation of grid expansion projects that may not fit to the, potentially very different, grid utilization patterns of other outlook scenarios, i.e. various high RES scenarios. More results on this topic can be found in the master thesis by F. Co- maty [192], supervised by the author of this doctoral thesis, as well as in a jointly written report on the challenges of the energy transition for the Swiss and European power systems made for the Schweizerische Akademie der Technischen Wissenschaften (SATW)[193]. 222 Chapter 9. Quantitative Simulation Studies (a) Power Flow Patterns (Year 2010). (b) Power Flow Patterns (Year 2050). Figure 9.14: EU-29 DispatchColor Simulations Coding: – Weekly Power Averaged Flow Line Patterns Loading (own illustration of [ 192 ]). Power Transfer Corridor (dark blue: 0%, dark red: 100%). 9.4. Simulation Studies of Various Power System Cases 223

Limits to RES Integration

Another intriguing eﬀect that was revealed through the analysis of the simulations of the interconnected European power system, is that RES curtailment tends to rise in line with rising RES energy shares. The simulation results indicate that there is indeed a limitation to RES grid integration above a certain threshold of the annual wind & PV energy share. This “invisible ceiling” surprisingly seems to be largely independent of the speciﬁc scenario setup. As is shown by Fig. 9.15, starting with a RES energy share of about 20% of annual load demand RES curtailment starts to rise in all analyzed IRENE-40 scenarios. The here conducted simulations correspond to a performance benchmark, i.e. a central dispatch optimization is conducted, no grid bottlenecks are considered, perfect prediction of wind & PV as well as load demand time-series is assumed and RES integration has dispatch priority. The simulated RES integration is thus also a best case. Curtailment results for real-world power systems with imperfect forecasts and non- negligible grid constraints, would be noticeable higher.

Figure 9.15: RES Curtailment as a Function of RES Energy Share (own illustration). 224 Chapter 9. Quantitative Simulation Studies

9.5 Obtaining Operational Flexibility from Dynamic Line Rating

An assessment of the beneﬁts from employing Dynamic Line Rating (DLR) instead of more conservative Nominal Line Rating (NLR) for softening line constraints in (predictive) power dispatch and, thus, improving the grid integration of variable RES such as windPV units. This section is largely based on the semester thesis by Bolun Xu [194], supervised by the author of this doctoral thesis, and a resulting joint publication [195].

9.5.1 Motivation for Dynamic Line Rating

Unlike Nominal Line Rating (NLR), DLR takes advantage of the fact that the physical power transmission capacity of overhead lines is a function of ambient conditions, i.e. temperature, wind speed, wind angle and solar insolation. DLR is hence often less conservative than NLR as the latter assumes significantly more challenging ambient conditions. A simulation study has been performed on a six-node benchmark system loosely based on the German power system. Simulations with high time resolution, i.e. 15 min., were accomplished using a predictive power dispatch scheme that directly incorporates line constraint information. Historic load demand, wind &PV power feed-in profiles, as well as scaled-up profiles for high RES scenarios are used. Dispatch impacts of line constraints derived via DLR and NLR are compared and their differing effect on RES grid integration is evaluated.

9.5.2 Dynamic Line Rating Modeling

Steady-state Heating Balance

The rating of the transmission line is determined based on the heating balance of the conductor in steady-state, as deﬁned by a CIGRE´ standard [196]. A simpliﬁed version of the heating balance equation is

PJ + PS = PC + PR , (9.8) 9.5. Operational Flexibility from Dynamic Line Rating 225 where PJ is Joule heating, PS is solar heating, PC is convective cooling and PR is radiative cooling.

The resulting DC current rating (IDC) of Eq. 9.8 is then s PC + PR − PS IDC = , (9.9) RDC[1 + α(TAvg − 20)] where RDC is the DC resistance, α is the temperature coeﬃcient of the 1 resistance and TAvg is the average temperature of the conductor .

The equivalent AC rating, IAC, can be calculated as

IDC IAC = . (9.10) p −5 1.0123 + 2.319 · 10 IDC

Procedures for obtaining PS, Pc and Pr are given by CIGRE´ in [196].

1Temperature is assumed to be distributed coherently across the conductor, thus, conductor surface temperature is equal to TAvg.

Figure 9.16: Current Rating of Overhead Line as a Function of Ambient Conditions with Reference Conditions marked as Red Circles [195]. 226 Chapter 9. Quantitative Simulation Studies

As shown in Fig. 9.16, wind speed (V) has the largest impact on line m rating IAC, which increases from 700A (at V = 0 s ) to around 3300A (at m 2 25 s ), constituting an increase of 371% . Besides this, the wind attack angle (δ) and the ambient temperature (TAmb) also have a significant effect on IAC, with an increase of 35% and a decrease of 41% in line rating, respectively. The global solar radiation (S), in comparison, has a small effect on line rating. In our simulations IAC dropped by only 5% of it’s initial value for high solar insolation levels. DLR profiles are calculated from temperature, wind speed and solar radiation profiles. The temperature profile is reconstructed from the daily minimum and maximum temperature using a sinusoidal approximation [197, 198], while wind speed and solar radiation profiles are reconstructed from wind & PV feed-in time-series [198]. Fig. 9.17 depicts a reconstruction example.

Figure 9.17: Reconstruction of Ambient Conditions for DLR (own illustration [195]).

2Horizontal section in wind angle curve is due to the fact that wind cooling power in this region is smaller than the conductor’s natural cooling power. 9.5. Operational Flexibility from Dynamic Line Rating 227

In our study, the German power system is chosen as the reference for the benchmark model used for the power dispatch simulation. This is motivated by the fact that in Germany, wind conditions are more favorable in the north whereas solar insolation conditions are more favorable in the south. In turn, most wind turbines are installed in the northern part, while the majority ofPV units are installed in the south [199]. If Germany is to increase its produced energy share from variable RES units, it will be facing the problem to transmit the wind and solar power nationwide. This is especially true for the north-south transmission corridors, which constitute more and more a transmission capacity bottleneck within Germany [200]. This situation makes it thus a ﬁne benchmark case for testing the performance of DLR.

A E

B F

C D

(a) Benchmark Zones. (b) Network Topology.

Figure 9.18: Illustration of Germany-based Six-Node Benchmark Model (own illustration [195]). 228 Chapter 9. Quantitative Simulation Studies

Results

Simulations are performed with actual or scaled renewable feed-in and load profiles. The rating of the transmission lines is set to correspond either to the NLR or the DLR value. The dispatch performance of the two power system setups is then compared. As simulations with the originally available energy feed-in/out time-series profiles of the full- year 2011 did not exhibit curtailment for both NLR and DLR setups, the profiles were scaled-up by increasing both wind & PV shares while decreasing dispatchable, conventional generation capacities. With these artificially scaled profiles, adopting DLR allowed 15,209 GWh more energy per year to be transmitted through the network, an increase of 66.7% when compared to the NLR case. Figure 9.20 shows a comparison between NLR and DLR for the transmission line between benchmark zones A (BREMEN) and B (COLOGNE). The NLR case has a load curtailment of 2,729 GWh, i.e. 0.5% of yearly load demand, counted by summing curtailments in all six zones, while total wind generation curtailment is 1,072 GWh, i.e. 1.1% of yearly wind feed-in. In the DLR case, load and wind generation curtailments are 2,325 GWh, i.e. 0.4%, and 46 GWh, i.e. 0.05% – a reduction of 15% and 95.7% compared to NLR. No PV curtailment occurs in either setup. Figure 9.21 shows the curtailment for zone A (BREMEN) in December 2011, for which wind feed-in curtailment was significantly reduced when using DLR. The comparison of line loading of zone A (BREMEN) to zone B (COLOGNE) during this period is shown in Fig. 9.19.

Figure 9.19: Line Loading from Zone A (BREMEN) to Zone B (COLOGNE) in December 2011 (red: DLR, blue: NLR). 9.5. Operational Flexibility from Dynamic Line Rating 229 Figure 9.20:(year Transmission 2011). Corridor of Zone A (BREMEN) to Zone B (COLOGNE): NLR versus DLR 230 Chapter 9. Quantitative Simulation Studies Figure 9.21: PredictiveDecember Dispatch 2011 and using NLR curtailment, Curtailment orange:(upper of PV and Feed-In/Out curtailment). middle Curtailments plot) for or Zone DLR A(lower (BREMEN) plot) in (red: load curtailment, blue: wind Chapter 10

Summary & Conclusion

Summary

Part I An overview of the on-going paradigm change in power system operation was given. Some of the important new challenges to power system operation & control are discussed. The presented challenges do mainly relate to the large-scale deployment of variable RES generation units but also to increasing power market activity and rising electricity demand in conjunction with only limited grid reinforcement at the same time. This part concludes with a discussion of opportunities for mitigating these operational challenges. This doctoral thesis argues that one of the key means for mitigating the challenges is to acquire, and use, additional sources of operational flexibility. Part II An overview of established modeling frameworks for power & energy systems was given. Notably, the Network-Preserving Model Frame- work and the Energy Hub Concept were presented and the motivation for new, complementary modeling frameworks is discussed. The Power Nodes Modeling Framework and new contributions to it were presented in the following. This part is concluded with a discussion of operational flexibility in power systems and how it can be modeled, both for individual units as well as for aggregations, i.e. pools, of different power system units, i.e. generators and energy storage.

231 232 Chapter 10. Summary & Conclusion

Part III An analysis of operational flexibility in power systems was presented. First, a qualitative analysis of the flexibility of individual power system units and small pools was accomplished. Then, a quantitative analysis of the operational flexibility of large-scale power systems using a predictive power dispatch optimization was conducted and results presented.

Conclusion

Operational flexibility in power system operation and its role for mitigation of disturbances and RES grid integration was discussed and analyzed from different angles, ranging from power system modeling approaches to analytic approaches inspired by well-known control theory concepts to first qualitative and then quantitative simulation-based assessments. The provision of (additional) operational flexibility can be enabled by introducing more sensing, i.e. sensor elements, computation, i.e. operation optimization schemes, as well as control, i.e. actuators, into power system operation and planning. Improving controllability & observability of power system processes will surely help to improve power system operation & management, i.e. allowing it to be more secure, efficient and stable. One noteworthy idea is the concept of a control-based grid adaptation as an alternative to conventional hardware-based grid adaptation for the operational challenges related to large-scale RES deployment. It allows a, potentially cost-saving, trade-off between computation & communication, for which costs have been exponentially falling in the past, and conventional grid upgrade options, for which costs stayed the same or have even risen. Ex- ponential ICT cost reductions help make many power system communication, control and optimization schemes technically and economically viable. To analyze this new manifold of grid operation and planning options, novel modeling, analysis and optimization tools are needed. This thesis aims to provide new ideas and yet academic tools for doing just that as well as pinpointing future research in the right directions. I hope that my doctoral thesis provides some qualitative and quantitative insights in this respect.

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Curriculum Vitae 16 September 1981 Born in Halle (Saale), Germany

Research Oct. ’08–March 2014 Research Assistant at Power Systems Laboratory, ETH Zurich, Switzerland May–July 2012 University of California, Berkeley Energy and Resources Group (Prof. D. Callaway) Berkeley, CA, USA April–June 2012 Paciﬁc Northwest National Lab Advanced Power&Energy Systems (N.Lu, Y.Makarov) Richland, WA, USA June–Sept. 2007 California Institute of Technology Control & Dynamical Systems (Prof. R. Murray) Pasadena, CA, USA 1999 – 2000 Student trainee at Humboldt-Universit¨at Solid-State Physics, (Prof. T. Masselink, Dr. U. Muller)¨ Berlin-Mitte, Germany

Education 2004–2007 Double-degree studies of Engineering Cybernetics Dipl.-Ing. (kyb), Universität Stuttgart, Germany Diplômede Master recherche Supélec, France 2001–2004 General Engineering Science (Pre-Diploma) TU Hamburg-Harburg, Germany 2001 A-levels (Abitur) at Heinrich-Hertz-Gymnasium Berlin-Friedrichshain, Germany 1998–1999 Senior year at Shawnee Mission West High School Overland Park, KS, USA

253 254 Curriculum Vitae

Industry Sept. ’07–Aug. 2008 Analyst at International Energy Agency (IEA), Paris, France May–Sept. 2006 Trainee at Réseau de Transport d’Electricité(RTE)´ Département Méthodes et Appui Versailles, France Aug. ’00–Sept. 2001 Student trainee at Fraunhofer FIRST (FUEGO satellite project, Dr. S. Montenegro) Berlin-Adlershof, Germany 1998, 1999, 2001 R&D student trainee and intern at Siemens AG Berlin-Spandau, Germany Scholarships 2007–2008 Carlo-Schmid Fellowship Studienstiftung des Deutschen Volkes (German Na- tional Academic Foundation) and DAAD (German Academic Exchange Service) 2003–2007 Study Scholarship, Stiftung der Deutschen Wirtschaft (German Business Foundation) Awards 2014 PSCC 2014 Best Paper Selection

2013 IEEE ISGT Europe 2013 Best Poster Award (Co-Author and Supervisor) 2013 IEEE PES General Meeting 2013 Best Paper Award (Co-Author) 2013 IEEE PowerTech 2013 Best Paper Selection (Top 5) (Co-Author and Supervisor) 2007 St. Gallen Wings of Excellence Award 2007 Selected Contribution, St. Gallen Symposium 2007 2000 2nd price at Jugend forscht (Youth researches) Berlin State Competition (Work Environment) 1997 3rd price at Jugend forscht (Youth researches) Berlin State Competition (Technology)