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Georgios Rogdakis, s073726

Electromagnetic validation of fault-ride through capabilities of fixed-speed wind turbines

Master’s Thesis, September 2010





Electromagnetic validation of fault-ride through capabilities of fixed-speed wind turbines

This report was prepared byGeorgios Rogdakis, s073726

SupervisorsRodrigo Garcia-Valle CET DTU

Ivan Arana Aristi DONG Energy

Release date: November 23, 2010Category: 1 (public)

Edition: First

Comments: This report is part of the requirements to achieve the Master of Science in Engineering (M.Sc.Eng.) at the Technical University

of Denmark. This report represents 30 ECTS points.Rights: ©Georgios Rogdakis, 2010

Department of Electrical EngineeringCentre for Electric Technology (CET)Technical University of DenmarkElektrovej building 3252800 Kgs. LyngbyDenmark

www.elektro.dtu.dk/cetTel: (+45) 45 25 35 00Fax: (+45) 45 88 61 11E-mail: [email protected]





Preface

This is report is the result of the work carried out by Georgios Rogdakis, studentat the Technical University of Denmark (DTU), in fulfillment of the requirements for

obtaining the degree of Master of Science in Wind Energy. The project has beencompleted in the period from February to September 2010 in cooperation with theCentre for Electric Technology at DTU and DONG Energy.

The supervision has been undertaken by Rodrigo Garcia from CET DTU and IvanArana from DONG Energy.

I hereby declare that this thesis was composed by myself, that the work containedherein is my own except where explicitly stated otherwise.

November 23, 2010Georgios Rogdakis

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Acknowledgements

I would like to thank my supervisors Rodrigo and Ivan for giving me the opportunity to in-vestigate a very interesting topic. I also appreciate their guidance, support and inspiration

throughout the project. Their comments formulated useful inputs towards the solutions of theproblems rising during the last months.

I would also like to thank the employees of Electrical Department and Siemens Wind PowerA/S that have been very helpful in all the inquiries I have had.

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Abstract

The scope of the present project is the development and validation of an electro-magnetictransient model of the fixed-speed wind turbines. The research work will be focused on the

development of a model of a fixed-speed wind turbine with fault-ride through capabilities,simulating its behavior during island operation. Based on that, the behavior of the windturbines during the island operation will be investigated. The developed model should besuitable for electro-magnetic transient studies and the software tool that will be used is PSCAD.

In the first stage of the project, data available from field measurements acquired fromswitching operations in Nysted Offshore Wind Farm are studied. As it is unknown whatexactly happens after the disconnection of the radial, in this part it will be attempted tounderstand the behavior of the wind turbines. In the second part of the project, the modelof the wind turbine will be developed. The process of the model development is based onexperience from previous research work, appropriate for switching transient studies.

In the final stage, the model will be validated with the voltage and current measurements.As some parameters of the model are unknown, a sensitivity analysis will be performed toinvestigate the effect of the parameters on the system behavior. Finally, the generic control

model of the capacitor banks will be developed and the behavior of the wind turbines whilethey are on low- and high-level of production will be simulated.

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vi



Contents

Contents vii

List of Figures ix

List of Tables xv

Introduction 1

1 Introduction 1

1.1 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Work by others . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 Wind Energy Systems 5

2.1 Wind turbine configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 Technical regulations for the interconnection of Wind Farms to the grid . . . . 7

3 Measurement Analysis 11

3.1 Nysted Wind Farm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.2 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.3 Measurement analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.3.1 Preliminary analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.3.2 Space Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.3.3 Transformation into sequence components . . . . . . . . . . . . . . . . . 223.3.4 FFT analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.4 Capacitor banks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4 Nysted Offshore Wind Farm Modeling 334.1 Transmission and Collection Grid Modeling . . . . . . . . . . . . . . . . . . . . 344.2 Wind Turbine Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.2.1 Aerodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.2.2 Shaft system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.2.3 Induction Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394.2.4 Capacitor banks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

5 Validation of the model 45

5.1 Comparison of the instantaneous values of currents and voltages . . . . . . . . 465.2 Sequence components analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

5.2.1 Voltage and current at the three locations . . . . . . . . . . . . . . . . . 495.2.2 Active and reactive power comparison . . . . . . . . . . . . . . . . . . . 545.2.3 FFT analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

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5.3 Distributed cable model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

6 Sensitivity analysis 65

6.1 Sensitivity analysis on the wind turbine parameters . . . . . . . . . . . . . . . . 666.1.1 Scenario A1: Low inertia- Low shaft stiffness . . . . . . . . . . . . . . . 666.1.2 Scenario A2: Low inertia- High shaft stiffness . . . . . . . . . . . . . . . 696.1.3 Scenario A3: High inertia- Low shaft stiffness . . . . . . . . . . . . . . . 716.1.4 Scenario A4: High inertia- high shaft stiffness . . . . . . . . . . . . . . . 74

6.2 Sensitivity analysis on the switching of the capacitor banks . . . . . . . . . . . 766.2.1 Scenario B1- The capacitor banks switching operations occur only in

A01 and A09 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 766.2.2 Scenario B2- The capacitor banks have the same operation in all wind

turbines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 796.2.3 Scenario B3- The capacitor banks remain connected and disconnect at

the 275 ms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

6.2.4 Scenario B4- Different steps of the capacitor banks connecting at A01 . 846.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

7 Capacitor control and assessment of over-voltages in different production

levels 89

7.1 Capacitor bank control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 897.2 Over-voltages during low-level production . . . . . . . . . . . . . . . . . . . . . 917.3 Over-voltages during nominal power production . . . . . . . . . . . . . . . . . . 967.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

8 Discussion and future work 103

8.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1038.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

Bibliography 107

Appendix 111

A Appendix A-Measurement analysis 111

B Appendix B-Validation 115

C Appendix C-Different steps of the capacitor banks connecting at A01 123

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List of Figures

2.1 Performance characteristics of wind rotors[1] . . . . . . . . . . . . . . . . . . . 5

2.2 Wind turbine configurations [2] . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.3 Voltage profile after symmetric three-phase faults [3]. . . . . . . . . . . . . . . . 8

3.1 Nysted Offshore Wind Farm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.2 Locations of the measuring system [4] . . . . . . . . . . . . . . . . . . . . . . . 123.3 Voltage in the three measuring points. Upper plot : voltage at the platform.

Middle plot : voltage at A01. Lower plot : voltage at A09 . . . . . . . . . . . 133.4 Current in the three measuring points. Upper plot : current at the platform.

Middle plot : current at A01. Lower plot : current at A09 . . . . . . . . . . . 133.5 Current in the three measuring points from 60ms to 120ms. Upper plot : cur-

rent at the platform. Middle plot : current at A01. Lower plot : current at A09 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.6 Voltage in the three measuring points from 250ms to 330ms. Upper plot : volt-age at the platform. Middle plot : voltage at A01. Lower plot : voltage at A09 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.7 Current in the three measuring points from 250ms to 330ms. Upper plot :current at the platform. Middle plot : current at A01. Lower plot : current at A09 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.8 Active Power measurements, 10 min average [5] . . . . . . . . . . . . . . . . . 163.9 Reactive Power Measurements, 10 min average [5] . . . . . . . . . . . . . . . . 163.10 Active and reactive power at the transformer platform calculated through space

vector transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.11 Active and reactive power at A01 calculated through space vector transformation 183.12 Active and reactive power at A09 calculated through space vector transformation 193.13 Active and reactive power at all three locations before the radial disconnection.

Left upper plot : Active Power at the transformer platform. Right upper plot : Reactive Power at the transformer platform. Left middle plot : ActivePower at A01. Right middle plot : Reactive Power at A01. Left lower plot :Active Power at A09. Right lower plot : Reactive Power at A09. . . . . . . . 19

3.14 Current at the transformer platform from 80ms to 120ms . . . . . . . . . . . . 203.15 Current at the transformer platform from 80ms to 120ms after the correction. . 213.16 Current at the transformer platform from 80ms to 120ms . . . . . . . . . . . . 213.17 Sequence components of the voltage at the transformer platform. Upper plot :

Zero sequence component. Middle plot : Positive sequence component. Lower

plot : Negative sequence component. . . . . . . . . . . . . . . . . . . . . . . . . 223.18 Sequence components of the current at the transformer platform. Upper plot :

Zero sequence component. Middle plot : Positive sequence component. Lower

plot : Negative sequence component . . . . . . . . . . . . . . . . . . . . . . . . . 233.19 Positive sequence voltage at A01. . . . . . . . . . . . . . . . . . . . . . . . . . . 243.20 Positive sequence voltage at the three locations. . . . . . . . . . . . . . . . . . . 25

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3.21 Power at the transformer platform calculated through sequence components and space vector transformation. Upper plot : Active power production. Lower

plot : Reactive power consumption . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.22 Power at A01 calculated through sequence components and space vector transformation. Upper plot : Active power production. Lower plot : Reactive power consumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.23 Power at A09 calculated through sequence components and space vector transformation. Upper plot : Active power production. Lower plot : Reactive power consumption. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.24 Power at A01 calculated through sequence components and space vector transformation between 80 ms and 200 ms. . . . . . . . . . . . . . . . . . . . . . . . 27

3.25 Spectrogram of the current at A01 wind turbine from 0 ms to 500 ms. . . . . . 283.26 FFT analysis on phase B of the measured current at A01 and A09 from 0 ms

to 500 ms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.27 FFT analysis on phase B of the measured current at A01. The signal is divided

in five stages according to figure 3.19. . . . . . . . . . . . . . . . . . . . . . . . 29

3.28 Voltage control set points [6]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.1 Generic block-diagram of the fixed-speed wind turbine. . . . . . . . . . . . . . . 344.2 Simple transformer equivalent circuit with the secondary winding referred to the

primary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.3 Model of the aerodynamics of the wind turbine rotor. . . . . . . . . . . . . . . . 364.4 Two-mass model of the shaft implemented in PSCAD. . . . . . . . . . . . . . . 394.5 Induction generator model implemented in PSCAD. . . . . . . . . . . . . . . . . 404.6 Equivalent circuit of a double squirrel-cage induction generator. . . . . . . . . . 414.7 Equivalent circuit of a single squirrel-cage induction generator. . . . . . . . . . 414.8 Model used for the representation of the capacitor banks included in the wind

turbine. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

5.1 Measured and simulated voltage at the transformer platform from 0 ms to 500 ms. Upper plot : Phase A. Middle plot : Phase B. Lower plot : Phase C. . . 46



5.4 Measured and simulated current at the transformer platform from 0 ms to 500 ms. Upper plot : Phase A. Middle plot : Phase B. Lower plot : Phase C. . . 48

5.5 Measured and simulated current at the transformer platform from 60 ms to 120 ms. Upper plot : Phase A. Middle plot : Phase B. Lower plot : Phase C. . . 48

5.6 Measured and simulated current at the transformer platform from 60 ms to 120

ms. Upper plot : Phase A. Middle plot : Phase B. Lower plot : Phase C. . . 495.7 Measured and simulated current at A01 from 270 ms to 330 ms. Upper plot :Phase A. Middle plot : Phase B. Lower plot : Phase C. . . . . . . . . . . . . 49

5.8 Measured and simulated current at A09 from 270 ms to 330 ms. Upper plot :Phase A. Middle plot : Phase B. Lower plot : Phase C. . . . . . . . . . . . . 50



5.11 Sequence components of the measured and simulated voltage at the transformer platform. Upper plot : Zero-sequence component. Middle plot : Positive-sequence component. Lower plot : Negative-sequence component. . . . . . . . . 52

5.12 Sequence components of the measured and simulated current at the transformer platform. Upper plot : Zero-sequence component. Middle plot : Positive-sequence component. Lower plot : Negative-sequence component. . . . . . . . . 52

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5.13 Positive-sequence component of the voltage at A01. . . . . . . . . . . . . . . . . 535.14 Zero-sequence component of the current at A01 and A09. Upper plot : A01.

Lower plot :A09. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

5.15 Active power production at the three measuring points. . . . . . . . . . . . . . 545.16 Active power production at the three measuring points after the radial discon-nection. Upper plot : Transformer platform. Middle plot : A01 wind turbine.Lower plot : A09 wind turbine . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

5.17 Reactive power at the three measuring points . . . . . . . . . . . . . . . . . . . 565.18 FFT analysis on the current at A01. . . . . . . . . . . . . . . . . . . . . . . . . 575.19 Frequency-Dependent (Phase) model of the cable. . . . . . . . . . . . . . . . . . 585.20 Instantaneous voltage at A01 from 60 ms to 120 ms. The results obtained from

the distributed cable and π-section model are compared with the measurements . 595.21 Instantaneous current at A01 from 60 ms to 120 ms. The results obtained from

the distributed cable and π-section model are compared with the measurements . 595.22 Instantaneous voltage at A01 from 260 ms to 380 ms. The results obtained from

the distributed cable and π-section model are compared with the measurements . 59

5.23 Instantaneous current at A01 from 260 ms to 380 ms. The results obtained from the distributed cable and π-section model are compared with the measurements . 60

5.24 Positive sequence component of the voltage at A01. . . . . . . . . . . . . . . . . 615.25 FFT analysis at phase B of the voltage. Upper plot : FFT at A01. Lower

plot : FFT at A09. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 615.26 FFT analysis at phase B of the current. Upper plot : FFT at A01. Lower

plot : FFT at A09. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

6.1 Instantaneous voltage comparison at A01-Scenario A1 . . . . . . . . . . . . . . 676.2 Instantaneous current comparison at A01-Scenario A1 . . . . . . . . . . . . . . 686.3 Instantaneous voltage comparison at A01-Scenario A2 . . . . . . . . . . . . . . 696.4 Instantaneous current comparison at A01-Scenario A2 . . . . . . . . . . . . . . 70

6.5 Instantaneous voltage comparison at A01-Scenario A3 . . . . . . . . . . . . . . 726.6 Instantaneous current comparison at A01-Scenario A3 . . . . . . . . . . . . . . 736.7 Instantaneous voltage comparison at A01-Scenario A4 . . . . . . . . . . . . . . 746.8 Instantaneous current comparison at A01-Scenario A4 . . . . . . . . . . . . . . 756.9 Instantaneous voltage and current comparison at A01-Scenario B1 . . . . . . . 776.10 Instantaneous voltage and current comparison at A09-Scenario B1 . . . . . . . 786.11 Instantaneous voltage and current comparison at A01-Scenario B2 . . . . . . . 796.12 Instantaneous voltage and current comparison at A09-Scenario B2 . . . . . . . 806.13 Voltage at A01 from 250 ms to 330 ms. . . . . . . . . . . . . . . . . . . . . . . 816.14 Instantaneous voltage and current comparison at A01-Scenario B3 . . . . . . . 826.15 Instantaneous voltage and current comparison at A09-Scenario B3 . . . . . . . 836.16 Voltage at A01 from 250 ms to 330 ms. . . . . . . . . . . . . . . . . . . . . . . 84

6.17 Instantaneous voltage and current comparison at A01-Scenario B4 . . . . . . . 856.18 Instantaneous voltage and current comparison at A09-Scenario B4 . . . . . . . 866.19 Measured and simulated current at A01 from 270 ms to 330 ms. The figure is

from the simulation in Chapter 5. Upper plot : Phase A. Middle plot : PhaseB. Lower plot : Phase C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

7.1 Voltage control set points [6]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 907.2 Voltage control logic implemented in PSCAD. . . . . . . . . . . . . . . . . . . . 917.3 Instantaneous voltages at A01. The control of the capacitor banks is enabled

faster in the simulation that the reactive power is supplied to the grid. . . . . . 927.4 Current at the capacitor banks at A01. Upper plot : Reactive power supplied

to the grid. Lower plot : Reactive power absorbed from the grid. . . . . . . . . 937.5 RMS voltage at A01 measured for the control of the capacitor banks. Upper

plot : Reactive power supplied to the grid. Lower plot : Reactive power absorbed from the grid. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

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7.6 Positive sequence component of the voltage at A01. . . . . . . . . . . . . . . . . 94

7.7 Active power production in the two simulated cases. Upper plot : Total activepower production. Middle plot : Active power production at A01. Lower plot :

Active power production at A09. . . . . . . . . . . . . . . . . . . . . . . . . . . 957.8 Reactive power production in the two simulated cases. Upper plot : Total reac-tive power production. Middle plot : Reactive power production at A01. Lower

plot : Reactive power production at A09. . . . . . . . . . . . . . . . . . . . . . 95

7.9 Instantaneous voltage at A01. The radial disconnection occurs at 15 sec. . . . . 96

7.10 Instantaneous voltage at A01. The capacitor banks in case of the nominal power operation disconnect 50 ms later and they connect again at 15.2 sec. . . . . . . 97

7.11 Current at the capacitor banks. . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

7.12 RMS voltage at MV side of the transformer at A01. The measured voltage isused for the voltage control of the capacitor banks. . . . . . . . . . . . . . . . . 98

7.13 Instantaneous voltage at A01. Connection of the capacitor banks at low-level power production occur at 15.655 sec . . . . . . . . . . . . . . . . . . . . . . . . 99

7.14 Positive sequence voltage at A01. . . . . . . . . . . . . . . . . . . . . . . . . . . 997.15 Active power production at the three locations for the two simulated cases. Up-

per plot : Active power production at the transformer platform. Middel plot :Active power production at A01. Lower plot : Active power production at A09. 100

7.16 Reactive power production at the three locations for the two simulated cases.Upper plot : Reactive power at the transformer platform. Middle plot : Reac-tive power at A01. Lower plot : Reactive power at A09. . . . . . . . . . . . . . 100

7.17 Positive sequence voltage at A01 for the three simulated cases. . . . . . . . . . . 101

A.1 Sequence components of the measured voltage at A01. Upper plot : Zero se-quence component. Middle plot : Positive sequence component. Lower plot :Negative sequence component . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

A.2 Sequence components of the measured current at A01. Upper plot : Zero se-quence component. Middle plot : Positive sequence component. Lower plot :Negative sequence component . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

A.3 Sequence components of the measured voltage at A09. Upper plot : Zero se-quence component. Middle plot : Positive sequence component. Lower plot :Negative sequence component . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

A.4 Sequence components of the measured current at A09. Upper plot : Zero se-quence component. Middle plot : Positive sequence component. Lower plot :Negative sequence component . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

B.1 Measured and simulated voltage at A01 from 0 ms to 500 ms. Upper plot :Phase A. Middle plot : Phase B. Lower plot : Phase C. . . . . . . . . . . . . 115


B.3 Measured and simulated voltage at the A01 from 270 ms to 330 ms. Upper

plot : Phase A. Middle plot : Phase B. Lower plot : Phase C. . . . . . . . . . 116



B.6 Measured and simulated voltage at the A09 from 270 ms to 330 ms. Upper

plot : Phase A. Middle plot : Phase B. Lower plot : Phase C. . . . . . . . . . 117

B.7 Measured and simulated current at A01 from 0 ms to 500 ms. Upper plot :Phase A. Middle plot : Phase B. Lower plot : Phase C. . . . . . . . . . . . . 117

B.8 Measured and simulated current at A09 from 0 ms to 500 ms. Upper plot :Phase A. Middle plot : Phase B. Lower plot : Phase C. . . . . . . . . . . . . 118

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B.9 Sequence components of the measured and simulated current at A01. Upper

plot : Zero-sequence component. Middle plot : Positive-sequence component.Lower plot : Negative-sequence component. . . . . . . . . . . . . . . . . . . . . 118

B.10 Sequence components of the measured and simulated voltage at A01. Upper


B.11 Sequence components of the measured and simulated current at A09. Upper


B.12 Sequence components of the measured and simulated voltage at A09. Upper


B.13 Instantaneous voltage at A01 from 0 ms to 500 ms. The results obtained from the distributed cable and π-section model are compared with the measurements. 120

B.14 Instantaneous voltage at A01 from 260 ms to 380 ms. The results obtained from the distributed cable and π-section model are compared with the measurements. 121

B.15 Instantaneous current at A01 from 0 ms to 500 ms. The results obtained from the distributed cable and π-section model are compared with the measurements. 121

C.1 Instantaneous voltage comparison at A01 from 0 ms to 500 ms-Scenarion B4 .Upper plot : Phase A. Middle plot : Phase B. Lower plot : Phase C. . . . . 123

C.2 Instantaneous current comparison at A01 from 0 ms to 500 ms-Scenarion B4 .Upper plot : Phase A. Middle plot : Phase B. Lower plot : Phase C. . . . . 124

C.3 Instantaneous voltage comparison at A09 from 0 ms to 500 ms-Scenarion B4 .Upper plot : Phase A. Middle plot : Phase B. Lower plot : Phase C. . . . . 124

C.4 Instantaneous current comparison at A09 from 0 ms to 500 ms-Scenarion B4 .Upper plot : Phase A. Middle plot : Phase B. Lower plot : Phase C. . . . . 125

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xiv



List of Tables

3.1 Active and Reactive Power before disconnection of the radial . . . . . . . . . . 15

5.1 Switching operations in the simulation . . . . . . . . . . . . . . . . . . . . . . . 45

6.1 Scenarios based on different values of H WTR and K . . . . . . . . . . . . . . . 666.2 Scenarios based on different times for the capacitor banks switching . . . . . . . 66

xv





Chapter 1

Introduction

The rate of electricity production from Wind Power is growing rapidly the last 25 years. Sincethe early 1970s when the first organized attempt of introducing another way of electricityproduction besides oil and its subsidies, the technology related to wind turbines has beenimproved. By the end of 1990s wind energy had become one of the most important sustainableenergy resources. The first wind turbines introduced were of the size of several kW whereasnowadays the wind turbines are over 3 MW and their production is expected to grow evenmore the next few years.

Furthermore, the goal set by European Union that by 2020 the rate of the electricityproduction should be at least 20%, led to the development of wind farms instead of individualwind turbines. From the early 2000s the development of offshore wind farms has grown rapidly

and it is of a vital importance to achieve the goal from EU. Even though the cost of thedevelopment of an offshore wind farm could be even double in respect with an onshore windfarm according to the European Environment Agency [7], the advantage of higher averagewind speed could make the investment more attractive. According to [8] the wind velocity at15 meters from the shore could be even 20-25% higher. In addition, the lower turbulence levelsin offshore comparing with the turbulence created by the landscape onshore could optimizethe power production.

1.1 Objectives

The main objective of the thesis was the development of a model of the fixed-speed windturbines suitable for electro-magnetic transient simulations. The model was validated with realmeasurements from the disconnection of a radial in Nysted Offshore Wind Farm. During theswitching operation the wind turbines were in operation. Once the model of the wind turbinewas validated, the effect of the radial disconnection on the over-voltages will be assessed whilethe wind turbines are in different production level.

As the behavior of the wind turbines after the radial disconnection was not known, part of the thesis was dedicated on the measurement analysis in order to extract as much informationas possible. Under this scope, different approaches were adopted and the results were discussed.

1.2 Work by others

The development of wind turbine models has been described in literature [9], [10]. The main

concepts that need to be taken into consideration while modeling mathematically the compo-nents of a wind turbine were described. In addition, according to the phenomenon investigateddifferent modeling approach should be adopted. In cases of voltage stability investigation of



2 1.2 Work by others

power systems with large wind farms an aggregated model could be more appropriate insteadof the representation of the whole wind farm [11], [12]. Furthermore, the degree of complexityregarding the components of the model has a significant impact on the results and different

models regarding the shaft system and the generator were presented [9], [13].Similar work for fixed-speed wind turbines has been done in [13]. The study was relatedto the investigation of the behavior of the wind turbine during a voltage dip. The model of the wind turbine the mechanical part of the wind turbine corresponding to the shaft systemand the induction generator. For each of the components two approaches were adopted; thedetailed and the simplified models. The behavior of the different models was investigated andcompared with field measurements acquired from a voltage dip event in a wind turbine. Thestudy was performed in two transient stability simulation tools, PSS/E and Power Factory.In [14], the comparison of the simplified and the detailed model of the induction generatoris performed in PSS/E, but both models are compared as well with the model available inPSCAD. The results showed an agreement between the fifth order model in PSS/E and themodel in PSCAD.

Even though the modeling of the wind turbines and the different aspects on that have

been investigated, there are not many studies regarding transient or temporary over-voltages.Temporary over-voltages could occur during island operation of a wind farm. Although anevent such as the disconnection of a wind farm while it is operating is rare, it could happen. In[15] the disconnection of a wind farm was analyzed and the simulation of similar events in windfarms was performed. The investigation has shown that after similar switching operations thelevel of active power production would affect the voltage increase rate. Therefore, the activepower supply of the wind turbines to the collection grid of the wind farm should be interruptedas soon as possible. In addition, reactive power compensation should be interrupted as well oract accordingly for preventing over-voltages.

The island operation of wind turbines is also described in [16] and [17]. The work is basedon the same experiment of island operation of a wind farm at Rejsby Hede in Denmark. In [16],the experiment was described and the preliminary analysis is presented. In addition, different

methods of estimating the frequency of the system were used to show that different methodsgive consistent results. In [17], the model of the wind farm was developed and validated withthe available measurements. The induction generator was represented by a fourth order modelwhile the mechanical part by the two-mass model. The simulation tool used for the simulationof the model was the PSS/E and the results were validated with the measurements presentedin [16].

The two-mass model representation of the shaft system of fixed-speed wind turbines is basedon [11], where it has been shown that for fixed-speed wind turbines there is electromechanicalinteraction between the shaft and the grid. Consequently, the studies involving a model of fixed-speed wind turbine, apart from the generator model, the aerodynamic model and theblade-angle control model, must include the shaft model. In [13], as it was mentioned before,two different modeling approaches for the mechanical model were studied; the two-mass andthe simple mass model. It was verified as well that the two-mass model was necessary tosimulate accurately enough the electromechanical oscillations.

The aim of the present project is that the model of the wind turbine developed will be ingood agreement with instantaneous voltage and current measurements following a switchingoperation. However, switching transient studies in large offshore wind farms focus mainly onthe energizing of the cables of the collection grid [5], [18]. In [5], the collection grid of Nystedwas modeled and validated with field measurements. The events studied were the energizingof the first and the second radial, with different switching moment and the energize of thetransformer in the last wind turbine of the first radial while seven wind turbines were underproduction. Even though, it was not under the scope of the present project, the modeling of the collection grid of the wind farm was based on the considerations presented in [5].

As the measurement available were from the disconnection of one radial of the wind farm,the wind turbines were in island operation. Similar work has been done in [19] and in [20].

In [19], the model of the wind farm was developed in both PSCAD and DIgSILENT PowerFactory and the results were compared with the measurements. However, the island operation



Chapter 1 3

of two wind turbines was simulated only in PSCAD. The results have shown discrepanciesbetween simulated and measured voltages, as the transients after the islanding are higherin the simulation results. However, the simulated currents show a closer to the measured

currents behavior. In [20], the impact of wind farm integration in the power quality of weakgrids was studied. Among other experiments, the over-voltages during island operation weresimulated. Several simulations were performed, with the capacitors connecting to the grid andthe capacitors disconnecting from the islanded grid in different moments. The transient over-voltages were higher if the capacitors were connecting in the grid at maximum voltage. It wasconcluded that when the wind farm was in island operation the capacitors should disconnectas soon as possible to avoid high over-voltages.



4 1.2 Work by others



Chapter 2

Wind Energy Systems

2.1 Wind turbine configurations

The first wind turbines used for producing electricity were simple and not always effective. Thegrowth of the wind turbines market led to the development of the wind turbine industry andthe design of more reliable wind turbines. Also, the need for higher electricity production fromrenewable energy sources along with the development of wind farms resulted in new designsof the control of wind turbines that could extract more wind power.

Based on the constructional design, wind turbines could be classified into those that theirrotor has a vertical axis of rotation and those that their rotor has an horizontal axis of rotation

[1]. The dominant design is the the horizontal axis wind turbines and the main reason is theirefficiency in respect with the efficiency of the vertical axis wind turbines. A comparison be-tween the performance characteristics of wind rotors can be seen in figure 2.1. The comparisonis based on the C p−λ curve and as it can be seen the three-bladed horizontal axis rotor is themost efficient among the other designs.

Figure 2.1: Performance characteristics of wind rotors[1]

Wind turbines can be also classified based on the generator that they are equipped with



6 2.1 Wind turbine configurations

and also based on their ability to control their speed. Related to the latter there are mainlytwo categories, the fixed-speed and the variable speed wind turbines. As denoted by thenames, variable speed wind turbines have the ability to adjust their rotational speed while the

fixed-speed have almost the same speed indifferent from the wind speed. The generators usedin wind turbines are either induction (asynchronous) or synchronous generators. The typicalwind turbine configurations are illustrated in figure 2.2.

In figure 2.2, type A, B and C are equipped with induction generators. More specifically,type A has a squirrel cage induction generator (SCIG) while type B and C have a woundrotor induction generator (WRIG). Type D wind turbines could be equipped with a WRIGor a synchronous generator; either permanent magnet (PMSG) or a wound rotor synchronousgenerator. Usually, fixed-speed wind turbines use squirrel cage induction generators (type A)and variable speed use the other three configurations of figure 2.2.

Figure 2.2: Wind turbine configurations [2]

Wind turbine designs can be also differentiated from the way that they perform the blade

control. There are three different types; the stall, the active stall and the pitch control. Thestall and the active stall control are normally associated with the fixed-speed wind turbineswhereas the pitch control is used in the variable speed wind turbines. With stall control



Chapter 2 7

wind turbines, which is the most simple and low-cost design, there is no control of the poweroutput. They are designed in such way that they optimize their production in a certain windspeed, after which due to the aerodynamic stall occurring at the blades the power output is

limited [1]. Even though stall controlled wind turbines were very popular during 1980s and1990s, nowadays is mainly used in small wind turbines that normally do not have blade pitchadjustment [1].

Active stall control is a more complex design than the stall control but maintains the powercharacteristics of a stall-regulated wind turbine [2]. Active stall wind turbines are also knownas "Danish concept" as it was mostly implemented by the danish wind turbine manufacturersuntil the early 2000 [11]. The operation of active stall wind turbines can be divided into twomodes. The first mode is for wind speeds higher than the rated where the pitch angle isadjusted so that the power output remains constant and equal to the rated. If the wind speedis higher than the rated speed, the pitch angle changes in the way that the angle of attack of the wind increases [21]. As angle of attack is defined the angle between the chord line and thewind direction [22]. The second mode of operation is for wind speeds less than the rated speed.In this case, the power of the wind turbine should be optimized which can be done through

the appropriate pitch angle. According to the aerodynamic design of the wind turbine, at agiven wind speed corresponds a pitch angle that the power output is the maximum.

As mentioned before, fixed-speed wind turbines are operating with a rotational speed thatis almost constant. Variable speed wind turbines can vary their rotational speed and adjustit according to the desirable power output. Variable speed wind turbines are equipped withsynchronous generators, doubly-fed induction generators or asynchronous generators. Forthose equipped with synchronous generators, the turbine is totally decoupled from the powersystem through converters. This is a common practice as wind fluctuations cause differentoperational speed and as a result the output voltage and the frequency will vary [1]. Usingconverters, the power quality produced from these wind turbines is improved. In the case of doubly fed induction generators, the stator of the generator is directly connected to the gridbut the rotor is connected to a converter. Through this converter the torque or the speed of the

machine can be controlled [23]. Normally, variable speed wind turbines are pitch controlled.In pitch controlled wind turbines, for wind speeds below rated the pitch angle of the blades isadjusted so that it maximizes the power output. For wind speed above rated, the pitch anglevaries so that the angle of attack is decreased and the power output is at its rated [23].

2.2 Technical regulations for the interconnection of Wind

Farms to the grid

The wind turbines used in Nysted Offshore Wind Farm are active stall fixed-speed wind tur-bines with induction generator. The term fixed-speed comes from the fact that the rotationalspeed of the wind turbine in normal operation is almost constant. This is due to the stator

of the generator connected to the power system while the rotor of the generator is coupledto the rotor of the wind turbine. As a result, the rotational speed of the wind turbine variesaccording to the variations in the slip of the induction generator. As those variations are small,not more than 2% , the speed is considered to be fixed [9]. As fixed-speed wind turbines aredesigned to operate more effectively in their rated wind speed, a different design could be ap-plied. In this design, known as multi-speed generator system, two constant speeds are chosen[1]. It is an intermediate design between the fixed and variable speed wind turbines and eventhough it does not have the advantages of variable speed operation it can increase the energyproduction for the fixed-speed wind turbines. The lower speed is used for low wind speedswhile the higher is used for medium and high wind speeds that the wind turbine can operateat its nominal power. Two different constant speeds of the generator can be achieved with theuse of a pole-changing induction generator, where two windings with different number of poles

are used. For the wind turbines used in Nysted, the low wind speed winding has 6 poles whilethe medium and high wind speed winding has 4 poles.For the operation of the induction generators, reactive power absorption is required. De-



8 2.2 Technical regulations for the interconnection of Wind Farms to the grid

pending on the level of the active power production, the required amount of reactive power willbe different. Higher power production means that the induction generator is operating withhigher slip and consequently the reactive power needed will be higher. If the wind turbines

are connected to the grid, the reactive power needed will be absorbed from the power system.However, in order to improve the power factor, reactive power compensation is a commonpractice. This can be achieved either with the use of capacitor banks for each wind turbine orwith reactive power compensation through STATCOMs or VSCs.

The advantage of the fixed-speed wind turbines is that they are simple, reliable and well-proven. On the contrary, the uncontrollable reactive power consumption and the limitedpower quality control are the main disadvantages of the specific configuration [2]. It is easilyunderstandable that the effects of the limited power control on the power system would beeven more severe in case of a large wind farm. To prevent power quality problems and also todetermine the behavior of the wind turbine during different faults in the power system, systemoperators have introduced severe restrictions in the grid codes [3][24][25].

The grid codes describe the active and reactive power regulation during steady state op-eration and set the limits on the impact of the wind farm on the voltage quality. In addition,

they describe the behavior of the wind turbines in case that a fault occurs in the grid. Underthis scope, the wind turbines are not allowed to disconnect from the network if the fault isof a certain duration and the voltage remain within specified limits. The operation duringand after a fault is known as fault-ride through. Especially in the danish grid code figure 2.3illustrates the voltage profile during symmetric three-phase fault. It is stated that if during afault the voltage is above a certain level ( 0.25 per unit), then the wind turbine must remainconnected and try to support the voltage [3]. After the fault, if the voltage remain abovethe curve in figure 2.3 the wind turbines must remain connected to the grid. As long as theyare connected, they should supply reactive power to the grid and support the voltage. If thewind turbine is equipped with power electronics, then the control of the reactive power willbe performed through them. Otherwise, the reactive power needed will be provided by thecapacitor banks.

Figure 2.3: Voltage profile after symmetric three-phase faults [3].

Nysted Offshore Wind Farm consists of fixed-speed wind turbines equipped with inductiongenerators. For the reactive power compensation, each wind turbine is connected with capac-itor banks that are able to provide full load compensation. The capacitor banks are separatedin steps and depending on the reactive power demand steps could connect or disconnect. Asmentioned before, in case of fault in the grid the wind turbines need to remain connected andprovide reactive power to the grid. To comply with this norm of the grid codes, the capacitor

banks should connect as soon as the fault is detected and provide the reactive power neededfrom the grid.The experiment that will be analyzed in Chapter 3 is the island operation of a radial of



Chapter 2 9

Nysted Offshore Wind Farm. Previous work has shown that when the wind farm is discon-nected from the grid the voltage will increase if the reactive power in the isolated grid is higherthan the necessary [20]. In [3] is described that the temporary over-voltages should be lim-

ited to 1.3 per unit of the output voltage and reduced to 1.2 per unit after 100 ms. In caseof over-compensation of the isolated grid, the decrease of the voltage occurs by disconnect-ing the capacitor banks that provide reactive power to the induction generators. In general,when islanding occurs the reactive power supply should disconnect as soon as possible to avoidover-voltages [2], [20].



10 2.2 Technical regulations for the interconnection of Wind Farms to the grid



Chapter 3

Measurement Analysis

3.1 Nysted Wind Farm

Nysted Offshore Wind Farm is consisted of 72 wind turbines with rated power 2,3 MW.The wind farm was commissioned in December 2003. The arrangement of the wind farm isillustrated in 3.1.

Figure 3.1: Nysted Offshore Wind Farm

The wind turbines are connected in 8 radials (from A to H). The radials are connected tothe platform where the park transformer is situated. Each radial has 9 wind turbines and thecable of the radial is of 36 kV. The park transformer is 3-winding (180/90/90 MVA;132/33/33kV). Each wind turbine has a transformer (2.5 MVA; 33/0.69 kV) and is connected to theradial through a switch on the Medium Voltage (MV).

3.2 Measurements

In 2007 field measurements were done in Nysted Offshore Wind Farm. Three GPS synchronisedmeasuring systems were developed and installed in the Wind Farm [4]. The measurement



12 3.3 Measurement analysis

system could monitor high frequency transients; the voltage and the current in three differentlocations in the network of the Wind Farm were recorded simultaneously with sampling rate2.5 MHz.

The three points in the network that the measuring system was located can be seen infigure 3.2 and they are in:

• The main transformer on the offshore platform, after the circuit breaker of the radial A

• The first wind turbine of the radial A, A01

• The last wind turbine of the radial A, A09

Figure 3.2: Locations of the measuring system [4]

For the field measurements several switching transients were generated and recorded. How-ever, only the disconnection of the radial feeder is investigated in the present work.

3.3 Measurement analysis

3.3.1 Preliminary analysis

The switching operation that will be simulated in PSCAD will be the disconnection of the linebreaker of the radial A. An overall view of the voltage and current measurements in the three

locations are depicted in figure 3.3 and 3.4 respectively.On each location, the measurement on each phase are plotted as "-a-", "-b" and "-c-" re-

spectively. Observing carefully figure 3.3 and figure 3.4 useful information can be extracted.In figure 3.4, the current in the transformer platform drops to zero at t=0.08s that denotesthat this is the time of the switching operation. In the same figure it can be seen that after theradial disconnection, the current in A01 and A09 does not drop to zero. This can be verified infigure 3.5. This implies that the wind turbines remain connected after the radial disconnectionand the capacitive current is fed into the isolated radial. In figure 3.5 the time of the switchingoperation can be also seen clearly as the current at the transformer platform drops to zero.

In figure 3.3 at t=0.275s there is a second switching operation that caused high transientover-voltages. The transients in the voltages and the currents in the three locations provokedby the second switching operation can be seen in figures 3.6 and 3.7 respectively. The origin

of the transients at this time is unknown and will be investigated later in the report.Apart from the voltage and current measurements, the active and reactive power productionof all the wind turbines of the radial are available and presented in figures 3.8 and 3.9. Even



Chapter 3 13

Figure 3.3: Voltage in the three measuring points. Upper plot : voltage at the platform. Middle plot : voltage at A01. Lower plot : voltage at A09

Figure 3.4: Current in the three measuring points. Upper plot : current at the platform. Middle plot : current at A01. Lower plot : current at A09




Figure 3.5: Current in the three measuring points from 60ms to 120ms. Upper

plot : current at the platform. Middle plot : current at A01. Lower

plot : current at A09

Figure 3.6: Voltage in the three measuring points from 250ms to 330ms. Upper

plot : voltage at the platform. Middle plot : voltage at A01. Lower

plot : voltage at A09

though they are prsented in 10 minutes average, it is clear enough that the wind turbineswere in operation before the radial disconnection. The active and reactive power of A01 windturbine, A09 wind turbine and the total power transmitted through the radial are presentedin Table 3.1.

As it is expected, after the radial disconnection there is no active power transmission tothe grid. However, as shown earlier, there is a small current at A01 and A09. This is due tothe fact that the wind turbines are still connected and feed current to the isolated radial [19].



Chapter 3 15

Figure 3.7: Current in the three measuring points from 250ms to 330ms. Upper

plot : current at the platform. Middle plot : current at A01. Lower

plot : current at A09

Table 3.1: Active and Reactive Power before disconnection of the radial

Nysted

P [MW] Q [MVAr]Total 17.19 1.86First 1.79 0.16Last 2.10 0.16

In figure 3.9 it should be also mentioned that A01 wind turbine has a different behavior fromthe rest. After the switching operation, some of the capacitor banks in A01 remain connectedas there is reactive power transmission. This is not the case with the other wind turbines of the radial.

The measurements were acquired in 2007 and there is no information whether the phasesequence of the voltages is associated with the phase sequence of the currents in each location.

To avoid any misinterpretation of the results this will be investigated. The active and reactivepower will be calculated from the measurements and then validated with the data presentedin figures 3.8, 3.9 and in table 3.1. The active and reactive power can be calculated throughequations 3.1, 3.2.

p(t) =3

i=1

ui(t) ∗ ii(t) (3.1)

q(t) = (u1(t) − u2(t)) ∗ i1(t) + (u2(t) − u1(t)) ∗ i2(t) + (u3(t) − u1(t)) ∗ i3(t) (3.2)

The calculation of the reactive power in 3.2 is only valid for fundamental components. In this




Figure 3.8: Active Power measurements, 10 min average [5]

Figure 3.9: Reactive Power Measurements, 10 min average [5]



Chapter 3 17

case, the harmonic contents due to the switching operation will lead to insufficient results forthe calculation of the instantaneous reactive power. For this reason, other ways to calculateboth active and reactive power are investigated.

3.3.2 Space Vectors

Space vectors have been used for the control of the induction machines and the converters butthey can also be used for the representation of the instantaneous values of the voltage and thecurrent [16], [26]. However, it was found out afterwards, that the space vector transformationshould be applied only in balanced power systems where the zero sequence component is zero[27]. It is unknown whether the system after the radial disconnection is balanced, so forthe time being only the steady state before the islanding will be considered as valid. Afterthe space vector transformation of the voltage and the active and the reactive power will becalculated to verify that it is in accordance with the measurements.

The equation used for the space vector transformation is:

xα(t) = 23 (xa(t) − 12 xb(t) − 12 xc(t)) (3.3)

xβ(t) =2

3(

√ 3

2xb(t) −

√ 3

2xc(t)) (3.4)

where xa, xb and xc are the three phases of the current and the voltage, while xα and xβ arethe space vectors. For the calculation of active and reactive power equation 3.5 and equation3.6 will be used.

p(t) =3

2(eα(t)iα(t) + eβ(t)iβ(t)) (3.5)

q(t) =

3

2 (−eβ(t)iα(t) + eα(t)iβ(t)) (3.6)

After implementing equations 3.3 and 3.5 in MATLAB the results are presented in figures3.10, 3.11 and 3.12 and are compared with the measurements presented in figures 3.8, 3.9 andin table 3.1. As mentioned earlier, the measurement presented in the figures are 10 minutesaveraged. The data presented in the table are before the radial disconnection but it is unknownexactly when they were recorded.

The results from the active power calculation are in accordance with both the 10 minutesaveraged data and the table 3.1. However, in the reactive power calculation some discrepanciescan be seen. According to table 3.1 only the reactive power absorbed at A09 seems to agreewith the measurements. In figure 3.11 it could be derived that after the radial disconnection,reactive power is supplied to the system. However, this changes at 200 ms and the reactive

power is oscillating around zero. In figure 3.12, A09 absorbs reactive power but after the 200ms it starts supplying reactive power to the grid. Nevertheless, as mentioned earlier, there aresome uncertainties regarding this method after the radial disconnection. A closer view of thecalculated active and reactive power before the disconnection are shown in figure 3.13.

As one can observe in figure 3.13, there are oscillations in active and reactive power atthe transformer platform. These oscillation are quite large and they might be present due tomeasurement or calculation errors. However, as the same oscillations are in figure 3.10 evenafter the radial disconnection leads to the hypothesis that this is mainly due to measurementerrors. In figure 3.14, if only the current at the transformer platform is plotted it can be seenthat after the disconnection the current is not zero as it should be.

Figure 3.14 implies that the oscillations in the power are due to a measurement error.Through MATLAB the component of the current after the disconnection will be subtracted

from the measurements. The results can be seen in figure 3.15. Again, some oscillation inphase C are still present but this time they are much smaller and around zero. By calculatingagain the space vectors for the transformer platform, the outcome from the calculation of the




Figure 3.10: Active and reactive power at the transformer platform calculated through space vector transformation

Figure 3.11: Active and reactive power at A01 calculated through space vector transformation



Chapter 3 19

Figure 3.12: Active and reactive power at A09 calculated through space vector transformation

Figure 3.13: Active and reactive power at all three locations before the radial dis-connection. Left upper plot : Active Power at the transformer plat-form. Right upper plot : Reactive Power at the transformer platform.Left middle plot : Active Power at A01. Right middle plot : Reac-tive Power at A01. Left lower plot : Active Power at A09. Right

lower plot : Reactive Power at A09.




Figure 3.14: Current at the transformer platform from 80ms to 120ms

power is presented in figure 3.16. Oscillations in the power are also present at A09 but thiscannot be fixed without risking the damage of the measurements as the wind turbine is stillproducing after the disconnection of the radial. In this case is more preferable not to interferein the measurement data. The corrected data of the measurements at the transformer platform

will be used throughout the report.



Chapter 3 21

Figure 3.15: Current at the transformer platform from 80ms to 120ms after the correction.

Figure 3.16: Current at the transformer platform from 80ms to 120ms




3.3.3 Transformation into sequence components

In the previous section, the transformation of the voltage and current measurements into spacevectors was presented. Due to uncertainties regarding the application of the method after

the radial disconnection, the transformation into symmetrical components will be used. Thetransformation into symmetrical components is a method that is being used for the analysis of unbalanced systems or faults [28], [29], [26]. In the present report, only the equations that de-scribe the transformation will be presented. Further information regarding the transformationcould be readily found in the literature [28], [29].

The zero, positive and negative sequence components are equal to:

V s = AV p (3.7)

where A is the matrix equal to:

A =

1 1 1

1 a

2

a1 a a2

(3.8)

anda = 1ej120 (3.9)

After implementing the transformation of the three-phase system into the sequence com-ponents in MATLAB, the results are depicted in figures 3.17 and 3.18 for the voltage and thecurrent in the main transformer respectively.

Figure 3.17: Sequence components of the voltage at the transformer platform. Up-

per plot : Zero sequence component. Middle plot : Positive sequence component. Lower plot : Negative sequence component.

In balanced power systems, the zero sequence voltage is zero [28]. Before the radial discon-nection at t=0.08s it could be considered as balanced as the zero sequence voltage in figure3.17 is almost zero. However, after the disconnection there is zero sequence component of the

voltage, so the system cannot be considered as balanced. This fact enhances the decision toconsider trustful the results from the space vector transformation only before the disconnectionof the radial. Furthermore, as shown in figure 3.18 the zero-sequence component of the current



Chapter 3 23

Figure 3.18: Sequence components of the current at the transformer platform. Up-

per plot : Zero sequence component. Middle plot : Positive sequence component. Lower plot : Negative sequence component

at the transformer platform is not exactly zero. It is reminded that the wind farm transformeris ∆-connected and the current should have no zero-sequence component [28]. The existingzero component could be either due to measurement errors or due to calculation errors duringthe transformation to the sequence components.

In [4] the measuring system is described. The measuring system for the currents is aRogowski-coil sensor from Powertek. The specifications can be found in [4] and in [30]. In [30]the datasheet for the CWT3 used can be found. According to the performance characteristicsthe system is capable of measuring currents above 300 mA and up to 600 A. This means thatthe current probes are not designed to measure the very low current as the zero sequencecomponent should be. The sequence components of the voltage and the current in A01 andA09 can be found in the Appendix A. It would be interesting though to discuss the positivesequence voltage at A01, presented in 3.19.

According to the shape of the waveform and the switching operations performed, the datacould be separated in 5 stages for the analysis. Stage A is the steady state before the islanding

of the wind turbines from 0 ms to 80 ms. Stage B is during the radial disconnection, whenthe first transients occur and lasts from 80 ms to 100 ms. Stage C is from 100 ms to 275 msduring which the wind turbines of the radial are into island operation. It can be seen that thevoltage increase until t=200 ms and then it starts decreasing. When wind turbines are isolatedfrom the grid they can produce over-voltages [31]. Among other, the over-voltages could occurdue to reactive overcompensation in the isolated system [20]. The fact that the magnitude of the voltage starts decreasing after 200ms could be an indication that the capacitor banks aredisconnected. This will lead the induction generators to be excited from the radial and absorbreactive power that eventually leads to the reduction of the voltage magnitude [15]. Stage D isbetween 275 ms and 320 ms when the high transient over-voltages occur. This is possibly dueto capacitor banks switching. A similar study in India has shown that when capacitor banksconnect similar transients with the transients observed in the current project are produced

[20]. The main difference is that in the current study the connection of the capacitors occurduring island operation while in [20] the wind farm is connected to a weak grid. Stage E isfrom 320 ms until 500 ms when the voltage magnitude decreases.




Figure 3.19: Positive sequence voltage at A01.

In figure 3.20 the positive sequence voltage at the three measuring points is depicted. Itcan be seen that the highest over-voltages appear in the transformer platform, then in A09and the smallest magnitude is at A01. It should be mentioned though that also the level of the voltage magnitude is the same at the steady state (V platform > V A09 > V A01).

For the calculation of the power delivered to the grid from the sequence components, equa-tion (3.10) will be used [28]:

S p = 3 ∗ (V 0 ∗ I ∗0 + V 1 ∗ I ∗1 + V 2 ∗ I ∗2 ) (3.10)

After implementing equation (3.10) in MATLAB the results are presented in figures 3.21,3.22 and 3.23. The power calculated from the sequence components is presented with the powercalculated from the space vector transformation in the same figure to ease the comparison.It can be seen that there is very good agreement between the results from the two methods.This agreement could lead to the conclusion that the system remain balanced even after thedisconnection of the radial. Supposing that the current probe could measure very low current,

this would be possible to verify through the zero sequence component of the current thatshould be zero in case of balanced systems.

Observing more carefully figure 3.23 one could see that after the islanding of the radial,A09 wind turbine is feeding active power to the cable. However, this is not the case withA01 wind turbine as after the disconnection it absorbs active power. This can be also seenin figure 3.24, where the active power absorbed varies from 0.1 MW to 0.3 MW. This can beexplained based on the power production of the wind turbines. As A09 is producing morepower (according to the calculations around 2.2 MW instead of 1.9 MW of A01) it will rotatefaster. After the isolation of the system, as the active power will flow into the isolated radial.As a result, the wind turbines that rotate faster will be operating as generators by feedingpower to the system while the wind turbines that rotate slower will be operating like motorsand will be absorbing power [19].



Chapter 3 25

Figure 3.20: Positive sequence voltage at the three locations.

Figure 3.21: Power at the transformer platform calculated through sequence com-ponents and space vector transformation. Upper plot : Active power

production. Lower plot : Reactive power consumption





Chapter 3 27

Figure 3.24: Power at A01 calculated through sequence components and space

vector transformation between 80 ms and 200 ms.

3.3.4 FFT analysis

An alternative approach for investigating the behavior of the system is the frequency analysisof the measurements. Variations on the voltage or current frequency are an important issueof the Power Quality aspect. Power quality is a complicated and lately deeply investigatedissue. Even the definition of the power quality could be different in various sources. In [32],the definition of power quality is based on the consumers and as a power quality problem isdefined "Any power problem manifested in voltage, current or frequency deviation that resultsin failure or misoperation of customer equipment". In [33], according to the International

Electrotechnical Commission (IEC), power quality is defined as "Characteristics of the elec-tricity at a given point on an electrical system, evaluated against a set of reference technicalparameters". In the latter, it can be seen that there is no direct connection to the consumer.However, regardless the definition, power quality is an important issue. Wind turbines have aserious impact on the power quality of a power system either due to wind fluctuations or dueto the components that they are consisted of.

As it has been shown earlier in the Chapter, the island operation of the wind turbines leadsto temporary and transient over-voltages that could harm the equipment. After the secondswitching operation, at 275 ms, the voltage waveform is distorted due to harmonic contents.In similar cases, where harmonics are present, a spectrum analysis is performed to identifythe harmonic components [34], [35]. The power spectrum analysis is usually performed withthe Fast Fourier Transformation (FFT). Depending on the event that disturbs the system,the frequency response will vary as it depends on the resonance of the system. In [34], it is

presented that during a capacitor bank energization the presence or not of another capacitorwill have a different impact on the spectrum of the transients. The difference on the spectrumcan be justified from the different resonances of the system. The resonant frequency of asystem can be determined by (3.11):

f =1

2 ∗ π ∗√

LC (3.11)

It is easily understandable that in case of different capacitors, the oscillatory circuit thatis formed between the capacitor connected and the capacitances and inductances already con-nected will have a different eigenfrequency. As a result, through the harmonic analysis of the

measurements, the resonances of the system could be estimated and be used for the validationof the model.In the beginning, a general perspective of the power spectrum should be investigated.




Following this, the spectrogram of the current at A01 is depicted in figure 3.25. The reasonthat A01 is chosen for the frequency analysis should be looked into figure 3.7. It can be seenthat the effect of the second switching operation at 275 ms is much more severe in A01 than in

A09. This could imply that the switching operation occurs in A01 or in a wind turbine close toA01. As it is expected, in figure 3.25 the dominating frequency before the radial disconnectionis 50 Hz. At t=80 ms and at t=275 ms the power spectrum is different. It can be observedthat instead of only the 50 Hz other frequencies are present as well. Especially at the secondswitching operation, the harmonics of the frequency with significant amplitude are close to1000 Hz.

Figure 3.25: Spectrogram of the current at A01 wind turbine from 0 ms to 500 ms.

Based on the difference in the current waveform in A01 and A09, an FFT analysis will beperformed for the two measuring points. The results can be seen in figure 3.26. It can be seenthat there are significant differences as in the current at A09 there are almost no harmonics.On the contrary, in the current at A01, the 5th harmonic is the one with the highest amplitudeafter the fundamental. The difference between the two spectra is most likely due to the factthat the switching operation at 275 ms occurs at or closer to A01 rather than A09.

Following the segmentation introduced in 3.19, an FFT analysis is performed on each of the five stages at the current in A01 wind turbine. The results of the analysis can be found infigure 3.27. In stages A, C and E the dominating frequency is 50 Hz as it is expected as thereare no severe disturbance during those stages that could give rise to higher harmonics. Duringthe radial disconnection (stage B) there is a peak around 900 Hz, while in stage D there aretwo dominating frequencies, at 250 Hz and at 800 Hz. The difference in the results in figures3.26 and 3.27 can be explained from the different content of the analyzed data; in the former,the whole dataset is analyzed, while in the latter each stage is analyzed independently.



Chapter 3 29

Figure 3.26: FFT analysis on phase B of the measured current at A01 and A09 from 0 ms to 500 ms.

Figure 3.27: FFT analysis on phase B of the measured current at A01. The signal is divided in five stages according to figure 3.19.



30 3.4 Capacitor banks

3.4 Capacitor banks

Based on the analysis performed earlier and the research in the literature, [20] and [34], it is

derived that the switching operation that provokes the high transient over-voltages at 275 msis due to capacitor energization. However, the reactive power calculated from the sequencecomponents show that before the radial disconnection A01 and A09 were almost fully compen-sated. From the total reactive power it could be also assumed that the A02-A08 were almostfully compensated. This means that after the radial disconnection, the capacitor banks at A01should disconnect and then connect again at 275 ms. As the capacitor used in the nine windturbines are the same, the same behavior would be expected.

From the information available, the Power Factor Correction (PFC) system that the windturbines are equipped with, is based on the Elspec Equalizer/Activar components. In theuser’s manual of the Equalizer it is mentioned that during the power factor control mode,the voltage control is necessary for the limitation of the grid voltage into safe limits [6]. Thevoltage control mode can be concisely presented in figure 3.28. The voltage control mode isbased on voltage measurements acquired from the grid. While the voltage remains between

the limits 95%-105% of its nominal value, the control of the capacitor banks is in power factorcontrol mode. In this mode, the steps of the capacitor banks are connecting or disconnectingin the basis of correcting the power factor of the wind turbines. More specifically, if the windspeed increases and more reactive power is needed, then the capacitor banks will connect.

In the voltage control mode, If the voltage exceeds the 95% or the 105% of its nominalvalue, then the control enters in voltage control mode. This means that the control will startconnecting or disconnecting capacitor steps respectively to control the voltage. If the voltageexceeds a critical point, either upper (120%) or lower (60%), the control will act immediatelyby disconnecting or connecting all the capacitor. When the voltage is into acceptable limitsagain, the control will start connecting or disconnecting capacitors in steps; one step everycycle.

Figure 3.28: Voltage control set points [6].

Figure 3.28 shows an indication that the assumptions regarding the second switching op-

eration could be possible. Even though is not clearly mentioned in the User’s manual whereexactly is the voltage measured and whether it is the RMS, the magnitude or even the instan-taneous value of the voltage, it shows that the immediate disconnection or connection of the



Chapter 3 31

capacitor banks could occur. However, there are some inquiries regarding the time betweenthe measurement of the voltage and the switching operations as well as whether the sameoperations occur simultaneously at all the nine wind turbines of the radial.

With the information available, both the measurements and the capacitor User’s manual, itcould be derived that after the radial disconnection all the capacitor banks disconnect but onlythe capacitor banks in A01 connect again. The latter is based on the difference in the currentmeasurements in A01 and A09. After the development and the validation of the model of thefixed-speed wind turbine, a sensitivity analysis will be performed to investigate the impact of different switching operations on the voltage and the current at the three measuring locations.

3.5 Summary

In the present Chapter the analysis of the available measurements is performed in order tounderstand the behavior of the wind turbine after the disconnection of the radial. It is remindedthat only the switching operation at 80 ms is known. For the verification of the voltage and

current sequence the calculation of the active and reactive power was needed. The measurementdata were transformed into space vectors and their symmetrical components and the activeand reactive power was calculated. The results of the calculations show a very good agreementfor both the methods used. In the results of the reactive power there was a difference betweenthe reactive power at the transformer platform between the calculation from the voltage andcurrent measurements and the measurements presented in table 3.1. As the measurementsgiven are from 10 minuted averaged values they will be used only as an indication and thegoal would be the simulation results to be close to the calculated results from the active andreactive power measurements.

To facilitate the procedure of understanding the behavior of the system, the data werediscretized according to figure 3.19. It was attempted to understand and interpret the behaviorof the wind turbine separately in each stage. It was assumed that the high transient over-voltages observed at 275 ms are caused by one or several switching operations. Based onliterature research, it seems that the switching operation is the capacitor banks connectingat A01. The research on the manual of the capacitor banks that are used as power factorcompensators at Nysted has shown that the connection of the capacitor banks could be possible.

Finally, an alternative approach of the analysis of the measurements was presented. TheFFT analysis has been used previously in the literature in capacitor switching studies. Differ-ent amount of capacitor banks connecting or being already connected could have a differentresonant frequency. With the FFT analysis the harmonic frequencies were estimated and theycould be used in the validation process later on the report.



32 3.5 Summary



Chapter 4

Nysted Offshore Wind FarmModeling

In this chapter the model of the Nysted Offshore Wind Farm developed in PSCAD will bedescribed. The present work is a continuation of [5], where the switching transients in the windfarm where modeled. Scope of the thesis is the development of the model of the fixed-speedwind turbine that is used in Nysted wind farm. Taking this into account, the transmissionand the collection grid is based on the model developed and validated in [5], [36].

The simulation tool that is used is PSCAD. PSCAD (Power Systems CAD) is a powerfulgraphical user interface to EMTDC solution engine. EMTDC stands for ElectromagneticTransients including DC and solves differential equations for electromagnetic systems in the

time domain [37].PSCAD is used in both academical and professional level for planning, design, operate and

advanced research of power systems. Among other, studies conducted using PSCAD are [37]:

• Power system studies consisting of rotating machines, turbines, transformers, transmis-sion lines, cables, loads etc.

• Over-voltages because of a breaker operation

• Studies of the power system response after a fault

• Control system design of FACTS and HVDC

PSCAD offers many models that can be found in the library provided with the program.The models included are from the simplest and most common like resistors, capacitors and

inductors to more complex AC and DC machines, wind turbines, inertial models and HVDCcontrollers. For the development of the model of the fixed-speed wind turbine in PSCAD,some of the components used were models provided in the tool (i.e. induction generator) whileothers were developed through the generic control systems (i.e. shaft model).

A generic model of a fixed-speed wind turbine should be consisted of the following parts[9], [10]:

• The aerodynamics model

• The shaft model

• The induction generator model

• The blade-angle control

• The capacitor banks

A generic block-diagram of the fixed-speed wind turbine is depicted in figure 4.1. Eachblock of the diagram represents a component of the wind turbine.





Chapter 4 35

sequence leakage reactance and the no-load and copper losses [36]. Regarding the wind turbinetransformer it was also modeled as a simple transformer model but in this case the saturationcharacteristics were included [36]. In [19], it can be seen that including the saturation effect

in the transformer and generator models would have a different impact on the current duringthe transients. As the park transformer is not part of the studied system after the radialdisconnection, the saturation effect was not included in the model. All the data regarding thetransformers of the wind farms can be found in [5].

Figure 4.2: Simple transformer equivalent circuit with the secondary winding re-ferred to the primary.

4.2 Wind Turbine Modeling

4.2.1 Aerodynamics

The power delivered through the drive train of the wind turbine to the generator depends onthe aerodynamic properties of the rotor. The design of the rotor has a crucial effect on theoverall efficiency of the energy conversion in the wind turbine as it determines the proportionof wind energy that will be converted into mechanical energy. However, high efficiency shouldbe also combined with the limitation as much as possible of the dynamic loads on the rotorthat affect the lifetime of the wind turbine.

The available power from the wind power is represented by the well-known equation (4.1):

P aero =

1

2 ∗ (ρ ∗ A ∗ C p(λ, β) ∗ V 3

w) (4.1)

where

ρ is the air density in kg/m2,A the area swept by the rotor m2,C p the power coefficient,λ equal to λ = R∗ω

V w,

β the pitch angle,V w the wind speed in m/s.

The power coefficient denotes the wind power at the wind turbine that can be extractedfrom the available wind power and depends on the pitch angle and the tip speed ratio [22].



36 4.2 Wind Turbine Modeling

As mentioned before in chapter 2, in case of fixed-speed operation, the rotor speed ω is fixedto the electric speed of the power grid and under normal operation it only varies accordingto the induction generator slip variations. This implies that the fixed-speed wind turbine will

operate at maximum efficiency at the wind speed that the optimal C p occurs. The active stallcontrol will be activated for wind speeds above rated to keep the power equal to the rated andfor wind speeds below rated to maximize the power output [21].

The switching transients that occur after the disconnection of the radial feeder last for afew milliseconds. Consequently, the wind speed could be considered as steady throughout thesimulations. In addition, for the initial simulations of the model, the power coefficient willbe considered as steady and that there is no control of the pitch angle. The model of theaerodynamics of the rotor implemented in PSCAD can be seen in figure 4.3.

Figure 4.3: Model of the aerodynamics of the wind turbine rotor.

The design of the rotor has a crucial effect on the efficiency of the energy conversion.The parameter that depends on the rotor design is the power coefficient that correspondsuniquely to a certain tip speed ratio and a pitch angle. During the control of the wind turbinethe relationship between Cp and the tip speed ratio for certain pitch angle plays the mostimportant role in the power output of the wind turbine. Due to lack of information regardingthe rotor aerodynamics, some assumptions need to be made. Initially, as the wind speed isassumed to be constant for the 500 ms of the measurements time, the power coefficient will beassumed constant as well.

The disconnection of the wind turbines while they are under operation will lead to theincrease of their rotational speed. As soon as it is detected, the blade-angle control will startpitching the blades to regulate the speed. Due to the total loss of the load demand power, the

speed will start increasing quickly like there was a fault in the power system. However, duringa fault in the system with a duration of 100 or 150 ms, the control might not be able to operatefast enough. This denotes that the wind turbines may operate as passive stall wind turbines[38], [39]. The total duration of the measurements is 500 ms with the islanding occurring at80 ms. The short duration of the operation along with the lack of the data regarding the timeconstants of the active stall control have led to the assumption that during the simulation thewind turbines will operate as passive stall as mentioned in [38] and [39]. The representationof the blade-angle control will be with the power coefficient C p that will remain constant forthe entire simulation. It should be noted that in case that the speed of the wind turbinesexceeds certain limits they will disconnect. However, the limits are not known and it will beconsidered that they remain connected throughout the simulation.

From the measurements available, it can be seen that the power output of A01 is around

1.8 MW, while the power output of A09 is around 2.2 MW. These values are close to the ratedpower, so it will be assumed that the wind speed is close to the rated wind speed. In [21] therated wind speed of an active stall fixed-speed wind turbine with 2 MW rated power is 11.8



Chapter 4 37

m/sec. As the wind turbine is similar it will be considered that the rated wind speed is between12 − 13 m/sec. It is assumed that the rated speed is at 13 m/sec as it is an offshore windfarm and the average wind speed is higher than onshore. For A09 wind turbine, knowing wind

speed, the C p can be easily found so that the power output is equal to the power calculatedfrom the measurements. It is considered that the wind speed is the same across the radial, sothe C p will be less for A01 so that it can produce power equal to the calculated in Chapter 3.

The power production of the other wind turbines of the radial can be found from the10 minutes averaged values in figure 3.8. However, two specifications need to be taken intoconsideration; the total power output of the radial should be equal to the total power calculatedin Chapter 3 and the wind speed is the same in all the wind turbines. Once these specificationsare fulfilled, the different level of production between the wind turbines can be determinedthrough different power coefficients.

In figure 4.3, the wind speed is provided to the system through the Wind Source model.From the available options of the model only the mean wind speed at the reference height isset equal to 13 m/s as explained earlier. The wind power that can be used from the windturbine as it is described by equation (4.1) is labeled as Pw . The rotor diameter is assumed to

be around 80 m, based on [21], whereas for the air density ρ the standard value of 1.225 kg/m2was used as there are no information regarding the air temperature and pressure. As the inputfor the mechanical model and the induction generator will be the aerodynamic torque, thetransformation from the aerodynamic power needs to be performed. After transforming theaerodynamic power into the per unit system, then the aerodynamic torque is calculated fromequation(4.2):

T aero =P aero

ωWTR

(4.2)

where

ωWTR is the wind rotor speed in per unit,

4.2.2 Shaft system

The wind turbine consists of several physical components such as the blades, the low-speedshaft, the gearbox, the high-speed shaft and the generator. Previous investigations [9] haveshown that in case of transient stability or fault studies the drive train of the wind turbineshould not be represented as lumped mass model but as a two-mass model. This is due to

the fact that the shaft system is not considered absolutely stiff. The shaft is subjected to themechanical torque applied from the wind turbine rotor and the electrical torque due to theelectromagnetic field of the generator. As a result, the shaft will be subjected to torsion whichwill vary when the electrical or the mechanical torque changes. When the wind turbine facesa sudden event such as a wind speed change or a grid frequency transient, oscillations on theshaft torsion will occur.

In [13] both mechanical models were used, lumped and two-mass model and the results onthe simulations were discussed. It was concluded that for the representation of the electrome-chanical oscillations the two-mass model is essential. Therefore the two-mass model will beincluded in the wind turbine model; the first mass represents the low-speed shaft that includesthe hub and the blades of the wind turbine rotor and the high-speed shaft that represents thegenerator rotor. The moments of inertia of the low and high speed shaft along with the shaft

stiffness should be provided by the manufacturer. However, only the inertia of the generatorwas provided.The equation applied to describe the shaft system is based on the equation of motion [40]:




J ∗ dωm

dt= T m − T e (4.3)

where

T m is the mechanical torque in N ∗ m,T e is the electromagnetic torque in N ∗ m,ωm is the angular velocity of the rotor in mech.rad/s andJ is the moment of inertia in kg ∗ m2

When there is an unbalance between the torques, the machine would either accelerate ordecelerate. The gradient of the change on the speed depends on the moment of inertia. Whenthe shaft is represented as a lumped model, then the moment of inertia in equation (4.3)

stands for both the turbine and generator moment of inertia. The T m is the torque of thewind power that acts on the wind turbine and T e the electrical torque of the generator. Forthe two mass model representation of the shaft system, equation (4.3) will be used to describethe motion in both masses. The state equations that describe the model can be found in [9]and are presented in equations (4.4)-(4.6):

2 ∗ H WTR ∗ dωWTR

dt= T WTR − T WTG − DWTG ∗ ωWTR (4.4)

2 ∗ H WTG ∗ dωWTG

dt= T WTG − T E − DWTG ∗ ωWTG (4.5)

dθs

dt= ω0 ∗ (ωWTR − ωWTG) (4.6)

where H WTR and H WTG are the inertia constant of the wind turbine rotor and generatorrespectively and they can be calculated through equations (4.7) and (4.8), [9]:

H WTR = 0.5 ∗ J WTR ∗ ω0

S BASE ∗ N 2ME ∗ N 2EE

(4.7)

H WTG = 0.5 ∗ J WTG ∗ ω0

S BASE

∗N 2EE

(4.8)

where

S BASE is the base power of the wind turbine in MV A,N ME is the gear box ratio,N EE is the the generator pole-pairs andω0 is the base system speed in rad/s

In equations (4.4)-(4.6), the parameters of the wind turbine rotor are denoted with WTR whilethe parameters of the generator with WTG. All the values of the parameters in equations (4.4)-(4.8) are in the per unit system apart from the base power S base and the base speed ω0 that

is equal to the base speed of the power grid:

ω0 = 2 ∗ π ∗ f = 314rad/s (4.9)



Chapter 4 39

The mechanical torque applied to the generator can be calculated from equation (4.10),

[9]: T WTG = K s ∗ θs − Ds ∗ (ωWTG − ωWTR) (4.10)

DWTR, DWTG and Ds are the damping coefficient of the rotor, generator and shaft respectively.K s is the shaft stiffness and θs is the shaft torsion. It should be noted here that there is noinformation available regarding the values of DWTR, DWTG, Ds and K s. Their values alongwith the value of the inertia of the wind turbine rotor was based on the typical values found inthe literature [9], [11]. However, the range of the typical values was broad so many simulationshad to be performed to find the values that were representing as close as possible the measuredvoltage and currents. Later on, in Chapter 6 a sensitivity analysis will be performed for thevalues of the inertia constant of the wind turbine rotor and the shaft stiffness. It will beshown that the frequency and the magnitude of the current and the voltage after the radial

disconnection are affected by changes in the values of the two parameters.The implementation of the two-mass model in PSCAD based on equations (4.4), (4.5),

(4.6) and (4.10) can be seen in figure 4.4.

Figure 4.4: Two-mass model of the shaft implemented in PSCAD.

The aerodynamic torque is used as the input to the model and the output is the mechanicaltorque applied to the generator rotor. The model presented actually comprises only one massthat represents the low speed shaft of the wind turbine, the wind turbine rotor. The generator

rotor, that lies in the high speed side, is included in the induction generator model.

4.2.3 Induction Generator

Previous studies have shown that the appropriate model for electromagnetic transient studiesis the fifth-order model [9], [13]. For the representation of the induction generator of the windturbine, the already existing model in PSCAD will be used. The model can be seen in figure4.5.

The state equations that describe the fifth-order model of the induction machine trans-formed in dq components can be found in [40], [41] and are presented in equations (4.11)-(4.14):

uDs = Rs

∗iDs +

dλDs

dt −ωe

∗λQs (4.11)

uQs = Rs ∗ iQs +dλQs

dt− ωe ∗ λDs (4.12)




Figure 4.5: Induction generator model implemented in PSCAD.

uDr = Rr ∗ iDr +dλDr

dt− λQr ∗

dθr

dt(4.13)

uQr = Rr ∗ iQr +dλQr

dt+ λDr ∗

dθr

dt(4.14)

The subindices s and r stand for the stator and rotor quantities respectively. The u and i denote the voltage and the current respectively in the stator and the rotor while the parameterλ represents the flux linkages. The parameter θr is the integral over time of the electromagneticfield speed in the rotor [9].

The expressions for the flux linkages are [40]:

λDs = X s ∗ iDs + X m ∗ iDr (4.15)

λQs = X s ∗ iQs + X m ∗ iQr (4.16)

λDr = X r ∗ iDr + X m ∗ iDs (4.17)

λQr = X r ∗ iQr + X m ∗ iQs (4.18)

The electrical parameters of the machine are the stator resistance and reactance, denotedby Rs and X s, the rotor resistance and reactance, denoted by Rr and X r, and the mutual

reactance denoted by X m. All the parameters in equations (4.11)-(4.18) are in the per unitsystem apart from the ωe, the electrical system speed given by equation (4.9) that is in el.rad/s and the rotor angle, θr, that is in el. rad.

The model described above is the fifth-order model of the induction machine. However,in stability studies the third-order model is used as well. The difference between the twomodels is that in the latter the stator flux linkage transients ( dλDs

dtand

dλQsdt

) are neglected.As the electromagnetic transients should be as accurate as possible for the present study, thefifth-order model is chosen.

There are two sets of data that could be used in PSCAD to model the induction generator.The first set of data is the representation of the equivalent circuit of the generator whilstthe second set comprises the parameters of the generator at the starting and at the full-loadoperation. The second set of data is defined among other by the slip of the generator at full

load, the power factor at rated load, the number of poles and the starting torque. From theinformation available both sets could be used. It needs to be mentioned that the squirrel-cageinduction machine in PSCAD is modeled as a double squirrel-cage machine to account for



Chapter 4 41

the deep bar effect of the rotor cage. A double squirrel-cage induction generator providesthe desirable characteristics to obtain high efficiency at full-load operation, that is low rotorresistance, and at the same time keep the starting current low by having high rotor resistance

at the starting of the machine [40]. However, the wind turbines are equipped with singlesquirrel-cage induction generators. The equivalent circuits of a double and a single squirrel-cage machine can be seen in figures 4.6 and 4.7 respectively.

Figure 4.6: Equivalent circuit of a double squirrel-cage induction generator.

Figure 4.7: Equivalent circuit of a single squirrel-cage induction generator.

In [40] it is stated that a double-cage rotor may be represented by an equivalent single-cagerotor. The equations that describe this representation are [40]:

Rr(s) = Rr0 ∗m2 + m ∗ s2 ∗ R1

Rr0

m2 + s2(4.19)

X r(s) = X 1 +Rr0 ∗ m∗R1

R2

m2 + s2(4.20)

where

Rr0 =R1 ∗ R2

R1 + R2

(4.21)

m =R1 + R2

X 2(4.22)




However, as it is shown in equations (4.19) and (4.20) both the resistance and the reactancewill be depended on the slip of the generator. As this could have an impact on the torque-speed characteristic of the machine it was decided to disable the effect of the second cage by

applying high values on the second-cage resistance and reactance, following the instructionsfrom PSCAD support. In addition, as the data for the representation of the equivalent circuitare available, the dataset that for the representation of the generator includes the equivalentcircuit will be used.

The machine can be either torque or speed control. As the wind speed is assumed to besteady for the simulation time, the machine can be controlled in the torque mode. This iscommon practice in simulations of wind farms that last several seconds as it simulates moreaccurately changes in speed in case of voltage dips. In PSCAD manual help is mentioned thatgenerators in torque control mode should be started in speed control mode to avoid the highstarting transients and then be switched to torque control. The control mode of the inductiongenerator is defined by the control signal S2M in figure 4.5. As long as the the generatorcontrol is in speed mode, the input torque is at 1 pu. After switching to the torque controlmode, the torque input is the torque calculated from the two-mass model described earlier.

It should be noted as well that once the induction machine model is used as a generator thetorque input should be negative.

4.2.4 Capacitor banks

The capacitor banks are also included in the model of the wind turbine. Each wind turbineis equipped with capacitor banks of 1356 kVAr nominal power. The capacitors are designedfor reactive power compensation of a 2.3 MW wind turbine as there is no other mean forcompensation. The behavior of the capacitor banks was described earlier; here the modelof the capacitor will be presented. In PSCAD there are two capacitor models available; thecapacitor and the three-phase capacitive load. The difference between the two models is thatin the latter the inductance value is calculated based on the data entered by the user, while

in the former it is not included. The model chosen is the capacitive load and it can be seen infigure 4.8.

Figure 4.8: Model used for the representation of the capacitor banks included inthe wind turbine.

As it was explained earlier, the behavior of the capacitor banks has a great influence on thesystem when it is in island operation. From the measurement analysis it was derived that thetransient over-voltages at 275 ms are due to the connection of capacitors in A01. Althoughthe connection is in accordance with the information regarding the voltage control mode of the capacitors, the different behavior of A01 and A09 as well as the unknown behavior of theintermediate wind turbines lead to the simplification of the control of the capacitor banks.Instead of the control based on the over-voltages and dip voltages, the time that they willconnect and disconnect is predefined. The time of the switching operations is based on themeasurement analysis and tests performed during the simulations.

The capacitor banks are disconnecting due to their voltage control when the upper criticalvoltage limit is exceeded. It is assumed that in this case the capacitor banks in each wind tur-

bine will be disconnected at the pre-defined moment as one big step. However, the connectionof the capacitor banks at A01, once the voltage has not exceeded the grid fault threshold, willoccur in steps. The capacitor banks are connecting in steps of 90 kVAr, so at the moment of



Chapter 4 43

the connection of the capacitors at A01, 15 steps of 90 kVAr will switch in. In Chapter 6 of the report, the sensitivity analysis performed would comprise different switching operationsregarding the capacitor banks of the wind turbines. When the wind turbine model is validated,

the voltage control of the capacitor banks will be implemented and added to the model.

4.3 Summary

The development of the model has been based on the recommendations introduced in [9] and[11]. The nature of the experiment along with the intention to develop a model as simple aspossible led to the assumption that during the simulation of the experiment, the blade-anglecontrol of the wind turbine will not operate. As the wind speed is assumed to remain constantduring the experiment, the power coefficient of the wind turbine remains constant as well. Asa result, throughout the simulation the aerodynamic torque is constant.

The two-mass model is chosen for the representation of the mechanical part of the windturbines. According to [9], there is a strong coupling between the generator rotor speed and

the active and reactive power production that must be represented in power system stabilitystudies. In [13] the implementation of the mechanical model as one mass has shown thatthe oscillations in rotor speed cannot be represented accurately. In the present model, thegeneral considerations regarding the representation of the shaft system are taking into account.Therefore, it is considered that the mechanical representation of the wind turbine as onelumped mass will not be accurate enough.

Regarding the induction generator, in stability studies two models are commonly used; thefifth-order and the third-order mode. The difference between the two models was explained andas the study is related to the electromagnetic transients a model of the generator as detailedas possible should be used. Therefore, the available model from PSCAD has been chose. In[14] was shown that the PSCAD model has similar results with the fifth-order model of themachine used in tools that simulate stability studies.

Finally, the capacitor bank is modeled as three-phase capacitive loads, in which its in-ductance value is also calculated based on the capacitance. Until the model is validated thecapacitor bank control will be based on time and not the voltage control described earlier.



44 4.3 Summary



Chapter 5

Validation of the model

The model described in Chapter 4 will be applied in PSCAD and will be validated withthe measurements analyzed in Chapter 3. As it was mentioned in Chapter 3, there are twoswitching operations during the time of the measurements. The first switching operation is thedisconnection of radial A while the second switching operation seems to be capacitor banks thatconnect to the isolated system, based on [20]. As explained, it is assumed that it is the capacitorbanks at A01 that switch in. From the reactive power calculations and measurements A01 isalmost fully compensated, which means that the capacitor banks will have to be switched outfirst. As both the time of the disconnection and whether they disconnect in one or in severalsteps are unknown, new assumptions will be made. Based on that, the disconnection of thecapacitor banks will be assumed for all the 9 wind turbines of the radial but the connection

only for A01. The available measurements are only from 2 wind turbines and the results canbe only verified based on those measurements. The switching operations that take place inthe simulation are presented in Table 5.1.

Table 5.1: Switching operations in the simulation

Time [ms] Switching operation80 Radial disconnection

226 Disconnection of the capacitor banks at A06246 Disconnection of the capacitor banks at A03, A08

256 Disconnection of the capacitor banks at A04266 Disconnection of the capacitor banks at A01,

A02, A05, A07 and A09275 Connection of the capacitor banks at A01.

The connection occurs in 14 steps of 90 kVAr300 Disconnection of the capacitor banks at A01

For the validation of the model the results of the simulation will be compared with themeasurements. Initially, the instantaneous voltages and currents from the simulation will beused for the comparison. Further on, the simulation results will be transformed to the sequence

components. To ensure transparency, the transformation will be done with the same code as inChapter 3. After the transformation, the results will be compared with the results presentedin Chapter 3 and finally a similar FFT analysis will be performed.



46 5.1 Comparison of the instantaneous values of currents and voltages

5.1 Comparison of the instantaneous values of currents

and voltages

In figures 5.1 - 5.3 , the comparison of the instantaneous voltage at the transformer platformcan be seen.

In 5.1, the results of the whole simulation are depicted while in figures 5.2 and 5.3 thereis a closer view on the time of the switching operations. In figure 5.2, there is a discrepancyas the transients observed in the voltage measurements after the radial disconnection are notreproduced in the simulations. On the contrary, in figure 5.3, the transients after the switchof the capacitor are reproduced. The switching occurs at the same point of the waveform andthe impact on the magnitude of the transient over-voltages is comparable in phases A and C.However, the harmonics created after the operation do not have the same duration as in themeasurements. This possibly could happen because the capacitor banks in A01 do not switchin simultaneously but in steps or because the same switching operation could occur in otherwind turbines as well.

From the comparison shown in figure 5.1 is very interesting to point out the difference inthe frequency of the signals. Before the radial disconnection, as it is expected, the frequencyof the system is the same. Until the second switching operation the frequency of the signalsremains in the same level, even though one could notice that they are not exactly the same.After the switch of the capacitor banks though, it seems that in the beginning the frequencyin the simulation is less than the frequency in the measurements, to end with almost the samefrequency again. A possible reason that this happens is the different values in the inertia of thewind turbine rotor and the shaft stiffness between the simulation and the real wind turbines.As there were no information available, the values used were in the typical range that can befound in the literature [9]. The frequency difference could be also explained from the differentsize of the capacitor banks that connect in the measurements or even from the different timethat the capacitor banks switch off (see Table 5.1). However, it should not be disregardedthat the voltage magnitude between the switching operations and also the transients during

the switch of the capacitors are similar.The results of the simulation are the same for the voltage at the other two measuring

points (A01 and A09) as the results presented in figures 5.1 - 5.3 and they can be found in theAppendix B.

Figure 5.1: Measured and simulated voltage at the transformer platform from 0 ms to 500 ms. Upper plot : Phase A. Middle plot : Phase B. Lower plot :

Phase C.

In figures 5.4 and 5.5 the simulated current in comparison with the measured current atthe transformer platform is depicted. In figure 5.5, it can be seen that the magnitude of



Chapter 5 47

Figure 5.2: Measured and simulated voltage at the transformer platform from 60 ms to 120 ms. Upper plot : Phase A. Middle plot : Phase B. Lower

plot : Phase C.

Figure 5.3: Measured and simulated voltage at the transformer platform from 270 ms to 330 ms. Upper plot : Phase A. Middle plot : Phase B. Lower

plot : Phase C.



48 5.1 Comparison of the instantaneous values of currents and voltages

the simulated current before the radial disconnection is similar to the measured. Based onthat, it could be considered that the production of the radial in the simulation is equal tothe measured power production. However, this will be verified when the power production is

calculated. From figure 5.6, it can be derived that the radial disconnection in the simulationoccurs at the same point of the current waveform as in the measurements. The exact time of the disconnection is at t=78 ms when the first zero crossing is at phase C.

Figure 5.4: Measured and simulated current at the transformer platform from 0 ms to 500 ms. Upper plot : Phase A. Middle plot : Phase B. Lower plot :

Phase C.

Figure 5.5: Measured and simulated current at the transformer platform from 60 ms to 120 ms. Upper plot : Phase A. Middle plot : Phase B. Lower

plot : Phase C.

In the analysis of the measurements and in the beginning of the present chapter, based onthe current measurements at A01 and A09 it was assumed that the switch of the capacitorbanks was at A01. This can be verified in figures 5.7 and 5.8 where the current at A01 and A09is illustrated. The time of the switching operation in the simulation is in agreement with themeasurements and also the magnitude of the transient currents is similar to the measurements.

However, as it was expected after the discussion of the voltage waveform at the transformerplatform the frequency of the current in the simulation is not the same with the measurements.In figures 5.9 and 5.10 it is verified that a small current is still fed into the isolated system and



Chapter 5 49

Figure 5.6: Measured and simulated current at the transformer platform from 60

ms to 120 ms. Upper plot : Phase A. Middle plot : Phase B. Lower plot : Phase C.

that the wind turbines are still connected. In the same figures, it is shown that the transientsin the current after the radial disconnection have not been reproduced in the simulations. Theoverall view of the current in A01 and A09 can be found in the Appendix B.

Figure 5.7: Measured and simulated current at A01 from 270 ms to 330 ms. Upper

plot : Phase A. Middle plot : Phase B. Lower plot : Phase C.

5.2 Sequence components analysis

5.2.1 Voltage and current at the three locations

In this section, only the most important results will be presented. However, all the results canbe found in the Appendix B. It is reminded that the comparison is between the simulationresults and the measurements corrected as suggested in Chapter 3. In figures 5.11 and 5.12the zero, positive and negative component of the voltage and the current at the transformer

platform respectively are depicted. It can be seen that the measured and simulated values aresimilar. However, some differences exist, especially in the zero-sequence component of both thevoltage and the current. In the zero-sequence voltage, before the disconnection of the radial,



50 5.2 Sequence components analysis









Chapter 5 51

both the measured and the simulated voltages are zero. The main difference is located in thetransients during the disconnection of the radial and until the end of the simulation. Themagnitude of the transients is higher in the measurements and this can be explained from the

fact that the radial disconnection does not have the same influence on the voltage waveformin the simulations. In figure 5.2 it can be seen that the magnitude of the transient voltageduring the radial disconnection is not the same in the simulation and the measurements. Thisdifference might be the reason for the difference in the zero sequence component of the voltage.

After the radial disconnection, the magnitude of the zero-component of the simulatedvoltage remains almost constant but still higher than zero. On the contrary, on the measuredvoltage, the magnitude of the zero-sequence component is not constant as it reduces until itreaches the value of the simulated voltage. In addiction, in the measured voltage oscillationsare present this is not the case in the simulations.

Similarly, in figure 5.12 where the sequence components of the current are presented, themain differences can be observed in the zero component. As with the voltage, the magnitudeof the transients are higher in the measured than in the simulated current. However, in thiscase before the radial disconnection the simulated zero component is almost zero while the

measured zero component is not, as it was explained in Chapter 3. The simulated current isin agreement with what can be found in the literature for the zero-sequence components of the currents in ∆-connected systems.

The sequence components of the voltage in A01 and A09 are similar to the results shownin figure 5.11 and they can be found in the Appendix B. Here, only the positive-sequencecomponent of the voltage at A01 is presented in figure 5.13. It is clear that the simulatedvoltage is similar to the measured both during the transients and the temporary over-voltagesbetween the two main switching operations. This is another evidence that even though theexact switching operations are unknown, the assumed in Table 5.1 produce results similar tothe measurements. The main differences that can be spotted are mainly between the two mainswitching operations and after the connection of the capacitor banks at A01. The higher levelof the simulated voltage between 100 ms and 200 ms could be due to the capacitor banks that

they disconnect in different times than the assumed.After the second switching operation at 275 ms the simulated and the measured voltage

present a different behavior. It seems that the measured voltage decreases with steady slopewhereas the simulated voltage oscillates. The measured voltage drops to zero with the sameslope as it can be seen in figure 5.13. However, in the simulations after the 500 ms presentedhere, the voltage drops to zero but it presents oscillations. The difference could be due to thedisconnection of the wind turbines after this point in the measurements due to over-speeding.

However, the sequence components of the currents at A01 and at A09 present differenceswith the measured. The differences are located only in the zero component that is presentedin figure 5.14. The positive and negative-sequence components can be found in the AppendixB. In figure 5.14 the main difference can be spotted in the A01, as the zero component of thesimulated current is equal to zero for the whole simulation while the zero component of themeasured current is oscillating close to zero. To add on that, the measured current is risingfrom 200 ms until it reaches its peak value at the time when the capacitor banks connect. InA09 the oscillations at the zero component of the measured current are high but its value isvery low that it could be considered as zero.




Figure 5.11: Sequence components of the measured and simulated voltage at the transformer platform. Upper plot : Zero-sequence component. Mid-

dle plot : Positive-sequence component. Lower plot : Negative-sequence component.

Figure 5.12: Sequence components of the measured and simulated current at the transformer platform. Upper plot : Zero-sequence component. Mid-

dle plot : Positive-sequence component. Lower plot : Negative-sequence component.



Chapter 5 53

Figure 5.13: Positive-sequence component of the voltage at A01.

Figure 5.14: Zero-sequence component of the current at A01 and A09. Upper

plot : A01. Lower plot :A09.




5.2.2 Active and reactive power comparison

The comparison between the simulated and measured active and reactive power is for theverification of the state of the wind turbines. The active power transferred from the three

locations is presented in figure 5.15.

(a) Active power production from 0 ms to 500 ms. Upper plot: Transformer platform.

Middle plot: A01 wind turbine. Lower plot: A09 wind turbine

(b) Active p ower production before the radial disconnection. Upper plot: Trans-

former platform. Middle plot: A01 wind turbine. Lower plot: A09 wind

turbine

Figure 5.15: Active power production at the three measuring points.

As it can be verified, the production of A01, A09 as well as the total production of theradial is in accordance with the power production calculated from the measurements. It canbe also verified that after the radial disconnection the wind turbines are still connected. Thiscan be seen in figure 5.15a and it is more clear in figure 5.16. As it was explained in Chapter3, after the disconnection some of the wind turbines will have a negative slip and some of them will have a positive slip. Depending on their production and their angular velocity, thewind turbines with negative slip will be producing and the wind turbines with positive slipwill be consuming power. The wind turbines that before the disconnection were producing

more, therefore their slip was higher, they will continue producing power. As an example, infigure 5.16, A09 wind turbine that was producing almost at rated speed is producing powerwhile A01 that was producing less is consuming power [19].



Chapter 5 55

Figure 5.16: Active power production at the three measuring points after the radial

disconnection. Upper plot : Transformer platform. Middle plot : A01wind turbine. Lower plot : A09 wind turbine

The reactive power calculated after the sequence components transformation can be seenin figure 5.17. The reactive power consumed at A01, A09 and in total from the radial is inaccordance with the reactive power calculated from the measurements. The main differencescan be seen in the total reactive power absorbed and the reactive power absorbed from A01during the disconnection of the radial.




(a) Reactive power at the three measuring points from 0 ms to 500 ms. Upper plot:

Transformer platform. Middle plot: A01 wind turbine. Lower plot: A09 wind

turbine

(b) Reactive power at the three measuring points before the radial disconnection.Upper plot: Transformer platform. Middle plot: A01 wind turbine. Lower

plot: A09 wind turbine

Figure 5.17: Reactive power at the three measuring points





58 5.3 Distributed cable model

in figure5.19. The cable that represents the root cable of the radial is different regarding itslength. The information regarding the properties of each cable were retrieved from [5].

Figure 5.19: Frequency-Dependent (Phase) model of the cable.

Due to computational problems in the simulations some changes were essential. Initially,the solution step was reduced to 3 µs from 50 µs in the previous simulations. In addition,instead of the analytical approximation for the calculation of the earth ground return path forthe cable used in [5], the numerical integration is used. According to the manual [37], althoughthis calculation of the ground impedance is accurate enough adds a significant amount of timeon the simulation. It should be noted as well that the Frequency-Dependent (Phase) model isrepresented in the three phase system. Consequently it needs to be merged into a single linediagram as it is illustrated in figure 5.19.

For the simulation of the differentiated model of the radial, the same switching operationsapplied to the initial model and described in Table 5.1 are performed. For the easier comparison

of the simulation results obtained with the distributed cable model and the π-section modelwith the measurements, the voltage and the current at A01 are illustrated in figures 5.20-5.23.As it can be seen, the results of the two models are similar. The switching transients observedin the voltage and current measurements due to the radial disconnection were not representedwith any of the models (figures 5.20 and 5.21). The main difference can be spotted in thetransients due to the connection of the capacitor banks at 275 ms in figure B.14. It seemsthat the effect is more severe in the distributed cable model than in the π-section. Withthe π-section model, the frequency of the transient over-voltages is not the same with themeasurements as the disturbance lasts for less time. On the contrary, with the distributedcable model, the disturbance due to the capacitor connection lasts for more time than in themeasurements. It can be also seen that the magnitude of the transient over-voltages at the timeof the capacitor banks connection is different in the two cable approaches, with closest to themeasurements the results from the distributed model. Similar observations can be concluded

from figure 5.23.



Chapter 5 59

Figure 5.20: Instantaneous voltage at A01 from 60 ms to 120 ms. The results obtained from the distributed cable and π-section model are compared

with the measurements

Figure 5.21: Instantaneous current at A01 from 60 ms to 120 ms. The results obtained from the distributed cable and π-section model are compared


Figure 5.22: Instantaneous voltage at A01 from 260 ms to 380 ms. The results obtained from the distributed cable and π-section model are compared




60 5.3 Distributed cable model

Figure 5.23: Instantaneous current at A01 from 260 ms to 380 ms. The results obtained from the distributed cable and π-section model are compared


The aforementioned can be verified by plotting the positive sequence component of thevoltage at A01 in figure 5.24. The magnitude of the transient over-voltages due to the capacitorbanks connection with the distributed cable model are closer to the measurements. However,the oscillations observed after the 300 ms are not visible in the measurements as they aredamped soon after the switching event. Similarly to the analysis performed in Chapter 3, in

figures 5.25 and 5.26 the frequency analysis on phase B of the current and voltage in A01 andA09 respectively is presented.

In figure 5.25 the difference in the harmonic components between the cable models andthe measurements in each location is obvious. It can be seen that in the measured voltagethere is a peak around 800 Hz, but in case of the π-section model the peak is around 700 Hz.Regarding the results from the simulation with the distributed cable model, there is one peakaround 750 Hz but there is also one higher peak at 650 Hz. The 650 Hz component of thevoltage is not observed neither in the simple cable model nor in the measured voltage.

Similar observations can be seen in figure 5.26 where the frequency analysis is performedin phase B of the current at A01 and A09. Here, differences can be seen both between thesimulated cases and the measured current but can be also seen between the two locations. Thelatter was expected as the switching operation provokes high transients only in A01 where

it occurred. At A01, the low frequency component at around 250 Hz is similar in the twosimulated cases but it is slightly different for the measured values. In addition, the harmonicfrequency at 650 Hz in the simulation with the distributed cable is also present in the current,while the differences observed around 800 Hz are similar with the differences analyzed in theFFT at the voltage.

In figures 5.25 and 5.26 it can be seen that the 13th harmonic that is present in both voltageand current is also present in both locations A01 and A09. This could be associated with themodeling of the cable as in case of the simple π equivalent model for the cable is not observed.Apparently, the representation of the full frequency impedance of the cable created a resonancewith the capacitor banks at this frequency. In the simulations performed in the next chapters,the π-section model will be used for the representation of the cables as the results comparedwith the distributed model and the measurements are in good agreement.



Chapter 5 61

Figure 5.24: Positive sequence component of the voltage at A01.

Figure 5.25: FFT analysis at phase B of the voltage. Upper plot : FFT at A01.Lower plot : FFT at A09.



62 5.4 Summary

Figure 5.26: FFT analysis at phase B of the current. Upper plot : FFT at A01.Lower plot : FFT at A09.

5.4 Summary

Following the development of the model, in the present chapter, the model is validated withthe available data. The radial disconnection occurs at 80 ms and the nine wind turbines of theradial are in island operation. In Table 5.1 the switching operations of the capacitor banks aredescribed. As the behavior of the wind turbines was unknown after the radial disconnectionthe simulation was based on the measurement analysis that revealed that at 275 ms thereis capacitor banks connection. However, several simulations were performed with differentswitching operations.

The simulation that reproduced the results closest to the real measurements and presentedin the present Chapter, are according to table 5.1. The comparison of the simulated resultshas been following the measurement analysis; first the instantaneous values of the voltageand the current in all three measuring locations are compared with the measurements, whilethe transformation into sequence components follows. The active and reactive power arecalculated and through the FFT analysis, the harmonics induced to the system are presented.It is important to note that the transformation to sequence components and the FFT analysisare performed by using the same MATLAB code as in the measurement analysis section.

It can be seen that there is a good agreement between the simulated and measured in-

stantaneous values of the voltage and the current in all locations. After the transformation tothe sequence components, the positive sequence voltage has similar waveform to the positivesequence measured voltage. The main discrepancies are focused at the moment of the radialdisconnection, as the the transients in the voltage and the currents are not reproduced in thesimulations. Furthermore, the active power production of A01, A09 and the total power pro-duction from the radial are close to the power calculated from the measurements. Here, themain difference can be spotted in the reactive power calculated at the moment of the radialdisconnection. In addition, the reactive power before the disconnection is close to the reactivepower calculated from the measurements.

Finally, the most detailed model for the representation of the cables of the collection gridwas used due to the fact that the transients observed in the measurements during the radialdisconnection are not represented in the simulation results. The results of the study showed

that using a frequency dependent model for the cables would give different results from a simpleπ-section model. Especially the FFT analysis depicts different harmonic components betweenthe cable models and the measurements. The comparison showed that even though the π-



Chapter 5 63

section model is simplified it can represent accurately enough the measurements. Throughoutthe report, if is not referred otherwise the π-section will be used as the cable model.



64 5.4 Summary



Chapter 6

Sensitivity analysis

In the present Chapter, the main uncertainties introduced in the project will be discussed.Yet from the development of the model, some parameters were unknown and had to be chosenbased on the typical values found in the literature. In this case, the shaft stiffness and theinertia of the wind turbine rotor were the unknown factors. As both the wind turbine rotor andthe shaft are included in the two-mass model, it is easily understandable that it is importantto have the appropriate values so that the model is as accurate as possible.

In Chapter 4, the development of the model was presented, while in Chapter 5 the modelis validated. The values for the aforementioned parameters were chosen from the range of thetypical values found in the literature [9], [11]. To ensure that the values chosen give a resultas close as possible to the measurements, a sensitivity analysis will be performed. Sensitivityanalysis is a method used broadly to investigate the effect of errors or uncertainties in the studycase. In [42], for the investigation of possible discrepancies between the actual and the mea-sured values of the turbine inertia and the shaft stiffness, a sensitivity analysis was performed.In addition, in [43] the sensitivity analysis was performed to study the effect of the differentparameters that characterize the drive train and the generator on the transient stability of thewind turbines. In the present work, the sensitivity analysis will be used differently. As thevalues of the parameters are unknown, the sensitivity analysis will be used as a guide to showthat the values used in Chapter 4 are those that led to the most realistic outcome.

Apart from the uncertainties introduced from the unknown parameters of the wind turbines,equally critical for the validation of the model is the switching sequence of the capacitor banks.It is explained in Chapter 3 the logic behind the control of the capacitor banks. However, asthe measurements are only from 2 wind turbines of the radial, assumptions were made. The

assumptions were based on the control strategy and the measurement analysis. To verify thatthe approach followed in Table 5.1 is similar to what happened during the measurements, thesensitivity analysis will be repeated with the switching time and the quantity of the capacitorbanks switching as a variable parameter.

Based on the previous, the chapter can be divided into two sections. The first sectionwill be the sensitivity analysis regarding the values of the parameters of the model that wereassumed during the development of the model. The unknown parameters were:

• The inertia of the wind turbine rotor J WTR or the inertia constant H WTR

• The shaft stiffness K

For values used for the parameters were the typical that were found in the literature [9].However, the range was quite broad, i.e. the inertia constant of the wind turbine rotor could

vary from 2.5 s to 12.5 s , while the shaft stiffness could vary from 0.15 s to 1.2 s. Due tothis broad range of H WTR and K the following method was followed. In [11] a similar windturbine was used (rated power 2 MW), so the values of the specific parameters of this wind



66 6.1 Sensitivity analysis on the wind turbine parameters

turbine were used as a starting point. As the rated power is similar it is adopted that theinertia constant of the wind turbine rotor would not be much different, so the parameter thatwas changed in the whole range was the shaft stiffness. Four scenarios are formulated with

different values for the parameters and are presented in Table 6.1:

Table 6.1: Scenarios based on different values of H WTR and K

Inertia constant H WTR Shaft stiffness K

Scenario A1 3.5 s 0.15 sScenario A2 3.5 s 1.2 sScenario A3 4.5 s 0.15 sScenario A4 4.5 s 1.2 s

The second section of the Chapter will include the sensitivity analysis regarding the switch-ing of the capacitor banks. Scenarios based on different switching time for the capacitor banksare formulated and simulated. Based on this analysis, the outcome will show that even thoughthe information regarding the switching time of the capacitor banks is limited, the scenariopresented in Chapter 5 is the closest to the measurements. The scenarios are presented inTable 6.2.

Table 6.2: Scenarios based on different times for the capacitor banks switching

Switching operations

Scenario B1 Capacitor switching operations occur only at A01 and A09.They switch out at 200 ms and switch in at 275 ms.

Scenario B2 The capacitor banks in all nine wind turbines have the same behaviortheir switching operations occur at the same time.

Scenario B3 There is no switching operation of the capacitor banksuntil 275 ms where all disconnect.

Scenario B4 The capacitor banks connect in different steps than the 90 kVAr.

In the first section of the Chapter, from the results obtained from the sensitivity analysison the wind turbine parameters only the instantaneous voltages and currents at A01 will bepresented and compared with the measurements. It is expected that the impact of the changeswould be similar to all three locations, respectively. In the second section, the discussion willbe for both the wind turbines, A01 and A09, as the different switching operations will affect

both turbines in different ways.

6.1 Sensitivity analysis on the wind turbine parameters

6.1.1 Scenario A1: Low inertia- Low shaft stiffness

Following the first scenario presented in Table 6.1 the results obtained can be seen in figures6.1 and 6.2.

In figure 6.1a and more clearly in figure 6.1b it can be seen that there is a difference inthe frequency of the system. At the moment of the second switching operation the simulatedvoltage is almost half a period ahead of the measured voltage. In addition, the magnitude of thevoltage between the two main switching operations is higher in the simulations. Furthermore,

even the magnitude of the transient over-voltages is different as in the phases ’-a-’ and ’-c-’ of the simulated voltage is higher than the measurements whilst in phase ’-b-’ the impact of theswitching operation is almost unnoticeable.



Chapter 6 67

(a) Instantaneous voltage comparison from 0 ms to 500 ms.

(b) Instantaneous voltage comparison from 230 ms to 330 ms.

Figure 6.1: Instantaneous voltage comparison at A01-Scenario A1




(a) Instantaneous current comparison from 0 ms to 500 ms

(b) Instantaneous current comparison from 230 ms to 330 ms.

Figure 6.2: Instantaneous current comparison at A01-Scenario A1



Chapter 6 69

The same could be mentioned for the current at A01 as well in figure 6.2. Comparing thesimulated current with the measurements the impact of the capacitor banks connection at 275ms is more severe on phases ’-a-’ and ’-c-’ of the simulated current but less severe on phase

’-b-’. In addition, similarly with the frequency of the voltage, the frequency of the two signalsis different. However, is should be mentioned that at after 400 ms in figure 6.1a the simulatedand the measured voltage have the same magnitude and frequency. On the contrary, in thecurrent shown in figure 6.2a the magnitude and the frequency of the two signals do not agree.

6.1.2 Scenario A2: Low inertia- High shaft stiffness

For this simulation, the inertia is kept the same but now the shaft stiffness is the highestpossible from the range of the typical values. The results are presented in figures 6.3 and 6.4.

(a) Instantaneous voltage comparison from 0 ms to 500 ms



In this scenario, the different shaft stiffness has an impact on both the voltage magnitude

and the frequency. It can be seen that in this case, the magnitude of the simulated voltage afterthe radial disconnection and before the connection of the capacitor banks is almost the samewith the measurements. At the same time period, the frequency of the voltage is closer to the









Chapter 6 71

frequency of the measured voltage, but still close to the switching operation at 275 ms it startsdeviating. As presented in figure 6.3b the impact of the connection of the capacitor banks isdifferent in the simulation. Even though the time of the switching operation is the same in

all the simulations, here it occurs in a different point on the voltage waveform. Especially inphase ’-b-’ in the simulated voltage the switching operation occurs almost 180o earlier in thevoltage waveform than the actual point in the measurements.

In figure 6.4 the results of the simulation regarding the current at A01 are illustrated. Inthis case, the transients at 275 are similar but as it is depicted in figure 6.4b they occur earlierthan the measurements. Comparing scenario A1 with scenario A2 it could be said that theshaft stiffness of the wind turbine has an effect on the voltage and current after the radialdisconnection. It seems that with higher shaft stiffness the response of the system is closer tothe measurements.

6.1.3 Scenario A3: High inertia- Low shaft stiffness

In scenario A3, the stiffness of the shaft is low, similar to scenario A1. The inertia constant of

the wind turbine rotor will be high in this case and its impact on the simulation results willbe investigated. The results are presented in figures 6.5 and 6.6.

In figure 6.5 the difference in the frequency and the magnitude between the simulated andthe measured voltages can be noticed. Observing carefully figure 6.6 as well, it could be saidthat the results from the present scenario are similar to the results from the scenario A1.Indeed, the low shaft stiffness has produced discrepancies in the frequency and the magnitudeof the voltage that were not that significant when the stiffness was high. In addition, thetransients in the current at 275 are similar to the results in scenario A1, as in phases ’-a-’ and’-c-’ the impact of the switching operation is higher in the simulation than in the measurements.

The similarities between scenarios A1 and A3 can be also seen in both voltage and currentafter t = 400 ms. In the voltage, the frequency and the magnitude between simulation andmeasurements are exactly the same. Regarding the current, the frequency and the magnitude

between simulation and measurements are not the same. More specifically, the current inphase ’-c-’ in the simulation is higher than the current in phase ’-c-’ in the measurements.From the discussion of the three simulated scenarios, it is indicated that the shaft stiffness

has a higher influence in the temporary over-voltages during the island operation of the windturbines. In addition, the transient over-voltages during the connection of the capacitor bankshave also higher magnitude in case of the higher shaft stiffness than in the case with the lowstiffness.









Chapter 6 73







6.1.4 Scenario A4: High inertia- high shaft stiffness

The last scenario for the first part of the sensitivity analysis comprises high inertia constantfor the wind turbine rotor and high shaft stiffness. The results are illustrated in figures 6.7

and 6.8.




Following the discussion in scenario A3, the results of the present simulation confirm theproposal that the shaft stiffness has the most significant impact on the temporary and thetransient over-voltages. In figure 6.7 the frequency and the magnitude of the voltage afterthe radial disconnection in the simulation and the measurements are closer. Moreover, thetransient over-voltages at 275 ms are not that high as observed in the measurements. Regardingthe current, figure 6.8 shows also similar results as in scenario A2. The transients due to theconnection of the capacitor banks are similar between the simulated and the measured currentbut for the simulation the switching operation occurs earlier.

Following the 4 scenarios simulated, it could be concluded that the shaft stiffness hasan significant role on the temporary and the transient over-voltages. If the shaft stiffness isrepresented with a different value than its actual the effect would be either worse (if it is higher



Chapter 6 75






76 6.2 Sensitivity analysis on the switching of the capacitor banks

than the actual) or more conservative (if it is lower than the actual). The inertia of the windturbine rotor does not seem to influence the results as much as the shaft stiffness. However,it should be noted here that in the validated model, the inertia constant was lower than the

inertia values in the sensitivity analysis (H WTR=2.5s) while the shaft stiffness is between thetwo extreme values presented in the chapter (K s=0.6s). Further investigation could be done inthis section to study the exact impact of the two parameters and especially the shaft stiffness,that seems to be the most crucial, on the over-voltages. In this case though, the actual valuesshould be provided so that results of the study would be more accurate. Finally, according tothe sensitivity analysis the representation of the mechanical part of the wind turbine from thetwo-mass model is necessary.

6.2 Sensitivity analysis on the switching of the capacitor

banks

6.2.1 Scenario B1- The capacitor banks switching operations occur

only in A01 and A09

In scenario B1 it is only the capacitor banks at A01 and A09 that switch out and then switchin at 275 ms. This scenario is based on the information regarding the control of the capacitorbanks and disregards the behavior of the wind turbines that there is no measurement available(A02-A08). For those wind turbines it will be considered that the capacitor banks remainconnected throughout the simulation. The results are presented in figures 6.9-6.10.

The main differences can be spotted during and after the disconnection of the capacitors,as before this switching operation the measured and simulated voltages and currents are inagreement. The transients on the current at A01 are similar to the measured. However, thetransients in the current at A09 are much higher in the simulations. In addition, after the thedisconnection of the capacitor banks, the current and the voltage at both wind turbines have

significantly higher magnitude compared with the measurements. This is due to the fact thatthe capacitors in the A02-A08 are still connected and provide reactive power to the inductiongenerator. As a result, the wind turbines as long as they remain connected they keep feedingthe isolated system with current.

From the present scenario, it could be concluded that the capacitor banks at A09 are notconnecting at 275 ms. In addition, after the switching operation at 275 ms there should beno capacitor banks connected as in that case the current and the voltage magnitude would behigher as shown here.



Chapter 6 77

(a) Instantaneous voltage comparison between measurements and simulation from 0

ms to 500 ms.

(b) Instantaneous current comparison between measurements and simulation from 0

ms to 500 ms.

Figure 6.9: Instantaneous voltage and current comparison at A01-Scenario B1





ms to 500 ms.


ms to 500 ms.




Chapter 6 79

6.2.2 Scenario B2- The capacitor banks have the same operation in

all wind turbines

Scenario B2 is based on the control of the capacitors banks described earlier. In this case, thecapacitor will have the same operation in all wind turbines, which means that the capacitorswill switch out and in at the same time. The disconnection of the capacitor banks will be at200 ms and the connection at 275 ms. After the connection, the capacitors will disconnectfollowing the conclusions from scenario B1. The results can be found in figures 6.11-6.12


ms to 500 ms.


ms to 500 ms.


The simultaneous switching operations of all the capacitor banks in the wind turbines,being already an unlikely scenario, does not reproduce similar to the measurements results.The impact of the connection of the capacitor banks on the voltage is more severe than in the

measurements. As it can be seen in figure 6.13, the transient over-voltages at A01 can reach70 kV while in the measurements the transient over-voltages reach 45 kV. On top of that,the transients in the currents are different. In A01, as depicted in figure 6.11b, the effect the





ms to 500 ms.


ms to 500 ms.




Chapter 6 81

magnitude of the transient current is less than in the measurements while in A09, as illustratedin figure 6.12b the impact is more severe in the simulations.

As a conclusion from the present scenario, the results presented here show that the simul-

taneous connection of the capacitor banks at 275 ms during the time that the measurementswere acquired could not have happened. However, the disconnection of the capacitor banksat 200 ms might have occurred. The results from the simulation do not show any significantdifference regarding this switching operation. In reality, though, it would be difficult to happeneven the minimum delay in the control of the capacitors would have an impact on the switchingmoment. In figure 3.20 it was illustrated that the magnitude of the voltage after the radialdisconnection was different in the three measuring locations. This difference on the voltagemagnitude could be expected for the other wind turbines as well and it is easily understand-able that this difference would activate the voltage control of the capacitors in different timefor each wind turbine. Consequently, for the measurement representation, the simultaneousswitching operations of all the capacitor banks could be considered as invalid.

Figure 6.13: Voltage at A01 from 250 ms to 330 ms.

6.2.3 Scenario B3- The capacitor banks remain connected and dis-

connect at the 275 ms

Scope of this scenario is to clarify that the switching operation that occurs at 275 ms is notthe disconnection of the capacitor banks. The worst case is considered, where the capacitorsdisconnect simultaneously in all nine wind turbines of the radial. The results of the simulationare presented in figures 6.14-6.15.

In figures 6.14a and 6.15a it can be seen that the transient over-voltages at 275 ms have

significant differences with the measurements. In figure 6.16 this is more obvious. The transientover-voltages do not have similar magnitude to the measurements whereas the system is notexcited almost at all. The high frequency oscillations that can be seen in the measurements arenot shown in the simulation. This is apparently due to the fact that the switching operationsare not the operations that occur in the measurements. This can be verified from the currentwaveforms as well, as the disconnection of the capacitors do not provoke any current transients.





ms to 500 ms.


ms to 500 ms.




Chapter 6 83


ms to 500 ms.


ms to 500 ms.





Figure 6.16: Voltage at A01 from 250 ms to 330 ms.

6.2.4 Scenario B4- Different steps of the capacitor banks connecting

at A01

For the validation of the model, as the switching operation that occur at 275 ms was consideredthe connection of the capacitor banks at A01. The capacitor banks are in steps of 90 kVAr withnominal power 1350 kVAr. In Chapter 5 it was considered that all the steps are connectingsimultaneously, which means that 15 steps of 90 kVAr power connected at 275 ms. In theinformation available about the Dynamic Power Factor Correction system installed in Nystedit is mentioned that the capacitors are organized in teams; 90 kVAr is one team, 180 kVAr isthe second team and there are 3 teams of 360 kVAr. In the present scenario the simultaneousconnection of the 5 teams is considered.

Due to the good agreement between the results from the simulation and the measurements,only the figures illustrating the transients at 275 ms in A01 and A09 will be presented here.The overall views of the voltage and the current at A01 and A09 can be found in the AppendixC.



Chapter 6 85


ms to 330 ms.


ms to 330 ms.






ms to 330 ms.


ms to 330 ms.




Chapter 6 87

As it is shown in figures 6.17 and 6.18 there is a good agreement between the simulatedand measured values at both locations. However, the transients due to the connection of thecapacitors are not totally represented in the simulation. In A01, even though the magnitude

of the transients in both the voltage and the current is similar to the measurements, thedisturbance is damped quite fast. This is more obvious in the current in figure C.4 especiallyif it is compared with figure 6.19 from Chapter 5 that is presented here as well to facilitate thecomparison. In figure 6.19, the current transients are almost fully reproduced, while in figureC.2 the results are similar but not very close to the measurements.

The aforementioned can be verified in figure 6.18 where the comparison of the transientsin the voltage and the current at A09 is depicted. Especially in the current in figure C.4, thetransients in the current are not represented in the simulation. Consequently, even though theresults from scenario B4 are very close to the measurements they do not reproduce exactlythe measurements. In particular, the transients are damped quite fast and if the results fromthis scenario are compared with the results from the simulation in Chapter 5, the switchingoperation simulated in Chapter 5 has better response.

Figure 6.19: Measured and simulated current at A01 from 270 ms to 330 ms. The figure is from the simulation in Chapter 5. Upper plot : Phase A.

Middle plot : Phase B. Lower plot : Phase C.



88 6.3 Summary

6.3 Summary

In the present Chapter the sensitivity analysis regarding parameters that could affect theresults of the simulation and were unknown are presented. As described, the main uncertaintiesare the unknown values of the wind turbine rotor inertia, the shaft stiffness and the exactmoments of the switching operations of the capacitor banks.

The values of the unknown parameters were based on typical values that can be found inliterature [9], [11]. The results have shown that the temporary and transient over-voltagesdepend mainly on the shaft stiffness. However, this suggestion it can only be based on thecomparison between the simulation results and the available measurements. In order to verifythe dependence of the over-voltages from the shaft stiffness the actual data should be provided.Based on that, the sensitivity analysis would be more significant. It is also very importantto notice the dependence of the results from the two unknown parameters, as it means thatthe two-mass model is necessary for similar studies as well. In general, the two-mass model isessential for stability studies. As it is suggested here, the two-mass model is also necessary forelectromagnetic transient studies as well.

The second part of the sensitivity analysis includes the different switching operations of the capacitor banks. Four scenarios of different switching operations were performed and thethe results have verified that the assumptions made in the previous chapters were correct. Thecapacitor banks disconnect before 275 ms, probably not at the same time, and at 275 ms it isonly the capacitor banks at A01 that connect and provoke the high transient over-voltages. Ithas been shown that the connection of the capacitor banks occurs in 15 steps of 90 kVAr andalso that after this switching operation the capacitor banks at A01 need to be disconnectedagain.



Chapter 7

Capacitor control and assessmentof over-voltages in different

production levels

In the previous Chapters it was shown that the high transient over-voltages observed in figure3.6 are due to connection of the capacitor banks in A01. Based on the information regardingthe control of the capacitor banks this behavior could be expected. However, as it was shownin Chapter 6 the capacitor banks were connected only in A01. Due to the different behaviorof the capacitor banks, in the model developed in Chapter 4, the control of the capacitors wasmodeled through a simple breaker that performed the switching operations on specific time.

In the present chapter, the control of the capacitor banks will be developed. The controlwill be designed based on how the wind turbines should operate during island operation. Fur-thermore, simulations with the wind turbines producing in low and high-level will be performedand the results regarding the over-voltages will be discussed.

7.1 Capacitor bank control

As a reminder, figure 7.1 describes the logic behind the control of the capacitor banks. Itshould not be disregarded that the wind turbines used in Nysted are in compliance with thegrid codes [3]. This is depicted in the voltage control mode of the capacitor banks. If thevoltage is below a certain level, that is considered to be a threshold for a grid fault for a

certain time that can be defined from the user, then all the available capacitor groups areconnecting. Similar is the logic for the maximum safe voltage, which is normally the 120%of the nominal voltage. If the voltage exceeds this upper threshold, all the capacitor banksdisconnect immediately.

Apart from the upper and lower thresholds for the voltage control, there is an intermediatelevel as well. If voltage exceeds the upper or the lower voltage threshold, but not the corre-sponding critical thresholds, then the voltage control acts by disconnecting or connecting stepby step capacitor banks. This continues until the voltage is within the normal values again,that the control changes from voltage to power factor correction mode. As soon as the systemreturns to normal operation, the steps that were disconnected are connecting or vice versa.

To simulate the control of the capacitor banks, a simplified version of the control describedin figure 7.1 will be implemented in PSCAD. Only two extreme values will be taken into

account, one as the critical upper voltage (120% of the voltage nominal value) and one asa lower voltage threshold. For the lower voltage limit the gird fault threshold could be onechoice but for the present simulations the 90% of the nominal voltage will be considered as the



90 7.1 Capacitor bank control

Figure 7.1: Voltage control set points [6].

threshold. It was not possible to develop the model of the full control of the capacitor banksdue to time limits, as there were many parameters that should be taken into account. Some of the parameters were the several thresholds and the switching operation performed, switchingthe capacitors in steps or in total for different thresholds, introduce time delay for each windturbine as from the measurements it does not seem that they operate simultaneously.

Therefore, the control logic approach is simple and includes two critical voltage thresh-olds. However, as there is no fault introduced, the lower voltage threshold is chosen 90%, asmentioned earlier. The capacitor banks are switching as one step in all switching operations.Furthermore, the measurement voltage that the control will be based upon is the MV at thetransformer at each wind turbine, as introduced by the manual [6]. As the voltage controlcannot be based on the instantaneous values of the voltage, the RMS value of the voltageneeds to be calculated. The lower and upper voltage thresholds will be based on the per unitvalues of the RMS measured voltage.

The implementation of the voltage control logic is presented in figure 7.2. The RMS voltageis measured at the MV side of the transformer at each wind turbine and after transformationto its per unit value it is used for the control. The limits are set to 1.2 and 0.9 per unit and

the comparison is performed with the Hysteresis Buffer component. According to PSCADmanual [37], the Hysteresis Buffer component is used for converting a real into a logic signal.In addition, the transition to the new logic state is avoided until the input signal has movedacross the defined threshold.

The Edge Detector component and the counter are used to limit the switching operations of the capacitor banks. This operation is chosen for practical reasons, as it is not possible within1 sec the capacitor banks to switch several times. In simulations performed while testing thecontrol logic it was found out that numerous switching operations of the capacitor banks wereperformed following the radial disconnection as after disconnecting the capacitor banks thevoltage was decreasing and after connecting the capacitor banks the voltage was increasing.The command of opening or closing the breaker of the capacitor banks was controlled withan OR gate. When the voltage is higher than the predefined threshold, the breaker will

open. Finally, it should be noted that the amount of the capacitor banks participating in theswitching operations after the radial disconnection was equal to the amount of the capacitorbanks connected in the steady state before the radial disconnection.



Chapter 7 91

Figure 7.2: Voltage control logic implemented in PSCAD.

7.2 Over-voltages during low-level production

The peculiarity of this simulation is that the wind turbines used in Nysted have two differentinduction generators as explained in Chapter 2. The first generator is used for low wind speedsand the second for medium and high wind speeds. In this way the efficiency of the wind turbineis higher. In the low wind speed configuration the nominal power output of the wind turbineis 400 kW instead of the 2300 kW in high wind speed. In addition, the equivalent circuit of the generators is similar to the circuit depicted in figure 4.7 but the value of the parametersare different. Along with the induction generator model, the aerodynamic model needs to beadjusted as the base for the per unit values is the nominal power of the wind turbine.

The change in the induction generator configuration has an impact on the reactive powerconsumption as well. In case of the low power configuration, the reactive power consumptionat nominal operation is 225 kVAr. It was found out in [15] that if the wind turbines are fully-compensated or supply reactive power to the grid, then the increase rate of the voltage willbe larger than when they absorb reactive power. Furthermore, it is stated that the rate of thevoltage is also connected with the power production level. This is due to the current of the

wind turbines that charges the cable during the island operation. If the production is low, thecurrent will be low and the increase rate of the voltage will be lower as well.

For the low production level of the wind turbines, two simulations will be performed; onewhile the radial is supplying reactive power to the grid and one while the radial is absorbingreactive power. The results can be seen in figures 7.3-7.8.

The radial disconnects at 15 sec and after that the operation of the capacitor banks isbased on their control. In figure 7.3, where the voltage at A01 is depicted, it can be seen thatthe radial disconnection occurs at 15 sec as the voltage magnitude starts increasing after thismoment. However, the voltage waveform is not the same in the two simulations. It seems thatin the case that the radial is supplying reactive power to the grid, the voltage magnitude ishigher. The high transient over-voltages at 15.24 and 15.67 sec are due to the connection of thecapacitor banks in the two simulations. The connection is performed faster in the simulation

that the reactive power is supplied to the grid and the impact is more severe.In figure 7.3, the effect of the disconnection of the capacitor banks is also visible in thecase that the reactive power is supplied to the grid as it provokes switching transient over-



92 7.2 Over-voltages during low-level production

Figure 7.3: Instantaneous voltages at A01. The control of the capacitor banks is enabled faster in the simulation that the reactive power is supplied to

the grid.

voltages as well. However, the disconnection of the capacitor banks is not that severe in thesimulation that the reactive power is absorbed from the grid. It should also be mentioned thatthe disconnection of the capacitors occurs later in the reactive power consumption simulation,around t = 15.55 sec as the magnitude of the voltage starts decreasing, while in the reactivepower supply simulation occurs at 15.18 sec. The time difference is due to the different increaserate of the voltage in the two simulations as when the reactive power is supplied to the grid,the voltage increases faster.

In figure 7.4, the current at the capacitor banks in the two simulations is presented. It isverified that in the reactive power supply simulation, the capacitor banks disconnect aroundt = 15.18 sec while in the second simulation they disconnect around t = 15.55 sec. It should bealso noted that after the connection of the capacitors, in the first case they remain connectedfor less time than in the second case. Obviously, this is because the effect of the capacitorconnection is more severe and also the higher amount of reactive power provided from thecapacitors lead to a faster voltage increase in the reactive power supply simulation.It should

also be noted that current in the capacitor in the first case after the radial disconnection ishigher than the current in the second case. This is most likely associated with the excess of reactive power that is different in the two cases.

As mentioned before, the control logic is based on the RMS measured value measured at theMV side of each wind turbine. In figure 7.5 the RMS measured voltages in the two simulationsare presented. The thresholds for the voltage control are the 120% and 90% of the nominalvalue and is shown that the control is working as it was defined. It can be seen in figure 7.5that after the radial disconnection the voltage magnitude increases in both cases. However,when the reactive power is supplied to the grid the voltage increases faster. In this case, thehigher amount of reactive power supplied to the isolated system causes over-compensationof the generator and increase of the voltage. After the disconnection of the capacitor banksthe voltages start reducing until they drop to 90% of their nominal value when the control

reconnects the capacitors. Finally, when the voltage reaches again the upper limit the capacitorbanks disconnect and the voltage drops to zero, as no reconnection is allowed by the control.A different view of the over-voltages in the two simulated case is illustrated in figure 7.6.



Chapter 7 93

Figure 7.4: Current at the capacitor banks at A01. Upper plot : Reactive power supplied to the grid. Lower plot : Reactive power absorbed from the

grid.

Figure 7.5: RMS voltage at A01 measured for the control of the capacitor banks.Upper plot : Reactive power supplied to the grid. Lower plot : Reac-

tive power absorbed from the grid.



94 7.2 Over-voltages during low-level production

Here, it is more obvious that the connection of the capacitor banks is more critical in theswitching transient over-voltages in case of reactive power supply to the grid. In addition,in the same case, after the radial disconnection the voltage magnitude increases faster and

activates the control of the capacitor banks earlier.

Figure 7.6: Positive sequence component of the voltage at A01.

In figures 7.7 and 7.8, the active and reactive power status of the wind turbines are pre-sented. In figure 7.7, it can be seen that the active power produced is the same in the twowind turbines and a little higher in the total production in case of reactive power consumption.However, as the difference is small it is considered as identical active power production in bothsimulations. In figure 7.8 the difference between the two cases is illustrated. As it is shown,the total reactive power supplied to the grid is around 0.5 MVAr while the absorbed reactivepower is 0.2 MVAr. Even though the difference for each particular wind turbine is not large,the higher amount of reactive power available in the isolated radial in the case of reactive powersupply leads to the faster activation of the capacitors control system. The results presentedhere are in accordance with the conclusion of the Danish TSO investigation shown in [15], asin general the impact of the radial breaker switching operation is more severe if reactive poweris supplied to the grid.



Chapter 7 95

Figure 7.7: Active power production in the two simulated cases. Upper plot :Total active power production. Middle plot : Active power production

at A01. Lower plot : Active power production at A09.

Figure 7.8: Reactive power production in the two simulated cases. Upper plot :Total reactive power production. Middle plot : Reactive power pro-

duction at A01. Lower plot : Reactive power production at A09.



96 7.3 Over-voltages during nominal power production

7.3 Over-voltages during nominal power production

In this section, the behavior of the wind turbines during island operation while they areproducing their nominal power will be simulated. In the previous section it was shown thatthe over-voltages increase faster in case that the reactive power is supplied to the grid. Here,the effect of high and low-level of active power production of the wind turbines on the over-voltages will be discussed. The results are presented in figures 7.9-7.15.

In figure 7.9 the effect of the different power production level during the island operationon the voltage at A01 is illustrated. In case of the nominal power operation shortly afterthe radial disconnection the capacitor banks disconnect as well. Following this, the voltagestarts reducing until 200 ms later when the capacitor banks connect. The switching transientover-voltages provoked from this switching operation reach almost 50 kV. These can be seenmore clearly in figure 7.10. It should also be mentioned that the disturbances observed 50 msafter the radial disconnection are most likely due to the disconnection of the capacitor banks.To verify the switching time of the capacitor banks, the current at the capacitors in the twosimulations is presented at figure 7.11. It is indeed shortly after the radial disconnection that

the capacitor banks also disconnect as the current drops to zero.

Figure 7.9: Instantaneous voltage at A01. The radial disconnection occurs at 15 sec.

Similarly, when the capacitor current in the simulation with low active power productiondrops to zero the capacitors are disconnected. However, it should be noticed that the discon-nection of the capacitors occur more than 500 ms later than in the other case. This indicatesthat the increase rate of the voltage is higher in the case of high active power production.This can be implied as well from figure 7.10, but is more clear if the RMS voltage used for thecontrol of the capacitors is plotted in figure 7.12.



Chapter 7 97

Figure 7.10: Instantaneous voltage at A01. The capacitor banks in case of the nominal power operation disconnect 50 ms later and they connect

again at 15.2 sec.

Figure 7.11: Current at the capacitor banks.




Figure 7.12: RMS voltage at MV side of the transformer at A01. The measured voltage is used for the voltage control of the capacitor banks.

In figure 7.12 it can be seen that in the simulation with nominal power production, thechange rate of the voltage is higher than in the simulation with low power production. Morespecifically, within the first 500 ms after the radial disconnection, the control of the capacitor

banks has already been activated twice for the upper voltage threshold. On the contrary, inthe simulation with low-level power production, in order for the control to be activated twicefor the upper voltage threshold it takes more than 1 sec.

In figure 7.13 the switching transients due to the connection of the capacitor banks whilethe wind turbines are in low-level power production is shown. It can be seen that the ef-fect of the switching operations on the switching transient over-voltages is similar in the twosimulated cases. In figure 7.14 the positive sequence component of the voltage is depicted.The aforementioned observations regarding the increase rate of the voltage and the transientover-voltages due to the switching operations can be derived as well as from the analysis of figure 7.14.

For the complete comparison of the two cases, the active and reactive power productionare illustrated in figures 7.15 and 7.16. The difference in the active power production isobvious while at the same time the difference in the reactive power consumption is also signifi-

cant.Even though in the nominal power production simulation all the capacitor banks availableare connected, the wind turbine still absorb reactive power. From the comparison of the twosimulations, it could be derived that the level of the active power production is related withthe rate of the voltage as introduced in [15]. In the simulation where the wind turbines wereproducing their nominal power, the increase rate of the voltage was higher than in the casewith the low power production.



Chapter 7 99

Figure 7.13: Instantaneous voltage at A01. Connection of the capacitor banks at low-level power production occur at 15.655 sec

Figure 7.14: Positive sequence voltage at A01.




Figure 7.15: Active power production at the three locations for the two simulated cases. Upper plot : Active power production at the transformer plat-form. Middel plot : Active power production at A01. Lower plot :

Active power production at A09.

Figure 7.16: Reactive power production at the three locations for the two simulated cases. Upper plot : Reactive power at the transformer platform.Middle plot : Reactive power at A01. Lower plot : Reactive power

at A09.



Chapter 7 101

7.4 Summary

In the present chapter a simple control logic of the capacitor banks was introduced. Thecontrol logic is based on the User’s Manual of the Power Factor Compensator units used inNysted Offshore Wind Farm [6]. The voltage control of the capacitor banks is using the RMSmeasured voltage at the MV side of the transformer of each wind turbine. As it is not a fullcontrol model, it is based on two voltage limits; the upper voltage limit set by the 120% of the voltage nominal value and a lower voltage set by the 90% of the voltage nominal value.Exceeding the first limit, the control will disconnect all the capacitor banks while exceedingthe latter the control will connect all the available capacitor banks.

After including the capacitor control component into the initial model of the wind turbine,two study cases were investigated. The first study case was while the wind turbine was inlow-level power production operation, simulating a day with low wind speed. In this case, thewind turbine is operating with the "low power generator" where the nominal power output is400 kW. Two simulations were performed while the wind turbine was in this operation mode,one with the wind turbines absorbing reactive power and one with the wind turbines supplying

reactive power to the grid. The results showed that the over-voltages were influenced by thestate of reactive power compensation of the generator. When the generator was supplyingreactive power to the grid, the increase rate of the voltage was higher than in the other case.In addition, in the former simulation, the connection of the capacitor banks provoked higherswitching transient over-voltages than in the latter.

The second study case was to investigate the impact of high and low power production levelin the over-voltages. A new simulation was performed while the wind turbines were operatingin nominal power and the results were compared with the results from the simulation of theprevious case that reactive power was consumed. The comparison has shown that the impacton the transient over-voltages during the switching operation of the capacitor banks weresimilar but the increase rate of the voltage was higher in the case of nominal power operation.It could be mentioned that at the same time after the radial disconnection due to higher

current the cables are charged faster when the wind turbines are in nominal operation.As a final comparison, the positive sequence voltage at A01 in the three simulated cases ispresented in figure 7.17 to illustrate the results from all the simulation cases. As it is depicted,the highest rate of voltage increase occurs at nominal power operation but the highest switchingtransient over-voltages when reactive power is supplied to the grid. As discussed earlier, theresults are in agreement with the investigation from the Danish TSO presented in [15].

Figure 7.17: Positive sequence voltage at A01 for the three simulated cases.



102 7.4 Summary



Chapter 8

Discussion and future work

8.1 Discussion

The Scope of the project was the development of a model of a fixed-speed wind turbine . Themodel was validated with voltage and current measurements acquired from an experimentperformed in Nysted Offshore Wind Farm in 2007. The experiment performed was the discon-nection of radial A of the wind farm, while the wind turbines were in operation. This switchingoperation and the field measurements of the voltage and the current in three locations werethe available information.

As the behavior of the wind turbines after the radial disconnection was unknown, Chapter

2 was devoted in literature research. The main interest was to present the different typesof wind turbines, and present the technical regulations regarding the interconnection of windfarms to the power system. From this research, knowledge regarding the fault-ride throughcapabilities of the fixed-speed wind turbines was acquired. Nysted consists of this type of wind turbines and the experience through the research was used during the analysis of themeasurements.

In Chapter 3, the analysis of the measurements was performed. The measurements availablewere from three locations, after the circuit breaker of radial A at the main transformer, the firstwind turbine of radial, A01 and the last wind turbine of radial A, A09. Scope of the analysis wasto understand the exact behavior of the wind turbines during the island operation that couldbe applied in the development of the model. In addition, different ways of analyzing the datawere investigated in order to extract as much information as possible. From the measurementanalysis it was concluded that after the disconnection of the radial, the high transients observed

at 275 ms were due to capacitor connection. The reactive power measurements revealed thatbefore the disconnection the wind turbines were almost fully compensated as the reactivepower consumption was very close to zero. Combining these information, it was assumedthat the capacitor banks disconnected after the islanding of the radial. This assumption wasenhanced from the voltage waveform as after 150 ms from the radial disconnection, the voltagestarts decreasing. After the islanding of the radial the reactive power needed by the inductiongenerators is absorbed from the capacitors and the cable capacitance. Therefore, the voltagedecrease that was observed could be due to the disconnection of the capacitor banks and theloss of the reactive power needed by the generators.

Furthermore, the User’s Manual of the Dynamic Power Factor Correction system used inNysted confirmed this assumption. According to it, if the over-voltages exceed a certain limit,the capacitor banks must disconnect immediately. It is also mentioned that in case that the

voltage drops below a critical level, then all the capacitor banks should connect immediately.This is related to the fault-ride through capabilities of the fixed-speed wind turbines mentionedin Chapter 2. Connecting the capacitor banks as soon as the fault is detected is in accordance



104 8.1 Discussion

with the specifications of the grid codes regarding the supply of reactive power during andafter the fault. Consequently, it was assumed that the switching operation at 275 ms was theconnection of the capacitor banks that was based on the fault-ride through capabilities of the

wind turbines. In addition, based on the differences in the current measurements in A01 andA09, it was assumed that the connection of the capacitors occurred only in A01.After the assumptions regarding the behavior of the wind turbines, the model was developed

in order to be simulated and confirm the aforementioned. The development of the model ispresented in Chapter 4 and is based on the recommendations found in literature. Previousstudies in the fixed-speed wind turbine modeling were investigated even though the literaturefound was mainly for stability studies. The model included the aerodynamics of the windturbine, the mechanical part and the induction generator. The blade-angle control was notincluded in the model as it was assumed that due to the short duration of the experiment, itwould not have enough time to operate. This assumption was based on the fact that betweenthe radial disconnection and the moment of the high transient over-voltages the difference isonly 200 ms. At the moment of the disconnection, the difference between the active powerproduction and demand will accelerate the wind turbines. From the moment that the fault

is registered and the moment that the blades start pitching reasonable time will have passed.However, the time of interest in the present study is 250 ms that the blade-angle control ishighly unlikely to be activated and start operating as well. In addition, no data regarding theactive stall system were provided. For these reasons it was decided to assume that the activestall control will not have any influence on the over-voltages observed.

As a result, the aerodynamic model was based on a constant power coefficient as the windspeed was also assumed constant throughout the experiment. The mechanical part of the windturbine and the induction generator though, were modeled according to the recommendationsfrom [9]. The two-mass model representation was adopted for the shaft system while for theinduction generator the fifth-order model was chosen. Although the data for the inductiongenerator were provided, the inertia of the wind turbine rotor and the shaft stiffness were not.Their values were looked up from the literature and were chosen based on their range and on

data from similar wind turbines. Regarding the model of the capacitor banks control, takinginto consideration the different operation in the two wind turbines with the available data,it was decided to be with simple time logic. The moments of the switching operations werebased on the measurement analysis performed in Chapter 3.

Once the logic behind the development of the model was explained, the experiment wassimulated and the data were presented in Chapter 5. As explained in the chapter, the resultsof the simulation are very close to the measurements, despite the uncertainties introduced.The assumptions regarding the development of the model and the switching operations of thecapacitor banks were confirmed. The main difference can be spotted in the transient voltagesduring the radial disconnection that in the simulated model have not been reproduced. Exceptfor this, the results from the simulation are in very good agreement with the measurements.In the same chapter, the use of a more detailed representation of the model of the cables wasinvestigated. The results of the study showed that if the distributed cables had been used inthe model of the radial, the disconnection of the capacitor banks would be more severe dueto the low damping. For this reason, in the following simulation the Π equivalent was used torepresent the cables.

Following the validation of the model, the main uncertainties introduced in the study wereinvestigated. Chapter 6 was divided into two section; the first section is about the sensitivityanalysis of the unknown parameters of the two-mass model while the second part includesthe sensitivity analysis regarding the switching operation of the capacitor banks. In the firstpart it was shown that especially the shaft stiffness has a significant impact on the temporaryover-voltages. Thus, the use of the two-mass model was essential for the present study. Inthe second part, it was shown that the only switching operation that occurs at t = 275 ms isthe connection of the capacitor banks at A01. It can be seen in the results that the capacitorbanks do not have the same behavior in all the wind turbines. In this case, the impact of the

simultaneous connection of the capacitor banks in all the wind turbines would be more severeon the transient over-voltages.



Chapter 8 105

In the last chapter, the control of the capacitor banks was developed based on the descrip-tion found in the manual. The control is defined by two limits, one for the over-voltages andone when the voltage drops below a certain level. As this is the behavior that the wind tur-

bines should have in case of over-voltages, simulations with different level of power productionwere performed and their impact on the over-voltages was discussed. The results shown arein accordance with the conclusions from the study of the Danish System Operator presentedin [15].

8.2 Future work

As a conclusion, it could be derived that despite the assumptions in the development of themodel, it reproduces accurately enough the behavior of the wind turbines during the time of the experiment. The voltage and current measurements that were available were reproducedfrom the model. The validated model could be used in the assessment of the over-voltagesduring different switching operations. However, the assumptions regarding the blade-angle

control of the wind turbines should be always taken into consideration. This means that themodel should be used in studies that the time duration is not enough for the blade-anglecontrol to operate. Especially if the event lasts for several seconds, the active stall controlwould have time to operate. In this case, the blade-angle control have to be developed andincluded in the model of the wind turbine. In addition, if the wind turbines remain in islandoperation for considerable time they might be disconnected from the grid due to over-speedingprotection. However, for the implementation of the control, the appropriate data should beprovided otherwise it could lead to wrong results.

In Chapter 7 the model of the control of the capacitor banks is developed. However, it isnot complete as according to figure 7.1 there are several levels before the critical limits for theover-voltages and the faults. While the voltage does not exceed the critical limits, the controlis more conservative.In these levels, the switching operation of the capacitors occurs in steps;in every cycle, one step of the capacitor banks is switching.

Furthermore, if the actual data of the inertia of the wind turbine and the shaft stiffnessare provided their impact on the system could be investigated. More specifically, if all theparameters are known, the influence of the shaft stiffness on the over-voltages could be assessedindependently and verify whether the suggestion made in the present report is valid.





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Appendix A

Appendix A-Measurement analysis

Figure A.1: Sequence components of the measured voltage at A01. Upper plot :Zero sequence component. Middle plot : Positive sequence compo-

nent. Lower plot : Negative sequence component



112 A Appendix A-Measurement analysis

Figure A.2: Sequence components of the measured current at A01. Upper plot :Zero sequence component. Middle plot : Positive sequence compo-


Figure A.3: Sequence components of the measured voltage at A09. Upper plot :Zero sequence component. Middle plot : Positive sequence compo-




Chapter A 113

Figure A.4: Sequence components of the measured current at A09. Upper plot :Zero sequence component. Middle plot : Positive sequence compo-




114 A Appendix A-Measurement analysis



Appendix B

Appendix B-Validation

Figure B.1: Measured and simulated voltage at A01 from 0 ms to 500 ms. Upper




116 B Appendix B-Validation



Figure B.3: Measured and simulated voltage at the A01 from 270 ms to 330 ms.Upper plot : Phase A. Middle plot : Phase B. Lower plot : Phase C.





Chapter B 117



Figure B.6: Measured and simulated voltage at the A09 from 270 ms to 330 ms.Upper plot : Phase A. Middle plot : Phase B. Lower plot : Phase C.

Figure B.7: Measured and simulated current at A01 from 0 ms to 500 ms. Upper





Figure B.8: Measured and simulated current at A09 from 0 ms to 500 ms. Upper


Figure B.9: Sequence components of the measured and simulated current at A01.Upper plot : Zero-sequence component. Middle plot : Positive-

sequence component. Lower plot : Negative-sequence component.



Chapter B 119

Figure B.10: Sequence components of the measured and simulated voltage at A01.Upper plot : Zero-sequence component. Middle plot : Positive-sequence component. Lower plot : Negative-sequence component.

Figure B.11: Sequence components of the measured and simulated current at A09.Upper plot : Zero-sequence component. Middle plot : Positive-sequence component. Lower plot : Negative-sequence component.




Figure B.12: Sequence components of the measured and simulated voltage at A09.Upper plot : Zero-sequence component. Middle plot : Positive-sequence component. Lower plot : Negative-sequence component.

Figure B.13: Instantaneous voltage at A01 from 0 ms to 500 ms. The results obtained from the distributed cable and π-section model are compared

with the measurements.



Chapter B 121

Figure B.14: Instantaneous voltage at A01 from 260 ms to 380 ms. The results obtained from the distributed cable and π-section model are compared


Figure B.15: Instantaneous current at A01 from 0 ms to 500 ms. The results obtained from the distributed cable and π-section model are compared







Appendix C

Appendix C-Different steps of thecapacitor banks connecting at A01

Figure C.1: Instantaneous voltage comparison at A01 from 0 ms to 500 ms-Scenarion B4 . Upper plot : Phase A. Middle plot : Phase B. Lower

plot : Phase C.



124 C Appendix C-Different steps of the capacitor banks connecting at A01

Figure C.2: Instantaneous current comparison at A01 from 0 ms to 500 ms-Scenarion B4 . Upper plot : Phase A. Middle plot : Phase B. Lower

plot : Phase C.

Figure C.3: Instantaneous voltage comparison at A09 from 0 ms to 500 ms-Scenarion B4 . Upper plot : Phase A. Middle plot : Phase B. Lower

plot : Phase C.



Chapter C 125

Figure C.4: Instantaneous current comparison at A09 from 0 ms to 500 ms-Scenarion B4 . Upper plot : Phase A. Middle plot : Phase B. Lower

plot : Phase C.







Gr Msc Thesis

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