Modelling and Control of an ACDC System with Significant Generation from Wind

Modelling and control of an ACDC system with signiﬁcant generation from wind

Author: Stefanie Tatjana Gertraud Supervisor: Ingeborg Kuenzel Prof. Bikash C. Pal (CID: 00485684)

A report submitted in fulﬁlment of requirements for PhD examination.

Control and Power Group Dept. of Electrical and Electronic Engineering Imperial College London

July 2, 2014

1 Declaration of Originality and Copyright Declaration

The work in this thesis is my own and all other material used is referenced accordingly. The copyright of this thesis rests with the author and is made available under a Creative Commons Attribution Non-Commercial No Derivatives licence. Researchers are free to copy, distribute or transmit the thesis on the condition that they attribute it, that they do not use it for commercial purposes and that they do not alter, transform or build upon it. For any reuse or redistribution, researchers must make clear to others the licence terms of this work.

2 Abstract

This PhD project investigates the modelling and analysis of an AC-DC system with synchronous and asynchronous generation (wind farms). The GB network is undergoing major changes including the installation of large amounts of wind generation. Wind farm developments further offshore will be connected via DC connections, such as the eastern link. The first two chapters of the thesis will provide an outline of these changes to the GB system, and the impact of those changes on the frequency response capability of the GB system. In continuation the thesis will engage in modelling details of an AC system with integration of DC technology and wind. The modelling aim is a comprehensive grid representation in a multi-machine small signal stability framework. The inclusion of multi-terminal voltage source converter HVDC links adds further complexities giving rise to difficult research issues. First the solution of an ACDC power flow is described. This solution is then used for the initialization of a dynamic model of the GB network. This model includes the eastern link (represented by a six voltage source converter multi- terminal DC grid) and three offshore wind farms (representing Doggerbank, Hornsea and East Anglia ONE). The modelling and results of this simulation will be discussed in detail. The impact of increased wind integration into the GB system is further discussed with respect to the wind farm inertial response capability. An important factor for the inertial response capability is the wake effect. The wake effect describes a reduction in wind speed throughout a wind farm, caused by upstream wind turbines. The reduced wind speed at downstream turbines impacts the inertial response that can be expected from the wind farm. The thesis will conclude by summarising how the inclusion of more wind and HVDC technology impacts on the GB system and the modelling required.

3 List of publications

The following publications have been written during this work:

1. S. Kuenzel , P. L. Kunjumuhamed , B. C. Pal and I. Erlich, ”Impact of Wakes on Wind Farm Inertial Response”, IEEE Trans. On Sustainable Energy, Vol.5, no.1, pp.237-245, Jan. 2014 Further accepted for presentation and publication in the Proceedings of the 2014 IEEE PES General Meeting, Washington DC, Jul. 2014

2. S. Kuenzel , P. L. Kunjumuhamed and B. C. Pal, ”Frequency Response Capacity of the GB System in 2030”, 12th Wind Integration Workshop, London, Oct. 2013

3. S. Kuenzel , P. L. Kunjumuhamed , B. C. Pal and I. Erlich, ”Windfarm inertial response capability considering wake eﬀect”, 11th Wind Integration Workshop, Lis- bon, Nov. 2012

4 Acknowledgements

I would like to thank those who have supported me during my PhD. This work would never have been possible without my supervisor Prof. Bikash Pal. I am very grateful for his continuous guidance, research direction and feedback throughout this research. His support motivated me to learn more and more. I enjoyed working with him, since he is both extremely knowledgeable and kind. I would further like to express my gratitude to Dr. Linash Kunjumuhammed from whom I picked up a lot of the required day-to-day power systems knowledge. He was always there to help and explain. My examiners Dr. Lie Xu and Prof. Thomas Parisini had to dedicate time for reading my thesis and for the examination. Hence I would like to voice my appreciation for their signiﬁcant eﬀort. My sincere gratitude lies with Dr. Jenny Cooper at National Grid. It was my wish to be able to pursue a PhD degree, while keeping up-to-date with the industry. It is thanks to her that I was able to maintain regular visits to National Grid, who helped to fund this work. During those visits I worked with the teams of Mark Perry, Dr. Mark Osborn and Dr. Vandad Hamidi. I would like to thank them and their teams for taking the time for discussions, organizing my visits and inviting me for the PowerFactory training course. A thank you also goes to Mark Horley, who invited me to attend the frequency response testing at Ormonde wind farm. I would like to thank Prof. Istvan Erlich, for the three month I spent at his institute in Duisburg, giving me the chance to work at another university and learning from the experience. I would like to thank my colleagues, friends and extended family for being there. They have been a source of great support.

5 Contents

List of Figures 9

1 Introduction 18 1.1InternationalPerspective...... 19 1.2EuropeanPerspective...... 21 1.3UKPerspective...... 22 1.4TrendinoﬀshoreandDCdevelopments...... 23 1.5ResearchContributions...... 26

2 Ancillary services in UK system 28 2.1 GB system in 2030 ...... 29 2.1.1 Generation...... 29 2.1.2 Load...... 30 2.2FrequencyResponse...... 30 2.3Responsebytechnology...... 31 2.3.1 Conventionalgeneration...... 32 2.3.2 Wind...... 32 2.3.3 Otherrenewables...... 33 2.3.4 Interconnector...... 34 2.3.5 Nuclear...... 35 2.3.6 Loads...... 35 2.4Conclusion...... 36

3 Powerflow solution and validation for CSC and VSC links 37 3.1Introduction...... 37 3.2NewtonRaphsonMethod...... 38 3.3ACpowerflow...... 42 3.4ACDCpowerflowwithCurrentSourceConverter(CSC)...... 44 3.5Initialvalidation...... 47 3.6ACDCsimulationPowerfactoryvs.Matlab...... 48 3.7ACDCpowerflowwithVSC...... 52 3.8Conclusion...... 55

4 Modelling of the GB system with multi-terminal VSC connected wind farms 56 4.1Introduction...... 56

6 CONTENTS

4.2Selectionofparameters...... 59 4.3 Representation of the physical system through modelling components . . . 61 4.4Multi-areaACDCpowerflowcalculation...... 63 4.4.1 ACpowerflowandconvertervariables...... 65 4.4.2 PowerflowinDCGrid...... 66 4.4.3 Reverseslackconvertercalculation...... 68 4.4.4 Powerflowsolution...... 70 4.5 Dynamic modelling of the VSC MTDC grid ...... 73 4.6 Dynamic modelling and initialization of the offshore AC grids ...... 82 4.7Conclusion...... 84

5 Small signal analysis of the GB system with multi-terminal VSC connected wind farms 86 5.1Evaluationofstatematrixandeigenvalues...... 94 5.2EigenvalueAnalysis...... 103 5.2.1 Controllertuning...... 111 5.3Conclusion...... 121

6 Impact of Wakes on Wind Farm Inertial Response 122 6.1Introduction...... 122 6.2WakeEﬀect...... 124 6.2.1 Reviewofpreviouswork...... 124 6.2.2 Jensen’smodelindetail...... 125 6.3Windenergyconversionprocess...... 127 6.3.1 Inertialresponseprovisionmechanism...... 127 6.3.2 DFIGmodel...... 130 6.4Wakeeﬀectvalidation...... 131 6.5Quantifyingtheimpactofwakeoninertialresponse...... 135 6.6 Evaluating the duration of wind turbine response according to wind speed 139 6.7Conclusion...... 142

7 Conclusion and Future Work 144

Appendices 147

A Dynamic modelling of wind power plants 148 A.1 Dynamic modelling of DFIG ...... 148 A.2 Dynamic modelling of generic wind park model ...... 151

B Dynamic modelling of synchronous machines 154 B.1Excitationsystem...... 154 B.2Governorcontrol...... 154 B.3Machinemodel...... 155

C Test system parameters 157

D GB system parameters 158

7 CONTENTS

References 161

8 List of Figures

1.1Trendinincreasingwindturbinesize[1]...... 19 1.2Historicalinstalledwindcapacityglobally[2]...... 19 1.3 Worldwide installed wind capacity by June 2013 [3] ...... 20 1.4 Additional installed wind capacity during first half of 2013 [3] ...... 21 1.5InstalledgenerationcapacityinEurope[4]...... 21 1.6 Additional installed capacity in Europe during 2013 [4] ...... 22 1.7 Historical wind power installation in the UK, showing installed capacity [5, 6] 23 1.8 Historical UK wind power installations as percentage of electricity use [5] . 23 1.9ComparisonofinvestmentcostsofACandDCconnections[7]...... 24 1.10Comparisonofcurrentandvoltagesourceconverter[8]...... 25 1.11 LHS: Wind farm capacity accross UK (31.12.2012), blue offshore, red onshore, Wind Farm Capacities Map, Department of Energy and Climate Change, [9], RHS: Offshore wind farm developments, UK Offshore wind report 2012, The Crown Estate, [10] ...... 26

2.1 Change in generation mix for 2030 under gone green scenario, UK Future EnergyScenarios,NationalGrid[11]...... 29 2.2 Under frequency response, National Grid, Grid Code [12], P denoting pri- maryresponse,Ssecondaryresponse...... 30 2.3 Over frequency response, National Grid, Grid Code [12], H denoting high- frequencyresponse...... 31

2.4 Inertia emulation for wind turbines [13], where the torque command Tref consists of three components Tω,ref ,Tin,ref and Tf,ref for rotational, inertial andfrequencycontrolrespectively...... 33 2.5 2012 Mix of renewables other than wind [14] ...... 33 2.6 VSC frequency control by changing active power order, where the outer PI controller sets the active power order according to the frequency error, the active power error determines the reference for the quadrature component of the phase reactor current while the reactive power error determines the directcomponent...... 35

3.1FlowchartforNewtonRaphsonmethod...... 40 3.2ACnetwork...... 41 3.3 Results gained with Matlab and Powerfactory, red denoting Matlab results, blackPowerfactoryresults...... 43 3.4SequentialACDCpowerﬂowmethod...... 44

9 LIST OF FIGURES

3.5Currentsourceconverterlink...... 45 3.6PowerﬂowsolutionforDCnetwork...... 46 3.7 DC solution compared to results in book by Arrillaga and Watson[15], green denotingMatlabresults,blackresultsfrombook...... 48 3.8ACDCCSCnetworkparameters...... 50 3.9 ACDC solution compared to PowerFactory, green denoting Matlab results, blackPowerfactoryresults...... 51 3.10VSCconnection[16]...... 52 3.11 ACDC solution for VSC link, green denoting Matlab results, black deﬁned systemparameters...... 54

4.1 GB system with offshore DC grid and three offshore wind farms ...... 59 4.2 Comparison of slack converter step response with DC link capacitance of 1mF and 10mF, when offshore wind farm output connected to converter I isreducedby1%...... 60 4.3 Parameters of offshore DC grid and three offshore wind farms ...... 61 4.4 Simulation set-up of a large multi-machine system with onshore and off- shorewind,MTDCnetworkandoffshoreACgrid...... 62 4.5ACandDCnetworksinanetworkasshowninFigure4.1...... 63 4.6 Program structure for a load flow solver containing multiple AC networks andaDCgrid...... 64 4.7 Simulation of four AC systems in one AC load flow via matrix aggregation 64 4.8 Circuit diagram of symmetrically grounded, mono-polar two-terminal VSC circuit,includingconverterACside...... 65 4.9 GB system with offshore development, bus numbers are included in blocks, upper numbers denote load buses, lower numbers generators ...... 70 4.10Initialvoltagesandanglesacrossthesysteminp.u...... 71 4.11Initialpowerinjectedacrossthesystemin100MWbase...... 71 4.12Reactivepoweracrossbuses...... 72 4.13Currentsinjectedacrossthesystem...... 72 4.14Initialconditionsforoffshoredevelopment...... 73

4.15 Circuit of VSC grid with two converters for dynamic analysis, where Vdc is the voltage potential from line to ground across a single capacitor . . . . . 74 4.16Referenceframeconversion,fromDQtodq...... 74 4.17OverviewoftheVSCmulti-terminalDCgrid...... 75 4.18Dynamicmodelofmulti-terminalDCgrid...... 76 4.19Innercurrentcontrolleroftheconverterstations...... 78 4.20CircuitcomponentsinACoﬀshoregrids...... 83

5.1 Real power at offshore wind farms, during active power step at wind farm I 87 5.2 Reactive power at offshore wind farms, during active power step at wind farmI ...... 87 5.3 Real power at offshore converters, during active power step at wind farm I 88 5.4 Reactive power at offshore converters, during active power step at wind farmI ...... 88 5.5 DC voltage at all converters, during active power step at wind farm I . . . 89

10 LIST OF FIGURES

5.6 DC current at all converters, during active power step at wind farm I . . . 90 5.7 DC power at all converters, during active power step at wind farm I . . . . 90 5.8 Active power at onshore converters, during active power step at wind farm I 91 5.9 Reactive power at onshore converters, during active power step at wind farmI ...... 91 5.10Governorresponsetooffshorewindpowerstep...... 92 5.11Changeinvoltagemagnitudefrominitialvalues...... 92 5.12Changeincurrentmagnitudefrominitialvalues...... 93 5.13 Change in voltage angles from initial values relative to reference bus . . . . 94 5.14 Change in current angles from initial values relative to reference bus . . . . 94 5.15 Test system for comparison of analytical and “linmod” state-space model . 96 5.16 Comparison of analytical and “linmod” eigenvalues; “linmod” solution in blackcircle,analyticalinredstar...... 102 5.17 Comparison of analytical and “linmod” eigenvalues; “linmod” solution in blackcircle,analyticalinredstar...... 103 5.18 GB system with offshore development, for participation factor discussion bus numbers are included in blocks, upper numbers denote load buses, lowernumbersgenerators...... 104 5.19 Eigenvalues of GB system, colour coded by damping, green star >= 0.15, 0.15 >orange triangle >= 0.05, red circle <0.05...... 105 5.20 Eigenvalues of GB system, zoomed in on pole pairs, colour coded by damping, green star >= 0.15, 0.15 >orange triangle >= 0.05, red circle <0.05 . 107 5.21 Eigenvalues of GB system, zoomed in on low damped pole pairs, colour coded by damping, green star >= 0.15, 0.15 >orange triangle >= 0.05, red circle <0.05...... 108 5.22 Logarithmic plot of eigenvalues of GB system, colour coded by damping, green star >= 0.15, 0.15 >orange triangle >= 0.05, red circle <0.05 . . . . 109 5.23 Inner current control gain sensitivity of Mode 5, where gains are varied from 0.025 to 1000 from black triangle to pink circle ...... 111 5.24 Inner current control gain sensitivity of Mode 6, where gains are varied from 0.025 to 1000 from black triangle to pink circle ...... 112 5.25 Outer control gain sensitivity of Mode 5, where gains are varied from 0.025 to 1000 from black triangle to pink circle, the quadrature gains correspond to real power control and the direct integral gains to reactive power control 113 5.26 Outer control gain sensitivity of Mode 6, where gains are varied from 0.025 to 1000 from black triangle to pink circle, the quadrature gains correspond to real power control and the direct integral gains to reactive power control 113 5.27 Outer control gain sensitivity of Modes 5 and 6 to changes in DC voltage controller gains, where the direct gain is varied from 40 to 0.1 and integral gainfrom50to0.1fromblacktriangletopinkcircle...... 114 5.28 Power system stabilizer [17], with active powerflow from bus 60 to bus 62 as input and reference power at converter IV as output ...... 114 5.29 Comparison of critical modes, black triangle for original system without any PSS, black circle for system with additional PSS at converter IV, stars for change in time Ta, where red is critically damped and orange sufficiently damped...... 115

11 LIST OF FIGURES

5.30 Power system stabilizer for synchronous machine excitation system with washoutfilter,gainandphasecompensation[18]...... 116 5.31 Comparison of critical modes, triangles for original system without any PSS, circles for system with additional PSS at converter IV [17], squares with PSS at converter and generator at Bus 2. Stars show movement of poles when Kdamp sync is increased, red is critically damped, orange suffi- cientlydampedandgreenwelldamped...... 117 5.32 Angle difference between Bus 5 and 37, where the blue solid line is the system without any power system stabilizers, the red dashed line for the system with a power system stabilizer at the converter station, and the green dashed and dotted line is for the system with a PSS both at the converterandatthegeneratorlocatedatBus2 ...... 119 5.33 Zoomed view of angle difference between Bus 5 and 37, where the blue solid line is the system without any power system stabilizers, the red dashed line for the system with a power system stabilizer at the converter station, and the green dashed and dotted line is for the system with a PSS both at the converterandatthegeneratorlocatedatBus2 ...... 119 5.34 Difference between synchronous speed and speed of generator at Bus 2, where the blue solid line is the system without any power system stabilizers, the red dashed line for the system with a power system stabilizer at the converter station, and the green dashed and dotted line is for the system with a PSS both at the converter and at the generator located at Bus 2 . . 120 5.35 Zoomed view of difference between synchronous speed and speed of generator at Bus 2, where the blue solid line is the system without any power system stabilizers, the red dashed line for the system with a power system stabilizer at the converter station, and the green dashed and dotted line is for the system with a PSS both at the converter and at the generator locatedatBus2...... 120

6.1SchematicofN.O.Jensenwakemodel...... 125 6.2DiagramforBetzlawwithtwoturbines...... 127 6.3Powercurveofwindturbine...... 127 6.4 Power coefficient of wind turbine depicting inertial response without de- loading (solid arrow for turbines in OPPT region; dashed arrow for rated regime)...... 129 6.5Flow-diagramofDFIGwindturbinesimulation...... 130 6.6PitchcontrolofDFIGturbine...... 131 6.7LayoutHornsRevWindFarm...... 132 6.8 Comparison between Horns Rev wind measurements [19] and calculation . 133 6.9 Absolute value of worst matches for each wind direction and speed between HornsRevpowermeasurements[19]andcalculation...... 134 6.10 Power loss in wind farm through wake effect depending on wind direction and speed, for a wind farm with rated power output of 160 MW ...... 134 6.11 Power loss in wind farm through wake effect relative to expected power productiondependingonwinddirectionandspeed...... 135 6.12Totalpowerofdifferentrows...... 136

12 LIST OF FIGURES

6.13Torqueofturbinesindifferentrows...... 137 6.14Rotationalspeedofturbinesindifferentrows...... 138 6.15Pitchangleofturbinesindifferentrows...... 138 6.16Windfarmpoweroutputwithandwithoutwakeeffect...... 139 6.17 Rotational speed in radians/second of turbine during additional power command of 10% at 0 seconds at 4.9 m/s wind speed, point indicates moment turbinereachesminimumrotationalspeed...... 140 6.18 Response in turbine torque during additional power command of 10% at 0 seconds at 4.9 m/s wind speed, point indicates moment torque starts to dropoff...... 140 6.19 Time of additional 10% power command capability of DFIG turbine according to wind speed, solid line indicating limitation due to torque drop, doted line limitation due to minimum rotational speed of the turbine, dashed and dotted line indicating turbine overall capability ...... 141

A.1Overviewofgenericwindpowerplantmodel...... 151 A.2 Generic control model, ﬁrst selector for V or Q control, second selector Q controlasinfullconverterorDFIGturbine...... 152 A.3Genericgenerator/convertermodelofwindpowerplant...... 152

B.1Governorcontrolmodel...... 155

13 Acronyms

AC alternating current ACDC alternating current direct current AVR Automatic voltage regulator CCS carbon capture and storage CSC current source converter CHP combined heat and power DC direct current DFIG doubly fed induction generator EU European Union EWEA European Wind Energy Association FCIG full converter induction generator GB Great Britain HVDC high voltage direct current ICT information and communications technology LCC line commutated converter LHS left hand side MTDC multi-terminal direct current OPPT optimal power point tracking PI proportional integral PQ real power reactive power PSS power system stabilizer PWM pulse width modulation p.u. per unit PV photovoltaic RHS right hand side RoCoF rate of change of frequency SRIG slip ring induction generator UK United Kingdom UNFCCC United Nations Framework Convention on Climate Change VSC voltage source converter

14 List of symbols

ipr phase reactor current [A] 2 A1 overlap of wake and turbine [m ] iprd phase reactor direct current [A] 2 A2 turbine blade area [m ] iprd ref phase reactor direct current refer- Cdc capacitance of DC line [F] ence [A] Cp power coefficient [] iprq phase reactor quadrature current Cpmax maximum power coefficient [] [A] Ct thrust coefficient [] iprq ref phase reactor quadrature current Ddamping per unit damping [Nm] reference [A] Dturb turbine diameter [m] iq quadrature current at system bus Ed transient direct voltage behind [A] equivalent impedance of stator iqr rotor quadrature current [A] circuit [V] Ivec column vector of N ones [] Edc transient direct voltage source J jacobian matrix [mixed] 2 proportional to flux linkage to Jturb moment of inertia [kg/m ] treat transient saliency [V] KA gain of excitation system [] Efd direct excitation voltage [V] k decay parameter [] Emech kinetic energy [J] L inductance [H] Eq transient quadrature voltage be- Ldc inductance of DC line [H] hind equivalent impedance of sta- Lpr inductance of phase reactor [H] tor circuit [V] N number of DC converter stations f frequency [Hz] [] fref target frequency [Hz] P active power [W] Δf difference between target and ac- Pc converter active power [W] tual frequency [Hz] Pac alternating current power [W] ic converter current [A] Pdc direct current power [W] icc DC line current [A] Pe turbine output power [W] ICC matrix of DC line currents [A] Pnew inertial response command [W] idc DC terminal current [A] Pold power output before response [W] id direct current at system bus [A] Pref active power target[W] idr rotor direct current [A] Ps slack real power at DC slack bus [W] ioff offshore current leaving wind- Pt power extracted from wind [W] farms [A] Q reactive power [Var] ic off offshore converter current [A] Qc converter reactive power [Var] ion onshore current leaving wind- Qref reactive power target [Var] farms [A]

15 List of Symbols

Qs stator reactive power [Var] Vd system voltage direct component Qs slack reactive power at DC slack bus [V] [Var] Vdc nominal DC voltage [V] Rturb turbine radius [m] Vdc ref nominal DC reference voltage [V] Rerr error vector [mixed] Vdif DC voltage difference matrix [V] Rresistance[Ω] Vdr direct rotor voltage [V] Ra resistance in stator equivalent cir- Voff offshore voltage at windfarm [V] cuit [Ω] Von onshore voltage at windfarm [V] Rdc resistance of DC cables [Ω] Vq system voltage direct component Rpr resistance of phase reactor [Ω] [V] Sc apparent power at converter bus Vqr quadrature rotor voltage [V] [VA] Vqr ref quadrature rotor reference volt- Ss apparent power at system bus age [V] [VA] Vs system voltage [V] T torque [Nm] Vs system voltage magnitude [V] TA delay time of excitation system Vs ref system voltage magnitude refer- [sec] ence [V] Td delay time [sec] VsD system voltage direct component Te electrical torque [Nm] in DQ frame [V] Te ref electrical torque reference [Nm] VsQ system voltage quadrature com- Tref old torque reference before response ponent in DQ frame [V] [Nm] Vsq system voltage quadrature com- Tt turbine torque [Nm] ponent in dq frame [V] u total wake [] Vsq ref system voltage quadrature com- up single wake from upstream tur- ponent reference [V] bine [] vw wind speed at turbine [m/s] v free wind speed [m/s] x distance between turbines [m] Vb base voltage [V] xd direct reactance in stator equiva- Vc converter voltage [V] lent circuit [Ω] VcD converter voltage direct compo- xd transient direct reactance in sta- nent in DQ frame [V] tor equivalent circuit [Ω] Vcd converter voltage direct compo- xvar vector of unknowns [mixed] nent in dq frame [V] xq quadrature reactance in stator Vc off converter voltage at offshore sta- equivalent circuit [Ω] tions [V] xq transient quadrature reactance in VcQ converter voltage quadrature stator equivalent circuit [Ω] component in DQ frame [V] X reactance [Ω] Vcq converter voltage quadrature Δxvar update for vector of unknowns component in dq frame [V] [mixed] ΔVc update vector converter voltage Y admittance matrix [S] real and imaginary part [V] Ydc direct current admittance matrix [S]

16 List of Symbols

Z impedance [Ω] Zb base impedance [Ω] Zpr impedance of phase reactor [Ω] β pitch angle [deg] δ system voltage angle [rad/sec] λ tip speed ratio [] λopt optimal tip speed ratio [] ρ air density [kg/m3] ω system frequency [rad/sec] ωb system frequency base value [rad/sec] ωturb rotational speed of blades [rad/sec] ωturb old rotational speed before response [rad/sec] Δω diﬀerence between target and actual system frequency [rad/sec] Δωturb diﬀerence between optimal and actual speed of blades [rad/sec]

17 Chapter 1

Introduction

Global warming and limited reserves of fossil fuels are major concerns of the current age. This led to climate change agreements on international as well as national level. The United Nations Framework Convention on Climate Change (UNFCCC), was signed in 1992 by 165 parties [20], with the aim to stabilize greenhouse gas concentrations in order to avoid dangerous interference with the climate system. In 1997, the Kyoto Protocol signed by 83 countries set legally binding targets for a reduction in green house gas emissions. This agreement was further supported by the Bali Action Plan in 2007, the Copenhagen Accord in 2009 and the Cancún agreements signed in 2010. The European Climate Change Programme was initiated in 2000 [21], to realize the targets set forth in the Kyoto Protocol on a European level. The European Union Emission Trading Scheme (2005) was introduced as part of this program, to enable greenhouse gas emissions trading. In the year 2000, the British government launched the United Kingdom’s Climate Change Programme [22], to cut emissions. The UK further introduced the Renewables Obligation for electricity suppliers in 2002 and the Climate Change Act in 2008 for further reductions in emissions. This concern over green house gas emission levels has triggered a large interest in renewable generation sources, in particular wind. During the early development of wind turbine design, individual turbines had relatively small turbine diameters and hence also low power ratings. Since then major research and design effort by the manufacturers has led to turbines with increasingly large diameters, which capture the wind energy of a much larger area. This trend can be clearly seen in Figure 1.1. While the market cost of wind turbines during the first years of this trend was very high, around 2013 a more saturated market led to a decrease in wind turbine prices, which in turn makes wind turbines more cost competitive [3].

18 Chapter 1. Introduction

Figure 1.1: Trend in increasing wind turbine size [1]

1.1 International Perspective

While there were only about 31 GW of wind installed globally in 2002, by 2013 over 318 GW of wind generation had been installed world wide [2]. This is a ten-fold increase during the last eleven years with steadily increasing trend of wind power installations, shown in Figure 1.2.

Historical wind power installations gobally 400

300

200

100 Installed wind capacity [GW] 0 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013

Figure 1.2: Historical installed wind capacity globally [2]

China has the largest installed wind capacity worldwide with 80.8 GW [3]. The second largest player is the US with 60 GW. In Europe Germany, Spain and the UK have the largest installation of wind power plants. China, USA, Germany, Spain and India account for 73% of the installed wind capacity world wide. While China has the largest installed

19 Chapter 1. Introduction capacity of all countries, Europe is the continent with the largest capacity.

Wind capacity world wide 100

20 Installed capacity [GW]

0 China USA German Spain India UK Italy France Canada Denmark Portugal Sweden Australia Brazil Japan Others

Figure 1.3: Worldwide installed wind capacity by June 2013 [3]

Figure 1.4 shows the additional capacity installed in each country during the ﬁrst half of 2013. China has the largest installed capacity and has further installed a large amount of new wind generation during the ﬁrst half of 2013. During this period China made up about 39 % of all new installations. The UK managed to add 1.331 GW during this time, which makes it the second biggest market world wide. It is closely followed by India and Germany with 1.243 GW and 1.143 GW of new installations respectively. USA, the country with the second largest installed capacity, surprisingly hardly had any new installations (1.6 MW). The cause for this is the production tax credit. Many wind farms were connected in 2012 in fear of the expiry of the production tax credit, which were planned for connection in 2013. This low level of new installations is a short term phenomena, not expected to last [3].

20 Chapter 1. Introduction

Additional installation during first half of 2013 6

Added capacity [GW] 1

0 China UK India Germany Sweden Australia Denmark Canada Brazil Italy France Spain Japan Portugal USA Others

Figure 1.4: Additional installed wind capacity during ﬁrst half of 2013 [3]

1.2 European Perspective

Installed generation across Europe is currently still dominated by conventional generation, such as coal and gas. However wind and solar do signiﬁcantly contribute into the generation mix, as seen in Figure 1.5; the generation level of wind (117 GW) being close to the capacity of nuclear (122 GW).

Installed generation accross Europe 250

200

150

100

50 Installed generation capacity [GW] 0 Gas Coal Hydro Nuclear Wind PV Fuel Oil Biomass Others

Figure 1.5: Installed generation capacity in Europe [4]

The newly installed generation, depicted in Figure 1.6 across Europe clearly shows the commitment towards renewable generation. Both wind and PV were deployed large scale across Europe, with added installation of 11 GW each. Wind and PV are the main additions into the European generation mix, followed by about 7.5 GW of gas generators. All other types of generation show much lower installation volumes.

21 Chapter 1. Introduction

New power generation capacity installed in Europe during 2013 12

4 Added capacity [GW] 2

0 Wind PV Gas Coal Biomass Hydro Concentrated Fuel Oilsolar Waste Geothermal Ocean

Figure 1.6: Additional installed capacity in Europe during 2013 [4]

1.3 UK Perspective

The UK government agreed to the EU Renewable Energy Directive, which targets 15% of all energy from renewables by 2020 [23]. This commitment to renewables can be seen in the development of large numbers of windfarms. The UK has become a significant participant in the global wind market. In 2009, the amount of installed windpower in the UK was at 4.05 GW, by 2013 this number had increased to 10.98 GW [5]. The steady increase in installed wind power capacity can be seen in Figure 1.7. As Figure 1.8 shows, the increased wind power generation makes up an increasing proportion of the electricity consumption, hence leading to the displacement of synchronous generation technologies. The UK transmission system is going to face unprecedented operational challenges in the next 5 to 10 years, as this trend continues. The challenges are envisaged to be contributed by factors such as location, characteristics of new generation and planned retirement of an increasing number of centralised synchronous generators and their service to network control. New generation will be more difficult to balance, since wind generation is highly intermittent and nuclear generation currently has a constant output that cannot compensate for fluctuations as conventional coal and gas fired plants do. Conventional plants will need to retire, as resources are limited and the EU Renewables Directive demands a reduction of green house gases by 34% by 2020 compared to levels in 1990 [24, 25]. A discussion tackling the challenge of providing sufficient auxiliary services in a changing UK system is provided in Chapter 2.

22 Chapter 1. Introduction

Figure 1.7: Historical wind power installation in the UK, showing installed capacity [5, 6]

UK wind power installations 10

Percentage of electricity use [%] 0 2008 2009 2010 2011 2012 2013

Figure 1.8: Historical UK wind power installations as percentage of electricity use [5]

1.4 Trend in oﬀshore and DC developments

As offshore wind farms increase in size, they are being built further out into the sea. In AC cables the maximum transmission distance is limited by the reactive power flow, due to the large cable capacitance [26]. Further, as the distance between the onshore connection point and the offshore development increases, so does the length of the cable required for connection. At a certain distance, the break-even distance, the deployment of HVDC transmission over AC becomes beneficial. Figure 1.9 illustrates the cost of AC and DC according to distance. While the AC terminal cost is lower than the DC one, the

23 Chapter 1. Introduction incremental cost according to cable length is higher for AC. At a distance greater than the break-even point, DC will be the more cost eﬀective solution. For subsea cables the break-even distance is quoted to be around 50 km [7].

Figure 1.9: Comparison of investment costs of AC and DC connections [7]

Once it is clear that a DC connection is preferential, the converter type and converter topology have to be chosen. There are two types of converters, namely voltage source converters (VSC) and current source converters (CSC), which are also referred to as line commutated converters (LCC). Both converter types can be seen in Figure 1.10. CSCs use thyristors while VSCs use insulated gate bipolar transistors. There are several reasons why VSCs may be preferential in offshore developments over CSCs. CSC are larger and heavier than VSCs. The CSC absorbs reactive power, while the VSC can control real and reactive power independently and reactive power can be absorbed or injected. Therefore the CSC requires AC filters for reactive power compensation and against harmonics. In comparison VSC technology has insignificant levels of harmonic distortion [8]. While VSCs are self-commutating devices, CSCs rely on a relatively strong AC network for commutation. Hence only VSC technology has black start capability. CSCs can experience commutation failure, when the commutation voltage is reversed before the appropriate valves turns off , finally leading to a shortening of the bridge [18]. Since VSCs are quickly able to change the direction of power flows and are self-commutating and hence do not suffer commutation failure, they are suitable for multi-terminal applications [27]. In VSCs the powerflow can be reversed by changing the current direction, in CSCs the voltage polarity needs to be changed to reverse powerflow [27]. This limits the cable choice for CSC applications. Extruded cables cannot be used

24 Chapter 1. Introduction when polarity is changing, due to the excessive dielectric stress in the cable [28]. Extruded cables are cheaper than mass impregnated cables, which are used for polarity reversal [27].

Figure 1.10: Comparison of current and voltage source converter [8]

As can be seen at the LHS of Figure 1.11, a large amount of onshore wind farm installations has mainly taken place in Scotland. Demand growth will still be dominated in the south in England, where far fewer onshore wind installations have taken place. Hence the secure transfer of energy across the Scotland-England interconnector is going to be a major problem, since it is already operating at its capacity limit. For improved transfer of energy the existing AC transmission route is being reconductored and reinsulated. The installation of series capacitors is envisaged to further improve the transfer capability by reducing the transmission angle and by increasing system stability [29]. However Ref. [30] warns that the series compensation may introduce sub-synchronous resonance into the GB system. The inability to gain the necessary right-of-way for more inland AC lines, made offshore high voltage DC transmission a winning alternative to transport the total Scottish surplus during windy days. DC was chosen over AC for the offshore link due to the relatively long transmission distance, as discussed earlier. The offshore DC transmission plan will also allow for connection of larger offshore wind farms, such as round three wind farms. Even though offshore windfarms are more costly than their onshore counterpart, a significant part of wind installations is being deployed offshore. The first reason is that wind speeds offshore are higher than onshore, offering much higher generation levels. Further gaining planning permission for any kind of onshore installation has become increasingly difficult. The planned regions for offshore developments in the UK can be seen on the RHS of Figure 1.11.

25 Chapter 1. Introduction

Figure 1.11: LHS: Wind farm capacity accross UK (31.12.2012), blue offshore, red onshore, Wind Farm Capacities Map, Department of Energy and Climate Change, [9], RHS: Offshore wind farm developments, UK Offshore wind report 2012, The Crown Estate, [10]

Integration of DC technology, in particular multi-terminal grids, with large offshore windfarms into the GB system is a non-trivial task, that requires careful modelling and analysis. Challenges include the modelling of a power source, that is intermittent and subject to physical phenomena, such as aero- and fluid- dynamics. Maintaining sufficient response capabilities for different timescales and ensuring system stability.

1.5 Research Contributions

This work investigates how the inclusion of more wind and HVDC technology impacts the GB system and the modelling required. The prediction for the 2030 gone green scenario [11] is used together with relevant frequency response literature, to determine the challenges that this change in generation and demand may cause and the technological capabilities already available. In continuation powerﬂow solutions for an AC as well as ACDC network with CSC and VSC technology are found using Matlab. Results of the earlier two cases are validated against an equivalent simulation in PowerFactory. The functionality of the DC link is

26 Chapter 1. Introduction confirmed against results from Arrillaga and Watson [15]. The GB system with a multi-terminal VSC for the connection of offshore wind farms is modelled and analysed in the following chapter. The set-up is similar to that of the eastern link with the three wind farms aiming to represent Doggerbank, Hornsea and East Anglia One. This section describes of the powerflow solution of a multi-terminal DC grid, with multiple AC networks. The solution is necessary to initialize the system. The step response of the system is shown and discussed. A multi-machine test system, including offshore wind, an HVDC link and offshore AC line is used to validate the linearization of such a system using the ”linmod” function provided by Matlab. The system matrix is calculated analytically from the differential algebraic equations of the system and using the inbuilt function. The results of the analytical and Matlab solution are compared. The eigenvalue and participation factor analysis of the GB study case is conducted, analyzed and discussed. It is shown how modes of critical damping can have significant participation from the VSC grid and how the damping can be improved with power system stabilizers. Since the wind speed across a wind farm varies due to wake effect, the modelling of the wake effect is discussed. The wake model is validated against actual wind farm measurements. The wake effect model is then used to show how inertial response provided by a wind farm differs due to wake effect, compared to a free wind speed scenario.

27 Chapter 2

Ancillary services in UK system

Real time balancing of electricity generation and demand in a power system is a necessary and very challenging task. An unbalance between the two is immediately reflected in a frequency change of the AC system. Operators have an extensive experience in balancing a network with a considerable amount of conventional generation, as has been the case in the past. However, in future power systems this task has to be handled differently. This is because of a change in the types of generators and a change in demand (e.g. electric vehicles). Predictions of the types of generation and demand that will be connected to the GB network are available in the public domain [11]. This chapter aims to analyse which of these technologies are capable of providing frequency support according to the available literature. Some generation provides only short term response and some technologies are more adequate for reducing rather than for increasing their power output. Hence the capability of providing response is split into inertial, primary and secondary response as well as low-frequency and over-frequency response. National Grid constantly balances generation and demand to keep the system frequency within a statutory limit of 1% of nominal frequency (50 Hz) [31]. The system is balanced via a combination of different mechanisms such as inertial response, primary frequency control and secondary frequency control. When the demand exceeds generation levels, low-frequency response is necessary. Over-frequency response is used when there is a surplus of generation. The future GB system will have a different generation mix, to that seen in the past, and different loads. During this change, sufficient frequency response capabilities need to be available to ensure system security. Raised levels of intermittent renewable generation, such as wind and solar, increase the need for response services. Converter connected generators cause a loss of effective system inertia and renewable generation introduces a weather dependent change in the geographic location of power generation. Furthermore it is not straight forward to use renewable generators for frequency response services. The prediction for the 2030 GB generation mix [11] is used

28 Chapter 2. Ancillary services in UK system together with relevant frequency response literature, to determine the challenges that this change may cause and the technological capabilities already available. Three predictions, namely slow progression, gone green and accelerated growth are provided in [11]. The gone green scenario is chosen for this work, which assumes that renewable targets are met on time.

2.1 GB system in 2030

2.1.1 Generation

Figure 2.1: Change in generation mix for 2030 under gone green scenario, UK Future Energy Scenarios, National Grid [11]

Major drivers of the change in generation mix are the EU and UK government targets for renewable generation and greenhouse gas emissions [11]. Those targets include the Renewable Energy Directive, which demands 15% of the UK’s energy from renewables by 2020. The Climate Change Act introduced limits on the amount of greenhouse gases that can be emitted in the UK [11]. Figure 2.1 shows the change in generation mix by 2030 compared to 2012. It can be seen that coal and oil/pumped storage based generation decreases while all other generation increases. Renewable generation, in particular wind, shows the most signiﬁcant increase reaching 70.9 GW [11].

29 Chapter 2. Ancillary services in UK system

2.1.2 Load

Figure 2.1 further shows peak demand in the UK is forecasted to increase only mildly by 2030. This is caused by three main factors. The weak economy causes a reduction in demand. Load levels are further reduced by energy eﬃciency improvements. Finally load is masked by small embedded generation, which is treated as negative demand [32]. The larger change is present in the behaviour of demand. It is expected to be more ﬂexible and price sensitive [32], due to smart meters, which are due to be installed in most households by 2020 [33]. These meters will provide the operator with up-to-date information about demand levels and enable demand-side management. Electricity demand will increase by 19 TWh due to 3.2 million electric vehicles on the grid and another 3.2 TWh due to electric heat pumps.

2.2 Frequency Response

Frequency response can be split into several categories. One distinction is between under- frequency and over-frequency. Under-frequency, as in Figure 2.2, occurs when the demand is larger than the generation level. This commonly occurs due to loss of generation. The response to an under-frequency event can be split into several categories according to the time scale. During the ﬁrst 10 seconds of a frequency dip synchronous generation increases, since generators are coupled to grid frequency. After 10 seconds generators providing primary frequency response will be fully available and providing response for at least 20 seconds. At this point secondary frequency response will take over.

Figure 2.2: Under frequency response, National Grid, Grid Code [12], P denoting primary response, S secondary response

Over-frequency response, as seen in Figure 2.3, occurs due to a generation surplus and works similar to under-frequency response. The high-frequency response or reduction

30 Chapter 2. Ancillary services in UK system in generation is required to be fully available within 10 seconds of the frequency rise.

Figure 2.3: Over frequency response, National Grid, Grid Code [12], H denoting high- frequency response

National Grid has investigated future response requirements under the gone green scenario [34]. The response requirements for high frequency are not expected to change much. The requirement for primary and secondary response increase signiﬁcantly from the year 2019/20 due to the introduction of 1800 MW power stations, which increases the largest credible loss from 1320 MW to 1800 MW [34]. A further slight increase in primary and secondary requirements for the 2020 scenario was found due to the signiﬁcant increase in installed wind capacity. A decrease in system inertia caused by the large scale integration of asynchronous generation would lead to increasing dynamic response requirements. Ref. [34] discusses the possibility to amend the grid code to include a requirement for ‘synthetic inertia’ for plant that does not provide inertia. Ref. [35] reported that the future response requirements will be greater than those of the current GB system, due to the integration of more intermittent generation. The inertial, primary and secondary response of a power system are impacted by the integration of renewables, especially during low load situations [35].

2.3 Response by technology

Since the future GB system will have increased low frequency response requirements and the behaviour of both generation and load on the system is changing, it is interesting to see which of the expanding generation technologies can deliver frequency response services. To examine the current state of the art the relevant literature has been surveyed.

31 Chapter 2. Ancillary services in UK system

2.3.1 Conventional generation

By 2030 a significant amount of coal fired plants will be retired due to stricter emission requirements. Remaining plants will either run limited hours or be converted to carbon capture and storage (CCS) plants. Gas generation is predicted to increase, even though carbon capture and storage technology is only starting to be installed around 2030 [11]. Gas fired plants, which will constitute a significant part of the generation fleet, are a well- tested and well-known technology. They have fast ramp rates and relatively low minimum generation levels; they can be shut down and started up quickly. These capabilities mean that they make good intermediate and peaking units for load following [36].

2.3.2 Wind

Wind generation will be a major part of generation in the 2030 system, as can be seen in Figure 2.1. Hence its capability to support the system is very important. An overview [37] of the grid code requirements on wind generation has shown that turbines in the GBsystemarerequiredtobeabletoprovidecontinuous operation in a range from 47.5 Hz to 52 Hz. This is a larger frequency range than that of other countries with a high wind penetration, such as Denmark, Germany, Spain, Ireland or China [37]. Knowing that wind turbines can operate in a large range of frequencies, their capability to provide a response to frequency deviations is of interest. In general wind turbines can change their output very fast which means they can be used for various frequency response tasks. The fastest response to system changes is inertial response. Wind turbines connected to the grid via power electronic converters do not react to frequency drops by increasing their power output in the same way as synchronous machines. To overcome this and to be able to use the fast ramp rate of wind generators major research effort has been undertaken in the field of inertia emulation [13],[38],[39]. [39] modified the DFIG control system to introduce an inertial response. They found that the kinetic energy supplied by the DFIG was greater than that of a fixed-speed wind turbine. [40] concluded their work by warning that systems with a large share of emulated inertia by wind turbines have a higher uncertainty due to variations in the regional wind conditions. They recommend analysis of the location of wind generation with local wind forecasts as part of the dynamic study. Further work has been conducted on the primary frequency response of wind turbines using the kinetic energy stored in the turbine [13, 41] and the possibility to curtail the wind for load following [42]. Wind turbines can also very quickly reduce their output in response to over frequency [43]. Even though wind turbines have the technical capability to support all types of frequency response, as shown in [44], curtailing wind power is very

32 Chapter 2. Ancillary services in UK system

Figure 2.4: Inertia emulation for wind turbines [13], where the torque command Tref consists of three components Tω,ref ,Tin,ref and Tf,ref for rotational, inertial and frequency control respectively expensive [45]. Hence wind turbines are more likely to participate in short under-frequency response services and over-frequency response, since those services do not require keeping a reserve.

2.3.3 Other renewables

Most renewable power in the 2030 GB system is produced by wind generation; further renewable technologies include marine and hydro generators, biomass and solar PV. A project of the University of Kassel in cooperation with several companies has set out to prove the viability of a system that contains only renewable sources. For this project they linked 12.6 MW of wind, 5.5 MW of solar, 4 MW of biogas systems and a pump water storage with a capacity of 8.48 GWh. To balance the system the project used combined heat and power plants fuelled on biogas and pumped water storage while wind and solar produce the bulk power [46].

Figure 2.5: 2012 Mix of renewables other than wind [14]

In the UK most of the solar generation is micro generation embedded in the distribution system. There are several reasons that limit PV generators to contribute to frequency

33 Chapter 2. Ancillary services in UK system response. They would need to be coordinated via smart meters or other forms of communication. They are an intermittent form of generation, hence their response is stochastic. Further, since they are renewable generation it would be expensive to run them below their maximum capability and they do not carry any kinetic energy that could be used for inertial response. The main discussion around solar PV and frequency response has been the increased operating reserves required for its integration into the system [47]. Hydro generation is known to have a relatively fast response, which means it can do load following [36]. An incident in West China provided some experience of balancing a system with large frequency perturbations only with hydro power plants [48]. A study of the incident concluded that hydro generation can provide primary frequency response; however hydro-turbines react slower than steam turbines, due to large dead-bands and suffer from reverse action. This means that as the hydro-turbine tries to increase its output, the output initially drops, which can lead to a larger frequency nadir [48]. Marine technologies are still under development with many different possible concepts under investigation. In mid 2011 three wave and five tidal devices were reported to be in the full-scale demon- stration stage [49]. At the same time about another 15 devices each for wave and tidal were only in the concept stage. Without clear knowledge which marine technology or technologies will be championed for large scale implementation it is too early to speculate about their ability to provide the system with frequency services. A number of generators running or considering to run on bioenergy in the UK are converted coal fired plants. Tilbury B power station [50] has been converted to operate on wood pellets, Eggborough power station has started to burn pellets in addition to coal [51]. Ironbridge is planning to operate with a mix of wood pellets and coal [52]. Drax is planning to convert some of its generation units to biomass [53] as well as Rugeley Power station [54]. Since these plants have previously been coal-fired stations it may well be possible that the frequency response behaviour of these bioenergy generators will not differ from their pre-conversion behaviour. The same holds for landfill gas fired plants.

2.3.4 Interconnector

Interconnectors commissioned after the 1st of April 2005 need to be able to provide mandatory frequency response according to the H/04 Grid code modification [55]. BritNed is the first interconnector affected by this grid code modification. Frequency response tests for BritNed with a flow of 500 MW in both directions have been reported accordingly [56]. The interconnector Basslink, connecting Tasmania with south-east Australia, is an example of an interconnector that can be used for frequency control of either of the two AC networks [57]. The Estlink also has the capability for frequency control by changing the

34 Chapter 2. Ancillary services in UK system power order according to the frequency deviation [58]. [59] reports about the frequency control operation of the VSC link Caprivi connecting Namibia and Zambia. During several months of operation the south western Zambian grid was left in an island situation with only one generator in the network. The VSCs island mode was used to maintain the system frequency.

Figure 2.6: VSC frequency control by changing active power order, where the outer PI controller sets the active power order according to the frequency error, the active power error determines the reference for the quadrature component of the phase reactor current while the reactive power error determines the direct component

2.3.5 Nuclear

In the UK, the nuclear generation has traditionally been treated as a base generation. Reactors of the Magnox type had technical limitations that meant that those plants did not oﬀer load following [60]. Newer nuclear plants have load following capabilities. The pressurized water reactor Sizewell B in the UK for example has been demonstrated in automatic frequency response operation mode [61]. This function is not normally called upon, since it aﬀects the plant lifetime and hence is an expensive service. Other countries such as France and Germany have more frequently used nuclear plants in load following mode [60]. Even without the technical limitations of the past, this technology is likely to remain a base load in the UK for economic reasons [61].

2.3.6 Loads

The concept of adjusting demand levels in order to improve the balance between demand and generation in a power system is not new. National Grid has contracts with some loads that can reduce their demand by at least 3MW, to be able to use them as short term operating reserves [62]. Unlocking the potential of smaller loads for response services requires communication with those loads, which has not been available in the past. Such

35 Chapter 2. Ancillary services in UK system a participation of loads in frequency response services is termed demand-side response. The quantity of available demand-side response depends on the flexibility of the load and the access to control the load. In the future communication with smaller loads such as households will be via smart meters. Increased flexibility in demand is expected with an increase in heat pumps [63] and electric vehicles. Electric vehicles have been predicted to be able to provide 6% of the daily balancing requirement for the year 2020 [64]. Ref. [65] studied the primary frequency response from electric vehicles in the Great Britain power system. The performance of the frequency response depended on the vehicle charging scheme. They also found that it may be sufficient for parts of the electric vehicle fleet to participate in the primary response. The use of smart meters to provide primary frequency response via domestic load control has been investigated by [66] for the UK for 2020. They reported that 1GW of controllable loads would be required for the 2020 scenario, due to large amounts of converter connected generation. They further mention that the time delay in frequency measurement at the household side is critical when using demand-side management for primary frequency response. Benefits and challenges for demand-side management have been analysed by [67]. The main benefits include a reduction in the necessary generation margin, improved efficiency in network investments and the ability to balance a system with a high penetration of intermittent generation. Challenges were the necessary ICT infrastructure, the need for an increased understanding of possible benefits of demand-side management and its competitiveness with other approaches.

2.4 Conclusion

The response requirements of the future GB system are predicted to increase [34]. Gas and renewable generation will increase as well as the capacity of interconnectors and nuclear. Loads will comprise increasing amounts of electrical heat pumps and electric vehicles. Gas generation has always played an important part in balancing the system. Hydro generation and plants run on biomass can also contribute to the frequency response of the system. Major research eﬀort has gone into the frequency support by wind plants. Due to the high cost of keeping a reserve wind generation is most ﬁt for over-frequency and short-term (inertial and perhaps primary) under-frequency support. New interconnectors are required to be able to provide mandatory frequency response. Further system support may be available through the roll-out of smart meters. Using this technology, loads such as heat pumps and electric vehicles could reduce the demand levels during under-frequency events.

36 Chapter 3

Powerﬂow solution and validation for CSC and VSC links

3.1 Introduction

Power flow computation is the basic task to all advanced network control formulations. The powerflow solution is the first step when determining the initial conditions of a system, which are needed for dynamic models. Hence this chapter explores powerflow solutions for a variety of network types, including pure AC, and AC-DC with the DC part containing CSC or VSC technology. The Gauss-Seidel method was the first mathematical method to provide a load flow solution. The Newton method improves the convergence speed of the load flow solution. During the early ’70s the fast-decoupled load flow was developed, while latest extensions include the representation of HVDC lines [68]. Some of the basic concepts of the ACDC power flow are introduced by Radhakrishna [69]. Panosyan et al. [70] modify the Newton-Raphson method for ACDC power flows, keeping the residual vector and the Jacobian matrix for the AC network unchanged and adding a new vector and a new matrix representing the modifications due to the DC link. Osaloni et al. [71] recommend the unified Broyden method instead of the Newton- Raphson method, which uses more iterations while providing a faster computation time. Arrillaga et al. [72], Arifoglu [73] and Smed et al. [74] describe the integration of the DC power flow equations into the fast decoupled AC-load flow including the theory of DC per unit conversion. Silva et al. [75] improve upon this algorithm for weak AC systems by accounting for the dependence of the reactive power consumption of the converter according to the voltage. Gengyin et al. [76] concentrate on the power flow containing VSCs. Purchala et al. [77] provide an analysis of all the assumptions that have to hold

37 Chapter 3. Powerflow solution and validation for CSC and VSC links for a valid DC power flow. Milano [78] has addressed the effectiveness of different solution methods for a pure AC power flow. The development of increasingly effective ACDC power flow programs has shown an advantage in separately solving the AC and DC power flows as described in [15]. This allows for simple integration of DC power flow programs into pre-existing AC power flow solvers. The separate handling and interfacing between AC and DC further allows for changes in the representation of DC technology, without needing to alter the AC power flow solver. Simulation speed and convergence rate are further topics of interest in the area of power flow programs.

3.2 Newton Raphson Method

The Newton Raphson Method in polar coordinates uses the inverse Jacobian matrix to update angles and voltage elements [79]. ΔP J J Δδ = 1 2 (3.1) ΔQ J3 J4 Δ|V |/|V | The fast decoupled Newton Raphson Method exploits the loose coupling between the real power and the voltage and the reactive power and the phase angle respectively. This approximation allows for the oﬀ-diagonal elements of the Jacobian Matrix to be set to zero. ΔP J 0 Δδ = 1 (3.2) ΔQ 0 J4 Δ|V |/|V | Through expansion of the expression and inversion of the relevant Jacobian elements, separate equations for ΔP and ΔQ are gained. This improves the speed of calculation since only J1 and J4 need to be inverted instead of J and also improves memory requirements in the computation. δ J −1 P Δ = 1 Δ (3.3) |V |/|V | J −1 Q Δ = 4 Δ (3.4)

The elements of J1 and J4 in the Cartesian form are as follows:

The diagonal elements of J1 are deﬁned as the change in Pk with a change in δk,where B is the susceptance and G the admittance.

∂P k 2 = −Qk −|Vk| Bkk (3.5) ∂δk

38 Chapter 3. Powerﬂow solution and validation for CSC and VSC links

The oﬀ-diagonal elements of J1 represent the change in Pk with a change in δj,where E and F are the real and imaginary component of the voltage respectively.

∂Pk = Fk(GkjEj − BkjFj) − Ek(BkjEj + GkjFj) (3.6) ∂δj

The diagonal elements of J4 are deﬁned as the change in Qk with a change in |Vk| .

∂Q k 2 |Vk| = Qk −|Vk| Bkk (3.7) ∂|V |k

The oﬀ-diagonal elements of J4 represent the change in Qk with a change in |Vj| .

∂Qk |Vj| = Fk(GkjEj − BkjFj) − Ek(BkjEj + GkjFj) (3.8) ∂|Vj| To solve Equation 3.3 and 3.4 the calculated values for the real and reactive power mismatch are required. The power mismatch is the power injected into the node minus all power ﬂowing out of the node. Hence:

n P P sp − E G E − B F F G F B E Δ k = k [ k( kj j kj j)+ k( kj j + kj j)] (3.9) j=1 n Q Qsp − F G E − B F − E G F B E Δ k = k [ k( kj j kj j) k( kj j + kj j)] (3.10) j=1 TheupdatevaluesΔδ and Δ|V | are then used to ﬁnd the new δ and |V | for the next iteration.

δnew = δold +Δδ (3.11)

|Vnew| = |Vold|(1 + Δ|V |) (3.12)

Following these calculations according to the flowchart in Figure 3.1, the program will iterate through the steps until convergence of the real and reactive power, within a predefined precision, is reached. In programming this succession, it is important to note the different nature of bus bars. In every AC network one generator bus is fixed to function as the slack bus, as indicated in Figure 3.2 . This bus will provide the voltage and angle reference (typically |V | =1andδ = 0). Since the voltage and angle are fixed at this bus, P and Q are generated according to the power flow calculation. All other generator buses in the network will be set to be PV buses. The real power and the voltage magnitude at these buses are fixed, while the reactive power and the

39 Chapter 3. Powerﬂow solution and validation for CSC and VSC links

Figure 3.1: Flowchart for Newton Raphson method phase angle can be varied. It is common to provide a maximum and minimum value for Q that cannot be exceeded. When the power ﬂow solution violates these limits, the bus is set to be a PQ bus. The Q value will be the value that was violated. All buses, that are not generator buses, are PQ buses. The real and reactive power at these buses is known and the voltage and angle are calculated. In the load ﬂow calculation the slack bus is not included in the Jacobian matrix since it can generate any P and Q required. The PV buses are only included in the Jacobian

J1,sinceJ4 corrects for mismatches in Q, which can be generated freely. [79]

40 Chapter 3. Powerﬂow solution and validation for CSC and VSC links Figure 3.2: AC network

41 Chapter 3. Powerﬂow solution and validation for CSC and VSC links

3.3 AC power ﬂow

The described algorithm was written in Matlab for the parameters given in Figure 3.2. The results from Matlab were compared to those gained by a simulation in PowerFactory. PowerFactory requires some values to be entered in actual values rather than per unit values. The conversion formula is:

BaseMV A Z = Z (3.13) p.u. Ω 2 VL(kV ) B(μS) V (kV )2 B = L (3.14) p.u. 106 BaseMV A Results gained with Matlab compared to PowerFactory are displayed in Figure 3.3. The major discrepancies to Matlab results, indicated in red, appear for the reactive power with a deviation of 0.21 Mvar. This is an error of 0.147 %, which seems acceptable. These differences can be due to rounding errors or slight differences in models. The overall result, of both models matching well, confirms the correct computation in the Matlab model.

42 Chapter 3. Powerﬂow solution and validation for CSC and VSC links Figure 3.3: Results gained with Matlab and Powerfactory, red denoting Matlab results, black Powerfactory results

43 Chapter 3. Powerﬂow solution and validation for CSC and VSC links

3.4 ACDC power ﬂow with Current Source Converter (CSC)

The solution of any ACDC power flow problem can be found using two different methods, namely the unified and sequential method [15]. In the unified method the solution of the AC and DC system is found simultaneously, while the real and reactive part of the solution are treated iteratively. This leads to an iterative scheme named PDC, QDC, which can be simplified to P, QDC. In the sequential method the AC and DC solutions are found iteratively. This has the advantage that the DC system can be modelled by a fixed PQ injection in the AC powerflow and vice versa the AC system is modelled by fixed terminal voltages in the DC flow. This decoupling allows for a very simple integration of DC flows in an AC network, without the need to alter the AC power flow solver. As such the sequential method uses an iterative scheme of PQ, DC. A diagram of the sequential method is shown in 3.4.

Figure 3.4: Sequential ACDC powerﬂow method

The flow through the DC line using CSC technology is modelled by a set of three equations describing converter operation, and two control equations per converter, according to [15]. Hence a DC link would be described by ten equations, five for the rectifier and

44 Chapter 3. Powerﬂow solution and validation for CSC and VSC links

Figure 3.5: Current source converter link

five for the inverter. A diagram for such a link is provided in Figure 3.5. XC is the commutation reactance, which is the reactance between the commutating voltage and the converter valves [80]. k is the per unit ratio of the AC versus DC current, where √ 1 k 3 20.995 α γ a 1 = pi . is the firing delay angle, is the extinction advance angle and is the transformer off-nominal tap ratio. At the rectifier side the operation is described by:

0=Vd5 − k1a5V5cosφ5 (3.15)

V − k a V cosα 3 I X 0= d5 1 5 5 + π d5 C5 (3.16)

0=Vd5 + Vd4 − Id5RL (3.17)

The control equations that were chosen for the rectiﬁer are α control and DC power α P sp transmission. min, the minimum ﬁring angle, and the DC power d are the selected reference values.

0=cosα − cosαmin (3.18) V I − P sp 0= d5 d5 d (3.19)

For the inverter following equations must hold:

0=Vd4 + k1a4V4cosφ4 (3.20)

V − k a V cos π − γ 3 I X 0= d4 1 4 4 ( )+π d4 C4 (3.21)

0=Id4 + Id5 (3.22)

The control regime at the inverter side is set to γ control and DC voltage control. γ V sp min, the minimum extinction advance anlge, and the DC voltage d4 are the selected

45 Chapter 3. Powerﬂow solution and validation for CSC and VSC links reference values.

0=cos(π − γ) − cos(π − γmin) (3.23) V − V sp 0= d4 d4 (3.24)

The DC powerﬂow solution ensures that all these equations hold. Initially the residual value δR of all these equations with the current DC values x is calculated. The eﬀect of a change in variables on the ten converter equations is given by the matrix A. A is the matrix of the Jacobian values for the converter equations with regard to the DC variables. Using Equation 3.25, it is possible to calculate update values for the DC variables. The updated values can then be used to recalculate the residual value δR. This process is repeated, until all elements of δR are close to zero within a predetermined precision [15], as shown in Figure 3.6.

δR =[A]δx (3.25)

Figure 3.6: Powerﬂow solution for DC network

46 Chapter 3. Powerﬂow solution and validation for CSC and VSC links

3.5 Initial validation

To test, whether the DC part of the simulation is working correctly, it was compared to a solution gained by Arrillaga and Watson in “Computer Modelling of Electrical Power Systems” [15]. The results of the comparison can be seen in Figure 3.7, where the solution provided in the book is indicated in black and the Matlab solution is indicated in green. Following the book, reactances are in p.u. on a 100 MVA base, whereas the link resistance in Ohm has been converted to p.u. accordingly. Angles are referred to in degrees, voltages inkVandcurrentsinAmps.PowersareonanMVAbase.

As a control scheme Pdc, α and Vdc, γ were used. Excluding the tap changer position, all values match well, with the largest discrepancy being 0.377%. The tap changer positions show larger differences. This could be due to an accumulation of errors from rounded values provided in the book. Further it is not clear whether the AC voltages given are on 100kV base and what the % solution for a refers to. When back-substituting the solution values provided in the book into the equation provided by the authors for the DC voltage in terms of the commutating voltage, the value for a results as 0.9722 or 1-0.0278. 0.0278 is in good agreement with the 2.8% shown in the solution. This suggests that the authors use a different definition of the tap position in the solution, which is 1-a. The values for φ can be checked by calculating the inverse tangent of the reactive over the real power, and are found to match with the solution provided. Overall the comparison indicates a correct operation of the CSC powerflow.

47 Chapter 3. Powerﬂow solution and validation for CSC and VSC links

Figure 3.7: DC solution compared to results in book by Arrillaga and Watson[15], green denoting Matlab results, black results from book

3.6 ACDC simulation Powerfactory vs. Matlab

With the programs for the AC powerflow and the DC powerflow, the sequential method can be implemented, as depicted in Figure 3.4. A layout of the network, used for simulation, as can be seen in Figure 3.8, was also created in PowerFactory. The results of both simulations can be seen in Figure 3.9, where Matlab results are indicated in green. The results are found to match well, except for the reactive power flow. The maximum mismatch in the reactive powerflow is 2.07 Mvar. These mismatches are found in the reactive power at the DC link and at the slack bus. If the reactive power in the DC link differs between Matlab and PowerFactory, this will automatically be true for the slack

48 Chapter 3. Powerflow solution and validation for CSC and VSC links bus. In a simulation of the AC part of the network in Matlab, with the terminal P and Q values found by PowerFactory, the major mismatch was found to be only 0.21 Mvar at the slack bus. This mismatch is the same magnitude that was found in the first AC power flow comparison. It is hence obvious that the difference between both models occurs due to different reactive power at the DC link terminals. The functionality of the DC link was tested in comparison to a solution gained by Arrillaga and Watson in “Computer Modelling of Electrical Power Systems” [15], and found to be acceptable. In the DC link the transmission of real power and the tap changer setting as well as DC voltage and current matches PowerFactory results well. The difference in reactive power between the DC link models may occur for example since the Matlab simulation is assuming an ideal transformer, while PowerFactory might be using a more detailed model. All real powers, voltages and phase angles gave extremely good matches well below 1%. This provides a good confidence in the developed algorithm. To fully confirm results, the inbuilt PowerFactory converter model will need further investigation to make necessary adjustments, to match the Matlab model.

49 Chapter 3. Powerﬂow solution and validation for CSC and VSC links iue38 CCCCntokparameters network CSC ACDC 3.8: Figure

50 Chapter 3. Powerﬂow solution and validation for CSC and VSC links Figure 3.9: ACDC solution compared to PowerFactory, green denoting Matlab results, black Powerfactory results

51 Chapter 3. Powerﬂow solution and validation for CSC and VSC links

3.7 ACDCpowerﬂowwithVSC

Having completed the ACDC power flow with CSC technology with the DC link as in 3.5, the DC link is modelled to contain VSC technology instead. The power flow algorithm will still alternate between AC and DC iterations as before. The AC section will actually stay unchanged while the DC section will contain equations describing the VSC model. As before some control equations are set. In this case, the PMQM control scheme was chosen, specifying the modulation factor (M) at both ends and the real power (P) on one end and the reactive power (Q) on the other end. For each converter any two variables can be choosen as control equations. As the modulation factor M, describing the ratio of the output voltage Vc to it maximum possible value, has to stay between 0 to 1 [16], it simplifies matters to choose M as one control equation, since otherwise parameters need to be chosen that ensure M to be inside the region or control equations need to be switched, once the limit is reached.

Figure 3.10: VSC connection [16]

Based on Figure 3.10 the real and reactive power can be calculated as [16]:

P = BtVtVcsin(δ) (3.26)

Q = BtVt(Vccos(δ) − Vt) (3.27)

Ignoring converter losses AC side power equals DC side power [16]:

VdId = BtVtVcsin(δ) (3.28)

For a two level PWM VSC the relationship between converter voltage and DC voltage is [16]:

Vc = kMVd (3.29)

52 Chapter 3. Powerﬂow solution and validation for CSC and VSC links

The modulation factor allows for a variation in AC voltage, without a change in DC voltage. The factor k, that relates the DC voltage with the AC converter voltage in a √ 6 basic two-level three-phase (non-PWM) VSC is π [16]. If the DC link is set up for the PMQM control scheme, as indicted in Figure 3.11, four equations will ﬁx M at both terminals and P and Q for the two terminals respectively, P sp Qsp M sp M sp where 4 , 5 , 4 and 5 are the reference values.

V I − P sp 0= d4 d4 4 (3.30)

B V kM V cosδ − V − Qsp 0= t 5( 5 d5 5 5) 5 (3.31)

M − M sp 0= 4 4 (3.32)

M − M sp 0= 5 5 (3.33) The equation relating DC current and AC voltage can be found from Equation 3.28 and Equation 3.29.

0=Id4 − BtkM4V4sinδ4 (3.34)

0=Id5 − BtkM5V5sinδ5 (3.35)

From Ohm’s law:

0=Vd4 − Vd5 − Id4RL (3.36)

Since there can only be one current in a line, the current seen from two opposite reference points has to add to zero:

0=Id5 + Id4 (3.37)

Thus by ﬁxing 4 variables, there are 8 unknowns (Vd4, Vd5, δ4, δ5, M4, M5, Id4, Id5)and 8 equations. This is suﬃcient to solve the DC section as before with the CSC algorithm. The calculation will be conducted by creating an 8 x 8 Jacobian matrix comprising of the derivatives of all eight equations for all eight variables. The network for calculation and results gained can be seen in Figure 3.11.

53 Chapter 3. Powerﬂow solution and validation for CSC and VSC links iue31:AD ouinfrVCln,gendntn albrsls lc endsse parameters system deﬁned black results, Matlab denoting green link, VSC for solution ACDC 3.11: Figure

54 Chapter 3. Powerﬂow solution and validation for CSC and VSC links

A comparison to a VSC link in PowerFactory was not conducted since a validated version of a VSC module, similar to that of the CSC, with inbuilt transformer, was not available at the time. To model a VSC link in PowerFactory the industry practice is to use a PWM block for the VSC converter module. The converter transformer and phase reactor are added as separate components. The overarching VSC control, that allows the converter to control e.g. the voltage magnitude at the system side, has to be implemented using basic programming (DSL) blocks.

3.8 Conclusion

Major work has already been conducted in the field regarding the ACDC power flow with different algorithms and under different conditions. Various converter types and topologies have been investigated for modelling purposes. In this chapter powerflow solutions for an AC as well as ACDC network with CSC and VSC technology have been found using Matlab. Results of the earlier two cases were validated against an equivalent simulation in PowerFactory. The results showed that there was a good match in the AC power flow model, with the largest mismatch of 0.147% occurring at the LV side of the transformer. The ACDC CSC power flow model converged to values matching those of PowerFactory except for reactive power flow. Mismatches for the reactive power seem to originate from a discrepancy in the converter transformer models. The functionality of the DC link was confirmed against results from Arrillaga and Watson [15]. The ACDC VSC model converged to the results seen in Figure 3.11.

55 Chapter 4

Modelling of the GB system with multi-terminal VSC connected wind farms

4.1 Introduction

While the dynamic characteristic of the Scottish and English interconnected AC system is well understood and can be managed by generator additional control (power system stabilizer) the dynamic performance of the system in the presence of wind generation and HVDC transmission is not well investigated. This calls for a multi-machine stability model including wind, HVDC technology and synchronous generators. Existing research tends to concentrate on specific aspects of the network individually. Some research investigates into wind farm modelling; other work is conducted on voltage source converter (VSC) modelling, or fault level analysis of combined technologies. The modelling details of the grid are neither very systematic nor in multi machine small signal stability framework, which is often necessary for planning studies for the interconnected utilities. Ref [81] used a small AC test system to study the interactions of two separate DC links in the network. Using state-space modelling and participation factor analysis they found that tightly connected infeeds can interact with each other. However, this does not occur when infeeds are connected via a large impedance. They conclude by stressing the importance of small-signal interaction studies for the installation of multi-infeed HVDC systems. A dynamic study of a DFIG model and a simple DC link connected to an infinite AC grid was conducted by [82], to design a damping controller for the rectifier current regulator of the DC link, capable of mitigating the power fluctuations from the wind farm. Ref [83] designed a methodology for the selection of droop gains using a four-terminal grid.

56 Chapter 4. Modelling of the GB system with multi-terminal VSC connected wind farms

A comparison between a three-terminal test rig and simulations was executed in [84]. Three topologies were discussed, namely, two wind farms to one onshore point, one wind farm and multiple onshore points and a T-shaped connection of a wind farm into a DC link. The authors report a good agreement between test rig and simulation results. The small signal analysis and control design of a four-terminal system, of which two terminals are connected to offshore wind farms (fixed-speed induction-generators) and the other two to a three bus AC grid has been demonstrated by [85]. [86] studied a three-terminal line commutated converter (LCC) set-up with variable wind on one terminal and conventional plant on the next, to buffer power fluctuations from the wind and a load center on the last terminal, including considerations for fault ride through. At the wind side a 500 MVA VSC converter is used to supply the commutation voltage for the 2000 MW LCC. [87] developed a voltage-current droop control for a four-terminal system with two offshore wind farms and two onshore stations connecting to the AC system. The authors derive power share ratios that lead to minimal system copper loss. A hybrid HVDC system was proposed by [88], consisting of two offshore VSC terminals and two onshore LCC terminals, connected to two independent AC networks. They described power sharing, between stations and a black start principle for this four converter system, where one of the LCCs works as a charging source by reversing polarities through the operation of DC switches. They further discussed frequency support from the offshore wind farm, via the DC network, where wind power plants are releasing kinetic energy and the droop control of the onshore stations is adjusted to give frequency support from one AC grid to the other. Yao et al. [89] are looking at the transient properties of a VSC and the control schemes related to the converter. Their main objective is the analysis of a single and three phase fault on the windfarm or AC grid side. Their models do not appear to explore small signal analysis. Livani et al. [90] are tackling the voltage stability, while mainly concentrating on variable wind speed, three phase faults and 20% voltage sags on the grid side. Jovcic [91] models the interconnection of a number of windturbines, where some of them are connected to one rectifier only. The focus lies mainly in the possible loss of synchronism of a group of wind turbines that are connected to the same rectifier, when windspeeds differ and change over time. He further addresses whether a group of windfarms at different frequencies can be connected to the same inverter using VSC rectifiers. His models are based only on an AC terminal with a load, not on an AC grid with different components such as synchronous generators. Livermoore et al.[92] review research in the field of multi- terminal DC technology for the use of offshore windfarms. Ludois et al. [93] provide a benchmarking of the three converter techniques, namely current source converter (CSC), VSC and Bridge of Bridge converter (BoBC). Their benchmarking is for the application of a windfarm with an AC grid that is characterised as weak or strong. The paper is not

57 Chapter 4. Modelling of the GB system with multi-terminal VSC connected wind farms concerned with the precise properties of the AC network. Spahi et al. [94] compare the first two and HVAC as an alternative for connecting windfarms to the onshore grid. They categorize the use of the different technologies by power of the windfarm and distance to the shore. Their models do not include the onshore network and are with regards to single and three phase faults. Li et al. [95], Sommerfelt [96], Padiyar et al. [97], Zhao et al. [98], Chan et al. [99] and Zhang et al. [100] provide a model for VSC. Li et al. [95] give a dynamic model for VSC, testing it on a network of two AC parts and a DC line. No exact details of the AC grid are included and the analysis is limited to a short time fault and sudden change in power. Sommerfelt [96] looks at the influence of a windfarm connected to the Norwegian grid via VSC and AC cables respectively. The main emphasis is given to fault analysis and the modelling of the windfarm is kept to a minimum. Chan et al. [99] use a real time station (RTS) to test the computer model of a VSC in a real system representing a windfarm and demand. Zhao et al. [98] develop a simplified model for a VSC that can be used in the transient analysis of AC networks. Zhang et al. [100] provide a model for the VSC ignoring the switching ripples and hence increasing simulation speed. Ding et al. [101] extend the analysis to modular multi-level VSC. Padiyar et al. [97] give a procedure to design the optimal control parameters for VSC. Many publications in the field concentrate on specific network components, e.g. the DC grid, and use very simplified AC system models or infinite buses to represent the AC system. While certain phenomena can be studied in isolation, other interactions may only become apparent when the whole network with all relevant components is represented. Such a comprehensive model also allows for the study of various phenomena at a time. A system model that incorporates all relevant technologies, like AC, HVDC, wind farms and conventional generation with up to date models can provide valuable information. It will be useful in predicting how the different parts of the GB network interact, as the contribution of wind generation and the inclusion of HVDC technology increases. The simulation includes the GB system [102] with an offshore HVDC grid at the east coast, connecting to three offshore wind farms. This is similar to the situation at the east coast of the GB system after the connection of Dogger Bank, Hornsea and East Anglia One. In this simulation Doggerbank has a capacity of 3 GW, while the other wind farms are 1.2 GW each. This is in line with the information on the first tranche of installations [103, 104, 105]. The DC links are of VSC type. The connections are not simple point to point, but interconnected (MTDC) to allow for flow along the desired corridors. The world’s first HV multi-terminal (three terminals) VSC link has started operation in China in December 2013. This proves the feasibility of multi-terminal VSC applications and provides motivation for further research on the topic [106]. Figure 4.1 shows the simplified GB system with the distribution in generation mix. It also shows

58 Chapter 4. Modelling of the GB system with multi-terminal VSC connected wind farms the MTDC grid, the oﬀshore AC network and the oﬀshore wind farms.

Figure 4.1: GB system with oﬀshore DC grid and three oﬀshore wind farms

The parameters of the network, generation and demand levels are presented in the Appendix D.

4.2 Selection of parameters

Various parameters are required for the system model. The output power of three wind farms connected via converters I to III is chosen as 3 GW, 1.2 GW and 1.2 GW respectively. These parameters resemble the predictions for the connection of the ﬁrst tranche of wind turbines in Dogger Bank, Hornsea and East Anglia wind farms [103, 104, 105]. A nominal DC voltage of 550kV, has been cited for the connection of Dogger Bank [107]. This work assumes a symmetrically grounded mono-polar conﬁguration [108] using a con-

59 Chapter 4. Modelling of the GB system with multi-terminal VSC connected wind farms ventional two level converter, in which a potential of 550 kV across the two DC coupling capacitors leads to a reference DC voltage of 275kV across each capacitor, due to the symmetrical grounding. DC cable parameters have been estimated using the length of the DC lines. The distance from the wind farms to the shore is provided in [103, 104, 105] while the distance between the wind farms was estimated using wind farm coordinates provided in [109, 110]. Dogger Bank, Hornsea and East Anglia wind farms have a distance of 125 km, 150 km and 43.4 km from the shore respectively. Using the wind farm coordinates the distance between Dogger Bank and Horn Sea was estimated as 125.2 km and between Horn Sea and East Anglia One as 211.2 km. Khatir [111], reports per kilometer parameters for a DC line. The resistance is given as 0.015 Ω /km and the inductance as 0.792 mH/km. The capacitance of the DC line is negligible compared to the DC linking capacitor in conventional two level converter configurations. This would not hold true for a multi- level configuration. The DC link capacitor is reported as 0.2 mF by [112] and 10 mF by [113]. 1 mF was chosen for this simulation and provided a good transient behaviour, as can be seen in Figure 4.2. The larger DC link capacitor lead to a delayed response with significantly larger overshoot. The DC link capacitance has a major influence on the dynamic behaviour of a VSC grid and should be chosen with care.

Comparison of step response with different DC link capacitance 26.9

26.85

26.8

26.75

26.7

26.65

26.6 With DC link capacitance 10 mF 26.55 With DC link capacitance 1mF

26.5 Real power at onshore slack converter VI (100 MW) 0 5 10 15 20 25 30 Time (seconds)

Figure 4.2: Comparison of slack converter step response with DC link capacitance of 1mF and 10mF, when oﬀshore wind farm output connected to converter I is reduced by 1%

A base AC voltage is required for p.u. conversion of the oﬀshore AC developments and converter stations. Dogger Bank wind farm is expected to have a voltage somewhere between 132kV and 245kV [114] at the collector stations (the network location were

60 Chapter 4. Modelling of the GB system with multi-terminal VSC connected wind farms strings of wind turbines are connected). Hence 230kV is used for p.u. conversion of the new development. 100 MVA is the base power used. [115] provide offshore wind farm parameters, including equivalent parameters of the collector system. The parameters [115] provide for transformer inductance are also used for the inductance of transformer and phase reactor inductance of any converter stations. The resistance of the converter transformer and phase reactor has been assumed to be negligible and set to zero in line with information provided in [108]. All models include the resistance term to allow for modelling of different systems, that make the modelling of the converter transformer and phase reactor losses desirable. Following all information, calculation and appropriate base conversion, system parameters for the offshore developments are displayed in Figure 4.3.

Figure 4.3: Parameters of oﬀshore DC grid and three oﬀshore wind farms

4.3 Representation of the physical system through modelling components

The simulation model consists of five components; namely wind farm model, offshore line model, VSC MTDC model, synchronous machine model and a network representation. Wind farms have been represented by a behavioural model similar to the one described in [116]. The modelling of synchronous machines has been described in [117, 18]. The offshore AC transmission line model, consisting of line resistance, inductance and capacitance can be derived from standard equations using reference frame transformation [118].

61 Chapter 4. Modelling of the GB system with multi-terminal VSC connected wind farms

[102] provides a description of the GB network. [108] provides information regarding the model development of the VSC DC grid. The modelling of the DC grid and oﬀshore AC connection are discussed in this section. The modelling details of synchronous machines and wind generation are discussed in the appendices, since they are well known, and added only for reference and completeness sake.

Figure 4.4: Simulation set-up of a large multi-machine system with onshore and oﬀshore wind, MTDC network and oﬀshore AC grid

The onshore network is a Y matrix, that determines all onshore voltages, when current injections across the network are known. The onshore voltage is seen by the synchronous generators, the onshore converter stations and onshore wind generation. At least one synchronous generator in the onshore network is on governor control [18], meaning the torque command will be adjusted to keep the frequency at a set value, e.g. 50 Hz. The offshore grid does not contain any generation on governor control, because the offshore frequency is determined by the power electronics. There are no synchronous machines in the offshore system to cause a frequency response to a power mismatch. To ensure a power balance at the offshore grid it is essential for the converter to pass any offshore power directly into the DC grid. This can be ensured by setting the offshore converters to control both the voltage magnitude and phase angle, either at the system bus or the converter bus. In this case, the converter bus voltage is controlled. The converter switching is very fast, justifying the assumption of a fixed converter voltage. Since the offshore systems consist of a wind power plant and a line, with the voltage at the converter end fixed, the wind turbine generators offshore are set to reactive power control mode, rather than voltage control mode. The wind turbine model provides a current output, according to a given voltage at its terminal. Hence for the interconnection between the

62 Chapter 4. Modelling of the GB system with multi-terminal VSC connected wind farms

wind turbine and the converter bus the converter bus voltage Vc off and the current at the wind turbine ioff are known. This is sufficient to determine the voltage at the wind turbine Voff and the converter current ic off . The offshore converter voltage and current as well as onshore voltage and system frequency are known to the multi-terminal VSC model, which is then able to determine the current injections by the onshore converters into the main AC network.

4.4 Multi-area ACDC powerﬂow calculation

The initialization of the modelling blocks describes the initial conditions at steady state without any disturbances. The initial conditions need to be provided at all integrator blocks within the model. The first step in finding the initial conditions is the solution of the powerflow, in this case an ACDC powerflow. The powerflow solution provides the necessary information to calculate the initial values for both the synchronous machines, HVDC and the wind power plants.

Figure 4.5: AC and DC networks in a network as shown in Figure 4.1

The simulated system consists of four individual AC networks (the GB system and three offshore grids) and one DC grid. Every AC system requires a slack bus. While a generator is chosen in the onshore system to provide this function for the offshore grids this is not an optimal choice. In a practical system wind generation produces as much power as possible and this power is then exported to the grid. To reflect this in the powerflow, the wind turbine should not act as the slack. Since the offshore buses connected to the converter buses pass any power that arrives from the wind farm into the DC grid, they act as slack buses and are simulated as such for the load flow. The DC grid also requires a slack bus. This DC slack can be situated at any of the onshore converter stations, since the offshore stations already act as AC slack buses. In this manner a slack bus has been allocated for every grid. Figure 4.6 shows the program structure for the solution of the load flow problem. It is noteworthy that the powerflow solution for the four AC networks is found in one joint operation by aggregating all the AC network information in one impedance matrix, with four disjoint parts. This concept is illustrated in Figure 4.7, where Z1 represents the

63 Chapter 4. Modelling of the GB system with multi-terminal VSC connected wind farms

Figure 4.6: Program structure for a load ﬂow solver containing multiple AC networks and aDCgrid

impedance matrix for the main AC grid, and Z2 to Z4 the matrices for the three oﬀshore AC grids. Each of these AC grids must contain at least one AC slack bus. This is an extension to work in [108], which focuses on cases with only one AC and DC system.

Figure 4.7: Simulation of four AC systems in one AC load ﬂow via matrix aggregation

The DC power flow is responsible for modelling any power flow outside the AC system buses. This includes the converter AC side, such as the phase reactor, transformer and the DC connection. Chapter 3 provided the powerflow solution of a CSC and VSC link,

64 Chapter 4. Modelling of the GB system with multi-terminal VSC connected wind farms taking into account firing angle control and modulation respectively. Internal converter control of the firing angle or PWM is an extremely fast phenomena in the μs range [108]. The internal converter control is modelled by a delay in the μs range in this chapter for simplicity and simulation speed. The converter operation can be modelled as a black box, assuming the desired converter waveform is generated by the internal converter control [108]. Figure 4.8 shows an equivalent circuit of a two-terminal mono-polar VSC system, that is symmetrically grounded [108]. The figure shows a two-terminal system for ease of understanding, the six-terminal system studied in this work can be represented in the same fashion. It can be seen, that the overall DC voltage is twice the nominal DC voltage, due to the symmetrical grounding [108]. During steady state simulation the DC line model consists exclusively of ideal resistances, since inductance and capacitance only have an impact on changes in current and voltage. Hence they will be included in the circuit model for dynamic simulation.

Figure 4.8: Circuit diagram of symmetrically grounded, mono-polar two-terminal VSC circuit, including converter AC side

As can be seen from Figure 4.6 the load flow solution of the whole network requires four iterative processes, one for the AC powerflow, one for the DC powerflow, one for finding the AC bus voltage and angle at the DC slack converter and finally an overarching iterative process for coordination between AC and DC networks.

4.4.1 AC powerﬂow and converter variables

To start the program all known parameters are defined and an initial guess is required for all unknowns. In the first instance the AC powerflow is solved using the initial values. The solution of the AC powerflow is an iterative process, applying any suitable solution method such as Newton Raphson or fast decoupled Newton Raphson. A detailed description of standard AC load flow methods is provided in [79]. Once the AC powerflow has converged, all parameters on the AC side are known, apart from those on the AC converter buses. The calculation of these parameters is trivial since both complex voltage and apparent power are known on one side of the impedance and

65 Chapter 4. Modelling of the GB system with multi-terminal VSC connected wind farms the voltage and power on the other side are to be determined. The current is calculated as [108]:

∗ ipr =(Ss/Vs) (4.1)

Since the AC side voltage, the current and the line impedance are known the converter side voltage can be calculated [108]:

Vc = Vs + iprZpr (4.2)

Hence the converter power is known [108]:

∗ Sc = Vcipr (4.3)

4.4.2 Powerﬂow in DC Grid

Assuming loss-less conversion of the converters, the real power on the AC side should be of the same magnitude as that on the DC side. Power leaving the AC system, and as such appearing as a load with negative sign, will appear as generation in the DC system, with a positive sign and vice versa.

Pdc + Pac = 0 (4.4)

Any power flow problem requires one slack bus per grid, to account for losses. While the real power is known and can be fixed for all other converters, one converter has to be selected as DC slack bus. For this converter the real power is unknown, but the DC voltage is fixed. The well known equations for DC current and power, as described in [108] are used to find expressions for current in terms of admittance, voltage and power. The admittance matrix is real rather than complex, since DC circuits in power flow calculations only have resistance terms, due to zero frequency.

idc =YdcVdc (4.5)

The formula for DC power has a factor two, since the symmetrically grounded converter topology has a voltage potential of twice the nominal DC voltage.

Pdc =2Vdcidc (4.6)

The current can also be expressed as [108]:

66 Chapter 4. Modelling of the GB system with multi-terminal VSC connected wind farms

Pdc idc = (4.7) 2Vdc Hence it is true that:

Pdc 0=YdcVdc − (4.8) 2Vdc The current term has been eliminated from this equation. For each converter either the voltage or power are known. This matrix equation is split into N scalar equations, where N is the number of converter stations.

N−1 Pdc 1 0= Y1iVdc i +Y1NVdc N − i=1 2Vdc 1 . . N−1 Pdc N−1 (4.9) 0= YN−1iVdc i +YN−1NVdc N − i=1 2Vdc N−1 N−1 Pdc N 0= YNiVdc i +YNNVdc N − i=1 2Vdc N By default the DC slack converter is chosen to be the converter station with the highest number, this simpliﬁes the programming, while still maintain a generic code. The order of the converter stations can be chosen freely, since it does not depend on the order of AC buses. The solution of the DC voltages and DC slack power is found via the Newton Raphson method using the equations shown in (4.9). The vector of unknowns is [108]: ⎡ ⎤ V ⎢ dc 1 ⎥ ⎢ . ⎥ ⎢ . ⎥ xvar = ⎢ ⎥ (4.10) ⎣ Vdc N−1⎦

Pdc N The Jacobian Matrix J of the DC equations is found from the equations shown in (4.9). Where the rows of the matrix correspond to the equations and the columns to the variables. As such J(1,2) is derivative of the ﬁrst equation with respect to the second variable. The Jacobian J(a,b) is as follows: ⎧ ⎪ Pdc a ⎪ Y + if a=b= 1 to N-1 ⎪ aa 2V 2 ⎨⎪ dc a − 1 J(a, b)= if a=b= N ⎪ 2Vdc N ⎪ ⎪ 0ifb=Nandb=a ⎩⎪ Yab if b=Nandb =a

67 Chapter 4. Modelling of the GB system with multi-terminal VSC connected wind farms

The variables xvar are initialised, from these values an error vector Rerr can be calculated from the RHS of the equations shown in (4.9). The error in the guess for xvar is estimated using Equation (4.11). This equation is solved for Δxvar by left hand division.

JΔxvar = Rerr (4.11)

In the next iteration xvar is updated by Δxvar according to Equation (4.12).

xvar = xvar − Δxvar (4.12)

This process is repeated until all elements of the error vector Rerr are close to zero within a predeﬁned precision. Once the DC iteration has converged all DC voltages and the DC power at the DC slack bus are known.

4.4.3 Reverse slack converter calculation

The power at the AC converter bus of the DC slack converter is the equal and opposite of the power calculated for the DC slack power, according to Equation (4.4). The AC bus interfacing with the DC slack bus is treated as PQ bus, hence a change in the apparent power, will change the result of the AC load flow. The AC voltage on the system side is known and the apparent power at the converter side is known. To achieve this the reactive power at the converter side is fixed at a constant value. In this case the reactive power was fixed during the very first execution of the calculation of converter variables to the reactive power of the converter. Since the apparent power on the converter side and the complex voltage on the AC system side are known, we can use another Newton Raphson iteration process to determine the converter voltage and the apparent power on the system side of the slack converter. The power at the converter side is calculated as follows:

∗ V − V P + jQ = c s V (4.13) c c Z c Splitting all variables into real and imaginary components gives:

∗ V + jV − V − jV P + jQ = cQ cD sQ sD (V + jV ) (4.14) c c R+jX cQ cD The complex denominator is eliminated by multiplying both nominator and denominator by the complex conjugate, this leads to:

2 2 ∗ (Pc + jQc)(R +X )=((VcQ + jVcD − VsQ − jVsD)(R − jX)) (VcQ + jVcD) (4.15)

68 Chapter 4. Modelling of the GB system with multi-terminal VSC connected wind farms

The terms are multiplied out, taking the conjugate as indicated, then the equation is split into real and imaginary terms, leading to two equations:

Equation for real terms: 2 2 − − − − 2 2 0=R(VcQ + VcD VsQVcQ VsDVcD)+X(VsQVcD VsDVcQ) Pc(R +X ) (4.16)

Equation for imaginary terms: 2 2 − − − − 2 2 0=X(VcQ + VcD VsQVcQ VsDVcD)+R(VsDVcQ VsQVcD) Qc(R +X ) (4.17)

These equations are used to ﬁnd the converter voltage via the Newton Raphson method. The Jacobian matrix for this is formed by taking the derivative of both equations with respect to the real and imaginary parts of the converter voltage:

J(1, 1) = R(2VcQ − VsQ) − XVsD J(1, 2) = R(2V − V )+XV cD sD sQ (4.18) J(2, 1) = X(2VcQ − VsQ)+RVsD

J(2, 2) = X(2VcD − VsD) − RVsQ

The slack converter voltage is initialised, from this value an error vector Rerr is calculated from the RHS of equations (4.16) and (4.17). The error in the guess for the converter voltage is estimated using Equation (4.19). This equation is solved for ΔVc by left hand division.

JΔVc = Rerr (4.19)

In the next iteration Vc is updated by ΔVc according to Equation (4.20).

Vc = Vc − ΔVc (4.20)

This process is repeated until all elements of the error vector Rerr are close to zero within a predeﬁned precision. Once the slack converter iteration has converged the converter voltage at the slack bus is known. At this point the power at the system bus is calculated for the DC slack converter.

∗ V − V P + jQ = s c V (4.21) s slack s slack Z s

69 Chapter 4. Modelling of the GB system with multi-terminal VSC connected wind farms

If the calculated Ps slack + jQs slack is the same as the apparent power at this bus from the AC powerﬂow solution the whole ACDC simulation has converged and results can be used for further work. Otherwise the apparent power at the slack converter is updated and the process starts again from the AC powerﬂow.

4.4.4 Power ﬂow solution

The load ﬂow solution for the AC networks can be seen in Figures 4.10, 4.11, 4.12 and 4.13. The last six buses represent the three oﬀshore wind farms. The bus numbers referred to in Figures 4.10, 4.11, 4.12 and 4.13 are shown in Figure 4.9, where upper numbers denote load buses and lower numbers generator buses.

Figure 4.9: GB system with oﬀshore development, bus numbers are included in blocks, upper numbers denote load buses, lower numbers generators

70 Chapter 4. Modelling of the GB system with multi-terminal VSC connected wind farms

Figure 4.10: Initial voltages and angles across the system in p.u.

Figure 4.10 shows the voltage magnitude (in blue) and angle (in green) for all buses. It can be seen that both the voltage magnitude and angle stay within reasonable values. It can further be seen that the voltage drop in oﬀshore wind farms is larger than in the onshore network.

Figure 4.11: Initial power injected across the system in 100 MW base

Figure 4.11 shows the power drawn by the loads in the network in green and the power injected by the generators in blue. The last nine blue peaks and troughs are related to the offshore wind generation and the converter stations. The last three peaks are power injection into the AC grid from the three wind farms. The three troughs show the power drawn out of the offshore AC grid into the DC grid. The next three peaks going from right to left represent the power injection from the DC grid into the AC grid. The reactive power injection from generation and reactive loads can be seen in Figure 4.12. The currents injected throughout the AC network can be seen in Figure 4.13, where the offshore network and onshore converters can be clearly identified again by the last nine peaks and troughs.

71 Chapter 4. Modelling of the GB system with multi-terminal VSC connected wind farms

Figure 4.12: Reactive power across buses

Figure 4.13: Currents injected across the system

The power flow throughout the whole offshore development, including the DC grid is illustrated in Figure 4.14. In a symmetrically grounded mono-polar configuration [108] the DC power is calculated using twice the DC voltage. This has been indicated in the figure by a times two sign in the DC side of the converter block. The upper two onshore converter stations are in PQ mode, where all set values are shown in Figure 4.14. Any surplus power arriving from the offshore wind farms is directed to the DC slack bus, using the north-south connection between offshore converters. This can be seen from the current flows in the DC grid. Similarly, at times of low wind generation, this north-south connection can be used to aid the constraint north-south corridor in the AC grid. Power can be injected into the DC grid at converter IV and re-enter the AC grid at converter VI.

72 Chapter 4. Modelling of the GB system with multi-terminal VSC connected wind farms

Figure 4.14: Initial conditions for oﬀshore development

4.5 Dynamic modelling of the VSC MTDC grid

The dynamic model for the HVDC grid has been designed with the assumption that the DC slack converters are at the converter stations with the highest number. This does not limit the flexibility in any way, as the order of the converter stations can be freely chosen and does not depend on the order of the AC stations. This simple assumption does allow for some simplification of the power flow program as well as dynamic modelling. As indicated in Figure 4.15, the dynamic model of the voltage source converter grid encompasses the dynamic behaviour of the connection between the system and converter AC buses, where the filter is neglected. The model further includes the dynamics of the DC grid, with DC link capacitors, cable resistance and inductance. For simplicity a two-terminal system is shown in Figure 4.15, however the concept remains the same for a larger number of converter stations. At offshore converter stations the converter voltage is fixed, through the fast converter control and the modelling of dynamics from the converter transformer or phase reactor are incorporated in the offshore model, as can be seen in Figure 4.4. The converter dq-reference system is chosen such that the q-axis is aligned with the system voltage, as can be seen in Figure 4.16. This means that the angle between the

73 Chapter 4. Modelling of the GB system with multi-terminal VSC connected wind farms

Figure 4.15: Circuit of VSC grid with two converters for dynamic analysis, where Vdc is the voltage potential from line to ground across a single capacitor system DQ-reference frame and the dq-reference frame is the system voltage angle. This alignment leads to a simpliﬁcation of the dynamic equations since Vsd is zero. The orientation of the direct and quadrature axis has been extensively discussed in the literature. An IEEE Committee report [119] on phasor diagrams in 1969 concluded it is preferred for the direct axis to lead the quadrature axis by 90◦.“Using this principle, the quadrature axis can be taken as the real axis. The direct axis then becomes the imaginary axis ...” [119]

Figure 4.16: Reference frame conversion, from DQ to dq

Figure 4.17 shows the variables involved in the simulation of the multi-terminal VSC grid. Each converter station can control two variables, the variables that were chosen for control purposes for the simulation case are indicated in red. Starting at the offshore side, the voltage magnitude and angle at the converter station are fixed by the fast acting converter. The current injected into the converter bus can then be determined from the wind power plant model in combination with the offshore AC grid model, discussed in Section 4.6. The offshore AC converter power is hence known. The converters are modelled as ideal lossless converters. Hence the DC power at the offshore stations is known. Two onshore converter stations are set on P, Q control. The onshore voltage is determined by the system model, according to the current injections by all generators

74 Chapter 4. Modelling of the GB system with multi-terminal VSC connected wind farms and converters. The input of onshore system voltage allows for the real and reactive power references to be converted to reference values for q- and d- components of phase reactor current reference. Once the phase reactor current is known the converter voltage can be determined. At this point the power at the AC converter bus is known and hence the DC power. One converter station onshore is the DC slack converter station. This station controls the DC voltage at its terminal and thus provides a voltage reference for the DC grid. Any mismatch between injected power, power drawn and power losses will pass through this bus. In the DC grid ﬁve buses have a known DC power and one has a ﬁxed DC voltage. Simulation of the DC grid with the respective cable parameters is used to determine the DC power at the DC slack converter bus and hence the real power at the AC converter bus. The DC slack converter station can control one more quantity, either the reactive power or Vsq. In this case the converter regulates the reactive power. Pc is equal to

Vcqipqr q + Vcdipqr d. Since the direct component current reference is already determined by the Q control, the equation for Pc can be used to determine the quadrature current reference at the DC slack bus.

Figure 4.17: Overview of the VSC multi-terminal DC grid

Figure 4.18 shows the dynamic modelling blocks of the multi-terminal VSC grid. External signals are shown in green. These signals are reference signals and a selector for

Vs or Q control mode, they further include voltage and frequency of the onshore grid and converter voltage and current for the oﬀshore grids.

75 Chapter 4. Modelling of the GB system with multi-terminal VSC connected wind farms iue41:Dnmcmdlo ut-emnlD grid DC multi-terminal of model Dynamic 4.18: Figure

76 Chapter 4. Modelling of the GB system with multi-terminal VSC connected wind farms

The output of the block is the current injection by the onshore converters into the AC grid. Blocks and signals related to the DC network are shown in blue, other components responsible for the AC converter side are shown in black. Each block has been labelled with a number in red, for ease of referring. The converter dq-reference system is chosen such that the q-axis is aligned with the system voltage. Block 1 in Figure 4.18 is responsible for this alignment, which leads to a simplification of the dynamic equations since Vsd is zero. Block 2 re-aligns the converter current entering the AC network with the system DQ-reference frame. A voltage source converter can regulate the voltage magnitude at the system bus or the reactive power via the direct current reference. At the same time it can regulate either real power or for the DC slack buses, DC voltage, using the quadrature current reference. Blocks 3, 4, 5, 6 are the proportional integral (PI) controllers used for this purpose. The integrator blocks are initialised to correspond with the power flow solution of the output signal. In this case iprd for Blocks 3 and 4 and iprq and idc for Blocks 5 to 6 respectively. The power drained from the AC grid is the same as the power injected into the DC grid, if converter losses are neglected. In other words the AC side power and DC side power should cancel, as shown in Equation (4.4). In Block 7 this relationship is used to find the quadrature current reference.

2Vdcidc + Vcdiprd + Vcqiprq = 0 (4.22)

(−2Vdcidc − Vcdiprd) iprq ref = (4.23) Vcq Block 8 simply concatenates the two quadrature current references, using the fact that the converters are numbered in such a way, that the DC slack buses have the highest number. Block 9 has a selector input, which is a vector specifying for each converter, whether it is in voltage or reactive power control mode. The direct current reference for each converter will be selected according to the voltage or reactive power control mode. The direct and quadrature current references are then used in the inner current controller, Block 10, together with the system voltage magnitude and frequency. The inner current controller uses the reference values to control the direct and quadrature currents as well as the dq-components of the converter voltage. The inner current controller is best understood, starting with the dynamic equation of the AC system containing the converter phase reactor and transformer [108].

di (t) V (t) − V (t)=L pr +R i (t) (4.24) c s pr dt pr pr

77 Chapter 4. Modelling of the GB system with multi-terminal VSC connected wind farms

Figure 4.19: Inner current controller of the converter stations

This relationship can be converted to real and imaginary components in DQ-reference frame.

d (V + jV ) − (V + jV )=L (i + ji )+R (i + ji ) (4.25) cQ cD sQ sD pr dt prQ prD pr prQ prD

Since the signals are rotating AC voltages, it is desirable to use a rotating reference frame, such that the signals appear stationary. This rotating dq-reference frame is achieved by multiplying all signals by ejωt,whereω is the frequency of rotation in radians π rad per seconds. In this case this is 2 50 [ sec ]. Since the rotation of the signals is already expressed by the exponential term the signals themselves are not rotating.

d ejωt j − − j ejωt jejωt ejωt j (Vcq + Vcd Vsq Vsd)=Lpr dt( iprq + iprd)+Rpr (iprq + iprd) (4.26)

The derivative term in the equation is expanded using the product rule.

78 Chapter 4. Modelling of the GB system with multi-terminal VSC connected wind farms

jωt e (Vcq + jVcd − Vsq − jVsd)= d d jωejωt ejωt − ωejωt jejωt ejωt j Lpr( iprq + dtiprq iprd + dtiprd)+Rpr (iprq + iprd) (4.27)

This equation can be divided by ejωt and split into two equations for real and imaginary terms.

d 1 Rpr iprq = (Vcq − Vsq)+ωiprd − iprq (4.28) dt Lpr Lpr

d 1 Rpr iprd = (Vcd − Vsd) − ωiprq − iprd (4.29) dt Lpr Lpr These equations are in actual values. To convert them in p.u. values we can replace all actual values by p.u. values times base values.

d V ω V R p.u.Z ω V p.u. b b p.u. − p.u. ωp.u.ω p.u. b − pr b b p.u. b iprq = p.u. (Vcq Vsq )Vb + biprd p.u. iprq (4.30) dt Zb Lpr Zb Zb Lpr Zb Zb

d V ω V R p.u.Z ω V p.u. b b p.u. − p.u. − ωp.u.ω p.u. b − pr b b p.u. b iprd = p.u. (Vcd Vsd )Vb biprq p.u. iprd (4.31) dt Zb Lpr Zb Zb Lpr Zb Zb

Several base values can be cancelled from these two equations. Further, as mentioned the dq-reference frame was chosen, such that Vsd is zero, which means that Vsd can be eliminated from the equation.

d ω R p.u.ω p.u. b p.u. − p.u. ω p.u. − pr b p.u. iprq = p.u. (Vcq Vsq )+ iprd p.u. iprq (4.32) dt Lpr Lpr

d ω R p.u.ω p.u. b p.u. − ω p.u. − pr b p.u. iprd = p.u. Vcd iprq p.u. iprd (4.33) dt Lpr Lpr

The base conversion of inductance introduces ωb terms that do not cancel, further the ω term introduced by the rotating reference frame remains an actual value and not a per unit value. Using Laplace transform the equation can be rearranged, such that only terms con- p.u. p.u. taining iprq and iprd respectively appear on the LHS of the equation.

p.u. s p.u. p.u.ω ω p.u. − p.u. ω p.u. p.u. iprq ( Lpr +Rpr b)= b(Vcq Vsq )+ Lpr iprd (4.34)

79 Chapter 4. Modelling of the GB system with multi-terminal VSC connected wind farms

p.u. s p.u. p.u.ω ω p.u. − ω p.u. p.u. iprd ( Lpr +Rpr b)= bVcd Lpr iprq (4.35)

p.u. p.u. The terms appearing on the LHS with iprq and iprd respectively are the denominator p.u. of the transfer function, while the terms on the RHS are the input required to ﬁnd iprq p.u. and iprd . This can be seen in the two transfer functions on the RHS of Figure 4.19. The p.u. p.u. initial conditions of the transfer functions are iprq and iprd as determined by the ACDC power ﬂow program.

p.u. p.u. PI controllers with process variables iprq and iprd respectively are used for the inner current controller where the RHS terms are the control input. Hence the initial conditions of the PI controllers are the RHS terms. Vsq is an input to the inner current controller and ω p.u. p.u. −ω p.u. p.u. the cross coupling terms Lpr iprd and Lpr iprq respectively are determined by the p.u. p.u. PI controllers with process variables iprd and iprq . Hence the control input determines p.u. p.u. the reference value for Vcq and Vcd respectively.

The converter power electronics have a delay Td in adjusting the converter voltage to the reference value, this can be modelled through an additional delay block. In this case the delay time has been chosen as 10.3μs, according to [120], where the typical turn-on and turn-off switching times for an IGBT module are given as 3.9μsand6.4μs respectively. The power electronics may respond slower, due to the control delay of the IGBT switching. In general the switching is rather fast with a delay around the 100 μs range and will only be of concern for fast phenomena. As can be easily seen from Figure ω p.u. ω p.u. 4.19, the initial conditions for the delay blocks are bVcq and bVcd . Block 11 in Figure 4.18 includes the offshore converter current and voltage d- and q-components in the vectors for converter currents and voltages across all converters in dq-frame. Block 12 determines the DC currents for both onshore and offshore converters alike, excluding any DC slack buses. Using Equation (4.4), Block 12 calculates the DC currents as shown in Equation (4.36).

−Vcdiprd − Vcqiprq idc = (4.36) 2Vdc Block 13, concatenates the DC currents from converters in power control mode with the DC currents from the converters in DC voltage control. Looking at the DC grid in Figure 4.15 following equations hold true [108]:

dV C dc 1 = i − i (4.37) dc dt dc 1 cc

80 Chapter 4. Modelling of the GB system with multi-terminal VSC connected wind farms

dVdc 2 Cdc dt = idc 2 + icc (4.38)

d icc − − Ldc dt = Vdc 1 Vdc 2 Rdcicc (4.39)

The difference in sign for icc between Equation (4.37) and (4.38) occurs due to the definition of the current directions for icc and idc. To be consistent and to facilitate simple calculation methods icc will be defined to be pointing in the same direction as the idc vector of the converter bus with the lower converter number. For example the current icc flowing between converter two and three, will be defined in the same orientation as the idc current of the second converter. Block 14 is responsible for the calculation of the DC voltages at all buses using the current flows in the DC network, as described in Equations (4.37) and (4.38). While the implementation of previous blocks was obvious from the equations, due to their vector nature, the implementation of Block 14 is less trivial. It is desirable to keep the implementation as generic as possible, to allow for any topological changes in the study case. An implementation has been chosen that allows the representation of Equation (4.37) and

(4.38) for any number of converter stations. The branch currents icc can be represented as a skew symmetric matrix ICC, where the size is equivalent to the number of converter stations N. This matrix is initialised during the ACDC power ﬂow, once all DC voltages are known. Using the DC voltages, a skew symmetrical matrix of size N can be built, showing the voltage potential between nodes. For a three-terminal system the matrix would be as follows: ⎡ ⎤ 0 V − V V − V ⎢ dc 1 dc 2 dc 1 dc 3⎥ ⎢ − − ⎥ ⎢ Vdc 2 Vdc 1 0 Vdc 2 Vdc 3⎥ Vdif = ⎢ ⎥ (4.40) ⎣ Vdc 3 − Vdc 1 Vdc 3 − Vdc 2 0 ⎦

The ICC Matrix can be calculated using element wise multiplication of the purely real admittance matrix Y and V , the minus sign occurs since Y (1, 2) = −1 : dc dif dc Rdc(1,2)

ICC = −Ydc · Vdif (4.41)

The resulting matrix ICC is a skew symmetrical matrix, this means that the sign diﬀerence in current ﬂow direction between Equation (4.37) and (4.38) is accounted for in the matrix, such that when ICC is multiplied by a column vector Ivec of N ones, the resulting vector icc is the sum of all the branch currents at the node where icc has the same orientation as idc. Hence Equation (4.37) can be used for all buses.

81 Chapter 4. Modelling of the GB system with multi-terminal VSC connected wind farms

d Vdc − Cdc dt = idc ICCIvec (4.42) This formulation is beneficial, since it enables us to find the DC voltage at all converter stations in a single operation, using a single matrix equation, independently of the number of converter stations. As we have seen in Equation (4.35), the per unit conversion of a formula containing differential terms introduces ωb terms that do not cancel. Hence the relationship shown in Equation (4.43) requires careful conversion for the application in a per unit system. This conversion leads to:

C p.u. dV p.u. dc dc p.u. − p.u. = idc ICC Ivec (4.43) ωb dt Block 15 represents the dynamics shown in Equation (4.39). The skew symmetrical branch current matrix can be found using Equation (4.45) after ﬁnding Vdif according to

Equation (4.40). The matrix Vdif is easily implemented by multiplying the column vector of DC voltages with a row vector of ones of equal length. This will lead to a matrix X. T The matrix Vdif is simply X − X .

d ICC − Ldc dt = Vdif RdcICC (4.44) As before this relationship needs to be carefully converted, if it is to be applied in a per unit system. The per unit equation is:

L p.u. dI p.u. dc CC p.u. − p.u. p.u. = Vdif Rdc ICC (4.45) ωb dt

4.6 Dynamic modelling and initialization of the oﬀ- shore AC grids

As shown in Figure 4.4 the wind farms are connected to the DC grid via offshore AC connections. This model block represents all network components from the wind plant terminal to the DC converter bus. The inductance of the phase reactor and the AC network in Figure 4.20 can be represented by one equivalent inductance. The offshore grid also has a certain resistance and capacitance to ground. The model allows for a conductance to ground, that is taken as zero during the following simulations. This network can be expressed by two differential equations:

di (t) V (t) − V (t)=L c off +Ri (t) (4.46) off c off off dt c off

82 Chapter 4. Modelling of the GB system with multi-terminal VSC connected wind farms

Figure 4.20: Circuit components in AC oﬀshore grids

d t t − t Voff ( ) t ioff ( ) ic off ( )=C dt +GVoff ( ) (4.47) Noting the similarity between Equation (4.46) and Equation (4.24), the previous derivation can be used and the per unit dq- reference form of Equation (4.46) can be determined without much effort. Assuming the offshore frequency is held at its reference value by fast converter control, ω = ωb.

p.u. s p.u. p.u.ω ω p.u. − p.u. ω p.u. p.u. ic off q( Loff +R b)= b(Voff q Vc off q)+ Loff ic off d (4.48)

p.u. s p.u. p.u.ω ω p.u. − p.u. − ω p.u. p.u. ic off d( Loff +R b)= b(Voff d Vc off d) Loff ic off q (4.49)

Equation (4.47) is converted to a per unit dq-reference frame, following the same procedure.

d j − − j j j ioff Q + ioff D ic off Q ic off D =Cdt(Voff Q + Voff D)+G(Voff Q + Voff D) (4.50)

After expressing the rotation of the signals as ejωt this equation becomes:

d ejωt j − − j ejωt jejωt ejωt j (ioff q + ioff d ic off q ic off d)=Cdt( Voff q + Voff d)+G (Voff q + Voff d) (4.51) This equation is simplified by applying the product rule:

jωt e (ioff q + jioff d − ic off q − jic off d)= d d jωejωt ejωt − ωejωt jejωt ejωt j C Voff q +C dtVoff q C Voff d +C dtVoff d +G (Voff q + Voff d) (4.52)

83 Chapter 4. Modelling of the GB system with multi-terminal VSC connected wind farms

This equation is divided by ejωt and split into real and imaginary parts. The real terms are: d − − ω ioff q ic off q =CdtVoff q C Voff d +GVoff q (4.53)

The imaginary terms are:

d − ω ioff d ic off d =CdtVoff d +C Voff q +GVoff d (4.54)

These equations are expanded into per unit and base components.

V V Cp.u. d Cp.u. Gp.u. p.u. b − p.u. b p.u. − ωp.u.ω p.u. p.u. ioff q ic off q = Voff qVb bVoff dVb + Voff qVb (4.55) Zb Zb Zbωb dt Zbωb Zb

V V Cp.u. d Cp.u. Gp.u. p.u. b − p.u. b p.u. ωp.u.ω p.u. p.u. ioff d ic off d = Voff dVb + bVoff qVb + Voff dVb (4.56) Zb Zb Zbωb dt Zbωb Zb

After cancelling all possible base terms, these equations become:

Cp.u. d Cp.u. p.u. − p.u. p.u. − ω p.u. p.u. p.u. ioff q ic off q = Voff q Voff d +G Voff q (4.57) ωb dt ωb

Cp.u. d Cp.u. p.u. − p.u. p.u. ω p.u. p.u. p.u. ioff d ic off d = Voff d + Voff q +G Voff d (4.58) ωb dt ωb Equations (4.48), (4.49), (4.57) and (4.58) describe the dynamic behaviour of the offshore AC links. The ACDC powerflow solution is used to initialise the model. The dynamic modelling of the multi-terminal VSC grid and the offshore AC grid have been discussed in detail in this chapter. The dynamic modelling of wind power plants and synchronous machines is well known and details are given in Appendix A.2 and B respectively.

4.7 Conclusion

In this chapter the modelling of the GB system with multi-terminal VSC connected wind farms was described. The selection of parameters was discussed and a study case was chosen, that may resemble the connection of the ﬁrst tranche of Dogger Bank, Horn Sea and East Anglia One. For the connection to land a six-terminal VSC grid model was conﬁgured, where the length of DC cable was chosen according to wind farm coordinates.

84 Chapter 4. Modelling of the GB system with multi-terminal VSC connected wind farms

The chapter discussed how the overall system was represented by modelling various components. For the initialization of the system a powerﬂow with several AC grids and a multi-terminal DC grid had to be solved. This process is described in detail. The dynamic model development for the multi-terminal DC grid and the oﬀshore AC grids is discussed in this chapter, whereas the dynamic modelling of synchronous machines and wind power plants can be found in the Appendices. In Chapter 5 the developed dynam- ical model will be used to investigate the small signal analysis of the GB network with multi-terminal VSC connected wind farms.

85 Chapter 5

Small signal analysis of the GB system with multi-terminal VSC connected wind farms

Using the dynamic system model described in Chapter 4, simulations are carried out to observe the behaviour of the GB system (including onshore conventional and wind generation) with an offshore DC grid and offshore wind farms. The model is initially tested by running it for a long time without any perturbations, to check that values stay at their initial values. After this is confirmed, disturbances are introduced in the system. The most promi- nent change is a small step in the power command of the largest wind farm. A step change is the most influential in terms of the impact on dynamics. The wind farm drops its power output by 1% at five seconds. At 10 seconds, the power command returns to its original value. It can be seen in Figure 5.1 that the power at the 3 GW offshore wind farm decreases at 5 seconds by 1%, which means to 2.97 GW and increases again to 3 GW at 10 seconds. During this time the power at the other two wind farms stays unaltered. The offshore wind plants are all set on reactive power control, rather than the voltage control that their onshore counterparts operate in. This means that the reactive power should be controlled to the same value, irrespective of the change in real power. During the power step at wind farm I, the reactive power is maintained at the initial value. Two spikes can be seen in Figure 5.2 at the times where the step occurs, due to the time it takes the controller to adjust to the changes. It can also be seen how this change propagates through the AC offshore grid to the appropriate offshore converter. The line model contains a capacitance, representative of the wind turbine and collector system capacitance, a resistance representative of the collector system and an inductance to represent the collector system as well as converter

86 Chapter 5. Small signal analysis of the GB system with VSC connected wind farms

Real Power at offshore wind farms 30.1

30 12.0001 12.0001

29.9 12 12 29.8

11.9999 11.9999 29.7 Real power at wind farm I (100 MW)

29.6 Real power at wind farm II (100 MW) 11.9998 Real power at wind farm III (100 MW) 11.9998 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 Time (seconds) Time (seconds) Time (seconds)

Figure 5.1: Real power at oﬀshore wind farms, during active power step at wind farm I

Reactive power in offshore wind farms −0.24 −0.1197 −0.1197

−0.26 −0.1198 −0.1198

−0.1199 −0.1199 −0.28

−0.12 −0.12 −0.3 −0.1201 −0.1201

−0.32 −0.1202 −0.1202 Reactive power wind farm I (100 MVar) Reactive power wind farm II (100 MVar) −0.1203 −0.34 Reactive power wind farm III (100 MVar) −0.1203 0 5 10 15 20 25 30 0 5 10 15 20 25 30 5 10 15 20 25 30 Time (seconds) Time (seconds) Time (seconds)

Figure 5.2: Reactive power at oﬀshore wind farms, during active power step at wind farm I transformer and phase reactor. The losses in the collector system can be seen in Figure 5.3 during the initial condition. Further the power drop at the wind farm leads to a power drop at the respective converter bus. After the power drop at the wind farm is removed, the power at this converter returns to the original value. The power loss can also be seen at the other two oﬀshore converter buses, the power at those buses stays undisturbed, as the wind farm power is unchanged. As can be seen in Figure 5.4 the change in wind farm real power does not only introduce a step in real power on the converter side, but also a step in reactive power. The other converters maintain their initial values, since there is no change at their respective wind farms. The drop in converter power is equivalent to a drop in DC power i.e. the product of DC current and DC voltage has to drop. A voltage drop can be seen in Figure 5.5, for

87 Chapter 5. Small signal analysis of the GB system with VSC connected wind farms

Real power at offshore converter buses 28.85

28.8 11.7726 11.7726 28.75 11.7724 11.7724 28.7

28.65 11.7722 11.7722

28.6 11.772 11.772 28.55 11.7718 11.7718 28.5 Converter I real power (100 MW) Converter II real power (100 MW) Converter III real power (100 MW) 11.7716 28.45 11.7716 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 Time (seconds) Time (seconds) Time (seconds)

Figure 5.3: Real power at oﬀshore converters, during active power step at wind farm I

Reactive power at offshore converter terminals −1.02 3.2059 3.2059

−1.04 3.2058 3.2058 −1.06

3.2057 −1.08 3.2057

−1.1 3.2056 3.2056

−1.12 3.2055 3.2055 −1.14 Reactive power at converter I (100 MVar) Reactive power at converter II (100 MVar) 3.2054 Reactive power at converter III (100 MVar) 3.2054 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 Time (seconds) Time (seconds) Time (seconds)

Figure 5.4: Reactive power at oﬀshore converters, during active power step at wind farm I converter I. Converters II to V lower their voltages accordingly. Converter VI, in green, is on DC voltage control. Even though the voltage at this terminal drops at the time of the step, the controller ensures that the voltage is returned to its original value. It can also be seen, that after the wind farm power is returned to its initial value the DC voltages start to return to their initial values. Converters II to V are controlled to maintain a constant DC power, in this way the voltage drops and rises appear as a mirror image for those DC currents, see Figure 5.6. The power at converter I dropped i.e. both the DC voltage and current should drop, where the peaks in the voltage curve are cancelled in the shape of the DC current. Power is injected into the DC system at converters I to III from the windfarms, and drained from the DC system into the main AC system at converters IV to VI. This explains why the

88 Chapter 5. Small signal analysis of the GB system with VSC connected wind farms

DC voltages at all converter terminals

1.212

1.273 1.25 1.211 1.272 1.249

1.271 1.248 1.21 1.27 1.247 1.209 1.269 1.246 1.208 1.268 1.245 DC voltage at converter I (p.u.) DC voltage at converter II (p.u.) 1.267 1.244 DC voltage at converter III (p.u.) 1.207 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 Time (seconds) Time (seconds) Time (seconds)

1.229 1.198

1.256 1.228 1.197 1.255 1.227 1.196 1.254

1.253 1.226 1.195 1.252 1.225 1.194 1.251 DC voltage at converter VI (p.u.) DC voltage at converter V (p.u.) 1.193 DC voltage at converter IV (p.u.) 1.224 1.25 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 Time (seconds) Time (seconds) Time (seconds)

Figure 5.5: DC voltage at all converters, during active power step at wind farm I

later three DC currents are negative. With a reduction in power injection by the oﬀshore side, the DC slack converter VI has less power to inject into the AC system. This means the magnitude of the DC current is reduced. The DC voltage control at converter VI is acting to keep the DC voltage at its reference value. Hence the change in current should account for the whole change in output power during steady state. The DC voltage peaks that appear during control action at converter VI that were seen in Figure 5.5 are opposed by the DC current shape. Figure 5.7 validates that the control indeed maintains the DC power at the appropriate levels. The power injected at converter I drops, while the power at converters II and III remain undisturbed. The power at converters IV and V are also maintained at their reference values, since they are in PQ control mode. The power at these buses is negative since it is power drained from the DC system, it will appear as power injected i.e. with a positive sign on the AC side. As the power injected by the wind farm drops, the power reaching the AC system drops accordingly. As the simulated network has negligible transformer and phase reactor resistance, the power seen on the DC side is practically the power appearing on the AC system buses. This is seen in Figure 5.8. All three onshore converters are in reactive power control mode, and hence the reactive

89 Chapter 5. Small signal analysis of the GB system with VSC connected wind farms

DC currents at all converter terminals 11.32 4.73 4.875

11.3 4.725 4.87 11.28

11.26 4.72 4.865

11.24 4.715 4.86 11.22

DC current at converter I (p.u.) 11.2 DC current at converter II (p.u.) 4.71 0 5 10 15 20 25 30 DC current at converter III (p.u.) 0 5 10 15 20 25 30 0 5 10 15 20 25 30 Time (seconds) Time (seconds) Time (seconds) −11.05 −4.77 −4.875

−4.775 −4.88 −11.1 −4.78 −4.885

−4.785 −4.89 −11.15

−4.79 −4.895 −11.2 −4.795 −4.9 DC current at converter VI (p.u.) −4.8 DC current at converter V (p.u.) −4.905 −11.25 DC current at converter IV (p.u.) 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 Time (seconds) Time (seconds) Time (seconds)

Figure 5.6: DC current at all converters, during active power step at wind farm I

DC power at all converter stations 28.8 11.7726 11.7726

28.7 11.7724 11.7724

11.7722 11.7722 28.6

11.772 11.772 28.5 11.7718 11.7718 DC power at converter I (100 MW) DC power at converter II (100 MW) 28.4 DC power at converter III (100 MW) 0 5 10 15 20 25 30 5 10 15 20 25 30 0 5 10 15 20 25 30 Time (seconds) Time (seconds) Time (seconds) −11.9994 −11.9994 −26.5

−11.9996 −11.9996 −26.6 −11.9998 −11.9998

−12 −12 −26.7 −12.0002 −12.0002

−12.0004 −12.0004 −26.8

−12.0006 −12.0006 DC power at converter IV (100 MW) DC power at converter V (100 MW) DC power at converterV I (100 MW) −26.9 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 Time (seconds) Time (seconds) Time (seconds)

Figure 5.7: DC power at all converters, during active power step at wind farm I

90 Chapter 5. Small signal analysis of the GB system with VSC connected wind farms

Real power at onshore system buses for converters IV to VI 12.0002 12.0002 26.95

26.9

12.0001 12.0001 26.85

26.8

12 12 26.75

26.7

11.9999 11.9999 26.65

26.6 Real power at onshore converter V (100 MW) Real power at onshore converter IV (100 MW) 11.9998 11.9998 Real power at onshore converter VI (100 MW) 26.55 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 Time (seconds) Time (seconds) Time (seconds)

Figure 5.8: Active power at onshore converters, during active power step at wind farm I power is maintained at the reference values; see Figure 5.9.

Reactive power at system buses of onshore converters IV to VI 0.1635 0.1723 −1.1380

0.1630 0.1722 −1.1381

0.1625 0.1721 −1.1382

0.1620 0.1720 −1.1383

0.1615 0.1719 −1.1384

0.1610 0.1718 −1.1385 Reactive power at converter IV (100 MVar) Reactive power at converter V (100 MVar) 0.1605 0.1717 Reactive power at converter VI (100 MVar) −1.1386 0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 5 10 15 20 25 30 Time (seconds) Time (seconds) Time (seconds)

Figure 5.9: Reactive power at onshore converters, during active power step at wind farm I

The onshore generator governor adjusts the torque command of the relevant synchronous machine to maintain the system frequency at its reference value. This way it reacts to a mismatch between the generation and demand by increasing or reducing its power output. During the drop in power from oﬀshore generation the governor in Figure 5.10 increased the generation level. Since the excitation control is acting to keep the voltage magnitude at the reference value, the reactive power of the governor machine also changes (Figure 5.10). Since both the synchronous machines and onshore wind power plants are set to control

91 Chapter 5. Small signal analysis of the GB system with VSC connected wind farms

Governor response 18.1 3

18.05 2.99 18

17.95 2.98

17.9 2.97 17.85 Real power (100 MW) 2.96 17.8 Reactive power (100 MVar) 17.75 2.95 0 5 10 15 20 25 30 0 5 10 15 20 25 30 Time (seconds) Time (seconds)

Figure 5.10: Governor response to oﬀshore wind power step voltage magnitude it is not surprising that the change in voltage magnitude is rather small and settles down, after the disturbance has been removed. The largest excursion is seen at the governor machine (yellow trace in Figure 5.11), since the behaviour of this machine is highly coupled with system changes.

−4 x 10 Change in voltage magnitudes 0.5

−0.5

−1

−1.5

−2 Change in voltage magnitude (p.u.) −2.5 0 5 10 15 20 25 30 Time (seconds)

Figure 5.11: Change in voltage magnitude from initial values

Figure 5.12 shows the change in current magnitudes. The green square trace in the negative region of the ﬁgure shows the drop in injected power from the DC slack converter. The large yellow excursion is the governor response to this disturbance. By default one generator is the reference bus with a phase angle of zero degrees, all other angles are then deﬁned relative to this angle. The angles before and after the

92 Chapter 5. Small signal analysis of the GB system with VSC connected wind farms

Change in current magnitudes

0.2

0.1

−0.1

−0.2

−0.3

−0.4 Change in current magnitude (p.u.) 0 5 10 15 20 25 30 Time (seconds)

Figure 5.12: Change in current magnitude from initial values disturbance should be the same in relation to the reference bus. The change of angles relative to the reference bus with respect to their initial values is shown for voltages and currents across the whole onshore AC grid. It can be seen that for voltages as well as currents, there are changes of angle relative to the reference bus only during the disturbance and the settling time. Before and after the disturbance relative angles are as calculated during the initialization. The largest excursion is seen in the relative voltage and current angle change of the governor machine (yellow trace in Figures 5.13 and 5.14).

93 Chapter 5. Small signal analysis of the GB system with VSC connected wind farms

Change in voltage angle relative to reference bus 0.1

0.08

0.06

0.04

0.02

−0.02

−0.04

Relative voltage angle change (degrees) −0.06 0 5 10 15 20 25 30 Time (seconds)

Figure 5.13: Change in voltage angles from initial values relative to reference bus

Change in current angle relative to reference bus 0.3

0.25

0.2

0.15

0.1

0.05

−0.05

Relative current angle change (degrees) −0.1 0 5 10 15 20 25 30 Time (seconds)

Figure 5.14: Change in current angles from initial values relative to reference bus

5.1 Evaluation of state matrix and eigenvalues

The dynamics of a system along with powerﬂow equations is described by diﬀerential and algebraic equations of inputs, outputs, state variables, algebraic variables and constants.

94 Chapter 5. Small signal analysis of the GB system with VSC connected wind farms

The diﬀerential equations in vector form are expressed as:

dx F x, z dt = ( ) (5.1)

While algebraic equations are written as follows:

0=G(x, z) (5.2)

Using the diﬀerential and algebraic equations a state-space representation of the system can be found. A state-space representation consists of four matrices, relating state variables and inputs with the change in state-variables and outputs. When investigating a system in the closed loop form, which means there are no input variables or output variables in the system, the matrix of interest is the system matrix A. This matrix describes how the state-variables relate to a change in state variables. The A-matrix is found via partial derivatives using the chain rule [121], [122], to eliminate the algebraic variables: dF x, z ∂F x, z ∂F x, z ∂G x, z −1 ∂G x, z A ( ) ( ) − ( ) ( ) ( ) = dx = ∂x ∂z ∂z ∂x (5.3)

If a system model is created in Simulink for time domain simulation, the state-space model can be extracted using the function “linmod” [123]. Such programs often rely on perturbation methods, the results of which are known to be inaccurate due to scaling issues. The Simulink documentation claims to have largely overcome this, through the use of pre-programmed Jacobians for most blocks. The question arises whether “linmod” provides an accurate linearization if the system concerned is a multi-machine system including HVDC and wind plant dynamics. To check this a two machine system is chosen, including an offshore wind power plant connected via a offshore AC line and a DC link. The system matrix is then determined analytically using Equations (5.1), (5.2) and (5.3). The same system is implemented in Simulink and the A-matrix is found by calling the function “linmod” [123]. This system can be described by 36 differential equations. 22 algebraic equations were used to describe the relationship between variables. All of the following equations are in per unit, while this is not explicitly shown in the variable names, to avoid an overly complex notation. Six differential equations are needed for each synchronous machine. Another 12 differential equations are required to described the DC link. The offshore AC grid is described by four differential equations. Eight equations are needed for the description of the wind power plant. The differential equations for the two synchronous machines and their respective ex-

95 Chapter 5. Small signal analysis of the GB system with VSC connected wind farms

Figure 5.15: Test system for comparison of analytical and “linmod” state-space model citation systems are [117] (see Appendix B):

dE −E (x − x )i E q 1 = q 1 + d1 d1 sd1 + fd1 (5.4) dt Tdo1 Tdo1 Tdo1

d − − Eq 2 Eq 2 (xd2 xd2)isd2 Efd2 dt = + + (5.5) Tdo2 Tdo2 Tdo2

dE −E (xq1 − x )isq1 d1 = d1 − q1 (5.6) dt Tqo1 Tqo1

dE −E (xq2 − x )isq2 d2 d2 − q2 dt = (5.7) Tqo2 Tqo2 | |− 2 2 dE −E KA1( Vs ref1 Vsd1 +Vsq1 ) fd1 = fd1 + (5.8) dt TA1 TA1 | |− 2 2 dE −E KA2( Vs ref2 Vsd2 +Vsq2 ) fd2 = fd2 + (5.9) dt TA2 TA2

dE −E (x − x )isq1 dc1 = dc1 + d1 q1 (5.10) dt Tc1 Tc1

dE −E (x − x )isq2 dc2 = dc2 + d2 q2 (5.11) dt Tc2 Tc2

dδ 1 = ω − ω (5.12) dt 1 b

96 Chapter 5. Small signal analysis of the GB system with VSC connected wind farms

dδ 2 ω − ω dt = 2 b (5.13)

dw T w E i w E isq1wb (x − x )isd1isq1wb D (ω − ω ) 1 = m1 b − d1 sd1 b − q1 − d1 q1 − damp1 1 b (5.14) dt 2H1 2H1 2H1 2H1 2H1

dw T w E i w E isq2wb (x − x )isd2isq2wb D (ω − ω ) 2 = m2 b − d2 sd2 b − q2 − d2 q2 − damp2 2 b (5.15) dt 2H2 2H2 2H2 2H2 2H2

The diﬀerential equations for the DC link are:

dω (ω − ω ) hvdc = 2 hvdc (5.16) dt Tmeas

dN d −K Q V dt = iqd( ref2 + sq3isd3) (5.17)

dN dc = K (V − V ) (5.18) dt idc dc ref2 dc 2

dV (i − i )ω dc 1 = dc 1 cc b (5.19) dt Cdc1

dV (i + i )ω dc 2 = dc 2 cc b (5.20) dt Cdc2

di (V − V − R i )ω cc = dc 1 dc 2 dc cc b (5.21) dt Ldc

V d ω ( cq ω 2 − V ) ω isq3 b ωb sq3 Rpr2isq3 b = + isd3ωhvdc − (5.22) dt Lpr2 Lpr2

disd3 Vcd ω 2 Rpr2isd3ωb = − isq3ωhvdc − (5.23) dt Lpr2 Lpr2

Vcd ω 2 dV (Vcd ref 2 − )ωb +Lpr2isq3(ωhvdc − ωb) cd ω 2 = ωb (5.24) dt Td

Vcq ω 2 dV (Vcq ref 2 − )ωb − Lpr2isd3(ωhvdc − ωb) cq ω 2 = ωb (5.25) dt Td

97 Chapter 5. Small signal analysis of the GB system with VSC connected wind farms

dN vd K i − dt = iid( prd ref2 isd3) (5.26)

dN vq = K (i − i ) (5.27) dt iiq prq ref2 sq3 The diﬀerential equations for the oﬀshore AC grid are:

dic off q −Roff ωbic off q (Voff q − Vc off q)ωb = + + ωbic off d (5.28) dt Loff Loff

dic off d −Roff ωbic off d (Voff d − Vc off d)ωb = + − ωbic off q (5.29) dt Loff Loff

dVoff q (ioff q − ic off q)ωb Voff qωbGoff = + + ωbVoff d (5.30) dt Coff Coff

dVoff d (ioff d − ic off d)ωb Voff dωbGoff = + − ωbVoff q (5.31) dt Coff Coff The differential equations for the wind power plant are:

dV ref w =(Q − Q )K (5.32) dt ref gen wqi

dE qd ref w V − V K dt =( ref w term) wqv (5.33)

dP (P − P ) g = gen g (5.34) dt 0.05

d Npg . P − P dt =01( g ord) (5.35)

dE E − E qd w = qd ref w qd w (5.36) dt S0T

di i − i p w = p ref w p w (5.37) dt S1T 2 2 − dV Voﬀ q + Voﬀ d Vterm term = (5.38) dt 0.001

sin−1 Voﬀ q − dV ( V ) Vangl angl = oﬀ d (5.39) dt 0.05

98 Chapter 5. Small signal analysis of the GB system with VSC connected wind farms

22 algebraic equations are required to fully describe the system. Two equations describe each synchronous machine and another six network equations for the main AC system. The HVDC link adds another six algebraic equations. The full description of the wind power plant requires six.

The algebraic variables in the synchronous machine equations are isq1, isq2, isd1 and isd2. The algebraic equations for the two synchronous machines are:

V − − 0= sq1 Eq 1 xd1isd1 +Ra1isq1 (5.40)

V − − 0= sq2 Eq 2 xd2isd2 +Ra2isq2 (5.41)

V − − 0= sd1 Ed 1 Edc1 + xd1isq1 +Ra1isd1 (5.42)

V − − 0= sd2 Ed 2 Edc2 + xd2isq2 +Ra2isd2 (5.43)

The HVDC link has six algebraic variables iprq ref2, iprd ref2, Vcq ref 2, Vcd ref 2, idc 2 and idc 2. The six algebraic equations for the HVDC link are:

0=iprd ref2 + Kpqd(Qref2 + Vsq3isd3) − Nd (5.44)

0=idc 2 − Kpdc(Vdc ref2 − Vdc 2) − Ndc (5.45)

Vcd ω 2isd3 Vcq ω 2iprq ref2 0=2Vdc ref2idc 2 + + (5.46) ωb ωb

0=2Vdc 1idc 1 − Vc off dic off d − Vc off qic off q (5.47)

0=ωbVcd ref 2 − ωbLpr2isq3 − Nvd − Kpid(iprd ref2 − isd3) (5.48)

0=ωbVcq ref 2 − ωbVsq3 + ωbLpr2isd3 − Nvq − Kpiq(iprq ref2 − isq3) (5.49)

The algebraic equations for the main AC network are shown below, where the elements of R and X are the real and imaginary components of the system’s Z-matrix, including any loads. The AC network voltage variables are Vsq1, Vsd1, Vsq2, Vsd2, Vsq3 and δ3.

99 Chapter 5. Small signal analysis of the GB system with VSC connected wind farms

0=R11(isq1cos(δ1)−isd1sin(δ1))−X11(isq1sin(δ1)+isd1cos(δ1))+R12(isq2cos(δ2)−isd2sin(δ2))

−X12(isq2sin(δ2)+isd2cos(δ2))+R13(isq3cos(δ3)−isd3sin(δ3))−X13(isq3sin(δ3)+isd3cos(δ3))

− (Vsq1cos(δ1) − Vsd1sin(δ1)) (5.50)

0=R21(isq1cos(δ1) − isd1sin(δ1)) − X21(isq1sin(δ1)+isd1cos(δ1)) + R22(isq2cos(δ2) − isd2sin(δ2))

− X22(isq2sin(δ2)+isd2cos(δ2)) + R23(isq3cos(δ3) − isd3sin(δ3)) − X23(isq3sin(δ3)+isd3cos(δ3))

− (Vsq2cos(δ2) − Vsd2sin(δ2)) (5.51)

0=R31(isq1cos(δ1) − isd1sin(δ1)) − X31(isq1sin(δ1)+isd1cos(δ1)) + R32(isq2cos(δ2) − isd2sin(δ2))

−X32(isq2sin(δ2)+isd2cos(δ2)) + R33(isq3cos(δ3) − isd3sin(δ3)) − X33(isq3sin(δ3)+isd3cos(δ3))

−(Vsq3cos(δ3) − Vsd3sin(δ3)) (5.52)

0=X11(isq1cos(δ1) − isd1sin(δ1)) + R11(isq1sin(δ1)+isd1cos(δ1)) + X12(isq2cos(δ2) − isd2sin(δ2))

+R12(isq2sin(δ2)+isd2cos(δ2)) + X13(isq3cos(δ3) − isd3sin(δ3)) + R13(isq3sin(δ3)+isd3cos(δ3))

−(Vsq1sin(δ1)+Vsd1cos(δ1)) (5.53)

0=X21(isq1cos(δ1) − isd1sin(δ1)) + R21(isq1sin(δ1)+isd1cos(δ1)) + X22(isq2cos(δ2) − isd2sin(δ2))

+R22(isq2sin(δ2)+isd2cos(δ2)) + X23(isq3cos(δ3) − isd3sin(δ3)) + R23(isq3sin(δ3)+isd3cos(δ3))

−(Vsq2sin(δ2)+Vsd2cos(δ2)) (5.54)

0=X31(isq1cos(δ1) − isd1sin(δ1)) + R31(isq1sin(δ1)+isd1cos(δ1)) + X32(isq2cos(δ2) − isd2sin(δ2))

+R32(isq2sin(δ2)+isd2cos(δ2)) + X33(isq3cos(δ3) − isd3sin(δ3)) + R33(isq3sin(δ3)+isd3cos(δ3))

−(Vsq3sin(δ3)+Vsd3cos(δ3)) (5.55)

100 Chapter 5. Small signal analysis of the GB system with VSC connected wind farms

The equations for the wind power plant required for the algebraic variables (Pgb, Pgen,

Qgen, ip ref w, ioﬀ q and ioﬀ d)are:

0=Pgb − 0.08(Pg − Pord) − Npg (5.56)

Pord − Pgb 0=ip ref w − (5.57) Vterm

0=Pgen − ip wVterm (5.58)

Q − 0= gen Eqd wVterm (5.59)

sin cos − 0 = dﬁgbas(Eqd w (Vangl)+ip w (Vangl)) ioﬀ q (5.60)

− cos sin − 0 = dﬁgbas( Eqd w (Vangl)+ip w (Vangl)) ioﬀ d (5.61)

The initial conditions for the offshore AC grid are fully known from the ACDC powerflow solution, where the q- and d- component are simply the real and imaginary components. The DC link can also be initialised very easily from the powerflow solution. All AC variables are transformed to a d- q- reference, such that the AC system voltage is aligned with the q- axis. This concept has been discussed in Section 4.5 and is shown in Figure 4.16. This means that δ(3) is the angle of the AC voltage at the onshore system bus. The wind power plant can be directly initialised from the differential and algebraic equations. The derivative terms of the differential equations in steady state are zero by definition. While the system powers, voltages and currents are already known from the powerflow, other variables are easily calculated, using the wind power plant equations.

For the synchronous machines the load angle δ and Efd are first initialised according to Equations (B.2) and (B.3) in the appendix. Then the remaining variables can be initialized using the differential and algebraic equations, with derivative terms set to zero. The test system parameters are all listed in Appendix C. A comparison of the two system matrices shows that the values match very well. Since the dimension of the matrix is 36 times 36 it is not shown, for space reasons. Another way to check whether the solution matches well is to compare the eigenvalues. The eigenvalues of both solution methods are shown in Figure 5.16. Even though at first glance the solutions seem to match well, it is difficult to see the values at the RHS well.

101 Chapter 5. Small signal analysis of the GB system with VSC connected wind farms

Comparison of eigenvalues 4000

3000

2000

1000

ω 0 j

−1000

−2000

−3000

−4000 −10 −8 −6 −4 −2 0 2 σ 4 x 10

Figure 5.16: Comparison of analytical and “linmod” eigenvalues; “linmod” solution in black circle, analytical in red star

To avoid multiple zoomed views of the same set, a good option is to compare the eigenvalues using a logarithmic view. Since we have chosen a stable system there are no eigenvalues with positive real part. Figure 5.17 shows nicely that the eigenvalues found via “linmod” are in good agreement with the analytical solution. The logarithmic scale allows us to check the match across a broad range of values. The pole pairs of the system are listed in Table 5.1 both for the “linmod” and analytical solution. It can be seen that the values match extremely well. Any residual mismatch may occur due to the accuracy of parameters used for the analytical solution. For all practical purposes the poles found by the two methods are identical.

Table 5.1: Pole pairs of system using “linmod” and analytical method Number Eigenvalue using “linmod” Eigenvalue using analytical method 1 -2.8390120786 + 3972.1686921i -2.8390120766 + 3972.1686915i 2 -7.27254359949 + 3216.79690180i -7.27254359992 + 3216.79690132i 3 -18.5372038171 + 110.25406759i -18.5372038148 + 110.25406762i 4 -13.169977593096 + 99.867555307i -13.169977593617 + 99.867555299i 5 -1.037953393266 + 8.583221210041i -1.037953393519 + 8.583221210539i

102 Chapter 5. Small signal analysis of the GB system with VSC connected wind farms

Comparison of eigenvalues in log scale 4000

2000

ω 0 j

−2000

−4000 −100,000−10,000 −1000 −100 −10 −1 −0.1 −0.01 −0.001 σ

Figure 5.17: Comparison of analytical and “linmod” eigenvalues; “linmod” solution in black circle, analytical in red star

The comparison of the A-matrix or eigenvalues shows that “linmod” indeed provides an accurate state-space model for this kind of system. It is hence fair to use this function for the eigenvalues analysis of the GB system including DC technology and oﬀshore wind.

5.2 Eigenvalue Analysis

The step response of a system gives an indication of the system behaviour. However a full judgement of system stability would require the knowledge of interaction within the system with regard to various disturbances in the system. Eigenvalue analysis provides a complete picture of possible interactions and instabilities. To show clearly where the participating states for modes are located, the GB system is shown with all bus numbers in Figure 5.18. The numbers in the upper half of the blocks are the load buses at the node. The numbers in the lower half are the generators connected to the node. The generation at node 31, has been removed, such that it is also a load bus. The frequency signal for the offshore development is located at generator Bus 16 and the generator at Bus 20 has a governor enabled. The offshore buses are simply numbered through, starting at the converter side of the first windfarm. The purpose of giving offshore buses a higher bus number than onshore developments, is that it facilitates splitting results into onshore and offshore parts.

103 Chapter 5. Small signal analysis of the GB system with VSC connected wind farms

Figure 5.18: GB system with oﬀshore development, for participation factor discussion bus numbers are included in blocks, upper numbers denote load buses, lower numbers generators

Figure 5.19 shows the eigenvalues of the entire system i.e. the GB system, the HVDC grid, the oﬀshore wind power plants and oﬀshore AC connections. Only pole pairs represent an oscillatory behaviour. The decay of the oscillation is described by the damping factor, which can be directly calculated from the eigenvalue [18].

−σ ζ = √ (5.62) σ2 + ω2 The damping factor can also be used to approximate the settling time of the oscillations within a certain tolerance (e.g. 0.01 for 1%). Oscillations that die down quickly, have less impact on the system, which makes settling time an important indicator [124].

104 Chapter 5. Small signal analysis of the GB system with VSC connected wind farms

−ln(tolerance) Ts = ζω (5.63) “In power systems, electromechanical oscillations with damping ratios greater than 0.05 are considered satisfactory. ... 0.15 has been speciﬁed in some interconnected systems.” [125] This rule of thumb is used to divide eigenvalues into three groups. Namely those with a high damping ratio, satisfactory eigenvalues and critical eigenvalues. They are marked as green stars, orange triangles and red circles respectively in the eigenvalue plots. The eigenvalues on the left side of Figure 5.19 represent rapidly decaying non oscillatory modes, which are of no concern to system stability.

Eigenvalue plot of GB system with HVDC grid and offshore wind farms 3000

2000

1000 ω

j 0

−1000

−2000

−3000 −12 −10 −8 −6 −4 −2 0 σ 4 x 10

Figure 5.19: Eigenvalues of GB system, colour coded by damping, green star >= 0.15, 0.15 >orange triangle >= 0.05, red circle <0.05

Figure 5.20 shows a closer view of the critical poles, that are of interest. A group of poorly damped poles can be seen with a frequency above 260 Hz. A small signal multi- terminal VSC study by [85], reports interactions between converters of similar frequencies, ranging between 3169 Hz and 207 Hz. Table 5.2 gives the eigenvalue information for those modes. The modes are clustered around two frequencies, 261 Hz (near 5th harmonic) and 361 Hz (near 7th harmonic). Using Equation (5.63) the settling time for the modes is estimated. It can be seen that even though the damping factors of the modes are low (1.4 % to 2.1 %), the high frequency leads to a very fast settling time of around 0.2

105 Chapter 5. Small signal analysis of the GB system with VSC connected wind farms seconds. The eigenvalues determine the frequency of oscillation and the damping. All super-synchronous modes have participation factors from the oﬀshore network components. The main participation factors are attributed to the AC collector system cable capacitance and inductance. The frequency of the modes matches that reported in [85]. The super-synchronous frequencies are close to the 5th and 7th harmonic of the 50 Hz system. The converters should be designed to ﬁlter these high frequencies out, to prevent the excitation of high frequency resonance.

Table 5.2: Super-synchronous eigenvalues with critical damping Number Eigenvalue Frequency [Hz] Damping Settling time factor[%] within 1% [sec] 1 -35.2 + 2270.8i 361.4 1.6 0.1 2 -35.2 + 2270.8i 361.4 1.6 0.1 3 -32.7 + 2269.1i 361.1 1.4 0.1 4 -34.0 + 1642.7i 261.4 2.1 0.1 5 -34.0 + 1642.7i 261.4 2.1 0.1 6 -30.0 + 1641.4i 261.2 1.8 0.2

To observe the sub-synchronous modes of critical damping, the zoomed view in Figure 5.20 is required. It shows various pole pairs with good or suﬃcient damping. There is a cluster close to zero, that requires a closer look. This is shown in Figure 5.21.

The poles on the far left of Figure 5.21 are of good or suﬃcient damping, while those poles further to the right include six pole pairs of critical damping. The poles may aﬀect system stability, so they require further analysis. The eigenvalue information is provided in Table 5.3, while the participation factors are discussed in Table 5.4.

Table 5.3 shows the critically damped sub-synchronous modes of the system. The frequency of the modes ranges between 0.7 Hz to 1.5 Hz. Since the sub-synchronous modes have a much lower frequency by deﬁnition, than super-synchronous ones, modes with a similar damping factor have a much longer settling time. The sub-synchronous modes settle to a precision of 1% within 16.9 seconds to 44.7 seconds or to a precision of 2% within 14.4 seconds to 37.9 seconds.

106 Chapter 5. Small signal analysis of the GB system with VSC connected wind farms

Eigenvalue plot of GB system, zoomed in on pole pairs

2000

1000 ω

j 0

−1000

−2000

−35 −30 −25 −20 −15 −10 −5 0 σ

Figure 5.20: Eigenvalues of GB system, zoomed in on pole pairs, colour coded by damping, green star >= 0.15, 0.15 >orange triangle >= 0.05, red circle <0.05

Table 5.3: Sub-synchronous eigenvalues with critical damping

Number Eigenvalue Frequency [Hz] Damping Settling time Settling time factor[%] within 1% [sec] within 2% [sec] 1 -0.2 + 9.6i 1.5 2.1 22.8 19.3 2 -0.2 + 9.4i 1.5 1.8 27.6 23.4 3 -0.3 + 9.1i 1.5 3 16.9 14.4 4 -0.1 + 8.9i 1.4 1.2 44.7 37.9 5 -0.1 + 6.8i 1.1 2.1 31.7 26.9 6 -0.2 + 4.4i 0.7 4.3 24.2 20.5

To find the cause of the interaction participation factor analysis is used. Participation factors describe the contribution of each state variable to a mode. Since state variables have a physical meaning in power systems, the participation factors determine the influence of physical components on the mode. A detailed discussion of participation factor calculation for linear systems can be found in [126]. Some of the modes will have a large number of participating states. Hence only the states with the largest and hence significant participation factors are shown. The participation factors for the modes in Table 5.3 are shown in Table 5.4 to investigate the cause of these sub-synchronous poorly damped

107 Chapter 5. Small signal analysis of the GB system with VSC connected wind farms

Eigenvalue plot of GB system, zoomed into low damped poles

0 ω j

−5

−10

−1.2 −1 −0.8 −0.6 −0.4 −0.2 0 σ

Figure 5.21: Eigenvalues of GB system, zoomed in on low damped pole pairs, colour coded by damping, green star >= 0.15, 0.15 >orange triangle >= 0.05, red circle <0.05 eigenvalues. The first mode is caused by the interaction of several synchronous generators in the north of Scotland, mainly between network locations one and two. The second mode is similarly caused by synchronous machines in Scotland, where the interaction is located further south, around network locations three and four. The third mode shows another synchronous machine interaction between generators in the south of England. The fourth mode has contribution from synchronous generators in the north of Scotland as well as south of England. While an interaction between synchronous machines is a well known phenomenon, it is interesting to see how converter stations participate into some of the critical modes. The fifth mode is of large interest, as it describes the interaction of the DC grid with synchronous generation in the north of Scotland. The participation factor analysis shows the interaction is caused by the DC line currents. The behaviour of the line current is determined by the resistance and inductance of the DC cabling. This resistance and inductance is in turn determined by the cable type and transmission distance. This mode shows that HVDC can have a significant impact on system stability and any DC developments should be designed taking this into consideration. The sixth mode has the characteristic frequency of the well known Scotland-England inter-area mode. It has participation from a wind power plant in the south of Scotland and synchronous

108 Chapter 5. Small signal analysis of the GB system with VSC connected wind farms generation in Scotland and England, as would be expected. What is rather interesting is the signiﬁcant participation into the mode by the DC grid. As before, participation from the DC grid is due to the DC line current, which is related to the DC line resistance and inductance. Another participation into the mode is from the phase reactor current between the converter and system bus of the DC slack converter. The participation of a converter station into the inter-area mode is of particular interest, since the inter-area mode is a limiting factor of the transfer capability of power from Scottish generators down to English demand centres. The design of oﬀshore DC grids may determine whether inter- area modes in the future GB system degrade or improve in damping. An overview over all modes, apart from the pole at the origin, can be gained using a logarithmic plot, as shown in Figure 5.22. As before the modes are colour coded according to their damping. This plot enables us to simultaneously observe the six super- synchronous and the six sub-synchronous modes, that have been discussed before using zoomed views of the same eigenvalue plot. The draw back of this representation is that it only represents poles on the LHS, such that it can only be used to investigate stable modes.

Logarithmic plot of modes 2500

2000

1500

1000

500 ω

j 0

−500

−1000

−1500

−2000

−2500 −10^6 −10^5 −10^4 −10^3 −10^2 −10^1 −1 −10^−1 −10^−2 σ

Figure 5.22: Logarithmic plot of eigenvalues of GB system, colour coded by damping, green star >= 0.15, 0.15 >orange triangle >= 0.05, red circle <0.05

109 Chapter 5. Small signal analysis of the GB system with VSC connected wind farms

Table 5.4: Participation to sub-synchronous modes

Mode Mode Participation Gen. Bus Network Description Num. Num. Num. location 1 -0.2 + 9.6i 1 1 2 1 Synch. gen. static exc. Efd 0.283 3 5 2 Synch. gen. static exc. Efd 0.187 2 3 2 Synch. gen. static exc. Efd 0.161 3 5 2 Synch. torque angle loop ω 2 -0.2 + 9.4i 1 6 10 4 Synch. gen. static exc. Efd 0.312 4 7 3 Synch. gen. static exc. Efd 3 -0.3 + 9.1i 1 27 39 22 Synch. torque angle loop δ 0.309 30 43 25 Synch. torque angle loop δ 4 -0.1 + 8.9i 1 30 43 25 Synch. torque angle loop δ 0.651 17 26 12 Synch. torque angle loop ω 0.550 28 40 23 Synch. torque angle loop ω 0.468 4 7 3 Synch. torque angle loop ω 0.452 1 2 1 Synch. torque angle loop ω 0.428 32 45 26 Synch. torque angle loop δ 5 -0.1 + 6.8i 1 n/a n/a conv. IV Converter DC line current to I 0.846 n/a n/a conv. III Converter DC line current to VI 0.822 1 2 1 Synch. torque angle loop ω 0.712 3 5 2 Synch. torque angle loop δ 0.650 2 3 2 Synch. gen. static exc. Efd 0.569 3 5 2 Synch. torque angle loop ω 0.527 2 3 2 Synch. torque angle loop ω 6 -0.2 + 4.4i 1 5 12 6 Wind power plant voltage control 0.516 n/a n/a conv.VI Converter phase reactor direct current 0.187 n/a n/a conv. III Converter DC line current to II 0.097 3 5 2 Synch. torque angle loop δ 0.096 16 24 12 Synch. gen. static exc. Efd

110 Chapter 5. Small signal analysis of the GB system with VSC connected wind farms

5.2.1 Controller tuning

Two of the critically damped modes have participation from converter stations. The participation into the modes comes from the dynamic behaviour of currents due to line inductance both on the AC and DC side of converter stations. Since this represents a physical parameter, determined by cable type and transmission distance, it cannot be chosen at will. The dynamic behaviour of the converter can be inﬂuenced by the controller gains both of the inner current control and the outer controllers. Initially the gains of these controllers were chosen such that the step response to a change in reference value was neither under- nor over-damped. For the outer controller the proportional and integral gain for Q, P and Vdc respectively were selected as -25, -200, 1, 200, 40 and 50. The inner controller proportional and integral gains for both the direct and quadrature components were chosen as 1 and 0.1. The sensitivity of the modes under investigation can be found by changing the controller gains both of the inner current control and the outer controllers. Figure 5.23 shows the change in Mode 5 according to a change of the inner current control gains. The top two graphs show the sensitivity to a change of the proportional and integral gain for the q-component. The sensitivity to a change in the proportional and integral term of the d-component are also investigated. Even though gains are varied over a wide range from 0.025 to 1000, there is no signiﬁcant change of the mode. Thus adjusting the gains of the inner current controllers does not improve Mode 5.

Sensitivity to quadrature proportional gain Sensitivity to quadrature integral gain 6.7981603 6.79816018 ω ω j 6.7981602 j 6.79816017

6.79816016 −0.1452000 −0.1451998 −0.1451996 −0.1451997 σ −0.1451996 σ Sensitivity to direct proportional gain Sensitivity to direct integral gain

6.79816020 6.7981601905 ω ω j j

6.79816015 6.7981601895 −0.14519966 −0.14519964 −0.14519962 −0.1451996560 −0.1451996552 σ σ

Figure 5.23: Inner current control gain sensitivity of Mode 5, where gains are varied from 0.025 to 1000 from black triangle to pink circle

Figure 5.24 shows Mode 6 for a variety of inner current controller gains. For Mode 6 the sensitivity to a variation of inner current controller gains is extremely low, as seen before for Mode 5.

111 Chapter 5. Small signal analysis of the GB system with VSC connected wind farms

Sensitivity to quadrature proportional gain Sensitivity to quadrature integral gain 4.4050 4.404465

ω 4.404460 ω j 4.4045 j 4.404455

−0.19075 −0.19070 −0.19065 −0.19060 −0.19055 −0.190750 −0.190748 −0.190746 σ σ Sensitivity to direct proportional gain Sensitivity to direct integral gain

4.404462 4.404461178 ω ω

4.404461 j j 4.404461176 4.404460 4.404461174 −0.19073925 −0.19073920 −0.19073915 −0.190739104 −0.190739100 σ σ

Figure 5.24: Inner current control gain sensitivity of Mode 6, where gains are varied from 0.025 to 1000 from black triangle to pink circle

Since no significant impact was observed when altering the inner current controller gains, the outer controller gains are investigated. All onshore converters are in Q control. Two of the onshore converters are in P control while the last onshore converter is the DC slack converter and controls the DC voltage. Initially the proportional and integral gains of the P and Q controllers are altered to investigate their impact on the modes of interest. Figure 5.25 shows the change in Mode 5 according to a change of the outer controller P and Q gains, where the q-component is from the real power control and the d-component from the reactive power control. The top two graphs show the sensitivity to a change of the proportional and integral gain for the q-component. As before gains are varied from 0.025 to 1000. The sensitivity of Mode 5 to changes in quadrature or direct gains is very low. The sensitivity of Mode 6 to changes in outer controller gains can be seen in Figure 5.26, where gains are varied from 0.025 to 1000. As before gains show no significant impact on the mode. Finally the sensitivity of both modes (Mode 5 and Mode 6) is investigated, when altering the gain parameters of the DC voltage controller. This controller is responsible for maintaining the DC voltage of the DC slack converter at the reference level. Both the integral and proportional gain were varied, as seen in Figure 5.27. The modes both stayed around the same value. This means that altering the gains of the controller does not aid the damping of either mode. Two of the critically damped modes of the system had significant participation from the VSC converter stations. Sensitivity analysis of the controller gains of the converters has shown that the gains have little or no influence on the modes under consideration.

112 Chapter 5. Small signal analysis of the GB system with VSC connected wind farms

Sensitivity to quadrature proportional gain Sensitivity to quadrature integral gain

6.798160 6.79818 ω ω j 6.798158 j 6.79816 6.798156 −0.145199 −0.145198 −0.145197 −0.1452 −0.14518 −0.14516 σ σ Sensitivity to direct proportional gain Sensitivity to direct integral gain 6.7981603 6.79816020 6.7981602 ω j ω j 6.7981601 6.79816016 −0.14519968 −0.14519965 −0.14519962 −0.14519975 −0.14519965 σ σ

Figure 5.25: Outer control gain sensitivity of Mode 5, where gains are varied from 0.025 to 1000 from black triangle to pink circle, the quadrature gains correspond to real power control and the direct integral gains to reactive power control

Sensitivity to quadrature proportional gain Sensitivity to quadrature integral gain 4.4065 4.4045

ω 4.4055 ω j j 4.4045 4.4044 −0.19074 −0.19072 −0.19070 −0.1918 −0.1914 −0.191 −0.1906 σ σ Sensitivity to direct proportional gain Sensitivity to direct integral gain

4.404462

4.404461 ω ω j j 4.404460 4.404460 −0.1907394 −0.1907392 −0.1907390 −0.1907390 −0.1907385 −0.1907380 −0.1907375 σ σ

Figure 5.26: Outer control gain sensitivity of Mode 6, where gains are varied from 0.025 to 1000 from black triangle to pink circle, the quadrature gains correspond to real power control and the direct integral gains to reactive power control

Hence supplementary control is required to improve the damping of the inter-area mode, this is done using the VSC network. A common way to improve the damping in a system is to add power system stabilizers (PSS) at the appropriate synchronous machines. The simulations of the GB system initially do not assume PSS. In the next section PSS are included to improve the damping of the critical modes under study. [17] describes a simple PSS based on a single input single output power oscillation damper. This is implemented with the parameters provided by [17], where the power input is the power ﬂowing between Bus 62 and 60. The power system stabilizer with all relevant parameters is shown in Figure

5.28. The parameters Tw, Kdamp, Ta and Tb are given as 10, 0.35, 0.55 and 0.2 respectively.

113 Chapter 5. Small signal analysis of the GB system with VSC connected wind farms

Sensitivity of Mode 5 to proportional gain Sensitivity of Mode 6 to proportional gain 4.40452 6.7981604 4.40450 ω ω j j 4.40448 6.7981602 4.40446 −0.190750 −0.190746 −0.190742 −0.1451996 −0.1451995σ −0.1451994 σ Sensitivity of Mode 5 to integral gain Sensitivity of Mode 6 to integral gain 6.798160191 4.4044614

ω 6.798160190 ω j j 4.4044612 6.798160180 −0.145199657 −0.145199647σ −0.145199637 −0.190739 −0.190738σ −0.190737

Figure 5.27: Outer control gain sensitivity of Modes 5 and 6 to changes in DC voltage controller gains, where the direct gain is varied from 40 to 0.1 and integral gain from 50 to 0.1 from black triangle to pink circle

Figure 5.28: Power system stabilizer [17], with active powerﬂow from bus 60 to bus 62 as input and reference power at converter IV as output

The modes of the system before the integration of the PSS, after the integration and with a change in parameters are investigated. The difference in the critical modes can be seen in Figure 5.29, where the black triangle is the original mode and the black circle is the mode when including the PSS. It shows very clearly that Mode 6, the inter-area mode is shifted significantly to the LHS, making the mode more stable. The new damping is 14.1% rather than 4.3% without the PSS, the new damping is close to the boundary for a high damping ratio. Mode 5 is shifted very slightly to the RHS, changing the damping from 2.1% to 2.0%. Hence the supplementary controller has a beneficial effect for system stability by improving the damping of the inter-area mode, however some modes, in particular Mode 5, are affected negatively.

The stars in Figure 5.29 indicate the modes when the time Ta of the lead-lag com- pensator is reduced from 0.55 to 0.001 to show the movement of poles. The pink star indicates the lowest value. For very low values of Ta, up to 0.25, the damping of Mode

6 is critical. For a value of 0.3 the damping becomes suﬃcient. For this value of Ta,the

114 Chapter 5. Small signal analysis of the GB system with VSC connected wind farms damping of Mode 5 compared to the base case has only degraded by 0.011%. At the same time the inter-area mode has sufficient damping. While this offers a good option, the tuning of the other parameters should also be investigated. The movement of the poles during a change in Tb or Tw, is similar to that for Ta and hence not advantageous for adjusting the damping. Another option is to adjust the gain parameter, leading to a similar shift in modes. A gain of 0.04 was found to be sufficient for moving the inter-area mode into the sufficiently damped region.

System modes with and without PSS

Original Mode 5 6.5 with PSS

6 ω j 5.5

5 with PSS Original Mode 6 4.5

−0.65 −0.6 −0.55 −0.5 −0.45 −0.4 −0.35 −0.3 −0.25 −0.2 −0.15 σ

Figure 5.29: Comparison of critical modes, black triangle for original system without any PSS, black circle for system with additional PSS at converter IV, stars for change in time Ta, where red is critically damped and orange suﬃciently damped

The damping of the inter-area mode was increased from 4.3% to 14.1% using the PSS at converter IV with parameters as in [17]. At the same time Mode 4 and 5 were further degraded, which is undesirable, since they are critical sub-synchronous modes, with already very low damping factors. To improve the damping a further PSS can be implemented at the synchronous machine at Bus 2, which has a high participation factor into Mode 5 (0.822). The PSS used is shown in Figure 5.30. Parameters Tw s, Ta s, Tb s and Kd sync were chosen as 10, 0.25, 0.01 and 0.04 respectively, using sensitivity analysis. Figure 5.31 shows all sub-synchronous modes of critical damping of the original system in triangles. When the PSS as described in [17] is implemented at converter IV, the modes are as shown by the markers in circular shape. The Modes of the system with a PSS at the converter station as well as synchronous machine are shown as squares. To show

115 Chapter 5. Small signal analysis of the GB system with VSC connected wind farms

Figure 5.30: Power system stabilizer for synchronous machine excitation system with washout filter, gain and phase compensation [18] the movement of poles between the case of only one PSS at the converter station and the case of a PSS at the converter and one at the synchronous machine the gain Kd sync was reduced to 0.001 and the pole movement is indicated by star markers. The modes for all three cases, that are seen in Figure 5.31 are further listed in Table 5.5 with their respective damping factors. In Figure 5.31 the relative shift in modes for the three cases is easily visible. The PSS as in [17] shows a major improvement of the inter-area mode compared to the base case. However three of the other critical modes are altered. One mode is shifted to the left, which would be beneficial for damping. The other modes are shifted further right, further degrading the damping. As can be seen in Table 5.5 these are modes, which already have very low damping. This is clearly undesirable. The modes of the case with two PSS at the converter and synchronous machine are shown as squares. The stars clearly show how the modes are improved from the case of only one PSS at the converter, as the gain of the second PSS at the synchronous machine is increased. As can be seen from the table, or the marker colour, the inter-area mode is further improved, from the original critical damping, to sufficient damping using the PSS at the converter, to being well damped after the integration of the second PSS. Further Mode 5 is shifted far into the sufficiently damped region (13.3%). Another significant shift to the left can be seen for Mode 4, which had a very low damping in both previous cases. The damping has improved from about 1.2% to 2.5%. The main focus of this study was the impact of HVDC developments on the critical sub-synchronous modes. Table 5.5 and Figure 5.31, clearly show that those modes can be sufficiently or even well damped through the integration of PSS both at a converter and synchronous machine. The inclusion of both PSS does not show a significant impact on Mode 1 and 2. Mode 3 shows a minor and Mode 4 a significant improvement in damping.

116 Chapter 5. Small signal analysis of the GB system with VSC connected wind farms is sync damp K 0 Mode 5 Conv. PSS Mode 2 Mode 4 Orig & Conv. PSS 0.2 Original Mode 5 − Mode 1 Original Mode 6 Mode 4 both PSS Mode 3 0.4 − σ 0.6 − Mode 6 Conv. PSS 0.8 − Mode 6 both PSS 1 − Mode 5 both PSS Critical modes of system without PSS, with PSS at converter VI and synchronous machine

9 8 7 6 5

j ω increased, red is critically damped, orange suﬃciently damped and green well damped Figure 5.31: Comparisonat of critical converter modes, IV triangles [17], for squares original with system PSS without at any converter PSS, and circles generator for system at with Bus additional 2. PSS Stars show movement of poles when

117 Chapter 5. Small signal analysis of the GB system with VSC connected wind farms

Table 5.5: Sub-synchronous eigenvalues with critical damping for the original, PSS at converter and two PSS case Number Original Original PSS Conv. PSS Conv. both PSS both PSS Eigenvalue damping Eigenvalue damping Eigenvalue damping factor [%] factor [%] factor [%] 1 -0.2 + 9.6i 2.1 -0.2 + 9.6i 2.1 -0.2 + 9.6i 2.1 2 -0.2 + 9.4i 1.8 -0.2 + 9.4i 1.8 -0.2 + 9.4i 1.8 3 -0.3 + 9.1i 3 -0.3 + 9.1i 3.1 -0.3 + 9.1i 3.1 4 -0.1 + 8.9i 1.2 -0.1 + 8.9i 1.1 -0.2 + 9.0i 2.5 5 -0.1 + 6.8i 2.1 -0.1 + 6.8i 2 -0.1 + 7.3i 13.3 6 -0.2 + 4.4i 4.3 -0.6 + 4.5i 14.1 -0.7 + 4.5i 15.2

Figure 5.32 shows the angle difference between Bus 5 and 37. The generator at Bus 5 had a significant torque angle participation into both Mode 5 and Mode 6. The figure shows the oscillations of the original system as a blue solid trace. The response with a PSS at converter bus IV, is seen as a red dashed trace. It can be clearly seen that the behaviour is improved. The response of the system with a second PSS at the generator of Bus 2, is shown with a green dashed and dotted line. The oscillations in this case are smaller than those of the red trace. Too show this more clearly a zoomed view is shown in Figure 5.33. The zoomed view in Figure 5.33 shows that the amplitude of oscillations of the green trace is smaller that that of the red trace. This signifies that the behaviour is further improved by the second PSS at Bus 2. The second PSS alters the voltage reference of the excitation system of the the synchronous machine at Bus 2 in order to reduce oscillations in generator speed. This can be seen in Figure 5.34. The blue solid trace is the response of the original system. The red trace is the response after inclusion of a PSS at converter station IV. The green trace is the response after inclusion of a PSS at Bus 2. To see the difference in oscillations more clearly a zoomed view is shown in Figure 5.35. Figure 5.35 shows that the oscillations of the original system (solid blue) are reduced after inclusion of a PSS at the converter (red dashed). The green dashed and dotted line, corresponds to the behaviour of the system with both PSS. The green line has less oscillations due to the additional PSS. After investigating the modes of the system and the time domain response, it can be concluded that the system is most stable with a PSS both at converter station IV and at the generator of Bus 2.

118 Chapter 5. Small signal analysis of the GB system with VSC connected wind farms

Angle difference between bus 5 and 37 0.5875

0.587

0.5865

0.586 Angle difference between bus 5 and 37 (degree) 0.5855 0 5 10 15 20 25 30 Time (seconds)

Figure 5.32: Angle diﬀerence between Bus 5 and 37, where the blue solid line is the system without any power system stabilizers, the red dashed line for the system with a power system stabilizer at the converter station, and the green dashed and dotted line is for the system with a PSS both at the converter and at the generator located at Bus 2

Angle difference between bus 5 and 37

0.5874

0.5873

0.5872

0.5871

0.587

0.5869

0.5868

0.5867 Angle difference between bus 5 and 37 (degree)

5 6 7 8 9 10 11 12 Time (seconds)

Figure 5.33: Zoomed view of angle diﬀerence between Bus 5 and 37, where the blue solid line is the system without any power system stabilizers, the red dashed line for the system with a power system stabilizer at the converter station, and the green dashed and dotted line is for the system with a PSS both at the converter and at the generator located at Bus 2

119 Chapter 5. Small signal analysis of the GB system with VSC connected wind farms

−3 x 10 Change in generator rotational speed ( Bus 2 ) 4

−2

−4

−6 (radians/second) s ω

−

−8 ω −10

−12

−14 0 5 10 15 20 25 30 Time (seconds)

Figure 5.34: Diﬀerence between synchronous speed and speed of generator at Bus 2, where the blue solid line is the system without any power system stabilizers, the red dashed line for the system with a power system stabilizer at the converter station, and the green dashed and dotted line is for the system with a PSS both at the converter and at the generator located at Bus 2

−3 x 10 Change in generator rotational speed ( Bus 2 )

−1 (radians/second) s ω −2 −

ω −3

−4

−5 10 11 12 13 14 15 16 17 18 19 Time (seconds)

Figure 5.35: Zoomed view of diﬀerence between synchronous speed and speed of generator at Bus 2, where the blue solid line is the system without any power system stabilizers, the red dashed line for the system with a power system stabilizer at the converter station, and the green dashed and dotted line is for the system with a PSS both at the converter and at the generator located at Bus 2

120 Chapter 5. Small signal analysis of the GB system with VSC connected wind farms

5.3 Conclusion

Results of dynamic simulations of the complete system have been shown and discussed. The use of “linmod” [123] has been justified by validating the program against the analytical solution for a two-machine AC network including a DC link to an AC connected wind power plant. The state-space representations gained via the two solution methods, matched well. This enabled the further eigenvalue analysis to be conducted via the use of “linmod” [123]. The eigenvalue analysis showed that the system studied contained super-synchronous and sub-synchronous modal interactions. The critically damped sub-synchronous modes showed well-known characteristics, such as the inter-area mode. Some of the modes mainly rooted from the interaction between synchronous machines, which is a well understood phenomenon. Other modes showed a significant interaction with converter stations. The mode which has the characteristic frequency (0.7 Hz) of the well known Scotland-England inter-area mode was investigated among the critically damped sub-synchronous modes using participation factor analysis. It has participation from generation in Scotland and England, as would be expected. It further has significant participation into the mode by VSC converter stations. The inter-area mode is a limiting factor of the transfer capability of power from Scottish generators down to English demand centres. The design of offshore DC grids has potential to influence the damping of the inter-area mode in the future GB system, and an appropriate control design should be performed. The tuning of the converter controller gains, showed no significant impact on either of the two critical modes, with significant participation from the DC grid. Hence a power system stabilizer was implemented at converter station IV to improve the damping of the inter-area mode (Mode 6). The damping of Mode 5 was improved by including a PSS at the synchronous machine of Bus 2. This additional PSS further improved the damping of Modes 6 and 4. Using both PSS Mode 6 is well damped and Mode 5 sufficiently damped. This is a major improvement compared to the system without any PSS.

121 Chapter 6

Impact of Wakes on Wind Farm Inertial Response

6.1 Introduction

Inertial response from wind generators is important since it limits the rate of change of frequency (RoCoF) during generation and load imbalance. It is automatically provided by synchronous machines due to their direct coupling with system frequency. When synchronous generators are replaced by asynchronous generators, the RoCoF deteriorates. Asynchronous generators can be made to offer inertial response through suitable control action. The amount of response is dependent on the wind speed at the turbine. The wind speed at a turbine blade is influenced by the upstream turbine - known as the wake effect. This work models and quantifies the impact of the wake on the inertial response of the wind farm. The modelled wake effect is compared with measured data from a wind farm. The research contribution demonstrates that the wake effect has a significant influence on the actual inertial response capacity. One important aspect in interconnected power system operation is to maintain AC system frequency within a tight specification. The grid operator adopts a balancing service to do this. The mechanical inertia of the entire system determines the initial rate at which the frequency changes following large events such as a loss of generation or demand. The initial rate of change of frequency (RoCoF) is very important in the current and more so in the future context of AC power system operation with an increasing mix of generation from wind and solar sources. Many small embedded generators are connected to the grid and have protective relays operating on the principle of RoCoF. Depending on the protection setting, a high RoCoF triggers the protection to disconnect the embedded generators from the network. This leads to a further acceleration in the fall of frequency.

122 Chapter 6. Impact of Wakes on Wind Farm Inertial Response

National Grid, UK is currently reviewing the connection requirements for all generation installed in the future since the company recognizes that the RoCoF on the network is increasing, which impacts the security and stability of the system [127]. Generally, the first 5 seconds [128] from the loss of large power stations are important as the RoCoF depends primarily on the inertia of the system. Inertial response is naturally provided by synchronous machines due to the stored energy in the rotating mass of the rotor. In a system where asynchronous generators are replacing large centralised synchronous generators, the stored energy and hence inertial response is influenced by many factors such as the technology of generators, the pitch angle, operating speed of the wind turbine and the wind velocity. The natural inertial response present in fixed speed squirrel cage induction generator (Type 1), slip-ring induction generator (SRIG, Type 2), variable speed doubly fed induction generator (DFIG, Type 3) and full converter induction generator (FCIG, Type 4) varies [129]. Type 1 and Type 2 provide a larger inertial response, while Type 3 provide a weak and Type 4 a negligible amount, because of the decoupling from the network through a power electronic interface. A comparative study between the inertial response of a squirrel-cage induction generator and DFIG [130] shows that the inertial response of a DFIG depends on the bandwidth of the rotor current controller and a slow control can offer a response for 5 to 10 seconds. A supplementary DFIG control can significantly improve turbine response by introducing emulation of inertia [131, 132, 133]. It can either be delivered by methods of de-loading [134, 135, 136] or turbine inertia in the optimal regime [136, 41] and further overproduction (more than rated capacity) in the rated regime [41]. In all cases uniform wind speed across all wind turbines in the wind farm is assumed. In reality wind slows down while travelling from one turbine to the next. This is known as wake. The net wind speed meeting the downstream turbine drops. In the sub-rated regime (optimum power tracking mode) the slowing down of wind speed affects the power output and operating speed and therefore the stored energy. In the rated regime the power output is not affected but the pitch angle drops. This reduces the capability to produce extra power to slow down the RoCoF when needed. Hence the wake has the effect of progressively reducing the inertial response capacity in the downstream arrays of turbines in a wind farm. It is important to quantify the true volume of inertial response from a wind farm considering the effect of wakes. The value of doing this is obvious as it will help the grid operator to determine the appropriate amount of fast primary response and the appropriate setting of RoCoF relays. A simulation of the impact of wake effect on the inertial response capacity is conducted. The results of the wake effect simulation are compared with measured wind speeds from different turbine locations in an actual offshore wind farm in Horns Rev in

123 Chapter 6. Impact of Wakes on Wind Farm Inertial Response

Denmark [19]. The impact of the wake on the inertial response capacity is demonstrated by comparing two scenarios. In one all turbines operate at free wind speed and in the other turbines operate at different wind speeds according to the wake effect. The wind farm in both cases is provided with a command for 10% additional power for 10 seconds and the difference in response due to the wake effect is observed. It is shown clearly that the wake effect reduces the inertial response capacity from the wind farm. Inertial response that does not rely on a de-loading operation is considered in this work. De-loading leads to spilling of wind and hence wasting green power. The next section describes the wake effect modelling for quantification of inertial response.

6.2 Wake Eﬀect

6.2.1 Review of previous work

The rotation of a wind turbine introduces turbulence in the wind stream in the immediate vicinity of the turbine. The result is a drop in the average wind speed in the downstream wind flow. This is known as the wake. The turbines in the wake corridor operate at a reduced wind velocity and therefore produce less output when operating in sub-rated regime. The research on the wake effect so far has concentrated around model development [137, 138, 139, 140, 141], validation against measurements [137, 142, 143] and the mini- mization of the wake effect through optimal turbine placement [144]. N.O. Jensen [137] proposed a semi-empirical model of the wake effect. This was based on earlier measurements of wakes in wind farms by Vermeulen et al. in 1979 [145]. Later J.F. Ainslie [138] used an eddy viscosity turbulence model to calculate the wake under different meteorological conditions including wake meandering in two dimensions. This model was the first to include the impact of wake meandering on the wake deficits. Wake meandering describes changes in the wake direction due to the variability of wind direction caused by large-scale air movements [146]. The knowledge of ambient turbulence intensity, friction velocity, influence of stability on the mixing processes and the standard deviation of wind directional fluctuations is required for this modelling [138]. Thomsen et al [139] developed a method including the prediction of wake deficit and wake meandering for aero-elastic simulations. The main aim of their work was to unify the wake simulations for fatigue loading and power production using detailed and complex modelling [146]. Ref [147] conducted dynamic modelling regarding the change of output power with wind direction and step up of wind speed. Finite volume techniques were applied in [140] to calculate the wind speed change on a mesh throughout a wind farm. To model the wake

124 Chapter 6. Impact of Wakes on Wind Farm Inertial Response influence in wind farms, [141] used lumped equivalent wind turbines. Measurements of a test wind farm at the Netherlands Energy Research Centre were reported in [142]. They find that their model predicts the wake expansion well, however it under-predicts velocity deficits and overestimates the turbulence directly behind the rotor. Ref [143] showed that the direction measurement by wind turbines was not equivalent to the true wind direction. The true wind direction was found using two-parameter-matching for a better fit with measurements. An equilateral triangle mesh for optimal micrositing of turbines was proposed by [144]. According to their work this method improved upon the square mesh method, in particular when the mesh was orientated according to the prevalent wind direction. Surprisingly there is no effort in quantifying the effect of wakes on the inertial response volume. This work is based on Jensen’s model since it gives good results for engineering applications [148] and since it is much simpler than that proposed in [138, 146] and [139]. In a comparison study [149] the original Jensen model provided the best fit with wind farm measurements compared to various other wake modelling techniques. The aim of this work is to quantify the impact of wakes on the inertial response. The value of the contribution and its importance is obvious, when seen in the context of the changes and challenges outlined in the introduction.

6.2.2 Jensen’s model in detail

Jensen’s wake model assumes that the wake expands in a cone-like fashion away from the turbine blades, as shown in Figure 6.1. The strength of the wake decays downstream as the area aﬀected increases. At a distance x from the upstream turbine, the diameter of the disturbed air increases from the turbine diameter Dturb to Dturb +2kx,kbeingthe decay parameter. The wind speed vw at any downstream turbine is v-uv, v being the free wind speed and u being the wake.

Figure 6.1: Schematic of N.O. Jensen wake model

The wake produced by one upstream turbine up, with a thrust coeﬃcient Ct,iscal-

125 Chapter 6. Impact of Wakes on Wind Farm Inertial Response culated as [148]: √ 1 − 1 − C u = t (6.1) p (1 + 2kx )2 Dturb

m 7 s It is shown that generic algebraic relations for Ct such as v are not accurate since Ct varies with turbine type [150]. It is recommended to use the relevant manufacturer’s data or determine Ct using the Blade Element Method with suﬃcient available data [150].

The total wake u can be calculated from the individual wakes up of the upstream turbines that are inﬂuencing the turbine under consideration using a sum of squares while considering partial overlap [143]: A1 2 u = ( up) (6.2) A2

where the area of the smaller circle A2 is the turbine blade area and the area of the circle-circle intersection A1 is the section of the blade surface that cuts the wake. The detailed expression for A1 as a function of blade radius, the wake radius at the point of intersection and the distance between the wake and turbine blade center is available in [151]. Wind farms are generally designed to have a spacing of several turbine diameters between each turbine. The reason for this is a difference in the wake of a turbine in the near-field and far-field. In the near-field the turbine shape has an impact on the shape of the wake and the turbine generated turbulence is high [152]. In the far-field the main source of turbulence is atmospheric and some turbulence is caused by second order effects of shear forces. The turbine generated turbulence in this region is insignificant [153]. Hence wind turbines are spaced far enough, such that turbines are only affected by each others far-field. In the far-field of a turbine the main impact on other wind turbines is the reduced wind velocity and wind speed is free from turbulence. Jensen’s wake model, which is valid for the far-field, assumes a homogeneous wind direction and wind speed. Modelling of large wind farms is a challenging task, due to micro- as well as meso-scale effects creating heterogeneous wind direction and speed as well as turbulence. The meso-scale behaviour is also influenced by the interaction of the wakes of several turbines with the atmosphere. Complex terrain, such as changing surface roughness or proximity to shore further changes the airflow [154]. Despite these modelling challenges, Jensen’s wake model is commonly used in the simulation of wind farms. It provides reasonable results, which can compete with other wake simulation approaches [149].

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6.3 Wind energy conversion process

6.3.1 Inertial response provision mechanism

The power (Pt), that a DFIG turbine extracts from wind is dependent on the speed of the blade rotation and the orientation of the blades. A wind turbine has kinetic energy

(Emech) stored in the rotational mass of the blades and the turbine rotor. A DFIG turbine has two options for inertial response. It can increase its output power (Pe), either by extracting more Pt from wind or by releasing some of the Emech. The amount of power that can be delivered depends on the wind speed at the turbine in both cases.

Figure 6.2: Diagram for Betz law with two turbines

The calculation of Pt uses the upstream wind speed just before the airflow expands due to the disk actuator (turbine blades), at a location y, as seen in Figure 6.2. Such an expansion is not modelled. The distance from y to the actuator is short compared to the distance between turbines. Therefore the wind speed predicted by the Jensen model for location y does not differ much from the wind speed calculated at the location of the turbine blade. Hence vw calculated by Jensen’s model at the location of the turbine can be used in the power equation for the wind speed which is unaffected by the actuator disk.

Figure 6.3: Power curve of wind turbine

Wind turbines have diﬀerent operating regions. At very low wind speeds (around

127 Chapter 6. Impact of Wakes on Wind Farm Inertial Response

4m/s) and very high windspeeds (around 25 m/s) wind turbines do not operate. At medium wind speeds the turbine extracts as much power as possible and at relatively high wind speeds the power is limited according to the turbine rating. These diﬀerent operating regions can be seen in the power curve in Figure 6.3

The power Pt that a turbine can extract from the wind is proportional to the power contained in the air passing through the turbine blades. This depends on the wind speed vw, air density ρ and turbine radius Rturb.ThepowercoeﬃcientCp represents the eﬃciency of extraction, with a theoretical maximum of 59.3% (Betz Limit) [155]. Cp is a function of pitch angle β and tip speed ratio λ:

1 2 3 P = ρπR C (λ, β)vw (6.3) t 2 turb p

The approximate relationship of Cp with tip speed ratio and pitch angle is [156]:

116 4.06 C (λ, β)=0.5( − − 0.4β − 5) p λ +0.08β β3 +1 21 0.735 exp(− + ) (6.4) λ +0.08β β3 +1

Figure 6.4 shows the Cp curve, indicating methods for inertial response without de- loading. The λ-axis represents the tip speed ratio, where ωturb is the rotational speed of the blades:

ω R λ = turb turb (6.5) vw

At a constant wind speed vw and ﬁxed turbine radius Rturb,theλ-axis is directly proportional to the rotational speed ωturb of the turbine; any movement along the λ-axis towards zero represents slowing down of the turbine, releasing stored kinetic energy and hence increasing the power output. The rotational speed providing the optimal tip speed ratio λopt , at which a turbine can extract maximum power, is reached at:

λoptvw ωturb = (6.6) Rturb

As seen in (6.4) the pitch angle of the blades β, impacts the shape of the Cp curve.

A turbine operates at maximum Cp and hence zero β and λopt when the power output is below rated. This is optimum power point tracking (OPPT). In the rated regime the turbine will have a lower λ and higher β to limit the power output and rotational speed at the rated values. Without de-loading, a turbine in the OPPT region can only provide a response by

128 Chapter 6. Impact of Wakes on Wind Farm Inertial Response

Figure 6.4: Power coeﬃcient of wind turbine depicting inertial response without de- loading (solid arrow for turbines in OPPT region; dashed arrow for rated regime)

slowing down and releasing the kinetic energy. The kinetic energy stored in a rotational body, in this case the turbine blades and rotor, is [157]:

1 E = Jω2 (6.7) mech 2 turb

where J is the moment of inertia of the rotating body. Equation (6.6) describes the relation between turbine rotational speed and wind speed for the OPPT region. In this region a reduction in wind speed through the wake leads to lower rotational speed and hence less stored Emech.

The change of the operating point on the Cp curve as a result of releasing kinetic energy is shown by the solid arrow in Figure 6.4. The operating point is shifted from the maximum power point to a lower level and as a result the turbine will be able to extract less wind power.

A turbine in the rated regime can provide short term overproduction via pitch control and slowing down. If only the pitch control is used to provide the response, no movement along the λ-axis will be observed. In the rated regime the lower wind speeds caused by wake eﬀect lead to a reduction in pitch angle. This reduces the headroom for inertial response available through pitch control. The overproduction is equivalent to the over- loading of the mechanical and electrical parts of the turbine. This means the duration and amount of overproduction are limited.

Because of the reduction in rotational speed or pitch angle caused by the wake eﬀect, modelling of the inertial response capability should always include the impact of the wake on the power output.

129 Chapter 6. Impact of Wakes on Wind Farm Inertial Response

6.3.2 DFIG model

The inertial response supplied by the wind turbines in a farm is investigated through representative DFIG models in Simulink. The model shown in Figure 6.5 includes an OPPT controller and pitch angle control. Both controllers are designed with wind turbine rotational speed as an input, rather than a measurement of wind speed, which is not always readily available [158]. The OPPT controller calculates the torque reference from the rotational speed of the turbine, assuming Cpmax is 0.411 [158]:

0.5C ω2 ρπR 5 T = pmax turb turb (6.8) eref λ3 opt The equation is derived from the deﬁnition of the tip speed ratio, the equation of wind power output and the equation relating turbine torque and power.

Figure 6.5: Flow-diagram of DFIG wind turbine simulation

The pitch control, shown in Figure 6.6 compares the turbine rotational speed with the rated rotational speed to determine the adequate pitch angle. The ﬁrst stage uses a proportional and integral gain to compute the reference pitch. The second stage represents the lag due to blade inertia. The pitch angle is rate limited according to the speed at which the actuator can adjust the pitch angle. The pitch angle of any turbine is limited by the minimum and maximum value the blades can turn to, representable by a saturation block. Parameters for the controller are 150 and 25 for proportional and integral gain respectively. The lag time is 0.3 seconds [116]. The pitch angle is bound between 0◦ and 27◦ and has a rate limit of 10◦/s. Using the pitch angle from the pitch controller and information of wind speed and rotational speed, the turbine algebraic model in Figure 6.5 is solved to obtain the output

130 Chapter 6. Impact of Wakes on Wind Farm Inertial Response

Figure 6.6: Pitch control of DFIG turbine torque from the wind turbine using power coeﬃcient calculations. The torque reference found by the OPPT control is used to determine vqrref in the rotor side controller. The machine stator equations model the electrical behaviour of the induction generator, while the turbine generator model is a two-mass model representation of the behaviour of the drive train and rotating mass. A detailed description of the machine stator, rotor and generator equations, which are found in Appendix A.1, is provided in [159].

6.4 Wake eﬀect validation

This section validates the wake simulation presented in Section 6.2 against Horns Rev measurements [19]. The Horns Rev wind farm consists of 8 rows of 10 turbines arranged in a parallelogram layout with a 7.2◦ tilt as shown in Figure 6.7. The distance between each row and column is approximately 7 turbine diameters. The simulation uses the wind farm layout and turbine parameters presented in [19]. Horns Rev measurements at each turbine and three meteorological masts were obtained during one year in ten minute intervals. At the turbines power, pitch, nacelle measured wind speed and direction, nacelle position and yaw misalignment were registered. The masts provide information on wind speed and direction. Using a power curve the available information was used to estimate the wind speed at each turbine location. A detailed description of the measurements and the evaluation techniques used is provided in [19]. The measurements are available for wind speeds around 6 m/s, 8 m/s and 10 m/s. These measurements exist for wind directions of 270◦, 221◦ and 312◦, within a directional sector of ±5◦ for 221◦ and 6 m/s and ±1◦ for all other cases.

From the discrete set of output powers and Ct values with wind speed in [19], power output and Ct curves are produced. Below the cut-in speed of 4 m/s both parameters are set to zero [160]. The decay parameter k is important since it determines the wind speed recovery. Sørensen et al. [149] found that a decay coefficient of 0.04 (default value in commercial programs for offshore) was too low for Horns Rev wind farm. They further reported that at Klim wind farm a decay coefficient of 0.075 was a good choice. Using

131 Chapter 6. Impact of Wakes on Wind Farm Inertial Response

Figure 6.7: Layout Horns Rev Wind Farm

up, Ct and Dturb available from the measurements, the decay coefficient was optimized to provide a simulation with the best match with available measurements. The optimization conducted for this work has found a higher decay coefficient of 0.073 gave the best match for Horns Rev, which is in line with the decay coefficient reported for the Klim wind farm.

With the help of (6.1) and (6.2) the wake is calculated utilizing the Ct value obtained for each individual turbine. The computed wind speed at each turbine and turbine power are compared against the measured data. Figure 6.8 displays the measured and calculated wind speeds for different initial values (6 m/s, 8 m/s and 10 m/s) and wind directions (270◦, 221◦ and 312◦). Generally the measured and calculated velocity of the wind are close to each other as can be seen from Figure 6.8. The computed max. error is 4.82% for a wind speed of 5.99 m/s at angle of 221◦. The measured wake tends to be smaller than the computed one due to wake meandering [19]. This difference increases with increasing directional sector and hence it is not surprising that the largest mismatch of wake occurred for the case of ±5◦ (the largest directional sector). Further inaccuracies in the measurements are caused by the varying offset of the nacelle position registration and inaccuracy in power measurements [19]. In addition to local wind speeds, the power output in the simulation and measurements were compared. The most significant output power errors for each wind direction and speed are shown in Figure 6.9 with the worst mismatch of -10.99% at 312◦ at 10 m/s. The total power of the wind farm was also compared with the total measured power. The maximum error is 6.12%. While this margin is not negligible, it is much smaller than the error of not considering the wake effect. Wake effect modelling is an intricate task, since

132 Chapter 6. Impact of Wakes on Wind Farm Inertial Response

Figure 6.8: Comparison between Horns Rev wind measurements [19] and calculation

measurements carry uncertainty of calibration and are limited to available measurement points [161]. A variety of physical conditions can affect the wake effect, such as the atmospheric stability and local or temporal changes in wind speed and direction. There are further uncertainties in the model, such as the exact thrust coefficient for each turbine and knowledge of the precise surface roughness throughout the wind farm. For this reason the error margin observed is reasonable and comparable with values reported in [162]. Figure 6.10 displays power losses in the wind farm due to the wake, which are computed for different wind speeds and directions. Along the wind directions for which the turbines are aligned in a row, power loss is large. As expected the peaks are lower for larger spacing between turbines. As the cut-in speed is reached losses increase with the wind speed. After 11 m/s the losses drop, since the thrust coefficient and the steepness of the power curve decrease towards the rated regime at 17 m/s. When all turbines have reached the rated output, the exact wind speed does not affect the wind farm power output. Figure 6.11 presents the wake losses in Figure 6.10 relative to the expected power according to the wind speed. Large relative losses of up to 90% can be seen around cut-in wind speeds. Figure 6.10 shows that the actual power loss is small, however it can be significant for the network when this large percentage error is made on a large number of wind farms. At close to cut-in speeds it is important to know how many generators

133 Chapter 6. Impact of Wakes on Wind Farm Inertial Response

2 Power output mismatch [%]

0 10 8 221 270 Wind speed [m/s] 6 312 Wind direction [degree]

Figure 6.9: Absolute value of worst matches for each wind direction and speed between Horns Rev power measurements [19] and calculation

Figure 6.10: Power loss in wind farm through wake eﬀect depending on wind direction and speed, for a wind farm with rated power output of 160 MW

are actually operating. In the OPPT region the relative power loss mainly depends on the wind direction, rather than speed. From 11 m/s the losses start to drop towards

134 Chapter 6. Impact of Wakes on Wind Farm Inertial Response

Figure 6.11: Power loss in wind farm through wake effect relative to expected power production depending on wind direction and speed zero. At 14 m/s the losses have reduced to about 1% of the expected power output. This validates the effectiveness of the simulation based on Jensen’s model. This result is very useful to quantify the inertial response capacity with a high degree of confidence which is considered next.

6.5 Quantifying the impact of wake on inertial response

We consider a wind farm with a similar capacity and layout as that of Horns Rev for quantifying the impact of the wake on the total inertial response. Horns Rev wind farm [19] consists of 80 turbines. A plausible wind speed scenario for individual generators in the wind farm is found with the validated wake effect model. At a wind direction of 353◦ and a free wind speed of 13 m/s local wind speeds of 13 m/s, 12.27 m/s, 11.73 m/s, 11.42 m/s, 11.33 m/s, 11.30 m/s, 11.28 m/s and 11.27 m/s are present at ten turbines in each row. The aggregate power output for turbines operating at the same wind speed in a row is used. In this case eight distinct wind speeds are present at ten turbines each, hence eight DFIG models connected in parallel represent the wind farm. The top plots in Figure 6.12 to 6.15 represent the first row of the wind farm - the subsequent plots reflect the other rows. Because of the wakes, they receive less wind speed. Without the wake effect all rows will be the same as row one.

135 Chapter 6. Impact of Wakes on Wind Farm Inertial Response

For inertial response simulations the Cp relationship in (6.4) was used as an analytical method to link the pitch angle and rotational speed to the wind power extracted by the turbine. This model is for a turbine of 2.3 MW and a radius of 38.76 m [157] entering the rated regime at 12.46 m/s. In order to study inertial response by considering the wake eﬀect, each of the eight DFIG models, as shown in Figure 6.5 is supplied with a local wind speed according to the wake simulation. During the response this model is supplied with an additional power command Pnew, with Teref as in (6.9) as its torque reference, where Trefold, Pold, ωturb old and ωturb are the pre-disturbance torque, power and rotational speed and the current rotational speed respectively. In this work, 10% additional power for inertial response are demanded in response to a loss of generation such that Pnew is 1.1 times Pold.

PnewTrefoldωturb old Teref = (6.9) Poldωturb The DFIG model responds in the manner depicted in Figure 6.4, reducing the rotational speed in the OPPT region and ﬁrst reducing the pitch angle and then slowing down if necessary in the rated regime. Figure 6.12 shows the power output of each row of wind turbines responding to a 10% additional power command at 10 seconds for a duration of 10 seconds. After the response, the original reference torque is restored and the recovery period can be observed. The ﬁrst row operating at 13 m/s is the only row not to exhibit a recovery period.

Figure 6.12: Total power of diﬀerent rows

Figure 6.13 shows the change in torque during the response for one turbine for each

136 Chapter 6. Impact of Wakes on Wind Farm Inertial Response wind speed. The turbine rows operating in rated regime have torque curves resembling the power curves, whereas for all others the torque ramps up during response and down after the initial torque reference mechanism is restored.

Figure 6.13: Torque of turbines in diﬀerent rows

This torque response becomes clear when observing the rotational speed of the turbines during the response and recovery period in Figure 6.14. The front row of turbines does not experience significant changes in rotational speed. The turbines in the OPPT region slow down at 10 seconds to release kinetic energy for the additional power output requested. Once the additional power command is removed at 20 seconds the turbines speed reach their original speed, through the recovery phase. The turbines in the front row provide the response without slowing down due to the pitch response in Figure 6.15. At 13 m/s this is the only row operating in the rated regime with a pitch angle above 0◦. When this pitch angle is reduced, additional power can be extracted from the wind for a duration that depends on the overrating capacity of all turbine components. The total power output is shown in Figure 6.16. The simulation is based on a free wind speed of 13 m/s and a wind direction of 353◦ before, during and after the response to a 10% additional power command. Before the additional power command is applied, the total output power is 179.6 MW without the wake effect taken into consideration. It is clearly seen from the plot that the total output is substantially less (146 MW) when the wake effect is considered. After the additional power demand of 10% is applied the total output is 197.5 MW without the wake effect and 160.4 MW with the wake effect taken into consideration. The true worth of the frequency response capability of the wind

137 Chapter 6. Impact of Wakes on Wind Farm Inertial Response

Figure 6.14: Rotational speed of turbines in diﬀerent rows

Figure 6.15: Pitch angle of turbines in diﬀerent rows

farm is comparably less (in this case by 37.1 MW). After the additional power demand is withdrawn the wind farm experiences a major recovery period, that would not be predicted in the rated regime. During the recovery period the power produced is much lower than that before the response; potentially aggravating the problem. In a lower wind speed case where all wind turbines operate in the optimal power point tracking region, wake eﬀect still has a major impact on the wind farm response as can be seen in Figure 6.12. In this case the trace of row 2, may be the respone of the front row, while the lower traces represent the subsequent rows. I this region the wake leads to a reduction in power before, during and after the response, with all rows showing a recovery period.

138 Chapter 6. Impact of Wakes on Wind Farm Inertial Response

Figure 6.16: Wind farm power output with and without wake eﬀect

6.6 Evaluating the duration of wind turbine response according to wind speed

Section 6.5 has shown the impact of the wake eﬀect on a wind farm supplying 10% inertial response for 10 seconds. Since inertia has been an inbuilt characteristic of conventional generation, no regulation is set in place to determine the level of inertial response synthetic inertia should produce. This work is based on an increase of power by 10% from original production, following the 10% additional output set out in the Grid Code by National Grid UK for primary response [163]. The Grid Code also requires primary response to be fully available 10 seconds following the event. This means that inertial response should be able to cover at least up to 10 seconds, so another interesting question is if this can be guaranteed at all wind speeds and if the wind turbines could provide response for longer to support primary frequency response. Results of response capability were taken for a variety of wind speeds to establish a capability curve of the wind turbine according to wind speed. Two factors were of interest to the overall capability. The moment when the turbine cannot be slowed down further, because it has reached the minimum rotational speed, as seen in Figure 6.17, and the time when the torque and hence additional power output started to drop oﬀ, as can be seen in Figure 6.18. Figure 6.17 shows the rotational speed of the turbine at a wind speed of 4.9m/s when an additional power command of 10% is sent to the turbine at 0 seconds. At low wind speeds the pitch angle is already zero degrees; the turbine slows down as soon as the additional power command of 10% is sent to the turbine. After about 28.7 seconds the turbine reaches the minimum rotational speed, which was chosen according to rotational speed during cut-in, as 0.8208 radians/second, indicated in Figure 6.17. Figure 6.18 shows the turbine torque during the inertial response. The turbine torque

139 Chapter 6. Impact of Wakes on Wind Farm Inertial Response

Figure 6.17: Rotational speed in radians/second of turbine during additional power command of 10% at 0 seconds at 4.9 m/s wind speed, point indicates moment turbine reaches minimum rotational speed

Figure 6.18: Response in turbine torque during additional power command of 10% at 0 seconds at 4.9 m/s wind speed, point indicates moment torque starts to drop oﬀ and hence the turbine output power starts to drop oﬀ when the turbine is not able to maintain the additional power command. When the turbine slows down increasingly

140 Chapter 6. Impact of Wakes on Wind Farm Inertial Response quickly, the kinetic energy stored in the rotation of the turbine blades decreases and at the same time as the power extraction from the wind decreases. This leads to an exponential increase in the torque command. The cascade PI controllers in the rotor-side converter of the DFIG do not adjust the voltage reference sufficiently quickly to maintain the torque at the reference level. For 4.9 m/s this happened after about 25.76 seconds, as indicated in the figure. For a wind direction of 270 degrees using 2 degree bins wake measurements at Horns Rev [19] name wind speeds along one out of eight rows of ten turbines as 10.09 m/s, 8.82 m/s, 8.77 m/s, 8.66 m/s, 8.61 m/s, 8.49 m/s, 8.41 m/s and 8.36 m/s, while wind speed at the last two turbines is not stated. To keep the wind farm size of 80 turbines a wind farm layout of 10 rows and eight columns with the same 560m spacing and 7.2 degree alignment of columns West of North is assumed. This ensures the wake effect on inertial response presented is not overestimated. The wind farm presented will have ten turbines at each of the above wind speeds.

Response capability of wind turbine 35

Response capability of 10% additional power [seconds] 0 4 6 8 10 12 14 Wind speed [m/s]

Figure 6.19: Time of additional 10% power command capability of DFIG turbine according to wind speed, solid line indicating limitation due to torque drop, doted line limitation due to minimum rotational speed of the turbine, dashed and dotted line indicating turbine overall capability

141 Chapter 6. Impact of Wakes on Wind Farm Inertial Response

Figure 6.19 shows the duration a turbine can supply additional 10% power output considering wind speed. A minimum response capability of additional 10% power output for approximately 10.4 seconds can be provided for all wind speeds exceeding about 4.17 m/s. It can further be seen that in the low wind speed region the maximum time of additional power output is 26.46 seconds at a wind speed of 4.7 m/s. For higher wind speeds the 10% additional power is proportionally higher, the kinetic energy in the turbine is higher due to faster rotational speed while power losses from wind power extraction during slow down are more severe. This leads to shorter response times. From about 12.3 m/s the turbine capability increases because the pitch angle can be reduced from a higher value to zero increasing the power output by increasing the extraction from the wind. It is generally true that any response that is above the rated output of the turbine will further be limited by the duration all turbine components can tolerate the higher stresses. This has not been modelled since it will depend highly on the manufacturer specific components. This means that turbines operating during higher wind speeds have a limited response time, even though this is not indicated by rotational speed or torque models. At the respective wind speeds from Horns Rev wind farm turbines could produce 10% additional power for 12.6 seconds to 15.3 seconds for 10.09 m/s to 8.36 m/s respectively. 12.6 seconds should be taken as the time the wind farm will release additional 10% power output compared to initial power production, because those turbines that have reached their capability limit will release less power as they have to stop slow down and are at alowerpointontheCp curve, meaning they can extract less power from the wind and will eventually need to recover their initial rotational speed. Neglecting the wake effect every turbine would operate at 10.09 m/s and be able to release 122.06 kW. The response capabilities using wind speeds measured at Horns Rev are: 122.06 kW, 81.53 kW, 80.15 kW, 77.17 kW, 75.84 kW, 72.71 kW, 70.68 kW and 69.43 kW. For the specific example there are 10 equivalent rows with eight columns with above response capability, this means the wind farm can release an extra 6.50 MW instead of 9.76 MW for about 12.6 seconds. This means a real wind farm will release 3.25 MW less power than would be expected from the free wind speed data.

6.7 Conclusion

A wake model simulation approach is presented and validated against measurements from Horns Rev [19]. Power losses due to the wake in a wind farm are computed for various sets of wind speed and direction. It is shown that the drop in the wind speed due to the wake effect reduces the wind farm power output significantly. The losses as percentage of total wind farm output are very much influenced by the wind speed and direction.

142 Chapter 6. Impact of Wakes on Wind Farm Inertial Response

This significantly affects the inertial response of the wind farm. Even though a wind farm can offer inertial response, this often introduces a recovery period during which the MW output is very low. Thus the wake model must be taken into consideration while computing the fast primary frequency control requirement. This work also discusses the duration, during which a turbine can release additional 10% of power. This duration is dependent on the wind speed. It was shown that above wind speeds of about 4.17 m/s all turbines should be able to release additional 10% of their original power output for at least 10.4 seconds, at which point primary response is required to be fully available according to the Grid Code [163]. It was also shown that the duration each turbine can sustain this additional power output depends on the exact wind speed and how the wind power plant additional power output differs from a case where wake effect has been neglected. In the Horns Rev example for 10.09 m/s free wind speed the difference was 6.50 MW instead of 9.76 MW for 12.6 seconds.

143 Chapter 7

Conclusion and Future Work

This work has investigated how the inclusion of more wind and HVDC technology impacts the GB system and the modelling required. Wind integration has increased due to concerns around global warming and limited reserves. Climate change agreements have been signed as a result on international and national level. The installation of wind generation over the years has been discussed, showing a steady increase. The UK is a major player in the global wind market. Wind installations are not only increasing in volume, they also make up a large proportion of the generation mix and recently added generation. Thus they are contributing an increasing percentage of the electricity use. Wind installations in the UK take place onshore, with the largest installations in the north of the GB network. Offshore installations are being rolled out in three rounds, where the later installations are further offshore, requiring DC connections. Predicted changes for the GB system have been discussed, including the change in generation mix and demand. In particular the frequency response capability of the future GB system was highlighted. The prediction for the 2030 GB generation mix [11] was used together with relevant frequency response literature, to determine the challenges that this change in generation and demand may cause and the technological capabilities already available. The gone green scenario is chosen for this work, which assumes that renewable targets are met on time [11]. In continuation powerflow solutions for an AC as well as ACDC network with CSC and VSC technology have been found using Matlab. Results of the earlier two cases were validated against an equivalent simulation in PowerFactory. The results showed that there was a good match in the AC power flow model. The ACDC CSC power flow model converged to values matching those of PowerFactory except for reactive power flow. Mismatches for the reactive power seem to originate from a discrepancy in the converter transformer models. The functionality of the DC link was confirmed against results from Arrillaga and Watson [15]. The ACDC VSC powerflow solution was found using Matlab. A comparison to a VSC link in PowerFactory was not conducted since a validated version of such was

144 Chapter 7. Conclusion and Future Work not available at the time. The GB system with a multi-terminal VSC for the connection of offshore wind farms was modelled and analysed in the following chapter. The set-up was similar to that of the eastern link with the three wind farms aiming to represent Doggerbank, Hornsea and East Anglia One. This section included the description of the powerflow solution of a multi-terminal DC grid, with multiple AC networks. The solution provided the necessary information for finding the initial conditions of the system. The step response of the system was shown and discussed. A multi-machine test system, including offshore wind, an HVDC link and offshore AC line were used to validate the linearization of such a system using the ”linmod” function provided by Matlab. The system matrix was calculated analytically from the differential algebraic equations of the system and using the inbuilt function. The results matched extremely well. Therefore the inbuilt function was chosen for further system analysis. The eigenvalue analysis revealed six super-synchronous and sub-synchronous modes each, that were critically damped. Some of the modes mainly rooted from the interaction between synchronous machines. Other modes showed a significant interaction with converter stations. One of the critically damped modes with significant participation from the VSC grid, is the inter-area mode. A power system stabilizer (PSS) was implemented at converter station IV to improve the damping of the inter-area mode. A second PSS was introduced at a generator in Northern Scotland. Using two PSS the inter-area mode is well damped and one of the other originally critically damped modes is sufficiently damped. One aspect of the integration of offshore wind into the GB system is to ensure the system stability. Another question is whether the newly installed wind generation can provide any of the services, that the conventional generation it replaces used to provide. This question has been touched upon in the second chapter. A detailed discussion is provided for the wind farm inertial response capability. The work has shown how the duration of response from a turbine depends on the wind speed. Since the wind speed across a wind farm varies due to wake effect, the modelling of the wake effect has been discussed. The model was validated against actual wind farm measurements. The wake effect model was then used to show how inertial response provided by a wind farm differs due to wake effect, compared to a free wind speed scenario. This work has highlighted, that the GB system is undergoing major changes, such as the inclusion of large scale offshore wind farms and HVDC grids, which require special modelling efforts. The changes need to be reflected in small signal stability models. At the same time wind generation needs to be modelled with care, since it’s fuel source wind is not straight forward to predict and is affected by aerodynamic phenomena, such as the wake effect. It has been shown how changes in the GB system, bring various new complexities

145 Chapter 7. Conclusion and Future Work to power system considerations, such as impact on stability, reserves needed on the system and modelling of renewable generation. Successful integration of multi-terminal DC and large offshore as well as onshore wind developments requires a careful study of various aspects and in varying detail. Future work should entail a more detailed study of offshore networks, including the details of the offshore AC grid and individual wind turbine generators and possible interaction of the DC grid converter control and wind power plants. While the interaction of synchronous machines in a power system is well-know, the introduction of converter controls and wind turbine controls gives rise to new sources of instability. Interactions between different controls, leading to oscillations below system frequency, are termed sub-synchronous control interactions. Such a sub-synchronous control interaction has occurred in Texas between a wind power plant and a series compensated line, leading to sever damage of the wind generators [164]. Some research has suggested that supplementary wind turbine control can be used to avoid sub-synchronous control interactions or even dampen sub-synchronous interactions caused by the interaction of other system components [165, 166, 167]. Researchers have warned that the future GB system may face sub-synchronous resonance issues, due to the installation of series compensation [30]. Under such a circumstance the capability of wind farms to dampen sub-synchronous resonance via additional control would be extremely valuable and should be further investigated.

146 Appendices

147 Appendix A

Dynamic modelling of wind power plants

Modelling the dynamic behaviour of wind farms is a challenging task as it depends on the exact turbine types, wind farm layout, wind farm cabling and line parameters. When the behaviour of individual generators is of interest, the turbine model used should contain a representation of the mechanical and electrical system. For system level studies a generic wind park model that is tuned and veriﬁed against measurements may be appropriate. [116] provide such generic wind park models and oﬀshore network equivalent circuits, that have been developed using actual measurements. In this work a wind power plant similar to the generic model presented in [116] was used for larger system studies. While a detailed electro-mechanical model was used for the discussion of wakes throughout wind farms.

A.1 Dynamic modelling of DFIG

A detailed dynamic model of a DFIG provided in [159] has been used in Chapter 6, where the behaviour of single turbines in a wind farm was of interest. The pitch control, optimal power point tracking and power extraction by the blade were discussed inside the chapter. The dynamic equations of the drive train, induction generator and rotor side converter control are provided in the appendix, since a detailed description is available in [159]. The drive train is represented by a two-mass model [159]. It describes the transfer of energy from the rotating wind turbine blades to the generator. In the following equations

ωelB is the electrical base speed, Ht is the turbine inertia constant, Hg the generator inertia, k is the stiﬀness and c the damping coeﬃcient of the shaft.

148 Appendix

d 1 ωt = (Tt − Tsh)(A.1) dt 2Ht

d 1 ωr = (Tsh − Te)(A.2) dt 2Hg

d T kθ c θ sh = tω + dt tω (A.3)

d θ ω ω − ω dt tω = elB( t r)(A.4)

The electrical torque of the induction generator can be found as follows, where Lm is the mutual inductance:

Te =Lm(iqsidr − idsiqr)(A.5)

The generator of the DFIG wind turbine is represented as a voltage source behind a transient impedance, where the current injected into the grid is the sum of the stator and 2 grid side converter AC currents [159]. L = L − Lm ,whereL is the stator inductance s ss Lrr ss and L the rotor inductance. T is Lrr .K is deﬁned as Lm . R = R + R and rr r Rr mrr Lrr 1 s r 2 R2 =Kmrr Rr. Xm is the mutual reactance. The DFIG stator and rotor can be described by following equations [159]:

L d ωre e s − ω qs − ds − iqs = R1iqs + sLsids + vqs +Kmrrvqr (A.6) ωelB dt ωs ωsTr

L d ω e e s − − ω r ds qs − ids = R1ids sLsiqs + + vds +Kmrrvdr (A.7) ωelB dt ωs ωsTr

d ω e 1 − r − qs − eqs =R2ids +(1 )eds Kmrrvdr (A.8) ωsωelB dt ωs ωsTr

1 d ω e − − − r − ds eds = R2iqs (1 )eqs +Kmrrvqr (A.9) ωsωelB dt ωs ωsTr

eds iqr = − − Kmrriqs (A.10) Xm

eqs idr = − − Kmrrids (A.11) Xm The rotor side converter can control real and reactive power independently. As such one control loop, providing the direct rotor voltage reference can maintain either reac-

149 Appendix tive power or voltage magnitude, while the other control loop for the quadrature rotor voltage reference regulates either real power or torque. The control loops are cascade PI controllers, with direct and quadrature rotor reference current respectively as the intermediate control output. The following equations show an example where the voltage and torque are being controlled. Equations A.12 to A.15 represent the cascade PI controllers for voltage control, while Equations A.16 to A.19 correspond to the cascade PI torque control.

d N =K (V − V ) (A.12) dt i dr I i d s ref s

0=idr ref − KP i d(Vs ref − Vs) − Nidr (A.13)

d N =K (i − i ) (A.14) dt v dr I v d dr ref dr

0=vdr ref − KP v d(idr ref − idr) − Nv dr (A.15)

d − dtNi qr =KI i q(Te ref Te) (A.16)

0=iqr ref − KP i q(Te ref − Te) − Niqr (A.17)

d − dtNv qr =KI v q(iqr ref iqr) (A.18)

0=vqr ref − KP v q(iqr ref − iqr) − Nv qr (A.19)

The total power of the DFIG can be calculated from the voltages and currents. It is assumed that the GSC is operated in unity power factor, which makes the grid side converter reactive power zero. If the system is in a dq-reference frame with the system voltage aligned with the q-axis, vds is also zero.

Ptot = Ps + Pr = vqsiqs + vqriqr + vdridr (A.20)

Qtot = −vqsids (A.21)

Stot = Ps + Pr = vqsiqs + vqriqr + vdridr − jvqsids (A.22)

150 Appendix

Stot∗ vqriqr + vdridr itot = = iqs + jids + (A.23) vqs vqs The total current injection by the DFIG wind turbine can be calculated from the power and voltage. For the current injection into the grid the current should be in the according p.u. system and rotated to correspond with the system reference frame, rather than in dq-frame.

A.2 Dynamic modelling of generic wind park model

Figure A.1 shows an overview of the wind power park modelling block. The wind park module requires system voltage as input. The dq-reference frame and the beneﬁts of alignment of the q-axis with the system voltage have been discussed in Section 4.5. The model presented by [116] use the same alignment, such that Vterm is the quadrature voltage component and the direct component is zero.

Figure A.1: Overview of generic wind power plant model

The control model in Figure A.2 regulates the direct and quadrature current com- mands to ensure the real power and either reactive power or control voltage are maintained at their reference values. The control voltage ”...can be terminal voltage or remote bus voltage or ﬁctitious remote bus voltage.” [116] In this work the oﬀshore wind power plants operate on reactive power control, since the voltage at the DC grid converter is controlled by the VSC. The onshore wind power plants take the terminal voltage as the control voltage. The two machine test system, used reactive power control, as described in [116] for type four turbines (a cascade control), whereas the UK system study used the

151 Appendix reactive power control [116] provide for DFIG turbines (direct control).

Figure A.2: Generic control model, ﬁrst selector for V or Q control, second selector Q control as in full converter or DFIG turbine

The generator/converter model in Figure A.3 represents the delay between the real or quadrature command and their actual values. The quadrature voltage and current represent the real power generated. Because of the current conjugate in the power formula, the reactive power is equal and opposite to the quadrature voltage times the direct current. The complex current in the dq-reference frame is known from the direct and quadrature components by deﬁnition.

Figure A.3: Generic generator/converter model of wind power plant

152 Appendix

As shown in Figure A.1 the current has to be returned to the original reference frame, before it can be used as a current injection into the power system model. The power system model is representative of any other components present in the system, such as oﬀshore AC lines, synchronous machines, HVDC grids and the onshore network. The power system model uses the current injected by the wind farm to determine the voltage across the system, providing the input to the wind power plant model.

153 Appendix B

Dynamic modelling of synchronous machines

B.1 Excitation system

All synchronous generators in the network are equipped with excitation systems to allow control of the voltage magnitude or reactive power. Modern power plants tend to use static excitation systems, in which all parts are stationary and which provide a fast response. Excitation system models can be very detailed, when the exact physical set-up and vendor are known. A more generic representation is often chosen, where the excitation system is represented by a simple transfer function between the voltage deviation and the ﬁeld voltage with a gain KA and a delay time TA for the automatic voltage regulator (AVR).

E K fd = A (B.1) |Vs ref−|Vs 1+sTA

The gain KA can vary from values as low as 10 all the way into the hundreds. The excitation system should be designed to react fast to keep the voltages at their reference values, leading to a large gain. At the same time the gain should be selected that does not degrade the system stability. A gain of 60 was used in this work, to fulﬁl this requirement. The time delay of the AVR is set to 0.02 seconds, according to [168].

B.2 Governor control

As discussed, at least one generator in the system is required to operate as a governor to balance demand and generation and to maintain the frequency at its reference value. The governor response was modelled according to [18].

154 Appendix

Figure B.1: Governor control model

B.3 Machine model

The synchronous machine is modelled including a ﬁeld circuit with one equivalent damper on the q-axis [117]. The wb is chosen to be the same as ws, such that the p.u. value is 1. To ﬁnd the machine reference frame the induced voltage is calculated according to [117]:

Eq0 δ0 = Vterm Vangle +(Ra + jxq)iterm iangle (B.2)

The ﬁeld voltage can be initialized as [117]:

Efd0 = Eq0 − (xd − xq)id0 (B.3)

The equivalent stator equation of the synchronous machine is provided by [117] considering transient saliency. Transient saliency occurs when the reactance of the synchronous machine diﬀers between d- and q- axis.

j − j j j Eq + (Ed + Edc) (Ra + xd)(iq + id)=Vq + Vd (B.4)

Handling the transient saliency using a dummy rotor coil the relationship between the quadrature current iq and Edc becomes [117]:

E x − x dc = d q (B.5) iq 1+sTc Ed and Eq can be expressed as follows [117]:

(x − x )i + E E = d d d fd (B.6) q s 1+ Tdo

E −xq + x d = q (B.7) s iq 1+ Tqo The electrical generator torque [117], taking saliency into account, can be calculated using Equation B.8.

155 Appendix

− Te = Edid + Eqiq +(xd xq)idiq (B.8) The rotor mechanical equations describe the relationship between the rotor movement and the electrical system [117]:

2H dw w − wb = Tm − Te − Ddamping (B.9) wb dt wb The load angle diﬀerential equation is [117]:

dδ = w − w (B.10) dt b

156 Appendix C

Test system parameters

The parameters of the test system used in Chapter 4 to validate the use of ”linmod”, are listed here: The Z-matrix of the example system is: ⎡ ⎤ 0.3998 + j0.4746 0.3998 + j0.2370 0.3993 − j0.001 ⎢ ⎥ Z = ⎣ 0.3998 + j0.2370 0.3398 + j0.2370 0.3993 − j0.001⎦ (C.1) 0.3993 − j0.001 0.3993 − j0.001 0.3987 − j0.001

The oﬀshore AC system and wind generator parameters are:

Table C.1: Parameters of oﬀshore AC system and wind generator

−4 Roff 0.00128 Vc off q 0.98503 ic off q 0.09047 Pgen 3.831 · 10 −5 Loff 0.05311 Vc off d -0.00449 ic off d -0.20078 Qgen −2.2984 · 10 Coff 0.20708 Voff q 0.99581 ioff q 0.09046 Pgb 0 Goff 0 Voff d 0.00005 ioff d 0.00543

The DC link parameters are:

Table C.2: Parameters of DC link

Rdc 0.07881 Vdc 1 1.19861 idc 1 0.03755 Vc q 2 ref 0.89561 Ldc 1.56877 Vdc 2 1.19565 idc 2 -0.03755 Vc d 2 ref 0.00501 Cdc 1 8.9833 Vdc ref 2 1.19565 icc 0.03755 Cdc 2 8.98326 Vc q 1 0.9850 ωhvdc 376.991

157 Appendix D

GB system parameters

The parameters of the GB system, analyzed and simulated in Chapter 4, are listed here, where the voltage at all onshore generator buses is 1.01 p.u.:

Node Bus Real React. Type 6 12 11.906 Wind Power Power 58 -12.936 -3.15 Load [100 [100 7 13 10.290 Nuclear MW] MW] 14 3.963 Wind 1 1 7.092 Wind 59 -8.195 -1.710 Load 2 6.897 Hydro 8 60 -1.293 -0.374 Load 53 -5.148 -1.020 Load 9 61 -1.43 -0.530 Load 2 3 7.225 Gas 10 15 1.200 Gas 4 1.675 Wind 16 3.179 Coal 5 0.153 Hydro 17 10.120 Nuclear 54 -5.643 -1.13 Load 18 1.565 Wind 3 6 2.959 Wind 62 -28.171 -4.650 Load 7 4.694 Hydro 62 12 0.162 HVDC 55 -6.105 -1.050 Load 11 19 6.123 Gas 4 8 18.218 Coal 20 17.801 Coal 9 0.298 Wind 21 20.155 Nuclear 10 3.742 Hydro 22 10.613 Wind 56 -14.388 -3.170 Load 63 -36.960 -7.600 Load 5 11 7.569 Nuclear 12 23 11.842 Gas 57 -5.522 -1.280 Load 24 3.640 Nuclear

158 Appendix

25 0 no gen. 71 -22.209 -6.480 Load 26 17.714 Hydro 20 37 10.120 Nuclear 64 -13.079 -3.38 Load 72 -11.301 -3.058 Load 13 65 -27.764 -7.660 Load 72 26.837 -1.138 HVDC 14 66 -20.141 -5.665 Load 21 38 4.286 Gas 15 27 59.277 Coal 73 -7.722 -2.022 Load 28 0.2721 Wind 22 39 5.511 Gas 67 -28.963 -6.940 Load 74 -20.02 -6.65 Load 16 29 23.967 Gas 23 40 42.860 Gas 30 39.394 Coal 41 26.80 Coal 31 0 no gen 42 0 no gen. 68 -17.677 -6.550 Load 75 -52.074 -13.37 Load 68 12 0.172 HVDC 24 76 -15.598 -5.280 Load 17 32 15.137 Coal 25 43 17.144 Gas 69 11.891 3.710 Load 77 -107.07 -29.020 Load 18 33 0.784 Gas 26 44 14.083 Gas 34 16.787 Coal 45 22.706 Coal 70 -58.982 -19.35 Load 78 -15.664 -4.340 Load 19 35 21.767 Gas 27 46 8.844 Nuclear 36 12.611 Wind 47 8.674 Wind

159 Appendix

79 -5.027 -1.380 Load 28 48 15.613 Gas 49 1.196 Coal 50 0 no gen. 80 -30.261 -8.410 Load 29 51 6.4596 Gas 52 7.399 Nuclear 81 -28.347 -3.560 Load

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