Optimal Diversification of Heat Sources for Largeaustrian District

DISSERTATION

Optimal Diversiﬁcation of Heat Sources for Large Austrian District Heating Systems

ausgeführt zum Zwecke der Erlangung des akademischen Grades eines Doktors der technischen Wissenschaften

unter der Anleitung von Ao. Univ. Prof. Dipl.-Ing. Dr. techn. Reinhard Haas E370 - Institut für Energiesysteme und elektrische Antriebe

eingereicht an der Technischen Universität Wien Fakultät für Elektrotechnik und Informationstechnik

von Dipl.-Ing. Nikolaus Rab, M.Sc. (WU)

Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. Wien, 2019 Nikolaus Rab tuwien.at/bibliothek Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. tuwien.at/bibliothek The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. Kurzfassung

Zahlreiche Studien sprechen der Fernwärme eine bedeutende Rolle innerhalb nachhaltiger Energiesysteme der Zukunft zu. Heutzutage sind gasbefeuerte Kraft-Wärme- Kopplungsanlagen ein zentrales Standbein großer Fernwärmesysteme in Österreich. Die stark fallenden Börse-Strompreise der vergangenen Jahre erschweren zusehends einen wirtschaftlichen Betrieb dieser Anlagen. Diese Strompreisentwicklungen stellen dadurch eine wirtschaftliche Bedrohung für diese Fernwärmesysteme als Gesamtes dar und zeigen gleichzeitig die Bedeutung einer ausgewogenen Diversiﬁkation des Fernwärmeerzeugungs- Portfolios auf. In der vorliegenden Dissertation wird zunächst eine detaillierte Analyse der wirtschaftlichen Charakteristika sowie der Risikoexposition verschiedenster Fernwär- metechnologien durchgeführt. Dabei werden mehrere wissenschaftliche Beiträge gemacht. Zum einen wird als Grundlage für die Investitionsentscheidungen in eine Fernwärmetechno- logie unter Unsicherheit die Verteilung zeitlich gemittelter Primärenergiepreise (levelized input energy prices) mittels Ergebnisse aus der asiatischen Optionspreistheorie hergeleitet. Zum anderen wird eine dynamische Kostenallokation für Kraft-Wärme-Kopplungsanlagen auf Basis des aktuellen Deckungsbeitrages der Stromerzeugung eingeführt. Schließlich wird ein nicht-konvexes Optimierungsmodell zur Selektion von Fernwärmeportfolien bei unterschiedlicher Risikoaversion entwickelt. Die Anwendung des Modells zeigt für die drei großen österreichischen Fernwärmesysteme Wien, Linz und Graz deutlich die Bedeu- tung einer Integration von Niedertemperatur-Abwärmequellen mittels Wärmepumpen für die Möglichkeit langfristig stabile und wettbewerbsfähige Fernwärmepreise für den Endkunden bereitzustellen. Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

iii tuwien.at/bibliothek Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. tuwien.at/bibliothek The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. Abstract

Numerous recent studies foresee district heating play an important role in the development of future sustainable energy systems. Today large Austrian district heating systems mainly rely on combined heat and power plants fueled by natural gas. Due to changes in the electricity market in the last years, these plants have rather poor economic prospects. The electricity price development endangers the economic viability of the existing district heating systems and indicates the need for a proper diversification of price risks. Within this thesis an in-depth analysis of the financial characteristics and risk exposures of different district heating generation technologies is carried out. Hereby new scientific contributions are made by deriving the distribution of levelized input energy prices for the purpose of enabling district heating investment decisions under uncertainty based on insights gained from Asian option theory. Furthermore, a dynamic cost allocation of combined heat and power plants depending on the actual contribution margin of electricity generation is introduced. Finally, a non-convex optimization model is developed for the optimal selection of district heating generation portfolios for different levels of risk aversion. The application of this model for the district heating systems of Vienna, Linz and Graz particularly stresses the value of including low-temperature heat sources via heat pumps for ensuring stable and competitive prices for district heating customers. Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

v tuwien.at/bibliothek Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. tuwien.at/bibliothek The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. Contents

Kurzfassung iii

Abstract v

Contents vii

1 Introduction 1 1.1 Motivation ...... 1 1.2 URBEM-DK ...... 3 1.3 State of the Art ...... 3 1.4 Core Objectives ...... 4 1.5 Scientiﬁc Contributions and Structure of the Thesis ...... 5

I Economic Characteristics of District Heating in Austria 7

2 Demand and Supply 9 2.1 District Heating Load ...... 10 2.1.1 Variation Over Time ...... 10 2.1.2 Load Duration Curve (LDC) ...... 13 2.2 District Heating Sources ...... 16 2.2.1 Combustion Plants ...... 16 2.2.2 Waste Heat ...... 21 2.2.3 Heat Pumps ...... 23 2.2.4 Non-Combustible Renewables ...... 26 2.2.5 Technical Parameters ...... 27 2.2.6 Financial Parameters ...... 30

3 Input Energy 35 3.1 Markets and Prices ...... 36 3.1.1 Fossil Fuels ...... 36 3.1.2 Wood Fuels ...... 39 Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. 3.1.3 Electricity ...... 39 3.1.4 Volatilities and Correlations ...... 41

vii tuwien.at/bibliothek 3.2 Long-Term Uncertainties ...... 44 3.2.1 Stochastic Dynamics of Energy Prices (Pt)t≥0 ...... 44 3.2.2 Distribution of Levelized Energy Prices P¯ ...... 46 3.3 Input-Related Costs ...... 48 3.3.1 Transmission and Transportation Costs CT ...... 48 3.3.2 Taxes ...... 51

4 Cost Curves of Single DH Technologies 53 4.1 Fixed and Variable Costs ...... 54 4.1.1 Heat-Only Technologies ...... 55 4.1.2 CHP Technologies ...... 56 4.1.3 Waste Heat Technologies ...... 60 4.2 Cost Curves ...... 62

II District Heating Generation Portfolio Selection 65

5 Generation Expansion Planning 67 5.1 Introduction to GEP ...... 68 5.1.1 Inclusion of Existing Plants ...... 69 5.2 Convex Programming GEP ...... 70 5.2.1 Reformulation of the Standard GEP ...... 70 5.2.2 Analytical Characteristics ...... 72 5.2.3 Linearisation ...... 74 5.3 Mixed-Integer Linear Programming (MILP) GEP ...... 76 5.3.1 Discretisation and Extension of the Standard GEP ...... 76 5.3.2 Flexibility Modeling ...... 76 5.3.3 Program Formulation ...... 81 5.4 Discussion ...... 85

6 Modern Portfolio Theory 87 6.1 Standard Portfolio Theory ...... 88 6.1.1 Program Formulation ...... 88 6.1.2 Analytical Characteristics ...... 89 6.1.3 Discussion ...... 90 6.2 Integrated Portfolio Theory ...... 91 6.2.1 Risk-Averse Stochastic Programming ...... 91 6.2.2 Convex Quadratic Programming Approximation ...... 94 6.2.3 Solution Algorithm ...... 95

7 Large District Heating Systems in Austria 99 7.1 Characteristics ...... 100 Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. 7.1.1 Annual District Heating Generation ...... 100 7.1.2 Main Technical Characteristics ...... 101

viii tuwien.at/bibliothek 7.2 Generation Portfolios and Available Heat Sources ...... 102 7.2.1 Combustion Plants with Renewable Fuels ...... 102 7.2.2 Combustion Plants With Fossil Fuels ...... 103 7.2.3 Waste Heat Sources ...... 106 7.2.4 Non-Combustible Renewables ...... 108 7.2.5 Heat Pumps ...... 108 7.3 Mean-Variance Optimal Expansion Strategies ...... 110 7.3.1 Input Data for the IPT model ...... 110 7.3.2 Selected Generation Portfolios ...... 114

8 Conclusions and Outlook 123 8.1 Key Role of Portfolio Diversiﬁcation ...... 123 8.2 Transformation of Large DH Systems in Austria ...... 124 8.3 Outlook for Future Research ...... 125

A Mathematical Proofs 127 A.1 Generation Expansion Planning ...... 127 A.2 Modern Portfolio Theory ...... 131

List of Figures 133

List of Tables 135

Bibliography 137 Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

ix tuwien.at/bibliothek Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. tuwien.at/bibliothek The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. CHAPTER 1

Introduction

1.1 Motivation

Numerous recent studies including Heat Roadmap Europe [46] see District Heating (DH) play an important role in the implementation of future sustainable energy systems. Today DH systems already play a major role in the heat supply of several Northern, Central and Eastern European countries, see Figure 1.1. For example 28% of all Austrian citizens are supplied by DH. [80]. There are several factors that make district heating an important part of future sustainable energy systems, three of which will hereby be covered by the author:

Waste Heat Recovery: District heating systems allow for the inclusion of waste heat • from both industrial and incineration processes, heat that would otherwise be lost. This helps improve the environmental balance, as no additional heat generation is required. An example would be Vienna who in 2015, despite having a large DH system, managed to supply 35% of their DH by waste heat recovery.

Central Management: A DH system’s central management enables the actions • needed for a transition to a low-carbon heating system to be much simpler, faster and targeted, compared to the alternative of changing individual heating systems.

Stable Heat Prices for Customers: District Heating is highly adaptable to a large • variety of fuels and heat sources. This leads to diversiﬁcation opportunities of DH providers, which in turn can translate to competitive and stable heat prices for customers. Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

1 tuwien.at/bibliothek DH supply [in %] 100 40 35 30 25 20 15 10 5 0 no data

Figure 1.1: Share of citizens supplied by district heating per country in the European Union (2013). [80]

Large Austrian DH systems mainly rely on combined heat and power (CHP) plants fueled by natural gas. Historically, thermal power plants were built in Austria in order to complement the hydro power plants during the winter, when water availability is lower and electricity demand is higher. Since these thermal power plants have been especially used for electricity generation in winter when also heat demand is high, the usage of their waste heat oﬀered a huge district heating potential [223]. Due to changes in the electricity market in the last years, which have also led to lower electricity prices, these plants have rather poor economic prospects. [112] This price development endangers the economic viability of existing DH systems and indicates the need for a proper diversiﬁcation of their price risks. This conclusion is also supported by a survey conducted amongst executives of the Swedish District Heating Association, revealing that it is of the utmost importance for future competitiveness to manage "risks Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. impacting fuel prices", i.e. the exposure of fuel prices to risk, well. [174]

2 tuwien.at/bibliothek 1.2 URBEM-DK

This thesis was conducted within the doctoral program Urban Energy and Mobility Systems (Doktoratskolleg Urbanes Energie- und Mobilitätssystem, URBEM-DK). URBEM-DK was established by the Wiener Stadtwerke Holding AG (Vienna Public Utilities Company) and the Vienna University of Technology. It covered the interdisciplinary work of 10 PhD students supervised by 10 professors working for five different faculties and aimed to "research and develop an interactive environment for analyzing scenarios for the way to sustainably supply a secure, affordable and livable city by the example of the City of Vienna in a holistic and interdisciplinary approach". [90] Apart from this thesis, the following topics were further addressed during the program:

1. Future heat demand and supply of the building stock.

2. Analysis of energy consumption and mobility behaviour of the population.

3. Future electricity and heat load proﬁles of residential and oﬃce bullpens.

4. Technical analysis of the future district heating and natural gas grid infrastructure.

5. Technical analysis of the future electricity grid infrastructure.

6. Planning of information and communications technology structures for control of the urban energy supply.

7. Future choice of transport mode in the urban area.

8. Implementation of a visualization tool of the results within the URBEM-DK.

9. Management of the URBEM-DK smart city application.

1.3 State of the Art

The search for an optimal power plant portfolio selection was ﬁrst formulated and implemented as a mathematical optimization problem for Électricité de France in 1957. [178] This approach later became known as the Generation Expansion Planning (GEP) program and quickly came to be well-established in both the operations research literature and the energy sector. A ﬁrst large computer implementation as a linear programming program subject to several technical and operational constraints was achieved in 1974 by the International Atomic Energy Agency (IAEA) as Wien Automatic System Planning (WASP) [129]. For several decades GEP models have only been used for electricity generation portfolios that had several technologies available: hydro power, nuclear and thermal power plants Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. with gas, coal, oil and lignite as fuel inputs. In contrast to electricity generation portfolios, DH generation portfolios typically only comprised a CHP plant with additional heat-only

3 tuwien.at/bibliothek boilers (HOB) as backup. Therefore optimization programs for DH generation systems mainly focused on the optimal sizing of the CHP plants, e.g. in [181] for a fossil fuel CHP system and in [256] for a biomass fuel CHP system. The recent need and desire for DH portfolio diversiﬁcation led to the creation and adoption of mathematical models for investment planning of DH plants. This comprises several approaches:

Comparison of possible investments based on a simple economic evaluation, e.g. • [258], Comparison of possible investments based on a detailed linear programming model • for economic dispatching, e.g. [97], Optimal investments determined by a Linear GEP, e.g. [28] (for Vienna) and [87] • (for Graz and Salzburg).

Today, the detailed modeling of economic dispatching and generation expansion programs of DH systems is of fundamental importance for DH systems operators. In order to include an optimal diversification of energy price risks, the Modern Portfolio Theory (MPT) was first adapted to optimal power plant portfolio selection by Bar- Lev and Katz in 1976 [15]. Since the 2000s this approach has gained growing interest in academia and has been constantly further developed, however, an application and implementation for DH systems is still missing. Nevertheless, the issue of energy price risks in investment planning for DH systems has been addressed in simpler approaches such as the analysis of a large number of different fuel price scenarios, as in [254]. This thesis aims to close this research gap and to introduce a suitable application of Modern Portfolio Theory to the expansion of DH generation capacity.

1.4 Core Objectives

When considering proper diversification for Austrian DH systems, several steps emerge. First, a detailed analysis of the cost structure and risk exposure of existing DH generation systems in Austria needs to be conducted. Second, a proper method for determining optimally diversified portfolios with competitive customer prices needs to be identified. The review in Chapter 6 reveals a research gap in the application of the standard diversification theory to the DH system expansion planning, thus requiring the development of a new mathematical framework. Finally, this new method is to be applied to the largest DH systems in Austria in order to successfully fulfill the need for a proper diversification for future Austrian DH systems. These three core objectives may be described in more detail as follows: Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. 1. Analysis of the financial characteristics and risk exposures of DH generation in large DH systems in Austria. This thesis aims to accurately define the cost curves of

4 tuwien.at/bibliothek all DH technologies available in Austria. Furthermore, the volatility and correlation of their variable costs as well as major risks of their investment costs should be identiﬁed.

2. Identiﬁcation of the most suitable adaptation of Modern Portfolio Theory for determining optimally diversiﬁed DH generation portfolios. A further goal of this thesis is to develop a new approach for the use of Modern Portfolio Theory in DH generation expansion planning programs. This comprises an analysis of the assumptions and main characteristics of the MPT in power plant portfolio selection as well as the development of a mathematical framework for a model dealing with DH plant portfolio selection.

3. Determination of optimally diversified generation portfolios for large DH systems for 2030 in Austria. The ultimate goal of the thesis is to offer an overview of optimally diversified DH generation portfolios with competitive customer prices for the three largest DH systems in Austria for 2030. This overview will also include a detailed description of the distribution of the generation costs of each of the three systems.

In addition to the core objectives of this thesis, its inclusion into the URBEM-DK doctoral program in itself entails a supplementary core objective, namely properly sharing the results of this thesis with the other PhD students from the program and in return implementing the results from the thesis of those same PhD students. This particularly refers to the future DH generation park in Vienna and its cost characteristics at delivery as well as to the future development of the DH demand as an important input.

1.5 Scientiﬁc Contributions and Structure of the Thesis

The thesis is organized into two parts: Economic Characteristics of District Heating in Austria and District Heating Generation Portfolio Selection. The first part focuses on satisfying the first two core objectives, i.e. the analysis of the financial characteristics and risk exposures of DH generation in large DH systems in Austria. It comprises the study of DH demand and supply technology characteristics in Chapter 2, an in-depth analysis of the economic characteristics of the DH input energies in Chapter 3 as well as the study of the economic evaluation of single DH technologies in Chapter 4. Most notable scientific contributions are:

Contribution 1 (Distribution of Levelized Energy Prices) • In the standard literature on MPT adapted to power plant portfolio selection (e.g. [13]) a competitive market for power plants is assumed, i.e. they can be traded like Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. ﬁnancial assets. Subsequently the volatility of yearly input energy price returns can be regarded as a suitable risk measure for power plant investment decisions. For

5 tuwien.at/bibliothek DH plants this assumption has to be rejected, as DH systems are typically local monopoles and therefore no market for trading these plants exists. To overcome this obstacle the concept of the distribution of levelized energy prices, i.e. the distribution of the average input energy price over a plant’s lifetime is introduced. This new approach allows for an adequate method to cover uncertainties for the investment planning of DH plants and uses insights gained from Asian option theory.

Contribution 2 (Dynamic Cost Allocation for CHP Plants) • Academic literature supports a static cost allocation among electricity and heat generation in CHP plants based on a joint products costing or a by-products costing approach, depending on the technical characteristics of the plant. [103] Due to the high volatility of electricity prices such a static approach may sometimes lead to unreasonable cost allocations during the plant’s lifetime. Therefore the author proposes a dynamic cost allocation method that depends on the actual contribution margin of electricity generation.

The second part focuses on the second and third core objectives, i.e. on identifying the most suitable adaptation of the Modern Portfolio Theory for the determination of optimally diversiﬁed DH generation portfolios in Chapter 6 and on the determination of an actual portfolio for large urban Austrian DH systems in 2030 in Chapter 7. Its main contribution to the scientiﬁc literature is given by:

Contribution 3 (Integrated Portfolio Theory as Non-Convex Optimization) • In the standard literature on MPT adapted to power plant portfolio selection (Integrated Portfolio Theory) the possibility of reversals in the merit order is excluded by assumption, see e.g. [225, 126, 51]. This is justiﬁed by the empirically low occurrence of such reversals in the typical one year holding period of the power plant for the analysis. This assumption is crucial as it leads to mathematically simple convex or even quadratic optimization programs. For DH technologies the reversal of a merit order has been frequently observed. If this assumption of no such reversals is dropped, the Integrated Portfolio Theory leads to a generalized Risk-Averse Two-Stage Stochastic Program. Based on the insights gained from [271], a Deterministic Equivalent Formulation of the program is obtained be the author with a corresponding solution algorithm presented in Chapter 6 as one major contribution of this thesis. Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

6 tuwien.at/bibliothek Part I

Economic Characteristics of District Heating in Austria Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

7 tuwien.at/bibliothek Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. tuwien.at/bibliothek The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. CHAPTER 2

Demand and Supply

From the demand perspective District Heating (DH) is characterized by huge demand variation over time, mainly caused by variations in outdoor temperature throughout the year. This time-variation plays a critical role in technology selection for DH portfolios and imposes additional costs since especially supplying peak demand is expensive. From the supply perspective, DH is highly adaptable to a large variety of heat sources. These heat sources include combustion of different fuels in heat-only boilers, waste heat of electricity generation in combined heat and power (CHP) plants, geothermal and solar heat, sea, lake, river or sewage water that can be used by employing heat pumps and waste heat of several industrial processes. This leads to diversification opportunities for DH providing companies, which can imply more stable and competitive prices for customers. In Figure 2.1 an overview of a simplified DH system is given: heat sources and customers are connected via supply and return lines enabling the satisfaction of the time-varying demand of these customers by a portfolio of different heat plants. First, Section 2.1.1 gives an overview of the origins of variations in the DH load i.e. the aggregate of the consumers’ heat demand and heat losses that inevitably occur during distribution. The duration of different DH load levels arising over the course of a year can be analysed by using a Load Duration Curve (LDC). Its definition and empirical as well as parametric estimations are provided in Section 2.1.2, which additionally contains an analysis of the LDC and a case study on the Viennese DH load. Second, Section 2.2 provides an overview of DH generating technologies and their role in Austria. They can be grouped into heat-only boilers (HOB), combined heat and power (CHP) plants, non-combustible renewables and heat pumps and waste heat sources. Finally, their main technical and financial parameters are discussed and summarized. Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

9 tuwien.at/bibliothek Supply Line (90-150◦C) Demand Section 2.1

Input Energy Heat Plant Chapter 3 Section 2.2 Customer 1 Customer 2

Return Line (60◦C) Pump

Figure 2.1: Simpliﬁed illustration of a DH system: One or several heat plants are connected via a supply and return line to the customers. (Source: Own illustration)

2.1 District Heating Load

2.1.1 Variation Over Time The load of a district heating system is characterized by large variation throughout the year. This variation is mainly caused by ﬂuctuating diﬀerences between outdoor temperature and the desired temperature inside the buildings being supplied by DH, see [272, 95]. In Figure 2.2, the daily minimum and maximum DH load of the Viennese DH system, for the year 2012, are shown. The observed hourly load varied in this year from rd 175 MWth to 2397 MWth. The maximum load was observed on February 3 at 08:00 am, corresponding to an outside temperature of -13.1 ◦C, the minimum load on August 11th at 08:00 am, when an outside temperature of 27.5 ◦C was observed. The relationship between outside temperature and DH load in Vienna is depicted in 2.3. Below a temperature of roughly 15 ◦C, the DH load rises approximately linearly with the outside temperature decline. This can be attributed to the additional DH demand for space heating. Above the same temperature of roughly 15 ◦C, the DH load is low and does not change much as temperature increases. This part of the load can be attributed to a constant demand for hot water supply. From a modeling perspective, the relationship between outside temperature and the corresponding DH load L(T ) is most commonly illustrated through either piecewise linear functions, sigmoid functions or a combination of these two approaches, see [121] and [270, Section 4.1]. Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

10 tuwien.at/bibliothek DH load [in MW] 0 400 800 1200 1600 2000 2400 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Time [months]

Figure 2.2: Daily maximum DH load (upper line) and daily minimum DH load (lower line) of the Vienna DH system in 2012. (Source: own illustration; Data: Wien Energie)

A simple representation of the load as a function of the outside temperature L(T ) has been estimated in accordance with [270, Section 4.1.2] for Viennese data based on the following function:

2 B A + , if T 0 ◦C, 1 + exp(CT ) ≥ L(T ) =  (2.1)   BC A + B T, else, − 2   with parameters A, B, and C. A can be interpreted as the minimum load, A + B as the load when the outside temperature is 0◦C and C as the steepness and curvature parameter of the function L(T ). The resulting parametric estimation obtained via non-linear OLS regression is depicted in Figure 2.3 as the black line crossing the bright area. The regression function captures the main shape of the relationship between temperature and load well, however it tends to underestimate the load for very high temperatures and overestimate it for very low temperatures. Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. In addition to outside temperature, other factors have been identiﬁed to inﬂuence the DH load:

11 tuwien.at/bibliothek Meteorological factors: • Apart from the outside temperature, wind and solar radiation also have a small but significant influence on the DH load, see [272]. Wind increases the DH load due to air infiltration, as warm air is replaced by cold air. Solar radiation decreases DH load by increasing the temperature of the buildings’ outer walls, which in turn decreases the heat flow from the inside to the outside of a building.

Customer social behaviours: • The social behaviour of customers typically leads to two peaks during the day: one heat demand peak in the morning and one peak in the afternoon, see [95]. Such daily variations occur due to diﬀerent time preferences of heat demand for cooking, showering or variations in the desired room temperatures, as shown in [294]. DH load [in MW] 400 800 1200 1600 2000 2400

− 10 0 10 20 30 40 Temperature in Vienna [in °C]

Figure 2.3: Joint density of outside temperature and DH load for Vienna (26.304 joint observations on an hourly basis in 2012–2014). Bright regions are characterized by many observations of temperature and DH load, whereas in dark regions no such observations have been made. The estimated regression function L(T ) (black line) based on Equation 2.1 (A = 130, B = 1346 and C = 0.129) ﬁts the data acceptably and reﬂects the convex Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. relationship of the two observation variables. (Source: own illustration and computations; Data: Wien Energie)

12 tuwien.at/bibliothek 2.1.2 Load Duration Curve (LDC) A. Deﬁnition The distribution of a DH load throughout a year may be described by a Complementary Cumulative Distribution Function (CCDF). A CCDF displays how long in total the DH load stays above a particular level in one year. In mathematical notation this corresponds to the total length of the time intervals for which the load L(t), given in MWth, exceeds some level l, also given in MWth:

8760 F¯(l) := λ t [0, 8760] : L(t) > l = 1 dt, { ∈ } {L(t)>l} Z0 where t stands for the time in one year given in hours, λ denotes the Lebesgue measure assigning any closed interval [a, b] its length b a and 1A the indicator function for a set A. −

In the analysis of the relationship between generating capacity requirements and capacity utilization for DH systems, the inverse of the CCDF, known as Load Duration Curve (LDC), is very useful, see [187] for further details. A LDC D(t) therefore determines which load level matches a particular duration d. Mathematically this corresponds to inverting the CCDF F¯(l), such that we have

D F¯(l) = l for any load level l. This yields the formal deﬁnition:

D(d) := inf l : F¯(l) d . { ≥ } In particular, for a continuous and strictly monotonically decreasing LDC D(d), the CCDF is the inverse function of the LDC

F¯ = D−1.

B. Classiﬁcation of Load Levels Based on their duration, load levels can be segmented into three groups, as suggested in [192, Section 1.2]: Peak load, Intermediate load and Base load. Peak load comprises the DH load levels that are exceeded within a maximum of 15% of time within a year, i.e. 1314 hours. Intermediate load comprises the DH load levels that are exceeded at least at one point in time throughout a year, but at maximum 15% of the time within the span of a year. Base load represents the DH load levels that are exceeded at any point in time during the year. For the data on the Vienna DH load this segmentation is depicted as example in Figure 2.4. Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

13 tuwien.at/bibliothek C. Estimation The DH load can be observed only in discrete points in time. Such discrete measurements will be typically an hourly time series for at least one year. Such a time series can be used for estimating the LDC D(d). However there exist two fundamentally diﬀerent approaches:

1. Empirical LDC: The empirical or non-parametric LDC is a step function generated by the arrange- ment of all observed load levels in a descending order of magnitude. If we order the hourly observed DH heat load levels of one year l1, . . . , l8760 from the biggest to the smallest, such that

l l l , o(1) ≥ o(2) ≥ · · · ≥ o(8760) where o : 1,..., 8760 1,..., 8760 is a suitable permutation, we obtain the { } 7→ { } empirical LDC simply via

lo(1) if d = 0, DEmp(d) := (l if d (0, 8760] o(⌈d⌉) ∈ where . denotes the ceiling function. ⌈ ⌉ 2. Parametric LDC: Alternatively, a parametric model of the LDC can be estimated. In [221], a six-parameter model of a continuous LDC is proposed having the following representation δ δ D(d) = 1 α d β dγ + , (2.2) − − 1 + exp(ǫ(d ζ)) − 1 + exp( ǫζ) − − where the maximum load D(0) and the time interval [0, 8760] are normalized to 1 and [0, 1], respectively. The parameters α, β, γ, δ, ǫ and ζ can be ﬁtted via non- linear OLS regression. Note that also other parametric models are being employed, for example the more simple approach in [255], which uses polynomial functions. Parametric models have the advantage that they yield a continuous LDC.

The rest of this thesis uses the parametric estimation for the LDC given by Equation 2.2. For modelling purpose this is necessary as typically a continuous LDC is needed. Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

14 tuwien.at/bibliothek D. Example In Table 2.1, the estimated coefficients of the parametric LDC defined in 2.2 are given for hourly data on Viennese DH load for the years 2012–2014 (26304 observations). The fitted LDC is very close to the step-function approximation by the empirical LDC with an average absolute distance of just 4.99 MWth. The maximum load D(0) for Vienna is given by nearly 2497 MWth. Furthermore, the resulting estimated LDC is depicted in Figure 2.4.

Table 2.1: Non-linear OLS regression coeﬃcients of the parametric model given by Equation 2.2. Estimation was based on observed hourly DH load for Vienna in 2012–2014. (Source: own illustration and computations; Data: Wien Energie)

α β γ δ ǫ ζ -0.113 0.814 0.252 -0.211 -11.523 0.450

Peak load DH load [in MW] Intermediate load

Base load 0 400 800 1200 1600 2000 2400 0 2000 4000 6000 8000 Duration [in hours]

Figure 2.4: Load duration curve and classiﬁcation of load levels into base, intermediate and peak load for Vienna. Estimation was based on hourly DH load observations for 2012–2014. The parametric LDC based on Equation 2.2 is given by the coloured regions, the empirical LDC by the solid black line. (Source: own computations; Data: Wien Energie) Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

15 tuwien.at/bibliothek 2.2 District Heating Sources

2.2.1 Combustion Plants Combustion plants in DH systems generate heat from a renewable (e.g. wood chips) or fossil fuel source (e.g. natural gas, fuel oil or coal) by a combustion process and can be roughly categorized into either Heat-Only Boilers (HOBs) or Combined Heat and Power (CHP) plants. Unlike HOBs, CHP plants generate both electricity and heat from a fuel source, with diﬀerent CHP technologies being available including steam turbine, gas turbine and combined cycle gas turbine plants [160, 75, 4, 241]. When compared to the separate generation of heat and electricity, CHP plants can save both fuel and costs [142]. Therefore, CHP plants generate the majority of heat for DH systems in several EU member countries, as can be seen in Figure 2.5. In Austria, as of 2015, DH from combustion plants has been equally generated by CHP plants and HOBs [248]. Overall, as of 2015, there are CHP plants with capacities of 8.980 MWth and 6.075 MWe [62, p. 32], with the majority being supplied by natural gas, see Figure 2.6a. What is more, CHP plants also contribute a fair amount to Austria’s electricity generation: 25% of all Austrian power plant capacities are CHP plants [62, p.28]. Typically only very small Austrian electricity generating combustion plant facilities do not supply DH. [29, p. 21].

Share of heat from CHP plants in DH [in %] 100 90 80 70 60 50 40 30 20 10 0 no data

Figure 2.5: Share of DH generation by CHP plants in several EU member countries Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. as of 2013. In many countries CHP plants supply the majority of DH. (Source: own illustration; Data: [80])

16 tuwien.at/bibliothek Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. tuwien.at/bibliothek The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. Suc:onilsrto;Dt:[ Data: illustration; own (Source: lignite on based completely was Austria in generation DH 1970 in Although (1970–2014). n ulol int sn ogri s sne20) hl uloldopdt eysmall very a to dropped oil fuel while 2006), (since use in longer no is lignite oil, fuel and h er20.Ca a lasbe fmnriprac oAsra Hgeneration. DH Austrian to importance after minor built of i.e. plants, been biomass facilities, always and gas has 1980-2000, natural Coal between in built 2000. increase type, year huge HOB the a and to CHP due both Austria of occurred in development (b) This HOBs share. and (a) plants CHP for input fuel by generation DH 2.6: Figure

DH Generation [in GWh] DH Generation [in GWh]

9017 9018 9019 0020 002015 2010 2005 2000 1995 1990 1985 1980 1975 1970 2000 4000 6000 2015 2010 2005 8000 2000 1995 1990 1985 1980 1975 1970 2000 4000 6000 8000 10000 12000 Coal Lignite Oil Fuel Gas Natural Biomass Fuel Oil Fuel Gas Natural Biomass 248 b etol Boilers Heat-only (b) a H plants CHP (a) ]) 17 A. Heat-Only Boilers (HOBs) Heat-Only Boilers (HOBs) generate DH by burning a fuel in a furnace and using the resulting ﬂue gases to heat up water [4, 75]. In Austria the main fuel used in HOBs is woody biomass, see Figure 2.6b. In the past 20 years (1996–2015), 913 medium- and large-size biomass HOBs (i.e. boilers with a capacity exceeding 1 MW) have been installed in Austria, yielding a total of 2.565 MW [116]. However, biomass HOBs are primarily used for small, rural DH systems. In large, urban DH systems, HOBs predominantly employ fossil fuels, see [29, p. 21].

B. Gas Turbine CHP Plant A gas-turbine CHP plant uses natural gas or fuel oil as an input, see [143, Chapter 4–6] [98, Chapter 4]. The fuel input is injected into highly pressurized and high-temperature air. Subsequently, fuel and air are combusted (800-1200 ◦C) and expanded through a turbine. This process generates electricity by employing a generator. The hot exhaust gas of the turbine is then used for heating up water in a waste heat recovery boiler. This open cycle gas turbine process is also illustrated in Figure 2.7. As of 2015 the signiﬁcance of gas-turbine CHP plants in Austria is negligible.

Fuel Input Gas Turbine Process

Combustor

Electricity Air Compressor Gas Turbine Output

Exhaust gas Waste Heat Boiler

Heat Output

Figure 2.7: Simpliﬁed illustration of an open cycle gas turbine CHP plant. (Source: own illustration based on [143, Figure 6.6]) Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

18 tuwien.at/bibliothek C. Steam Turbine CHP Plant A steam turbine CHP plant typically uses coal or biomass as fuel input. Via combustion of the fuel input highly pressurized, high-temperature steam (500 ◦C, 200 bar) is generated out of a highly pressurized, low-temperature working fluid. [266, Section 6.3.2] This working fluid is typically water. The steam is transferred to a turbine, where its pressure is reduced below atmospheric pressure (30 ◦C, 0.04 bar) via expansion over the turbine blades. This process generates electricity by employing a generator. The low-pressure exhaust steam of the steam turbine is transferred to a condenser in order to recover the liquid state of the working fluid via cooling. This process produces heat that is not useful for a DH system. In order to generate heat that is of use to a DH system, a higher extraction temperature and therefore higher extraction pressure of the steam is required (90-140 ◦C, 0.7-4 bar). [266, Section 6.3.2] This medium-pressure steam can be extracted from the turbine and used for DH via a heat exchanger. The steam extraction decreases the amount of electricity generated. After the steam is condensed to a liquid, a pump is used to again increase the pressure of the working fluid. An illustration of a steam turbine CHP plant is given in Figure 2.8.

Fuel Input Steam turbine process

Boiler Live steam

Electricity Pump Steam Turbine Output

Exhaust Feedwater steam Condenser

Condensate

Heat exchanger Heating steam

Heat Output

Figure 2.8: Simpliﬁed illustration of a steam turbine CHP plant. (Source: own illustration

19 tuwien.at/bibliothek A steam turbine can operate in a CHP mode, i.e. with maximum extraction of medium- pressure steam for DH and subsequently co-generating heat and electricity, as well as in a condensing mode, with full electricity generation (via condensation in the steam turbine) and no heat extraction for DH at all. By controlling the amount of medium-pressure steam extracted, the ratio of electricity to heat generation becomes adjustable. If the system comprises no condenser at all and can only operate in CHP mode, the steam turbine is referred to as back-pressure steam turbine (BP), otherwise as extraction-condensing steam turbine (EC). [143, Section 6.4.2 and 6.4.3]

In Austria several large steam turbine CHP plants exist, most of which are of backpressure steam turbine type that have wood chips as fuel input. However, the two largest steam turbine plant operating in 2015 in Austria have a extraction-condensing steam turbine: a wood chip plant located in Vienna and the Mellach coal CHP plant, which supplies the majority of the Graz DH demand. A detailed description of these two plants can be found in Section 7.2.1 and 7.2.2, respectively. Furthermore, an overview of steam turbine CHP plants supplying more than 100 GWhth in 2015 in Austria is given in Table 2.2.

Table 2.2: Steam turbine CHP plants with more than 100 GWhth of yearly DH generation in Austria as of 2015. (Source: own compilation)

Plant Fuel Type MWth GWhth/a Source

Mellach (Graz) C EC 230 900 [26, p. 73][247] Simmering (Vienna) WC EC 35 225 [228][278, p. 45] Linz-Mitte WC BP 21 160 [172, p. 10][170, p. 40] Klagenfurt-Süd WC BP 15 125 [263, p. 6–7] Timelkam (Vöcklabruck) WC BP 15 100 [69, p. 11] C: coal, WC: wood chips.

D. Combined Cycle Gas Turbine (CCGT) CHP Plant Combined Cycle Gas Turbine (CCGT) CHP plants consist of gas turbine units, heat recovery steam generators and steam turbine CHP units. First, the fuel (natural gas or fuel oil) is burnt in the combustors of the gas turbines. The exhaust heat of the gas turbines is then used as heat input in heat recovery steam generators that are part of the steam turbine CHP units [143, Section 5.3. and 6.5.2]. These steam turbines are typically extraction-condensing steam turbines such that a CCGT can operate in a CHP mode and a condensing mode.

In Austria CCGT CHP plants can be found mainly in large-scaled DH systems, see Table Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. 2.3. All of them are fueled by natural gas. The largest Austrian DH system, the Vienna DH system comprises the three largest CCGT CHP plants of the country: Simmering 1,

20 tuwien.at/bibliothek Simmering 3 and Donaustadt 3 (1050 MWth, 2750 GWhth/year). A detailed description of these plants can be found in Section 7.2.2.

Table 2.3: CCGT CHP plants with more than 200 GWhth of yearly DH generation in Austria. (Source: own compilation)

Plant Fuel MWth GWhth/a Source

Simmering 1 (Vienna) NG 450 1250 [280, p. 14][278, p. 45] Simmering 3 (Vienna) NG 350 850 [280, p. 14][278, p. 45] Donaustadt (Vienna) NG 250 650 [280, p. 14,28] Linz-Süd NG 150 350 [172, p. 14][170, p. 40] Salzburg-Mitte NG 130 300 [237, p. 5] Linz-Mitte NG 170 200 [169, p. 8][170, p. 40] NG: natural gas.

2.2.2 Waste Heat A. Incineration Incineration is a waste treatment process involving the combustion of organic substances contained in waste materials. Incineration facilities are not primarily meant for energy generation, but nevertheless they produce a substantial amount of high-temperature steam as a by-product. This steam can be recovered for DH, electricity and process steam generation, typically by using a steam turbine with heat and steam extraction. [226, Section 3] In Austria, 13 large incineration facilities exist. Their number increased rapidly over the course of the past years due to the interdiction of landﬁlling as a waste treatment alternative. [25, p. 27] As of 2015, the usage of waste heat is quite diverse among the incineration facilities: six facilities use the steam primarily for DH generation, four of which are located in Vienna (Flötzersteig, Spittelau, Simmeringer Haide, Pfaﬀenau) and two in Upper Austria (Linz and Wels). In addition, the incineration plant Arnoldstein is expected to supply its waste heat to the Villach DH system beginning with 2018. Furthermore note that the steam of the incineration plant Dürnrohr is also used to a smaller, but notable extend for the Sankt Pölten DH system, see Table 2.4 for an overview. On the other hand, incineration facilities with primary electricity generation (Zistersdorf ) and steam generation for industrial processes (Niklasdorf, Lenzing, Dürnrohr) exist in Austria [25, p. 108, 153] too. Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

21 tuwien.at/bibliothek Table 2.4: DH systems with a minimum supply of waste heat from incineration facilities of 100 GWhth per year in Austria. (Source: own compilation)

DH system Plants GWhth/a Source Vienna 4 1600 [279, p. 25] [280] Linz 1 350 [170, p. 40] Sankt Pölten 1 200 A [83, p. 15] Wels 1 150 [204] Villach 2 100 B [141] A The steam of the incineration facility is not supplied to the Sankt Pölten DH system directly but used as additional fuel input in the nearby coal steam turbine CHP plant. [82, p. 18] B Heat extraction for DH expected to start operation in 2018.

B. Industrial Waste Heat Energy-intensive industries including the pulp and paper, chemical, metal and refinery industries, have been traditional investors in CHP facilities for their own supply of electricity and process steam, see [285, Section 3.7.3]. Most of these industries produce the fuel input of their CHP plants as a by-product such as waste gases (in the chemical and refinery industries) or wood-based wastes (in the pulp and paper industry). Heat can be extracted from these industrial CHP facilities and supplied to a local DH system. In addition, several industrial processes generate extractable heat (i.e. heat contained in flue gases of process steam or waste heat from cooling systems, see [259, Section 7.4.3.1] for a detailed description) as a by-product. Many of these industrial processes generate waste heat at above 100 ◦C, which can be directly integrated into a DH system through the use of heat exchangers [4, 127]. The biggest industrial waste heat suppliers for Austrian DH systems are given in Table 2.5. Most widespread for large-scale Austrian DH systems is waste heat supply from the pulp and paper as well as the steel industry. The largest amount of waste heat for DH purposes from one single site is extracted from industrial CHP plants at the only refinery in Austria near Vienna, the Schwechat refinery.

Table 2.5: Extraction of industrial waste heat for Austrian DH systems that exceed 100 GWhth per year. (Source: own compilation)

Company Industry Major DH system GWhth/a Source OMV Reﬁnery Vienna 700 A voestalpine Steel Linz 180 [185, p. 74] Sappi GratkornB Paper Graz 150 [66] Zellstoﬀ Pöls Paper Aichfeld 110 [66] Schweighofer-Fiber Paper Salzburg 100 [242, p. 13] A See Section 7.2.3 for a detailed description. Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. B Heat extraction for the Graz DH system is expected to start operation in 2017 or 2018.

22 tuwien.at/bibliothek 2.2.3 Heat Pumps A. Characteristics Low-temperature heat sources can be used for district heating by employing large- scale heat pumps [75, 96, 4]. The conversion to a higher temperature is based on a thermodynamic refrigeration cycle consuming either electricity (compressor heat pump) or hot steam (absorption heat pump). Although heat pumps are rarely used in Austrian DH systems, they are well-established in Nordic countries. In Sweden for example, 10–18% of DH is generated by heat pumps since 1986 [12]. It is believed that in 2030 and 2050 a large share of district heating generation in Europe will come from heat pumps [46]. Based on a survey of 97 heat pumps in several European DH systems, the supply temperature of heat pumps for district heating purposes is most commonly in the range of 70–90 ◦C and 37% exceed a supply temperature of 80 ◦C[49]. These heat pumps use various diﬀerent heat sources including sea, lake and river water (2–9 ◦C), sewage water (10–20 ◦C), low-temperature industrial waste heat (14-46 ◦C), ﬂue gases (11-40 ◦C), low-temperature geothermal sources (15-74 ◦C) and solar heat storages (10-40 ◦C). An overview of the heat sources of compressor heat pumps for DH in Europe is further provided by Figure 2.9.

Sewage Water

Solar Heat Storage District Cooling Flue Gas

Geothermal Heat

Industrial Waste Heat Ambient Water

Figure 2.9: Share of installed capacities per heat source of DH compressor heat pumps in Europe based on a survey of 149 units with 1580 MWth. (Source: own illustration, Data: [50, Table 2] Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

23 tuwien.at/bibliothek B. Integration into DH Systems In large Austrian DH systems supply line temperatures during the winter (110-150◦C) are well above the feasible supply temperatures of a heat pump (< 90◦C). In order to overcome this shortfall, there exist two diﬀerent strategies for integrating heat pumps into DH systems:

One possibility is to use heat pumps to preheat the return line of a DH network before • entering a combustion plant [200]. This yields a low and achievable temperature lift for the heat pump, which translates into a low consumption of either electricity or hot steam. However, this conﬁguration has some disadvantages, as mentioned in [27, p. 15]: both heat losses in the system and the required fuel input of the combustion plant increase due to the higher return line temperature. Moreover, the heat pump cannot supply heat other than through a coupled generation with a combustion plant.

Alternatively, the heat pump can directly supply heat. In order to satisfy the • required supply line temperatures heat pumps can be either used for preheating during the winter or preferably, for supplying subsystems with lower supply line temperature requirements. Notably, in the latter setting the heat pump can work independently of other heat suppliers. For example in Graz heat pumps with 11.5 MWth should supply the low-temperature DH subsystem Reininghaus from 2017 with a required supply line temperature of just 68◦C. [212]

C. Available Heat Sources for Absorption Heat Pumps Absorption heat pumps require a low-temperature (40-50 ◦C) heat source as well as a high-temperature steam source (> 160 ◦C) as input energies. Preferably, absorption heat pumps are built near sites, where a hot steam source is already used for the DH supply. In this case, using this hot steam as input energy for the absorption heat pump would not impose any costs as no additional steam generation is necessary. [76, Section 40] In Austria, the most promising applications for absorption heat pumps are:

Flue gases of combustion plants (flue gas condensation): • Absorption heat pumps can recover heat from flue gas condensation for DH and can extract steam from combustion plants for the temperature lift. One notable such application in Austria is incorporated into the DH system Salzburg: the Biomass CHP plant in Hallein with a thermal capacity of 30 MWth performs a flue gas condensation with 3 MWth recovered by an absorption heat pump. This heat pump, driven by the 165 ◦C steam of the CHP plant, yields an additional generation of 15 GWhth per year due to the absorption heat pump [230, p. 109–122]. Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

24 tuwien.at/bibliothek Industrial waste heat: • It is often the case that the temperature of industrial waste heat either exceeds or falls behind the temperature needed for DH. With an absorption heat pump, the low-temperature industrial waste heat can be lifted to the required temperature by using high-temperature waste heat for hot steam generation. A successful example in Austria can be found in the DH system of Innsbruck-Hall-Wattens: waste heat ◦ from a cooling tower of 2.5 MWth with 40 C can be used for DH by using an absorption heat pump supplied by ﬂue gases from a melting furnace (170◦C) [246].

D. Available Heat Sources for Compressor Heat Pumps Compressor heat pumps require a low-temperature (0-50 ◦C) heat source as well as electricity as input energies. In comparison with absorption heat pumps, they can achieve higher temperature lifts, but the electricity consumption leads to higher operation costs. [76, Section 40] In Austria, the most promising applications for compressor heat pumps are:

Industrial waste heat: • Many industries do not produce enough high-temperature waste heat so as to energetically drive absorption heat pumps. In this case, compressor heat pumps can be used for lifting the temperature of low-temperature industrial waste heat. A successful example in Austria includes waste heat from the food processing industry (Tirol Milch) used for supplying the DH system Wörgl by employing three compressor heat pumps with a total capacity 4.1 MWth [21, p. 4]. Sewage water: • Sewage water from local residential drainage systems exhibits relatively high temperatures during the heating season with values under 10◦C being rather rare, see [238]. Two distinct approaches exist for heat recovery with compressor heat pumps, see for example [285, Section 6.3.2.4] and [238]: heat recovery before or after sewage treatment. In the ﬁrst case, the stream temperature is typically between 12 and 25◦C and located within residential areas, however the stream is contaminated and possible heat extraction is limited as stream temperatures should not fall below the required design temperature of the cleaning process. In the second case, the process stream is cleaner and can be cooled down by up to 8 Kelvin which is also desirable for the water fauna. However, sewage treatment plants are located outside residential areas, resulting in higher access costs. In Austria, only one realized sewage water source heat pump for DH exists in 2015: in Amstetten, raw sewage water is used to supply a small low-temperature DH system (maximum 45 ◦C). The raw sewage water has an average temperature of 22 ◦C, a Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. mass ﬂow of 130 l/s and is being cooled down by 0.34 K. [3, p.27].

25 tuwien.at/bibliothek Ground water and river water: • The usage of ground water and/or river water for DH systems via compressor heat pumps has been considered for several Austrian cities including Vienna, Linz and Graz, see [54], [114, Section 2.12.1 and 2.12.4], [114, Section 2.12.4] and [286]. However, there are no such installations yet. River water is typically easily accessible, but has very low temperatures during the heating season. Ground water has temperatures comparable to those of sewage water even during the winter, but is limited by the existence of water wells in the city.

2.2.4 Non-Combustible Renewables A. Geothermal Heat Sources Geothermal heat sources, i.e. heat stored below the earth’s surface, in hydrothermal reservoirs, are well suited to supply heat to DH systems, but are only available in specific locations, see [161] and [285, Chapter 4]. For the exploitation of such heat sources, at least two wells (i.e. a geothermal doublet) need to be drilled: a production and an injection well, both with a suitable depth so as to reach the hot water with the desired temperature from a hydrothermal reservoir. The extracted heat is approximately proportional to the mass flow m of the extracted water given in m3/h, as well as to the temperature difference of supply and return temperatures, T T , of the system, see [105, p. 10]. in − out In Austria, suitable geothermal heat sources for DH can be found in the Molasse basin in Upper Austria, in the Styrian Basin and in the Vienna Basin, see [104, 105]. Overall, a total of nine DH systems are supplied by geothermal heat in Austria as of 2015, seven of which are located in Upper Austria. Some of the geothermal facilities have been primarily installed for balneological use of the thermal water, however, three medium-sized geothermal DH systems also exist, see Table 2.6.

Table 2.6: Urban geothermal DH facilities in Austria as of 2015 with a minimum yearly geothermal DH generation of 30 GWhth. (Source: [105, 219, 43])

◦ ◦ Installation m [m3/h] Tin [in C] Tout [in C] MWth GWhth/a Braunau 2001 78 81 53 9.1 50 Ried/Innkreis 2014 55 87 65 5 40 Altheim 1990 77 105 70 11 30

B. Solar Heat Solar heating is a well-established technology for hot water preparation and space heating Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. in residential buildings. Furthermore it can also be used as a non-combustible renewable source in DH systems. [285, Section 5] Solar collectors provide a liquid-based heat transfer

26 tuwien.at/bibliothek to capture and transfer solar heat. Availability of solar heat varies strongly over time. Therefore, solar collectors are often combined with seasonal heat storage, since solar heat availability is at its lowest in the winter, when the DH demand is at its highest. [285, Section 5.2.2]

2 In Austria, for generating 1 GWhth of DH per year, 2000-2800 m of collector are needed. [189, Figure 3-25] In Austria, only ﬁve solar DH heating facilities with a collector area of more than 2800 m2 exist, integrated in two diﬀerent urban DH systems (Graz and Wels), see Table 2.7 for an overview of the facilities’ characteristics.

Table 2.7: Solar heat facilities with collector areas of more than 2800 m2 in urban Austrian DH systems as of 2014 (Source: [189, Table 2-1])

Facilities Capacity Installation 2 [per #] [in m ] [in GWhth/a] [per year] Graz 4 14.735 6 2002–2014 Wels 1 3.628 1–2 2011

2.2.5 Technical Parameters A. Energy Conversion Efficiency and Coefficient of Performance η For combustion plants the energy conversion efficiency η gives the ratio of the useful output of energy (either heat for HOBs or heat and electricity for CHP plants) to the lower heating value (LHV) of the fuel input. In the case of compressor heat pumps the term coefficient of performance (COP) is used for this indicator. For this technology η corresponds to the ratio of useful heat output to the electricity consumed by the heat pump: [76, Section 40]

Heat Output for HOBs,  Fuel Input   Heat and Electricity Output η :=  for CHP plants, (2.3)  Fuel Input   Heat Output  for compressor heat pumps. Electricity Input    For HOB and CHP plants, average energy conversion efficiencies from Austria as of 2014 Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. are given in Table 2.8. In general, efficiencies of about η = 80% can be achieved, where natural gas has the highest efficiencies for both technology types.

27 tuwien.at/bibliothek Table 2.8: Energy conversion eﬃciencies η of HOB and CHP plants of Austrian DH supplying companies on average for diﬀerent fuels. [248]

Energy conversion eﬃciencies η [in %] Natural Gas Wood chips Coal HOB 89% 84% – CHP 85% 83% 80%

For heat pumps, the COP mainly depends on the temperature of the heat source and the supply temperature of the DH system, see Table 2.9 and Figure 2.10. It ranges between 250% and 550% when varying the temperature of the heat source from 10 ◦C to 40 ◦C and the required supply temperature of the heat pump for the DH system from 80 ◦C to 90 ◦C. Table 2.9: Range of typical COPs of compressor heat pumps for DH systems for diﬀerent temperatures of the heat source and required supply temperatures of the DH system. (Source: [75, p. 112])

Heat Source Temperature 10 ◦C 20 ◦C 30 ◦C 40 ◦C 80 ◦C 2-7–3.5 2.9–4.0 4.0–4.9 4.4–5.5 Supply temperature 90 ◦C 2.5–3.3 2.7–3.7 3.5–4.4 4.0–5.1

B. CHP Plant Coefficients cσ and cβ The cogeneration of heat and electricity in a CHP plant can be characterized via two parameters: the power to heat ratio cσ, see [91], and the power loss coefficient cβ, see [264]. While the power to heat ratio gives the ratio of electricity and heat generation in CHP mode, the power loss coefficient gives the loss of electricity generation per additional unit of heat extracted in a CHP plant with extraction-condensing steam turbines at a fixed fuel input:

Electricity Output (CHP mode) cσ := (2.4) Heat Output (CHP Mode)

Electricity Output (Condensing Mode) Electricity Output (CHP Mode) cβ := − (CHP Mode) Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. Heat Output

28 tuwien.at/bibliothek 446 ●

326 ● 291 ● COP [in %] ● 261

● ● 191 170 100 200 300 400 500 600 0 5 10 15 20 25 30 35 40 Heat Source Temperature [in °C]

Figure 2.10: Range of minimum to maximum COP values of compression heat pump heating water from 60 to 90◦C. (Source: own illustration, Data: [76, p. 108])

Based on the power to heat ratio cσ and the power loss coefficient cβ, the separate energy conversion efficiencies for heat and electricity can be computed. Hereby, the energy conversion efficiencies in condensing mode for electricity generation ηe and in CHP mode CHP for electricity and DH generation, ηe and ηth, need to be distinguished, see [75, Annex 1].

Electricity output (condensing mode) cσ + cβ ηe := = η (2.5) Fuel input 1 + cσ

CHP Electricity output (CHP mode) cσ ηe := = η Fuel input 1 + cσ

Heat output (CHP mode) 1 ηth := = η (2.6) Fuel input 1 + cσ

Note that the following identities hold, see [75, Annex 1] for additional information:

CHP CHP CHP ηe ηe ηe η = ηth + ηe , cβ = − and cσ = . (2.7) ηth ηth Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

29 tuwien.at/bibliothek C. CEN/CENELEC Fuel Allocation Factors of CHP Plants fe and fth Based on a proposal of the oﬃcially recognized European Standardization Organizations CEN (European Committee for Standardization) and CENELEC (European Committee for Electrotechnical Standardization) [39, Section 6.2.5], the fuel input of a CHP plant operating in CHP mode plant may be allocated to DH and electricity generation according to the following rule: the additional amount of fuel needed in CHP mode to generate the same amount of electricity as in condensing mode should be regarded as fuel input for DH generation, the remaining part as fuel input for electricity generation. The Fuel Allocation Factors of CHP Plants fe and fth are then given as:

Fuel Input for Electricity Generation (CHP mode) cσ fe := = , (2.8) Fuel input (CHP mode) cσ + cβ

Fuel Input for DH Generation (CHP mode) cβ fth := = . Fuel input (CHP mode) cσ + cβ

D. Plants’ Lifetimes L The average lifetime of a plant of a certain technology is given in years and denoted by L.

2.2.6 Financial Parameters

A. Capital Expenditure and Operation and Maintenance costs CCAPEX, CFOM and CVOM Costs associated with heat generation in a DH plant can be grouped into four diﬀerent categories:

1. Capital expenditure (CAPEX) CCAPEX,

2. Fixed operating and maintenance (FOM) costs CFOM,

3. Variable operating and maintenance (VOM) costs CVOM and

4. Fuel and electricity input costs.

Their main components and billing characteristics are summarized in Table 2.10. CAPEX, FOM and VOM costs differ strongly both for different DH technologies, but also within single technologies, as a wide dispersion of these costs can be observed even when focusing on one DH technology in particular. In 2010 for example, the International Energy Agency (IEA) published a report, based on data from 190 power plants in 21 countries, stating Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. that cost data „vary widely from country to country; even within the same region there are significant variations in the cost for the same technologies“, see [236, p.20].

30 tuwien.at/bibliothek Table 2.10: Billing characteristics and main components of the four DH generation cost categories. (Source: own compilation based on [75, p. 13–15] and [138, p. 9])

Billing Billing Main Components Unit Frequency

CCAPEX capacity one-time Physical equipment, infrastructure and network connection. CFOM capacity annual Administration, operation staﬀ, maintenance and service agreements, network use of system charges and insurance. CVOM heat output frequent Consumption of auxiliary materials (e.g. fuel additives), residual treatment and output related maintenance and repair. Fuel costs fuel input frequent Fuel, fuel transmission and transportation, fuel consumption related taxes.

However, some of this observed cost dispersion within the same technology is systematic: most notably it can be stated that an economy of scale is present for DH plants, meaning that larger energy plants present cost advantages precisely due to their size. Typically, this eﬀect is represented as a one-parameter-function for CAPEX CCAPEX(c) and capacity c, denoted as EUR/MWth and MWth, respectively, see [45]:

a−1 CCAPEX(c) = CCAPEX(1) c .

For a scale parameter a < 1, an economy of scale is present. Evidence for DH plants has been found for example in biomass HOBs for Austria and Denmark in [265, p. 172] and for electrode HOBs in Germany with scale parameter a = 0.54 in [111]. Other systematic effects typically occur for renewable DH plants such as cost variations due to variations in the necessary drill depth for geothermal DH, see [240, p. 54] for further information, or due to different distances of low-temperature heat sources to the DH system. For selected DH technologies, CAPEX, FOM and VOM costs are given in Table 2.11 (combustion plants), Table 2.12 (non-combustible renewables) and Table 2.13 (heat pumps) for large-scale plants. For combustion plants two different sources are given per technology to capture price variations within each of these cost categories. Essential technical parameters for DH plants such as the energy conversion efficiency η, the power to heat ratio cσ and the power loss coefficient cβ, as well as the DH plants’ lifetime L are also indicated. Own assumptions are made by averaging over the financial parameters from the sources gathered, whereas technical parameters are chosen to fit well with the Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. characteristics of new plants in Austria. Fuel and electricity input costs are not provided in Table 2.11 and but extensively covered in Chapter 3.

31 tuwien.at/bibliothek Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. tuwien.at/bibliothek The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. 32 Table 2.11: Financial data of large-scale DH plant technologies. Own assumptions used for further modeling purposes are given in bold. (Source: own compilation; Data: references indicated in the table; Exchange Rates:197 [ ]; Inﬂation Rate: [81])

Financial Parameters Technical Parameters

Fuel CCAPEX CFOM CVOM η cσ cβ L 2015 2030 2015 2030 2015 2030

[EUR2015/Wth] [EUR2015/kWth] [EUR2015/MWhth] [%] [%] [%] [years] 0.87 0.87 – – 5.9 5.9 – 20 [75, p. 130] HOB Wood Chips 0.52 0.47 26 26 – – – 20 [68, p. 141–145]A 0.70 0.67 13 13 2.9 2.9 87 20 0.11 0.11 4 4 – – 97 30 [75, p. 134] HOB Natural Gas 0.09 0.09 5 5 – – – 20 [68, p. 141–145] 0.10 0.10 4 4 0.0 0.0 90 30 1.89 1.74 71 65 – – 85B 42 – [130] Steam Turbine CHP Wood Chips 1.93 1.59 68 56 – – 85B 45 20 [75, p. 70] 1.91 1.67 69 51 – – 85 42 20 1.33 1.30 52 51 5.2 5.2 91 102 25 30 [p. 40][138] CCGT CHP Natural Gas 1.40 1.30 48 48 4.0 4.0 90 134 13 25 [75, p. 50] 1.36 1.30 50 49 4.6 4.6 90 134 13 25 0.65 0.60 – – 3.4 3.4 83 92 25 [75, p. 44] Gas-turbine CHP Natural Gas 0.59 0.53 24 24 – – 80 70 20 [160] 0.62 0.57 12 12 1.7 1.7 82 85 25

η: energy conversion efficiency, cσ : power to heat ratio, cβ : power loss coefficient, L: DH plant lifetime. A Scenario ’central’. B The energy conversion efficiency η is not reported or only reported for including flue gas condensation. Furthermore η cannot be computed via Equations 2.7 using other reported quantities. For small-sized wood chip steam turbine CHP plants it is assumed that η = 85%, for CCGT CHP plants η = 90%. This enables the comparability between energy conversion efficiencies of existing Austrian plants, as already given in Table 2.8. C In all sources on financial data of CHP plants, figures are given in EUR/MWe or EUR/MWhe. Conversion to EUR/MWth or EUR/MWhth is carried out via the formulas: EUR/MWth = (cσ + cβ ) EUR/MWe, and EUR/MWhth = (cσ + cβ ) EUR/MWhe. Table 2.12: Financial data of large-scale non-combustible DH plant technologies. (Source: own compilation; Data: references indicated in the table; Exchange Rates: [197]; Inflation Rate: [81])

C C C CAPEX FOM VOM L 2015 2030 2015 2030 2015 2030

[EUR2015/Wth] [EUR2015/kWth] [EUR2015/MWhth] [years]

Solar (seasonal storage) 6.43 5.12 17 17 0.6 0.6 30 [75] Geothermal 1.52 1.27 38 32 – – 20 [161]

L: DH plant lifetime. Data on solar DH with seasonal storage correspond to a combination of solar collectors and storage systems, such that 1 2 MWth of installed capacity delivers 8760 MWhth of heat per year. This requires 17520 m of solar collectors (see [75, p. 3 145]) and 70080 m solar storage (see [75, p. 144]). Additionally, an absorption heat pump may be required to empty the storage, which is not included in the cost data.

Table 2.13: Financial data of large-scale DH heat pump technologies. (Source: own compilation; Data: references indicated in the table; Exchange Rates: [197]; Inﬂation Rate: [81])

C C C CAPEX FOM VOM L 2015 2030 2015 2030 2015 2030

[EUR2015/Wth] [EUR2015/kWth] [EUR2015/MWhth] [years]

Absorption HP (Waste Heat) 0.60 0.51 2 2 0.9 1.3 25 [76] Compressor HP (Waste Heat) 0.70 0.59 2 2 2.0 1.7 25 [76] Compressor HP (Water) 0.67 0.53 7 7 – – 20 [68]

L: DH plant lifetime.

For water source heat pumps diﬀerent price scenarios are given in [68]. The reported values correspond to the scenario ’low’.

The cost data given in Tables 2.11, 2.12 and 2.13 show huge differences among the DH technologies. While CAPEX is lowest for natural-gas fired HOBs, it is 10-40 times higher for non-combustible renewables. What is more, CHP plants have significantly higher CAPEX, FOM and VOM costs than their HOB counterparts.

B. Weighted Average Cost of Capital r The weighted average cost of capital (WACC) r of a DH system operator is the minimum return that it has to earn on its CAPEX in order to satisfy both its owners and creditors, see [8, Section 7] for a detailed discussion. Following a report on the WACC of Austrian natural gas and electricity distribution system operators [58, Section 9], the WACC for an Austrian DH system operator may be assumed to be on the same level, i.e. 6.42% (nominal interest rate). Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

33 tuwien.at/bibliothek When accounting for an annual inﬂation rate of 1.93%, as observed in the EU for 2002–2015, the WACC is given as r = 4.40% in terms of a real interest rate, following [8, Section 10.1].

C. Investment Risks Unlike other DH plants, the construction of geothermal DH plants poses a severe failure risk for an investor, see [11, Chapter 4]. According to a report based on 2613 geothermal wells worldwide, the failure rate of the ﬁrst well drilled in a new ﬁeld is 50%, as stated in [118, p. 18]. Furthermore, the relation between the number of drilled wells and their corresponding failure rate can be described by the following function:

p (n ) = 0.52 0.07 log(n ). failure well − well In Figure 2.11 the average failure rate is depicted for diﬀerent numbers of drilled wells for geothermal DH projects. Exploration Phase Probability of failure [in %] 0 10 20 30 40 50 0 10 20 30 40 50 Number of wells drilled per field

Figure 2.11: Average failure rate for diﬀerent numbers of drilled wells for geothermal DH projects. (Source: own illustration, Data: [118, p. 18]) Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

34 tuwien.at/bibliothek CHAPTER 3

Input Energy

Input energy for DH plants include fuels like natural gas, fuel oil, coal, lignite, wood chips and other renewable energy sources such as biogas, straw, peat and tall oil. In addition, electricity can be used as input for DH generation in compressor heat pumps. Input energies for DH plants differ greatly in their local availability, state of market integration, carbon footprint, production process (since some of them are by-products), macroeconomic interdependencies and price dynamics. The high volatility of several input energy prices causes substantial uncertainties for the investment planning of DH plants. On the other hand, the large variety of DH input energy possibilities provides several diversification opportunities for a DH system operator. First, the market structure and reference prices of input energies for DH in Austria are both discussed in Section 3.1. Historic price movements starting with the year 2002 are additionally depicted. This year corresponds to the first year of full market liberalization of electricity and natural gas and therefore represents the year of a major structural break in the Austrian energy market. Furthermore four stylized facts on long-term movements of prices of DH input energies are tested for statistical significance, see Section 3.1.4. Second, in Section 3.2 a Geometric Brownian Motion (GBM) is identified as a suitable model for the long-term stochastic dynamics of DH input prices. Additionally, as one main contribution of this thesis the distribution of the levelized prices for input energy over a plant’s lifetime under GBM modelling is furthermore introduced in Section 3.2.2. This new approach to cover uncertainties for the investment planning of DH plants uses insights gained from Asian option theory. Finally, Section 3.3 discusses input-related costs for DH input energies in Austria, i.e. national taxes and costs for the transmission or transportation of the fuel and electricity to the plant site. Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

35 tuwien.at/bibliothek 3.1 Markets and Prices

3.1.1 Fossil Fuels

A. Natural Gas

In continental Europe natural gas is still often priced via long-term, oil-indexed contracts with periodic reviews and minimum take-or-pay levels. Since the year 2000, several gas trading hubs have been established to work as virtual trading points. This increases ﬂexibility and competitiveness in the natural gas market [1, Chapter 10]. In Austria, energy plants claimed a share of 28% of the total natural gas demand in 2015, thus being one of its main consumers. Natural gas is mostly imported (in 2015 a share of only 17% of the total gas demand was produced locally), which stresses the importance of reliable reference pricing [85].

In Austria, the border price of natural gas, i.e. the monthly averaged import prices of Austrian gas suppliers, is calculated by the Austrian statistical oﬃce Statistik Austria and published by the Austrian regulator for natural gas markets E-Control [59]. The prices at the natural gas markets are commonly based on the higher heating value (HHV) of natural gas. For the conversion into EUR/MWhLHV the conversion factor: [147, p. 224] MWhLHV = 1.1074 MWhHHV

is needed. The time series of Austrian border prices of natural gas for 2002-2015 denoted in EUR/MWhLHV is given in Figure 3.1.

37.1 ● ] LHV /MWh 2015

● Price [in EUR 15 20 2515.11 30 35 40 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015

Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. Figure 3.1: Monthly average Austrian border price of natural gas as published by E-Control. (Source: Own illustration, Nominal values: [59], Inﬂation rate (HICP): [81])

36 tuwien.at/bibliothek Figure 3.1 shows that in Austria monthly border prices for natural gas varied strongly, having a minimum at 15.11 and peaking at 37.10 EUR2015/MWhLHV in October 2008, at the beginning of the Russia-Ukraine gas dispute. Border prices are suitable for large-scale district heating systems; for smaller operators higher price levels have been reported by E-Control, as summarized in Table 3.1.

Table 3.1: Natural gas prices for diﬀerent amounts of yearly consumptions in 2015. (Source: Border price: [59], Industry prices: [61])

Border Industry price

>90 GWhLHV 9–90 GWhLHV <9 GWhLHV

Price [in EUR/MWhLHV] 23.5 26.5 28.3 30.7

B. Fuel Oil

Fuel oil is a residue obtained from petroleum distillation in reﬁneries. In Austria, fuel oil is produced in the Schwechat reﬁnery near Vienna that is operated by OMV. Prices are reported by the Association of the Austrian Petroleum Industry (Fachverband der Mineralölindustrie). [86] Figure 3.2 displays historic prices for heavy fuel oil.

57.14 ● ] LHV /MWh 2015

● Price [in EUR 16.81 10 20 30 40 50 60 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015

Figure 3.2: Monthly average prices of heavy fuel oil in Austria, published by the Association of the Austrian Petroleum Industry for the time span 2005–2015. (Source:

37 tuwien.at/bibliothek C. EU Emission Allowances (EUA) In 2005 the European Union Emissions Trading System (EU ETS) was established and presently includes all 28 EU member states and 3 non-EU countries: Iceland, Liechtenstein and Norway. It works according to the ’cap-and-trade’ principle: [44] The ’cap’-component refers to the fact that the total amount of greenhouse gases that can be emitted by all participating installations (including heat and power plants) is capped. EU Emission Allowances (EUA) are auctioned off or allocated for free, and can subsequently be traded, which explains the ’trade’-component. The obligations imposed on entities covered by the EU ETS are implemented stepwise in certain phases, e.g. within the current phase three (2013-2020), free EUA allocation is no longer foreseen for electricity generation units, as opposed to the first two phases. In March 2005 the European Energy Exchange (EEX) launched a spot market for EUA, for which monthly average prices are given in Figure 3.3. Prices for EUAs are denoted in EUR per t CO2 emission, whereas emission factors differ for fossil fuels. For DH plants in Austria on average the following conversion factors are observed [284, Table 2a]:

0.288 t CO /MWh for fuel oil, • 2 LHV 0.198 t CO /MWh for natural gas. • 2 LHV

Phase 1 Phase 2 Phase 3

30.73 ● 29.06 ● / t] 2015

Price [in EUR 8.43 ● 0 10 20 30 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015

Figure 3.3: Monthly average EUA spot market prices traded at the European Energy

Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. Exchange (EEX), spanning a period between 2005 and 2015. (Source: Own illustration, Nominal values: Data provided by EEX, Inﬂation rate (HICP): [81])

38 tuwien.at/bibliothek 3.1.2 Wood Fuels Wood fuels for DH are typically sawmill by-products such as sawdust and wood chips. The wood fuel market is strongly connected to the forest-based industry, which therefore primarily determines the prices. The sawmill by-products in particular are typically used as raw material in the panel, pulp and paper industry and are increasingly pelletized to supply the individual heating market. In fact, Granger Causality tests reveal that in Austria the prices of sawdust and wood chips depend on the price of wood pellets [152]. In Austria, the prices for sawmill by-products are established monthly by a separate price committee for timber and published by the Vienna Commodity Exchange. These prices 3 for sawmill by-products are reported in EUR per loosely packed cubic metre (m loose, Schüttraummeter)[32]. However, the reported wood fuel price among biomass plant operators often diﬀers. This phenomenon can be explained by diﬀerences in [107, Section 3]:

1. wood chip quality (e.g. diﬀerent moisture content),

2. production costs (e.g. diﬀerent local topography),

3. ownership structures (e.g. forest owner is co-owner of the supplied heat plant).

For the conversion of the prices provided by the Vienna Commodity Exchange into EUR/MWhLHV, a moisture content of 35% will be assumed throughout this thesis. For spruce, this translates to:

0.745 MWh /m3 for wood chips (spruce) [20], • LHV loose 0.702 MWh /m3 for saw dust (spruce) [20, 140]. • LHV loose

The converted monthly prices for sawdust and wood chips are given in Figure 3.4 from 2002 until 2015. It shows that compared to fossil fuels, price ﬂuctuation for wood fuels is smaller, e.g. for wood chips it varied from 12 to 25 EUR2015/MWhLHV. As can be further seen in Figure 3.4 volatility and price levels increased after 2006. This may be attributed to an increased demand for wood chips from both new heating plants and the rising pellets market.

3.1.3 Electricity Electricity markets have been fully liberalized in Austria in October 2001. The Austrian Energy Exchange (EXAA) plays an essential role in this new market system. [89, p. 79–80] Energy supply companies, energy traders and industrial consumers have access to the electronic trading platform. Prices are set via daily auctions with delivery of power Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. on the following day. The monthly averages of these day-ahead spot-market prices are given in Figure 3.5.

39 tuwien.at/bibliothek Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. tuwien.at/bibliothek The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. utinEeg xhnefrtetmsa 0221.(ore w illustration, Own (Source: 2002–2015. timespan the for Exchange Energy Austrian ihtehgetpie curn nJl 08 ic hn ut tbedcieo prices of decline stable quite a then, Since 2008. July in occurring prices highest the with 0221.(ore w lutain oia ausi EUR/m in values Nominal illustration, Own (Source: 2002–2015. 40 the at [ traded values: electricity Nominal for prices spot-market day-ahead average Monthly 3.5: Figure energy renewable of amount costs. higher variable the low to very attributed at often operating is generation EUR which 97 observed, to been 20 has market form the varied Since prices volatility. market high stock average tremendously monthly a by liberalization characterized are prices Electricity timespan the [ to for (HICP): delivered Exchange rate (spruce/ﬁr) Commodity dust Vienna saw the and by chips published wood Austria, of in prices sawmills average Monthly 3.4: Figure

Price [in EUR2015/MWhe] Price [in EUR2015/MWhLHV] 20 40 60 80 100 5 10 15 20 25 20.42 ●

2002 81 2002 ,Cneso atr:[ factors: Conversion ], Saw Dust Saw Chips Wood 77

,Iﬂto ae(IP:[ (HICP): rate Inﬂation ], 2003 2003

2004 2004

2005 2005 11.61 ●

2006 2006

2007 20 2007 96.82 , ● 2008 140 2008 81 ]) ]) 2009 2009

2010 2010

2011 2011

2012 2012 3

2013 2013 25.35 loose ●

2014 [ : 2014 32 2015

2015 Inﬂation ], 2015 /MWh e , 3.1.4 Volatilities and Correlations The high volatility of DH fuel prices causes substantial uncertainties for the investment planning of DH plants. Some of these price movements are furthermore strongly correlated. In this context, several stylized facts on long-term movements of DH input energy prices, in particular their volatilities and correlations can be found in the literature:

(H1) Wood fuel price changes have lower volatilities compared to fossil fuel price changes [153].

(H2) Long-term price developments of fossil fuel prices are closely tied, proving the fact that all prices are similarly impacted by macroeconomic eﬀects [194].

(H3) In Europe, fossil fuel and EUA price changes inﬂuence electricity prices as the costs of generation based on these fuels makes up a large share of electricity prices [10].

(H4) Wood fuel prices show no co-movements with fossil fuel prices [198].

In order to verify these four stylized facts concerning long-term movements for the Austrian market, the returns of the sample yearly average DH fuel prices of 2002-2015 are used in an empirical analysis, following [135, Section 4.3]. Yearly average prices are used in order to exclude short-term and inter-annual seasonal eﬀects. The rates of return are used instead of absolute values since the stylized facts concern price changes. The 2015 2015 returns (Rt)t=2003 of a sample of yearly average DH fuel prices (Pt)t=2002 are deﬁned as logarithmic return, i.e.:

P R := log t , t 2003,..., 2015 . t P t−1 ∈ { } Their descriptive statistics can be found in Table 3.2. They give strong support to the stylized facts (H1)-(H4).

Table 3.2: Statistical characteristics of DH input energy price returns (Austria, 2002- 2015, yearly average prices). For fossil fuels EUA prices are included. (Source: Own computations)

Minimum Maximum Volatility Correlation [in %] [in %] [in %] [in %] E NG FO WC Electricity -55.81 52.11 28.24 100 80.51 71.54 -20.96 Natural Gas -30.87 30.27 22.93 100 82.82 -23.92

41 tuwien.at/bibliothek The hypotheses (H1)-(H4) can be tested by means of appropriate statistical techniques. An F-test is suitable to test for a significant difference of standard deviations of the DH input energy price returns in (H1)[162, Chapter 10]. Furthermore, a t-test is suitable for testing significance of correlations as needed for (H2)-(H4)[162, Chapter 13.1]. The null and alternative hypotheses H0 and HA are given as

F-test (one-sided): H0 : σ1 = σ2 HA : σ1 > σ2. t-test (one-sided): H0 : ρ1,2 = 0 HA : ρ1,2 > 0. t-test (two-sided): H : ρ , = 0 H : ρ , = 0. 0 1 2 A 1 2 6 th where σi denotes the standard deviation of the i sample and ρ1,2 the correlation coeﬃcient of the ﬁrst and second sample. Both tests require independent and identically normally distributed samples, which means that further tests are required to verify the validity of this assumption. First, we check for normality by employing Jarque-Bera [132, 133] and Shapiro-Wilk tests [243, 244] with null and alternative hypotheses:

H0 : data is normally distributed HA : data is not normally distributed.

While the Shapiro-Wilk test is based on an analysis of variances, the Jarque-Bera test checks whether the sample data has a skewness and kurtosis corresponding to a normal distribution. Second, we check for independence by employing Ljung-Box tests for a p lag [173] having as null and alternative hypotheses

p p H : Cor(Rt,Rt l) = 0, H : Cor(Rt,Rt l) = 0. 0 − A − 6 Xl=1 Xl=1 Hence, the Ljung-Box test veriﬁes whether any of a group of autocorrelations

Cor(Rt,Rt−1),..., Cor(Rt,Rt−p)

of a time series is statistically significant different from zero. The observed p-values of the Shapiro-Wilk, Jarque-Bera and Ljung-Box tests are reported in Table 3.3. The normality and independence hypotheses cannot be rejected for all four input energy price returns as all p-values are above a significance level of 5%. Since for all four DH input energies, i.e. electricity, wood chips, natural gas and fuel 2015 oil, the latter two including EUA prices, their yearly returns (Rt)t=2003 can be assumed to be independent and identically normally distributed, t- and F-tests can be used for testing (H1)-(H4). The corresponding hypotheses and observed p-values can be found in Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. Table 3.4.

42 tuwien.at/bibliothek Table 3.3: Observed p-values of the Jarque-Bera and Shapiro-Wilk tests on normality and Ljung-Box tests on independence for the returns of yearly average DH input energy prices including EUA (2002–2015). (Source: Own computations)

p-value [in %] Electricity Natural Gas Fuel Oil Wood chips Jarque-Bera 99.1 71.4 86.7 80.2 Shapiro-Wilk 84.4 58.3 99.4 77.6 Ljung-Box (one lag) 15.4 19.8 36.2 98.6 Ljung-Box (two lags) 34.4 43.6 45.3 5.2 Ljung-Box (three lags) 26.9 50.4 63.6 11.1

Table 3.4: Null and alternative hypotheses H0 and HA as well as the observed p-values for the F- and t-tests corresponding to the stylized facts (H1)-(H4). Tests are based on the returns of the observed yearly average DH input prices for 2002–2015, as deﬁned by equation 3.1.4. The favoured hypotheses for a level of signiﬁcance of 5% are underlined. (Source: Own computations)

Samples p-value H0 HA Test #1 #2 [in %] GW 2.96 (H ) σ = σ σ > σ F-test (one-sided) 1 OW 1 2 1 2 1.37

(H2)GO ρ1,2 = 0 ρ1,2 > 0 t-test (one-sided) 0.16 G E 0.04 (H ) ρ = 0 ρ > 0 t-test (one-sided) 3 O E 1,2 1,2 0.99 GW 39.83 (H ) ρ1,2 = 0 ρ , = 0 t-test (two-sided) 4 OW 1 2 6 97.40

E: Electricity, O: Fuel Oil incl. EUA, G: Natural Gas incl. EUA, W: Wood chips.

At a 5% significance level, the statistical tests favour (H1)-(H4) for the Austrian DH input market. In the case of (H1) a one-sided F-test is used to assess whether the volatility of wood chip returns is equal to that of natural gas or fuel oil returns. This null hypothesis is rejected for both fossil fuels for a level of significance of 5%. The tests on the correlation coefficients additionally reveal that fossil fuel returns and electricity returns are positively correlated, since the null hypothesis of no correlation is rejected in all three cases with the p-value being well below the 5% level. By contrast, the null hypothesis of no correlation between wood chip returns and fossil fuel returns Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. cannot be rejected as the p-values corresponding to their t-tests are well above 5%.

43 tuwien.at/bibliothek 3.2 Long-Term Uncertainties

3.2.1 Stochastic Dynamics of Energy Prices (Pt)t≥0 Energy commodity prices typically tend to move towards a stochastically ﬂuctuating and unobservable trend line representing long-run total marginal costs. In the short run, of course, deviations may appear, e.g. due to abnormal temperatures or a supply shock (see [218] for a statistical analysis on commodity prices based on 127 years, 1870-1996, of data). As far as investment planning is concerned, an adequate modeling of this long-run dynamics is of particular importance. According to a review by [99], Geometric Brownian motion (GBM) is the most appropriate tool to serve this purpose. This approach is also used in the Pilipovic model [217], which is one of today’s most well-established models in commodity pricing [150, p. 58]. GBM is the continuous-time, non-negative stochastic process widely used for the modeling of ﬁnancial assets. Its relative change is a combination of an expected relative growth rate µ and a standard normally distributed random deviation with volatility σ. If we denote the DH energy input price process (Pt)t≥0, with time index t in years and today’s price P0, the formal and explicit expression of a GBM is [102, Section 3.2.1]:

σ2 Pt = P0 exp µ t + σBt , t 0, − 2 ! ! ≥

where (Bt)t≥0 denotes a standard Brownian motion, cf. [102, Section 3.1.1]

1. B0 = 0 almost surely,

2. (Bt)t≥0 is almost surely continuous,

3. the increments Bt Bs and Bt Bs are independent, if 0 s < t s < t , 1 − 1 2 − 2 ≤ 1 1 ≤ 2 2 4. Bt Bs is normally distributed with mean 0 and variance (t s), if 0 s t. − − ≤ ≤

For any point in time t the DH input energy price Pt is a log-normally distributed random variable with probability density function [102, Section 3.2.1]:

2 1 2 1 1 ln x ln P0 µ 2 σ t fP (x) = exp − − − , x 0. t √2π xσ√t − 2σ2t  ≥     The expected value and variance of the input energy prices Pt are furthermore given by

µ t E(Pt) = P0 e ,

44 tuwien.at/bibliothek For estimating the two parameters µ and σ of a DH input price process (Pt)t≥0, the sample mean and standard deviation of the historic returns of the yearly average energy prices 2015 (Rt)t=2003, as deﬁned in Equation 3.1.4, can be used [128, Section 5.1.2][135, Section 4.3]. However, in order to comply with the properties of a GBM, observed returns need to be independent and identically normally distributed. For electricity, wood chips, fuel oil and natural gas, with the latter two including EUA prices, this has been successfully tested statistically in Section 3.1.4, see also Table 3.3. Hence the estimators for the two parametersµ ˆ andσ ˆ can be constructed as

1 2015 µˆ = Rt, 13 t =2003X 1 2015 σˆ = (R µˆ)2. v t u12 t − u =2003X t In Figure 3.6 some sample paths for wood chips pricing modelled as GBM are depicted. The parametrisation is based on the historic sample standard deviations of price return and a yearly growth rate µ of 1%. ] LHV /MWh 2015 Price [in Euro 10 20 30 40 50 60

2005 2010 2015 2020 2025 2030 2035 2040 Time [in years]

Figure 3.6: Historic prices for wood chips (until 2015) and sample paths of a GBM for future prices. The volatility of the GBM σ corresponds to the historic sample volatilities of the returns of yearly average prices from 2002–2015 (see Table 3.2), its expected growth rate µ is set to 1%. The interquartile range of future wood chip prices is furthermore Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. indicated by the shaded area. (Source: Own illustration and computations)

45 tuwien.at/bibliothek 3.2.2 Distribution of Levelized Energy Prices P¯ Levelized prices of input energy for DH are defined as the average energy price over a plant’s lifetime. When these prices are uncertain, they can be characterized by a probability distribution. Arguably, the magnitude of the levelized energy price is one key factor in determining the economic profitability of an energy plant. As stressed in [292] "‘the value of a real asset value is resultant of financial cash flows during operation of the project"’. Therefore the distribution of average prices should be considered in such investment decisions under uncertainty rather than just present prices or their return distribution. A first scientific contribution of this thesis is to introduce the concept of the distribution of levelized energy prices to DH investment decisions.

For an input energy price process (Pt)t≥0 as deﬁned in Section 3.2.1, the levelized price of input energy for DH is then given as a random variable P¯ via the transformation 1 L P¯ := P dt, L t Z0 where L denotes the life span of the plant. In the case of a GBM, this random variable can be further speciﬁed as

L 2 P0 σ P¯ := exp µ t + σ Bt dt. L − 2 Z0 ! !

Levelized energy commodity prices are well-studied in ﬁnancial mathematics namely in the form of Asian options. These are options whose payoﬀ is determined by the levelized commodity prices over some pre-set period of time They are traded frequently, in particular for oil and natural gas. [100] The pricing of Asian options from a mathematical point of view leads to an in-depth study of the distributions of the levelized commodity prices, see for example [291, 180] for an overview. In the case of the input energy price process (Pt)t≥0 being given by a GBM with drift µ and volatility σ, the non-centralized moments

n µn := E P¯ , n N ∈ can be expressed analytically through the following formula [101, p. 359]:

n n 2 2 P0 n! ν σ i µn = n n ωi,n exp + ν i L (3.1) L σ2 " σ2 2 ! !# Xi=0 n 2 with ω (x) = i,n (x + i)2 (x + j)2 j6=i − jY=0 2

46 tuwien.at/bibliothek No explicit representation of the probability density function of P¯ is known. The results of [157, 42] may be used to obtain values for the density function via Monte Carlo simulation. However, several approximations for the density function of P¯ are known to exist, see [94, 139]. The simplest approaches are based on matching the ﬁrst two moments of P¯ to the density of a two-parametric family. Two approaches can be found that oﬀer satisfactory results in terms of accuracy:

Log-normal distribution approximation, as proposed in [164] and [262], • Inverse gamma distribution approximation, as proposed in [186]. •

When using the log-normal distribution approximation, the location and scale parameters µP¯ and σP¯ can be computed as a function of the ﬁrst and second non-centralized moments µ1 and µ2 of the levelized input energy prices (see Equation 3.1):

µ2 µ µ = log 1 , σ = log 2 . P¯ µ P¯ µ2 √ 2 ! s 1

Figure 3.7 shows the density function corresponding to the distribution function of levelized wood chip prices upon implementation of the log-normal distribution approximation (L = 25 years). The interquartile range is furthermore highlighted: compared to Figure 3.6 displaying sample paths of a wood chips prices using the same parametrisation a much lower volatility for the levelized price can be seen.

16.97 ●

● 29.27 Density

0.000 0.02 0.04 10 20 30 40 50 60 70 Levelized Price of Wood Chips (25 years) [in Euro2015/MWhLHV]

Figure 3.7: Density function of the levelized price distribution of wood chips, using the log-normal distribution approximation. The volatility and mean parameter the underlying GBM coincide with the parametrisation used for Figure 3.6, the plant’s lifetime L is

47 tuwien.at/bibliothek 3.3 Input-Related Costs

3.3.1 Transmission and Transportation Costs CT A. Natural Gas In Austria, grid utilisation fees for natural gas transmission are set by the government regulator E-Control on an annual basis. The cost function of natural gas transmission is characterized by the presence of a significant economy of scale [290, 179]. In Austria, these cost advantages are transferred to the final consumer, since grid usage fees decrease with increasing yearly consumption [268]. There are different grid utilisation charges depending on the type of connection, with connections to the high-pressure gas network (i.e. with a pressure greater than 6 bar) exhibiting lower charges than connections to the low-pressure gas network. Large-scale DH plants are typically connected to high-pressure gas networks [65, Section 4.3.3]. Table 3.5 shows average Austrian grid utilisation fees in terms of marginal costs in 2015. The corresponding average cost for a given annual gas consumption are depicted in Figure 3.8. Table 3.5: Marginal grid usage fees for natural gas transmission with connection to the high-pressure gas network in Austria (weighted country average) for the year 2015. (Source: Regional charges: [268], Regional natural gas consumption : [60])

Consumption [in GWhLHV/year] 0 - 4.5 4.5-9 9-90 90-181 181-813 >813

Marginal Charge [in EUR/LHV] 1.78 1.42 1.11 0.79 0.74 0.72 ] LHV

● /MWh 1.16 2015

● 0.93 ● 0.83 ● ● 0.79 0.75 Costs [in EUR

0.50 0.750 1.00 1.25 1.50 250 500 750 1000 1250 1500 1750 2000 Annual Gas Consumption [in GWhLHV]

Figure 3.8: Average grid usage fees for natural gas transmission with connection to

Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. the high-pressure gas network in Austria (weighted country average) for the year 2015. (Source: Own illustration and computations)

48 tuwien.at/bibliothek For a large natural-gas supplied DH generation park, grid utilisation charges for an annual consumption of 200 GWhLHV will be on average 0.95 EUR/MWhLHV and 0.75 EUR/MWhLHV for 2000 GWhLHV as it can be seen in Figure 3.8 [268]. Note that in 2014, in order to allow more ﬂexibility for gas power plants, E-Control introduced an additional pricing system for users with a maximum capacity exceeding 400 MW. This pricing system oﬀers lower use of system charges (which would lead to lower FOM costs CFOM), but higher grid utilisation fees [57].

B. Wood Fuels The logistic chains and their economic characteristics for solid biomass plants in Austria and Bavaria have been intensively studied in [154, 287]. Transport costs for forest residues strongly depend on the distances of the biomass sources from the power plants. In [275, 276] a linear cost function depending on the transport distance d (in km) is used. In Table 3.6 ﬁxed and variable costs are given for three types of transportation modes.

Table 3.6: Fixed and variable transportation costs CT,fix and CT,var for one MWhLHV of wood chips with different transport modes. (Source: Nominal values: [275, 276], Inflation rate (HICP): [81])

Transport mode CT,ﬁx CT,var

[in EUR2015] [in EUR2015/100km] Truck 1.10 2.490 Train 2.33 0.347 Ship 2.68 0.142

For large-scale biomass plants a dis-economy of scale for fuel transportation costs is present since the average distance to cover increases with rising demand. This in turn implies that an increase in capacity associated with the rising demand would oﬀ-set the economy of scale for CAPEX, yielding a uniquely determined optimal plant size [134]. According to [88], average transportation costs can be computed approximatively when the location of wood fuel sources is assumed to be distributed uniformly in a circle around the biomass plants with an average amount of annually available wood fuel of ν 2 MWhLHV/km , see Figure 3.9 for an illustration.

When using a linear cost function, transportation costs CT denoted in EUR/MWhLHV can be computed via CT(c) := CT,ﬁx + d¯T(c) CT,var.

Hereby transportation costs depend on the average distance of transportation d¯T(c) and

49 tuwien.at/bibliothek The average distance of transportation d¯T(c) (in 100 km) is furthermore given by: 2 c h 0.5 d¯ (c) = . T 300 π ν η th Hereby h denotes the full load hours of DH generation (see Section 4.2 for a Deﬁnition) and ηth the energy conversion eﬃciency for DH generation.

DH plant

0.5 1 c h dmax = 100 π ν ηth

= Location of biomass source.

Figure 3.9: Locations of biomass sources uniformly distributed in a circle with a maximum distance of dmax (in 100 km) around a DH plant. (Source: Own illustration)

C. Electricity Grid utilisation charges for ﬁnal consumers of electricity are set by the E-Control on an annual basis. Charges depend strongly on the supply voltage and are lowest for the highest supply voltage [269]. Furthermore diﬀerences occur depending on thy supply region. Within this thesis charges for Vienna will be chosen to be representative for grid utilisation charges for large-scale DH systems. Assuming that compressor heat pump is connected to the Austrian network level 5 (Netzebene 5 ), i.e. medium voltage (10-30 kV), in 2015 end consumers would have been charged in Vienna [269]:

a grid utilisation fee of 8.50 EUR/MWh and • e a network loss fee of 1.19 EUR/MWh . • e

This results in total average electricity transmission costs of 9.69 EUR/MWhe, for the Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. year 2015. Note that if the compressor heat pump is directly supplied by a power plant no grid utilisation charges need to be paid. [196]

50 tuwien.at/bibliothek 3.3.2 Taxes

A. Energy Consumption Tax (Energieabgabe)TEC Austria enforces a national consumption tax on the usage of natural gas, coal and electricity for heat generation. The tax was introduced in 1996 to consolidate the federal budget and to increase the signiﬁcance of the ecological aspect in the tax system [184, Section 8]. For natural gas the consumption tax is given in EUR/m3. It can be converted 3 3 based on the conversion factor of 11.26 kWhHHV/m (10.17 kWhHHV/m ), as given by E-Control [268] for Austria (excluding Tyrol and Vorarlberg). Therefore, in 2015, a DH plant operator is charged for:

Electricity consumption: 15 EUR/MWh ,[31] • e Natural Gas consumption: 0.066 EUR/m3 (6.49 EUR/MWh ). [30, 268] • LHV In order to prevent double taxation, the energy consumption tax need not be paid when the respective energy is used for electricity generation, i.e. the tax is only applied for the amount of fuel that can be assigned to DH generation. The Austrian Supreme Administrative Court (Verwaltungsgerichtshof ), in its decision from September 25, 2012 stated that in case of natural gas CHP plants, only the additional amount of fuel needed in CHP mode to generate the same amount of electricity as in condensing mode should be regarded as necessary fuel input for DH generation [79]. This goes in accordance with the proposal of the oﬃcially recognized European Standardization Organizations CEN and CENELEC (European Committee for Standardization and the European Committee for Electrotechnical Standardization) [39, Section 6.2.5].

In particular, for one MWhLHV fuel input of natural gas the energy consumption tax for CHP mode operation is given by the formula

T EC = fth 6.49 EUR/MWhLHV,

where fth denotes the fuel allocation factor for heat generation in CHP plants, see Equation 2.8. In the case of a CCGT CHP plant with technical characteristics as shown in Table 2.11, only 8.8% of the fuel input is charged with the energy tax of 6.49 EUR/MWhLHV for the usage of natural gas. For a GT CHP plant no energy consumption tax has to be paid as fth = 0 per deﬁnition.

B. Renewable Energy Surcharge (Ökostromförderbeitrag)TRES For the consumption of electricity for DH generation, a percentage surcharge on grid utilisation and network loss charges for electricity has to be paid. It is set yearly by the government regulator E-Control and used for subsidies for renewable electricity generation. In 2015 the percentage surcharge was set at 30.76% based on the average Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. Austrian grid utilisation charges [267]. In 2015 this corresponded to 3.12 EUR/MWhe for compressor heat pumps connected to network level 5.

51 tuwien.at/bibliothek C. Utilization Tax (Gebrauchsabgabe) The utilization tax is set on community level and amongst other things, it charges the utilization and occupation of public ground by transmission networks for electricity and natural gas. For the majority of the Austrian communities, the transmission system operator (TSO) is charged only a utilization tax which is therefore included in the system use charges. For some communities including Vienna, the energy providing company is also charged, making the utilization tax an additional expense [63][215, p. 150]. For the purpose of modeling, it will be assumed that the utilization tax is already included in the average system use fees for electricity and natural gas transmission, as depicted in Section 3.3.1.

D. Overall Taxes for DH Input Energy In Table 3.7 all relevant taxes for natural gas, electricity and wood chip consumption for DH generation in Austria are summarized. It can be seen that for the consumption of electricity and natural gas in HOB, a substantial amount of taxes has to be paid. DH generation based on wood chips or CHP plants in general have no or almost no ﬁscal burden. Table 3.7: Energy consumption taxes (ECT), Renewable energy surcharge (RES) and overall taxes for the consumption of diﬀerent DH input energies in Austria as of 2015. The energy consumption tax of the CCGT CHP plant corresponds to a plant with technical characteristics as given in Table 2.11. (Source: Own compilation)

Taxes [in EUR/MWhLHV or MWhe] TEC TRES Total Electricity 15 3.12 18.12 HOB 6.49 – 6.49 Natural Gas CCGT CHP 0.57 – 0.57 GT CHP 0 – 0 Wood chips – – 0 Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

52 tuwien.at/bibliothek CHAPTER 4

Cost Curves of Single DH Technologies

Economic evaluations of single DH technologies require a comparability of their production costs. For DH plants, cost curves may be either denoted in EUR per MWth of installed DH capacity (Screening Curves) or in EUR per MWhth of generated DH (Levelized Cost of Heat Curves), see Section 4.2. Computation of these costs curves diﬀer severely among three categories of DH technologies: heat-only technologies, CHP technologies and waste heat technologies:

Heat-only technologies: This category comprises HOBs, non-combustible renewables • and heat pumps. Computations for these plants are straight forward as all cost components are entirely assigned to DH. Their proper aggregation to ﬁxed and variable costs can be found in Section 4.1.1.

CHP technologies: For CHP plants a cost allocation among DH and electricity • generation is required. As a second main contribution of this thesis a dynamic cost allocation is developed. This allocation method is based on the actual value of the contribution margin of electricity generation. Resulting ﬁxed and variable costs of DH supplied by CHP plants are discussed in Section 4.1.2 in detail.

Waste heat technologies: Finally, when considering incineration and industrial waste • heat, several structural diﬀerences to other DH sources can be observed. First, DH is clearly a by-product of minor economic importance and second, the facilities are often not owned by the DH system operator. This leads to several diﬀerences in the total cost determination as described more accurately in Section 4.1.3. Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

53 tuwien.at/bibliothek 4.1 Fixed and Variable Costs

For analysing the total generation costs of single technologies, it is beneﬁcial to narrow down the four cost categories presented in Table 2.10 to just two cost categories:

Fixed Costs F denoted in EUR/MW , containing all non-output-related costs, i.e. • th CAPEX and FOM costs and are paid on an annual basis, and

Variable Costs V denoted in EUR/MWh , containing all output-related costs, i.e. • th VOM cost and fuel and electricity input costs.

The formulas for computing ﬁxed and variable costs for heat-only technologies (HOB, heat pumps, non-combustible renewables), CHP technologies and waste heat technologies can be found in Equations:

Variable costs V Fixed costs F Heat-only technologies 4.2 4.1 CHP technologies 4.3 4.4 Waste heat technologies 4.6 4.5

Hereby the fixed and variable costs can be computed based on technical and financial parameters given in Table 4.1 and 4.2. Note that the levelized prices P¯Fuel and P¯E are random variables. Subsequently all fixed and variable costs that are computed based on these quantities are random variables too.

Table 4.1: Financial parameters required for computing ﬁxed costs F and variable costs V for a single DH plant. (Source: own compilation)

Parameter Meaning Unit Section

CCAPEX Capital expenditure EUR/MWth 2.2.6 CFOM Fixed operating and maintenance costs EUR/MWth/a 2.2.6 CVOM Variable operating and maintenance costs EUR/MWhth 2.2.6 CT Input energy transmission/transportation costs EUR/MWhLHV/e 3.3.1 CGC G component of electricity transmission tariﬀs EUR/MWhe 4.1.2 CA Access costs of waste heat technologies EUR/a 4.1.3 P¯Fuel Levelized fuel price including EUA EUR/MWhLHV 3.2.2 P¯E Levelized electricity price EUR/MWhe 3.2.2 PWH Price of waste heat (DH credit) EUR/MWhth 4.1.3 TEC Energy consumption tax EUR/MWhLHV/e 3.3.2 TRES Renewable electricity surcharge EUR/MWhe 3.3.2

54 tuwien.at/bibliothek Table 4.2: Technical parameters required for computing ﬁxed costs F and variable costs V for a single DH plant. (Source: own compilation)

Parameter Meaning Equation

cσ Power to heat ratio 2.4 cβ Power loss coeﬃcient 2.4 η Energy conversion eﬃciency 2.3

ηth Energy conversion eﬃciency in CHP mode for DH 2.6 fe CHP fuel allocation factor for electricity 2.8 fth CHP fuel allocation factor for DH 2.8 L Lifetime of a plant (in years) –

4.1.1 Heat-Only Technologies Heat-only technologies comprise HOBs, non-combustible renewables as well as heat pumps for exploiting low-temperature heat sources. Since these technologies generate heat as sole product, all their cost components of DH generation, as presented previously in Table 2.10, are fully attributed to the generation of DH. For one representative year of DH generation in Austria, these costs can be deﬁned as follows:

F := CCAPEX CRFL(r) + CFOM, (4.1) 1 V := C + P¯ + C + T + T , (4.2) VOM η Fuel/E T RES ECT see Table 4.1 and 4.2 for a deﬁnition of the used parameters. In the case of a HOB and a compressor heat pump the variable costs are a random variable, since they depend on the random variable P¯Fuel or P¯E. In the case of non-combustible renewables and absorption heat pumps the variable costs are deterministic and coincide with the VOM costs CVOM.

Furthermore note that the function CRFL(r) represents the Capital Recovery Factor and is deﬁned in accordance with [144, Section 3.5.3] as

L −1 r 1 −L if r > 0 CRFL(r) := = 1 (1 + r) (1 + r)l  −−1 l ! L if r = 0. X=1   The CRF is used for converting CAPEX into an equivalent annual payment. In general,

55 tuwien.at/bibliothek 4.1.2 CHP Technologies A. Cost Allocation Methods In the case of CHP plants, an allocation of joint costs for simultaneous generation of heat and electricity is required in order to enable the computation of total costs of DH generation. In general, the joint cost allocation method requires a distinction between joint products, i.e. products of equal value and by-products, i.e. products of secondary value. Such classiﬁcations may change over time and depend on the purpose of the joint cost allocation, see [117, p. 298]. In particular, two costing approaches can be distinguished, as done in [117, Chapter 7] and [55, Chapter 12]:

By-product costing: • When a good is classiﬁed as a by-product, revenues from its sales accounting for any additional processing costs, are typically deducted from the primary good.

Joint product costing: • First separable costs, i.e costs that are clearly assignable to one individual product, are allocated. For CHP plants, these comprise e.g. a heat exchanger needed for the usage of extracted heat for DH purposes. The remaining joint costs are assigned based on economical measures (e.g. expected revenues, net present values) or physical measures (e.g. ratio of electricity and DH generated by a CHP plant).

When considering how to allocate the costs of a CHP plant’s production to heat and electricity, it is important to distinguish between the plant’s fixed and variable costs, which are typically handled separately in the different cost allocation methodologies, see [103, Paragraph 5.2]. For CHP plants, the academic literature favours the joint product costing approach, equally stressing both fixed and variable costs, see [103]. A survey among 33 Swedish DH operating companies revealed that in practice the allocation principles are implemented differently by the companies: 25 companies treated electricity as a by-product, its revenues being subtracted as negative costs. On the other hand, only 3 companies regarded DH as a by-product while 5 other companies used joint product costing typically based on generated energy quantities, see [209, p. 12–13]. For large-scale CHP plants, power-to-heat ratios are typically high, which suggests that heat should be regarded as the by-product of electricity generation. However, in times of low electricity prices, the contribution margin of electricity generation by CHP plants may be negative. In this case, a plant operates only in order to supply heat. Subsequently, it is electricity that should be treated as a by-product of heat generation in such periods. Hence, a positive or negative contribution margin of electricity generation should decide whether heat or electricity should be treated as the by-product of cogeneration. Based Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. on this argument, a dynamic cost allocation for CHP plants is developed by the author as second main contribution of this thesis.

56 tuwien.at/bibliothek B. Additional Cost Component: G component of TSO Tariffs CGC The costs of electricity transmission can be divided among consumers and generators of electricity by the transmission system operator (TSO). In most European countries electric generators are only charged with a negligible generation component (G component) of the TSO tariffs or even not charged at all. [78] However, the G component in Austria is considerably high: It consists of two service fees per MWhe injected into the grid for financing the Frequency Containment Reserve and the Automatic Frequency Restoration Reserve. Additionally, transmission loss charges need to by paid by the electricity generator. This charge varies with the network level of power injection. In Austria, large-scale CHP plants mostly supply the high voltage grid (110kV, network level 3), see [288, Section 3.1]. In 2015, these plants had an average fee consisting of:

a system service fee of 2.51 EUR/MWh for ﬁnancing the Automatic Frequency • e Restoration Reserve, see [269]

a system service fee of 0.33 EUR/MWh for ﬁnancing the Frequency Containment • e Reserve, see [64, p. 10]

a transmission loss charge of 0.52 EUR/MWh , see [269, 267] • e

This yields a total average fee for electricity feeding of 3.36 EUR/MWhe injected into the grid in Austria as of 2015.

C. Variable Costs of CHP Plants The cost allocation of variable costs of CHP plants is based on the contribution margin of electricity generation. This contribution margin is sometimes referred to as spark spread in case of natural gas power plants, see [93, Chapter 19]. In general, is given for a price of electricity PE and a fuel price Pfuel as: f P + C CM(P ,P ) := (P C ) e fuel T + C , E fuel E GC c η VOM − − σ th see Table 4.1 and 4.2 for a deﬁnition of the used parameters. The proposed allocation method then treats DH or electricity as by-product dependent on the contribution margin of electricity:

CM(P ,P ) 0 Heat is by-product E fuel ≥ ⇒ CM(P ,P ) < 0 Electricity is by-product E fuel ⇒

In the ﬁrst case of DH being a by-product, the variable costs of DH generation in CHP mode are given by costs of the fuel input associated with DH generation according to Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. the CEN/CENELEC fuel allocation principle. In the second case of electricity being a by-product, these fuel costs are increased by the negative contribution margin of

57 tuwien.at/bibliothek electricity. Therefore the distribution of the variable costs can by computed via the formula:

P¯Fuel + CT TECT V = fth + CVOM + cσ max(0, CM(P¯E, P¯Fuel)). (4.3) ηth ! ηth −

Variable costs of a CCGT CHP plant allocated to DH generation according to Equation 4.3 are illustrated in Figure 4.1. Hereby variable costs for a deterministic natural gas price of 24 EUR/MWHLHV and a range of deterministic electricity prices are depicted.

] Price of Natural Gas (including EUA): 24 Euro/ MWh th LHV

Negative Contribution Margin of Electricicty Generation In CHP mode Share of Variable Costs Allocated to DH in CHP mode (CEN− CENELEC Allocation Principle) Variable Costs of DH Generation [in Euro/ MWh 0 5 10 15 20 25 30 35 40 45 50 55 20 25 30 35 40 45 50 55 60 65 70 75 80 Price of Electricity [in Euro/ MWhe]

Figure 4.1: Variable costs of a CCGT CHP plant allocated to DH generation for diﬀerent (deterministic) electricity prices and a ﬁxed (deterministic) natural gas price of 24 EUR/MWhLHV. Technical characteristics of the plant are chosen as given in Table 2.11. (Source: own illustration and computations)

C. Fixed Costs of CHP Plants

The allocation of ﬁxed costs for technical installations in CHP plants to DH generation and electricity generation exhibits several similarities to the allocation of variable costs. Separable costs of CAPEX and FOM costs can be identiﬁed as some installations (e.g. heat exchanger, connection to the DH grid) are only used for the purpose of generating DH. For example, for a CCGT CHP plant 16% of CAPEX and 46% of FOM costs are Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. separable costs, that do not occur for a CCGT power plant with no installations for DH extraction, according to [138, p. 40 and 80].

58 tuwien.at/bibliothek Therefore the joint fixed costs of electricity and DH generation of CHP plants Fjoint and the separable fixed costs of DH generation FDH can be defined as:

FDH = 0.16 CCAPEX CRFL(r) + 0.46 CFOM,

Fjoint = 0.84 CCAPEX CRFL(r) + 0.54 CFOM.

The allocation of joint costs may then be calculated based on the expected contribution margin of electricity generation throughout the plant’s lifetime E[CM(P¯E, P¯fuel)]. If the expected contribution margin is negative, the fixed costs are allocated fully to DH generation. In this case electricity is treated as by-product. Otherwise the contribution margin of electricity generation is used for covering the non-separable fixed costs to the maximum extend possible, while the remaining part of the non-separable fixed costs is covered by the contribution margin of DH (joint product costing), i.e.:

FDH + Fjoint if E[CM(P¯E, P¯fuel)] < 0,

F := FDH + 8760 E[CM(P¯E, P¯fuel)] if 0 8760 E[CM(P¯E, P¯fuel)] < Fjoint, (4.4)  ≤ F if 8760 CM(P¯ , P¯ ) F . DH E fuel ≥ joint   The share of ﬁxed costs of a CCGT CHP plant allocated to DH generation according to Equation 4.4 is illustrated in Figure 4.2, using the same parametrisation as for Figure 4.1.

Price of Natural Gas (including EUA): 24 Euro/ MWhLHV

Share of Joint Fixed Costs Allocated to DH Generation

Seperable Fixed Costs of DH Generation Share of Fixed Costs Allocated to DH Generation 0.0 0.2 0.4 0.6 0.8 1.0 20 25 30 35 40 45 50 55 60 65 70 75 80 Price of Electricity [in Euro/ MWhe]

Figure 4.2: Share of fixed costs of a CCGT CHP plant allocated to DH generation for different (deterministic) electricity prices and a fixed (deterministic) natural gas price of

Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. 24 EUR/MWhLHV. Technical characteristics of the plant are chosen as given in Table 2.11. (Source: own illustration and computations)

59 tuwien.at/bibliothek 4.1.3 Waste Heat Technologies

A. Price of Waste Heat PWH DH from incineration facilities and industrial processes is a by-product since its net realizable value is a lot smaller than that of their main product. In the case of incineration, the main product is a waste treatment process charged with a gate fee. These gate fees are paid by local authorities to contractors for the disposal and treatment of waste, meaning not only for the incineration facilities, but also for a mechanical biological treatment (MBT) of waste. The gate fee is meant to balance the net present values of waste management costs and revenues from by-products such as heat and, if existing, electricity generation over the facility’s lifetime, see [108, Section 7.3] and [191]. In either case, separable costs for DH supply associated with additional technical installations arise that need to be attributed to DH as a by-product. Moreover the revenues associated with the by-product need to be used such that they reduce the costs of the main product to some extent. Hence, the price of waste heat PWH, often referred to as heat credits, will exceed the costs for additional technical installations. The following heat credits have been reported for Austria:

Industrial Waste Heat: 19.7 EUR /MWh , see [175, p. 22] and • 2015 th Incineration: 22.6 EUR /MWh , see [124, p. 57]. • 2015 th

In Table 4.3, the revenues for diﬀerent products of a Municipal Solid Waste (MSW) incineration facility with a yearly waste treatment of 300.000 tons of MSW, are shown. It can be seen that waste treatment is by far the most important product of these facilities.

Table 4.3: Revenues for diﬀerent products of a Municipal Solid Waste incineration facility with a yearly waste treatment of 300.000 tons of MSW. (Source: own compilation; Nominal Values: [124, p. 57] in EUR/t; Inﬂation Rate (HICP): [81]); Conversion Factor: [182, p. 17])

Waste treatment District Heat Electricity

Revenue [in EUR2015/t] 131 45 7

B. Additional Cost Component: Access Costs CA Due to the fact that DH is only a by-product for incineration and industrial facilities, their distance relative to a DH system is of minor importance in their choice of location. Therefore, these facilities may be located at a considerable distance from the DH system. Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. Exploiting their waste heat potential therefore leads to additional access costs CA for transportation lines and subsequently to heat losses.

60 tuwien.at/bibliothek The amount of additional access costs can be considerable and is given in [29, p. 83] for Austria by an annualized cost of:

CA = dA 83.500 EUR/year.

Hereby dA denotes the distance of the facility producing waste heat to the DH system given in km. Several examples of realized and projected high-distance integration of incineration and industrial waste heat can be found in Austria:

Incineration: • The longest existing transmission line for DH in Austria connects the incineration facility Dürnrohr with the DH system in Sankt Pölten. It has a total length of 31 km, see [83, p. 4] and supplies 200 GWhth per year since 2009, see [83, p. 15]. Moreover, a 17 km line from the incineration facility Arnoldstein to the Villach DH system should start operation in 2018 with a projected yearly supply of 100 GWhth, see [141]. Industrial waste heat: • Starting in 2018, the Graz DH system will be annually supplied by 150 GWhth from the paper company Sappi Gratkorn via a transportation line with a length of 11 km. A further transmission line with a length of 19 km is additionally intended to connect the paper company FunderMax and the DH system of Klagenfurt, supplying it with 200 GWhth per year, see [263].

C. Fixed and Variable Costs If the waste heat facility is not owned by the DH system operator, take-or-pay contracts are typically in place. Hence the price of waste heat PWH needs to be paid by the DH system operator throughout all 8760 hours of the year. Therefore all generation costs will be covered by a ﬁxed costs factor: 1 F = C + 8760 P . (4.5) c A WH

The access costs CA need to be normalized by the capacity c of the waste heat. Consequently, there are no variable costs assigned to waste heat technologies:

V = 0. (4.6) Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

61 tuwien.at/bibliothek 4.2 Cost Curves

In general, cost curves express production costs in terms of the amount produced. For DH plants, these cost curves may be either given as costs per installed capacity in EUR/MWth or per generated heat in EUR/MWhth. In either case, the domain of the cost curves is given by the respective possible ratio of DH generation to plant capacity. These fractions are commonly referred to as Full Load Hours h: Annual Heat Output MWh h := in th = hours . Heat Capacity MW th The name stems from the fact that the full load hours represent the amount of time needed for generating the same annual heat output when operating at full capacity. Hence, full load hours h are per deﬁnition limited to the closed hour interval [0, 8760], representing one year worth of hours. When varying the full load hours, the average annual cost can be deﬁned through the two equivalent approaches mentioned above as follows, see [109, 37]:

Levelized Cost of Heat (LCOH) Curve: •

The LCOH curve corresponds to the generation costs of DH per generated heat in EUR/MWh for diﬀerent full load hours h [0, 8760]: th ∈ F (h) := + V. CLCOH h Screening Curve: •

The screening curve corresponds to the generation costs of DH per installed capacity in EUR/MW for diﬀerent full load hours h [0, 8760]: th ∈

(h) := F + V h. CSC

Figure 4.3 illustrates the LCOH and screening curve for a technology with low variable and high ﬁxed costs (geothermal DH) and a technology with high variable and low ﬁxed costs (natural gas HOB). It can be seen that, for a low amount of full load hours, average annual costs for the natural gas HOB are lower, while for a high number of full load hours geothermal DH would be economically preferable. Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

62 tuwien.at/bibliothek / MWh] / MW] 2015 2015 Fixed Costs Total costs [in TEuro

Levelized costs [in Euro Variable Costs 0 20 40 60 80 0 100 200 300 400 0 2000 4000 6000 8000 0 2000 4000 6000 8000 Full load hours [in hours] Full load hours [in hours]

(a) Natural Gas HOB / MWh] / MW] 2015 2015

Variable Costs Total costs [in Euro

Levelized costs [in Euro Fixed Costs 0 20 40 60 80 0 100 200 300 400 0 2000 4000 6000 8000 0 2000 4000 6000 8000 Full load hours [in hours] Full load hours [in hours]

(b) Geothermal DH

Figure 4.3: LCOH and screening curve for a technology with low variable and high ﬁxed costs (geothermal DH) and a technology with high variable and low ﬁxed costs (natural gas HOB). (Source: own illustration based on [27, Figure 45]) Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

63 tuwien.at/bibliothek Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. tuwien.at/bibliothek The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. Part II

District Heating Generation Portfolio Selection Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

65 tuwien.at/bibliothek Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. tuwien.at/bibliothek The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. CHAPTER 5

Generation Expansion Planning

Generation Expansion Planning (GEP) models are well-established in both the operations research literature and the energy sector for power plant portfolio selection. Their aim is to select a generation portfolio of power plants that minimizes the total costs of satisfying a time-varying demand over the portfolio’s lifetime. Thus, in GEP models the selection of cost-optimal generation portfolios additionally entails the search for an optimal operation schedule for each power plant. The optimal selection of an electricity generation portfolio was already addressed by Steinberg in 1943 by using a break-even point analysis, see [250]. A formulation as a mathematical optimization program was first proposed by Massé and Gibrat in 1957, see [178]. They developed their model in the mid-1950s for Électricité de France, making GEP one of the first industrial applications of Linear Programming (LP). This chapter gives an overview of the GEP modelling with particular focus on DH plant selection. It distinguishes between two different approaches:

Convex programming (Section 5.2): • GEP models formulated as a convex optimization program are characterized by a small number of decision variables, allowing for an in-depth analytical characterisa- tion of their solution. Mathematical challenges may arise when program extensions are considered, which could potentially make the GEP model unsolvable.

Mixed-integer linear programming (Section 5.3): • GEP models formulated as a mixed-integer linear optimization program allow for various linear extensions, since numerical solutions can be obtained even for higher-dimensional programs. However, the dynamics of such a higher-dimensional Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. program is diﬃcult to understand.

67 tuwien.at/bibliothek 5.1 Introduction to GEP

The present Section offers an introduction to GEP models applied to DH systems. In a standard GEP model, see [7, p. 271–272], the investor chooses capacities for finite number n N of different generation technologies. The investor aims to minimize the ∈ total costs of satisfying a time-varying DH load during one representative year. As discussed in Chapter 4, generation costs of a single DH technology can be computed based on its fixed and variable costs. Herby the variable costs may be a random variable for some technologies, i.e. most notably for HOBs, compressor heat pumps and CHP technologies. However, a GEP model is a deterministic optimization program. Hence within this chapter all parameters are assumed non-stochastic. For variable costs of DH generation their expected value may be used as input parameters for these standard GEP programs. In Chapter 6 this restriction will be dropped. A GEP model is characterised by the following collection of parameters and decision variables:

Parameters: • The n N DH generation technologies diﬀer by their real-valued ﬁxed F and ∈ variable costs V:

F1 V1 . n . n F := . R [in EUR/MWth] and V := . R [in EUR/MWhth],  .  ∈  .  ∈ F V  n   n      both given as column vectors. For DH generation technologies in Austria, these costs are provided as shown in Section 4.1. The time-varying DH load is speciﬁed by a continuous, non-negative function

L(t) [0, 8760] [in MWth], ∈ C see Section 2.1 for a detailed discussion. The time index t [0, 8760] corresponds ∈ to the point in time in 8760 hours of one representative year. Decision variables: • The investor decides the installed DH capacity c of each generation technology and the rate of heat ﬂow from the DH plants of each generation technology to the DH lines Q˙ (t) at any point in time t:

c1 Q˙ 1(t) . ˙ . c :=  .  [in MWth] and Q(t) :=  .  [in MWth] cn  Q˙ n(t)          ˙ Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. Furthermore, the rate heat ﬂow Qi(t) needs to be a continuous function for every generation technology i.

68 tuwien.at/bibliothek In vector notation, the standard GEP model for DH generation can be formulated as:

Program 1 (GEP: Standard Formulation, [7, p. 271–272])

8760 min F⊤ c + V⊤ Q˙ (t) dt. ˙ c, Q(t) Z0 s.t. 0 Q˙ (t) c, ( t [0, 8760]) (5.1) ≤ ≤ ∀ ∈ 1⊤ Q˙ (t) L(t), ( t [0, 8760]) (5.2) ≥ ∀ ∈ 0 c c¯. (5.3) ≤ ≤

where 1⊤ := (1, 1,..., 1) represents a vector of ones. The search for optimal capacities and DH generation schedules is subject to a number of constraints:

Rate of Heat Flow Constraint (5.1): • According to the first constraint, the rate of heat flow Q˙ (t) cannot exceed the corresponding installed DH capacity c. This constraint ensures that DH is only generated by existing technologies in the GEP model. Load Balance Constraint (5.2): • The second constraint forces the total rate of heat flow of all DH generating technologies 1⊤ Q˙ (t) to at least meet the instantaneous DH load L(t). The Load Balance Constraint is one of the central constraints of all energy models and ensures a valid interaction of demand and supply. DH Capacity Constraint (5.3): • The third constraint sets an upper bound c¯ for the installed DH capacity c. This constraint is necessary for including limited potentials of some DH sources, i.e. waste heat sources. Moreover it may be used in order to included existing plants into the model, see Section 5.1.1 for details.

5.1.1 Inclusion of Existing Plants The DH Capacity Constraint (5.3) allows for including existing plants of a certain technology i, having a capacity of cexist,i into Program 1. This can be done by artiﬁcially introducing an additional technology j with

c¯j := cexist,i. Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. Variable cots of technology j coincide with those of technology i, but for their ﬁxed costs no CAPEX is taken into account, i.e. CCAPEX,i = 0.

69 tuwien.at/bibliothek 5.2 Convex Programming GEP

5.2.1 Reformulation of the Standard GEP The standard GEP model (Program 1) may be reformulated as a linear program by introducing a discrete time horizon. This linear program would have a considerable amount of decision variables and constraints. In the early 1960s computers could not handle large amounts of constraints, which drove practitioners to come up with an alternative reformulation of the same program, captured by [216] for UK’s entire thermal system, see also [7, p. 286–288] for an overview. Their main insight was that in the standard GEP model (Program 1), the operating sequence of the technologies is decided by their variable costs only. Thus, the scheduling of the plants can be prearranged in ascending order of variable costs, the so-called merit order.

For this purpose we introduce the set of all n n dimensional permutation matrices n × P deﬁned as n := Pπ ,Pπ ,...,Pπ , P { 1 2 n! } whose illustratively chosen element Pπ represents the permutation π : 1, 2, . . . , n { } → 1, 2, . . . , n that orders the variable costs in an ascending order: { } V < V < < V . π(1) π(2) ··· π(n) Notably, the decision variables Q˙ (t) can be explicitly computed and subsequently omitted from Program 1. If, without loss of generality Pπ = I, the optimal generation can be represented as:

i−1 0, if L(t) cj  ≤ j=1  X  i−1 i−1 i ˙  Qi(t) = L(t) cj, if cj < L(t) < cj  −  j=1 j=1 j=1 X Xi X c , if c > L(t)  i j  j=1  X   for all t [0, 8760] and i 1, . . . , n . A proof for the validity of this representation is ∈ ∈ { } given in Proposition 1. The yearly DH generation Q for each technology i 1, . . . , n can be furthermore i ∈ { } represented as a function of the decision variables c by using a parametric load duration curve D(d), recall its deﬁnition from Section 2.1.2:

i c j=1 j D−1(ω) dω if i > 1, i−1  P cj Qi(c) = Z j=1 Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.   c1  P D−1(ω) dω if i = 1, Z0   70 tuwien.at/bibliothek for all t [0, 8760] Note that this representation can by computed by using the equality: ∈ 8760 Qi(c) := Q˙ i(t). Z0

An illustration of this representation of the yearly DH generation is given in Figure 5.1. Hence the yearly DH generation for each technology may be given as vector depending on the installed DH capacity as follows:

Qi(c) . Q(c) :=  .  [in MWth]. Q  n(c)    A detailed mathematical analysis of the reformulated GEP has been carried out in [253, 163]. We adopt their notation to give a re-formulation of Program 1:

Program 2 (GEP: Load Duration Curve Formulation, [253])

⊤ ⊤ min F c + (PπV) Q(Pπc) c s.t. 0 c c¯, (5.4) ≤ ≤ 1⊤ c D(0). (5.5) ≥

A rigorous proof that the optimal capacities of Program 1 and those of Program 2 are indeed the same is provided by Proposition 1. The two constraints used in Program 2 are:

Load Balance Constraint (5.5): • In contrast to Program 1, the Load Balance Constraint forces implicitly the total rate of heat ﬂow of all DH generating technologies to meet the instantaneous DH load L(t). This is done be ensuring that the total installed DH capacity exceeds the maximum DH load.

DH Capacity Constraint (5.4): • The second constraint coincides with the DH Capacity Constraint of Program 1. Notably it may be used as well in order to included existing plants into the model, see Section 5.1.1 for details. Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

71 tuwien.at/bibliothek MW

n i=1 ci = D(0) P

D(t)

c1+c2 −1 c1 + c2 Q2(c) = D (ω)dω Zc1 c2

d2 d1 d0 = 8760 Duration

Figure 5.1: Load Duration Curve D(d) with the notation for the GEP Program with merit-order dispatching (Program 2). For DH technology 2, the corresponding capacity is given by c2 and the corresponding annual DH generation by Q2(c) (surface of the shaded area). (Source: own illustration)

5.2.2 Analytical Characteristics The optimality conditions of the GEP model (Program 2) can be accurately characterized via the Karush–Kuhn–Tucker (KKT) theorem, see [253]. Since this program can be shown to be a convex program (see Proposition 2 for a exhaustive proof), any solution that satisﬁes the KKT conditions also yields a global optimum, see [163].

For discussing the analytical characteristics of Program 2 we consider two diﬀerent cases:

1. Exclusion of the DH Capacity Constraint:

If the DH Capacity Constraint ci c¯i is absent for all technologies i, existing ≤ plants cannot accounted for in the optimization. However, in this case the optimal capacities have an appealing representation, known as the Screening Curve Method of portfolio selection, as stated in [47] (see Section 4.2 for a more detailed discussion

If all technologies are included into the optimal portfolio, i.e. ci > 0 for all

72 tuwien.at/bibliothek n technologies i at the optimum, their optimal capacities (ci)i=1 satisfy:

D(di) D(di−1) if i > 1, ci = − (D(di) if i = 0.

Fi Fi − +1 if 0 < i < n, with d = Vi+1 Vi i  −  0 if i = n,

where 0 = dn < < d2 < d1 < d0 = 8760. ··· n The parameters (di)i=0 are duration levels that have a useful interpretation: for th the i technology di corresponds to the duration of DH generation and di+1 to the duration of DH generation at maximum capacity. (see Figure 5.1 for an illustration). n−1 The duration levels (di)i=1 are determined as intersection points of the Screening Curves, as deﬁned in Section 4.2:

(di) = (di), i 1, . . . , n 1 . CSCi CSCi+1 ∈ { − }

Herby (h) denotes the screening curve of the ith technology. At these intersection CSCi points, the higher ﬁxed costs of the ith technology are balanced out by the duration st di with the lower variable costs of the (i+1) technology, such that the total generation costs are equal for these two technologies.

2. Inclusion of the DH Capacity Constraint: In the general case, if all technologies are included into the optimal portfolio, i.e. n ci > 0 for all technologies i at the optimum, their optimal capacities (ci)i=1 satisfy:

D(di) D(di−1) if i > 1, ci = − (D(di) if i = 0.

(Fi + µi ) (Fi + µi) +1 +1 − if 0 < i < n, with d = Vi Vi i  − +1  0 if i = n,

where 0 = dn < < d2 < d1 < d0 = 8760 and µi 0 for all i. ··· ≥ Moreover the orthogonality criteria corresponding to the complementarity slackness of the KKT theorem,

µi = 0 ci =c ¯i µi(¯ci ci) = 0 ⊥ ⇔ − n holds. The parameters (µi) are the KKT multipliers of the DH Capacity Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. i=1 Constraints ci c¯i. They can be interpreted as is the shadow price of these ≤ constraints, i.e. the marginal costs of strengthening these constraints.

73 tuwien.at/bibliothek 5.2.3 Linearisation

A time-discrete version of the standard GEP model (Program 1) with hourly time steps would involve 8760 n decision variables. However, using the LDC formulation of GEP × (Program 2) as a starting point for linearisation, this number can be drastically decreased, as ﬁrst noticed by [17].

For reformulating Program 2 as a LP program, the interval [0,D(0)] of possible loads is replaced by a ﬁnite number B of (non-negative) load levels L1,...,LB, called load blocks. The replacement of the LDC by load blocks corresponds to an approximation of the LDC D(d) via a step function DS(d) with B steps:

B B

DS(d) = 1{d≤db}(d) Lb with Lb = D(0) (5.6) bX=1 bX=1

and some duration levels:

0 dB dB d = 8760. ≤ ≤ −1 ≤ · · · ≤ 1

In the most straightforward manner, the duration levels are chosen equidistantly, i.e.:

B + 1 b db = − 8760, b 1,...,B B ∈ { }

and the corresponding load blocks as:

D(db+1) D(db) if b 1,...,B 1 Lb = − ∈ { − } (D(0) D(dB) if b = B. −

The equidistant discretisation of a LDC into three load blocks is illustratively depicted in Figure 5.2. Note that this discretisation overestimates the actual DH load. Alternatively, the load blocks may also be chosen via a more accurate optimization approach, see e.g. [183, 208]. Herby the distance between the actual LDC and its step function approximation is to be minimized.

In the LP formulation of the GEP model based on a discrete LDC, the investor then decides upon the capacities cb of the DH generation technologies that are used to satisfy every load block b 1,...,B . The number of decision variables is therefore B n, ∈ { } × when n technologies are present. Adapting Program 2 yields the following formulation: Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

74 tuwien.at/bibliothek MW

D(d)

L1 Duration 1 2 d3 = 3 8760 d2 = 3 8760 d1 = 8760

Figure 5.2: Equidistant discretisation of the LDC D(d) into B = 3 load blocks L1,L2 and L3 with corresponding duration levels d1, d2 and d3. (Source: own illustration)

Program 3 (GEP with Discrete Load Duration Curve, [17])

B ⊤ ⊤ min F + db V cb cb bX=1 ⊤ s.t. 1 cb Lb and cb 0, ( b 1,...,B ) ≥ ≥ ∀ ∈ { } B cb c¯. ≤ bX=1

As the optimal capacities cb are determined for every load block separately, the overall optimal capacities for each technology are given via:

B c = cb. bX=1 Note that an explicit solution to Program 3 has been derived in [48, Proposition A]. Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

75 tuwien.at/bibliothek 5.3 Mixed-Integer Linear Programming (MILP) GEP

5.3.1 Discretisation and Extension of the Standard GEP The standard GEP Program can be reformulated as a Mixed-Integer Linear Program (MILP), see [122]. Such a reformulation of the GEP Program in MILP form allows the inclusion of several extensions, for the sake of a more accurate modelling, while retaining numerical solvability. Therefore, MILP GEP models oﬀer a huge advantage when compared to the convex programming GEP ones. In general, two forms of discretisation of the standard GEP are used to obtain a reformulation as MILP:

Discrete Time Interval: • Instead of a continuous time interval t [0, 8760], a discrete time interval, typically ∈ on an hourly level is used, i.e. h 1,..., 8760 . Most notably, the DH load is ∈ { } then given as the average DH load for each hour Lh, such that: h+1 Lh = L(t)dt, h 1,..., 8760 . ∈ { } Zh Discrete Number of Plants per Technology: • Instead of a continuous capacity interval c [0, c¯] for each technology, the number ∈ of plants Nr = 0, 1,... with rated capacity c per technology is used as decision { } variable.

A MILP GEP Program most notably allows to include additional constraints and decision variables associated with the optimal plant scheduling. Excluding such constraints might result in a sub-optimal portfolio selection with significantly higher operating costs, see [211]. For DH, a proper modelling of the flexibility of DH plants is typically included for this reason (e.g. in [28]): in particular, combustion plants can operate below full load and subsequently adjust their heat and, in case of CHP plants, electricity output. This operation flexibility is restricted by minimum levels of fuel input and characterized by different energy conversion efficiencies while operating below full load. A detailed MILP GEP including flexibility modelling is presented in Program 4. Other aspects of minor importance have been included in GEP MILP as well, see [122], and these extensions incorporate a more detailed system of e.g. reliability modelling (see [6]) or maintenance scheduling (see [14]).

5.3.2 Flexibility Modeling A. Feasible Operating Regions In a standard GEP model, a DH plant with capacity c can generate heat with a rate Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. of heat ﬂow Q˙ [0,c] at a constant power-to-heat ratio. However, for real combustion ∈ plants, two major diﬀerences exist:

76 tuwien.at/bibliothek Adjusting the fuel input: • By adjusting the fuel input, a different rate of heat flow Q˙ can be achieved. However, operation below a specific rate of heat flow cmin may not be achievable due to technical limitations or excessive emissions, see [241, Section 4.1.3] and [119, Selection 2.2.14]. Adjusting the steam extraction: • Extraction-condensing steam turbine and CCGT CHP plants may vary the steam extraction for DH generation continuously, yielding a large possible area of feasible combinations between generated power P and generated rate of heat flow Q˙ .

Typical minimum fuel input levels for diﬀerent heat generation technologies are given in Table 5.1. For extraction-condensing CHP plants, this provides four diﬀerent possible extreme operation points: the four possible combinations of operating with minimum/maximum fuel input and no/maximum steam extraction. The characteristics of these Operating Points (OP) are given in Table 5.2 and further depicted in Figure 5.3.

Table 5.1: Typical relative minimum load levels cmin/c (in %) for diﬀerent DH technologies. (Source: Own compilation)

Plant type cmin/c [in %] Source Gas Turbine 50 [22, p. 14] CCGT 40 [249, p. 4] Steam Turbine (Biomass) 20 [75, p. 67] HOB (Natural Gas) 15 [76, p. 123] Heat Pump 10 [76, p. 117–118]

Table 5.2: Characteristics of the extreme operating points (OP) of a CHP plant: operation with minimum/maximum fuel input and minimum/maximum power to heat ratio, i.e. condensing and CHP mode. (Source: own compilation)

OP Mode Fuel Input QP˙ −1 1 CHP cmin (ηth) cmin cσ cmin −1 2 CHP c (ηth) c cσ c −1 3 Condensing c (ηth) 0 (cβ + cσ) c −1 4 Condensing cmin (ηth) 0 (cβ + cσ) cmin

The Feasible Operating Region (FOR) of a CHP plant is then simply given by the convex hull of these extreme operating points [159]:

|OP| |OP| Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. Conv(OP) = (λi Pi, λi Q˙ i) ( i : λi 0) λi = 1 (Pi, Q˙ i) OP . (5.7)  ∀ ≥ ∧ ∧ ∈  i=1 i=1  X X 

  77 tuwien.at/bibliothek In case of an extraction type CHP plant, the resulting FOR is convex by definition and depicted in 5.3. Note that additional technical restrictions (e.g. a minimum steam input for the low-pressure turbine part) and additional alternative operating modes (i.e. supplementary firing) may lead to a different shape of the FOR in reality, see [235, Section 3.5.] for an overview of modelling techniques of the FOR. However, [5] reports that more detailed models do not offer a considerable advantage compared to the proposed modelling approach.

slope: -cβ 3 2

slope: cσ

4 1

Q˙ cmin c

Figure 5.3: FOR of a CHP plant with variable steam extraction (coloured region). The extreme operating points 1 and 4 correspond to minimum fuel input, 2 and 3 to maximum fuel input. Moreover, at the extreme operating points 1 and 2, the steam extraction is maximal, whereas at points 3 and 4 there is no steam extraction. cβ is the power loss coeﬃcient, cσ the power to heat ratio, see Deﬁnition 2.4 (Source: own illustration based on [75, Annex 1] and [5])

B. Off-Design Behaviour Since combustion plant configurations are optimised for maximum fuel input, operating at a part-load level is less efficient, see [241, Section 4.1.3] and [119, Section 2.2.14]. For CHP plants the ηe drops significantly, when the fuel input decreases. However, the additional waste heat can be mainly recovered for DH, leading only to a modest drop in the overall energy conversion efficiency, see [193, Section 5.1.4]. In contrast to CHP plants, the energy conversion efficiency of HOBs is approximately constant for a wide Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. range of fuel inputs, see [145, Section 12.4.1]. Therefore, specific Off-Design Behaviour modelling is only required for CHP plants, see [199].

78 tuwien.at/bibliothek Figure 5.4 shows the relative energy conversion efficiency for electricity generation of a CCGT and a gas turbine plant for different load levels in comparison to full load operation (Part Load Efficiency Factor FPL). It can be seen that a CCGT plant shows a much better off-design behaviour than a gas turbine plant. Typical part load efficiency factors at minimum load levels are furthermore given in Table 5.3.

CCGT LP modeling Gas Turbine LP modeling Part Load Efficiency Factor [in %] 80 85 90 95 100 50 60 70 80 90 100 Load Level [in %]

Figure 5.4: Part load efficiency factors (relative energy conversion efficiency for electricity generation in comparison to full load operation) for different load levels of a CCGT and a gas turbine plant. The approximation by a MILP GEP model is furthermore given as the dashed line. (Source: own illustration based on [53, Figure 1.7])

Table 5.3: Typical part load eﬃciency factors FPL of diﬀerent CHP technologies. (Source: Own compilation)

Plant type FPL [in %] Source Gas Turbine 80 [53, Figure 1.7] CCGT 90 [53, Figure 1.7] Steam Turbine (Biomass) 95 [75, p. 67]

When modelling combustion plants, the off-design behaviour of CHP plants needs to be considered in a model, otherwise their electricity output in a part load operation would be greatly overrated by the model, see [193, Section 5.1.4]. Two aspects need to be considered by the model: a lower energy conversion efficiency for electricity generation ηe and a higher energy conversion efficiency for DH generation ηth at minimum fuel input compared to maximum fuel input. Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. At a minimum load level, electricity output in CHP mode is given by FPL cσ cmin. The additional waste heat of electricity generation, (1 F ) cσ c , is allocated to useful heat − PL min 79 tuwien.at/bibliothek output (DH generation) and non-useful heat output (additional losses) proportionately, according to the overall efficiency η. DH generation at minimum load level therefore increases by η (1 F ) cσ c and the additional losses by (1 η) (1 F ) cσ c . The − PL min − − PL min corresponding power P and rates of heat flow Q˙ for all four extreme operating points of a CHP plant based on this allocation principle are given in Table 5.4.

Table 5.4: Characteristics of the extreme operating points (OP) of a CHP plant when accounting for oﬀ-design behaviour: operation with minimum/maximum fuel input and minimum/maximum power to heat ratio, i.e. condensing and CHP mode. (Source: own compilation)

OP Mode Fuel Input QP˙ −1 1 CHP cmin (ηth) (1 + (1 FPL) cσ η) cmin FPL cσ cmin −1 − 2 CHP c (ηth) c cσ c −1 3 Condensing c (ηth) 0 (cβ + cσ) c −1 4 Condensing cmin (ηth) 0 FPL (cβ + cσ) cmin

For modelling every feasible OP in an MILP program, it can be assumed that the FOR can still be described as a convex hull of the extreme OP, as given in Equation 5.7. This implicitly assumes a linear relationship between the fuel consumption of combustion plants and their heat and electricity output.

In reality, this relationship is non-linear and determined by several different effects, see [67, p. 611–623]. The resulting modelling error for the part load efficiencies of CCGT and gas turbine CHP plants is depicted in Figure 5.4. A more detailed modelling would be based on quadratic or third-order polynomials for the approximation of the variable costs as a function of the fuel input (alternatively polynomial approximations for the input-output functions or efficiency functions are used), see [235, p. 836–838] for an overview. However, for DH systems modelling, [199] reports that linear modelling is the most appropriate form in terms of accuracy and runtime.

C. Variable Costs of CHP Plants in MILP GEP For any feasible operating point of a CHP plant, variable costs should be calculated separately, as the ratio between fuel consumption of combustion plants and their heat and electricity output diﬀers. Under the assumption of a linear relationship between fuel consumption of combustion plants and their heat and electricity output, the variable costs of any feasible operating point V (P, Q˙ ) can be computed as convex combination of the variable costs of the four extreme operating points V1,...,V4, i.e.[159]:

Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. |OP| |OP| ˙ OP ˙ ˙ V (P, Q) = λi Vi with (λi)i=1 :(P, Q) = (λi Pi, λi Qi). Xi=1 Xi=1 80 tuwien.at/bibliothek The variable costs of the four extreme operating points V1,...V4 are given as: P + C + T V = c fuel T ECT + C c F (P C ) (5.8) 1 min η VOM σ PL E EF th − − P + C + T V = c fuel T ECT + C c (P C ) 2 η VOM σ E EF th − − P + C V = c fuel T + C (c + c )(P C ) 3 η VOM σ β E EF th − − P + C V = c fuel T + C (c + c ) F (P C ) . 4 min η VOM σ β PL E EF th − − See Table 4.1 and 4.2 for a deﬁnition of the used parameters.

D. Start-Up Costs Start-up costs arise in CHP plants due to the technical limitations on their start-up time. These restrictions are necessary to limit thermal stress through extreme temperature and pressure diﬀerences within thick-walled components of a plant, see [241, p. 59]. Start-up costs of CHP plants can be decomposed into two main factors, as done in [241, p. 60]: fuel-related start-up costs (additional fuel due to no or lower generation during ramping and additional manpower requirement) and depreciation costs (unit life shortening due to thermal stress).

Table 5.5: Typical start-up costs of CHP technologies for diﬀerent shut-down times (Sources: own compilation; Data based on [241, p. 62], [155, p. 13–14]; Exchange Rates: [197]; Inﬂation Rate: [81])

A Type Shut-Down Time Start-up costs [in EUR2015/MWth] CCGT Gas Turbine Steam turbine Hot Start 0–8 h 35.1 14.6 8.5 Warm Start 8–50 h 50.4 18.5 15.1 Cold Start > 50 h 69.4 34.1 23.4

A In all sources on start-up costs of CHP plants ﬁgures are given in EUR/MWe. Conversion to EUR/MWth is carried out via the formula: EUR/MWth = (cσ + cβ ) EUR/MWe. Hereby the coeﬃcients cσ and cβ are chosen according to Table 2.11.

5.3.3 Program Formulation In a MILP GEP model for DH generation portfolio selection the investor chooses to install a speciﬁc number of plants Nrn = 0, 1,... of each of the n N available heat { } ∈ generation technologies. The investor aims to minimize the total costs of satisfying a time-varying heat load during one representative year with 8760 hours indexed by Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. h 1,..., 8760 . Hereby the optimal plant scheduling includes the most important ∈ { } restrictions on the ﬂexibility of DH plants as discussed in Section 5.3.2.

81 tuwien.at/bibliothek ] th /MW 2015

CCGT Gas Turbine Steam turbine 0 10 20 30 40 50 60 70 Start− Up Costs [in EUR 0 10 20 30 40 50 60 70 80 90 100 Shut− Down Time [in h]

Figure 5.5: Typical start-up costs of CHP technologies for diﬀerent shut-down times (Sources: own illustration; Data: Table 5.5)

A MILP GEP model is characterised by the following collection of parameters and decision variables:

Parameters: • The parameters of a MILP GEP mainly model the characteristics of the n N ∈ available DH generation technologies. First, these plants diﬀer in their rated heating capacities

c1 . n c := . R [in MWth].  .  ∈  cN    Second, the plants diﬀer for each technology in their characteristics of their extreme operating points OPb with b 1, 2, 3, 4 , i.e. their hourly variable costs Vn,b,h and ∈ { } their rates of heat ﬂow Q˙ n,b:

˙ V1,b,h Q1,b . n ˙ . n Vb,h := . R [in EUR/h] Q :=  .  R [in MWth]  .  ∈ b . ∈ VN,b,h  Q˙     N,b      Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. for h 1,..., 8760 . The variable costs of extreme operating points Vn,b,h can be ∈ { } computed according to Equation 5.8, the rates of heat ﬂow according to Table 5.4.

82 tuwien.at/bibliothek Finally, in case of combustion plants, for each technology the DH plant is associated with start-up costs scn:

sc1 . n sc := . R [in EUR/start-up]  .  ∈  scN    As mostly no distinction is made between the start-up costs and the shut-down time of the plant for numerical performance, the cost of a warm start as given in Table 5.5 may be used as approximation for scn. In addition to plant characteristics, the hourly average of the head load is given as parameter for each hour h 1,..., 8760 : ∈ { }

Lh [in MWth].

Decision variables: • The investor decides upon the number of plants built Nrn = 0, 1,... of each { } generation technology:

Nr1 Nr := . Nn  .  ∈  NrN    Furthemore, the investor decides upon the generation schedule of each plant type by controlling the unit commitment variables during any hour h 1,..., 8760 , i.e. ∈ { } the number of operating plants per technology onn,h and the number of start-ups of plants per technology upn,h:

on1,h up1,h . n . n onh := . N , up :=  .  R .  .  ∈ h . ∈ + onN,h  upN,h          Finally the investor chooses in any hour h 1,..., 8760 the operating point of each ∈ { } plant type. This decision is modelled via setting the weights of the unique convex combination representation of the four extreme operating points that correspond to the desired operating point (see Equation 5.7):

λ1,b,h . n Λb,h := . R .  .  ∈ + λ Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.  N,b,h   

83 tuwien.at/bibliothek In vector notation, the a MIP GEP model for DH generation can be formulated as:

Program 4 (MILP GEP, [7, p. 271–272] [159])

8760 4 ⊤ ⊤ ⊤ min F (Nr c) + Λb,hVb,h + sc (uph c) . Nr, Λb,h onh uph ◦ ◦ ! hX=1 bX=1

s.t. onh Nr ( h 1,..., 8760 ) (5.9) ≤ ∀ ∈ { } ⊤ 1 Λ ,h Q˙ + Λ ,h Q˙ = Lh ( h 1,..., 8760 ) (5.10) 1 1 2 2 ∀ ∈ { } Nr c c¯ (5.11) ◦ ≤ 4 Λb,h = onh ( h 1,..., 8760 ) (5.12) ∀ ∈ { } bX=1 onh onh up ( h 2,..., 8760 ). (5.13) − −1 ≤ h ∀ ∈ { }

Hereby denotes the Hadamard product, i.e. the entrywise product of two matrices. ◦ Note that the three constraints as given in the standard GEP (Program 1) are present in the MIP GEP as well:

Rate of Heat Flow Constraint (5.9): • The ﬁrst constraint ensures that DH is only generated by existing technologies in the GEP model. For this purpose the number of operating plants is bounded by the number of installed plants for each technology.

Load Balance Constraint (5.10): • The Load Balance Constraint ensures that for any hour h the corresponding load Lh is equal to the total DH generation of all installed DH plants. In a MILP GEP this generation is competed the convex combination of the DH generation at the ˙ extreme operating points Qb with the weights Λh,b, see also the deﬁnition in Section 5.3.2.

DH Capacity Constraint (5.11): • The DH Capacity Constraint sets an upper bound on the number of plants Nr that can be installed per technology. Similar to Section 5.1.1, this constraint may be

84 tuwien.at/bibliothek For a MILP GEP two additional constraints are needed compared to a standard GEP:

FOR Constraint (5.12): • The FOR constraint ensures that power and rate of heat ﬂow of a operating plant stays within the FOR as given in Equation 5.7.

Start-Up Constraint (5.13): • The Start-Up Constraint is required in order to model change in the operation mode from shut down to generation mode uph. If it is desired to include the diﬀerence of hot, warm or cold start a time counter may be included as given in [9] vie additional constraints.

5.4 Discussion

A. Impact of Input Energy Price Uncertainties Generation Expansion Planning models assume a stable monopolistic world without any competition, and thereby little ﬁnancial uncertainty, see [56]. DH faces high ﬁnancial uncertainty due to volatile fuel costs, see Section 3.2. Due to the competition with several individual heating technologies, these risks cannot be transferred to the customer. Thus, input energy price uncertainties raise problems when employing a standard GEP to DH portfolio selection: the optimal portfolio depends strongly on the assumed future energy prices and may be sub-optimal when the energy price dynamics are other than expected.

CHP CCGT (existing)

] HOB Natural Gas (existing) th HP Sewage Water (new) /MWh 2015 LCOH [in Euro 20 30 40 50 60 70 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015

Figure 5.6: LCOH for diﬀerent technologies based on 5.000 full load hours. Deterministic Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. prices of input energy correspond to the past 12-month average for each indicated point in time. (Source: own illustration and computations)

85 tuwien.at/bibliothek For an illustration of this issue, the LCOH in case of 5.000 full load hours for three selected DH technologies are depicted in Figue 5.6. It can be seen that: "‘Uncertainties in fuel costs [. . . ] could lead to heat technologies going from being cost eﬀective to being less attractive technology choices."’ [41]

B. Necessity of Operating Constraints Linear GEP allow for the inclusion of several additional aspects if they can be modelled in a linear form. In DH GEP modelling these are most importantly operating constraints as minimum load levels, unit commitment and a more detailed modelling of the adjustable heat-power ratios in CHP plants. Not including these operating constraints may lead to a sub-optimal solution but not to a fundamentally diﬀerent portfolio selection. For DH a detailed investigation has been made in [199] Selected results for a one-month economic dispatching are given in Table 5.6. It can be seen that if ﬂexibility modeling constraints are present, low loaded CHP have to be shut down for some periods and are replaced by heat pumps instead. In an investment choice probably a smaller share of CHPs would therefore be considered to be optimal, nevertheless the modelling without operating constraints gives a good approximation.

Table 5.6: Load factors of diﬀerent CHPs and Heat pumps when modelling with and without including ﬂexibility modeling. (Source: [199])

Capacity Load Factor

[in MWth] [in %] Flexibility modeling no yes 180 50 49 300 73 77 125 56 59 CHP plants 175 42 19 485 43 23 131 100 100 Heat Pumps 400 22 28

In contrast to linear GEP modelling, convex GEP models provide valuable analytic insights and give a parsimonious modelling framework. Recent works focus on preserving this advantage of convex GEP and still consider operating constraints in heuristic models. Examples of these so-called enhanced or improved screening curve models can be found in [36, 293]. Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

86 tuwien.at/bibliothek CHAPTER 6

Modern Portfolio Theory

Modern Portfolio Theory (MPT) or Mean-Variance Analysis (MVA) is a tool developed to find the best allocation strategy for a risk-averse investor selecting a portfolio of risky assets. The standard MPT is formulated as a Quadratic Program (QP) and determines the optimal selection of assets so that the expected return is maximized for a given level of risk, defined as variance. MPT was introduced by Harry Markowitz in 1952 in [177], for which he was awarded a Nobel Prize in Economic Sciences. It became „by far the most recognized decision framework in the practice of business decision-making, including especially capital budgeting (e.g. whether to build a new factory), investment management (e.g. whether to increase the weight of oil stocks in a pension fund) and corporate financial valuation (e.g. whether a company is worth its current value on the stock market)“, see [137]. First applications of MPT to energy plant portfolio selection were presented by [15] and [13]. This application of MPT is challenging since GEP needs to be integrated into the standard formulation. Otherwise „results [...] are easily dismissed by regulators and practitioners as unacceptable, since load cycles play critical roles in fuel selection“, see [110]. This Integrated Portfolio Theory (IPT) leads to a program with a rather complex mathematical form of a generalized Risk-Averse Two-Stage Stochastic Program. As a third major contribution of this thesis the author derives a general Deterministic Equivalent Formulation of this program based on insights gained from [271] and provides a suitable solution algorithm. First, an introduction to standard MPT is given in Section 6.1. Then, the IPT, combining standard MPT and GEP, will be presented in Section 6.2. This includes the general stochastic program (Program 6) and its the deterministic equivalent (Program 7) as well as the solution algorithm in Section 6.2.3. Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

87 tuwien.at/bibliothek 6.1 Standard Portfolio Theory

6.1.1 Program Formulation In Modern Portfolio Theory (MPT), an investor is assumed to evaluate uncertain pay-offs P with a mean-variance utility function (for an introduction to MPT, see [34, Section 3], [84, Section 3] and [19, Section 7]). This mean-variance utility function is one of the most popular approaches towards decision making under uncertainty, in both economic theory and its practical applications, see [123, Section 2.3]. In this approach, utility from an uncertain pay-off P is represented by a function f of the first and second central moments of the pay-off’s distribution:

: P f(E(P ), Var(P )). U 7→

The function f is most commonly deﬁned as a linear combination of the 2 central moments:

β (P ) := E(P ) Var(P ), UMV − 2

with the risk aversion parameter β 0. ≥ Generally, in MPT the uncertain investment opportunities are characterized as a stochastic vector R, usually referred to as a return vector, with mean and covariance matrix:

R σ2 . . . σ 1 R1 R1Rn E . C . . . (R) = R =  .  and ov(R) = ΣR =  . .. .  , 2 Rn σ . . . σ    RnR1 Rn     

where n is the number of assets available to invest in. Throughout this thesis, ΣR is assumed to be positive deﬁnite.

Table 6.1: Different definitions for the economic profitability measure R, which are used in the application of MPT to energy generation portfolio selection. (Source: own compilation)

R Unit Examples (Levelized Cost of Energy) EUR/MWh [131, 232] − (Levelized Cost of Energy)−1 MWh/EUR [13, 18]

88 tuwien.at/bibliothek In the portfolio selection problem of energy plants, R corresponds to the economic profitability measure of the generation technologies. In the specialized literature several profitability measures have been used in the application of MPT, see Table 6.1. An overview of these profitability measures is provided by [109]. Their mathematical relationships are furthermore studied in [37]. The aim of the investor as the decision-maker is to find portfolio weights w that maximize the utility (P ) of their portfolio UMV P := w⊤R. This yields the following quadratic program :

Program 5 (Modern Portfolio Theory, [84, Section 3])

⊤ β ⊤ max MV(P ) = w R w ΣR w w U − 2 s.t. 1⊤w = 1, w 0. ≥

The ﬁrst constraint ensures that the portfolio weights sum up to one. Restrictions on the portfolio weights to be non-negative, as in the second constraint, are in general not necessary for ﬁnancial portfolios when short-selling is allowed.

6.1.2 Analytical Characteristics The set of optimal portfolio weights for all risk aversion coefficients β 0 is commonly ≥ referred to as efficient frontier, see Figure 6.1 for an illustration. Some analytical characteristics of the efficient frontier can be inferred (see [19, Theorem 7.1] for details). Suppose we define a set of assets I 1, . . . , n , ⊂ { } where n stands for the total amount of assets available to invest in. In this setting, the + range BI R of risk aversions β for which the assets from set I are included in the ⊂ optimal portfolio exclusively, i.e. ∗ ∗ BI := β 0 : w = 0, i I w > 0, i I { ≥ i ∀ 6∈ ∧ i ∀ ∈ } ∗ is a closed interval. Moreover, for any β BI , all optimal weights (w ) can be ∈ i i∈{1,...,n} represented as linear combinations of two fixed portfolio weights for this segment, such that mean and variance of this linear combination coincide with those of the desired Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. optimal portfolio. This result was first derived in [261] and is known as Two Fund Theorem.

89 tuwien.at/bibliothek Mean

Eﬃcient Frontier

= Feasible Portfolios = Individual Technologies

Variance

Figure 6.1: Area of feasible portfolios and the eﬃcient frontier, i.e. the set of optimal portfolios for diﬀerent risk aversion parameters β. (Source: own illustration)

6.1.3 Discussion When using MPT in energy plant portfolio selection, two critical remarks need to be pointed out:

1. Time-varying demand: Standard portfolio theory does not account for the need to satisfy a time-varying load over the portfolio’s lifetime. Its application is thus limited to special cases, most importantly when a private investor selects a portfolio of electricity generating plants in a liberalized market (for successful implementations see for example [234, 274]). It is not suitable for DH plants. To account for the time-varying load, the Integrated Portfolio Theory (IPT) has been developed, see Section 6.2.

2. Positively skewed generation costs: Variable costs V of energy plants are well known to have a positively skewed distribution. This causes some inconveniences from a theoretical point of view when employing the mean-variance utility function. Decision making under uncertainty should satisfy certain axioms of rational behaviour, the so-called von Neumann–Morgenstern axioms. In this setting the expected utility, i.e. E [ (P )] of Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. U an uncertain pay-oﬀ P is maximised. In the case of the mean-variance utility, one obtains the same result, if has the form U 90 tuwien.at/bibliothek β (P ) := E(P ) Var(P ) + E(P )2 . U − 2 However, this utility function (Quadratic Utility) has rather undesirable properties, see [16]). Alternatively, one would also obtain the same preferences, if attainable pay-oﬀ distributions, i.e.

P = w⊤R : 1⊤w = 1 w 0 { ∧ ≥ } only diﬀered in their location and scale parameters, i.e. form a Linear Class, see [40, 210]. This would require that R be symmetrically distributed, contradicting empirical observations.

6.2 Integrated Portfolio Theory

6.2.1 Risk-Averse Stochastic Programming A. Overview Integrated Portfolio Theory (IPT) combines Generation Expansion Planning (GEP) models with Modern Portfolio Theory (MPT). Hence, an investor with mean-variance utility function wants to solve the GEP Program when variable costs V are random, UMV i.e. are a random variable on some probability space (Ω, F , P) with

E(V) = V and Cov(V) = ΣV .

IPT models were ﬁrst researched by [225, 126], however, it wasn’t until later on that the theory received its name from [51]. The standard IPT has the rather complex mathematical form of a generalized Risk- Averse Two-Stage Stochastic Program (Program 6). Based on the insights gained from [253, 271], a Deterministic Equivalent Formulation of the program is obtained by the author (Program 8) with a corresponding solution algorithm presented in Section 6.2.3 as one major contribution of this thesis.

B. IPT as a Risk-Averse Two-Stage Stochastic Program Naturally the IPT Program can be formulated as a generalized Risk-Averse Two-Stage Stochastic Program. Such a program is an optimization program of the form

min min f(x, y, ω) , x∈X U y(ω)∈Y (x)×Ω ! Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. see also [195] for an introduction to this kind of problems. Hereby x X are the so- ∈ called first-stage decision variables and y Y (x) Ω the so-called second-stage decision ∈ × 91 tuwien.at/bibliothek variables. Furthermore, : R ω R is a function evaluating the utility from an U × 7→ uncertain pay-off and ω Ω an outcome on the probability space (Ω, F , P). Intuitively ∈ speaking, the decision-maker has to choose x X in the first stage before the random ∈ ω Ω is known and then, after the realization of the random quantity becomes available, ∈ chooses y(ω) Y (x) in the second stage. ∈ In the case of IPT this modelling framework can be interpreted as a risk-averse investor with utility facing two decisions that are taken in two different stages: UMV 1. First Stage: The decision-maker needs to make an investment decision by choosing the capacities- vector c before the realization of the random vectors for the variable costs V(ω) are known. 2. Second Stage: After the realization of the variable costs V(ω) becomes available, the investor optimizes the decisions for DH generation for each technology Q˙ (t, ω) for every point in time t in order to supply the DH load with minimal costs.

The risk-averse two-stage stochastic programming formulation is given in Program 6 for both the GEP in the standard formulation (Program 1) as well as the GEP in the Equivalent LDC Formulation (Program 2). In the second case the second-stage variables Q˙ (t, ω) are expressed in terms of the ﬁrst-stage variables, yielding an ordinary risk-averse stochastic program:

Program 6 (IPT: Stochastic Programming, [38]) . . Standard formulation: 8760 ⊤ ⊤ min MV F c + min V(ω) Q˙ (t, ω) dt , c U ˙ Q(t,ω) Z0 ! s.t. 0 Q˙ (t, ω) c, ( (t, ω) [0, 8760] Ω) ≤ ≤ ∀ ∈ × 1⊤ Q˙ (t, ω) L(t), ( (t, ω) [0, 8760] Ω) ≥ ∀ ∈ × 0 c c¯. ≤ ≤ Equivalent LDC Formulation:

⊤ ⊤ min MV F c + (Pπ(ω)V(ω)) Q(Pπ(ω)c) , c U s.t. 1⊤ c D(0), ≥

92 tuwien.at/bibliothek C. Deterministic Equivalent of the IPT Program One of the most common ways to solve a stochastic program is to build and solve a deterministic equivalent (DE). This can be done if the probability space Ω is discrete, i.e. only a ﬁnite number of possible outcomes ω Ω exists. In this case a stochastic program ∈ can be rewritten as a deterministic program in the following way:

min f(x, ω) = min P(ω) f(x, ω). x∈X x∈X ωX∈Ω Clearly, the probability space Ω is discrete, if the random parameters, i.e. in the case of the IPT Program V (ω) have a discrete distribution. However, as shown in Section 3.2.2, a suitable distribution for V (ω) would be the continuous multivariate log-normal distribution. Nevertheless, it was ﬁrst observed in [271] for the special case of two technologies only, that a deterministic equivalent for the IPT Program exists, even for continuously distributed parameters. A third major contribution of this thesis is the generalization of this idea for n technologies which is formulated in Program 7.A detailed proof of the equivalence of the DE with Program can be found in Proposition 3. Furthermore a solution algorithm for the DE is provided by the author in Section 6.2.3. The derivation of the DE builds on the LDC representation of the IPT Program (see

Program 6). Here only the permutation matrices (Pπ(ω))π∈Pn clearly have a discrete distribution with n! possible outcomes. By introducing the events

Mπ := ω Ω: V (ω) < V (ω) < < V (ω) , π n, { ∈ π(1) π(2) ··· π(n)} ∈ P that are going to be referred to as merit orders, a ﬁnite partition of the sample space Ω can be found. In the formulation of the DE (Program 7) the conditional distributions of (V Mπ)π are used as follows: | ∈Pn

V¯ := Pπ E(V Mπ), (6.1) |Mπ | ⊤ ⊤ Σ := Pπ [Cov(V Mπ)] P + (V¯ V¯ )(V¯ V¯ ) . |Mπ | π |Mπ − |Mπ −

Program 7 (IPT: Deterministic Equivalent Formulation)

⊤ β ⊤ min F c + P(Mπ) V¯ Q(Pπc) + Q(Pπc) Σ Q(Pπc) , c |Mπ 2 |Mπ πX∈Pn s.t. 0 c c¯, ≤ ≤ 1⊤ c D(0). (6.2) ≥ Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

93 tuwien.at/bibliothek 6.2.2 Convex Quadratic Programming Approximation A. Simplifying Assumptions and Methodology One of the most important advantages of the standard portfolio theory is that it is a convex quadratic program that can be solved fast and easily by standard algorithms, e.g. the dual method of Goldfarb and Idnani. [106] Trying to approximate the objective function of the IPT Program (Program 6) by a convex quadratic function in order to obtain a Convex Quadratic Program as well was ﬁrst suggested by [126] and [110]. This quadratic function approximation requires a two step procedure: [110]

1. Approximate the Load Duration Curve via a step function: First, in order to construct a Convex Quadratic Programming IPT, a linearised GEP is used as starting point. As discussed in Section 5.2.3, a GEP Program can be reformulated as a LP when the LDC D(d) is replaced by a step function DS(d) with B steps as given in Equation 5.6.

2. Consider generation per technology as ﬁrst stage decision variable: In the second, far more crucial step the linear GEP Program is combined with Modern Portfolio Theory. In contrast to the original IPT, generation per technology is hereby considered as ﬁrst stage decision variable, like the investment in capacities. This means generation is scheduled before the realization of the random variable costs is known and cannot be changed after this information is available. This kind of modelling leads to irrational generation schedules, when the change of the merit order occurs with a reasonable probability. Nevertheless, it is necessary in order to obtain a convex quadratic optimization program.

The resulting Convex Quadratic Programming IPT Program can be then stated as follows:

Program 8 (IPT with Quadratic Programming, [110])

B B ⊤ ⊤ β 2 ⊤ min F + db V cb + db cb ΣV cb , cb 2 bX=1 bX=1

⊤ s.t. 1 cb Lb, and cb 0, ( b 1,...,B ) ≥ ≥ ∀ ∈ { } B cb c¯, ≤ bX=1 Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

94 tuwien.at/bibliothek B. Discussion For the sake of simplification several studies including [225, 126, 51] assumed that electricity generation per technology is a first stage variable as well. This means, that generation has to be chosen by the investor before the actual realization of the random vector for the variable costs V is known. Arguably this is a rather non-problematic assumption for electricity generation, since a change in the merit order and therefore in the generation schedule is rather unlikely. However for DH generation, a change in the merit order is very likely, see also Figure 5.6. Therefore this simplification is not suitable for this purpose but may be valuable in order to construct a starting solution for Program 7.

6.2.3 Solution Algorithm A. General Idea As one further contribution by the author a suitable solution algorithm for the DE of the IPT Program (Program 7) is presented in this Section. This algorithm requires the IPT Program to be formulated as a Box-Constrained Non-Linear Program, i.e. an optimization program of the form:

minx f(x) s.t. xl x xu. ≤ ≤

Such a Box-Constrained Non-Linear Program with a smooth objective function f(x) can be solved successfully by algorithms based on projected Quasi-Newton Algorithms, such as the L-BFGS-B algorithm:[35] The L-BFGS-B algorithm is an iterative algorithm that requires a starting solution estimate c(0). For the IPT Program the solution of the quadratic programming approximation (Program 8) can be used. With each iteration k the L-BFGS-B Algorithm method forms then a quadratic approximation Ok(c) of the objective function O(c) around the current iterate c(k):

⊤ 1 ⊤ Ok(c) = O(c) + (c c(k)) c O(c(k)) + (c c(k)) Bk (c c(k)). − ∇ 2 − −

2 Hereby Bk denotes a positive-definite approximation of the Hessian matrix Ok(c) and ∇c c O(c(k)) the gradient of the objective function at the current iterate c(k). ∇ In general, Quasi-Newton methods approximate the Hessian matrix by a positive definite matrix using the gradient vectors. In the BFGS method, the approximation starts with some initial matrix B0. For every iteration the updated approximation Bk+1 satisfies the secant equation

Bk (O(c(k + 1)) O(c(k))) = c O(c(k + 1)) c O(c(k)). +1 − ∇ − ∇ Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. As there is no unique matrix satisfying this condition, the BFGS method chooses the symmetric matrix such that Bk Bk minimizes a weighted Frobenius norm. −1 − 95 tuwien.at/bibliothek Finally in every iteration step k the quadratic program

Ok(c) s.t. 0 c c¯ ≤ ≤ is solved approximatively. This is performed by using the gradient projection method in order to ﬁnd the set of active boundaries. These boundaries are then treated as equality constraints in the minimization of Ok(c).

B. Simplifying Assumption In order to obtain a box-constrained version of the IPT Program, the load balance constraint (Equation 6.2) is assumed to be binding, i.e.: 1⊤ c = D(0). (6.3) This will allow to implicitly include this constraint into the program. For this purpose th the variable cn corresponding to the installed DH capacity of the n will not be included into the objective function O(c). It can be recovered from the solution via: n−1 cn = D(0) ci. − Xi=1 However if cn < 0 the algorithm has to be re-run with a different technology chosen to th be the n technology until cn 0. ≥ For realistic parameters the load balance constraint will be binding in general. In this case, the box-constrained version coincides with the solution of the original program. The case of a non-binding load balance constraint would suggest that it is optimal to build more capacities than needed for supplying peak demand D(0) as this allows for more flexibility in plant scheduling when facing different possible merit orders.

C. Algorithm Requirements For the L-BFGS-B algorithm, several ingredients are required:

Input Parameters: • These parameters are made up of ﬁxed costs of the technologies F, as well as ¯ the conditional expectation and variance of variable costs, V|Mπ and Σ|Mπ , for all possible merit orders including their probability of occurrences P(Mπ). Box Constraints: • For the upper box constraints, for every technology a maximum capacity c¯i is required. If no maximum capacity exists, the maximum DH load may be used instead, i.e.c ¯i = D(0). Starting Solution Estimate:

Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. • The starting solution estimate c(0) can be obtained by solving the convex programming approximation of IPT as presented in Program 8.

96 tuwien.at/bibliothek Analytic Expressions of the Objective and Gradient Functions: • The analytic expression of the objective function O(c) can be derived based on the objective function in Program 7 and the condition stated in Equation 6.3:

O(c) :=F⊤ c(c˜) β + P(M ) V¯ Q(P c˜(c)) + Q(P c˜(c))⊤ Σ Q(P c˜(c)) ; π |Mπ π 2 π |Mπ π πX∈Pn n−1 ⊤ with c˜(c) := c1,...,cn−1,D(0) ci . − ! Xi=1

The gradient function of the objective c O(c) can then be computed to be: ∇

n−1 ⊤ c O(c) := F1,...,Fn−1, Fi + ∇ − ! Xi=1 P ′ ¯ ′ + (Mπ) Q (c) V|Mπ + β Q (c)Σ|Mπ Q(Pπc˜(c)) . πX∈Pn

Hereby the Jacobian matrix Q′(c˜) Rn−1 Rn is given as: ∈ ×

′ ∂ Q (c) i,j := [Q(Pπc˜(c))]j ∂ci

−1 j D ( k=1 c˜(c)π(k)) if π(i) = j < π(n) −1 j −1 j−1 D (Pk=1 c˜(c)π(k)) D ( k=1 c˜(c)π(k)) if π(i) < j < π(n)  j−1 −  D−1( c˜(c) ) if π(i) < j = π(n) − P k=1 π(k) P  −1 j =  D (Pk=1 c˜(c)π(k)) if π(n) = j < π(i) −  −1 j−1 −1 j D ( Pk=1 c˜(c)π(k)) D ( k=1 c˜(c)π(k)) if π(n) < j < π(i) −1 j−1 − D (Pk=1 c˜(c)π(k))P if π(n) < j = π(i)   0 P else.    D. Increasing Computational Performance For a given number of technologies n there are n! diﬀerent merit orders. As most of these Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. merit orders occur typically with a very low probability, the computational performance may be increased by neglecting such merit orders in the computations. For this purpose

97 tuwien.at/bibliothek the merit orders (Mπ)π∈Pn may be arranged by decreasing order according to their probability of occurrence with a permutation o : 1, 2, . . . , n! 1, 2, . . . , n! such that: { } 7→ { }

P(Mπ ) P(Mπ ) P(Mπ ). o(1) ≥ o(2) ≥ · · · ≥ o(n!)

Then for a threshold α [0, 1], the minimal numbers of merit orders mα can be computed, ∈ such that their total probability of occurrence exceeds 1 α, i.e. − p P mα := min p : (Mπo(i) ) > 1 α . p∈N ( − ) Xi=1

Then the computations may be restricted to p(α) merit orders only, i.e. by just considering the merit orders M ,M ,...,M . πo(1) πo(2) πo(mα) Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

98 tuwien.at/bibliothek CHAPTER 7

Large District Heating Systems in Austria

Three large DH systems with an annual DH generation of more than 1 TWhth exist in Austria, namely in its biggest cities: Vienna, Linz and Graz. Approximately 40% of the Austrian DH supply is dedicated to these DH systems. All three DH systems generate heat via fossil fuel-based CHP plants. However, their generation portfolios and available heat sources exhibit signiﬁcant diﬀerences:

Vienna: With an annual DH generation of roughly 6 TWh , the Viennese DH • th system is by far the country’s largest. It is based on three large CCGT CHP plants in addition to a signiﬁcant waste heat integration from ﬁve incineration facilities and the petroleum industry.

Linz: The DH system of Linz has an annual generation of 1 TWh and a well • th diversiﬁed generation portfolio with three main DH sources: small natural gas CCGT CHP plants, a biomass CHP plant and an incineration facility.

Graz: The DH system in the city of Graz is similar in size to that of Linz. The • vast majority of DH is supplied by a single coal CHP plant, which will be shut down in 2019. This will trigger a massive transformation of this DH system, complicated by a comparably low availability of waste heat sources.

This chapter presents a detailed summary of DH generation portfolios and available heat sources for Vienna, Linz and Graz in Section 7.2. Furthermore, a Modern Portfolio Theory model as presented in Section 6.2 is applied in order to determine the optimal Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. diversiﬁcation of these portfolios by the year 2030. Results of this analysis as well as parameter assumptions are then given in Section 7.3.

99 tuwien.at/bibliothek 7.1 Characteristics

7.1.1 Annual District Heating Generation The combined annual DH generation of Austria’s three largest urban DH systems – Vienna, Linz and Graz – is approximately 8 TWhth. (See Table 7.1). As previously mentioned, this corresponds to roughly 40% of the Austrian annual DH generation by energy utilities (20 TWhth). [248]. The remaining 12 TWhth are generated by medium- size DH heating systems with annual generations between 0.2 and up to 1 TWhth/a and small urban and rural DH systems. Due to the different technical and financial characteristics given by the distinct portfolio composition of the three largest urban DH systems, their analysis needs to be conducted separately. Although there exist only three such systems in Austria, their relative importance in the overall annual DH generation is significant. A detailed overview is provided in Figure 7.1.

Linz (Linz AG) Vienna

Graz

Salzburg Large (> 1000 GWh/ a) Klagenfurt

Sankt Pölten Medium Villach (200− 1000 GWh/ a) Wels Vöcklabruck Linz (KELAG) Small (< 200 GWh/ a)

Others

Figure 7.1: Annual DH generation of Austrian DH systems. (Source: Vienna, Linz (Linz AG) and Graz: see Table 7.1, Salzburg: [237], [205, p. 31], Klagenfurt: [263], Sankt Pölten: [202, p. 30]; Villach: [203, p. 13], Wels: [204, p. 32], Vöcklabruck: [52, p. 29], Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. Linz (Kelag Wärme): [185, p. 74], Overall DH Generation in Austria: [248])

100 tuwien.at/bibliothek 7.1.2 Main Technical Characteristics The three largest DH systems of Austria diﬀer in some of their main technical characteristics, including their overall size, the grid connection ratio within the supply area as well as the parameters of their transmission systems:

Size: Vienna is by far Austria’s largest system, belonging to the largest DH systems • of the European Union. [273] With an annual DH generation of approximately 6 TWhth, it is six times larger than the other two systems, Linz and Graz. In particular Linz exhibits a special situation with a second urban DH system available in addition to the main DH system, generating an extra 0.2 TWhth per annum. [185, p. 74]

Grid Connection Ratio: Despite the size of the Viennese DH system, within the • respective supply area heat generation via DH comes only second, after heat supply via natural gas. [92, p. 48] This translates into great opportunities of expansion of the DH system. In contrast, the grid connection ratio of residential buildings in Graz and Linz is very high (69% in Linz as of 2015 [171]).

Transmission System: The transmission system of Vienna has two network levels • with diﬀerent supply temperatures and pressures. This leads to a higher heat density and consequently to lower heat losses but also to higher supply temperatures of the main system compared to Linz and Graz.

A detailed overview is provided in Table 7.1.

Table 7.1: Technical characteristics of the three largest urban DH systems in Austria. (Sources: Vienna: Supply (2015): [279, p. 2], Losses (2015): [281], Network Length (2014): [282] Max. Supply Temperature [277]; Linz: Generation (2015): [170, p. 40], Supply (2015): [170, p. 61] Network Length (2015): [170, p. 61], Max. Supply Temperature (2013): [169, p. 10]; Graz: Generation (2015): [73, p. 66], Losses (2013): [72, p. 60, 78], Supply Temperature (2011) [70, p. 2] ) and total heat demands (2012): [29, Table 4-1]; own compilation and computations)

Vienna Linz Graz

Generation [in GWhth] 6260 1140 1050

Supply [in GWhth] 5680 1020 930 A Transmission Losses [in %] 9 10 11 Network Length [in km] 1210 300 380

Heat Density [in GWhth/km] 4.7 3.4 2.4 ◦ Supply Temperature at Full Capacity [in C] 145 130 120

A Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. includes personal need of DH system operator

101 tuwien.at/bibliothek 7.2 Generation Portfolios and Available Heat Sources

7.2.1 Combustion Plants with Renewable Fuels Investment subsidies and feed-in tariﬀs for biomass introduced in the early 2000s led to a huge increase of biomass CHP plants in Austria. For the three large-scale Austrian DH systems, the strategies concerning the integration of biomass CHP plants have been quite diﬀerent:

Vienna: Vienna desired a extraction-condensing steam turbine CHP plant with a • high energy conversion efficiency for electricity generation. Operation in condensing mode should maximise revenues from electricity feed-in tariffs granted from 2006- 2019 at 102 EUR/MWhe. Moreover, operation in CHP mode with DH generation should take place for only 2500 of the 8760 hours of a year. [228] The technical characteristics of the built CHP plant are summarized in Table 7.2. A changing economic environment has led to a different utilization of the Viennese plant during the past years: as initially planned 2430 full load hours for DH generation had still been reported in 2009. In the following years a continuous increase was observed, peaking at 6560 full load hours for DH generation in 2013. [278, p. 45]

Linz: In contrast to Vienna, Linz opted to build a back-pressure biomass CHP • plant with a high number of full load hours for DH generation. [166] Its technical characteristics are also summarised in Table 7.2. A second biomass CHP plant of similar size was planned in 2012, however the project became withdrawn. [206, p. 9]

Graz: In Graz there are no combustion plants with renewable fuels as of 2015. • The regional wood chip supply for a biomass combustion plant in Graz is limited to 170 GWhLHV of fuel input per year. This, in turn, limits the maximum capacity of a new biomass CHP to the range of 20-25 MWth.[114] However, the DH system operator prefers the installation of several small-scale biomass HOBs with a total capacity of up to 30 MWth over that of a single biomass CHP plant. The ﬁrst biomass HOB Hart/Raaba opened in 2016 with a yearly supply of 20 GWhth.[74]

Table 7.2: Technical characteristics (installed DH capacity, energy conversion eﬃciency η, power-to-heat ratio cσ and the power loss coeﬃcient cβ) of the wood chips steam turbine CHP plants in Vienna and Linz. (Source: own compilation)

Technical Parameters Generation/a Year MWth η [%] cσ [%] cβ [%] GWhth % Vienna 2006 35 80 50 20 225 4 [228][278, p. 45]

102 tuwien.at/bibliothek 7.2.2 Combustion Plants With Fossil Fuels For all three large-scale DH systems in Austria, fossil fuel combustion plants are of major importance. The annual DH generation as well as the share of DH from fossil fuel combustion plants in the overall DH supply for every DH system is given in Table 7.3.

Table 7.3: Installed DH capacities in MWth of fossil fuel combustion plants in Vienna, Linz and Graz and the annual share of the DH generation from fossil fuel combustion plants of the total DH supply. (Source: own compilation)

CHP plants HOB Generation/a Natural Gas Coal Natural Gas GWhth % Vienna 1200 – 1450 3800 61 [278, p. 45][280] Linz 320 – 150 630 54 [169][170, p. 40] Graz – 230 280 990 94 [247]

The individual fossil fuel combustion plants diﬀer quite strongly in their size and technical characteristics among the three Austrian large-scale DH systems:

Vienna: The Viennese DH system comprises two generation sites with fossil fuel • CHP plants: Simmering and Donaustadt (1200 MWth, 2900 GWhth/a) [278, p. 45][280, p. 14, 28] as well as ﬁve generation sites with fossil fuel HOBs: Spittelau, Kagran, Leopoldau, Arsenal and Inzersdorf. (1450 MWth)[280, p. 14] The largest plant in terms of annual DH generation of both Vienna and Austria is the CCGT plant Simmering 1 (1250 GWhth/a) with a DH capacity of 450 MWth. [280, p. 14][278, p. 45] It started operating in 2009 and originated from revamping the old Simmering 1/2 CHP CCGT plant built in 1978 with a capacity of just 280 MWth [136]. The new Simmering 1 plant comprises two new gas turbines together with the upgraded existing steam turbine, generator and condenser. [120] The original gas turbine built in 1978 is still used in 2015 as the reserve capacity Simmering 2 plant, providing an additional 150 MWth (150 GWhth/a). [280, p. 21][278, p. 45] Simmering 3, the second largest plant in terms of annual DH generation (850 GWhth/a) is located at the same generation site. [278, p. 45] Opened in 1992, it is the oldest CHP plant of Vienna and has a capacity of 350 MWth.[23, p. 50] Simmering 3 functions as a CCGT plant, where the heat input for the steam turbine is recovered from a gas turbine in combination with a steam boiler that can be ﬁred with either fuel oil or natural gas. [26, p. 84] This type of construction leads to a lower power-to-heat ratio cσ = 104%, compared to CCGT plants with no steam boiler, see Table 7.4. Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. The third Viennese CCGT plant Donaustadt 3 (650 GWhth/a) with a capacity of 250 MWth was opened in 2001. [280, p. 14,28] The plant is well-suited for operating

103 tuwien.at/bibliothek in condensing mode, since the energy conversion efficiency ηe = 58% is quite high. [280, p. 28] In contrast to the large expansion of CCGT CHP plants’ capacities by more than st 520 MWth in the first decade of the 21 century, the economic development of the years that followed led to a different outcome: In 2012 the CCGT CHP plants’ capacities were reduced by replacing the CHP plant Leopoldau with a natural gas HOB. Moreover, the start of operations of the large-scale CCGT CHP plant Simmering 4 scheduled for 2019, was postponed until further notice. [207, p. 8]

Linz: The Linz DH system comprises three generation sites with fossil fuel com- • bustion plants: Linz-Süd, Linz-Mitte and Dornbach. The largest plant in terms of annual DH generation is the CCGT plant Linz-Süd (340 GWhth/a). It comprises three gas turbine units, two of which are already operational since 1993, and the third one since 1997 [26, p. 49], as well as one back-pressure steam turbine unit and one extraction-condensing steam turbine unit [167], see Table 7.4 for technical characteristics. The latter unit is currently mothballed due to economic reasons. [207, p. 8] Due to its low power-to-heat ratio, the CCGT plant Linz-Süd is primarily used for DH generation.

Linz-Mitte (290 GWhth/a) comprises two small CCGT plants as well as 124 MWth of natural gas HOBs. The CCGT plants Linz-Mitte 1A and Linz-Mitte 1B started their operation in 2005 and 2010, respectively. While Linz-Mitte 1A was built as a back-pressure turbine, Linz-Mitte 1B was built as an extraction-condensing turbine, see 7.4 for further details. Linz-Mitte 1B oﬀers the highest energy conversion eﬃciency for electricity among all CHP plants in Linz when operating in condensing mode.

The third generation site Dornbach (<1 GWhth/a) is just used as back-up and comprises 14 MWth of natural gas HOB.

Graz: The Graz DH system is made up of four generation sites with fossil fuel • combustion plants: Mellach, Puchstraße, Neudorf-Werndorf and Thondorf. The largest plant in terms of annual DH generation is by far the coal extraction- condensing steam turbine plant Mellach (900 GWhth/a)[247]. It is operating since 1986 and is characterized by a low energy conversion eﬃciency factor ηe = 38% in condensing mode compared to natural gas ﬁred combustion plants, see [26, p. 73] and also Table 7.4 for details on its technical characteristics. The operation of the coal steam turbine plant is scheduled to cease in 2019. [201].

The second generation site, Puchstraße (100 GWhth/a) comprises 280 MWth of natural gas HOBs. Their DH capacity is extended by additional 190 MWth until 2017. [295] The other two generation sites Thondorf and Neudorf-Werndorf have been shut down due to economic reasons as of 2015. [114, p.26, 29]. Thondorf Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. comprised a gas-turbine CHP plant that was built in 1997 in order to supply the automobile manufacturer MAGNA Steyr. [260, p. 21] Outside the heating period

104 tuwien.at/bibliothek Power [in MW] Simmering 1 Simmering 3 Donaustadt Linz− Süd Linz− Mitte 1A Linz− Mitte 1B

0 100 200 300 400 500 600 700 800 Mellach

0 100 200 300 400 500 Heating capacity [in MW]

Figure 7.2: Feasible operation regions of all seven CHP plants located in Vienna, Linz and Graz. (Source: Own compilation and computations based on data given in Table 7.4 and methodology as described in Section 5.3.2)

Table 7.4: Technical characteristics (installed DH capacity, energy conversion efficiency η, power-to-heat ratio cσ and the power loss coefficient cβ) of natural gas and coal fired CHP plants in Vienna, Linz and Graz. (Source: own compilation)

Year MWth η [%] cσ [%] cβ [%] Simmering 1 2009 450 81 158 27 [136, 280] Vienna Simmering 3 1992 350 80 104 16 [23, p. 50] Donaustadt 2001 250 86 139 19 [280, p. 28] Linz-Süd 1993/97 150 85 105 9 [167, 26] Linz Linz-Mitte 1B 2010 86 87 131 13 [168] Linz-Mitte 1A 2005 85 88 121 0 [165]

Graz Mellach (coal) 1986 230 68 75 23 [26, p. 73] Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

105 tuwien.at/bibliothek it used to deliver 96 GWhth of DH per year on average (2006–2011) with a capacity of 35 MWth.[24, p. 28, 39] The CHP plant will most likely be replaced by HOBs ﬁred with natural gas (21 MWth). [114, p.26] The CHP plant Neudorf-Werndorf fueled with natural gas and fuel oil was used as reserve capacity for Mellach. [212, p. 1] Its replacement with natural gas HOBs with a capacity of 90 MWth is also planned. [188]. Overall, the three fossil fuel CHP plants in Mellach, Neudorf-Werndorf and Thondorf are planned to be replaced by new natural gas HOBs with a total capacity of 320 MWth.[188]

7.2.3 Waste Heat Sources In all three large DH systems in Austria, waste heat sources are used for DH supply. However, Linz and Graz still exhibit additional potential, which has not been explored as of 2015. The supply and additional potential of DH from waste heat is summarized for these three systems in Table 7.5.

Table 7.5: Supply by waste heat sources in GWhth for large-scale DH systems in Austria. (Source: Own compilation)

Industry Incineration Generation/a Supply Potential Supply GWhth % Vienna 600 600 1600 2200 35 [251, p. 54][279, p. 25] Linz 0 200 370 370 32 [214][170, p. 40] Graz 60 210A 0 60 6 [71, p. 19][66][222]

A This potential includes 150 GWhth distance of the facility producing waste heat to the DH system of 11 km.

Concerning the three large DH systems in Austria, the usage and potential of waste heat for DH is quite diﬀerent:

Vienna: In Vienna the vast majority of the industrial waste heat is extracted from • the OMV Schwechat refinery, covering roughly 10 % of the annual DH generation for 2010–2015. [280] The OMV Schwechat refinery comprises two large combustion plants using refinery residues as fuel providing electricity for the refinery as well as high-pressure steam. This high-pressure steam is used for processes within the refinery (e.g. steam cracking) and is additionally sold to the petrochemical company Borealis Schwechat (170 GWhth per year). Medium-pressure steam is furthermore extracted for the purpose of DH generation and delivered to three different DH systems: Vienna, Aiport Schwechat (110 GWhth) and Schwechat-Zwölfaxing (40 GWhth). [156, Chapter 11] [158] For the Vienna DH system a continuous supply with a capacity of 30 MW has

Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. th been ﬁxed yielding a minimum supply of 263 GWhth per year. [2, p. 177] This supply can be extended to a maximum capacity of 170 MWth, enabling a much

106 tuwien.at/bibliothek higher total heat extraction from the refinery. The extraction depends strongly on the overall DH demand and economic characteristics of the alternative heat generation. It therefore varies strongly over the course of time, e.g. 920 GWhth in 1989[251, p. 54] versus just 410 GWhth in 2003. [220, p. 12] Apart from the significant amounts of industrial waste heat supplied by the OMV Schwechat refinery, much smaller amounts of industrial waste heat are provided by the chemical and consumer goods company Henkel (3.5 MWth), the window and door manufacturers Hrachowina (1.5 MWth) and the confectionery company Manner (1 MWth). [146, p.67] [239, p. 14] In addition to industrial waste heat, four incineration facilities exist in Vienna that provide DH to the system: Pfaffenau (430 GWhth), Flötzersteig (420 GWhth), Spittelau (380 GWhth) and Simmeringer Haide (370 GWhth). [279, p. 25] [280] This yields a waste heat supply from incineration of roughly 1600 GWhth, which, combined with the approximately 600 GWhth from industrial waste heat, gives a total of around 35% of the Viennese DH demand that is supplied by high- temperature waste heat sources.

Linz: In Linz, industrial waste heat is only supplied to the grid of KELAG Wärme. • It constitutes around 90% of the DH generation (200 GWhth) and is solely supplied by the steel company voestalpine. [185, p. 74]. Further industrial waste heat potentials for Linz are remarkable, including additional supply by voestalpine and by chemical companies, i.e. DSM/DPx Fine Chemicals and AMI Agrolinz Melamine International totalling another 200–300 GWhth per year. [289] Including a waste heat potential of 200 GWhth into the Linz AG DH system is currently under investigation (2016-2017). [214] In addition, since 2012, waste from a new incineration facility operated by Linz AG is used for heat and electricity generation by employing an extraction-condensing steam turbine. In 2015 this yielded 370 GWhth of DH from incineration. [170, p. 40]

Graz: In Graz there is one major source of industrial waste heat: the steel company • Marienhütte which supplies 60 GWhth per year since 2011. Prior to that year only small amounts could be extracted (< 10 GWhth until 2000, 40 GWhth between 2003 and 2009). [71, p. 19] In addition, the paper company Sappi Gratkorn will supply 150 GWhth starting with 2017 or 2018 via a new 11 kilometer transmission line, as the facility is situated outside the current DH system. [66] At the time being, there are no incineration facilities that could supply DH to the Graz DH system and eﬀorts in that respect are low due to the expected particulate pollution. [222] Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

107 tuwien.at/bibliothek 7.2.4 Non-Combustible Renewables A. Solar DH with Seasonal Storage So far there exist no Solar DH facilities with seasonal storage in Austria. Graz has plans for a large-scale application in combination with absorption heat pumps that should yield an annual DH supply of 232 GWhth.[125, 188]

B. Geothermal DH Suitable geothermal heat sources that can be exploited in the medium-term are only available for the Vienna DH system. Their technical potential has been estimated at a minimum of 300 MWth.[104, p. 13]. The geothermal doublet Essling should have started operation in 2014. It should have had a capacity of 40 MWth with a source temperature of 150 ◦C and a source depth of 5000 m. [148, 149] However, the exploration wells failed and the project was abandoned in 2012. Since no proper exploration risk insurance was contracted, the drill costs had to be covered by the DH operating company Wien Energie. [229, p- 97–98] Nevertheless, the Sustainability Programme 2016 of Wien Energie concerning diversiﬁcation of DH sources still contains the possible exploration of the geothermal heat source potentials for the Vienna DH system. [283, p. 7]

7.2.5 Heat Pumps For all three large urban DH systems in Austria a substantial integration of heat pumps into the generation portfolio is either under investigation, planned or already partly under construction. The concerned heat sources are quite diverse:

Industrial Waste Heat: • The usage of low-temperature industrial waste heat is currently planned or already in realization in all three large urban DH systems: Linz has by far the largest potential with 400-700 GWhth per year from the steel and chemical industry only. [289] In combination with the exploitation of 40 MWth of high temperature waste heat sources, an integration of roughly 10 MWth from absorption heat pumps is under investigation. [214] In Graz an additional 50 GWhth will be supplied by the steel company Marienhütte in 2017 (7 MWth). In Vienna the most promising heat source is made up of computer centers with a technical potential of 380 GWhth per year [252, p. 90] which are also under review by the DH system operator [227, p.11] [283, p. 7] (corresponding to a conservative estimate of 35 MWth).

Sewage Water: • The usage of sewage waters for DH purposes has been announced as being under consideration only for Graz. At the sewage treatment plant Gössendorf a mass Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. ﬂow of 850 l/s is available on average. A maximum potential of 14 MWth has been identiﬁed and is under further investigation. [113, p. 21]

108 tuwien.at/bibliothek Surface Water: • For Vienna and Graz the usage of river water as heat source is considered. In Graz the water can be taken from the river Mur: if a maximum of 10% of the mass flow is used and cooled down by 1.5 Kelvin, a potential of 60 MWth exists. [114, Section 2.12.4] In Vienna, the usage of river water from the Danube and the Danube channel is under investigation. [286] In Linz river water from the Danube may be used as well. Comparing the minimum mass flow of the river Danube in Vienna and Linz with the mass flow of the river Mur in Graz based on [33], a rough estimate under the same assumptions would give a potential of 900 and 700 MWth, respectively.

In 2017 a ﬁrst heat pump installation with a total capacity of 27 MWth will be opened at the generation park site Simmering. [283, p. 7] Here the ﬂuvial water of the Danube channel is used as cooling water of the extraction-condensing plants Simmering 1 and 3 as well as the biomass CHP plant Simmering. This leads to it usually having a much higher temperature than raw river water.

Ground Water: • For Linz and Graz the usage of ground water as heat source is considered. In Linz 23 potential locations have been identified, some of them with a promising average temperature of 13 ◦C. By exploiting a mass flow of 2400 l/s, in total 85 MWth of compressor heat pump potential, supplying 560 GWhth per year, are available. These heat pumps can replace the CCGT CHP plants Linz 1B and Linz Süd. The goal is to supply the necessary electricity directly by the steam turbine of the incineration facility or the biomass CHP plant as both are likely to have very high full load hours in the future. [54] In Graz at least 20 wells at three locations with a mass flow of 450 l/s and an average temperature of 13 ◦C are available as heat sources, to be cooled down by 3 Kelvin. [114, Section 2.12.1] This yields the much smaller potential of 11 MWth, when compared to Linz. [213, p.15]

Table 7.6: Potentials for heat pumps in the DH systems of Vienna, Linz and Graz. (Source: own compilation; see references within this chapter)

Temperature η Potential [in MWth] Type ◦ [in C] [in %] Vienna Linz Graz

river water 6 231 900 700 60 Compressor HP ground/sewage water 14 259 0 85 25 industrial waste heat 40 439 35 40 7 Absorption HP – – 0 10 0 Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

109 tuwien.at/bibliothek In Table 7.6 the potentials of heat pumps for DH in Vienna, Linz and Graz are summarized. River water is assumed to have a seasonal average temperature of 6◦C, ground and sewage water 14◦C and waste heat 40◦C. Their corresponding coeﬃcient of performance η is based on the data depicted in Figure 2.10 and corresponds to the mean of the illustrated bandwidth.

7.3 Mean-Variance Optimal Expansion Strategies

7.3.1 Input Data for the IPT model The IPT Model (Program 7, Solution algorithm: Section 6.2.3) requires several input parameters: ﬁxed costs for the technologies, probabilities for each merit order, conditional mean and variance for the variable costs as well as capacity constraints and a DH load duration curve. These parameters are set for the computations as follows:

A. Technical and Financial Parameters For the computations of the fixed and variable costs according to the formulas summarized in Section 4.1, several technical and financial parameters are needed: see Tables 4.1 and 4.2 for an overview. Note that for heat-only technologies, CHP technologies as well as waste heat technologies different formulas and subsequently different input parameters are required. Unless these input parameters are not quantified in Section 4.1 (i.e. G component of electricity transmission tariffs CGC, price of waste heat PWH and access costs of waste heat technologies CA) the following rules have been applied in order to set the remaining parameters:

Parameters for existing technologies: • The capital expenditure CCAPEX as well as the ﬁxed and variable operating and maintenance costs CFOM and CVOM for existing technologies coincide with the values in Table 2.11 (combustion plants), Table 2.13 (heat pumps) and Table 2.12 (non-combustible renewables) for the year ’2015’. The energy conversion factor η for HOBs is set according to Table 2.8. The technical parameters for CHP plants, cσ, cβ and η, are computed as the weighted average based on Table 7.4 (fossil fuel CHP plants) and Table 7.2 (renewable fuel CHP plants). The weights were chosen according to the DH capacity and all plants considered were those opened in the year 2000 or later.

Parameters for newly installed technologies: • The ﬁnancial parameters (CCAPEX,CFOM and CVOM) as well as the technical parameters (cσ, cβ and η) and the plant’s lifetime L for newly installed technologies Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. coincide with the values in Table 2.11 (combustion plants), Table 2.13 (heat pumps) and Table 2.12 (non-combustible renewables) for the year ’2030’.

110 tuwien.at/bibliothek Weighted Average Cost of Capital: • The interest rate is chosen according to Section 2.2.6.

Input-Related Costs: • The Energy Consumption Tax TEC for natural gas and electricity consumption as well as the Renewable Energy Surcharge TRES for electricity consumption are computed based on Section 3.3.2.

In case of transmission and transportation costs CT (see Section 3.3.1 for details) diﬀerent computation methods are used depending on the input energy: for natural gas transmission costs an annual consumption of 200 GWhLHV will be assumed, resulting in costs of 0.95 EUR/MWhLHV. For wood fuels an average distance of transposition of 80 km covered by a truck is assumed leading to transportation costs of 3.09 EUR/MWhLHV. Finally, in case of electricity transmission the costs as indicated in Section 3.3.2 for medium voltage (10-30 kV) will be used.

B Long-run Dynamics of Input Energy Prices The prices of input energy are assumed to follow a multivariate geometric Brownian motion as discussed in Section 3.2.1. Subsequently the levelized energy prices that are used for computing the variable costs can be approximated by a multivariate log normal distribution according to Section 3.2.2. Hence mean, volatilities and correlations of the multivariate geometric Brownian motion need to be set ﬁrst:

Mean: • Expected prices of input energy are based on the Current Policies Scenario as described in [151], which have also been used for expansion strategies for Vienna in [92]. This scenario is characterized by an increase in fossil fuel prices towards their long-term means as current prices are quite low. In addition wood chip and EUA prices increase on a moderate level as a consequence of the continued implementation of climate change-mitigating policies. Electricity prices rise severely due to the high share of renewable energy plants and the upcoming gradual elimination of nuclear power plants. All of this combined will lead to a slightly positive Spark Spread. An overview of the expected input energy prices is given in Table 7.7.

Volatility and correlation: • For the volatilities σ and correlation of the multivariate geometric Brownian motion historic quantities of the energy prices are used as reported in Table 3.2. The resulting distributional parameters µP¯ and σP¯ of the log normal distributions of the levelized input energy prices are further given in Table 7.8 (see Section 3.2.2 for a detailed discussion). Interquartile ranges of the future input energy prices are

111 tuwien.at/bibliothek Table 7.7: Expected prices of input energy in 2040 according to the Current Policies Scenario. (Source: [151])

2015 2040

Natural Gas [EUR/MWhLHV] 23.5 31.89

Electricity [EUR/MWhe] 30.6 74.7

Wood chips [Euro/MWhLHV] 21.3 30.8 EUA [EUR/t] 7.6 33.7

Electricty Natural Gas (incl. EUA) Wood chips / MWh] 2015 Price [in Euro 20 40 60 80 100

2002 2006 2010 2014 2018 2022 2026 2030 2034 2038 Time [in years]

Figure 7.3: Interquartile ranges of input energy prices (coloured areas) and expected future prices (dashed lines) for the Current Policies Scenario. (Source: own illustration)

Table 7.8: Input parameters for the computation of the distribution of the levelized input energy prices with L = 25 years according to Section 3.2.2. (Source: own computations)

P0 µ σ µP¯ σP¯

Natural Gas (incl. EUA) [EUR/MWhLHV] 25.0 0.0173 0.2293 3.1739 0.7349 Electricity [EUR/MWhe] 30.6 0.0357 0.2824 3.4268 0.9730 Wood chips [EUR/MWhLHV] 21.3 0.0148 0.1333 3.1645 0.4099 Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

112 tuwien.at/bibliothek The variable costs are described by their expected values V¯ , variance-covariance matrix Σ ¯ as well as their conditional expectation vector V|Mπ and conditional covariance matrices

Σ|Mπ for all merit orders (Mπi )πi∈Pn . These quantities may be estimated base on a Monte Carlo simulation. For this purpose 105 sample vectors of input energy prices from the joint log normal distribution with mean µP¯ and variance-covariance matrix ΣP¯ are drawn. Based on these joint prices samples, the resulting joint samples of variable costs ˆ m (Vi)i=1 can then be computed according to the formulas given in Section 4.1.

In the next step, the frequency of observation for every merit order (Mπi )πi∈Pn is counted. Note that not all possible merit orders are considered in the solution algorithm: since the number of technologies for the investigated portfolios is rather large, a threshold of α = 1% is introduced in order to enhance computational performance as described in Section 6.2.3. Finally, based on the selected merit orders the estimators for the ¯ quantities V|Mπ and conditional covariance matrices Σ|Mπ as deﬁned in Equation 6.1 can be computed.

C. Exploration Risk of Geothermal DH As discussed in Section 2.2.6 there is a severe failure rate for drilling geothermal wells. In order to include this exploration risk into the IPT Program it will be assumed that there is a failure rate of 41% corresponding to an average rate in exploration phase, see Figure 2.11. The ﬁxed and variable costs of a new geothermal DH facility with exploration risk is then given by 59% by the costs of a geothermal DH plant and by 41% by the costs of a back-up technology. This back-up technology is assumed to be HOBs fueled with natural gas. Furthermore, it will be assumed that in the case of failure, 50% of the CCAPEX of the geothermal DH facility still has to be paid.

C. Maximum DH Capacity The installed DH capacities for the existing technologies are based on the information gathered on the existing plants in Section 5.1.1, i.e. Table 7.4 (fossil fuel CHP plants), Table 7.2 (renewable fuel CHP plants) and Table 7.5 (waste heat sources and incineration). Note that only plants will be considered that have been built in the year 2000 or later. For waste heat technologies the maximum capacities may be recovered form the annual DH supply by assuming 8760 full load hours. For new technologies several restrictions on the available potential exist: for heat pumps see Table 7.6 and for waste heat sources Table 7.5. As discussed in Section 7.2.4 potentials for geothermal DH only exist in Vienna (300 MWth according to [104, p. 13]). Moreover, in case of combustion plants with renewable fuels there is only a potential for biomass HOB in Graz (30 MWth, see Section 7.2.1). Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

113 tuwien.at/bibliothek D. DH Load Duration Curves The load duration curve will be modelled according to Equation 2.2. For all three DH systems the underlying parameters coincide with those reported in Table 2.1. However the DH systems differ by the maximum DH load D(0). When setting this parameter it has to be taken into account that large DH systems are believed to be further extendable by connecting additional existing buildings and newly contracted buildings to the grid. For Vienna this may lead to only a modest increase of DH demand by 4% until 2030, with a total expected yearly supply of 5890 GWhth, compared to 2015. [92, p. 85] In particular the increasing energy efficiencies of the buildings will mainly offset the increase of demand by new costumers. For all three large DH systems an increased yearly DH supply by 4% until 2030 will be assumed leading to a maximum DH load D(0) as reported in Table 7.9. Moreover a security margin requirement will be considered in the IPT program, i.e. total installed DH capacities need to exceed the maximum DH load D(0) plus 20%. This can be easily considered in the solution algorithm by representing the nth technology as

n−1 cn = 1.2 D(0) ci. − Xi=1 Table 7.9: Maximum DH load D(0) and required DH capacity (security margin requirement: 20%) in 2030 when assuming a 4% increase in DH demand for large DH systems in Austria. (Source: Table 7.1; own compilation and computations)

Vienna Linz Graz Maximum DH load 2550 465 415 Required DH capacitiy 3060 558 498

7.3.2 Selected Generation Portfolios A. Structure of Results In this section the mean-variance optimal portfolios based on the IPT Program (Program 7) for Vienna, Linz and Graz are presented. The solutions have been computed by applying the solution algorithm presented in Section 6.2.3 for diﬀerent levels of risk aversion β. Input parameters have been set according to Section 5.1.1. The following results are displayed:

Installed DH Capacities: • For all three DH systems the optimal installed DH capacities are given for existing Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. and newly installed technologies. Hereby a lowering of the installed DH capacities of existing technologies can be attributed to a shut-down of some capacities.

114 tuwien.at/bibliothek Expected annual DH generation per technology: • The expected annual DH generation is furthermore given as well for all three DH systems for existing and newly installed technologies. Note that unlike the installed DH capacities, the annual DH generation per technology is a random quantity as it depends on the realization of the fuel and electricity prices.

Quantiles and mean of the LCOH: • For every reported level of risk aversion β the corresponding mean of the LCOH as well as the lower and upper 2.5%, 5% and 10% quantiles are additionally reported. This enables an interpretation for the abstract quantity β. In particular, it allows for a comparison of diﬀerent mean-variance optimal portfolio choices from the investor’s perspective via showing the trade-oﬀ of decreasing risk and increasing costs expectations.

B. Results on Vienna As of 2015 the Vienna DH system is mainly supplied by CCGT CHP plants and waste heat from incineration and the petroleum industry. If the existing generation park remains unchanged, this would lead to an average LCOH of 35.97 EUR/MWhth in 2030. However the LCOH have a quite high dispersion, e.g. the upper 2.5% quantile corresponds to 77.13 EUR/MWhth. By adapting the DH generation portfolio this quantile can be well reduced below 65 EUR/MWhth without increasing the average LCOH above the level of existing portfolio, see Figures 7.4 and 7.5. All mean-variance optimal generation portfolios for Vienna favour the exploitation of the geothermal DH sources. This base load technology allows to reduce both installed DH capacity and DH generation of the CCGT CHP for all levels of risk aversion. In practice this would suggest that the oldest running CCGT CHP as of 2015, Simmering 3, should not be replaced by a new CCGT CHP plant, when the end of its lifetime is reached. Nevertheless the younger plants CCGT CHP plants Simmering 1 and Donaustadt 3 are still considered to be an optimal choice for the Viennese DH generation portfolio and no premature closure is beneﬁcial. A further reduction of cost risk in Vienna can be reached by installing new river-sourced heat pumps in the range of up to 200 MWth. Compressor heat pumps for low-temperature waste heat are only installed to a very modest extent, when a very high level of risk aversion is assumed. However, these energy sources may be more economically attractive when used additionally for cooling in summer and heating in the rest of the season. Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

115 tuwien.at/bibliothek Vienna: Installed DH capacities in 2030 2015 2030

Natural Gas HOB CCGT CHP (extraction− condensing) Low− temperature waste heat (Compressor Heat Pump) Installed Capacities [in MW] River water

Waste Heat from Incineration and Industry Biomass CHP Geothermal DH (extraction− condensing) 0 500 1000 1500 2000 2500 3000

0 1 2 3 4 5 6 7 8 9 10 11 12 Risk aversion

2015 2030

77.13 Average 73.53 95% range 90% range 67.63 66.52 80% range 64.54

● ● ● 35.97 ● ● 36.13 34.22 34.43 35.17 Levelized Costs of DH [in Euro/ MWh] 20 30 40 50 60 70 80 0 1 2 3 4 5 6 7 8 9 10 11 12 Risk aversion

Figure 7.4: Generation portfolio selection and levelized costs of DH for the Vienna DH system in 2030. (Source: own illustration) Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

116 tuwien.at/bibliothek Vienna: Expected annual DH generation in 2030 2015 2030

Natural Gas HOB

CCGT CHP (extraction− condensing) Low− Tempreture Waste Heat (Compressor HP)

River Water Installed Capacities [in MW]

Waste Heat from Incineration and Industry

Biomass CHP (extraction− condensing) Geothermal DH 0 1000 2000 3000 4000 5000 6000

0 1 2 3 4 5 6 7 8 9 10 11 12 Risk aversion

2015 2030

77.13 Average 73.53 95% range 90% range 67.63 66.52 80% range 64.54

● ● ● 35.97 ● ● 36.13 34.22 34.43 35.17 Levelized Costs of DH [in Euro/ MWh] 20 30 40 50 60 70 80 0 1 2 3 4 5 6 7 8 9 10 11 12 Risk aversion

Figure 7.5: Expected DH generation and levelized costs of DH for the Vienna DH system in 2030. (Source: own illustration) Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

117 tuwien.at/bibliothek Linz: Installed DH Capacities in 2030 2015 2030

Natural Gas HOB CCGT CHP (extraction− condensing and backpressure) Installed Capacities [in MW] Low− Tempreture Waste Heat (Absoprtion HP) Ground Water

Waste Heat from Incineration Biomass CHP (backpressure)

Industrial Waste Heat 0 50 100 150 200 250 300 350 400 450 500

0 1 2 3 4 5 6 7 8 9 10 11 12 Risk aversion

2015 2030

Average 74.93 95% range 90% range 65.84 80% range

56.89 53.71 51.1

● ● ● 32.48 ● ● 30.83 31.79 29.26 29.96 Levelized Costs of DH [in Euro/ MWh] 20 30 40 50 60

0 1 2 3 4 5 6 7 8 9 10 11 12 Risk aversion

Figure 7.6: Generation portfolio selection and levelized costs of DH for the Linz DH system in 2030. (Source: own illustration) Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

118 tuwien.at/bibliothek Linz: Expected annual DH generation in 2030 2015 2030

Natural Gas HOB

CCGT CHP (extraction− condensing and backpressure)

Ground Water Low− Temperature Waste Heat

Installed Capacities [in MW] Waste Heat from Incineration Biomass CHP (backpressure)

Industrial Waste Heat 0 200 400 600 800 1000 1200

0 1 2 3 4 5 6 7 8 9 10 11 12 Risk aversion

2015 2030

Average 74.93 95% range 90% range 65.84 80% range

56.89 53.71 51.1

● ● ● 32.48 ● ● 30.83 31.79 29.26 29.96 Levelized Costs of DH [in Euro/ MWh] 20 30 40 50 60

0 1 2 3 4 5 6 7 8 9 10 11 12 Risk aversion

Figure 7.7: Expected DH generation and levelized costs of DH for the Linz DH system in 2030. (Source: own illustration) Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

119 tuwien.at/bibliothek Graz: Installed DH Capacities in 2030 2015 2030

Natural Gas HOB

Gas Turbine CHP Solar DH (seasonal storage) Installed Capacities [in MW] Low− temperature waste heat (Compressor Heat Pump) River Water

Sewage and Ground Water Coal Wood Chips HOB CHP Industrial Waste Heat 0 100 200 300 400 500 0 1 2 3 4 5 6 7 8 9 10 11 12 Risk aversion

2015 2030

Average 82.31 95% range 90% range 80% range 72.92 69.6 65.67 CHP plants. abandonment from coal

● in Austrian to the ● 38.34 ● ● 36.05 34.17 34.61 urrent portfolio cannot be replicated Levelized Costs of DH [in Euro/ MWh] The c in 2030 due combustion

0 1 2 3 4 5 6 7 8 9 10 11 12 Risk aversion

Figure 7.8: Generation portfolio selection and levelized costs of DH for the Graz DH system in 2030. (Source: own illustration) Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

120 tuwien.at/bibliothek Graz: Expected annual DH generation in 2030 2015 2030

Natural Gas HOB

Gas Turbine CHP

Low− temperature waste heat (compressor heat pump)

River Water Solar DH (seasonal storage)

Sewage and Ground Water Wood Chips HOB Expected annual generation [in GWh]

Coal CHP Industrial Waste Heat 0 200 400 600 800 1000 0 1 2 3 4 5 6 7 8 9 10 11 12 Risk aversion

2015 2030

Average 82.31 95% range 90% range 80% range 72.92 69.6 65.67 CHP plants. abandonment from coal

● in Austrian to the ● 38.34 ● ● 36.05 34.17 34.61 urrent portfolio cannot be replicated Levelized Costs of DH [in Euro/ MWh] The c in 2030 due combustion

0 1 2 3 4 5 6 7 8 9 10 11 12 Risk aversion

Figure 7.9: Expected DH generation and levelized costs of DH for the Graz DH system in 2030. (Source: own illustration) Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

121 tuwien.at/bibliothek C. Results on Linz Linz has a similar share of DH generation by CCGT plants and waste heat sources as Vienna. In addition to Vienna, a considerable share of DH from a biomass CHP plant is present. With an average LCOH of 32.48 EUR/MWhth, and an upper 2.5% quantile of 74.93 EUR/MWhth, the generation costs of the current generation portfolio are slightly lower than in Vienna. Moreover the diversiﬁcation opportunities are even more promising for Linz: by adapting the DH generation portfolio, the upper 2.5% quantile can be well reduced below 52 EUR/MWhth without increasing the average LCOH above the level of existing portfolio, see Figures 7.6 and 7.7. In contrast to Vienna, a suitable amount of waste heat from industry as well as ground water as heat source for heat pumps is available. Integrating these new heat sources into the existing generation park leads to much more economically appealing portfolios. Similarly to Vienna, the CCGT CHP plant capacities are reduced. In the case of Linz this would suggest that the oldest CCGT CHP plant, Linz-Süd, should be closed after the end of its lifetime and not be replaced by a new CHP plant.

C. Results on Graz As of 2015 the vast majority of DH in Graz is supplied by the coal CHP plant Mellach, opened in 1986. Presumably the plant will be shut down in 2019. With a replacement by a new coal CHP plant being out of the question due to ecological reasons, the Graz DH system must undergo the most radical change in the near future. Moreover, compared to Vienna and Linz waste heat potentials are far more limited, as for example incineration is not available at all, yielding entirely different mean-variance optimal portfolio adaptations. Regardless of the risk aversion, industrial waste heat potentials are fully exploited, e.g. an additional 150 GWhth/year of waste heat from the paper company Sappi, requiring an additional 11km transmission line, has been identified as optimal to be built for all levels of risk aversion. As can be seen in Figure 7.9, industrial waste heat will be expected to generate more than 200 GWhth per year. Aside from industrial waste heat also wood chip HOBs and water-source heat pumps using ground water or sewage water will be installed for all level of risk aversion. However for low risk aversion, the existing potentials would not be fully exploited. In expectation, the full load hours for the heat pumps will be much higher than for the wood chip HOBs, as can be seen in Figure 7.9. Most notably, also a new gas turbine CHP plant is identified to be part of the optimal DH generation portfolio. Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

122 tuwien.at/bibliothek CHAPTER 8

Conclusions and Outlook

8.1 Key Role of Portfolio Diversiﬁcation

In this thesis the selection and adaptation of large-scale Austrian DH generation portfolios was addressed. As least-cost portfolios tend to have a high volatility in their long-term generation costs, Modern Portfolio Theory was applied to the district heating generation portfolio selection in order to obtain portfolios with stable and yet competitive generation costs. A risk aversion parameter was introduced in order to model the trade-oﬀ between low average costs and their high volatility. The main mathematical challenges have been the integration of the time-variation of the DH load and the frequent changes in the merit order of the generation technologies during the assessment time. Two key results can be highlighted by the author:

1. Large diversiﬁcation opportunities of price risks: The study of the mean-variance optimal portfolios of Vienna, Linz and Graz illustrates that price risks can decrease dramatically compared to the least cost solution with only a small increase in expected annual costs. This allows for both stable and competitive customer prices and stresses the importance of diversiﬁcation in generation portfolio planning.

2. Least-cost portfolios have a smaller number of different technologies: Furthermore the mean-variance optimal portfolios showed that optimal diversification does not only lead to a more balanced generation mix, but also to the consideration of technologies that would not be included in a least cost portfolio. For the portfolios of Vienna, Linz and Graz this was seen for several types of absorption and compressor heat pumps as well as for solar DH with seasonal storage. The benefit of price stability when including such technologies may be overseen by an investor who Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. chooses a least-cost technology portfolio.

123 tuwien.at/bibliothek 8.2 Transformation of Large DH Systems in Austria

Based on the results of the mean-variance optimal portfolio application for Vienna, Linz and Graz several general characteristics of the transformation of large DH systems in Austria may be highlighted:

Fossil fuel combustion plants: • Fossil fuel CHP plants used to be the main source of DH generation in large and medium-sized DH systems in Austria. Despite their current economic situation, natural-gas fired CHP plants will still play an important but less dominant role in DH generation. For Vienna and Linz a further operation of their new natural gas CHP plants is beneficial, whereas plants built before 2000 should not be replaced by new natural gas CHP plants. However, in Graz, where the coal CHP plant needs to be replaced, a new small gas-turbine CHP plant is favourable for any level of risk aversion. Renewable fuel combustion plants: • The desired regional supply of wood chips for biomass CHP and HOB plants sets a natural limit on their capacity. The investment for today’s existing small-sized steam turbine CHP plants required a considerable amount of subsidies in terms of feed-in tariffs. The examples of Vienna and Linz show that if the feed-in tariffs are not guaranteed any more, full load hours decline, but a continued operation is still preferable over a shut down. However, for future new installations, Graz illustrates that small wood chip HOBs are preferred over a wood chip CHP plant for new installations. Heat Pumps: • Heat pumps will be an important technology for generation portfolio diversification. With increasing risk aversion, several low-temperature heat sources for heat pumps are increasingly exploited in the DH systems of Vienna, Linz and Graz. Employing heat pumps that allow for using low-temperature heat sources such a sewage water is also very beneficial from an ecological point of view and goes along with a de-carbonisation of DH generation. Non-combustible renewables: • Geothermal DH is only available for Vienna. The analysis shows that due to its low generation costs, exploiting geothermal DH sources is highly recommendable even in the presence of a considerable amount of exploration risk. In contrast, solar DH with seasonal storage has very high generation costs but no price risk at all. It requires a very high number of full load hours for economic operation and is therefore only recommendable for DH systems with an available capacity of cheap

Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. waste heat sources that is too small for supplying base load. Hence, this technology is only installed in Graz for high risk aversion.

124 tuwien.at/bibliothek 8.3 Outlook for Future Research

When addressing the proposed research questions several new aspects and tasks arose that could not be included in this thesis. From the author’s perspective the three main aspects are:

Including large scale thermal energy storage: • In the current version of the IPT program, no large scale thermal energy storage (TES) (see [285, Chapter 7]) is considered. Such thermal energy storage makes it possible to increase DH generation when DH generation costs are low and to store the heat for times when DH generation costs are high. Therefore, the technology may be an economically viable extension to existing generation units in DH generation portfolios.

Considering an endogenous DH load due to demand-side management: • In the IPT program, DH demand is considered to be exogenous. That coincides with reality as costs for DH customers typically do not change depending on the current DH load or generation costs. Peak load pricing may be a method to trigger demand-side management and thus lower the overall cost for DH systems. This would lead to an endogenous DH load that needs to be incorporated into the IPT program.

Analysing the risk allocation among portfolio assets: • Understanding the risk proﬁle of a portfolio and identifying concentrations of risk is an important step in portfolio management. [257] The Euler principle of risk contribution is the most used and accepted one tackling this issue. [233, Section 2.1] [224]. In the case of the IPT program, this would allow a break down of the generation park’s total risk (variance) into to a sum of risk contributions of single technologies. The Euler principle of risk contribution has received some critical comments as in [245], but gained large acceptance both in the ﬁnancial literature and in practice [176, 233]. Therefore, it may lead to a better understanding of the economic risk structure of a DH generation portfolio. Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

125 tuwien.at/bibliothek Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. tuwien.at/bibliothek The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. APPENDIX A

Mathematical Proofs

A.1 Generation Expansion Planning

Proposition 1 (Equivalence of the LDC formulation) The optimal decision variables g(t)) of Program 1 can be expressed as

i−1 0 if j=1 cj L(t) i−1 i ≥ i−1 gi(t) = L(t) j=1 cj if Pj=1 cj > L(t) > j=1 cj  − ci P else. P P  for i 1, . . . , n . Furthermore the optimal decision variables c of Program 1 and Program ∈ { } 2 coincide.

Proof. 1st step. First we show that Program 1 can be reformulated as

T ⊤ min F c + Ot(c) dt. c Z0

⊤ s.t. Ot(c) = min V g(t) . g(t) 0 g(t) c, ( t [0,T ]) ≤ ≤ ∀ ∈ 1⊤ g(t) D(t)( t [0,T ]) ≥ ∀ ∈

Therefore, we need to show that integration and inﬁmum in Program 1 can be interchanged,

Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. i.e. 8760 8760 inf V ⊤ g(t) dt = inf V ⊤ g dt. g t 1 Rn gRn ( )∈L ( ) Z0 Z0 127 tuwien.at/bibliothek The equality holds according to Hiai and Umegaki’s interchange theorem [115, p. 435], a special case of Rockafellar’s interchange theorem [231] as

h(w) := V ⊤ w

is a real-valued and continuous function. 2nd step. Second we show that

i−1 0 if j=1 cj > L(t) i−1 i i−1 gi(t) = L(t) j=1 cj if Pj=1 cj > L(t) > j=1 cj  − ci P else. P P  for i 1, . . . , n . and t [0, 8760] is the solution for all sub problems ∈ { } ∈ ⊤ Ot(c) = min V g(t) . g(t) 0 g(t) c, ( t [0,T ]) ≤ ≤ ∀ ∈ 1⊤ g(t) D(t)( t [0,T ]) ≥ ∀ ∈

We use the Karush-Kuhn-Tucker conditions to verify optimality of the proposed solution. Since the subproblems Ot(c) are linear, the KKT conditions are necessary and suﬃcient for the unique optimum. The Lagrangian of the sub problems Ot(c) has the form:

L (g(t), λ, η, µ) = V⊤ g(t) + λ⊤ (g c) η⊤ g(t) + µ (D(t) 1⊤ g(t)) − − − where λ is the vector of KKT multipliers associated with the constraint g(t) c, η is the ≤ vector of KKT multipliers associated with the non-negativity constraint and µ the KKT multiplier of the constraint 1⊤ g(t) D(t). It is easy to verify that the non-negative ≥ multipliers

Vm Vi > 0 if i < m Vi Vm > 0 if i > m λi = − ηi = − µ = Vm (0 else. (0 else.

satisfy complementary slackness. Furthermore ∂L = 0. ∂g(t)

3rd step. In order to complete the proof it remains to be shown that

8760 g(t)idt = I1 + I2 Z0

8760 i−1

I1 := L(t) cj 1 i i−1 (t) dt c >L(t)> c 0  −  j=1 j j=1 j Z jX=1 8760   nP P o I2 := ci 1 i (t) dt c ≤L(t) Z0 j=1 j nP o Therefore we consider I1 ﬁrst:

8760 i−1

I1 = L(t) cj 1 i i−1 (t) dt c >L(t)> c 0  −  j=1 j j=1 j Z jX=1   n o 8760 D(0) P i−P1

= 1{uL(t)> c 0 " 0 # −  j=1 j j=1 j Z Z jX=1 8760  D(0)  nP P o = 1 (u) du 1 (t) dt i−1 {uL(t) Z Z j=1 j ! j=1 i−1 n o 8760 c P P j=1 j u u c t t = i 1{u

Proposition 2 (Convexity) Program 2 is convex, i.e. the objective function

⊤ ⊤ O(c) := F c + V¯ Q(Pσc)

is a convex function on the convex subset

⊤ Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. c : 0 c c¯ 1 c D(0) . { ≤ ≤ ∧ ≥ }

129 tuwien.at/bibliothek Proof. The objective function can be rewritten as

⊤ ⊤ O(c) : = F c + (V¯ ) Q(Pσc) n D(0) = F c + (V V ) D−1(ω)dω i i i i−1 i−1 − c1 Xi=1 Z j=1 P First, we consider the function

D(0) f(x) := D−1(ω)dω, x [0,D(0)]. ∈ Zx Using Leibniz’s rule for differentiation under the integral we find the first and second derivative to be: d f(x) = D−1(x) 0, dx − ≤ d d f(x) = D−1(x) 0. dx2 −dx ≥ The first inequality holds since D−1(x) > 0 as D−1(x) [0, 8760] per definition for ∈ x [0,D(0)]. Moreover the second inequality holds as D−1(x) is monotonically decreasing ∈ per definition implying d D−1(x) < 0 for all x [0,D(0)]. Hence we conclude that f(x) dx ∈ is a monotonically decreasing, convex function. Second, we consider the functions

i−1 D(0) g (c) := f c = D−1(ω)dω. i j i−1 j  c1 X=1 Z j=1   P The functions gi(c) are a composition of the monotone convex function f(x) and the i−1 linear (hence convex) function c j cj. Therefore these are convex functions too. 7→ =1 Finally, we consider the function P

n n D(0) h(c) := (V V )g (c) = (V V ) D−1(ω)dω i i−1 i i i−1 i−1 − − c1 Xi=1 Xi=1 Z j=1 P Per deﬁnition Vi > Vi−1. Hence h(c) is a weighted sum with non-negative weights (Vi Vi ) of convex functions gi(c) and therefore convex itself. − −1 Hence we conclude that the objective function O(c) is convex as it is the sum of two n convex functions i=1 Fi ci, which is even linear and h(c). P Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

130 tuwien.at/bibliothek A.2 Modern Portfolio Theory

Proposition 3 (Deterministic equivalent form) The optimal solutions for the decision variables c of Program 6 and Program 7 coincide.

Proof. According to Proposition 1, Program 6 may be rewritten in the form:

⊤ ⊤ β ⊤ min F c + E (PπV) Q(Pπc + Var (PπV) Q(Pπc) c 2 s.t. 0 c c¯ ≤ ≤ such that the optimal capacities c coincide with those of the original formulation. For ⊤ evaluating the expectation and variance of the variable costs (PπV) Q(Pπc), the law of total variance as well as the law of total expectation can be used. Therefore we introduce the set of events

Mπ := V (ω) < V (ω) < < V (ω) , { π(1) π(2) ··· π(n)}

or all permutations π n. For any continuous distribution of V, this set forms a ∈ P partition M of the sample space as

P Mπ = 1, P(Mξ Mζ ) = 0, ξ, ζ n and P(Mπ) > 0,   ∩ ∀ ∈ P π∈P[n   So we may use the laws of total variance and expectation to ﬁnd:

⊤ ⊤ ⊤ Var[(PπV) Q(Pπc)] = E(Var[(PπV) Q(Pπc) M]) + Var(E[(PπV) Q(Pπc) M]). | | ⊤ ⊤ E[(PπV) Q(Pπc)] = E[PπV) Q(Pπc) M]. |

Since Pπ and Q(Pπc) are M measurable we may simplify these expressions to arrive at:

⊤ ⊤ Var[(PπV) Q(Pπc)] = E((Pπ Var[V M]) Q(Pπc)) | ⊤ ⊤ + Q(Pπc) Pπ Var(E[V M]) P Q(Pπc) | π ⊤ ⊤ E[(PπV) Q(Pπc)] =Q(Pπc) Pπ E[V M] |

yielding the result. Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

131 tuwien.at/bibliothek Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. tuwien.at/bibliothek The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. List of Figures

1.1 Share of citizens supplied by district heating per country in the European Union (2013) ...... 2

2.1 Simplified illustration of a DH system ...... 10 2.2 Daily maximum and minimum DH load of the Vienna DH system (2012) . . 11 2.3 Joint density of outside temperature and DH load in Vienna (2012–2014) . . 12 2.4 Load duration curve and classification of load levels into base, intermediate and peak load for Vienna (2012–2014) ...... 15 2.5 Share of DH generation by CHP plants in several EU member countries (2013) 16 2.6 DH generation by fuel input for CHP plants and HOBs in Austria (1970–2014) 17 2.7 Simplified illustration of an open cycle gas turbine CHP plant ...... 18 2.8 Simplified illustration of a steam turbine CHP plant ...... 19 2.9 Share of installed capacities per heat source of DH compressor heat pumps in Europe ...... 23 2.10 Range of minimum and maximum COPs of compressor heat pumps . . . . . 29 2.11 Average failure rate for different numbers drilled wells for geothermal DH projects ...... 34

3.1 Monthly average Austrian border price of natural gas (2002-2015) ...... 36 3.2 Monthly average prices of fuel oil in Austria (2005–2015) ...... 37 3.3 Monthly average EUA spot market prices at EEX (2005-2015) ...... 38 3.4 Monthly average prices of wood chips and saw dust delivered to sawmills in Austria (2002–2015) ...... 40 3.5 Monthly average spot-market prices for electricity at EXAA (2002–2015) . . 40 3.6 Sample paths of a GBM for modeling future wood chip prices ...... 45 3.7 Density function of the levelized price distribution of wood chips ...... 47 3.8 Average grid usage fees for natural gas transmission with connection to the high-pressure gas network in Austria (2015) ...... 48 3.9 Locations of uniformly distributed biomass sources around a DH plant . . . . 50

4.1 Variable costs of a CCGT CHP plant for different electricity prices and a fixed natural gas price ...... 58 Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. 4.2 Share of fixed costs of a CCGT CHP plant allocated to DH generation for different electricity prices and a fixed natural gas price ...... 59

133 tuwien.at/bibliothek 4.3 LCOH and screening curve geothermal DH and a natural gas HOB ...... 63

5.1 Load duration curve D(t) with notation for the GEP with merit-order dispatching 72 5.2 Equidistant discretisation of the LDC D(t) into 3 load blocks with corresponding load factors ...... 75 5.3 One-segment model for a FOR of an extraction-type CHP plant ...... 78 5.4 Monthly average prices of fuel oil in Austria ...... 79 5.5 Typical start-up costs of CHP technologies for diﬀerent shut-down times . . . 82 5.6 LCOH for diﬀerent technologies based on 5.000 full load hours ...... 85

6.1 Area of feasible portfolios and the eﬃcient frontier ...... 90

7.1 Annual DH generation of Austrian DH systems ...... 100 7.2 Feasible operation regions of all seven CHP plants located in Vienna, Linz and Graz ...... 105 7.3 Interquartile ranges of input energy prices and expected future prices in the Current Policies Scenario ...... 112 7.4 Generation portfolio selection for the Vienna DH system ...... 116 7.5 Expected DH generation for the Vienna DH system in 2030 ...... 117 7.6 Generation portfolio selection for the Linz DH system in 2030 ...... 118 7.7 Expected DH generation for the Linz DH system in 2030 ...... 119 7.8 Generation portfolio selection for the Graz DH system in 2030 ...... 120 7.9 Expected DH generation for the Graz DH system in 2030 ...... 121 Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

134 tuwien.at/bibliothek List of Tables

2.1 Non-linear OLS regression coeﬃcients of the parametric LDC model for Vienna 15 2.2 Steam turbine CHP plants with more than 100 GWhth of yearly DH generation in Austria ...... 20 2.3 CCGT CHP plants with more than 200 GWhth of yearly DH generation in Austria ...... 21 2.4 Waste heat from incineration in Austrian DH systems ...... 22 2.5 Industrial waste heat in Austrian DH systems ...... 22 2.6 Geothermal DH facilities in Austria (2015) ...... 26 2.7 Solar heat facilities in urban Austrian DH systems (2014) ...... 27 2.8 Energy conversion eﬃciencies of HOB and CHP in Austria (2014) ...... 28 2.9 Range of typical COPs of compressor heat pumps ...... 28 2.10 Billing characteristics and main components of the four DH generation cost categories ...... 31 2.11 Financial data of large-scale DH plant technologies...... 32 2.12 Financial data of large-scale non-combustible DH plant technologies...... 33 2.13 Financial data of large-scale DH heat pump technologies...... 33

3.1 Natural gas prices for diﬀerent amounts of yearly consumptions (2015) . . . . 37 3.2 Statistical characteristics of DH input energy price returns (2002-2015) . . . . 41 3.3 Observed p-values of the Jarque-Bera and Shapiro-Wilk tests on normality and Ljung-Box tests on independence for the returns of yearly average DH input energy prices including EUA (2002–2015) ...... 43 3.4 Null and alternative hypotheses as well as the observed p-values for the F- and t-tests corresponding to the stylized facts ...... 43 3.5 Marginal grid usage fees for natural gas transmission with connection to the high-pressure gas network in Austria (2015) ...... 48 3.6 Transportation costs for one MWhLHV of wood chips ...... 49 3.7 Taxes for the consumption of diﬀerent DH fuels in Austria ...... 52

4.1 Financial parameters required for defining fixed and variable costs for a single DH plant ...... 54 Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. 4.2 Technical parameters required for computing fixed and variable costs for a single DH plant ...... 55

135 tuwien.at/bibliothek 4.3 Revenues for diﬀerent products of a Municipal Solid Waste incineration facility 60

5.1 Typical relative minimum load levels for different DH technologies ...... 77 5.2 Characteristics of the extreme operating points (OP) of a CHP plant . . . . . 77 5.3 Typical part load efficiency factors FPL of different CHP technologies . . . . 79 5.4 Characteristics of the extreme operating points (OP) of a CHP plant when accounting for off-design behaviour ...... 80 5.5 Typical start-up costs of CHP technologies for different shut-down times . . . 81 5.6 Load factors of DH plant with and without including flexibility modeling . . 86

6.1 Different definitions for the economic profitability measure R ...... 88

7.1 Technical characteristics of the three largest urban DH systems in Austria . . 101 7.2 Characteristics of the wood chip steam turbine CHP plants in Vienna and Linz102 7.3 Installed DH capacities in MWth of fossil fuel combustion plants in Vienna, Linz and Graz ...... 103 7.4 Technical characteristics of natural gas ﬁred CHP plants in Vienna and Linz 105 7.5 Supply by waste heat sources in GWhth for large-scale DH systems in Austria 106 7.6 Potentials for heat pumps in the DH systems of Vienna, Linz and Graz. . . . 109 7.7 Expected prices of input energy in 2040 according to the Current Policies Scenario...... 112 7.8 Input parameters for the computation of the distribution of the levelized input energy prices ...... 112 7.9 Maximum DH load D(0) and required DH capacity in 2030 ...... 114 Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

136 tuwien.at/bibliothek Bibliography

[1] M. Abbott, The Economics of the Gas Supply Industry, Taylor & Francis, 2016. 36 [2] M. Ableidinger, Arbter, W. H. Hauer, W. Rogalski, S. Sciri, and U. Volk, Wiener Abfallwirtschaftskonzept 2007: Anhang 1: Ist-Zustand der Wiener Abfallwirtschaft, Magistratsabteilung 48 - Abfallwirtschaft Straßenreinigung und Fuhrpark, 2007. https://www.wien.gv.at/umwelt/ma48/service/ pdf/ist-zustand2007.pdf. 106 [3] G. Adelberger, Abwasser als Energiequelle für Stadtwerke Am- stetten und deren Kraftwerk, 2016. Presentation: http://www. abwasserenergie.at/fileadmin/energie_aus_abwasser/user_ upload/AbwasserEnergieStadtwerke_20120327.pdf. 25 [4] E. Ahlgren, District Heating, Energy Technology Systems Analysis Pro- gram (ETSAP), E16 (2013). https://iea-etsap.org/E-TechDS/PDF/E16_ DistrHeat_EA_Final_Jan2013_GSOK.pdf. 16, 18, 22, 23 [5] C. Algie and Kit Po Wong, A test system for combined heat and power economic dispatch problems, in 2004 IEEE International Conference on Electric Utility Deregulation, Restructuring and Power Technologies. Proceedings, 2004, pp. 96–101. 78 [6] B. Alizadeh and S. Jadid, Reliability constrained coordination of generation and transmission expansion planning in power systems using mixed integer programming, IET Generation, Transmission & Distribution, 5 (2011), pp. 948–960. 76 [7] D. Anderson, Models for Determining Least-Cost Investments in Electricity Supply, The Bell Journal of Economics and Management Science, 3 (1972), pp. 267– 299. 68, 69, 70, 84 [8] S. Armitage, The Cost of Capital: Intermediate Theory, Cambridge University Press, 2005. 33, 34 [9] J. M. Arroyo and A. J. Conejo, Optimal response of a thermal unit to an Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. electricity spot market, IEEE Transactions on Power Systems, 15 (2000), pp. 1098– 1104. 85

137 tuwien.at/bibliothek [10] F. Asche, P. Osmundsen, and M. Sandsmark, The UK Market for Natural Gas, Oil and Electricity: Are the Prices Decoupled?, The Energy Journal, 27 (2006), pp. 27–40. 41

[11] P. A. Avato, N. Basarir, G. Beardsmore, M. Gehringer, Geother- mEx, T. Harding-Newman, C. Harvey, S. Jacob, Kasumi Yasukawa, O. S. Mertoglu, A. Pantelias, L. Rybach, H. Rüter, and M. Tönnis, Geothermal exploration best practices: guide to resource data collection, analysis, and presentation for geothermal projects, The World Bank Group, 2013. http: //documents.worldbank.org/curated/en/418111468350105471/ pdf/782280WP0IFC0I0Box0377330B00PUBLIC0.pdf. 34

[12] H. Averfalk, P. Ingvarsson, U. Persson, and S. Werner, On the use of surplus electricity in district heating systems, in Symposium on District Heating and Cooling, Swedish District Heating Association, 2014, pp. 469–474. 23

[13] S. Awerbuch and M. Berger, Applying portfolio theory to EU electricity planning and policy making, IAEA/EET Working Paper No. 03, (2003). 5, 87, 88

[14] G. A. Bakirtzis, P. N. Biskas, and V. Chatziathanasiou, Generation Expansion Planning by MILP considering mid-term scheduling decisions, Electric Power Systems Research, 86 (2012), pp. 98–112. 76

[15] D. Bar-Lev and S. Katz, A Portfolio Approach to Fossil Fuel Procurement in the Electric Utility Industry, The Journal of Finance, 31 (1976), p. 933. 4, 87

[16] D. P. Baron, On the Utility Theoretic Foundations of Mean–Variance Analysis, The Journal of Finance, 32 (1977), pp. 1683–1697. 91

[17] F. Beglari and M. A. Laughton, The combined costs method for optimal economic planning of an electrical power system, IEEE Transactions on Power Apparatus and Systems, 94 (1975), pp. 1935–1942. 74, 75

[18] M. Berger, Portfolio analysis of EU electricity generating mixes and its implica- tions for renewables, Technische Universität Wien, 2003. PhD Thesis. 88

[19] M. J. Best, Portfolio Optimization, Taylor & Francis, 2010. 88, 89

[20] Biomasseverband OÖ, Masse und Energieinhalt von Hackgut in Abhängigkeit vom Wassergehalt, 2016. https://www.biomasseverband-ooe.at/ uploads/media/Downloads/Publikationen/Umrechnungstabellen_ Brennstoff_Holz-BMV-OOe.pdf. 39, 40

[21] BIOS Bioenergiesysteme, Kurzinformation und Referenzen zum Unternehmen BIOS Bioenergiesysteme GmbH, 2014. https://www.bios-bioenergy.at/ Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. uploads/media/Firmeninfo-Ueberblick-inkl-Referenzen-DE.pdf. 25

138 tuwien.at/bibliothek [22] Black & Veatch, Cost and Performance Data for Power Generation Technologies. Prepared for the National Renewable Energy Laboratory, 2012. https://www.bv. com/docs/reports-studies/nrel-cost-report.pdf. 77

[23] S. Böhmer and M. Gössl, Optimierung und Ausbau von Fernwärmesystemen, Umweltbundesamt: REP-0074, 2009. http://www.umweltbundesamt.at/ fileadmin/site/publikationen/REP0074.pdf. 103, 105

[24] S. Böhmer, M. Gössl, C. Nagl, and W. Spangl, Analyse Fern- wärmeversorgung Graz, Umweltbundesamt: REP-0549, 2015. http://www. umweltbundesamt.at/fileadmin/site/publikationen/REP0549.pdf. 106

[25] S. Böhmer, I. Kügler, H. Stoiber, and B. Walter, Abfallverbrennung in Österreich: Statusbericht 2006, Umweltbundesamt: REP-0113, 2007. http://www. umweltbundesamt.at/fileadmin/site/publikationen/REP0113.pdf. 21

[26] S. Böhmer, I. Schindler, I. Szednyj, and B. Winter, Stand der Technik bei Kalorischen Kraftwerken und Referenzanlagen in Österreich, Umweltbundesamt: M- 162, 2003. www.umweltbundesamt.at/fileadmin/site/publikationen/ M162.pdf. 20, 103, 104, 105

[27] G. Bucar, K. Schweyer, C. Fink, R. Riva, M. Neuhäuser, E. Meiss- ner, W. Streicher, and C. Halmdienst, Dezentrale erneuerbare Energie für bestehende Fernwärmenetze, Bundesministerium für Verkehr, Innovation und Technologie. Berichte aus Energie- und Umweltforschung: Schriftenreihe 78/2006, 2005. https://nachhaltigwirtschaften.at/resources/edz_ pdf/0678_dezentrale_energieerzeugung_fuer_fernwaerme.pdf?m= 1469660750. 24, 63

[28] R. Büchele, Implementierung eines Investitions- und Optimierungsmodells zur kostenminimalen Jahresdeckung des Strom- und Wärmebedarfs innerhalb eines regionalen Energieparks: Beispielregion Wien, Technische Universität Wien, 2013. Master Thesis. 4, 76

[29] R. Büchele, R. Haas, M. Hartner, R. Hirner, M. Hummel, L. Kranzl, A. Müller, K. Ponweiser, M. Bons, K. Grave, E. Slingerland, Y. Deng, and K. Blok, Bewertung des Potenzials für den Einsatz der hocheﬃzienten KWK und eﬃzienter Fernwärme-und Fernkälteversorgung, 2015. https://ec.europa.eu/energy/sites/ener/files/documents/ Austria_MNE%282016%2950514.pdf. 16, 18, 61, 101

[30] Bundesgesetz (Konsolidierte Fassung), Erdgasabgabegesetz, 1996– Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. 2003. https://www.ris.bka.gv.at/GeltendeFassung.wxe?Abfrage= Bundesnormen&Gesetzesnummer=10005028. 51

139 tuwien.at/bibliothek [31] , Elektrizitätsabgabegesetz, 1996–2014. https://www.ris.bka.gv.at/ GeltendeFassung.wxe?Abfrage=Bundesnormen&Gesetzesnummer= 10005027. 51 [32] Bundesholzwirtschaftsrat, Holz-Kurier: unabhängig, tagesaktuell, international, Österreichischer Agrarverlag, 2002–2015. 39, 40 [33] Bundesministerium für Nachhaltigkeit und Tourismus, eHYD: Hydro- graphischen Archiv Österreich, 2018. https://ehyd.gv.at/. 109 [34] J. Burke, Markowitz Mean-Variance Portfolio Theory, University of Washing- ton, 2003. Lecture Notes: https://sites.math.washington.edu/~burke/ crs/408/fin-proj/mark1.pdf. 88 [35] R. Byrd, P. Lu, J. Nocedal, and C. Zhu, A limited memory algorithm for bound constrained optimization, SIAM Journal on Scientiﬁc Computing, 16 (1995), pp. 1190–1208. 95 [36] C. Batlle and P. Rodilla, An Enhanced Screening Curves Method for Consid- ering Thermal Cycling Operation Costs in Generation Expansion Planning, IEEE Transactions on Power Systems, 28 (2013), pp. 3683–3691. 86 [37] F. A. Campos, J. Villar, and C. Cervilla, Proﬁtability measures and cost minimization in electricity generation investments, in Conference Proceedings of the 12th International Conference on the European Energy Market, 2015. 62, 89 [38] R. Castellano and R. Cerqueti, Optimal Fuel Mix for Power Generation: hedging with renewables, in IV CICSE Conference "Structural Change, Dynamics, and Economic Growth", 2013. https://editorialexpress.com/cgi-bin/ conference/download.cgi?db_name=STCHANGE&paper_id=59. 92 [39] CEN/CENELEC, Manual for Determination of Combined Heat and Power (CHP), Workshop Agreement CWA 45547, 2004. 30, 51 [40] G. Chamberlain, A characterization of the distributions that imply mean— Variance utility functions, Journal of Economic Theory, 29 (1983), pp. 185–201. 91 [41] M. Chaudry, M. Abeysekera, S. H. R. Hosseini, N. Jenkins, and J. Wu, Uncertainties in decarbonising heat in the uk, Energy Policy, 87 (2015), pp. 623 – 640. 86 [42] J. Choi and K. Kim, The derivatives of Asian call option prices, arXiv preprint arXiv:0712.1093, (2007). 47 [43] B. Cociancig, Altheim in Upper Austria – an example of cascaded geothermal energy use, Geothermal Workshop Veli Lošinj, 2014. Presentation: https: Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. //www.fondazioneinternazionale.org/wp-content/uploads/2014/ 08/2014_Cociancig_Altheim_MND-Group_Hodonin-CZ.pdf. 26

140 tuwien.at/bibliothek [44] E. Commission, Eu emissions trading system (eu ets), 2019. https://ec. europa.eu/clima/policies/ets_en. 38

[45] W. H. Comtois, Economy of scale in power plants, Power Engineering, 1977 (1977), pp. 51–53. 31

[46] D. Connolly, H. Lund, B. V. Mathiesen, S. Werner, B. Möller, U. Pers- son, T. Boermans, D. Trier, P. A. Østergaard, and S. Nielsen, Heat Roadmap Europe: Combining district heating with heat savings to decarbonise the EU energy system, Energy Policy, 65 (2014), pp. 475–489. 1, 23

[47] A. J. Covarrubias, Expansion planning for electric power systems, IAEA Bulletin, 21 (1984), pp. 55–64. 72

[48] M. A. Crew and P. R. Kleindorfer, Optimal plant mix in peak load pricing, Scottish Journal of Political Economy, 22 (1975), pp. 277–291. 75

[49] A. David, Large heat pumps in European district heating systems, 2016. https://www.euroheat.org/wp-content/uploads/2016/04/ 160420_1600_1730_2nd-place_Andrei-David_presentation.pdf. 23

[50] A. David, B. V. Mathiesen, H. Averfalk, S. Werner, and H. Lund, Heat Roadmap Europe: Large-Scale Electric Heat Pumps in District Heating Systems, Energies, 10 (2017), p. 578. 23

[51] E. Delarue, C. d. Jonghe, R. Belmans, and W. D’haeseleer, Applying portfolio theory to the electricity sector: Energy versus power, Energy Economics, 33 (2011), pp. 12–23. 6, 91, 95

[52] G. Dell, Umsetzung des O.Ö. Energiekonzeptes: Berichtsjahr 2009, Land Oberösterreich, 2010. https://www.energiesparverband.at/ fileadmin/redakteure/ESV/Info_und_Service/Publikationen/ Umsetzungsbericht09.pdf. 100

[53] R. Doležal, Kombinierte Gas- und Dampfkraftwerke, Springer Berlin Heidelberg, Berlin, Heidelberg, 2001. 79

[54] P. Drucker, Großwärmespeicher mit Großwärmepumpen für die Stadt Linz – Vision oder ein zukünftiges urbanes Konzept?, VDI-Forum 2015, Linz, 2015. Presentation. 26, 109

[55] M. Dutta, Cost Accounting: Principles And Practice, Pearson Education, 2004. 56 Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. [56] I. Dyner and E. R. Larsen, From planning to strategy in the electricity industry, Energy Policy, 29 (2001), pp. 1145–1154. 85

141 tuwien.at/bibliothek [57] E-Control, Neuer Anreiz - Tarif für bessere Wettbewerbsfähigkeit der Gaskraftwerke: Die wegen Unwirtschaftlichkeit in die Schlagzeilen geratenen Gaskraftwerke sollen mit einem neuen Tarif wieder ﬁt gemacht werden., 2013. Press note: https://www.e-control.at/documents/20903/-/-/695f0b5f- 73f0-4ee0-b301-6aacb309d911. 49

[58] , Regulierungssystematik für die dritte Regulierungsperiode der Stromverteilernetzbetreiber 1. Jänner 2014 - 31. Dezember 2018, 2013. https://www.e-control.at/documents/20903/-/-/225b49e0-6534- 40e4-afa1-97d83f8edbde. 33

[59] , Erdgasimportpreisindex (EIPI), 2016. https://www.e-control.at/ documents/20903/449229/Importpreisindex-Gas.xls/06374a8b- 7a63-4ea2-b33b-faeebac6db02. 36, 37

[60] , Erdgasstatistik (Marktstatistik): Regionalisierte Verbraucherstruk- tur 2015, 2016. https://www.e-control.at/documents/20903/ 637684/MStErdGas-2015_JJ2VerReg.xlsx/2045c07e-a59c-4067- 9c1a-1f3f9184cdd2. 48

[61] , Gaspreisentwicklungen:berichtsjahr 2015, 2016. https://www.e-control. at/statistik/gas/marktstatistik/preisentwicklung. 37

[62] , Statistikbrochüre 2016, 2016. https://www.e-control.at/ documents/20903/388512/e-control-statistikbroschuere- 2016.pdf/e11c5759-8bcf-4548-9c96-3df8b4a1284a. 16

[63] , Steuern und Abgaben: Gebrauchsabgabe, 2016. https://www.e- control.at/marktteilnehmer/gas/gasmarkt/gaspreis/steuern- und-abgaben/gebrauchsabgabe. 52

[64] e3 consult, Ausgleichsenergiekosten der Ökostrombilanzgruppe für Wind- kraftanlagen: Bewertung Status Quo, internationaler Vergleich und Lö- sungsansätze zur Reduzierung der Kosten. Überarbeitung und Aktualisierung 2015, Studie im Auftrag der Interessengemeinschaft Windkraft Österreich, 2015. https://www.igwindkraft.at/mmedia/download/2015.06.25/ 1435215563773437.pdf. 57

[65] C. Edler, Das österreichische Gasnetz, Technische Universität Wien, 2013. Bach- elor Thesis. 48

[66] J. Edler, Industrielle Abwärmenutzung als Vorteil für Umwelt und Wirtschaft, 7. ExpertInnentag Umweltförderungen 2016, 2016. Presenta- tion: https://www.umweltfoerderung.at/fileadmin/user_upload/ Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. pics/allgemein/News/Expertinnentag_Vortrag_Edler.pdf. 22, 106, 107

142 tuwien.at/bibliothek [67] H. Effenberger, Dampferzeugung, VDI-Buch, Springer Berlin, Berlin, 2013. 80

[68] Element Energy, Research on district heating and local approaches to heat decarbonisation, A study for the Committee on Climate Change, 2015. https://www.theccc.org.uk/wp-content/uploads/2015/ 11/Element-Energy-for-CCC-Research-on-district-heating-and- local-approaches-to-heat-decarbonisation.pdf. 32, 33

[69] Energie AG Oberösterreich Kraftwerke, Umwelterklärung für das Kraftwerk Timelkam, gemäß EG-Öko-Audit-Verordnung Nr. 1221/2009 (EMAS-Verordnung), 2014. https://www.energieag.at/2013-KW- Umwelterklaerung-Timelkam.pdf?:hp=1;2;de. 20

[70] Energie Graz, Technische Anschlussbedingungen Fernwärme für die Planung, die Errichtung, den Betrieb und die Abänderung von Wärmeübergabestatio- nen und Kundenanlagen im Versorgungsgebiet der Energie Graz GmbH & Co KG, 2011. https://www.energie-graz.at/media/well-linked- media/egg-pdf/downloads_fernwarme/technisch/Technische- Anschlussbedingungen_gesamt.pdf. 101

[71] , Geschäftsbericht 2011, 2012. 106, 107

[72] , Geschäftsbericht 2013, 2014. 101

[73] , Geschäftsbericht 2015, 2016. 101

[74] Energie Steiermark, Neues Biomasse-Heizwerk in Hart eröﬀnet: Ab sofort "grünere" Fernwärme für Großraum Graz, 2016. Press note: https: //www.ots.at/presseaussendung/OTS_20160930_OTS0089/neues- biomasse-heizwerk-in-hart-eroeffnet-ab-sofort-gruenere- fernwaerme-fuer-grossraum-graz-bild. 102

[75] Energistyrelsen and Energinet.dk, Technology Data for En- ergy Plants: Generation of Electricity and District Heating, En- ergy Storage and Energy Carrier Generation and Conversion, 2012. https://energiatalgud.ee/img_auth.php/4/42/Energinet.dk. _Technology_Data_for_Energy_Plants._2012.pdf. 16, 18, 23, 28, 29, 31, 32, 33, 77, 78, 79

[76] Energistyrelsen and Energinet.dk, Technology data for energy plants: Up- dated chapters, august 2016, 2016. ... 24, 25, 27, 29, 33, 77

[77] Energy Exchange Austria, Historische Daten: Marktdaten, 2002–2015. https: //www.exaa.at/de/marktdaten/historische-daten. 40 Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. [78] ENTSO-E, ENTSO-E Overview of Transmission Tariﬀs in Europe: Synthesis 2016, 2017. https://docstore.entsoe.eu/Documents/MC%20documents/

143 tuwien.at/bibliothek ENTSO-E_Transmission%20Tariffs%20Overview_Synthesis2016_ UPDATED_Final.pdf. 57

[79] Erkenntnis (Verwaltungsgerichtshof), Geschäftszahl 2011/17/0096, 2012. http://www.ris.bka.gv.at/Dokumente/Vwgh/JWR_2011170096_ 20120925X02/JWR_2011170096_20120925X02.pdf. 51

[80] Euroheat & Power, Statistics Overview – Country by country / 2015 Sur- vey, 2015. https://www.euroheat.org/wp-content/uploads/2016/03/ 2015-Country-by-country-Statistics-Overview.pdf. 1, 2, 16

[81] European Central Bank, Harmonised Index of Consumer Prices (HICP), 2016. https://www.ecb.europa.eu/stats/macroeconomic_ and_sectoral/hicp/html/index.en.html. 32, 33, 36, 37, 38, 40, 49, 60, 81

[82] EVN Abfallverwertung Niederösterreich, EVN Abfallverwertung Niederösterreich MVA Dürnrohr: Umwelterklärung 2015, 2016. 22

[83] EVN AG and VERBUND Thermal Power, Umwelterklärung 2012 für den Standort Karftwerk Dürnrohr, 2013. 22, 61

[84] I. Evstigneev, T. Hens, and K. R. Schenk-Hoppé, Mathematical Financial Economics: A Basic Introduction, Springer International Publishing, 2015. 88, 89

[85] Fachverband der Gas- und Wärmeversorgungsunternehmungen, Zahlen- spiegel 2016: Erdgas und Fernwärme in Österreich, Wirtschaftskammer Österreich, 2016. https://www.fernwaerme.at/media/uploads/misc/ zahlenspiegel_2016.pdf. 36

[86] Fachverband der Mineralölindustrie, Jahresberichte, Wirtschaftskam- mer Österreich, 2005–2015. https://www.wko.at/branchen/industrie/ mineraloelindustrie/jahresberichte.html. 37

[87] M. Fenz, Erweiterung eines Investitions- und Optimierungsmodells zur kostenminimalen Strom-, Wärme- und Kälteversorgung mit Fokus auf Fernwärmeausbau und CO2-Emissionen : Beispielregionen Graz und Salzburg, Technische Universität Wien, 2015. Master Thesis. 4

[88] M. Fiala, G. Pellizzi, and G. Riva, A model for the optimal dimensioning of biomass-fuelled electric power plants, Journal of Agricultural Engineering Research, 67 (1997), pp. 17–25. 49

[89] K. Fischer and C. Rosenkranz, Handbuch Energiepolitik Österreich, LIT Verlag Münster, 2012. 39

[90] Forschungszentrum Energie und Umwelt, Urbanes Energie- und Mobil- Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. itätssystem (URBEM), Technische Universität Wien, 2013. https://urbem. tuwien.ac.at/home/. 3

144 tuwien.at/bibliothek [91] C. A. Frangopoulos, A method to determine the power to heat ratio, the cogenerated electricity and the primary energy savings of cogeneration systems after the European Directive, Energy, 45 (2012), pp. 52–61. 28

[92] S. Fritz, Economic assessment of the long-term development of buildings’ heat demand and grid-bounded supply, Technische Universität Wien, 2016. PhD Thesis. 101, 111, 114

[93] G. Fusai and A. Roncoroni, Implementing Models in Quantitative Finance: Methods and Cases, Springer Berlin Heidelberg, 2007. 57

[94] G. Fusai and A. Tagliani, An accurate valuation of Asian options using moments, International Journal of Theoretical and Applied Finance, 5 (2002), pp. 147–169. 47

[95] H. Gadd and S. Werner, Heat load patterns in district heating substations, Applied Energy, 108 (2013), pp. 176–183. 10, 12

[96] N. P. G. Garcia, K. Vatopoulos, A. K. Riekkola, A. P. Lopez, and L. Olsen, Best available technologies for the heat and cooling market in the European Union, Reference Report by the Joint Research Centre of the European Commission, 2012. http://publications.jrc.ec.europa. eu/repository/bitstream/JRC72656/eur%2025407%20en%20- %20heat%20and%20cooling%20final%20report-%20online.pdf. 23

[97] R. Gatautis and H. F. Ravn, Modelling of energy supply systems by the Balmorel model, Energetika, 2 (2005), pp. 8–20. 4

[98] W. Gawlik, Kraftwerke, Technische Universität Wien, 2016. Lecture notes. 18

[99] H. Geman, Mean reversion versus random walk in oil and natural gas prices, in Advances in Mathematical ﬁnance, 2007, pp. 219–228. 44

[100] H. Geman, Commodities and Commodity Derivatives: Modeling and Pricing for Agriculturals, Metals and Energy, Wiley, 2009. 46

[101] H. Geman and M. Yor, Bessel Processes, Asian Options, and Perpetuities, Mathematical Finance, 3 (1993), pp. 349–375. 46

[102] P. Glasserman, Monte Carlo Methods in Financial Engineering, Springer New York, 2013. 44

[103] C. Gochenour, Regulation of heat and electricity produced in combined-heat- andpower plants, 2003. http://documents.worldbank.org/curated/en/ 948891468771619606/pdf/272010paper.pdf. 6, 56 Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. [104] J. Goldbrunner, Status und aktuelle Entwicklungen der Geothermie in Österreich, Berichte der Geologischen Bundesanstalt, 92 (2012). 26, 108, 113

145 tuwien.at/bibliothek [105] , Austria – Country Update: Melbourne, Australia, 19-25 April 2015, in Proceedings World Geothermal Congress 2015, 2015. 26

[106] D. Goldfarb and A. Idnani, A numerically stable dual method for solving strictly convex quadratic programs, Mathematical programming, 27 (1983), pp. 1–33. 94

[107] M. Golser, K. P. Nemestothy, and R. Schnabel, Methoden zur Übernahme von Energieholz, Holzforschung Austria and Energieverwer- tungsagentur, 2004. https://www.forstholzpapier.at/images/FHP- Arbeitskreise_/AK_Energie/Methoden_Energieholz_2004.pdf. 39

[108] V. Goodship, Management, Recycling and Reuse of Waste Composites, Elsevier Science, 2009. 60

[109] Goswami, D. Yogi Goswami and Kreith, Frank, Energy Management and Conservation Handbook (Mechanical and Aerospace Engineering Series), CRC Press, 1 ed., 2007. 62, 89

[110] D. Gotham, K. Muthuraman, P. Preckel, R. Rardin, and S. Ruangpat- tana, A load factor based mean–variance analysis for fuel diversiﬁcation, Energy Economics, 31 (2009), pp. 249–256. 87, 94

[111] M. Götz, D. Böttger, H. Kondziella, and T. Bruckner, Economic Potential of the “Power-to-Heat” Technology in the 50Hertz Control Area, 2013. Presentation: https://tu-dresden.de/bu/wirtschaft/ee2/ressourcen/dateien/ lehrstuhlseiten/ordner_veranstaltungen_alt/ordner_enerday/ enerday2013/ed2013download/Gtz_Presentation.pdf?lang=de. 31

[112] M. Greller and F. Bieberbach, Entwurf eines technischen und ökologischen Strukturwandels in der Fernwärmeversorgung, Energiewirtschaftliche Tagesfragen, 65 (2015), pp. 14–17. 2

[113] W. Götzhaber, E. Meißner, G. Moravi, W. Prutsch, P. Schlemmer, R. Schmied, E. Slivniker, and M. Zimmel, Wärmeversorgung Graz 2020/2030 Wärmebereitstellung für die fernwärmeversorgten Objekte im Großraum Graz: Sta- tusbericht 2017, Grazer Energieagentur, 2017. https://www.energie- graz.at/media/wysiwyg/Unternehmen/Geschaftsbereiche/ Fernwarme/waermeversorgung-graz-statusbericht-2017.pdf. 108

[114] W. Götzhaber, E. M. Meißner, G. Moravi, B. Papousek, W. Prutsch, T. Schleifer, P. Schlemmer, R. Schmied, E. Slivniker, and M. Zimmel, Wärmeversorgung Graz 2020/2030: Ergebnisse der Fachworkshops und der Diskussionsbeiträge der Arbeitsgruppe, Grazer Energieagentur, 2014. https: //speicherinitiative.at/assets/Uploads/22-Fachworkshops- Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. Waermeversorgung-Graz-2020-2030-Ergebnisse.pdf. 26, 102, 104, 106, 109

146 tuwien.at/bibliothek [115] O. A. Hafsa and J.-P. Mandallena, Interchange of inﬁmum and integral, Calculus of Variations and Partial Diﬀerential Equations, 18 (2003), pp. 433–449. 128

[116] H. Haneder, Biomasse - Heizungserhebung 2015, 2016. https: //www.biomasseverband-ooe.at/uploads/media/Downloads/ Publikationen/Heizwerkserhebung/Biomasseheizungserhebung_ 2015.pdf. 18

[117] D. Hansen, M. Mowen, and L. Guan, Cost Management: Accounting and Control, Cengage Learning, 2007. 56

[118] T. Harding-Newman, J. Morrow, S. Sanyal, and Z. Meng, Success of Geothermal Wells: A Global Study, International Finance Corporation, World Bank Group, 2013. https://www.ifc.org/wps/wcm/connect/ 7e5eb4804fe24994b118ff23ff966f85/ifc-drilling-success- report-final.pdf?MOD=AJPERES. 34

[119] C. Harris, Electricity markets: pricing, structures and economics, John Wiley & Sons, 2011. 77, 78

[120] M. Heinrici, Repowering Simmering BKW 1/2, Fernwärmetage 2009, Linz, 2009. Presentation. 103

[121] M. Hellwig, Entwicklung und Anwendung parametrisierter Standard-Lastproﬁle, Technische Universität München, 2003. PhD Thesis. 10

[122] R. Hemmati, R. A. Hooshmand, and A. Khodabakhshian, Comprehen- sive review of generation and transmission expansion planning, IET Generation, Transmission & Distribution, 7 (2013), pp. 955–964. 76

[123] T. Hens and M. O. Rieger, Financial Economics: A Concise Introduction to Classical and Behavioral Finance, Springer Berlin Heidelberg, 2010. 88

[124] D. Hogg, Costs for Municipal Waste Management in the EU: Final Report to Directorate General Environment, European Commission, Eunomia Research & Consulting, 2002. http://ec.europa.eu/environment/waste/studies/ pdf/eucostwaste.pdf. 60

[125] M. Holter, Big Solar Graz – 245 GWh Solarenergie für die Fernwärme Graz, Highlights der Energieforschung 2016: Die Rolle der Wärmepumpe im zukünftigen Energiesystem, 2016. Presentation: https://nachhaltigwirtschaften. at/resources/iea_pdf/events/20160622_highlights_der_ energieforschung_2016_vortrag_holter.pdf?m=1469661474. 108 Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. [126] Y.-H. Huang and J.-H. Wu, A portfolio risk analysis on electricity supply planning, Energy Policy, 36 (2008), pp. 627–641. 6, 91, 94, 95

147 tuwien.at/bibliothek [127] M. Hummel, L. Kranzl, and C. Villotti, Assessment of the economic viability of the integration of industrial waste heat into existing grids, in Proceedings of the ECEEE 2014 Industrial Summer Study on Retool for a competitive and sustainable industry, 2014, pp. 537–545. 22

[128] S. M. Iacus, Option Pricing and Estimation of Financial Models with R, Wiley, 2011. 45

[129] International Atomic Energy Agency, Wien Automatic System Planning (WASP) Package: A computer Code for Power System Expansion Planning, Computer Manual Series No. 16, 2001. https://www-pub.iaea.org/MTCD/ Publications/PDF/CMS-16.pdf. 3

[130] International Energy Agency, Power generation assumptions in the new policies and 450 scenarios in the world energy outlook 2016, 2016. Supplement Excel Sheet. 32

[131] J. C. Jansen, L. Beurskens, and X. Van Tilburg, Application of portfolio analysis to the Dutch generating mix, Energy research Center at the Netherlands (ECN) report C-05-100, 2006. 88

[132] C. M. Jarque and A. K. Bera, Eﬃcient tests for normality, homoscedasticity and serial independence of regression residuals, Economics letters, 6 (1980), pp. 255– 259. 42

[133] , A test for normality of observations and regression residuals, International Statistical Review/Revue Internationale de Statistique, (1987), pp. 163–172. 42

[134] B. M. Jenkins, A comment on the optimal sizing of a biomass utilization facility under constant and variable cost scaling, Biomass and Bioenergy, 13 (1997), pp. 1–9. 49

[135] S. Jin, S. M. Ryan, J.-P. Watson, and D. L. Woodruff, Modeling and solving a large-scale generation expansion planning problem under uncertainty, Energy Systems, 2 (2011), pp. 209–242. 41, 45

[136] E. Johnson, Second Life, Living Energy, 3 (2010), pp. 44–49. 103, 105

[137] D. Johnstone and D. Lindley, Mean–Variance and Expected Utility: The Borch Paradox, Statistical Science, 28 (2013), pp. 223–237. 87

[138] Joint Research Centre of the European Commission, ETRI 2014 - En- ergy Technology Reference Indicator projections for 2010-2050, vol. 92496 of JRC, Publications Oﬃce of the European Union, 2014. https://setis.ec.europa. eu/system/files/ETRI_2014.pdf. 31, 32, 58 Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. [139] N. Ju, Pricing Asian and basket options via Taylor expansion, Journal of Compu- tational Finance, 5 (2002), pp. 79–103. 47

148 tuwien.at/bibliothek [140] M. Kaltschmitt, H. Hartmann, and H. Hofbauer, Energie aus Biomasse: Grundlagen, Techniken und Verfahren, Springer Berlin Heidelberg, 2016. 39, 40

[141] KELAG Wärme, Grüne Wärme aus Arnoldstein für Villach, 2016. Press Note: https://www.fernwaerme.at/aktuell/140/. 22, 61

[142] T. Kerr, Combined heat and power – Evaluating the beneﬁts if greater global investment., International Energy Agency, 2008. http://www.iea.org/ publications/freepublications/publication/chp_report.pdf. 16

[143] N. V. Khartchenko and V. M. Kharchenko, Advanced Energy Systems, Second Edition, Taylor & Francis, 2013. 18, 19, 20

[144] H. Khatib, Economic Evaluation of Projects in the Electricity Supply Industry, Institution of Engineering and Technology, 2003. 55

[145] F. C. Knopf, Modeling, Analysis and Optimization of Process and Energy Systems, Wiley, 2011. 78

[146] J. Koch, Optimierung der Strom- und Wärmeproduktion in der MVA Spittelau, Montanuniversität Leoben, 2008. Master Thesis. 107

[147] P. Konstantin, Praxisbuch Energiewirtschaft: Energieumwandlung, -transport und -beschaﬀung im liberalisierten Markt, Springer Berlin Heidelberg, 2013. 36, 37

[148] M. Kotschan, Das Geothermiezentrum Aspern: Erschließung einer nachhaltigen Energiequelle für Wien, in Tagungsband 5. PM-Bau Symposium 2011, 2011, pp. 42– 45. 108

[149] , Energie aus Wien für Wien - Die Geothermie als nachhaltiger Baustein in der Wiener Wärmeversorgung, 3. GGSC Erfahrungsaustausch Kom- munale Geothermieprojekte, 2012. Presentation: https://www.ggsc- seminare.de/pdf/2012_04_geothermie/06_kotschan_energie_aus_ wien_fuer_wien_2012-04-19.pdf. 108

[150] R. M. Kovacevic, G. C. Pflug, and M. T. Vespucci, Handbook of Risk Management in Energy Production and Trading, International Series in Operations Research & Management Science, Springer, New York, 2013. 44

[151] K. Kratena, M. Sommer, U. Eysin, and K. Rose, Energieszenarien 2050: Herausforderungen an die österreichische Energiewirtschaft, Österreichisches Institut für Wirtschaftsforschung, Strategy Lab, 2014. https://www.wifo.ac. at/jart/prj3/wifo/resources/person_dokument/person_dokument. jart?publikationsid=47185&mime_type=application/pdf. 111, 112

[152] C. Kristöfel, U. B. Morawetz, C. Strasser, and E. Schmid, Price cointe- Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. gration in the Austrian wood fuel market, in ETA-Florence Renewable Energies, 22nd European Biomass Conference and Exhibition, 2014, pp. 1330–1335. 39

149 tuwien.at/bibliothek [153] C. Kristöfel, C. Strasser, U. B. Morawetz, J. Schmidt, and E. Schmid, Analysis of woody biomass commodity price volatility in Austria, Biomass and Bioenergy, 65 (2014), pp. 112–124. 41 [154] M. Kühmaier, C. Kanzian, F. Holzleitner, and K. Stampfer, Wertschöp- fungskette Waldhackgut – Optimierung von Ernte, Transport und Logistik, in 2. Energietagung Raumberg-Gumpenstein 2010, 2010, p. 47 – 56. 49 [155] N. Kumar, P. Besuner, S. Lefton, D. Agan, and D. Hilleman, Power plant cycling costs, Intertek APTECH, 2012. https://www.nrel.gov/docs/ fy12osti/55433.pdf. 81 [156] U. Kutschera, B. Winter, S. Böhmer, H. Fallmann, C. Nagl, I. Schindler, K. Jamek, M. Scheibengraf, C. Schramm, I. Roder, H. Wiesenberger, A. Riss, R. Baumann, W. Spangl, I. Offenthaler, D. Müller, S. Weihs, P. Weiss, S. Aichmayer, B. Karigl, A. Aschauer, G. Sonderegger, J. Schneider, I. Szednyj, A. Chovanec, M. Tiefenbach, A. Freudenschuß, N. Glas, A. Hanus-Illnar, J. Grath, S. Hackl, W. Vo- gel, and B. Sebesta, Medienübergreifende Umweltkontrolle in ausgewählten Gebieten, Umweltbundesamt: M-168, 2004. http://www.umweltbundesamt. at/fileadmin/site/publikationen/M168.pdf. 106 [157] K. Kyounghee, Moment Generating Function of the Reciprocal of an Integral of Geometric Brownian Motion, Proceedings of the American Mathematical Society, 132 (2004), pp. 2753–2759. 47 [158] A. Lagger, V. Schalk, F. Sommer, A. Spreitzer, and C. Timmerer, En- ergieversorgung Region Schwechat, Institut für Verkehrssystemplanung – Technische Universität Wien, 2011. Project Work. 106 [159] R. Lahdelma and H. Hakonen, An eﬃcient linear programming algorithm for combined heat and power production, European Journal of Operational Research, 148 (2003), pp. 141–151. 77, 80, 84 [160] P. Lako, Combined Heat and Power, Energy Technology Systems Analysis Program (ETSAP), E04 (2010). https://iea-etsap.org/E-TechDS/PDF/E04-CHP- GS-gct_ADfinal.pdf. 16, 32 [161] , Geothermal Heat and Power, Energy Technology Systems Analysis Pro- gram (ETSAP), E07 (2010). https://iea-etsap.org/E-TechDS/PDF/E07- geoth_energy-GS-gct_ADfinal_gs.pdf. 26, 33 [162] D. C. LeBlanc, Statistics: Concepts and Applications for Science, vol. Bd. 2, Jones and Bartlett, 2004. 42 [163] N. Levin and J. Zahavi, Optimal mix algorithms with existing units, IEEE Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. Transactions on Power Apparatus and Systems, PAS-103 (1984), pp. 954–962. 71, 72

150 tuwien.at/bibliothek [164] E. Levy, Pricing European average rate currency options, Journal of International Money and Finance, 11 (1992), pp. 474–491. 47

[165] Linz AG, Eröﬀnung Fernheizkraftwerk Linz-Mitte NEU: Informationsunterlage zur LINZ-AG-Pressekonferenz, 2005. Press note: http://www.linz.gv.at/ presse/2005/200503_12603.asp. 105

[166] , Fernwärme aus Biomasse – Linz nimmt als erste Landeshauptstadt Öster- reichs ein Biomassekraftwerk in Betrieb: Informationsunterlage zur LINZ-AG- Pressekonferenz, 2005. Press note: http://www.linz.gv.at/presse/2005/ 200512_13347.asp. 102

[167] , Fernheizkraftwerk Linz-Süd, 2006. Information Brochure. 104, 105

[168] , Zweite Kraftwerkslinie im Fernheizkraftwerk Linz-Mitte wird eröﬀnet: In- formationsunterlage zur LINZ-AG-Pressekonferenz, 2010. Pressnote:http: //www.linz.gv.at/images/ko-kraftwerkslinie.pdf. 105

[169] , Fernwärme ist nicht zu (s)toppen, am punkt, 1 (2013), p. 10. 21, 101, 102, 103

[170] , Geschäftsbericht 2015, 2016. https://www.linzag.at/media/ dokumente/infomaterial_2/geschaeftsbericht-linzag-2015.pdf. 20, 21, 22, 101, 102, 103, 106, 107

[171] , Linzer Fernwärme-Oﬀensive – eine Erfolgsgeschichte! 70.000 Linzer Wohnungen an das LINZ AG-Fernwärmenetz angeschlossen, 2016. Press note: http://www.linz.gv.at/presse/2016/201604_82610.asp. 101

[172] , Die Kraftwerke der LINZ AG: Eﬃziente, umweltschonende Energieerzeugung, 2018. https://www.linzag.at//media/dokumente/linzag/folder- kraftwerke.pdf. 20, 21

[173] G. M. Ljung and G. E. P. Box, On a measure of lack of ﬁt in time series models, Biometrika, 65 (1978), pp. 297–303. 42

[174] K. Lygnerud, Risk Management in Swedish District Heating Companies, Bas Publishing, 2010. 2

[175] Magistratsabteilung 27 (Stadt Wien), Nutzung von Abwärmepotentialen in Wien, SEP-Koordinationsstelle, 2008. 60

[176] S. Maillard, T. Roncalli, and J. Teïletche, The Properties of Equally Weighted Risk Contribution Portfolios, The Journal of Portfolio Management, 36 (2010), pp. 60–70. 125 Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. [177] H. Markowitz, Portfolio selection, The Journal of Finance, 7 (1952), pp. 77–91. 87

151 tuwien.at/bibliothek [178] Massé P. and R. Gibrat, Application of Linear Programming to Investments in the Electric Power Industry, Management Science, 3 (1957), pp. 149–166. 3, 67

[179] O. Massol, A Cost Function for the Natural Gas Transmission Industry: Further Considerations, The Engineering Economist, 56 (2011), pp. 95–122. 48

[180] H. Matsumoto and M. Yor, Exponential functionals of Brownian motion, I: Probability laws at ﬁxed time, Probab. Surveys, (2005), pp. 312–347. 46

[181] Y. Matsumoto, Optimal multistage expansion planning of a gas turbine cogeneration plant, Journal of engineering for gas turbines and power, 118 (1996), p. 803. 4

[182] G. Mauschitz, Klimarelevanz der Abfallwirtschaft IV, Studie im Auftrag des Bundesministeriums für Land- und Forstwirtschaft, Umwelt und Wasser- wirtschaft, 2009. https://www.bmnt.gv.at/dam/jcr:275ce304-f369- 4a09-bfcc-113ad9212e3b/Endbericht%20Klimarelevanz%20der% 20Abfallwirtschaft%20IV%20Mauschitz.pdf. 60

[183] J. MAYBEE, P. Randolph, and N. URI, Optimal step function approximations to utility load duration curves, Engineering Optimization, 4 (1979), pp. 89–93. 74

[184] R. Mayer and D. Stibi, Energie und Steuern: Systematischer Überblick über die Ertrag-, Umsatz- und Verbrauchsteuern, Orac Steuerpraxis, LexisNexis-Verl. ARD Orac, Wien, 2005. 51

[185] A. Melcher, Industrial Heat Applications at KELAG Wärme GmbH – Sustainable Energy Eﬃciency between Tradition and Innovation, Conference Renewable Energy Carinthia, Velden, Wörthersee, (2014), pp. 71–75. 22, 100, 101, 107

[186] M. A. Milevsky and S. E. Posner, Asian Options, the Sum of Lognormals, and the Reciprocal Gamma Distribution, The Journal of Financial and Quantitative Analysis, 33 (1998), pp. 409–422. 47

[187] J. Monette, A mathematical model of an electrical utility’s load-duration curve, Omega, 10 (1982), pp. 94–96. 13

[188] G. Moravi, „Wärmewende“ im Großraum Graz: Rahmenbedingungen und Ziele auf dem Weg zu einer smarten Fernwärmeversorgung, Berliner Energietage 2017, (2017). 106, 108

[189] A. Müller, R. Büchele, L. Kranzl, G. Totschnig, F. Mauth- ner, R. Heimrath, and C. Halmdienst, Solarenergie und Wärmenetze: Optionen und Barrieren in einer langfristigen, integrativen Sichtweise (So- largrids), 2014. http://www.eeg.tuwien.ac.at/eeg.tuwien.ac.at_ Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. pages/research/downloads/PR_382_SolarGrids_publizierbarer_ endbericht_v11.pdf. 27

152 tuwien.at/bibliothek [190] J. I. Muñoz, Agustín A. Sánchez de la Nieta, J. Contreras, and J. L. Bernal-Agustín, Optimal investment portfolio in renewable energy: The Spanish case, Energy Policy, 37 (2009), pp. 5273–5284. 88

[191] J. D. Murphy and E. McKeogh, Technical, economic and environmental analysis of energy production from municipal solid waste, Renewable Energy, 29 (2004), pp. 1043–1057. 60

[192] P. K. Nag, Power Plant Engineering, Tata McGraw-Hill, 2002. 13

[193] H. Neuffer, F.-G. Witterhold, W. Pfaffenberger, A. Gregorzewski, W. Schulz, M. Blesl, U. Fahl, A. Voß, E. Jochem, and W. Manns- bart, Strategien und Technologien einer pluralistischen Fern-und Nahwärmever- sorgung in einem liberalisierten Energiemarkt unter besonderer Berücksichtigung der Kraft-Wärme-Kopplung und regenerativer Energien., AGFW-Hauptstudie. Band 1: Grundlagen der Kraft-Wärme-Kopplung, Zertiﬁzierungsverfahren und Förder- modelle, 2001. 78, 79

[194] S. Nick and S. Thoenes, What drives natural gas prices? — A structural VAR approach, Energy Economics, 45 (2014), pp. 517–527. 41

[195] N. Noyan, Risk-averse two-stage stochastic programming with an application to disaster management, Computers & Operations Research, 39 (2012), pp. 541–559. 91

[196] P. Oberndorfer, Rechtsgutachten zu Fragestellungen im Zusammenhang mit Power-to-Heat („P2H“), 2014. 50

[197] Oesterreichische Nationalbank, Interest rates and exchange rates – euro time series, 2018. https://www.oenb.at/zinssaetzewechselkurse/ zinssaetzewechselkurse?lang=en&mode=zeitreihenzumeuro. 32, 33, 81

[198] O. Olsson, J. Vinterbäck, A. Dahlberg, and C. Porsö, Price mechanisms for wood fuels, Eubionet3, (2010). 41

[199] T. Ommen, W. B. Markussen, and B. Elmegaard, Comparison of linear, mixed integer and non-linear programming methods in energy system dispatch modelling, Energy, 74 (2014), pp. 109–118. 78, 80, 86

[200] , Heat pumps in combined heat and power systems, Energy, 76 (2014), pp. 989– 1000. 24 Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. [201] orf.at, Verbund: Schluss für Steinkohle-Kraftwerk Mellach, 2017. Press note: https://steiermark.orf.at/news/stories/2831296/. 104

153 tuwien.at/bibliothek [202] Österreichische Vereinigung für das Gas- und Wasserfach & Fachver- band der Gas- und Wärmeversorgungsunternehmungen, Fernwärmestadt St. Pölten: Fernwärme Stadtportrait, Forum Gas Wasser Wärme, (2016), pp. 28–30. 100

[203] , Fernwärmestadt Villach: Fernwärme Stadtportrait, Forum Gas Wasser Wärme, (2016), pp. 12–14. 100

[204] , „Energiestadt“ Wels: Fernwärme Stadtportrait, Forum Gas Wasser Wärme, (2016), pp. 30–32. 22, 100

[205] , Salzburg: Fernwärme Stadtportrait, Forum Gas Wasser Wärme, (2017), pp. 28–31. 100

[206] Österreichs E-Wirtschaft, Zeit zum Handeln: Der Aktionsplan von Oesterre- ichs Energie zeigt die Schritte in die Stromzukunft auf, oesterreichs energie, (2012). 102

[207] , oestereichs energie: Fachmagazin der österreichischen E-Wirtschaft, 2014. 104

[208] E. A. Othman, N. Y. Dahlan, M. N. Mohd Nawi, T. Ahmad Nizam, and M. Z. Tahir, Optimal step-function approximation of load duration curve using Evolutionary Programming (EP), Jurnal Teknologi, (2015). 74

[209] C. Overland and A. Sandoff, Joint Cost Allocation and Cogeneration, SSRN Electronic Journal, (2014). 56

[210] J. Owen and R. Rabinovitch, On the class of elliptical distributions and their applications to the theory of portfolio choice, The Journal of Finance, 38 (1983), pp. 745–752. 91

[211] B. Palmintier and M. Webster, eds., Impact of unit commitment constraints on generation expansion planning with renewables: 2011 IEEE Power and Energy Society General Meeting, 2011. 76

[212] B. Papousek, Wärmeversorgung Graz 2020/30, 2016. 24, 106

[213] B. Papousek and E. Meißner, Alternativenergie - Potentiale in der zukünftigen Wärmeversorgung, 2015. 109

[214] H. Pauli, Abwärmeintegration im Linzer Fernwärmesystem Möglichkeiten und Szenarien für ein „Future District Heating System“, 2. Praxis- und Wissensforum Fernwärme/ Fernkälte, 2016. Presentation https: //www.ait.ac.at/fileadmin/mc/energy/downloads/News_and_ Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. Events/2016_11_15_2.Praxis_und_Wissensforum_FWK/B3_Pauli_ _Future_DH_System_AIT_15_Nov_16_Pauli_V3.pdf. 106, 107, 108

154 tuwien.at/bibliothek [215] S. Peroutka, Unbundling – Neue Aspekte der Rechnungslegung am Beispiel der Entﬂechtungsbestimmungen in der Elektrizitätswirtschaft, Universität Wien, 2002. PhD Thesis. 52

[216] D. Phillips, F. Jenkin, J. Pritchard, and K. Rybicki, A mathematical model for determining generating plant mix, in Proceedings of the Third IEEE PSCC, 1969. 70

[217] D. Pilipovic, Energy risk: valuing and managing energy derivatives, McGraw-Hill, New York, 1997. 44

[218] R. S. Pindyck, The Long-Run Evolution of Energy Prices, The Energy Journal, 20 (1999), pp. 1–27. 44

[219] R. Pixner, Erdwärme für Ried und Mehrnbach: Geothermie-Projekt ist eröﬀnet, Tips, 2015. https://tips.at/news/mehrnbach/wirtschaft-politik/ 313580-erdwaerme-fuer-ried-und-mehrnbach-geothermie- projekt-ist-eroeffnet. 26

[220] W. Pölz, Emissionen der Fernwärme Wien 2005: Ökobilanz der Treibhausgas- und Luftschadstoﬀemissionen aus dem Anlagenpark der Fernwärme Wien GmbH, Umweltbundesamt: REP-0076, 2007. http://www.umweltbundesamt.at/ fileadmin/site/publikationen/REP0076.pdf. 107

[221] A. Poulin, M. Dostie, M. Fournier, and S. Sansregret, Load duration curve: A tool for technico-economic analysis of energy solutions, Energy and Buildings, 40 (2008), pp. 29–35. 14

[222] W. Prutsch, Fernwärme als Schlüssel zur Wärmewende oder Auslauf- model? Die Zukunft der Fernwärme in Graz, Energiegespräche: "Fern- wärme - der Schlüssel zur Wärmewende oder Auslaufmodell?", 2016. Pre- sentation: http://www.eeg.tuwien.ac.at/eeg.tuwien.ac.at_pages/ events/egs/pdf/egs160301_prutsch.pdf. 106, 107

[223] R. Pumberger, E. Mair, and K. Prodinger, Fernwärmemarktpotential in Österreich, 1984. 2

[224] E. E. Qian, On the Financial Interpretation of Risk Contribution: Risk Budgets Do Add Up, Journal of Investment Management, 4 (2006). 125

[225] R. Doherty, H. Outhred, and M. O’Malley, Establishing the role that wind generation may have in future generation portfolios, IEEE Transactions on Power Systems, 21 (2006), pp. 1415–1422. 6, 91, 95

[226] T. Rand, J. Haukohl, and U. Marxen, Municipal Solid Waste Incineration: Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. Requirements for a Successful Project, no. 462 in World Bank technical paper, The World Bank, 2000. 21

155 tuwien.at/bibliothek [227] A. Rapottnig, Innovative Wege der Wärme- versorgung in Wien bis 2050, En- ergiegespräche: "Fernwärme - der Schlüssel zur Wärmewende oder Auslaufmod- ell?", 2016. http://www.eeg.tuwien.ac.at/eeg.tuwien.ac.at_pages/ events/egs/pdf/egs160301_rapottnig.pdf. 108

[228] Rechnungshof, Prüfungsergebnis: Wien Energie Bundesforste Biomasse Kraftwerk GmbH, (2006). https://www.rechnungshof.gv.at/fileadmin/ downloads/2006/berichte/teilberichte/wien/Wien_2006_02/ Wien_2006_02_1.pdf. 20, 102

[229] , Prüfungsergebnis: Erschließung Seestadt Aspern, 2015. https: //www.rechnungshof.gv.at/fileadmin/downloads/_jahre/2015/ berichte/teilberichte/wien/Wien_2015_02/Wien_2015_02_2.pdf. 108

[230] R. Rieberer, G. Zotter, D. Hannl, Moser, Harald, O. Kotenko, A. Zottel, T. Fleckl, and I. Malenkovic, IEA Heat Pump Pro- gramme Annex 35: Anwendungsmöglichkeiten für industrielle Wärmepumpen, Bundesministerium für Verkehr, Innovation und Technologie, 2014. https://nachhaltigwirtschaften.at/resources/iea_pdf/ endbericht_201517_iea_hpp_annex35_anwendungsmoeglichkeiten_ fuer_industrielle_waermepumpen.pdf?m=1469661961. 24

[231] R. T. Rockafellar, Integral functionals, normal integrands and measurable selections, in Nonlinear Operators and the Calculus of Variations: Summer School Held in Bruxelles 8–19 September 1975, 1976, pp. 157–207. 128

[232] N. Rodoulis, Evaluation of Cyprus’ Electricity Generation Planning Using Mean- Variance Portfolio Theory, Cyprus Economic Policy Review, 4 (2010), pp. 25–42. 88

[233] T. Roncalli, Introduction to Risk Parity and Budgeting, CRC Press, 2016. 125

[234] F. A. Roques, D. M. Newbery, and W. J. Nuttall, Fuel mix diversiﬁcation incentives in liberalized electricity markets: A Mean–Variance Portfolio theory approach, Energy Economics, 30 (2008), pp. 1831–1849. 88, 90

[235] F. Salgado and P. Pedrero, Short-term operation planning on cogeneration systems: A survey, Electric Power Systems Research, 78 (2008), pp. 835–848. 78, 80

[236] M. S. Salvadores and J. H. Keppler, Projected Costs of Generating Electricity: 2010 Edition, Energy Agency and OECD Nuclear Energy Agency, 2010. https://www.iea.org/publications/freepublications/

[237] Salzburg AG, Kraft-Wärme-Kopplung, 2013. Information Brochure. 21, 100

156 tuwien.at/bibliothek [238] F. Schmid, Sewage water: interesting heat source for heat pumps and chillers, 2008. http://www.bfe.admin.ch/php/modules/publikationen/ stream.php?extlang=en&name=en_508290240.pdf. 25

[239] R.-R. Schmidt and R. Geyer, Nah- und Fernwärme – Auseinan- dersetzung mit Innovationsaspekten, AIT Austrian Institute of Technol- ogy, 2016. https://www.arbeiterkammer.at/infopool/akportal/AIT_ Zukunftsaspekte.pdf. 107

[240] Y. Scholz, Möglichkeiten und Grenzen der Integration verschiedener regenerativer Energiequellen zu einer 100% regenerativen Stromversorgung der Bundesrepublik Deutschland bis zum Jahr 2050, Deutsches Zentrum für Luft- und Raumfahrt: Materialien zur Umweltforschung 42, 2010. https://www.umweltrat. de/SharedDocs/Downloads/DE/03_Materialien/2010_MAT42_DZLR_ Integration_Energiequellen_2050.pdf?__blob=publicationFile. 31

[241] A. Schröder, F. Kunz, J. Meiss, R. Mendelevitch, and C. von Hirschhausen, Current and Prospective Costs of Electricity Generation until 2050, Deutsches Institut für Wirtschaftsforschung: Data Documentation 68, 2013. https://www.diw.de/documents/publikationen/73/diw_01.c. 424566.de/diw_datadoc_2013-068.pdf. 16, 77, 78, 81

[242] Schweighofer Fiber, Umwelterklärung 2015, 2015. https: //www.schweighofer.at/fileadmin/files/all/Newsbilder/ Schweighofer_FIBER_Umwelterklaerung_2015.pdf. 22

[243] S. S. Shapiro and M. B. Wilk, An analysis of variance test for normality (complete samples), Biometrika, 52 (1965), pp. 591–611. 42

[244] S. S. Shapiro, M. B. Wilk, and H. J. Chen, A comparative study of various tests for normality, Journal of the American Statistical Association, 63 (1968), pp. 1343–1372. 42

[245] W. F. Sharpe, Budgeting and Monitoring Pension Fund Risk, Financial Analysts Journal, 58 (2002), pp. 74–86. 125

[246] SOLID Gesellschaft für Solarinstallation und Design, SOLID liefert 6 MW Absorptionswärmepumpe an TIGAS, 2015. Press note: https://www.solid.at/de/news-archiv/2015/227-solid-liefert- 6-mw-absorptionswaermepumpe-an-tigas. 25

[247] Statistik Austria, Energiebilanz Steiermark 1970 bis 2016 (Detailin- formation), 2017. http://www.statistik.at/wcm/idc/idcplg? Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. IdcService=GET_NATIVE_FILE&RevisionSelectionMethod= LatestReleased&dDocName=065506. 20, 103, 104

157 tuwien.at/bibliothek [248] , Gesamtenergiebilanz Österreich 1970 bis 2016 (Detailinfor- mation), 2017. https://www.statistik.at/wcm/idc/idcplg? IdcService=GET_NATIVE_FILE&RevisionSelectionMethod= LatestReleased&dDocName=029955. 16, 17, 28, 100

[249] M. Steck and W. Mauch, Technische Anforderungen an neue Kraftwerke im Umfeld dezentraler Stromerzeugung, in 10. Symposium Energieinnovation Graz, 2008. https://www.ffe.de/download/Veroeffentlichungen/ 2008_EnInnov_Steck.pdf. 77

[250] M. J. Steinberg and T. H. Smith, Economy Loading of Power Plants and Electric Systems, J. Wiley & sons, Incorporated, 1943. 67

[251] M. Stenitzer, S. Fickl, B. Papousek, and M. Cerveny, KliP Working Paper Nr. 3: Energieeinsatz und CO2-Emissionen in Wien, Magistratsabteilung 22, 1997. https://www.wien.gv.at/umwelt/klimaschutz/pdf/working- paper3.pdf. 106, 107

[252] R. Stollnberger, Industriell-gewerbliche Abwärmepotenziale und deren Nutzung für eine energieeﬃziente Entwicklung im Stadtgebiet von Wien, Technische Univer- sität Wien, 2016. Master Thesis. 108

[253] N. M. Stoughton, R. C. Chen, and S. T. Lee, Direct Construction of Optimal Generation Mix, IEEE Transactions on Power Apparatus and Systems, PAS-99 (1980), pp. 753–759. 71, 72, 91

[254] G. Sundberg and D. Henning, Investments in combined heat and power plants: Inﬂuence of fuel price on cost minimised operation, Energy Conversion and Man- agement, 43 (2002), pp. 639–650. 4

[255] M. Sunderkötter and C. Weber, Valuing fuel diversiﬁcation in power generation capacity planning, Energy Economics, 34 (2012), pp. 1664–1674. 14

[256] G. Taljan, G. Verbič, M. Pantoš, M. Sakulin, and L. Fickert, Optimal sizing of biomass-ﬁred Organic Rankine Cycle CHP system with heat storage, Renewable Energy, 41 (2012), pp. 29–38. 4

[257] D. Tasche, Risk contributions and performance measurement, Report of the Lehrstuhl für mathematische Statistik, Technische Universität München, 1999. 125

[258] T. Tereshchenko and N. Nord, Energy planning of district heating for future building stock based on renewable energies and increasing supply ﬂexibility, Energy, 112 (2016), pp. 1227–1244. 4

[259] M. Theißing, A. Kraußler, M. Muster, M. Schloffer, M. Tragner, and Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. Wanek Michael, Instationarität von industrieller Abwärme als limitierender Fak- tor bei der Nutzung und Integration in Wärmeverteil- und Wärmenutzungssystemen,

158 tuwien.at/bibliothek 2009. https://nachhaltigwirtschaften.at/resources/fdz_pdf/ endbericht_0934_industrielle_abwaerme.pdf?m=1469660207. 22

[260] M. Tieber, Eﬃzienz, Nutzen und Zukunftspotenzial von Fernwärmean- schlüssen, sowie Prüfung der Verwendung von Mitteln aus der Feinstaubrücklage, 2011. https://www.graz.at/cms/dokumente/10029027/5a4a85e6/ Fernw%C3%A4rme-Endbericht.pdf. 104

[261] J. Tobin, Liquidity preference as behavior towards risk, The review of economic studies, 25 (1958), pp. 65–86. 89

[262] S. M. Turnbull and L. M. Wakeman, A quick algorithm for pricing European average options, Journal of ﬁnancial and quantitative analysis, 26 (1991), pp. 377– 389. 47

[263] P. Unterluggauer, Positionspapier: Nachhaltige Alternativen für das Fer- nwärmesystem Klagenfurt, im Auftrag der AUSTROPAPIER – Vereinigung der Österreichischen Papierindustrie und der Österreichischen Plattenindustrie, 2015. https://news.wko.at/news/oesterreich/Positionspapier_ Nachhaltige_Alternativen_Klagenfurt_2015-04.pdf. 20, 61, 100

[264] D. Urošević, D. Gvozdenac, and V. Grković, Calculation of the power loss coeﬃcient of steam turbine as a part of the cogeneration plant, Energy, 59 (2013), pp. 642–651. 28

[265] S. van Loo and J. Koppejan, The Handbook of Biomass Combustion and Co-ﬁring, Earthscan, 2008. 31

[266] S. Van Loo and J. Koppejan, The Handbook of Biomass Combustion and Co-ﬁring, Taylor & Francis Group, 2012. 19

[267] Verordnung (Bundesminister für Wissenschaft, Forschung und Wirtschaft), Ökostromförderbeitragsverordnung 2015 und Ökostrompauschale-Verordnung 2015, 2014. https://www.ris.bka.gv. at/GeltendeFassung.wxe?Abfrage=Bundesnormen&Gesetzesnummer= 20009046&FassungVom=2015-12-31 and https://www.ris.bka.gv. at/GeltendeFassung.wxe?Abfrage=Bundesnormen&Gesetzesnummer= 20009047&FassungVom=2017-12-31. 51, 57

[268] Verordnung (E-Control), Gas-Systemnutzungsentgelte-Verordnung 2013 - Nov- elle 2015: GSNE-VO 2013 - Novelle 2015, 2014. https://www.ris.bka.gv. at/eli/bgbl/II/2014/370. 48, 49, 51

[269] , Systemnutzungsentgelte-Verordnung 2012 - Novelle 2015: SNE-VO 2012 Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. - Novelle 2015, 2014. https://www.ris.bka.gv.at/eli/bgbl/II/2014/ 369. 50, 57

159 tuwien.at/bibliothek [270] S. von Roon, T. Gobmaier, K. Wachinger, and M. Hinter- stocker, Statusbericht zum Standardlastproﬁlverfahren Gas, End- bericht der Forschungsgesellschaft für Energiewirtschaft, 2014. https: //www.ffegmbh.de/download/informationen/508_bdew_slp_gas/ Statusbericht_SLP_Gas_FfE_201411.pdf. 10, 11

[271] C. Weber and M. Sunderkötter, Mean-Variance Optimization of Power Generation Portfolios Under Uncertainty in the Merit Order, EWL Working Paper, (2011). 6, 87, 91, 93

[272] S. Werner, The heat load in district heating systems, Chalmers University of Technology, 1984. PhD Thesis. 10, 12

[273] S. Werner, International review of district heating and cooling, Energy, 137 (2017), pp. 617 – 631. 101

[274] G. Westner and R. Madlener, The beneﬁt of regional diversiﬁcation of cogeneration investments in Europe: A mean-variance portfolio analysis, Special Section: Carbon Reduction at Community Scale, 38 (2010), pp. 7911–7920. 88, 90

[275] E. Wetterlund, S. Leduc, E. Dotzauer, and G. Kindermann, Optimal localisation of biofuel production on a European scale, Energy, 41 (2012), pp. 462– 472. 49

[276] , Optimal use of forest residues in Europe under diﬀerent policies—second generation biofuels versus combined heat and power, Biomass Conversion and Bioreﬁnery, 3 (2013), pp. 3–16. 49

[277] Wien Energie, Technische Auslegungsbedingungen, Technische Richtline TR-TAB, 2013. https://www.wienenergie.at/media/files/2015/technische% 20richtlinie%20tr-tab%20technische%20auslegungsbedingungen_ 140557.pdf. 101

[278] , Umwelterklärung 2014 (Aktualisierung) der Strom- und Wärmeerzeugungsan- lagen von Wien Energie, 2014. https://www.wienenergie.at/media/ files/2014/umwelterkl%C3%A4rung_2014_128460.pdf. 20, 21, 102, 103

[279] , Jahrbuch 2015: Wien wächst – Wien Energie wächst mit, 2016. https://www.wienenergie.at/media/files/2016/we_ jahrbuch2015_geschuetzt_179859.pdf. 22, 101, 106, 107

[280] , Umwelterklärung 2016 der Strom- und Wärmeerzeugungsanlagen von Wien Energie, 2016. http://www.wienenergie.at/media/files/2016/ Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. umwelterkl%C3%A4rung_2016_final_188171.pdf. 21, 22, 103, 104, 105, 106, 107

160 tuwien.at/bibliothek [281] Wiener Stadtwerke, Nachhaltigkeitsbericht 2015: Wie die Wiener Stadtwerke wirken, 2014. https://www.wienerstadtwerke.at/media/files/2017/ wstw%20nachhaltigkeitsbericht%202015_196261.pdf. 101

[282] , Ökologie: Energieerzeugung & -bereitstellung: Fernwärme, 2015. 101

[283] , Nachhaltigkeitsprogramm 2016, 2016. 108, 109

[284] M. Wieser and A. Kurzweil, Emissionsfaktoren für die Österreichische Luftschadstoﬀ-Inventur, Umweltbundesamt BE-254, 2004. http://www. umweltbundesamt.at/fileadmin/site/publikationen/BE254.pdf. 38

[285] R. Wiltshire, Advanced District Heating and Cooling (DHC) Systems, Elsevier Science, 2015. 22, 25, 26, 27, 125

[286] B. Windholz, M. Lauermann, H. Ondra, and M. Höller, Einsatz von Wärmepumpen im Wiener Fernwärmenetz, 2. Praxis- und Wissensforum Fernwärme/ Fernkälte, 2016. Presentation: https://nachhaltigwirtschaften.at/ resources/iea_pdf/events/20161115_2_fernwaerme_fernkaelte_ praxis_und_wissensforum_vortrag10_windholz.pdf?m=1479990576. 26, 109

[287] S. Wittkopf, Bereitstellung von Hackgut zur thermischen Verwertung durch Forstbetriebe in Bayern, Technische Universität München, 2005. PhD Thesis. 49

[288] M. Wöhrer, Potentiale und technische Voraussetzungen für Notversorgungsinseln im österreichischen Hochspannungsnetz, Technische Universität Wien, 2014. Master Thesis. 57

[289] www.austrian heatmap.gv.at, Ergebnisse: Industriebedarf, 2015. http: //www.austrian-heatmap.gv.at/data/Industrie_ms_20170220.csv. 107, 108

[290] R. A. Yépez, A Cost Function for the Natural Gas Transmission Industry, The Engineering Economist, 53 (2008), pp. 68–83. 48

[291] M. Yor, Exponential Functionals of Brownian Motion and Related Processes, Springer Berlin Heidelberg, 2001. 46

[292] S. Zahra and R. Reza, Asian real option: New approach to project economic valuation, in 2012 International Conference on Information Management, Innovation Management and Industrial Engineering, vol. 2, Oct 2012, pp. 475–479. 46

[293] T. Zhang, R. Baldick, and T. Deetjen, Optimized generation capacity ex- Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek. pansion using a further improved screening curve method, Electric Power Systems Research, 124 (2015), pp. 47–54. 86

161 tuwien.at/bibliothek [294] M. Ziegler, Method for Establishing Scalable Load Profiles for Residential and Office Buildings to run an Urban Simulation Environment considering Construc- tion and Mechanical Engineering Technologies as well as the Impact of Social Differentiation, Technische Universität Wien, 2016. PhD Thesis. 12

[295] M. Zimmel, Ausfallsreserve Puchstraße –von der Idee bis zur Inbetriebnahme, Fer- nwärmetage 2017, 2017. Presentation: https://eventmaker.at/uploads/ 7509/downloads/ZIMMEL_-_Ausfallsreserve_Puchstrasse_- _von_der_Idee_bis_zur_Inbetriebnahme.pdf?force_download=1. 104 Die approbierte Originalversion dieser Dissertation ist in der TU Wien Bibliothek verfügbar. The approved original version of this doctoral thesis is available at the TU Wien Bibliothek.

162 tuwien.at/bibliothek