Modeling of Switching Transients in Nysted Offshore …etd.dtu.dk/thesis/242550/thesis_iaa.pdf · 3...

Iván Arana Aristi, s060768

Modeling of Switching

Transients in Nysted Offshore

Wind Farm and a Comparison

with Measurements

EMT Simulations with Power Factory and

PSCAD

Master of Science Thesis, June 2008

3

Modeling of Switching Transients in Nysted Offshore Wind Farm and a Comparison with Measurements, EMT Simulations in Power Factory and PSCAD

This report was drawn up by: Iván Arana Aristi Supervisor(s): Arne Hejde Nielsen Joachim Holbøll Ole Holmstrøm Poul Sørensen Troels Sørensen

DTU Elektro Centre for Electric Technology (CET) Technical University of Denmark Elektrovej Building 325 2800 Kgs. Lyngby Denmark www.elektro.dtu.dk/ Tel: (+45) 45 25 35 00 Fax: (+45) 45 88 61 11 E-mail: cet@ elektro.dtu.dk

Release date:

30 June 2008

Category:

1

Edition:

1st edition

Comments:

This report is part of the requirements to achieve the Master of Science in Wind Energy at the Technical University of Denmark.

This report represents 30 ECTS points.

Rights:

©Iván Arana, 2008

5

ABSTRACT

This report was prepared as part of the requirements to achieve the Master of Science in

Wind Energy with Electrical Engineering Specialization at the Technical University of

Denmark (DTU).

In the recent years there has been a particular interest in the collection grid of large

offshore wind farms. This is due to the expected increase in size, and investment, of

these wind power plants in the following years. However, the electrical conditions

present in the collection grid are not alike any other industrial application. The length of

MV cable is remarkable; as well as the number of switchgears and transformers. This

combination of components creates an electrical environment never assemble before.

In 2007 field measurements are done in Nysted Offshore Wind Farm, where three GPS

synchronized measuring systems have been built and used for simultaneous

measurement at three different locations in the wind farm. The measurement system and

the measurements performed were within the project entitled “Voltage conditions and

transient phenomena in medium voltage grids of modern wind farms”, funded by

Energinet.dk.

A comprehensive explanation of the modeling and transient phenomena, of some

electrical devices present in the collection grid of Nysted, was made; followed by a

simple case to compare the models -for some devices- in Power Factory and PSCAD.

Then, based on three measured switching events in the wind farm, three study cases

were created in both simulation programs. Here, the standard models of the electrical

devices were used to assemble the collection grid of Nysted and compare the results

from both simulations with the measurements.

After the digital models in both programs were evaluated, an assessment on the voltage

dip due to the sequential energization of different amount and combination of wind

turbine transformers was made. Finally, a comparison of both programs was created for

electromagnetic transient simulations; as well as guidelines to energize the collection

grid in large wind farms and a list of information required for switching transient

studies.

Kgs. Lyngby, 2008-06-30

7

ACKNOWLEDGEMENTS

This thesis work was conducted at DONG Energy. I would like to express my deepest

gratitude to my supervisor Troels Sørensen for providing me with the opportunity to

work in an excellent engineering environment and for all his time, guidance and

support.

I am grateful as well to Arne Hejde Nielsen, Joachim Holbøll, Poul Sørensen and Ole

Holmstrøm for their valuable discussions and supervision.

Special thanks goes to Mogens Henriksen and Asger Jensen, who believed in me since

the beginning.

I am extremely grateful as well with Saeed Rahimi for his help with the modeling part

and his constant guidance, suggestion and valuable input to this work.

I would like to acknowledge the other people who have helped and encouraged me. I

want to thank Braulio Barahona, Morten Lunow, Aleksander Derdowski, Daniel

Villarreal and particularly Ari Bronstein

To Javier, for being the best role model a son can have; to my sisters Lucia and Teresa,

and to my aunts Enriqueta and Silvia.

I also want to thank my friends in Denmark for being with me during these two years,

especially to Lucia, Cris, Mercè, Elie, Xavier, Leo, Andrzej, Bernt, Bing, Carlos, Iván

and Sonsoles. To my friends from Mexico: Ana, Mario, Juan Raul, Evelyn, Mariana,

Miguel, Jorge, Mauricio, Christian and Erick.

Last but not least, I am deeply indebted with Esperanza for her support and concern

during the entire period of my thesis.

http://server.oersted.dtu.dk/staff/person/mlu

http://www.elektro.dtu.dk/forskning/eltek/students/ad.aspx

9

TABLE OF CONTENTS

1 Preface.................................................................................................................... 23

1.1 Background ...................................................................................................... 24

1.2 Objectives ......................................................................................................... 24

1.3 Problem formulation ........................................................................................ 24

1.4 Method and limitations .................................................................................... 25

1.5 Work by others ................................................................................................. 27

1.6 Guide on how to read the report ....................................................................... 30

2 Switching transients .............................................................................................. 33

2.1 Switching transients studies ............................................................................. 33

2.2 Transient recovery voltage ............................................................................... 34

2.3 Inrush current calculations in transformers ...................................................... 35

3 Measurements at Nysted Offshore Wind Farm ................................................. 37

3.1 Nysted Offshore Wind Farm ............................................................................ 37

3.2 Measurements .................................................................................................. 38

3.3 Study cases ....................................................................................................... 41

3.3.1 Case 1. First closing of the line breaker for line A ................................... 41

3.3.2 Case 2. Second closing of the line breaker for line A............................... 45

3.3.3 Case 3. Closing of the breaker on wind turbine A9 .................................. 46

3.4 Analysis of voltage and current measurements ................................................ 49

3.4.1 Voltage dip standards................................................................................ 49

3.4.2 Rms calculations ....................................................................................... 50

3.4.3 Power calculations .................................................................................... 50

3.4.4 FFT in current ........................................................................................... 50

3.5 State of the NWP when the measurements were done ..................................... 53

3.6 Steady state for case 1 and case 2 .................................................................... 55

4 Electrical equipment in simulation programs .................................................... 57

4.1 Network ............................................................................................................ 57

4.2 Wave theory ..................................................................................................... 57

4.3 Switchgear ........................................................................................................ 60

4.3.1 Circuit breaker modeling .......................................................................... 61

4.3.2 Vacuum circuit breaker ............................................................................. 63

4.3.3 Vacuum circuit breaker modeling............................................................. 66

Table of contents

10

4.4 Transformers ..................................................................................................... 67

4.4.1 Simple transformer model ......................................................................... 68

4.4.2 Switching transient studies in transformers............................................... 69

4.4.3 Magnetic characteristic of the transformer ................................................ 71

4.4.4 Simple case simulation .............................................................................. 74

4.4.5 Further inrush current control.................................................................... 87

4.5 High voltage cables........................................................................................... 88

4.5.1 Cable modeling theory .............................................................................. 88

4.5.2 Cable modeling application ....................................................................... 88

4.5.3 Conductive materials ................................................................................. 89

4.5.4 Insulating materials ................................................................................... 90

4.5.5 Grounding .................................................................................................. 91

4.5.6 Sensitivity of transients ............................................................................. 91

4.5.7 Simple case in Power Factory ................................................................... 92

4.5.8 Simple case in PSCAD .............................................................................. 95

4.5.9 Comparison ............................................................................................... 97

4.6 Voltage source .................................................................................................. 98

4.7 Capacitors bank ................................................................................................ 99

4.8 Generator ........................................................................................................ 101

4.9 Summary ......................................................................................................... 103

5 System modeling .................................................................................................. 105

5.1 General procedure ........................................................................................... 105

5.2 Study case 1: Connection of Row A-I ............................................................ 108

5.2.1 Power Factory.......................................................................................... 108

5.2.2 PSCAD .................................................................................................... 114

5.2.3 Transient comparison .............................................................................. 116

5.2.4 Steady state comparison .......................................................................... 132

5.3 Study case 2: Connection of Row A-II ........................................................... 134

5.3.1 Power Factory and PSCAD ..................................................................... 134

5.3.2 Comparison ............................................................................................. 135

5.4 Study case 3: Switch A09 ............................................................................... 138

5.4.1 Power Factory.......................................................................................... 138

5.4.2 PSCAD .................................................................................................... 139

5.4.3 Wind turbine generator ............................................................................ 140

5.4.4 Comparison ............................................................................................. 141

5.5 Worst case switching- voltage ........................................................................ 156

5.6 Worst case switching -current ........................................................................ 156

5.7 Fit traveling time of the voltage wave ............................................................ 157

5.8 Summary ......................................................................................................... 161

Table of contents

11

6 Voltage dip at the PCC, due to the connection of different amount of

transformers at the same time ................................................................................... 163

6.1 Sequence energization .................................................................................... 164

6.2 Simulation in PF ............................................................................................. 166

6.3 Simulation in PSCAD .................................................................................... 169

6.4 Results ............................................................................................................ 172

7 Conclusions .......................................................................................................... 175

7.1 Results- simulation tools ................................................................................ 175

7.2 Results- required information ........................................................................ 176

7.3 Results- simultaneous energization of transformers ...................................... 176

7.4 Perspectives .................................................................................................... 177

7.5 Further work ................................................................................................... 177

A Non-simultaneous pole closing during three-phase transfromer energization in

Power Factory ............................................................................................................. 183

B Second study case plots ........................................................................................... 187

13

LIST OF FIGURES

Figure 1-1 Overview of case 1 and case 2 ...................................................................... 26

Figure 1-2 Overview of case 3 ........................................................................................ 27

Figure 1-3 Overview of sequential energization of transformers ................................... 27

Figure 1-4 Graphic overview of the project.................................................................... 32

Figure 2-1 Comparison of TRVs for cable systems and line-systems, adopted

from (Dufournet & Montillet, 2005) .................................................................... 34

Figure 3-1 Nysted Offshore Wind Farm ......................................................................... 37

Figure 3-2 Measurements locations, adopted from (Christensen, et al., 2007) .............. 38

Figure 3-3 Measurement at wind turbines, adopted from (Christensen, et al.,

2007) ...................................................................................................................... 39

Figure 3-4 Voltage waveforms for study cases. ............................................................. 39

Figure 3-5 Current waveforms for study cases ............................................................... 40

Figure 3-6 Case 1. Voltage 0-250 ms ............................................................................. 41

Figure 3-7 Case 1. Voltage 0-50 ms ............................................................................... 42

Figure 3-8 Case 1. Voltage 4,3-5 ms .............................................................................. 42

Figure 3-9 Case 1. Current 0-250 ms .............................................................................. 43


Figure 3-11 Case 1. Current 4,3-5 ms ............................................................................. 44

Figure 3-12 Case 2. Voltage 20-21 ms ........................................................................... 46

Figure 3-13 Case 2. Current 0-250 ms ............................................................................ 46

Figure 3-14 Case 3. Voltage 0-50 ms ............................................................................. 47


Figure 3-16 Case 3. Voltage and current 2,5-8 ms ......................................................... 48

Figure 3-17 Usual form of voltage change caused by motor starting, adopted

from (ENA, 1989.) ................................................................................................ 49

Figure 3-18 Case 1-A01. Current 0-500 ms ................................................................... 51

Figure 3-19 Case 1-A09. Current 0-500 ms ................................................................... 51

List of figures

14

Figure 3-20 Case 1-A01 and A09. FFT on current ......................................................... 52

Figure 3-21 Active power measurements, 10 min average ............................................. 53

Figure 3-22 Reactive power measurements, 10 min average .......................................... 54

Figure 4-1 Case 1. Voltage phase B 4,3-4,6 ms .............................................................. 60

Figure 4-2 Pre-strike effect in circuit breakers, adopted from (PSCAD User's

Guide, 2005) .......................................................................................................... 65

Figure 4-3 Transformer model used in (Popov, et al., 2001) .......................................... 68

Figure 4-4 Simple transformer equivalent ....................................................................... 68

Figure 4-5 Impedance magnitude and angle of a wind turbine transformer,

adopted from (Pedersen, et al., 2005) .................................................................... 70

Figure 4-6 A very detailed model adopted from (de Leon, et al., 1994) ......................... 71

Figure 4-7 Simple case-transformer. Power Factory system .......................................... 74

Figure 4-8 Simple case- transformer. Single phase a). Voltage, current and

flux. ........................................................................................................................ 75

Figure 4-9 Simple case- transformer. Single phase a). Voltage, current and

flux. 500 ms ........................................................................................................... 76

Figure 4-10 Current- flux characteristic of transformers in Power Factory .................... 77

Figure 4-11 Simple case- transformer. Single phase b). Voltage, current and

flux ......................................................................................................................... 77

Figure 4-12 Simple case- transformer. Single phase c). Voltage, current and

flux ......................................................................................................................... 78

Figure 4-13 Simple case- transformer. Single phase a), b), c), d) e) and f). Zero

crossing (top) and peak crossing (bottom). Voltage and flux ................................ 79

Figure 4-14 Simple case- transformer. Single phase, all. Voltage (top) and flux

(bottom).................................................................................................................. 80

Figure 4-15 Simple case- transformer. Three phase. Zero voltage switching ................. 81

Figure 4-16 Simple case- transformer. Three phase. Peak voltage switching. ............... 82

Figure 4-17 Simple case- transformer. Three phase. With residual flux.

Voltages ................................................................................................................. 83

Figure 4-18 Simple case- transformer. Three phase. With residual flux. Fluxes ............ 83

Figure 4-19 Simple case- transformer. Three phase. With residual flux. Current .......... 84

Figure 4-20 Residual flux and voltages. Left φd=0, φq=-1. Right φd=-1, φq=0 ............ 84

Figure 4-21 PSCAD transformer equivalence................................................................. 85

Figure 4-22 Simple case- transformer. PSCAD .............................................................. 86

Figure 4-23 Simple case-transformer. PSCAD. Results ................................................. 87

List of figures

15

Figure 4-24 Simple case- cable. Power Factory. Network ............................................. 92

Figure 4-25 Simple case- cable. Power Factory. Single core cables .............................. 93

Figure 4-26 Simple case- cable. Power Factory. Three phase cable .............................. 94

Figure 4-27 Simple case- cable. Power Factory. Cable system, basic data .................... 94

Figure 4-28 Simple case- cable. Power Factory. Cable system, EMT

simulations............................................................................................................. 95

Figure 4-29 Simple case- cable. PSCAD. Network ........................................................ 96

Figure 4-30 Simple case- cable. PSCAD. Cable configuration. ..................................... 96

Figure 4-31 Single case- Cable. Comparison ................................................................. 97

Figure 4-32 Capacitor bank .......................................................................................... 100

Figure 4-33 Capacitor bank impedance characteristic .................................................. 101

Figure 4-34 Simple case- Generator. Network ............................................................. 102

Figure 4-35 Simple case- Generator. Rotor speed ........................................................ 103

Figure 5-1 Simplified network for study case 1, 2 and 3 .............................................. 106

Figure 5-2 Case 1. Power Factory. HV network........................................................... 108

Figure 5-3 Case 1. Power Factory. MV network .......................................................... 109

Figure 5-4 Case 1. Power Factory. Sheath network ..................................................... 110

Figure 5-5 Case 1. Power Factory. A01........................................................................ 111

Figure 5-6 Case 1. Power Factory. Cable 50 mm ......................................................... 111

Figure 5-7 Case 1. Power Factory. Cable 50 cm .......................................................... 112

Figure 5-8 Case 1. Power Factory. Separation ............................................................. 112

Figure 5-9 Case 1. Power Factory. Phase voltage B ..................................................... 114

Figure 5-10 Case 1. PSCAD. HV network ................................................................... 115

Figure 5-11 Case 1. PSCAD. MV network .................................................................. 115

Figure 5-12 Case 1. PSCAD. A01 ................................................................................ 116

Figure 5-13 Case 1. Platform voltages (4,3-5,5 ms) ..................................................... 117

Figure 5-14 Case 1. Phase A voltage for each location (4,3-5,5 ms) ........................... 117

Figure 5-15 Case 1. Phase B voltage for each location (4,3-5,5 ms)............................ 118

Figure 5-16 Case 1. Phase C voltage for each location (4,3-5,5 ms)............................ 118

Figure 5-17 Case 1. Platform voltages (4-10 ms) ......................................................... 119

Figure 5-18 Case 1. Platform voltages (4-50 ms) ......................................................... 119

Figure 5-19 Case 1. Platform currents (4-5,5 ms) ........................................................ 120

Figure 5-20 Case 1. Platform currents (4-50 ms) ......................................................... 121

List of figures

16

Figure 5-21 Case 1. A01 currents (0-50 ms) ................................................................. 121

Figure 5-22 Case 1. A01 currents (0-500 ms) ............................................................... 122

Figure 5-23 Case 1. A01 currents FFT .......................................................................... 123

Figure 5-24 Case 1. A09 currents (0-50 ms) ................................................................. 123


Figure 5-26 Case 1. A09 currents (4-6 ms) ................................................................... 124

Figure 5-27 Case 1. A09 current phase B (4-6 ms) ....................................................... 125

Figure 5-28 Case 1. Rms current at platform................................................................. 125

Figure 5-29 Case 1. Rms current at A01 and A09 ......................................................... 126

Figure 5-30 Case 1. Active power at platform .............................................................. 127

Figure 5-31 Case 1. Active power at A01 and A09 ...................................................... 128

Figure 5-32 Case 1. Reactive power at platform ........................................................... 128

Figure 5-33 Case 1. Reactive power at A01 and A09 ................................................... 129

Figure 5-34 Case 1. Rms voltage at platform ................................................................ 130

Figure 5-35 Case 1. Rms voltage from measurements .................................................. 131

Figure 5-36 Case 1. Rms voltage from Power Factory .................................................. 131

Figure 5-37 Case 1. Rms voltage from PSCAD ............................................................ 132

Figure 5-38 Case 1. Power Factory. Steady state .......................................................... 133

Figure 5-39 Case 2. Platform voltages (20-22 ms) ....................................................... 135

Figure 5-40 Case 2. Platform currents (20-70 ms) ........................................................ 136

Figure 5-41 Case 2. A01currents (10-70 ms) ................................................................ 136


Figure 5-43 Case 2. Rms voltage at platform ................................................................ 137

Figure 5-44 Simplified network for study case 3 .......................................................... 138

Figure 5-45 Case 3. Power Factory. MV network. ....................................................... 139

Figure 5-46 Case 3. PSCAD. Induction generator ........................................................ 140

Figure 5-47 Active power characteristic of induction generator ................................... 141

Figure 5-48 Reactive power characteristic of induction generator ............................... 141

Figure 5-49 Case 3. Phase A voltage for each location (2-6 ms) .................................. 142

Figure 5-50 Case 3. Phase B voltage for each location (2-6 ms) .................................. 143

Figure 5-51 Case 3. Phase C voltage for each location (2-6 ms) .................................. 143

Figure 5-52 Case 3. A01 voltages (2-6 ms)................................................................... 144


List of figures

17

Figure 5-54 Case 3. A01 currents (300-400 ms) .......................................................... 145

Figure 5-55 Case 3. A09 currents (0-400 ms) .............................................................. 145

Figure 5-56 Case 3. A09 currents (0-50 ms) ................................................................ 146

Figure 5-57 Case 3. A09 currents (2-7 ms) .................................................................. 146

Figure 5-58 Case 3. Phase B currents in A09 (2-7 ms) ................................................ 147

Figure 5-59 Case 3. Rms currents at platform .............................................................. 147

Figure 5-60 Case 3. Rms currents at A01 and A09 ....................................................... 148

Figure 5-61 Case 3. Active power at platform.............................................................. 149


Figure 5-63 Case 3. Influence of generators inertia in active power at platform ......... 151

Figure 5-64 Case 3. Reactive power at platform .......................................................... 153

Figure 5-65 Case 3. Reactive power at A01 and A09 .................................................. 153

Figure 5-66 Case 3. Rms voltage at platform................................................................ 154

Figure 5-67 Case 3. Rms voltage from measurements.................................................. 154

Figure 5-68 Case 3. Rms voltage from Power Factory ................................................. 155

Figure 5-69 Case 3. Rms voltage from PSCAD............................................................ 155

Figure 5-70 Worst case switching at peak voltage ....................................................... 156

Figure 5-71 Worst case switching at zero voltage ........................................................ 157

Figure 5-72 Fit traveling time of voltage wave. Power Factory. Relative

permittivity. ......................................................................................................... 158

Figure 5-73 Fit traveling time of voltage wave. Power Factory. Frequency. ............... 158

Figure 5-74 Fit travelling time of voltage wave. Comparison ...................................... 160

Figure 6-1 Overview of sequential energization of transformers ................................. 163

Figure 6-2 Sequencial energization. Power Factory. Saturation exponent. .................. 164

Figure 6-3 Sequence energization. Power Factory. Vzero A01-A09 ........................... 166

Figure 6-4 Sequence energization. Power Factory. Vzero ........................................... 167

Figure 6-5 Sequence energization. Power Factory. Vpeak ........................................... 167

Figure 6-6 Sequence energization. Power Factory. Row B .......................................... 168

Figure 6-7 Sequence energization. Power Factory. Residual flux ................................ 168

Figure 6-8 Sequence energization. Power Factory. Reduced grid ................................ 169

Figure 6-9 Sequence energization. PSCAD. Vzero ...................................................... 170

Figure 6-10 Sequence energization. PSCAD. Vpeak ................................................... 170

Figure 6-11 Sequence energization. PSCAD. Vzero. Rms each cycle ......................... 171

List of figures

18

Figure 6-12 Sequence energization. PSCAD. Vpeak. Rms each cycle ......................... 171

Figure 7-1 Non-simultaneous pole closing with 0,02 ms apart ..................................... 184

Figure 7-2 Non-simultaneous pole closing with 2 ms apart .......................................... 184


Figure 7-4 Non-simultaneous pole closing with 5 ms apart .......................................... 185


Figure 7-6 Case 2. Phase A voltage for each location (20-22 ms) ................................ 187

Figure 7-7 Case 2. Phase B voltage for each location (20-22 ms) ................................ 187

Figure 7-8 Case 2. Phase C voltage for each location (20-22 ms) ................................ 188

Figure 7-9 Case 2. Phase A voltage for each location (20-20,5 ms) ............................. 188



Figure 7-12 Case 2. Platform currents (20-22 ms) ........................................................ 190

Figure 7-13 Case 2. A01currents (0-500 ms) ................................................................ 190


Figure 7-15 Case 2. A09 currents (20-21,5 ms) ............................................................ 191

Figure 7-16 Case 2. A09 current phase A (20-21,5 ms)................................................ 192

Figure 7-17 Case 2. A09 current phase B (20-21,5 ms) ................................................ 192

Figure 7-18 Case 2. Platform current (400-500 ms) ..................................................... 193

Figure 7-19 Case 2. Rms currents at platform ............................................................... 193

Figure 7-20 Case 2. Rms currents at A01 and A09 ....................................................... 194

Figure 7-21 Case 2. Active power at platform .............................................................. 194


Figure 7-23 Case 2. Reactive power at platform ........................................................... 195

Figure 7-24 Case 2. Reactive power at A01 and A09 ................................................... 196

Figure 7-25 Case 2. Rms voltage from measurements .................................................. 196

Figure 7-26 Case 2. Rms voltage from Power Factory .................................................. 197

Figure 7-27 Case 2. Rms voltage from PSCAD ............................................................ 197

19

LIST OF TABLES

Table 3-1 Harmonic current ratio ................................................................................... 52

Table 3-2 Steady state (0,5 s) for case 1 and case 2 ....................................................... 56

Table 4-1 Modeling guidelines adopted from (CIGRE, 1998) ....................................... 63

Table 4-2 Accepted values for equation (4.10)............................................................... 67

Table 4-3 Color nomenclature. Three phase, without residual flux. .............................. 81

Table 4-4 Color nomenclature. Three phase, with residual flux .................................... 82

Table 4-5 Material properties in cables .......................................................................... 89

Table 4-6 XLPE relative permittivity ............................................................................. 90

Table 4-7 Simple case- cable. Information ..................................................................... 92

Table 5-1 Input information and models in both simulation tools ............................... 107

Table 5-1 Case 1. Power Factory. Cable 50 mm .......................................................... 111

Table 5-2 Case 1. Power Factory. Cable 50 cm............................................................ 112

Table 5-3 Case 1. Power Factory. Pre-strike times....................................................... 113

Table 5-4 Case 1. Active and reactive power during the first cycle. ............................ 129

Table 5-5 Steady state values (at 25 cycles) for current and voltages .......................... 134

Table 5-6 Steady state values (at 25 cycles) for real and reactive power ..................... 134

Table 5-7 Reactive power comparison in MVAr .......................................................... 152

Table 6-1 Times for sequencial energization in seconds .............................................. 165

Table 6-2 Sequence energization results ...................................................................... 172

Table 7-2 Color nomenclature for appendix A ............................................................. 183

Table 7-3 Non-simultaneous simulation cases ............................................................. 183

21

LIST OF SYMBOLS

Symbol Unit Definition

C F Capacitance

G S Conductance

L H Inductance

R Ω Resistance

φd p.u. Residual flux in d-axis

φd p.u. Residual flux in q-axis

22

LIST OF ABBREVIATIONS

Abbreviation Meaning

CB Circuit breaker

CIGRE International Council on Large Electric Systems

DAQ Data acquisition

emt Electromagnetic transient

EMTP The Electromagnetic Transients Program

FFT Fast Fourier Transform

HF High frequency

HV High voltage

IEC International Electrotechnical Commission

IEEE Institute of Electrical and Electronics Engineers,

LV Low voltage

MV Medium voltage

NOWF Nysted Offshore Wind Farm

p.u. Per unit

PCC Point of common coupling

Power Factory Power Factory/DIgSILENT

PSCAD PSCAD/HVDC

rms Root mean square

TOV Transient Overvoltage

TRV Transient recovery voltage

UK United Kingdom

VCB Vacuum circuit breaker

WT Wind turbine

WTs Wind turbines

23

1 PREFACE

The offshore wind power in the UK is expected to increase largely in the following

years. In his first environmental policy speech in November 2007, Prime Minster

Gordon Brown announced that the present British reduction target for CO2 emissions

might have to be raised by 2050. This legislative objective promotes the increase of

renewable energy in the UK, and since wind energy is the most technically mature and

cost-effective of the new energies, it is predicted that the amount of wind power will

increase rapidly during the coming years.

So far there have been two calls for bids to develop UK offshore wind sites, known as

Round 1 and Round 2. The first phase‟s successful applicants were announced in 2001,

with leases awarded for 18 sites at 13 locations. In this pilot phase the sites were limited

to a maximum of 30 turbines. In 2003 the final results of Round 2 were announced, with

the right to develop 15 sites totaling 5,4-7,2 GW awarded to 10 companies or consortia.

Round 2 sites are larger than Round 1 sites and will utilize more powerful machines, at

greater distance from shore, with no maximum limit of turbines. Some of the sites are as

big as 1 GW.

The 90 MW Burbo Bank park of DONG Energy was connected last October. DONG

Energy will also build and operate the two offshore wind parks Walney Island with 151

MW and Gunfleet Sands with 173 MW off the British coast by 2010.

According to the British Engineering Recommendations P28, the voltage fluctuation at

the point of connection with the grid may be required to be as low as 3% during the

energization of a motor; and since the energization of a transformer is similar to the

direct-on-line starting of induction motors, this recommendation automatically applies

to the transformers.

For the thesis, site measurements of three switching operations in Nysted Offshore

Wind Farm were used to implement a digital model of the collection grid in Power

Factory and PSCAD. Then, the results from the switching operations in both programs

were compared to the measurements with acceptable agreement.

Finally, once the models have been verified, different combinations of transformers

were switched-in at different times, and the voltage drop at the point of common

coupling was compared. In general, the results from Power Factory regarding two

Preface

24

energizing sequences were contradictory, since a large voltage dip was present ever

though the inrush current had not increase dramatically.

Finally, a comparison of both programs was created for electromagnetic transient

simulations; as well as guidelines to energize the collection grid in large wind farms and

a list of information required for switching transient studies.

1.1 Background

The collection grid of large offshore wind farms are especially vulnerable to switching

operation, due to the electrical environment assemble in the sea. And since the wind

power plants are expected to increase in size and investment, the industry is particularly

interested in the prediction of possible risks to protect their wind farms.

The problem with switching transient studies is that the information needed for almost

every electrical device is very detailed, and the manufacturers are unwilling to provide

this information to the system designer.

On the other hand, there are grid requirements that the wind power plant has to comply

in order to connect with the network. This grid codes are defined by the Transmission

System Operator of each country, and some of them are not updated to regulate

correctly the operation of large wind power plants.

1.2 Objectives

The main aim of this thesis was to simulate three switching events in two simulation

programs and compare the results with measurements. Once the models were validated,

an assessment on the voltage dip due to the sequential energization of different amount

of wind turbine transformers was prepared, in order to create general guidelines to

energize the collection grid in large wind farms.

Another important goal of this thesis was to compare Power Factory and PSCAD for

electromagnetic transient simulations. In addition to this, it was also fundamental to

catalog the critical component data required for switching transient studies.

1.3 Problem formulation

The offshore wind farms are expected to increase in size and power; so far, there have

been successful applications in Denmark and the UK. However, the best way for

protection and risk assessment, is the accurate prediction of possible occurrences. On

this basis the project answers the following questions:

Are there major differences in the results from electromagnetic transients in

Power Factory and PSCAD?

How good can the simulation programs predict the transient behavior in cables

during energization?

Preface

25

What information is needed to simulate the possible events in the switchgear?

How accurate are the models for transformers, and what other information

would be relevant to obtain from the manufacturer for transient studies?

How good does the voltage dip, caused by the energization of a transformer, is

simulated in Power Factory and PSCAD?

1.4 Method and limitations

In order to create the digital network of Nysted Offshore Wind Farm, the available

information from each component had to be found and compare. This was a

complicated task since this wind power plant was installed in the year 2003, and some

changes were done from the first draft of the wind farm to the actual installation.

Then, based on the measurements log, relevant switching operations were selected as

the study cases to be simulated and compared between the two programs. Once the

events were selected, the state of the system was deduced from the available

measurements and the experience of the operator.

Afterwards, the standard models in Power Factory and PSCAD for the electrical devices

connected in the study cases were compared in both programs. Subsequently, three

study cases were simulated and compared in Power Factory and PSCAD. Just then, with

acceptable correspondence between the results from both digital systems and the

measurements, the voltage dip was assessed.

Since the results from the simulations were compared with measurements, it was

assumed from the beginning that the measurements were correct. As the comparison

from the third study case showed, the uncertainties of the measurement system are less

than 2%.

The measurement data and the results from the simulations were analyzed and

compared in MATLAB; here predefined subroutines and commands were used for the

analysis, but in general all the necessary code was created.

One very important value not available from the datasheets was the open circuit

characteristic of the transformer; however after several simulations using estimated

values, a saturated reactance was found to give similar results as the measurements. At

this stage it was also assumed that all transformers in the simulations had the same

characteristics. This was a reasonable assumption since no additional information was

available.

As explained further in the document, the pre-strike phenomenon in the vacuum circuit

breaker was not simulated, since there was no information about the breaker and the

time for the project was limited.

Preface

26

The residual flux in the transformer model in PSCAD was not used, since the scenario

for sequence energization of transformers with residual flux is not a realistic situation in

Nysted Offshore Wind Farm.

All the models used in Power Factory and PSCAD are standard models without

additional control parameters, or dynamic properties beside the transient phenomenon

simulated.

Every time a problem occurred in both simulation programs, the support team from each

program helped as much as they could, and the results presented here are the final

outcome after many preliminary simulations. However, one of the main objectives of

the project was to compare Power Factory and PSCAD for electromagnetic transient

studies, and some limitations were noticed for both simulation tool.

In general three systems were created from scratch in each program. The model for the

first and second study case is shown in Figure 1-1. The third study case is shown in

Figure 1-2, and the Figure 1-3 presents the network for the sequencial energization. In

these three figures the equipment in red color are the energized devices and the

equipment in black color are the non-energized devices prior to the switching event.

Additional discussion on each study case and modeling procedure was done further in

the report.

Figure 1-1 Overview of case 1 and case 2

Preface

27

Figure 1-2 Overview of case 3

Figure 1-3 Overview of sequential energization of transformers

1.5 Work by others

Switching transient studies in large offshore wind farms using PSCAD have been done

before in (Liljestrand, Sannino, Breder, & Thorburn, 2008), while in (R. King, 2008) the

simulation program used is EMTP-RV. In both papers the pre-strike during cable

energization, within the breaker is modeled. Sørensen, in (Sørensen, et al., 2007),

models the cable energization in Power Factory corresponding to the first case study of

this thesis. Abdulahovic, in (Abdulahovic & Thiringer, 2007) simulated, the

energization of a wind park radial (in the current project the radials in the wind farms

Preface

28

were referred to as rows). In this paper, the comparison between simulations and

measurements of the energization of a MV cable with several wind turbines is done,

with reasonable agreement between simulations and measurements.

Liljestrand concluded that the electrical stress on transformers during transients depends

on the wave propagation in the collection grid and their location in the system. King

focused on the voltage reflections and cable charging currents.

Sørensen conluded that there are some limitations in Power Factory when modeling

cables for switching transients studies. This paper is highly practical, with little

emphasis on theory, but it is the starting point for this project. In the paper, the authors

initially simulated with the basic equipment models; a lumped () parameter model for

the cables, a switch for the circuit breaker and a T-equivalent for the transformers.

Then, the frequency for fitting the distributed line parameter model with constant

parameters was calculated. Afterwords, an FFT on the simulated current with the

lumped model is made to identify the resonant frequency (1959 Hz).

Once the model is updated, the switching event is repeated. In the simulation results

they found a problem with the appearance of a voltage on phases that were not

connected yet.

Finally, they included a HV-ground capacitance in the transformer model to obtain the

current peaks that have been seeing on the measurements when the voltage waves arrive

at each transformer. At this stage they estimate a capacitance value and conclude that

the current peaks are very sensitive to this parameter.

The current project is important because no work has been done to compare the

behavior of standard models of electrical devices in offshore wind farms in both Power

Factory and PSCAD. Neither simulations nor measurements had been compared for

these very large wind farms when high quality measurements have been available.

Some work regarding the voltage dip due to sequential energization of different number

of transformers in wind farms has been carried out before in (Ma & Cadmore, 2006),

(Smith, 2005) and (Abdulahovic & Thiringer, 2007). In (Rioual & Sow, 2008) a study

of symathetic interaction during transformer‟s energization in wind farms was realized.

Ma investigated possible solutions to the fulfillment of the UK recommendations for

voltage dips in (Ma & Cadmore, 2006). Here, two types of transformers were compared

in two different sites (2x10 turbines and 1x17 turbines):

The standard design transformer with 7,35 p.u. peak current and 1,6 s to damped

the current.

The special design transformer with 4,04 p.u. peak current and 1 s to damped the

current.

Preface

29

For the study, site measurements were done to implement a realistic model in PSCAD.

Once the model in PSCAD has been verified, different amount of transformers are

switched in at the same time, and the voltage drop is compared at 0 ms and 30 ms.

The study results show that:

1. The higher the inrush current magnitude, the higher the voltage dips.

2. Voltage dips decrease when the number of transformers energized

simultaneously is reduced.

3. The energization inrush current is more rapidly damped when there are no

initially energized transformers than with formerly energized transformers.

4. The slow decay of the inrush current with initially energized transformers

prolongs the voltage dip.

5. The voltage dip increases if the voltage of one phase is around zero, when the

system is energized and the three phases are energized non-simultaneously.

Smith investigated the transient inrush current and system voltage drop during the

energization of wind turbine transformers, based on PSCAD simulations, in (Smith,

2005). Here, a generally accepted “worst case” scenario for transformer energization is

presented, where residual flux might be expected upon a random energization (-80%

one phase, +80% second phase and third phase zero).

The author compares two wind farms, one with 15 wind turbines (WTs) connected via a

33 kV and the second with 52 WTs at 33 kV divided in collection rows of nine WTs,

with two parallel step-up transformers to the 132 kV grid.

From the simulations it was found that in order to fulfill the P28 requirements at the

point of common coupling (PCC), fewer transformers could be energized

simultaneously at the smaller capacity wind farm with a 33 kV grid connection.

On the 52 WTs study case, a sympathetic inrush current assessment is made. Here nine

WT transformers are energized simultaneously with only one incoming transformer in

service, while the rest of the wind turbine transformers are on-line; this way achieving

the strongest sympathetic interaction between transformers. The event is made at zero

degrees switching angle and 0,8 pu residual flux. A “sympathetic magnetizing current”

in the on-line transformer around 12 cycles after switching is achieved.

Abdulahovic compared measurements and simulation results from PSCAD during the

energization of a wind park radial in (Abdulahovic & Thiringer, 2007). Here, the master

library components from PSCAD are used for the simulations. The authors divided the

transient event into the phenomena cable energization, followed by the transformer

magnetization. The measurements also show that the voltage rises slightly due to the

reactive power generated by the cable capacitance, at steady state.

Rioual and Sow used EMTP as a simulation tool in (Rioual & Sow, 2008), where the

phenomena of sympathetic interactions between transformers is present. Here, several

transformer are energized simultaneously, then the voltage dip and overvoltage are

calculated.

Preface

30

In the case where five transformers are energized sequentially, with a time delay of 4

seconds between each other, they concluded that due to sympathetic interaction, one of

the transformers is stressed five times during the total energizing procedure. They also

showed that the same transformer experience four times an offset in flux, which causes

high inrush sympathetic-currents. Another important contribution of this sequential

energization simulation is that the voltage dip increases as the energizing sequence

progresses.

Regarding the transformer energization, the current thesis is important because there are

three measurement cases used to compare the transformer characteristics and

realistically approximate and assess the voltage dip.

A very detailed modeling in PSCAD and experimental verification was done in (Daniel

& Gebre, 2008) for transformers and cables commonly used in offshore wind farms.

Here a comprenhensive explanation of the transient phenomena in VCBs, cables and

transformers was made.

For the cables, it was explained that the model that should be used in PSCAD for

switching transients is the “Frequency dependant (phase) model”. A step voltage on

different cables was measured to compare the simulations, obtaining a good agreement.

It was found that additional stray component need to be included in the models, in order

to obtain better results. It was also found that there is faster damping in the cables than

estimated in the simulation.

Regarding the VCB several simulations were done based on (Kondala & Gajjar, 2006)

but no comparison with measurements was made.

The work on the transformer modeling was very extensive; it achived agreement

between measurements, calculations and simulations of the transformer impedance

characteristic.

1.6 Guide on how to read the report

The project is divided in six main sections;

2) Switching transient

3) Network and measurements description

4) Electrical equipment explanation and comparison

5) System modeling

6) Voltage dip due to transformer energization sequence

7) Conclusions

The second section pre1sents some important definitions regarding the switching

transient studies. Here relevant information from current research and industrial

applications was gathered.

Preface

31

The collection grid at Nysted Offshore Wind Farm (NOWF) and the state of the system

under the measurement campaign is presented on the third section. Here the

measurements and study cases were explained and compared.

The electrical equipment in the collection grid of NOWF is presented and explained in

the fourth section. The main phenomena occurring during transient conditions and the

simulation methods used to represent switchgear, medium voltage cables, transformers,

induction generators and capacitor banks in Power Factory and PSCAD are explained.

Then, a comparison between Power Factory and PSCAD was made for some

component, with a simple case simulation.

After the model of each electrical device is understood and compared between Power

Factory and PSCAD, the collection grid of NOWF was created. In the fifth section, the

procedure to create the network in Power Factory and PSCAD is explained step by step.

Also in this section, the comparisons for each study case are presented between the

measurements and the simulation results from both Power Factory and PSCAD.

Once the simulations were done with the available information, additional models were

created to compare worst-case scenarios for both voltage and current switching to

previous study cases. In the last model the velocity of the travelling voltage wave was

“fitted” to the measurements.

In the sixth section the voltage dip when different number of transformers are being

energized simultaneously was simulated in Power Factory and PSCAD. Here, the

maximum number of transformers energized simultaneously while complying with the

UK grid code requirements was calculated.

The last section presents the conclusions of the overall project. Here, a comparison

between simulation softwares was made. In this section, a summary of the available and

necessary information to realize switching transients was presented. At last,

recommendations regarding the simultaneous energizing of different amount of

transformers were stated, as well as possible solutions.

Figure 1-4 shows graphically the overall project contents. The five main electrical

devices that compose the collection grid are shown, as well as the voltage source that

accounts for the connection to the transmission grid.

The colored rings represent layers of analysis for each device, where the first ring

encloses the theory and simulation basis, the second and third rings represent the Power

Factory and PSCAD simple-case simulations, the fourth ring corresponds to the

network simulation and comparison with measurements. The last ring contains the

voltage dip simulation due to transformer energization.

Preface

32

Figure 1-4 Graphic overview of the project

Switching transients

33

2 SWITCHING TRANSIENTS

Switching transients are caused by the operation of breakers and switches in a power

system. The switching operations are divided in two main categories: energization

phenomena and de-energization of the system elements.

Due to the complexity of the mathematical representation of the equipment involved,

digital simulation using electromagnetic transient (emt) simulation programs has a

major importance in the study of switching transients. Results from such studies are

useful for:

Overvoltage calculation

Insulation coordination

Transient recovery voltage (TRV) across circuit breakers

Transient mitigation devices

Inrush current calculations in transformers

Switching during normal operation, as well as during faults and outages, are the most

important switching conditions to consider, in a insulation coordination study for the

collection grid in an offshore wind farm.

Damaging switching operations depend to a large extent on the behavior of the

switching devices. Therefore, after a study, the system designer should verify with the

manufacturers that the electrical devices can withstand the calculated stress. At this

stage, the amplitude as well as the maximum rate-of-rise of the voltage are essential

parameters.

In the collection grid of offshore wind farms, the combination of vacuum circuit

breakers, cables, and transformers causes high-voltage high-frequency transients that

are suspected of contributing to the transformer failure in Middelgrunden (Larsen,

Sørensen, Christiansen, Naef, & Vølund, 2005) and Horns Rev (Sweet, 2004).

2.1 Switching transients studies

There are some modeling requirements that switchgear devices should comprise for

switching transients studies (Rashidi, et al., 2003):

Protection delay or clearing times

Maximum fundamental frequency switching voltage

Maximum capacitive switching capabilities


34

Reclosing sequence and whether they will be used

Rated TRV and maximum rate of rise of TRV

Mechanical closing time and variation in pole closing time. This is important if

point-in-wave closing is to be investigated

In practice, due to the secrecy of product development, there is no way of directly

comparing vacuum circuit breakers between manufacturers, except for the transient

recovery voltage (TRV).

2.2 Transient recovery voltage

According to the IEEE, the recovery voltage is the voltage that appears across the

terminals of a pole of a circuit breaker after interruption. This voltage can be considered

in two successive time intervals: one during which a transient voltage exists (TRV),

followed by a second during which a power frequency voltage alone exists (IEEE

Application Guide for Transient Recovery Voltage for AC High-Voltage Circuit

Breakers). There is ongoing work for the harmonization of TRVs in IEEE and IEC

Standards for AC high-voltage circuit breakers rated less than 100 kV.

In order to cover all types of networks in the range of rated voltage higher than 1 kV

and less than 100 kV the revision of the IEC 62271-100 has defined two types of

systems (Dufournet & Montillet, 2005): Cable systems and line systems. Both systems

have a TRV during a breaking of terminal fault at 100% of short-circuit breaking

current that does not exceed the two-parameters enveloped in the standard. Figure 2-1

shows the comparison of the TRVs for cable-systems and line-systems based on IEC

62271-100. It can be seen that the rise of recovery voltage (RRRV) for line-systems is

approximately twice the value for cable systems.

Figure 2-1 Comparison of TRVs for cable systems and line-systems, adopted from

(Dufournet & Montillet, 2005)


35

According to (Kondala Rao & Gajjar, 2006), it is posible for a generic model of VCB to

simulate current chopping, re-ignitions, virtual current choping and pre-strikes if certain

values are known. Some of the most important values are:

Rate of Rise of Restriking Voltage

Rate of Rise of Dielectric Strength

However, in reality it‟s impossible to obtain any of these values from the manufacturer.

Most of the time, circuit breakers are considered as ideal breakers for switching

transient studies focusing mainly on low voltage phenomena. The closing time of the

poles is normally simplified to simultaneous closing, where in reality the non-

simultaneous phenomenon is possible. To widen the switching transient studies,

variation on point-in-wave could be included.

2.3 Inrush current calculations in transformers

Transformer energization is a common occurrence in any electric power system. Most

of the time, energization results in the transformer needing a large inrush current, which

eventually decreases to a small magnetizing current. The length of time the transformer

demands the inrush current depends on the impedance of the system, including the

transformer characteristics.

The inrush current could cause a temporary voltage drop due to the impedance of the

system between the source and the energized transformer. If the short circuit MVA

available at the transformer bus is low, the resulting voltage drop can be significant.

Short duration voltage drops that are caused by faults or large inrush currents are called

voltage dips (IEC) or sags (IEEE).

The magnitude of the inrush current is a statistical variable depending on where on the

sinusoidal voltage curve the circuit breaker connects the transformer to the source. The

highest inrush current occurs when the circuit breaker connects the transformer, when

the voltage passes through zero.

Modern transformers tend to have higher inrush currents compared to transformers built

40 years ago. The reason for this is that modern low-loss core steel allows higher flux

densities in the core without unacceptable high core temperature as consequence.

In offshore wind farms, the system designer is more concered about the losses in the

transformer, due to its high costs, than in the transient phenomena. However, grid

requirements in the UK limit the voltage dip to 3% when an induction machine is

started, and this requirement is simply applied to transformer energization (ENA, 1989).

No standard update has been made for wind turbine transformer energizing or park

transformer energizing.


36

In practice, a study to assess the voltage dip due to transformer energization or inrush

current ratings would take into account point-in-wave switching, as well as different

levels (low/high) of residual flux in the transformer core.

In the last section of the project, some recommendations are included regarding the

available and required information to realize switching transient studies in offshore

wind farms.

37

3 MEASUREMENTS AT NYSTED OFFSHORE WIND FARM

Once the switching transients studies had been define, the measurements done in the

collection grid at Nysted Offshore Wind Farm (NOWF) are presented in this section.

The state of the system under the measurement campaign is presented as well. Here the

measurements and study cases are explained and compared.

3.1 Nysted Offshore Wind Farm

The wind farm is installed in the year 2003 and it‟s operated by DONG Energy who

owns 80% of the farm, while E.ON owns 20%. It consists of 72 wind turbines (WTs)

with a rated power of 2.3 MW. The turbines are arranged in a parallelogram, formed by

eight rows with nine WTs each. Figure 3-1 shows the arrangement. The WTs are

delivered by former Bonus, now Siemens Wind Power.

Figure 3-1 Nysted Offshore Wind Farm

The WTs are connected in “rows” of 36 kV submarine cables. Each row is then

connected to the platform by one “root” cable. The park transformer (180/90/90 MVA,

132/33/33 kV) is in the central position. Each feeder is connected by a VCB, followed

by the root cable. There are eight rows, from A to H, where A, B, C and D are

connected to one MV winding, and E, F, G, and H to the other MV winding.

The submarine cable is connected on the bottom of each WT where the armor and the

shield of the cables are grounded. Then the transformer (2,5 MVA, 33/0.69 kV) is

connected via switch disconnector-fuse on the MV. On the LV side of each transformer

Measurements at Nysted Offshore Wind Farm

38

only the capacitor bank to compensate the induction generator and a small load were

included in some of the simulations.

The WTs are interconnected with 36 kV cables of 505 m of length. Furthermore, the

HV grid (132 kV), sea cable (10.5 km) and land cable (18.3 km) were included in the

models.

During the entire document, the base voltage and current for per unit calculation was the

rms and not the emt magnitude, since the emt uses the amplitude of the waveform.

The voltage at the three measurement locations is the same (33 kV), while the base

current depends on the location. For the platform the nominal current of the cables was

used (420 A) as base current, while for the measurements in A01 and A09 the nominal

current of the transformer was used (43 A).

3.2 Measurements

A novel GPS synchronized measuring system for MV equipment to document high

frequency transients, was developed and installed in NOWF, Denmark (Christensen, et

al., 2007). Three voltages and three current were sampled at 2.5 MHz, in three different

locations in the network simultaneously and synchronized via GPS. The measuring

points can be seen Figure 3-2 and were located at:

The transformer platform after the circuit breaker from radial A

The wind turbine A01, the first turbine of the radial A

The wind turbine A09, the last turbine of the radial A

Figure 3-2 Measurements locations, adopted from (Christensen, et al., 2007)

Several switching transients were generated and recorded, but only the opening and

closing of the line breaker for radial A and the load breaking switch in turbine A09 were

covered in this work. In WTs A01 and A09, the measuring equipment was placed

between the MV switchgear and the transformer, as showed in Figure 3-3.


39

Figure 3-3 Measurement at wind turbines, adopted from (Christensen, et al., 2007)

The measurements to be replicated in Power Factory and PSCAD as study cases are

shown in the next subsection. The two first cases where the row A was energized (7 km

of cables and nine wind turbine transformers (WTT)) and then the third case where only

the last WTT (A09) of row A was energized, with seven other wind turbines under

production in the same row. The voltage for the three cases is shown in Figure 3-4.

Figure 3-4 Voltage waveforms for study cases.

In this figure, the top plot is the voltage at the platform during the initial 50 ms of the

recording of the first study case. The plot in the middle is the voltage at the platform

during the initial 50 ms of the recording of the second study case. The bottom plot is the


40

voltage at the wind turbine A09 during the initial 50 ms of the recording for the third

study case.

It can be seen in the second study case, that the voltage reaches 2 p.u. and has higher

oscillations after the switching occurred. In theory the system should be the same, only

the point-in-wave has changed. In the second case the voltage of phase A (Va) is closer

to the peak voltage than in the first study case.

In the third study case, it can be seen that the time between pole closing is larger than in

the first two cases. This is because in each WT, the breaker before the transformer is not

a vacuum- circuit breaker (VCB) but an air-blast breaker.

In the bottom plot of Figure 3-4 it can be seen as well some oscillation on the voltage

phase A (Va) when phase C and B has been connected. This oscillation could be caused

by the delta connection in the primary side of the wind turbine transformer. Since the

transformer is a three-phase core-type transformer; where the vector sum of the flux

should be zero at any time. Hence, in phase A some voltage might be induced.

The inrush currents for each study case are presented in Figure 3-5. Here the top plot is

the current at the platform during the initial 250 ms of the recording from the first study

case. The plot in the middle, is the current at the platform during the initial 250 ms of

the recording from the second study case. The bottom plot, is the current at the wind

turbine A09 during the initial 50 ms of the recording for the third study case.

Figure 3-5 Current waveforms for study cases

The current in the second and third case presents a flat top. This is due to measurement

errors. It‟s important to remember that 1 p.u. in the platform represents 420 A, while 1

p.u. in A09 is only 43 A.


41

Before the inrush current starts to flow, some current energize the MV cable. Deeper

analysis was done for each study case further in the thesis. At this stage it is important

to notice how the point-in-wave is very important for the inrush current. This can be

seen in the first and second case, since they are essentially the same system, but for the

initial cycles the current peaks are higher in the second study case.

From Figure 3-4 can be seen the difference in the switching angle for each study case.

In the first case the switching occurred before the voltage of phase B (green) reached a

negative peak value. In the second case the switching occurred after the voltage of

phase A (blue) reached a negative peak value. Finally, in the third case the switching

occurred almost when the voltage of phase C (red) reached a negative peak value

In the first two cases “half-wave-current” appears when the switching occurs, this are

due to the appearance of electric arcs in the switchgear. While the current spikes in A01

and A09 are caused by stray capacitances in the transformers.

3.3 Study cases

Once the study cases have been mentioned, the following subsection presents each

study case in detail.

3.3.1 Case 1. First closing of the line breaker for line A

The voltage measured in the three locations (platform, A01, A09) from 0 s to 0.25 s are

shown in Figure 3-6. Here it can be seen that, there are some transient overvoltages

(TOVs) at the beginning of the waveform. These are caused by reflections in the cables

that attenuates during the first milliseconds.

Figure 3-6 Case 1. Voltage 0-250 ms


42

If a zoom is made for the first 50 ms it can be seen that the transient due to the cable

energizing and reflections disappears in less than 50 ms after the closing (Figure 3-7).


If the voltage is visualized only from 4.3 ms to 5 ms the traveling wave can be analyzed.

In Figure 3-8 it can be seen how the voltage travels from the platform to the last wind

turbine (A09) in 45 μs and 45 μs later returns to the platform almost doubling the

voltage. It can be also seen that there is no simultaneous-pole-closing in the circuit

breaker on the platform.

Figure 3-8 Case 1. Voltage 4,3-5 ms


43

If the cable between the platform and the last wind turbine is 7 km, and it takes 45 μs to

the voltage wave to arrive, the velocity of the wave would be 157 km/s, 52% of the

speed of light (300 km/s) (Sørensen, et al., 2007). The same phenomena can be seen in

phase A and phase C.

From the voltage shape of phase B on A09, a doubling of the voltage can be recognized.

This occurred when an open-circuited line is energized, and the magnetic energy

associated with the current disappears when the current is brought to zero at the open

circuit. It reapers as electric energy, which manifest itself in the voltage increase

(Greenwood, 1991).

The current measured in the three locations from 0 s to 0.25 s is showed in Figure 3-9.

Here can be clearly seen two phenomena occurring: the cable energizing at the

beginning, followed by transformer energizing.

Figure 3-9 Case 1. Current 0-250 ms

If a zoom is made for the first 50 ms, it can be seen that the transient due to the cable

energizing disappears in less than 10 ms (Figure 3-10).

In Figure 3-10 a flat region on the phase C of the current on A01 can be seen. The value

present here is 2.858 pu (125 A), this is a measurement error due to the specified input

range in the data acquisition (DAQ) software, since the Rogowski-coil sensor used has a

peak current of 600 A (Christensen, et al., 2007).


44


Figure 3-11 Case 1. Current 4,3-5 ms

If the currents are visualized only from 4.3 ms to 5 ms (Figure 3-11), it‟s possible to see

current spikes with a value lower than 1 p.u., for less than 1 ms in A01 and A09, when

the voltage waves (Figure 3-8) arrive to each transformer. This is due to the charging of

capacitances in the MV transformer in the WTs. This phenomena has been reproduced

by (R. King, 2008) and (Sørensen, et al., 2007). This can be explain simply by the

instantaneous current caracteristc of the capacitor:

dv

i Cdt

(3.1)


45

where C is the stray capacitances of the WT transformers, that are being charged by the

dv/dt of the waves arriving at each transformer.

It can be also seen in Figure 3-11 that the current in the platform have “half-waves”

presumably caused by pre-strikes in the VCB as reported by (Liljestrand, Sannino,

Breder, & Thorburn, 2008). When the breaker closes to energize the cable on row A, the

circuit is almost closed before the contacts mechanically touch. Then, the system

voltage acts across the diminished pole gap, creating an increased dielectric stress

between the contacts, which can result on breakdown before the circuit mechanically

closes.

3.3.2 Case 2. Second closing of the line breaker for line A

This second case was not presented as thoughtfully as the first case, since is basically

the same event. The voltage on the three measurement location are shown in Figure

3-12 for the first millisecond after the closing. It can be seen that the voltage at the

platform and at the wind turbine A09 surpasses 2 pu several times. This is because the

closing in the VCB took place closer to the negative peak voltage of phase A. Then

when it reached the last wind turbine, the voltage increased further on, as explained

before.

It‟s important to notice that the energization of an individual phase does not affect the

voltage of the other phases. This is due to the shielding of each individual conductor

within the cable. Howerver, in reality there are some capacitances between phases due

to the close geometrical arrangement of the cable. These capacitances are responsible

for the small variations and decrease in voltage of phase C on the platform just before it

gets energized.

The current on the three measurement location for the first 250 ms is shown in Figure

3-13. The flat peak in two phases is noticeable in the three locations, and its explanation

is the same measurement error as explained before.

There is a higher inrush current in the second study case compared to the first one. This

is due to the point-in-wave in which the switching happened.

In Figure 3-13 and Figure 3-9, an oscillating current can be seen in A01. This current is

caused by a capacitor bank still connected on the LV side of the wind turbine

transformer. Analysis on the current waveforms for both cases, and an explanation of

the state of the system during the measurements was discussed in the following section.

However, it is very clear that the current in A01is different between the first and second

study cases.


46



3.3.3 Case 3. Closing of the breaker on wind turbine A9

The voltage at the three measurement locations, for the first 50 ms of the third study

case are shown in Figure 3-14. It is important to mention that no significant drop in the

platform voltage is noticeable, for this a half-cycle rms calculation were performed

further in the document.


47

The current for the first 50 ms is shown in Figure 3-15. Some currents are present in the

platform and in A01. It was shown later in the document that seven of the nine WTs of

row A (all except the ones with measurement equipment) were under production. Here

it‟s only important to notice that no significant change occurs on A01 after the switch in

A09 was closed.


The voltage and current in the WT A09 are presented in Figure 3-16. It can be seen that

the switch closes the phases not simultaneously. Between closing of phase C and B

there are 200 μs, and between phase B and A there are 2 ms.

There are some high frequency oscillations in the voltage after each phase closes, this

could be due to an arc on the breaker. When each phase is energized there are sudden

current raises, that cannot be explain easily by the charging capacitance in the

transformers, since they reach more than 1 p.u. and in the previous cases the current

spikes hardly reach 0,5 p.u.


48


After phase B has close, there is some voltage oscillation on phase A until it is

connected. This could be due to the coupling between phases in the HV side of the

transformer, since it is a delta connected three-phase core-type transformer.

Figure 3-16 Case 3. Voltage and current 2,5-8 ms

Once the measurements have been presented and analyzed, the required calculation for

its comparison with the results from the simulation in Power Factory and PSCAD, were

explained in the next subsection.


49

3.4 Analysis of voltage and current measurements

3.4.1 Voltage dip standards

Voltage dips are defined as a short-duration reduction in rms voltage (Bollen, 1999).

These phenomanas are produced by short-duration increase in current elsewhere in the

system, e.g. transformer energizing. International organizations like the IEEE, IEC and

CIGRE have been working in the stardarization of the voltage dip, however there is still

some work to be done (Bollen, et al., 2006).

The IEC 62000-4-30 distinguishes between single-channel and multi- channel

measurements. For multi-channel measurements the worst channel is taken for further

analysis when calculating single event indices. Thus for every half-cycle update of rms

voltage, the lowest of the values from the different channels should be used.

For the present report the half-cycle rms voltage was used to compare the voltage dip on

each study case, and further in the report to calculate the voltage dip due to

simultaneous energization of different amount of transformers.

Since one of the practical objectives of the theses is to assess the voltage dip due to

sequential energization of different amount of transformers in order to comply with the

UK requirements, the voltage change limitation based on this standard is presented here.

The following information was taken from (ENA, 1989.).

Figure 3-17 Usual form of voltage change caused by motor starting, adopted from

(ENA, 1989.)

In the UK the general limit on the allowable magnitude on voltage drop, caused by

motor starting, has been the accepted practice to control the risk of low voltages. The

Figure 3-17 shows the typical voltage of a motor with direct starting. Here is assumed

that the magnetizing inrush current last for 30 ms. In this case the recommended limit

for the voltage magnitude variation is DV .


50

3.4.2 Rms calculations

The formula to calculate the rms value of the voltage (3.2) and current (3.3)are:

2 2 2

1 2 1 ½½

½

Nrms

u u uU

N

(3.2)

2 2 2

1 2 1 Nrms

u u uI

N

(3.3)

Where the N is the number of samples per cycle. For the half-cycle rms voltage the first

value is obtained over the sample (1,½N), the next over the sample (½N+1,N), etc. For

the rms current the first value is obtained over the sample (1,N), the next over the

sample (N+1,2N), etc.

3.4.3 Power calculations

Another important parameters to compare the measurements and the results from the

simulations are the instantaneous real power (3.4) and instantaneous reactive power

(3.5):

, , , , , ,

1

1( )

N

A k A k B k B k C k C k

k

P v i v i v iN

(3.4)

, , , , , , , , ,

1

1(( ) ( ) ( ) )

N

B k C k A k C k A k B k A k B k C k

k

Q v v i v v i v v iN

(3.5)

Where k is the sample number. For the first and second study cases only one

measurements file was used since each file covers half a second. For the third study case

two consecutives measurements files were used, since each file cover only 200 ms.

Thus for the first and second study cases 1,25×106 samples, corresponding to 25 cycles

were analyzed for 18 signals. While only 1,00×106 samples, corresponding to 20 cycles

were analyzed for the third study case.

Nevertheless the instantaneous powers were not directly compared on the study cases.

The active and reactive powers were calculated with the average of each instantaneous

power every cycle. This method was found to be insufficient to calculate the active and

reactive power in a system with high harmonic contents, however this situation was

only present in A01.

3.4.4 FFT in current

The current in each phase measured at A01 during the first study case is shown in

Figure 3-18, while the current measured at A09 is shown in Figure 3-19.


51

Figure 3-18 Case 1-A01. Current 0-500 ms

It can be seen from this two figures that the equipment connected on the LV side of the

transformers is not the same in A01 and A09, assuming that the transformers are. To

discard possibilities on the equipment connected on the LV side of the transformer an

FFT analysis was done.

Figure 3-19 Case 1-A09. Current 0-500 ms


52

The results of this two FFT analysis are shown in Figure 3-20. It can be seen that there

are significant differences around 210 Hz between A01 and A09.

Figure 3-20 Case 1-A01 and A09. FFT on current

It was found from the FFT that apparently there is not the same equipment connected at

A01 and A09. The harmonic current/fundamental current ratio is presented in

Table 3-1. The forth harmonic on phase B in A01 presents the highest ratio with 1,16.

Table 3-1 Harmonic current ratio

I(100)/I(50) I(150)/I(50) I(200)/I(50) I(250)/I(50)

Case 1

A1

Ia 0,87 0,34 0,79 0,04

Ib 1,05 0,42 1,16 0,37

Ic 0,83 0,48 0,35 0,12

A9

Ia 0,61 0,32 0,24 0,18

Ib 0,90 0,10 0,66 0,40

Ic 0,59 0,32 0,24 0,19

It‟s not possible to realize the FFT analysis on other study cases since the current

waveforms are incomplete.

The main loads connected on the LV side of each WTT consist of yawing motors,

hydraulic pumps, cooling fans, lubrication equipment, heating elements and control

system. While there are other devices with high priority that are directly supplied from

the transformer like the hoist, control cabinets and cooling fans in the transformer.

Large loads were not included in any simulation since they are not part of the main

project objective. However it was found in the datasheets of the wind turbines that there

is a permanent load directly connected to the LV side of the transformer, of 0,37 kW

that was included in the simulations.

On the other hand, the capacitor banks that compensate for the reactive power

consumption of the asynchronous generator under production were included further on

in the report, while they were found to be relevant for the simulation.


53

3.5 State of the NWP when the measurements were done

The measurements of the opening and closing of row A on NOWF were done the 8 of

march 2007 between 16:50 and 17:00. The Figure 3-21 and Figure 3-22 present the 10

minutes average of the permanent measuring equipment in the turbines A01 to A09.

The measurements files used for the first two study cases, had a time stamp on the file‟s

name so the user can be sure of the time of the switching event. However for the third

case the files‟ name had been edited before and no record or log of the measurement

was kept. This brought problems for the last study case, since from the beginning of the

project it was assumed that the wind turbines without measurement equipment of row A

were not under production. Later on the project changes were made and simulations

with the generators were done.

Ac tive P ower

-

500

1.000

1.500

2.000

2.500

15:00 15:10 15:20 15:30 15:40 15:50 16:00 16:10 16:20 16:30 16:40 16:50 17:00 17:10 17:20 17:30 17:40 17:50

P [

kW

]

A1

A2

A3

A4

A5

A6

A7

A8

A9

Figure 3-21 Active power measurements, 10 min average

From the Figure 3-21it can be seen that between 16:50 and 17:20 the wind turbines

were almost under no production. While A09 and A01 does not start production at all

after this period. While the rest of the turbines returned to almost full production.


54

R eac tive P ower

-

50

100

150

200

250

300

15:00 15:10 15:20 15:30 15:40 15:50 16:00 16:10 16:20 16:30 16:40 16:50 17:00 17:10 17:20 17:30 17:40 17:50

Q [

kV

Ar]

A1

A2

A3

A4

A5

A6

A7

A8

A9

Figure 3-22 Reactive power measurements, 10 min average

The reactive power on each WT is shown in Figure 3-22. It is important to notice that

during the field test the turbine A01 kept injecting between 150 and 200 kVAr to the

grid. This shows that the capacitor bank in A01 remained connected.

The generators on NOWF are asynchronous machines with a capacitor bank to

compensate for the reactive power consumption during production. Hence, by knowing

the terminal voltage of the generator and the production, the slip can be calculated.

Once the slip is computed, the reactive power consumption can be estimated. Then, by

adding the measured reactive power at the LV side of the WTT and the calculated

reactive power consumption of the generator, the amount of reactive power from the

capacitor can be calculated.

It results that before the opening of the platform breaker 1260 kVAr were delivered by

each capacitor bank. This value could be used to calculate the resonance frequency of

the system during the first opening of the radial A. But due to time limitations this

analysis had to be left out of the scope of the theses

In order to fully understand the state of the system after closing the breaker in the

platform and energize row A (case 1 and case 2), the following subsection presents the

expected values for currents, voltage, real and reactive power for the mentioned cases.


55

3.6 Steady state for case 1 and case 2

The Table 3-2 presents the main characteristics of each wind turbine transformer under

normal conditions, as well as the comparison with a small low voltage load.

Once the nominal values are known, the current at the LV side of the transformer can be

calculated, for a small LV load as:

3 3 LLS I V (3.6)

Then, the equivalent current at the primary side of the transformer can be calculated as:

P P S SI V I V (3.7)

Then, the equivalent copper losses (3.8) and leakage reactive power (3.9) consumption

of the transformer, with lower current can be computed as:

2

1 1

2

2 2

P I R

P I R (3.8)

2

1 1

2

2 2

Q I X

Q I X (3.9)

Then the result can be multiplied by the total amount of transformers, obtaining the

steady state value that should be theoretically measured and simulated at the platform.

However, the reactive power production in the cables has to be included as well. For

this with the specific capacitance per length (3.10), the length of the MV cable (3.11),

frequency and voltage, the reactive power (3.12) can be calculated as:

1

2CX

fC

(3.10)

CC

XX

l

(3.11)

2

LL

C

VQ

X (3.12)

From Table 3-2 can be seen that the real and reactive power consumtion in the cables is

almost insignificant. Howerver, at steady state the cables would produce nearly 0,5

MVAr, where the iron losses in each transfromer acount for all the active power

consumtion in row A.

Once the measurements and the system have been explained, as well as the study cases;

the theory behind the electrical components that will be used for the simulations of the

study cases in Power Factory and PSCAD can be done.


56

Table 3-2 Steady state (0,5 s) for case 1 and case 2

Steady state power balance for row A P [kW] Q [kVAr]

Tra

nsfo

rme

rs

Three phase transformer characteristics

Nominal three phase apparent power [MVA] 2,50

Primary side nominal rms phase-phase voltage [kV] 33,00

Secondary side nominal rms phase-phase voltage [kV] 0,69

Positive sequence short circuit voltage [%] 8,30 206,43

No load losses (iron losses) [kW] 5,50

Nominal operation losses (copper losses) [kW] 21,00

High voltage side nominal current [A] 43,74

Low voltage side nominal current [A] 2.091,85

Three phase transformer under operation

Low voltage load [kW] 0,37

Low voltage side current [A] 0,31

High voltage side current [A] 0,10

Iron losses [kW] 5,50

Copper losses [kW] 0,00

Leakage reactance [kVAr] 0,00

Total power consumption 5,87 0,00

Total power consumption of nine transformers 52,83 0,00

Cab

les

Power consumed in cable sections

Current at high voltage side of each transformers [A] 0,10

Section Amount of current

Root A 0,92 0,00 0,00

A1-A2 0,82 0,00 0,00

A2-A3 0,72 0,00 0,00

A3-A4 0,62 0,00 0,00

A4-A5 0,51 0,00 0,00

A5-A6 0,41 0,00 0,00

A6-A7 0,31 0,00 0,00

A7-A8 0,21 0,00 0,00

A8-A9 0,10 0,00 0,00

Addition of power consumption in row A 0,00 0,00

Reactive power generated from the cable’s capacitance

Capacitance per phase [μF/km] 0.199

Cable length [km] 7,061

Nominal frequency [Hz] 50

Line to line voltage [kV] 33

Total power consumption in row A 0,00 -483,14

Overall total 52,83 -483,14

Steady state current at platform in feeder A [A] 8,50

57

4 ELECTRICAL EQUIPMENT IN SIMULATION PROGRAMS

In this section the network characteristics will be presented, as well as information

regarding wave theory. Then, the six main electric components used in the Power

Factory and PSCAD were explained and compared. This are:

Circuit Breaker

Transformer

Cables

Grid (Voltage source)

Capacitor bank

Generator

The theory behind each device and its application in offshore wind farms is presented.

Then, the explanation regarding the standard models in Power Factory and PSCAD, as

well as a simple case for comparison is presented for each device.

4.1 Network

In an offshore wind park, the turbines are connected in radials by MV cables, with

feeders coming from the wind park transformer to each radial. This property of the

collection network has an influence on the TOVs caused by the CB operations. The

large number of cables and transformers gives rise to reflections in the system. The

reflection points will cause different stress on the insulation of the equipment depending

on its location (Liljestrand, et al., 2008).

In cable systems the CB operation are the main source of TOVs, since the surge

impedance has direct impact on the time derivate of the TOVs and the surge impedance

of cables is low compared to overhead lines (OHL): the lower the surge impedance, the

higher the time derivate of the TOVs. The time constant for the voltage across a load

when hit by a step voltage, depends as:

loadsurgeCZ (4.1)

where the Zsurge is the surge impedance and Cload is the capacitance of the load.

4.2 Wave theory

The electrical devices are usually analyzed as lumped or concentrated models with

constant R, L and C parameters. In reality these parameters are actually distributed in

any circuit or piece of equipment. This way of modeling the electrical devices, has the

unique characteristic to support travelling waves of current and voltage. The

Electrical equipment in simulation programs

58

transmission line theory is well explain in [Greenwood A. 1991], and the reader is

invited to review this source, only the main information is included here.

The current and voltage waves travel along a lossless circuit at a velocity of:

LC

v1

(4.2)

With a approximation of the inductance

ln( / )L d r

(4.3)

And a approximation of a capacitance

ln( / )

Cd r

(4.4)

The velocity of the wave can be rewritten as

1

v

(4.5)

From equation (4.5) can be seen that the wave velocity is independent of the line

geometry, it is only dependant on the conductor relative permeability (μ) and the

insulation relative permittivity (ε).

The ratio of the amplitude of the voltage and current waves on a transmission line has

the dimension of impedance and is called characteristic impedance Z0 of the line, and

can be calculated as:

C

LZ 0 (4.6)

And it can be seen that unlike the wave velocity, v, the characteristic impedance

depends upon the line geometry. A typical value or characteristic impedance for OHL is

400 Ω, while for cables is between 30-80 Ω because the closer spacing makes C larger

and L smaller. The capacitance is further increased by the permittivity of the cable

dielectric.

When the cables are analyzed as transmission lines, some of the following items might

not be taken into account (Sluis, 2001):

Skin-effect for high frequencies

Losses in the dielectric medium between the conductors

Leakage current across string insulators

The influence of ground resistance

However, when a voltage or current wave travels along a cable with losses, the

attenuation caused by the properties of the transmission line, would decrease the

amplitude of the wave. This attenuation in the voltage wave was visible on the

measurements from the first and second study cases, which both of the simulation

programs were able to replicate.


59

When a wave arrives at a discontinuity in a line, where Z0 changes, some adjustments

occur in the wave, so the proportionality (Z0) is not to be violated. This adjustment takes

the form of the initiation of two new wave pair. The reflected voltage wave and its

companion current travel back in the line superimposed on the incident wave. The

refracted wave penetrates beyond the discontinuity. The amplitude of the reflected and

the refracted waves are such that the voltage to current proportionalities are preserved

for each, as demanded by Z0 of the line on which they are traveling; current and voltage

at the line discontinuity are themselves continuous, and the energy is conserved.

The magnitude of the reflected voltage wave at a junction point with characteristic

impedance ZA and ZB on the incident side and refractive side, respectively, can be

calculated as:

112 VVZZ

ZZV

AB

AB

(4.7)

the refracted voltage wave can be calculated by

113

2VV

ZZ

ZV

AB

B

(4.8)

Where V1 is the incident wave, V2 is the reflected wave and V3 is the refracted wave. ρ

and α are called reflected and refracted coefficient, respectively.

The Figure 4-1 shows the first milliseconds of the measurements of the first study case.

Here, the voltage of phase B is presented on the three measurement locations where the

voltage at the platform is shown in blue, the voltage at A01 in green and the voltage at

A09 in red. In the lower part of the figure, the color nomenclature is the same, but the y

axis is not voltage as in the upper part, here the distance between measurement locations

is shown.

The lower figure presents the position of the voltage wave in grey color. At T1 the

phase B is energized on the platform. At T2 the voltage arrives to A01 and at T3 the

voltage reaches A09.

It is possible to see the doubling of the voltage at T3, since the transformer would be

seen as an open circuit. Then once it has reach the end of the line the wave bounces

back to the platform, arriving to A01 at T4 and to the platform at T5. Here it‟s important

to notice that the voltage at the platform increases again, since the park transformer and

other feeders are connected at this point.

At T5 two gray lines leave the platform in direction to A09. The dark gray line

represents the position of the voltage wave if the velocity of the voltage had not

decreased. The light gray line is the position of the voltage at decreased velocity. From

this simple numerical equivalencies can be seem that the velocity of the wave diminish

after the first reflection period. The wave velocity reduction could be explained by the

change in relative permittivity due to frequency variations. Additional discussion on the

transient phenomena in cables and its simulation was done further in the report.

The orange lines represent the reflections each time the voltage reaches a wind turbine

between A01 and A09. From (4.8) can be seen that each time the voltage wave reaches

a transformer (high impedance) between the platform and A09, a small amount was


60

reflected back. Similar reflections appear as small variations in A01 (green voltage)

between T2 and T3, due to the change from copper core cables to aluminum core cables

at A02.

Figure 4-1 Case 1. Voltage phase B 4,3-4,6 ms

4.3 Switchgear

In an offshore wind farms like Nysted, the collection grid is relatively active, and not

passive as in a distribution network. Hence the switchgear plays a critical part in

controlling what is taking place. In general the switchgear is used to (Steward, 2004):

Isolate faulty equipment

Divide the network into sections for repair purposes


61

Reconfigure the network in order to restore the power production

Control other equipment

All switchgear must be capable of either closing or opening an electrical circuit. This

includes the switching device, associated control, measuring, protection and regulating

equipment.

The difference between a CB and a switch is that the CB can detect and interrupt a

short-circuit fault current, whereas a switch can do neither.

Any CB should meet thermal interruption requirements, interrupt at natural current zero

and withstand dielectric stresses caused during interruptions. Depending on the

extinguishing medium used, the CBs are classified as oil, air, air-blast, vacuum and SF6

CBs.

For this project only two types of the switching element from the collection grid of

NOWF were taken into account; a vacuum circuit breaker (VCB) as the breaking

element for each collection radial in the platform and a switch disconnector fuse on the

MV side of each WTT.

Due to time constrains during the project only a theoretical review of the switching

phenomena in CBs and the modeling of gas insulated CBs and VCBs was made. In the

simulations, the models used were the simplest with an ideal breaking action that is

independent of the arc, while the breakers were represented as ideal switch that opened

when the tripping signal was given.

4.3.1 Circuit breaker modeling

The following information about switching transient studies for gas insulated CBs, was

taken from the IEEE PES Task Force on Data for Modeling System Transients

“Parameter determination for Modeling System Transients-Part VI: Circuit breakers”.

For switching transients studies the switch is usually modeled as an ideal conductor

(zero impedance) when closed, and an open circuit (infinite impedance) when open.

There are a variety of options of closing time provided by commercial transient

programs, ranging from one-shot deterministic closing to multi-shot statistical or

systematic closing.

In normal operation a CB is in closed position, and some current is usually flowing

though the closed contacts. The CB opens its contacts when a tripping signal is sent to

it. The separation of the contacts causes the generation of an electric arc. There are

several levels of model complexity available in transient analysis applications (CIGRE,

1998):

1. The simplest model considers an ideal breaking action that is completely

independent of the arc. The breaker is represented as an ideal switch that opens


62

at the first current-zero crossing after the tripping signal is given. The model

may include a current margin parameter for approximate modeling of possible

current chopping. Such models are applicable in studies where the interaction

between the breaker arc and the surrounding network can be neglected. It can be

used to obtain the voltage across the breaker; this voltage is to be compared with

a prespecified TRV withstand capability for the breaker.

2. A more elaborate model considers the arc as a time-varying resistance or

conductance. The time variation is determined ahead of the time based on the

breaker characteristics and perhaps upon knowledge of the initial interrupting

current. This model can represent the effect of the arc on the system, but requires

advanced knowledge of the effect of the system on the arc. Arc parameters are

not always easy to obtain and the model still requires the use of precomputed

TRV curves to deliver the adequacy of the breaker.

3. The most advanced models represent breakers as a dynamically varying

resistances, whose value depends on the past history of voltage and currents in

the arc itself. This model can represent both the effect of the arc in the system

and the effect of the system in the arc. No precomputed TRV curves are

required. Most of these models rely on the first-order differential equation. This

type of model is generally developed to determine arc quenching capabilities.

Most models can be used to study the thermal period, some can be used to

determine arc re-ignitions due to insufficient voltage withstand capabilities of

the dielectric between breaker contacts. Their most important application cases

are short-line-faults (SLF) interruption and switching of small inductive

currents. They are exclusively applied to gas CBs.

Several models can be used to represent a CB in closing operation.

The simplest model assumes that the breaker behaves as an ideal switch whose

impedance passes instantaneously from an infinite value, when open, to a zero

value at the closing time. The performance can be represented at any part of the

power cycle. A closing operation can produce TOV whose maximum peaks

depends on several factors; for instance, the network representation of the source

side of the breaker, or the charge trapped on transmission lines in a reclosing

operation. One of the factors that has more influence on the maximum peak is

the instant of closing, which can be different for every pole of the three-phase

breaker.

Most transient programs allow users to analyze the influence of this factor and

obtain a statistical distribution of the switching overvoltages, usually provided in

the form of a cumulative distribution function. Two types of switches can be

represented.

o The closing time of the switch is systematically varied from a minimum to a

maximum instant in equal increments of time; this type is known as

systematic switch.

o The closing time is randomly varied according to either a normal or a

uniform distribution; this type is known as statistical switch. Data required


63

to represent these switches are the mean closing time, the standard deviation

and the number of switching operations.

The breaker model assumes that there is a closing time from the moment at

which the contacts starts to close to the moment that they finally make. The

withstand voltage decreases as the separation distance between contacts

decrease; an arc will strike before the contacts have completely closed if the

voltage across them exceeds the withstand voltage of the dielectric medium.

To summarize the modeling guidelines for CBs the next table from the same paper was

used.

Table 4-1 Modeling guidelines adopted from (CIGRE, 1998)

4.3.2 Vacuum circuit breaker

The vacuum breaker is, at least in principle, the simplest of all the breakers designs

from the mechanical construction with only a fixed and movable contact located in a

vacuum vessel. When the contacts are separated, the arc is supported by ionized metal

vapour derived from the contacts instead of by ionized gas as in other interrupters, and

at current zero collapse of ionization and vapour condensation is very fast, ensuring

interruption virtually independent of the rate of rise of re-striking voltage (Flurscheim,

1982).

Vacuum is used as an extinguishing medium for MV CBs. VCB are capable of

interrupting currents with a very high di/dt, typically in the range of 150-1000 A/μs

(Wong, Snider, & Lo, 2003).

The current interruption is performed by cooling the arc plasma so that the electric arc,

which is formed between the breaker contacts after contact separation, disappears. At

short circuit current zero, the instantaneous energy input to the arc is minimal, enabling


64

the arc to extinguish. Immediately after the extinction of the arc, the power network

reacts with a TRV that stresses the gap.

The arc that occurs in the vacuum interrupter is very different from the arcs in other

CBs. The “vacuum arc” is a contradiction in terms, since an arc, by definition contains

positive ions; however, a vacuum arc is an arc where the vapour to produce positive

ions is generated from electrodes by the arcing process itself. The physical processes in

the VCB are rather complex, but for simulation purposes some simplifications can be

made.

For the VCB different breaker models exists and they all take into account arc thermal

instabilities. However there is no universal precise arc model. The generic model of

VCB incorporates stochastic properties of different phenomena that take place in the

breaker opening process. The different properties that are generally considered are

(Wong, Snider, & Lo, 2003):

Random nature of the arcing time

Current chopping ability

The characteristic recovery dielectric strength between contacts when opening

The quenching capabilities of the high frequency current at zero crossing

Below the four main causes of overvoltage in VCB are presented, based on (Kondala &

Gajjar, 2006):

Current chopping

Voltage escalation due to multiple pre-ignitions

Virtual current chopping

Pre-strikes

Only the pre-strike phenomenon was explained since it is the only incident that was

measured in the study cases, being highly relevant during the energization of radial in a

wind farm. The pre-strike phenomenon during opening of a VCB is mentioned below.

4.3.2.1 Pre-strike

Traditional methods of representing the CB for energizing phenomena in transients‟

studies are to assume that the contacts can close on any part of the cycle. In reality,

there is a closing time between when the contacts start to close and when they finally

make. Somewhere in between, an arc may strike across the contacts as they close

(Rashidi, et al., 2003), this is known as “pre-strike”. The pre-strike effect in closing CBs

with finite closing time is shown in Figure 4-2.


65

Figure 4-2 Pre-strike effect in circuit breakers, adopted from (PSCAD User's Guide,

2005)

The vertical axis in Figure 4-2 is a measure of the withstand voltage across the CB

contacts. In the open position the withstand voltage of the CB will be a per unit value of

the rated voltage. The time varying value of the voltage across the contacts is depicted

as an absolute function of the alternating voltage across the contacts. As the contact

close, the withstand voltage reduces as the separation distance between the contacts

reduces. When the voltage across the contacts exceeds the reduced withstand voltage of

the insulating medium between them, and pre-strike occurs. As a result of the pre-strike,

there will be a greater tendency for effective closing to occur with rising or maximum

voltage across the contacts (PSCAD User's Guide, 2005).

4.3.2.2 Opening

In studying interrupting operations of a VCB the entire process can be divided into a

few stages (Kosmac & Zunko, 1995):

The contact starts to separate and the electric arc begins to burn. As is well-

known, the voltage/current characteristic of a VCB in a very wide current range

is almost constant, and the arc voltage drop for Cu/Cr contacts is approximately

20 V.

The current decreases and approaches zero value. At one specific point, a very

fast decrease occurs (chopping current). The slop di/dt can be 108A/s or even

higher. For load currents between 45 and 170 A the following empirical

expression based on measurements can be used to estimate the chopping current

[Weber, F.U., 1988]

Nch ZcbIai log1 (4.9)

in which ich is chopping current, I1 rms load current, a, b, c, contact dependant

constants and ZN the impedance of the network.


66

For operating condition not matching the current range some assumptions can be

made.

In the case of high and/or fault current, the chopping current is essentially

zero because of the high ionization of the space between contacts and

thermal electron emission from the cathode which assures a long mean-

free path for electrons and ions.

When low current are interrupted it can be expected instability of the arc

and higher value of the chopping current and the di/dt.

The voltage on the load side terminal of the breaker may- after the current is

chopped due to a high di/dt value and conversion of magnetic into electric

energy- reach very high values. The potential difference between the contacts

can be higher that the dielectric strength of the space between contacts, and re-

ignition of the arc may occur. But dielectric strength improves with time, and

after certain period a full dielectric strength is reached. Sometimes contact start

to separate just before zero current. In such cases –due to small contact gap- the

voltage needed for re-ignition is relatively small. If the TRV is sufficiently high

and fast, re-ignition occurs. The number of re-ignitions and HF zero current

passing are random. The quenching capabilities of the HF current passing are

random. The quenching capability of the HF current depends on the current

slope and is different for different rms values [Czarnecki, L 1984]. When

inductive current is interrupted, multiple re-ignition, voltage escalation and

virtual current chopping can be observed. Post-zero current may be presented

even after contacts are separated, and it is load-current dependant.

4.3.3 Vacuum circuit breaker modeling

When realizing a switching transient study, the component involved should be modeled

as accurately as possible. However is very complicated to obtain an accurate model of

the VCB when all the phenomena mentioned above should be included.

As mentioned before only a theoretical approach was made regarding the VCB

modeling. Nevertheles, how to model the dielectric strength in a VCB is shown below.

4.3.3.1 Dielectric strength

During the closing of a VCB, is assumed that no current was flowing though the breaker

previous the closing. Thus, the relevant breakdown voltage under the influence of the

TRV is equivalent to the cold gap breakdown voltage. The frequency of this voltage is

in kHz range. The linear dependency of the dielectric strength and contact distance is

assumed as (Helmer, et al., 1996):

BttATVRU open )(lim (4.10)

Where topen is the moment of contact opening, A is the rate of rise of dielectric strength,

B the breaker TRV just before current zero and TRVlim is the maximum dielectric

strength that the breaker can withstand (IEEE Std. C37.011, 1994):

3

2lim magppaf EkkTVR (4.11)


67

Where kaf is the amplitude factor (1,4), kpp is the first pole to clear factor (1,5) and Emag

is the breaker rated voltage.

The calculated value of the dielectric strength is incorporated by considering the normal

distribution with a standard deviation of 15%, since breakdown phenomena is statistical

in nature. Some accepted values for equation (4.10) are shown in Table 4-2 based on

(Gliiikowslti, et al., 1997).

Table 4-2 Accepted values for equation (4.10)

A [V/ms] B[kV]

High 17 3,4

Medium 13 0,69

Low 4,7 0,69

As a practical matter in PSCAD simulations, is important to notice that the breakers

have a close resistance of 0,1 Ω, as standard value. This was found to be one possible

source of discrepancy between the results from Power Factory and PSCAD in the study

cases 1, 2 and 3.

Once the transient phenomena presented in the first and second study cases within the

switchgear device has been explained and understood, the next electrical device should

be explained. In this case the following equipment is the transformer.

4.4 Transformers

In offshore wind farms the step-up transformers in each wind turbine have great

exposure to electrical transients. Hence this subsection is dedicated to the theory behind

the emt modeling of transformers for switching transient studies.

There is a large amount of literature about the behavior of transformers when subjected

to surges and transient conditions, thus a comprehensive survey is presented next.

A complete model for a transformer would require that every turn be represented and

that all mutual couplings, inductive and capacitive, with every other turn be included. In

practice such a model is unnecessary, and a simplified model would be sufficient. The

model chosen will depend on the purpose of the simulation.

For example, if the time for the simulation needed is only microseconds, no significant

current can penetrate the winding properly because of its inductance. Currents would

flow as displacement currents in the capacitive of the windings. Thus, to obtain the

initial voltage distribution the model required would comprise capacitive elements only

(Greenwood, 1991).

On the other hand, when the model is used for other studies, e.g. to calculate the

transient overvoltage caused by vacuum circuit breaker re-ignitions, a simple capacitive

model would not be sufficient.


68

When the transformer is switched in no-load, the transformer model should represent

the influence of the transformer winding and the transformer core. Since the VCB re-

ignitions contain oscillations with different frequencies, the transformer behavior is also

different because of the variable impedance of the transformer winding and the

frequency dependant losses (Popov, et al., 2001).

Figure 4-3 Transformer model used in (Popov, et al., 2001)

4.4.1 Simple transformer model

The transformer model shown in Figure 4-4 is a simplification used in practical

engineering applications, where the secondary winding is referred to the primary. Here

the losses that occur in real transformers have to be accounted for. R1 X1 R’2 X’2

Xm Rfe

Figure 4-4 Simple transformer equivalent

The major items to be considered in the construction of such a model are (Chapman,

2003):

Copper losses are resistive heating losses in the primary and secondary windings

of the transformer. (R1 and R`2)

Eddy current losses are resistive heating losses in the core of the transformer.

They are proportional to the square of the voltage applied to the transformer

(Rfe).

Hysteresis losses are associated with the rearrangement of magnetic domains in

the core during each half-cycle. They are complex, nonlinear function of the

voltage applied to the transformer (Rfe).

Leakage flux that escape the core and pass through only one of the transformer

windings are leakage fluxes. These escaped fluxes produce a self-inductance in

the primary and secondary coils, and the effects of this inductance must me

accounted for (X1 and X`2).


69

The magnetization current of the core is proportional (unsaturated region only)

to the voltage applied to the core and lagging the applied voltage by 90°, so it

can be modeled as a reactance (Xm)

The main component in a transformer model for switching in open circuit is the

magnetizing branch and the capacitance to ground of the winding. This capacitance can

be assumed as distributed uniformly over the length of the winding; hence a total

capacitance referred to a terminal can be calculated (Greenwood, 1991).

Capacitances between terminals and between windings can be required for simulations

of some low-frequency transients; in addition, their effect can be important in excitation

tests (Martinez, et al., 2005). Transformer windings and bushing capacitances can be of

critical importance for slow transient phenomena such as ferroresonance and other

resonance situations. In addition their value increases with transformer size. The

manufacturer can state capacitances for their product, although they can also be

estimated from construction details or from typical values listed in the literature.

4.4.2 Switching transient studies in transformers

During switching operations in the radial of an offshore wind farm, the wind turbine

transformers are subjected to high-voltage and high-frequency waves. During the

connection of a transformer, the insulation of the coils connected to the line terminals

might be subjected to a voltage concentration, however the severity of the stress

situation depends on the point-in-wave on which the switching takes place.

As explained in the previous subsection the closing and opening events in a CB are

extremely hard to predict. However it is important to remember that the electric arc in

CB is highly possible. Arcing in the breaker contacts produces trains of high frequency

waves, which impinge upon the transformer windings and represents a real problem to

the insulators (JH- Franklin, et al., 1983). If an intermittent arcing takes place the

situation may worsen, additional information is presented in subsection 4.4.2.2.

In offshore wind farms a careful design of the system is important since maintenance is

highly expensive, hence the use suitable protective devices is imperative.

4.4.2.1 Detailed transformer model for surges

For switching surge transient studies it is better to use a reduced order representation

with less detail compared to the very detailed transformer model needed for the

insulation studies. Usually a lumped parameter coupled-winding model with sufficient

number of R-L-C elements, gives the appropriate impedance characteristics at the

terminal within the frequency range of interest. The nonlinear characteristic of the core

should usually be included, although the frequency characteristics of the core are often

ignored. This may be an oversimplification as the eddy current effect prevents the flux

from entering the core steel at high frequencies thereby making the transformer appear


70

to be air-cored. This effect begins to be significant even at frequencies in the order of 3-

5 kHz (A.M. Gole, 1997).

For switching surges studies, the following approaches may be used (A.M. Gole, 1997):

The model may be directly be developed from the transformer characteristic e.g.

nameplate information or measurements. The standard EMTP models fall into

this category.

A model synthesized from measured impedance versus frequency response of

the transformer. An example of this is shown in Figure 4-5.

A very detailed model obtained from the transformer geometry and material

characteristic may be developed. The model is the reduced to one that is usable

in the time domain solution. An example of this approximation is shown in

Figure 4-6.

When possible, the following techniques can be used to validate the model (Martinez, et

al., 2005):

A frequency response obtained by simulation can be compared within the desire

bandwidth with the actual characteristic if available. This should be done for all

possible open and short circuit conditions on the windings.

Determining the fundamental frequency response in the form of open and short

circuit impedances is a standard check. The turns ratio or induced winding

voltages at fundamental frequency are of interest.

Comparison with factory test if available also validates the model if terminal

capacitances measurements are available a comparison between measurements

and computed response is useful

Figure 4-5 Impedance magnitude and angle of a wind turbine transformer, adopted from

(Pedersen, et al., 2005)


71

Figure 4-6 A very detailed model adopted from (de Leon, et al., 1994)

4.4.2.2 Transformer-breaker interaction

Occasionally, when a transformer is switched into or out of a system, the transient

voltage produced at the terminals of the transformer may contain high frequency

oscillatory components. This oscillatory voltage is the result of the system configuration

and the breaker characteristics. When this voltage has a frequency component near one

of the natural frequencies of the transformer, and is of sufficient magnitude and

duration, damage to the internal insulation structure of the transformer may result.

In the IEEE there is an ongoing standard project PC57.142 “A Guide To Describe The

Occurrence And Mitigation Of Switching Transients Induced By Transformer-Breaker

Interaction”.

Because the reduced amount of time for the project, no high frequency phenomenon in

the transformer was modeled.

4.4.3 Magnetic characteristic of the transformer

Transformer saturation is an important component of many low-frequency EMT

phenomena (Martinez, et al., 2005). In general, it needs to be modeled in transient

conditions with high flux. Many simulation programs are concerned with the details of

the transformer saturation curve. For most phenomena, the critical transformer

saturation parameters are the slope (air-core inductance) and the zero-current intercept

of the saturation curve. The location of the saturation representation in the transformer

model topology is also important

Saturation can be incorporated into a power transformer model using test

data/manufacturer‟s curves or estimating the key parameters from design details, core

material and transformer geometry. However, joints in the core structure can play a

significant role that is not reflected in the material data. Relationships needed to obtain a


72

saturation characteristic from transformer geometry (cross-section of core, magnetic

path length, number of turns) and standard values of core permeability are provided in

textbooks.

The saturation characteristic can be modeled by a piecewise linear inductance with two

slopes, since increasing the number of slopes does not significantly improve accuracy.

Except for very specific applications, a very accurate model is not required. A non-

linear iron core model of a three-phase, three-limb power transformer based on the

current-dependant characteristics of flux linkage in presented in (Dolinar, et al., 2006),

by three independent controlled voltage sources while secondary windings are opened.

The method used is relatively complex; however, it is possible to perform an accurate

numerical analysis of the saturation in the core.

4.4.3.1 Inrush current of the transformers during energization

The following information was taken from the ABB Transformer manual.

The magnitude of the inrush current is a statistical variable depending on where on the

sinusoidal voltage curve the circuit breaker connects the transformer to the source. The

highest inrush current occurs when the circuit breaker connects the transformer when

the voltage passes through zero.

On the other hand, when the circuit breaker disconnects the transformer from the

voltage source, some residual flux is trapped in the core, unless the disconnection takes

place exactly when the flux passes zero. Hence, the residual flux is also a statistical

variable. The residual flux will be at its maximum if the disconnection happens when

the flux has its maximum. The polarity of the residual flux may be positive or negative,

depending on the voltage before the disconnection, since the flux is the integral of the

voltage.

When a transformer with zero residual flux, is switched on when the instantaneous

value of the applied voltage is close to zero, which requires that the instantaneous value

of the flux in the magnetizing branch must be at peak value or lag by 90° to satisfy the

steady state equilibrium. Since the flux cannot instantly rise to peak value, it starts from

zero and reaches 1 pu after ¼ cycle and continues to increase until it becomes

approximately 2 pu ½ cycle after the switching. This phenomenon is commonly referred

to as the flux doubling-effect. However if there is any remnant flux present prior to

switching, and its polarity is in the same direction of the flux build-up after switching,

the maximum value can even exceed 2 pu (Nagpal, Martinich, Moshref, Morison, &

Kundur, 2006). The statistical probability that the absolute worst case will occur is not

high.

When the voltage changes direction, the current will decrease. But in the next cycle the

current will increase again. The curse of events will continue with gradually decreasing


73

the peak value of the current. The influence of the original residual flux will also

gradually disappear. The number of cycles before steady-state is reached varies from

less than 10 cycles for small transformers up to several minutes for larger transformers.

A characteristic of the inrush current is that it contains a second harmonic component

because of asymmetrical half-cycles. Inrush currents tend to be higher on modern

transformers compared to transformers build 40 years ago. The reason is that modern

low loss core steel allows higher flux densities in the core without unacceptable high

core temperature as consequence.

4.4.3.2 Voltage dip due to transformer energization

Transformer energization is a common occurrence in the electric power system. Most of

the times energization results in the transformer needing large inrush current, which

eventually decreases to a small magnetizing current. The time the transformer demands

the inrush current depends on the resistance and reactance of the equipment, including

the transformer magnetizing reactance.

The inrush current could cause a temporary voltage drop due to the impedance of the

system between the source and the energized transformer. If the short circuit MVA

available at the transformer bus is low, the resulting voltage drop can be significant.

Typically a voltage sag or dip is a decrease in the system voltage to between 0.1 pu and

0.9 pu at the power frequency lasting from half cycle to one minute (Nagpal, Martinich,

Moshref, Morison, & Kundur, 2006).

A simple back-of-the-envelope method can be used to obtain an indication of the

maximum inrush current and the expected voltage sag due to it from the equivalent

circuit (Nagpal, Martinich, Moshref, Morison, & Kundur, 2006).The following equation

uses the source reactance (X) and assumes that the transformer iron core behaves like an

air core at saturation, with a value of two times the short circuit impedance. Being the

short circuit impedance the sum of the primary (Xp) and the secondary leakage

reactance of the transformer (Xt). The inrush current cannot exceed:

tp

MAXinrushXXXZ

VI

2

1_

(4.12)

Thus, the maximum voltage sag can be estimated as

_

2sag MAX

p t

XV

X X X

(4.13)

And since the primary side can be assumed as half of the transformer reactance

t

MAXsagXX

XV

5,2_

(4.14)

During the energization of a single wind turbine transformer in Nysted, taking into

account the reactance for the collection cable, reactances in the park transformer,

reactances from the sea cable, land cable and the grid; the maximum voltage sag is

calculated to be 6%. However further in the report this value was found to be extremely


74

high in comparison with the actual measurements and the sequential energization results

from the simulation programs.

In the paper where this equation was used, the maximum voltage sag calculated with the

back-of-the-envelope method and the maximum voltage sag simulated were very close

when switching the three phases simultaneously at the zero crossing of one phase.

4.4.4 Simple case simulation

In order to compare the low frequency transformer model for energization from Power

Factory and PSCAD a simple case simulation was done.

First a comprehensible explanation of the residual flux and its influence on the inrush

current based on (JH- Franklin, et al., 1983) was done for single phase transfromers in

Power Factory. Then several simulations were done changing the residual flux and the

pole closing time between phases in Power Facotry.

Then, a brief comparisson between available standard models of transformers in

PSCAD was done. Finally a comparisson between the energization of the same

transfromer in both simulation programs was done, achieaveing similar results in both

cases.

4.4.4.1 Power Factory- single phase transformer

In order to simulate the switching of a single phase transformer in Power Factory the 5

limb transformer should be used with YN/YN connection, since the fluxes in all three

branches must add to zero in a 3 limb core delta-winding transformer.

The Figure 4-7 shows the simple case model for the simulations in Power Factory. The

AC voltage source connected to a bus feeding the high voltage side of the transformer,

while on the low voltage side of the transformer is connected to the LV bus with no load

or generation.

Figure 4-7 Simple case-transformer. Power Factory system


75

For single phase transformers there are six limiting conditions to consider for the

switching in a transformer;

a) At zero voltage with no residual flux

b) At zero voltage with residual flux with same polarity

c) At zero voltage with residual flux with opposite polarity

d) At peak voltage with no residual flux

e) At peak voltage with residual flux with same polarity

f) At peak voltage with residual flux with opposite polarity

Each of these conditions are explained and simulated below.

a) At zero voltage- no residual magnetism

Under normal conditions the magnetic flux in the core, being 90° out of phase with the

voltage, reaches its peak value when the voltage passes though zero. Due to the phase

displacement it is necessary for the flux to vary from a maximum in one direction to a

maximum in the opposite direction in order to produce on half cycle the required back

e.m.f in the primary winding, so that the total flux is embraced during the half cycle

corresponding to twice the maximum flux density.

At the instant of switching in, there being no residual magnetism in the core the flux

must start form zero, and to maintain the first half cycle of the voltage wave it must

reach a value corresponding approximately to twice the normal magnetic flux density.

35.0028.0021.0014.007.000-0.000 [ms]

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2-Winding Transformer: Phase Voltage C/HV-Side in p.u.

2-Winding Transformer: Phase Current C/HV-Side in p.u.

2-Winding Transformer: Magnetizing Flux C in p.u.

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Figure 4-8 Simple case- transformer. Single phase a). Voltage, current and flux.

The voltage (red), current (green) and flux density (blue) waves for the previous

condition are shown in Figure 4-8 and Figure 4-9. The maximum value of the flux

density, vary gradually from nearly approaching twice the peak in one direction only,

down to a normal peak value located symmetrically on each side of the zero axis as can

be seen in Figure 4-9.

As the magnitude of the no-load current is dependent upon the flux density, it follows

that the current waves also will initiate unsymmetrical, and that they will gradually


76

settle down to a steady state conditions. However, in the case of the flux density the

transient value cannot exceed twice the normal, where the transient current reaches a

value very many times the normal no-load current and can exceed the full-load current.

The reason for this high inrush current is to be found in the characteristic shape of the

B/H curve of transformer steel core, which is shown in Figure 4-10 as flux/current in

p.u. From this figure it can be see that the for a small increase in the flux (0,9 to 1,3

p.u.) the current would largely increase in comparison with the current under steady

state conditions.

In Figure 4-10 is shown the two slope representation of the core saturation in blue,

while the polynomial representation with a saturation exponent of 13 and 7, green and

red respectively, are shown as well. This are two standard ways to represent the variable

reactance in the transformer in Power Factory, but care should be taken when choosing

a polynomial representation, because some problems might arise as it will be explained

in the next section.

500.0400.0300.0200.0100.00-0.000 [ms]

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2.00

0.00

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Figure 4-9 Simple case- transformer. Single phase a). Voltage, current and flux. 500 ms


77

0.50000.40000.30000.20000.10000.0000 [p.u.]

2.0000

1.6000

1.2000

0.8000

0.4000

0.0000

[p.u.]

2-Winding Transformer: Phase Current C/HV-Side in p.u./Magnetizing Flux C in p.u.



Tw o-slopes

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Figure 4-10 Current- flux characteristic of transformers in Power Factory

b) At zero voltage-maximum residual magnetism having the same polarity to that to

which the flux would normally attain under equivalent normal voltage

conditions

If there is residual magnetism in the core at the instant of switching in and the residual

magnetism possesses the same polarity to that which the varying flux would normally

have, the phenomena described under (a) will be accentuated. This is, instead of the flux

wave starting at zero it will start at a value corresponding to the polarity and magnitude

of the residual magnetism in the core, and in the first cycle the flux will reach a

maximum higher than outlined in (a) by the amount of the residual flux. The theoretical

limit is three times the normal maximum flux density.

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Figure 4-11 Simple case- transformer. Single phase b). Voltage, current and flux


78

The Figure 4-11 illustrates the resulting transient flux/time distribution, while the inrush

current and voltage are showed as well. In this case the maximum value of the current

will be much higher and will take longer time to reach steady state conditions that in (a).

c) At zero voltage- maximum residual magnetism having a opposite polarity to

that to which the flux would normally attain under equivalent normal voltage

conditions

The converse of (b), where the residual magnetism has the opposite polarity as that

which is changing flux would normally attain, results in a diminution of the initial

maximum values of the flux, and consequently of the inrush current as can be seen in

Figure 4-12.

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Figure 4-12 Simple case- transformer. Single phase c). Voltage, current and flux

d) At maximum voltage- no residual magnetism

In this case at the instant of switching in, the flux should be zero, due to its 90° phase

displacement from the voltage, and with no residual magnetism in the core, the desired

conditions are obtain which produce the normal steady state time distribution of the

flux. That is, at the instant of switching in the flux start from zero, rises to normal

maximum in one direction, falls to zero, rises to normal maximum in the opposite

direction and again to zero, the wave being symmetrically disposed about the zero axis.

The no-load current, therefore, pursues its normal cause and does not exceed the

magnitude of the normal no-load current.

e) At maximum voltage-maximum residual magnetism having a polarity opposite to

that to which the flux would normally attain under equivalent normal voltage

conditions

This is the converse of the foregoing case, and the initial flux waves will again by

unsymmetrical disposed about the zero axis. For the same value of the residual

magnetism the total maximum flux would be the same as in case (e), but both flux and

current waves would initially be disposed on the opposite side of the zero axis.


79

f) At maximum voltage- maximum residual magnetism having a the same polarity

to that to which the flux would normally attain under equivalent normal voltage

conditions

In this case the residual magnetism introduces the transient component, so that the

initial flux waves are unsymmetrical disposed about the zero axis, high initial maximum

flux values are attained, and in the case where residual magnetism has the same value as

corresponds to the normal maximum flux density the inrush current will have a value

corresponding approximately to twice the normal maximum flux.

The voltage and flux for the six previous cases is shown in Figure 4-13. In the upper

plot the switching occurs when the voltage is zero, where the plot below presents the

fluxes when the switching occurs on the peak voltage.

40.0030.0020.0010.000.00 [ms]

3.75

2.50

1.25

0.00

-1.25

-2.50

Vc Opposite (e)

Zero (d)

Same (f)

40.0030.0020.0010.000.00 [ms]

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-2.50

Vc Same (b)

Zero (a)

Opposite (c)

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Figure 4-13 Simple case- transformer. Single phase a), b), c), d) e) and f). Zero crossing

(top) and peak crossing (bottom). Voltage and flux

The Figure 4-14 shows the fluxes (top) and currents (bottom) for all cases are compared

before. It can be clearly seen that the maximum current would happen during the

condition (b), where the switch closes on zero voltage and the transformer had resudial

flux on the same direction.


80

40.0030.0020.0010.000.00 [ms]

3.75

2.50

1.25

0.00

-1.25

-2.50

b

a

c

e

d

f

40.0030.0020.0010.000.00 [ms]

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-2.50

-5.00

b

a

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d

f

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Figure 4-14 Simple case- transformer. Single phase, all. Voltage (top) and flux (bottom)

4.4.4.2 Power Factory-three phase transformer

For three-phase transformers the previous operating principles are applicable, as long as

the normal magnetic relationships between different phases are considered, and each

phase is treated in combination with the remaining ones.

Normally the flux waves are simplified to sinusoidal functions in order to present the

phenomenon as clearly as possible, but the actual shape of flux and current waves will

be determined by the connections of the transformer windings and the type of magnetic

circuit.

A further simulation was done using a 3 limb delta winding transformer as the wind

turbine transformers in the collection grid of Nysted offshore wind farm.

First a comparison between switching when one of the phases was zero and peak

voltage was made. Then the residual flux during a zero voltage switching was varied in

the dq axis to obtain a worst case scenario. After these simultaneous pole closing, a non-

simultaneous pole energization of the transformer was done. Here, the switching was

made using the “worst case” (voltage on one of the phases was zero and the residual

flux on the other two was 0,8 with same polarity to that to which the flux would

normally attain under normal voltage conditions) for different times between pole

closing.

First a switching-in the transformer, was simulated, when one phase voltage was zero

(red) and then it was compared with a switching-in when the same phase voltage had

peak value. Figure 4-15 presents the voltages, fluxes and currents for the first case in

this comparison, where Figure 4-16 shows the results when he switching occurred on

peak voltage. The color nomenclature is shown in Table 4-3.


81

Form these two figures it can be seen that the highest current appears when the

switching happened in zero voltage crossing, with respect to the red phase, hence the

worst switching case is under the zero voltage crossing for any phase.

Table 4-3 Color nomenclature. Three phase, without residual flux.

Position Color Value

Top Blue Voltage phase A Green Voltage phase B Red Voltage phase C

Middle Light blue Magnetizing flux phase A Dark green Magnetizing flux phase B Pink Magnetizing flux phase C

Bottom Blue Current phase A Green Current phase B Red Current phase C

35.0028.0021.0014.007.0000.000 [ms]

3.000

1.800

0.600

-0.600

-1.800

-3.000

2-Winding Transformer: Phase Voltage A/HV-Side in p.u.

2-Winding Transformer: Phase Voltage B/HV-Side in p.u.


35.0028.0021.0014.007.0000.000 [ms]

3.000

1.800

0.600

-0.600

-1.800

-3.000

2-Winding Transformer: Magnetizing Flux A in p.u.

2-Winding Transformer: Magnetizing Flux B in p.u.


35.0028.0021.0014.007.0000.000 [ms]

4.000

2.400

0.800

-0.800

-2.400

-4.000

2-Winding Transformer: Phase Current A/HV-Side in p.u.

2-Winding Transformer: Phase Current B/HV-Side in p.u.


VI_2

Date: 6/19/2008

Annex: /10

Figure 4-15 Simple case- transformer. Three phase. Zero voltage switching


82

35.0028.0021.0014.007.0000.000 [ms]

3.00

2.00

1.00

0.00

-1.00

-2.00

-3.00

2-Winding Transformer: Magnetizing Flux A in p.u.

2-Winding Transformer: Magnetizing Flux B in p.u.


35.0028.0021.0014.007.0000.000 [ms]

3.00

2.00

1.00

0.00

-1.00

-2.00

-3.00

2-Winding Transformer: Phase Voltage A/HV-Side in p.u.

2-Winding Transformer: Phase Voltage B/HV-Side in p.u.


35.0028.0021.0014.007.0000.000 [ms]

4.000

2.400

0.800

-0.800

-2.400

-4.000

2-Winding Transformer: Phase Current A/HV-Side in p.u.

2-Winding Transformer: Phase Current B/HV-Side in p.u.


VI_1

Date: 6/19/2008

Annex: /9

Figure 4-16 Simple case- transformer. Three phase. Peak voltage switching.

Then, once the worst case switching is found, simulations with residual flux were done,

but only for this situation. Here, four cases were developed since the residual flux in

Power Factory can be only defined on d-q axis, and not independently on each phase.

These four cases are:

φd=0 and φq=1 (top-left)

φd=1 and φq=0 (top-right)

φd=0 and φq=-1 (bottom-left)

φd=-1 and φq=0 (bottom-right)

The voltages and fluxes for these cases are shown in Figure 4-17 and Figure 4-18,

respectively. Where the currents are presented in Figure 4-19. The color nomenclature is

shown in Table 4-4.

Table 4-4 Color nomenclature. Three phase, with residual flux

Left/right

Color Value

Voltages

Figure 4-17 Top/Bottom

Blue Voltage phase A

Green Voltage phase B

Red Voltage phase C

Flux


Light blue Magnetizing flux phase A

Dark green Magnetizing flux phase B

Pink Magnetizing flux phase C

Currents


Current phase A Current phase A

Current phase B Current phase B

Current phase C Current phase C


83

35.0028.0021.0014.007.0000.000 [ms]

3.000

1.800

0.600

-0.600

-1.800

-3.000

35.0028.0021.0014.007.0000.000 [ms]

3.000

1.800

0.600

-0.600

-1.800

-3.00035.0028.0021.0014.007.0000.000 [ms]

3.000

1.800

0.600

-0.600

-1.800

-3.000

35.0028.0021.0014.007.0000.000 [ms]

3.000

1.800

0.600

-0.600

-1.800

-3.000

Vvs(1)

Date: 6/19/2008

Annex: /6

Figure 4-17 Simple case- transformer. Three phase. With residual flux. Voltages

35.0028.0021.0014.007.0000.000 [ms]

3.000

1.800

0.600

-0.600

-1.800

-3.000

35.0028.0021.0014.007.0000.000 [ms]

3.000

1.800

0.600

-0.600

-1.800

-3.00035.0028.0021.0014.007.0000.000 [ms]

3.000

1.800

0.600

-0.600

-1.800

-3.000

35.0028.0021.0014.007.0000.000 [ms]

3.000

1.800

0.600

-0.600

-1.800

-3.000

psi vs

Date: 6/19/2008

Annex: /7

Figure 4-18 Simple case- transformer. Three phase. With residual flux. Fluxes


84

35.0028.0021.0014.007.0000.000 [ms]

6.000

3.600

1.200

-1.200

-3.600

-6.000

35.0028.0021.0014.007.0000.000 [ms]

6.000

3.600

1.200

-1.200

-3.600

-6.00035.0028.0021.0014.007.0000.000 [ms]

6.000

3.600

1.200

-1.200

-3.600

-6.000

35.0028.0021.0014.007.0000.000 [ms]

6.000

3.600

1.200

-1.200

-3.600

-6.000

I vs

Date: 4/5/2008

Annex: /7

DIg

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Figure 4-19 Simple case- transformer. Three phase. With residual flux. Current

It can be seen from Figure 4-19 that the highest currents are presented when φd=0, φq=-

1 (bottom-left) and when φd=-1, φq=0 (bottom-right). This can be explained from

Figure 4-18 (bottom-left) where the its noticeable that the magnetizing flux of phase B

(dark green), starts in 1 p.u.; where the magnetizing flux of phase C and A starts in 0,5

p.u. In Figure 4-18 (bottom-right) it can be seen that the magnetizing flux of phase B,

starts in 0 p.u.; where the magnetizing flux of phase C and A starts in 0,8 p.u. and -0,8

p.u., respectively. These two cases are shown graphically in Figure 4-20 where the same

color nomenclature for voltages and fluxes was used.

Figure 4-20 Residual flux and voltages. Left φd=0, φq=-1. Right φd=-1, φq=0


85

The problem with the residual flux defined in dq-axis is that there is no independence

between phases. The technical documentation of Power Factory is no very extensive in

this topic, where only few example cases refer to this phenomenon.

For the sequential transformer energization with residual flux in section 6, the case with

φd=-1, φq=0 was used since the inrush current is higher in this case, and is similar to the

“worst case” in (Smith, 2005).

Additional simulations were done with non-simultaneous closing of the breaker, with

and without residual flux, since in (Ma, et al., 2006) the authors mentioned that this

closing condition could lead to higher inrsh currents. But they don‟t mention the time

between each pole. Hence ten cases were done for five different closing times, with and

without residual flux as Table 7-2 in page 183 states.

It can be seen from Figure 7-1 to Figure 7-5 that the non-simultaneous closing does not

seems to worsen the inrush current. However additional work could be done in other

simulation programs where residual flux for each phase can be specified.

4.4.4.3 PSCAD-Single phase transformer

In PSCAD there are several single-phase and three-phase transformer models. In

general a three-phase transformer model can be made out of single phase transformer

models as Figure 4-21 shows of YD transformer.

Figure 4-21 PSCAD transformer equivalence

The transformer models in PSCAD are devided based on the classical approach and the

unified magnetic equivalent circuit (UMEC) approach.

The UMEC transformer models are based primarily on core geometry. Unlike the

classical transformer model, magnetic coupling between windings of different phases, in

addition to coupling between windings of the same phase, are taken into account

(PSCAD User's Guide, 2005).

For the current project the trasformers used are based on the clasical aproach. However

no simulations were done for the single-phase transformer.

mk:@MSITStore:C:\Program%20Files\PSCAD42\help\ol-help.chm::/EMTDC/Transformers/the_classical_approach.htm

mk:@MSITStore:C:\Program%20Files\PSCAD42\help\ol-help.chm::/EMTDC/Transformers/the_umec_approach.htm


86

4.4.4.4 PSCAD-three phase transformer

In this subsection the zero-voltage simultaneous pole energization of a transformer with

no residual flux was simulated in PSCAD (same event as Figure 4-15 in Power

Factory), in order to compare the same transformer model in both simulation programs.

The network used in this subsection is shown in Figure 4-22. Here the connection to the

grid is simulated as a voltage source, then a breaker is connected between the

transformer and the grid. On the low voltage side of the transformer a small load was

connected to avoid numerical problems.

It‟s important to notice that the grounding on the secondary side of the transformer is

simply connected with a “wire” device, as recommended in (PSCAD User's Guide,

2005).

In Figure 4-22 is possible to locate the voltage measurements on both sides of the

breaker and the current measurements in the primary side of the transformer.

The closing signals for the breaker are send individually for each phase, with a “Time

breaker logic” component used to control single and three phase breakers, to a signal

(BRKA, BRKB and BRKC) used to transfer data signals to the breaker.

Figure 4-22 Simple case- transformer. PSCAD

The results from the voltage and current measurements are send to an output channel,

that are further visualized in a graph, this measurements are shown in Figure 4-23.


87

Figure 4-23 Simple case-transformer. PSCAD. Results

The instantaneous voltage and currents are shown here with the color nomenclature as

stated on the upper side of each graph. If the current in Figure 4-23 is compared with

Figure 4-15 is possible to see the same shape and magnitude for the current. This proves

that both models match each other, regarding the saturated and un-saturated reactances

during energization.

In PSCAD the transformer model has an “inrush decay time constant” parameter that

gives the possibility to force a fast decay of the inrush current by artificially introducing

damping in the circuit. However this value was set to 0 for all the simulations, and the

inrush would be damped solely by the network.

4.4.5 Further inrush current control

There are possible solutions to reduce the residual magnetism in power transformers,

some of them are:

1. Switch off the load of the transformers before the primary circuit is opened

2. De-magnetization. Gradually reducing the applied voltage before switching the

transformer out of circuit. As the voltage decreases, the flux in the transformer

core also decreases.

3. De-energization. The transformer breaker can be controlled to achieve define

and repeatable remanent flux. Subsequent energization can be then matched

with known residual flux to minimize inrush current (ABB Controlled

Switching 2006-09).

On the other hand there are possible solutions to reduce the inrush current in power

transformers (Nagpal, Martinich, Moshref, Morison, & Kundur, 2006):


88

1. Include pre-insertion reactors, this adds impedance to the switched circuit and

thereby reduces the inrush. This is an expensive solution because an additional

substation is needed (Ma & Cadmore, 2006).

2. Transformers energized by segregated point-in-wave closing method requires

that the circuit breaker poles be switched at optimal instants to reduce or

eliminate inrush currents [Brunke, J.H., et al 2001]

Additional work should be done regarding a risk and economical analysis of the benefits

of reducing the residual flux, and inrush current in large offshore wind farms, since

maybe due to grid concerns or protection, specialized equipment would pay off.

4.5 High voltage cables

The cables used in the collection grid in Nysted Wind Farm are solid dielectric cables

with cross-linked polyethylene (XLPE) insulation. The XLPE cables have several

advantages over High-Pressure Fluid-Filled (HPFF) pipe-type cables that makes them

ideal for the use in offshore wind farms [Tziouvaras, D.A., 2006]:

Lower capacitance, resulting in lower steady-state charging current

Higher load-carrying capability

Lower losses

Lower maintenance cost because there is no dielectric fluid

No environmental risk due to insulating oil fluid leak

Immediate re-energization capabilities on system restoration

4.5.1 Cable modeling theory

Cables can be divided into two broad categories, shielded and unshielded. The effect of

the shield is to confine the electric field between itself and the conductor. Since the

current almost always returns through the conductor of the other phases, the magnetic

shield is not confined in the same way, it is nevertheless affected by the presence of the

shield and armoring because of eddy current induced within.

For low frequency transients the dominant attribute of the cable is the capacitance. The

cable can be therefore modeled as a capacitor in parallel with the load. For fast

transients, a distributed model is required. Because the conductors are in close

proximity it is necessary to consider the line and ground modes. Also when shields or

armor are grounded at one end only, a mode is added between this shield or armor and

the external ground plane.

In XLPE cables the skin effect, dielectric and semi-conductive layer losses are

responsible for a attenuation on the steep-fronted transient (Dick, et al., 1988).

4.5.2 Cable modeling application

According to the IEEE PES Task Force on insulated cable modeling (Gustavsen, et al.,

2005), there are several EMT programs that can accurately represent the frequency

dependence of the cables. These models require the same information: the series

impedance matrix Z and the shunt admittance matrix Y.


89

However other parameters are hard to obtain for cables system because the small

geometrical distance makes the parameters highly sensitive to errors. Furthermore, there

is no simple method to represent features like wire screens, semiconductive screens,

armor or lossy insulation materials.

The basic equations to represent insulated cables have the following form:

)()()(

)()()(

CjGY

LjRZ

(4.15)

where R is the series resistance, L the series inductance, G the shunt conductance and C

the shunt capacitance per unit length of the cable system. These quantities are (n x n)

matrices, being n the number of parallel conductors of the cable system. Both Z and Y

being frequency dependant quantities.

The series impedance Z and the shunt admittance Y are calculated automatically by the

cable constants routines within the program, using cable geometry and material

properties as input parameters. In general, the user must input:

Geometry

o Location of each conductor (x-y coordinates)

o Inner an outer radii of each conductor

o Burial depth of the cable system

Material properties

o Resistivity and relative permeability of all conductors

o Resistivity and relative permeability of the surrounding medium

o Relative permittivity of each insulating material

The calculation of Z and Y from the geometry and the material properties follows

similar procedure for all cable constant routines. However there are still challenges on

the impedance calculation, based on computing surface impedance and transfer

impedance of cylindrical metallic shields, as well as self and mutual ground

impedances. The standard routines in PSCAD include the skin effect but neglect the

proximity effect on the cable. However the losses due to these effects are small at

nominal frequency.

4.5.3 Conductive materials

Table 4-5 Material properties in cables

Resistivity Copper Aluminum Lead Steel

[m] 1,72E-8 2.83E-8 22E-8 18E-8

Stranded conductors are to be modeled as solid conductors, with an increased resistivity

to take into account the fill factor of the conductor, in order to achieve the correct

resistance. The corrected resistivity should be calculated as:

c

c

A

r2

'

(4.16)

Where, rc is the conductor radio and Ac the conductor area given from the manufacturer

for each phase. In the simulations of the next section, the corrected resistivity increased


90

about 7% due to the modification of equation (4.16) in the MV cables at Nysted

offshore wind farm.

In the same document it is mentioned that the resistivity of the surrounding ground

depends strongly on the soil characteristics, where a recommended value of 1 m for

wet soil.

The submarine cables in Nysted have a magnetic steel armor, consisting of a number of

round wires enclosing the three-phase cable; hence, the cable can be modeled using

“pipe-type” representation. Here, the permeability depends on the wire diameter, the

laying angle and the intensity of the circumferential magnetic field. This variation on

the permittivity arises problems with the calculation of the zero-sequence impedance of

the pipe-type cables, while zero-sequence impedance varies with the effective

permeability of the steel pipe, and the permeability of the steel pipe varies with the

magnitude of the zero-sequence current (Tziouvaras, 2006). However neither PSCAD

nor Power Factory supports armored three-phase cables.

4.5.4 Insulating materials

Table 4-6 XLPE relative permittivity

Relative permittivity XLPE

2,3

Most extruded insulations, are practically lossless up to 1 MHz. The losses are

associated with complex, frequency-dependant permittivity

'/'')(tan

)('')(')(

rr

rrr j

(4.17),(4.18)

where the tan is the insulation loss factor. This value should be set to zero, while non

of the available routines allows to enter a frequency-dependant loss factor and a

constant value would lead to inaccuracies.

As stated above, the main insulator of each conductor lays between to semiconductive

screens, unfortunately in the EMT programs it‟s not possible to specify these layers.

Therefore, a correction should be made in order to allow the insulation to extend

between the core and the sheath conductor, with the capacitance of the cable unchanged.

This can be done by

0

12

2

)/ln(

rrCr (4.19)

where the C is the cable capacitance, r1 the conductor radius, r2 the outer radius of the

insulation plus both semiconductive screens. In the simulations of the next section, the

corrected relative permittivity increased about about 10% due to the modification of

equation (4.19) in the MV cables at Nysted offshore wind farm.


91

4.5.5 Grounding

In submarine cables, the armor is usually thick for mechanical strength, thus preventing

any high- frequency flux to penetrate the armor, so no voltage drop will develop here.

However the armor and the sheath are grounded at both cable ends in the collection

grid. In reality, the outer metal wire armor is in contact with the soil, since it is only

covered with impregnated insulator.

With this connection, during transients, very small induced voltages would appear in the

sheath compared with voltages in the conductors. However the sheath and armor were

included in the studies when possible.

4.5.6 Sensitivity of transients

High-frequency cable transients propagate as decoupled coaxial waves between core

and sheaths, so the transient behavior of the cable is sensitive to the modeling of the

core, main insulation, semiconductors, and sheath. The sensitivity of coaxial waves can

be summarized as follows (Gustavsen, et al., 2005):

Increasing the core resistivity increases the attenuation and slightly decreases

propagation velocity

Increasing the sheath resistivity (or decreasing the sheath thickness) increases

attenuation

Increasing the insulation permittivity increases the cable capacitance. This

decreases the velocity of the surge impedance

With a fixed insulation thickness, adding semiconductive screens increases the

inductance of the core-sheath loop without changing the capacitance. This

decreases the velocity and increases the surge impedance

Since the sheath conductors are normally grounded at both ends, the potential along this

conductor is low compared to that of the core conductor, even in transient conditions.

As a result, the simulated transient on phase conductors are insensitive to the specific

properties of insulating materials external to the sheath.

Once the transient phenomena in cables and its modeling have been presented, the

simple study cases to compare Power Factory and PSCAD are explained.

For each simulation program four cases based in (Gustavsen, et al., 2005) has been done

with a fixed step value of 1 μs (145 kV, 5 km cable). The information for all the cases is

presented in Table 4-7. The different cases are:

3 mm lead sheath, 1 mm semiconductor on both side of the insulation

1 mm lead sheath, 1 mm semiconductor on both side of the insulation

0,211 mm copper sheath, 0 mm semiconductor on both side of the insulation

0,211 mm copper sheath, 3 mm semiconductor on both side of the insulation


92

Table 4-7 Simple case- cable. Information

Case Radius Resistivity Relative

permittivity

Outer radius Relative

permeability

Units [m] [Ω*m] [m]

1 Core 0,02 1,72E-08 1

Insulation 1 2,671 0,035 1

Sheath 2,20E-07 0,038 1

Insulation 2 2,3 0,043 1

2 Core 0,02 1,72E-08 1

Insulation 1 2,671 0,035 1

Sheath 2,20E-07 0,036 1


3 Core 0,02 1,72E-08 1


Sheath 1,72E-08 0,035211 1

Insulation 2 2,3 0,040211 1

4 Core 0,02 1,72E-08 1

Insulation 1 3,897 0,035 1

Sheath 1,72E-08 0,035211 1

Insulation 2 2,3 0,040211 1

4.5.7 Simple case in Power Factory

A step voltage on one of the phases of a cable has been modeled in Power Factory, as

the example in (Gustavsen, et al., 2005). The network for this simple case is shown in

Figure 4-24. Where the individual voltage sources for each phase are connected at

Terminal A. Here the conductor for the cable system is connected on one side, where

the other side of the cable is connected to Terminal B. The sheath conductor for the

cable system is connected between Terminal Sh A and Terminal Sh B.

Phase C

Phase B

Phase A

0.0000..

AC Voltag..

Sheath

0.0000..0.0000..0.0000..

0.0000..0.0000..0.0000..

Conducto

r

0.0000..0.0000..0.0000..

0.0000..0.0000..0.0000..

Terminal B0.0000.0000.000

Terminal A0.0000.0000.000

Terminal Sh B0.0000.0000.000

Terminal Sh A0.0000.0000.000

DIg

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Figure 4-24 Simple case- cable. Power Factory. Network


93

Once the sheath and the conductor network have been done, a cable system has to be

created, where the coupling between the sheath and the phases can be included. This

coupling can be seen in Figure 4-27.

Once the coupling has been created a single core cable element has to be added in the

Data Manager, since the cables are not standard components in Power Factory and they

are still under development.

The information needed for each single core cable (Table 4-7) must be set in the cable

type as Figure 4-25 presents. Then the geometrical position of each single core cable

has to be added in the cable definition, as Figure 4-26 shows.

Figure 4-25 Simple case- cable. Power Factory. Single core cables


94

Figure 4-26 Simple case- cable. Power Factory. Three phase cable

Figure 4-27 Simple case- cable. Power Factory. Cable system, basic data

Then, the cable system should be define as a distributed parameter, where the frequency

for parameter approximation (a frequency value representative of the range of frequency

expected for the study) should be used (Figure 4-28) (DigSILENT Technical

references). This cable system fixes this frequency during the entire simulation period,

which in the following section was proven to be give wrong results in the steady state of

the study cases 1 and 2.


95

Figure 4-28 Simple case- cable. Power Factory. Cable system, EMT simulations

4.5.8 Simple case in PSCAD

In this subsection the procedure to create the same study system for a cable, in PSCAD

as previously explained in Power Factory is shown.

First the cable interfaces for both sides of the cable has to be done, then the cable

configuration has to be added. It is important to notice that the cable interfaces and the

cable configuration has to have the same name (Cable1 in this case) in order for

PSACAD to understand that these are three parts of the same cable system. Then the

sheaths on each cable interface (S1) has to be grounded with a very low resistance to

avoid numerical problems.

Since the study case require that only one of the phases experience a step voltage, the

remaining phases on the same side of the cables had to be grounded, where in the other

side of the cable all phases were connected to a large resistance to emulate an open

circuit.


96

Figure 4-29 Simple case- cable. PSCAD. Network

Figure 4-30 Simple case- cable. PSCAD. Cable configuration.

In the cable configuration (Figure 4-30) the control constrains to solve the cable

behavior under transient condition, has to be define based on the recommendations of

the User‟s manual. Then coaxial cable constants for each single core cable are to be

define. Some of the information needed here is the position of each cable with respect to

each other and the soil, the thicknesses and electrical parameters of the cable conductors

and insulators, etc.


97

4.5.9 Comparison

The four cases, on each simulation program were done and the results were exported to

MATLAB in order to compare them. Figure 4-31 shows on the top the first two cases in

Power Factory (Va1PF, Va2PF) and PSCAD (Va1PSCAD, Va2PSCAD). Where the

lower part shows the last two cases in Power Factory (Va3 PF, Va4 PF) and PSCAD

(Va3PSCAD, Va4PSCAD).

Figure 4-31 Single case- Cable. Comparison

At first sight is noticeable that the response in Power Factory and PSCAD are very

different, however the main problem in Power Factory is that the voltage source is not

capable to realize step changes, and work independently with each phase. The

simulations were repeated in Power Factory several times with measurements files for

step voltages, capacitances between the conductor and sheath, etc.. However the

response never fit the results from PSCAD, or the figures on the paper from Gustavsen.

Nevertheless, some conclussions can be made from this comparisson, based on the cable

sensitivity under transeint conditions (subsection 4.5.6 in page 91):

In both simulation programs, an increase in the sheath resistivity (or decreasing

the sheath thickness) an increase in the attenuation is presented.

In both simulation program, an increase in the insulation permittivity increased

the cable capacitance, and this decreased the velocity of the voltage wave.


98

The rounding during first microseconds of the overvoltage, is not present in the

results from Power Factory. This phenomena is caused by the skin effect

representation in the core (frequency dependant).

Emphasis should be made in this comparison, since the results from Power Factory and

PSCAD are very different. The results presented in (Gustavsen, et al., 2005), are made

on EMTP-RV, where PSCAD is the graphical user interface of the simulation engine

EMTDC. Although the comparison was based on the simulation results from Gustavsen,

no measurements were done in the thesis on a cable.

However at Chalmers University of Technology, similar measurements on a real system

were reported in (Daniel & Gebre, 2008). Here, the authors initially charged a cable at

800 V and discharged through a COM-gap, to create a very steep fronted voltage.

Then the measurements were emulated using PSCAD with good agreement between

measured and simulated values. The frequency of oscillation and propagation delay in

the cable matched the measurements, although higher damping is observed in the real

system.

The results from Daniel & Gebre are important because they show that PSCAD results

can be trusted for a step voltage variation in a cable. On the other hand, the outcome of

the simulations done in the current thesis, reveal that the model in Power Factory for a

step voltage in a cable is inaccurate. However this conclusion cannot be extrapolated to

a real system, where other equipment is connected on both ends of a cable (study cases

in Nysted Offshore wind farm).

It was shown in the next section that Power Factory and PSCAD results, from a

switching event on a real system, are not as accurate as an insulation coordination study

would require.

Additional comments regarding the cable behavior under transient conditions in Power

Factory and PSCAD was done further in the report.

4.6 Voltage source

In the next section the study cases 1, 2, and 3, where simulation results in Power

Factory and PSCAD were compared with actual measurements, the grid connection at

132 kV was modeled as a voltage source with a series impedance that accounts for the

short circuit capacity and damping of the grid. These are important values for the

simulation since the “strength” of the system is simplified in this two values.

As stated in the section 2, 3 and subsection 4.5 the voltage source has key importance in

the switching transient studies. In section 2 and 3 was mentioned the importance of the

point-in-wave where the switching takes place since the overvoltages, reflections and

inrush currents are highly dependent in this parameter. In subsection 4.5 was shown

how the representation of independent voltage sources for each phase can result in


99

better simulation results. In section 6 one of the study cases to compare simulation

results has a decreased grid capacity, which has an influence on the voltage dip due to a

sequencial energization of a number of transformers.

In this subsection a comparison between voltage sources in Power Factory and PSCAD

was done, as well as a procedure to include accurately a voltage source for switching

transients.

First of all Power Factory has one very flexible AC voltage source, with many options

of control, while PSCAD Master Library includes three equivalent Thévenin voltage

source types. Each of these possesses distinctive features, so the system designer

should be aware of the differences.

In the three study cases and sequential energization of transformers, the Three-Phase

Voltage Source Model 3 was used. In this model it‟s possible to specify the positive

sequence and zero sequence source impedance. Here the source impedance is modeled

as aseries RL impedance. The difference with the other models in PSCAD is that this

source must be controlled externally, where the rms voltage and the phase angle are

inputs to the model, however these values can be constants.

Once the voltage source has been chosen for each simulation program, the magnitude

and phase of the voltage should be calculated based on the measurements. Here it‟s

important to notice that in both programs the phase angle is based on the moment when

the simulation begins, hence is recommended to start the simulation at time zero or with

variations every 20 ms.

From the measurements is possible to calculate the phase of the voltage, however care

should be taken, since there is a phase shift in the park transformer, and the initial angle

is defined differently in both programs.

Another important aspect of the switching transient studies is that the system should be

stable before the switching begins. In the case of the voltage source in PSCAD is

recommended that the voltage increase for 60 ms until the switching operations begins.

This is done by setting the “Voltage input time constant” to 0,06 s. This way the voltage

ramps up to 1 p.u. in three cycles to reduce start-up transients.

No simple case to compare the voltage sources in Power Factory and PSCAD was done.

However additional comment were realized further in the report.

4.7 Capacitors bank

The capacitor bank located on the low voltage side of the transformer on each wind

turbine, is in charge of compensate for the reactive consumption of the asynchronous

machine under generation.

In the first and second study cases there was a capacitor connected in A01, while in the

third study case additional capacitors were connected in A02, A03, A04, A05, A06, A07

and A08 since the generators in this wind turbines were under production.


100

It is a common use in the capacitor banks to include a reactor before the capacitors in

order to protect the banks, in this situation the reactor is indirectly defined by the degree

of inductance in the capacitor bank. This degree represents the ratio between the

inductive and capacitive reactance of the equipment. Hence if the reactive power

generation is known (Figure 3-22), as well as the nominal frequency and voltage on the

low voltage side of the transformer the reactance and capacitance can be calculated for

each case.

In Power Factory the capacitor banks in each wind turbines can be simply defined as a

Filter ABC-„D‟ with the rated reactive power and the degree in the bank. However in

PSCAD, the capacitance and inductance of the bank has to be calculated, as stated

before.

The capacitor bank in A01 with a rated capacity of 180 kVAr, and 5,6 % is presented in

Power Factory (left) and PSCAD (right) in Figure 4-32.

Figure 4-32 Capacitor bank

If the impedance characteristic of the bank is plotted (Figure 4-33) for different values

of inductance, is possible to see that if a wrong value of inductance is used, the

resonance frequency of the capacitor bank would change.

Is possible to see from Figure 4-33, that the resonance frequency for a value of 4,71E-4

H is around 210 Hz, similar to the resonance frequency achieved in the current at A01

(Figure 3-20-left). Hence, a capacitor bank is connected at A01. However, in the

PSCAD model of the filter, a value of 4,71E-5 H was used by mistake, as Figure 4-32

shows.


101

Figure 4-33 Capacitor bank impedance characteristic

Once the capacitor bank model was explained, the next electrical device left to explain

is the induction generator.

4.8 Generator

In the third study case, it was found after the active and reactive power calculation in

the measurements that seven of the nine wind turbines of row A were under production.

Thus in order to simulate this case as close to reality as possible, the generators were

included, nevertheless this was not part of the initial scope of the project.

The induction machine is relatively easy to define and use in Power Factory, where the

equivalent circuit should be defined, the nominal power, the operating condition

(motor/generator), the inertia, nominal frequency and number of poles pair.

In PSCAD the procedure is a little more complicated. First the model is set for a double

cage induction machine; here corrections had to be made to the equivalent model since

the equivalent model used in Power Factory is a single-cage machine. In reality the

double squirrel-cage induction machines are used to obtain high value of starting

resistance and low value of resistance at full load (Kundur, 1994). On page 294 of this

same book, the procedure to achieve an equivalent circuit for an induction machine with

double-cage rotor is presented. In this case the available information is on a single-cage

machine, and the required equivalent circuit for PSCAD should be calculated for certain

slip (under production).

Once the equivalent circuit is complete, the model is partially complete, since the

control has to be implemented. Here the machine has to be started in speed control

mode and then switched over to torque control after the initial transients of the machine


102

are over. The time to switch to torque control varies depending on the machine. This

change to torque control is important because in the wind turbines if there is a voltage

dip e.g. caused by a transformer energization, the machine would accelerate and

oscillate for several cycles, since it can be assume that the wind speed remains constant.

The equivalent circuit in Power Factory (left) and PSCAD (right) is shown in Figure

4-34. The simple study case here is to start the induction machine as a generator, then at

2 s one breaker would disconnect the machine for 10 ms. Here the machine would

accelerate since there is no electric torque to control it, then it would oscillate for

several cycles depending on the damping in the system and the inertia of the generators.

Figure 4-34 Simple case- Generator. Network

In Figure 4-35 the speed of the generators on both models are presented. The left side

plot of this figure is the results from Power Factory, while the plot in the right is the

calculated speed from PSCAD. Both simulations show the same behavior regarding the

oscillations. However the initial speed is not the same, this could be due to the fact that

the control of the machine in Power Factory is torque control for the entire simulation,

while for the PSCAD model the initial control speed set the velocity to 1.01 p.u.

Another difference is that the decreased speed after the re-connection of the machine is

lower in Power Factory than in PSCAD. Other important difference is that the system

seems to have larger damping in Power Factory than in PSCAD. Both of these

variations could be due to the different generator representation in the programs.

However, these disparities for the third study case are not really important.


103

Figure 4-35 Simple case- Generator. Rotor speed

Now that the main electrical devices in the collection grid of Nysted offshore wind farm

had been explained and compared between simulation programs, the computation of the

three main study cases was done in the next section.

4.9 Summary

In this section the electrical equipment needed to emulate the measurements of the three

study cases in Power Factory and PSCAD were explained. The theory behind the

modeling of a breaker was clarified. The transformer transient conditions were

explained based on theory and examples in Power Factory. Then, a satisfactory

comparison between the transformer model in Power Factory and PSCAD for

energizing studies was done.

The transient phenomena occurring in the cable during energization was presented, as

well as the guidelines for cable modeling. When a comparison was made between the

cable models in Power Factory and PSCAD, a clear difference was present due to the

simulated voltage source in Power Factory. After that, the voltage source models in

Power Factory and PSCAD were mentioned and compared.

The capacitor bank connected in the low voltage side of the transformer, which

compensates for the reactive power consumption of the induction generator under

production, was explained and compared in both simulation programs.

Finally the induction machine model in Power Factory and PSCAD, were compared

achieving similar results in a simple study case.

105

5 SYSTEM MODELING

5.1 General procedure

First of all, the information regarding the wind farm was gathered. Some of the

available information was:

The gird impedance and voltage level.

The sequence impedance and capacitance of the cables between the point of

connection with the transmission grid and the high voltage side of the park

transformer.

The impedance, rated power and voltage level of the three winding park

transformer.

The sequence impedance and capacitance of the submarine cables of the

collection grid.

The length of the cables between wind turbines and between the first wind

turbine of each row and the transformer platform.

The construction layers of the three phase cables, with its dimensions and

properties.

The short circuit voltage of the wind turbine transformers, the copper and iron

losses and the no-load current.

To account for the transformer energization the magnetizing reactances and knee

flux are required.

The high frequency capacitances between the HV windings to ground, LV

winding to ground and LV to HV windings.

The permanent LV load on each wind turbine.

The capacitors bank that compensates for the reactive power consumption of the

induction generator in each wind turbine.

The induction generator electrical representation.

Once all the available information was gathered the next step is to find the event to

simulate. In this project only three cases from many measured events were relevant. It

was decided that two “Energization of Row A” and one “Switch A09” were to be

simulated. On the first two cases the breaker on the platform that connects the row A is

closed, here the cable is energized follow by all the transformers in the row. In the last

case only the transformer in the wind turbine A09 was energized, and in theory, the rest

of the wind turbines were not under production, but as it was later demonstrated that

seven of the remaining turbines were almost at full production.

Once it was decided which events to simulate, the next step is to approach the

measurements files. Since they were made at 2.5 MHz and there are three voltages and

System modeling

106

three currents at three locations, the problem becomes quite large. The files for the first

two cases are divided each half second with a time stamp on the file‟s name, and one

file for each location. In these six files the data was unscaled 16-bit data from the DAQ,

so it had to be converted to kV and kA. For the third case the file‟s length is only 0,2 s

instead of 0,5 s from the two first cases. These measurements files are already scaled

and not conversion had to be made.

Once the files are located the time of the switching events had to be found. Since there

are samples every 400 ns the switching time for each phase is very precise. Another

important thing to calculate at this stage is the phase of the voltage, since it is very

important for switching studies. If the phase of the voltage is not the right one, the

reflection on the cable and the inrush current on the transformers would be different.

Just as a reminder the Figure 5-1 shows the simplified network of the study cases 1, 2

and 3. The three measurement locations can be located in blue color, while the “live”

equipment is shown in red, and the equipment without voltage in black.

Figure 5-1 Simplified network for study case 1, 2 and 3

The digital system of NOWF was created in both simulation tools, based on the

experience gained in the previous section. However, it‟s important to mention the

differences between both systems. The Table 5-1 shows a comparison of some of the

System modeling

107

models used for the transient simulations in both programs, as well as important

parameters for emt studies:

Table 5-1 Input information and models in both simulation tools

Equipment Attributes Power Factory PSCAD

Available Used Available Used

Circuit

breaker Detailed model No No Yes No

Tra

nsfo

rme

r

Models

2-winding

transformer

type

2-winding

transformer

type

Classical and

UMEC model Classical

Residual flux Yes Yes Yes No

High frequency

capacitances Yes Yes Yes Yes

Inrush decay

time constant No No Yes No

Cable 3 phase cable

with armor No No No No

Voltage

source Models

AC voltage

source

AC voltage

source

Voltage

source model

1, 2 and 3

Voltage

source model

3

Capacitor

bank Models Yes Yes No Yes

Induction

generator Models

Asynchronous

machine

Asynchronous

machine

Double- cage

induction

machine

Double- cage

induction

machine

Due to time limitations, the detailed circuit breaker model available in PSCAD was not

used to emulate the measured pre-strikes. However, there is no standard model in Power

Factory for this phenomenon.

The transformer models used in PSCAD was the classic model, since no detailed

information of the transformer was available besides the main electrical characteristics.

The residual flux of the transformer in Power Factory was used in the next section;

however there was no need for it in the study cases. Where the residual flux in PSCAD

was not used due to time constrains. The inrush decay time constant of the transformers

in PSCAD could be set to decrease the time to reach steady state after energization,

nevertheless there is no equivalent variable in Power Factory.

On the modeling of submarine cables, none of the simulation tools have the possibility

to model three-phase armored cables. Although, due to the grounding of the system, the

transients propagate as decoupled coaxial waves between core and sheath; and the

specific properties of the cable external to the conductor-insulation-sheath system have

no influence on the transient behavior of the cable.

The voltage source, capacitor bank and induction generator were simulated in Power

Factory and PSCAD as stated on the previous section, where no major difference were

expected.

System modeling

108

5.2 Study case 1: Connection of Row A-I

Assuming that the previous steps had been fulfilled the modeling of the network can

start. The modeling of the first case “Row A energization” was explained below. The

procedure for the second case is relatively the same, only the switching time is different.

However is important to model the second case because this time difference caused

higher transient overvoltages and higher inrush currents.

The procedure to create the model in Power Factory will be presented first and then the

procedure for PSCAD, afterwards the comparison between the measured and simulated

results was done.

5.2.1 Power Factory

The first thing to define in the network are the terminals or busbars, where the cables,

transformers, voltage sources, loads, capacitor banks and generators were connected. To

simplify things, and avoid confusion, the network was created based on the geometrical

arrangement of the network as Figure 3-1 shows.

Here the connection to the grid is in the top center part of the network, followed by the

HV cables to connect the park transformer. This part is shown in Figure 5-1.

LV load(8)

LV load(7)

LV load(6)

LV load(5)

LV load(4)

LV load(3)

LV load(2)

LV load(1)

LV load

Sea cableSea cable

A8-A9A8-A9

A7-A8(1)A7-A8(1)

A6-A7A6-A7

A5-A6A5-A6

A4-A5A4-A5

A3

-A4

A3

-A4

132 kV network

V~

A2-A3A2-A3

A1-A2A1-A2

Shunt/Filter

Lin

eL

ine

A8(1)A8(1)

A7(1)A7(1)

A6A6

A5A5

A4(1)A4(1)

A3(1)A3(1)

A2(1)A2(1)

A1(1)A1(1)

A9(2)A9(2)

H1

-H9

H1

-H9

G1

-G9

G1

-G9

F1-F

9F

1-F

9

E1

-E9

E1

-E9

DDCCBB

Ro

otH

Ro

otH

Ro

otG

Ro

otG

Ro

otF

Ro

otF

Ro

otE

Ro

otE

Ro

otD

Ro

otD

Ro

otC

Ro

otC

Ro

otB

Ro

otB

Ro

otA

Ro

otA

132/33/33 Transformer132/33/33 Transformer132/33/33 Transformer

Platform/Sea

Raadsand/B1

Radsted/Shore

H9G9F9E9

D9C9B9

A9(..A9

H1G1F1E1

D1C1B1

Platform Term 2/EFGH

A8

A7

A6(1)

A5(1)

A4

A3

A2

A1

Platform Term 1/ABCD

DIg

SIL

EN

T

Figure 5-2 Case 1. Power Factory. HV network.

Then on each winding of the transformer, four feeders are created with a MV submarine

cable to the first turbine of each row. Then, only the row A is further defined since the

measurements and the switching operations take place here only. The MV collection

grid of Nysted offshore wind farms created in Power Facotry is shown in Figure 5-3.

System modeling

109

LV load(8)

LV load(7)

LV load(6)

LV load(5)

LV load(4)

LV load(3)

LV load(2)

LV load(1)

LV load

Sea cableSea cable

A8-A9A8-A9

A7-A8(1)A7-A8(1)

A6-A7A6-A7

A5-A6A5-A6

A4-A5A4-A5

A3

-A4

A3

-A4

132 kV network

V~

A2-A3A2-A3

A1-A2A1-A2

Shunt/Filter

Lin

eL

ine

A8(1)A8(1)

A7(1)A7(1)

A6A6

A5A5

A4(1)A4(1)

A3(1)A3(1)

A2(1)A2(1)

A1(1)A1(1)

A9(2)A9(2)

H1

-H9

H1

-H9

G1

-G9

G1

-G9

F1-F

9F

1-F

9

E1

-E9

E1

-E9

DDCCBB

Ro

otH

Ro

otH

Ro

otG

Ro

otG

Ro

otF

Ro

otF

Ro

otE

Ro

otE

Ro

otD

Ro

otD

Ro

otC

Ro

otC

Ro

otB

Ro

otB

Ro

otA

Ro

otA


Platform/Sea

Raadsand/B1

Radsted/Shore

H9G9F9E9

D9C9B9

A9(..A9

H1G1F1E1

D1C1B1


A8

A7

A6(1)

A5(1)

A4

A3

A2

A1


DIg

SIL

EN

T

Figure 5-3 Case 1. Power Factory. MV network

In order to create the coupling between the conductors and the sheath, a sheath network

had to be created as Figure 5-4 presents. Here the grounding in the platform and in each

wind turbine had to be created with an AC voltage sources as the Technical References

explains. At this stage the user has to be very careful since the length of the conductor

and the sheath has to be the same in order for the cable system to work.

The name of each of the cables and sheath has to be define in a clear way since the

“connection” in the cable system is done in the Data Manager and not graphically, and

its complicated when 23 cables and 23 sheaths has to be connected in 23 cable systems.

System modeling

110

Sh_A

8-A

9S

h_A

8-A

9

AC Gnd(..

AC Gnd

Ac Gnd B1-B9

Ac Gnd A0-A1(..

Ac Gnd A0-A1(..

Ac Gnd A0-A1(..

Ac Gnd A0-A1(..

Ac Gnd A0-A1(..Ac Gnd D1-D9Ac Gnd C1-C9

Ac Gnd H9

Ac Gnd H1

Ac Gnd G9

Ac Gnd G1

Ac Gnd F9

Ac Gnd F1

Ac Gnd E9

Ac Gnd E1

Ac Gnd A0-A1(..

Ac Gnd A0-A1(..

Ac Gnd A1-A9

Ac Gnd A0-A1Ac Gnd D0-D1Ac Gnd C0-C1Ac Gnd B0-B1

Sh H

1-H

9S

h H

1-H

9

Sh G

1-G

9S

h G

1-G

9

Sh F

1-F9

Sh F

1-F9

Sh E

1-E

9S

h E

1-E

9

Sh_R

_H

Sh_R

_H

Sh_R

_G

Sh_R

_G

Sh_R

_F

Sh_R

_F

SH

_R

_ES

H_R

_E

Sh_D

Sh_D

Sh_C

Sh_C

Sh_B

Sh_B

Sh_R

_D

Sh_R

_D

Sh_R

_C

Sh_R

_C

Sh_R

_B

Sh_R

_B

Sh_A

7-A

8S

h_A

7-A

8

Sh_A

6-A

7S

h_A

6-A

7S

h_A

5-A

6S

h_A

5-A

6S

h_A

4-A

5S

h_A

4-A

5S

h_A

3-A

4S

h_A

3-A

4

Sh_A

2-A

3S

h_A

2-A

3S

h_A

1-A

2S

h_A

1-A

2

Sh_R

_A

Sh_R

_A

Station D1/Sheath D1Station C1/Sheath C1Station B1/Sheath B1

Station B9/Sheath B9

Station A1(5)/Sheath A6




Station A1(1)/Sheath A2 Station D9/Sheath D9Station C9/Sheath C9



Station A9/Sheath A9

Station A1/Sheath A1

Platform term 2/EFGH Sheath

Platform term 1/ABCD Sheath

H9G9

F9E9

F1E1

H1G1

DIg

SIL

EN

T

Figure 5-4 Case 1. Power Factory. Sheath network

Then the Single Core Cable Types, the Cable Definitions and Cable System Types have

to be created for the cables, as the subsection 4.5.7 in page 92 explained. Here is

important to notice that if the same cable is used in the collection grid, only one Single

Core Cable Type and Cable Definition can be used. However a Cable System Types has

to be created for each cable.

Once the cable systems were created, the electrical equipment connected on each wind

turbine has to be defined. Here a step-up transformer and a LV load were included in

each wind turbine terminal, where only in A01 a capacitor bank was include (Figure

5-5).

At this stage all the information regarding the voltage source, cables, transformers,

capacitor banks and filters has to be confirmed and verified before the switching

simulations begins, since finding a problem on the equipment in such a network is fairly

complicated.

Once the collection grid was complete, the switching events can be simulated based on

the measurements. The most important thing to remember here, is the switching time

and switching angle. The cubicle where the switching operation occurred can be seen in

Figure 5-5 at the end of the cable “RootA”.

System modeling

111

Figure 5-5 Case 1. Power Factory. A01

In Power Factory the distance between single phase conductors is set in the Cable

Definition. And base on the manufacturers datasheets a radial separation of 50 mm

between conductors can be calculated. The position of each phase is stated in Table 5-2

and shown graphically in Figure 5-6.

Table 5-2 Case 1. Power Factory. Cable 50 mm

A B C

X 0 0,0235 -0,0235

Y 0,98 1,03 1,03

Figure 5-6 Case 1. Power Factory. Cable 50 mm

However a comparison case had to be done in order to decrease the capacitive coupling

between phases, under sequential energization of the phases. Here a separation of 50 cm

System modeling

112

between phases horizontally placed was used, where the Table 5-3 presents the position

of each phase and Figure 5-7 shows graphically this separation.

Table 5-3 Case 1. Power Factory. Cable 50 cm

A B C

X -0,5 0 0,5

Y 1 1 1

Figure 5-7 Case 1. Power Factory. Cable 50 cm

6.0005.6005.2004.8004.4004.000 [ms]

40.00

20.00

0.00

-20.00

-40.00

6.0005.6005.2004.8004.4004.000 [ms]

40.00

20.00

0.00

-20.00

-40.00

6.0005.6005.2004.8004.4004.000 [ms]

40.00

20.00

0.00

-20.00

-40.00

DIg

SIL

EN

T

Figure 5-8 Case 1. Power Factory. Separation

The results from different simulation done in Power Factory are shown in Figure 5-8,

where the plots represent:

Top. 50 cm separation and 1950 Hz as frequency for parameter approximation.

Middle. 50 cm separation and 50 Hz as frequency for parameter approximation.

Bottom. 50 mm separation and 1950 Hz as frequency for parameter

approximation.

System modeling

113

From this figure it can be seen that the separation between phases and frequency for

parameter approximation are very important parameters for the emt simulations in

Power Factory. However is important to notice that a geometrical variation on the cable

has an influence on the impedance, nevertheless this variation gives reasonable results

for the study cases 1 and 2.

Another important difference at this stage, is that even with the relative permittivity

correction due to semiconductive layers on both sides of the insulation between the

conductor and the sheath, the velocity of the simulated voltage wave is different to the

measured one.

As mentioned before the pre-strike modeling was left out of the scope of the project due

to the reduced time for the theses. However sequential opening and closing operations

are possible to define in Power Factory. The Table 5-4 shows the closing and opening

times for the breaker operations, to emulate the measured pre-strike of the first study

case (Figure 3-11, page 44). Although, for the breaker to open/close, in emt simulation

in Power Factory, the breaker needs certain conditions to be met (zero crossing).

Therefore, no further simulations were done on this area.

Table 5-4 Case 1. Power Factory. Pre-strike times

Operation Phase B Phase A Phase C

Close 4,378 4,605 4,745

Open 4,472 4,700 4,837

Close 4,532 4,827 4,862

Open 4,625 4,956

Close 4,677 4,992

Open 4,775 5,088

Close 4,816 5,102

Another important result from Figure 5-8 is that it‟s not possible to achieve round

corners in the voltage steps after the closing of the breaker. Not even increasing

manually the resistivity of the conductor.

Another discovery here, is that it is not possible to notice the reflection of the voltage

waves when it arrives to the platform (at 4,47 ms for the green phase) and doubles, as

Figure 3-8 in page 42 shows. The voltage increases during the first ms of the event are

the reflection of the voltage wave bouncing between the platform and wind turbine A09.

If the voltage of phase B is plotted for each wind turbine of row A (Figure 5-9), it‟s

possible to see that the transformers are stressed non-uniformly, depending on the

position of it, within the collection grid as Liljestrand reported in (Liljestrand, et al.,

2008).

System modeling

114

4550.4514.4478.4442.4406.4370. [us]

0.40

0.00

-0.40

-0.80

-1.20

-1.60

-2.00

Platform

A1

A9

DIg

SIL

EN

T

Figure 5-9 Case 1. Power Factory. Phase voltage B

Further comparison between the results from Power Factory and the measurements was

done in the next subsections.

5.2.2 PSCAD

The procedure to create the model of Nysted offshore wind farm for transient

comparison of the study case 1 and 2 is presented in this subsection.

The procedure to create the network is in essence, the same as in Power Factory. Here

everything begins with the voltage source on the top, connecting the park transformer

through two HV cables, represented here as PI sections. Then on each winding, a

connection to three phase breakers, followed by a cable interfaces is made. The previous

mentioned models are shown in Figure 5-10. Here is important to remember that is

recommended that all the equipment is grounding with a small resistance using wires.

The Time breaker logic for the breakers “Row A”, “Row B,C,D” and “Row E, F, G, H”,

are shown in the top-right of Figure 5-10. To avoid numerical problem on the solution

the cables of the rows B, C and D were modeled together where the rows E, F, G and H

were also modeled together. The cables are modeled as explained in subsection 4.5.8 on

page 95. In Figure 5-11the cable interfaces and cable configuration for the cables

“RootA” , “RootBCD” and “RootEFGH” are shown.

System modeling

115

Figure 5-10 Case 1. PSCAD. HV network

Figure 5-11 Case 1. PSCAD. MV network

Then, on each wind turbine a breaker on the primary side of the wind turbine

transformer was connected, followed by a LV load. In wind turbine A01 a capacitor

bank was modeled as subsection 4.7 in page 99 explained. The capacitances for high

frequency studies in the transformers are shown in Figure 5-12. Where the capacitance

between the HV windings to ground, LV winding to ground and LV to HV windings are

shown as C1, C3 and C2, respectively.

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Figure 5-12 Case 1. PSCAD. A01

The same procedure is repeated for the eight remaining wind turbines, with the

exception that the voltages and current fore each phase are only measured in A01 and

A09.

5.2.3 Transient comparison

The following figures and explanation accounts for the comparison between

measurements and simulation results in Power Factory and PSCAD for the study case

number 1.

Throughout this subsection the instantaneous value of the current and voltage for the

measurements, results from Power Factory and PSCAD are plotted as “–m”, “-pf” and

“-ps” respectively. Where the rms values of the current and voltage for the

measurements, results from Power Factory and PSCAD are plotted as “m”, “PF” and

“PSCAD” respectively.

The same color nomenclature for instantaneous current and voltages for each phase was

used as well in this subsection; where the blue is used for phase A, green is used for

phase B and red is used for phase C. A common use of line nomenclature was used;

where the solid line represents the measurements, the dot-slash line represents the

results from Power Factory and the dashed line the results from PSCAD. However in

the rms, FFT and power comparison of the results another color and line nomenclature

was used.

The Figure 5-13 shows the first milliseconds of the three phases in the platform. It can

be seen that the overvoltages due to voltage reflections in the row are not replicated by

any software. As well is possible to notice a decrease on the voltage of phase C in

PSCAD, before this phase is energized.

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Figure 5-13 Case 1. Platform voltages (4,3-5,5 ms)

If each phase (A: Figure 5-14; B:Figure 5-15; C:Figure 5-16) is separated by location is

possible to see that the velocity of the wave in both simulation programs is higher than

the measured velocity.

Figure 5-14 Case 1. Phase A voltage for each location (4,3-5,5 ms)

For phase A the voltage at A09 (Figure 5-14-bottom) it can be seen that PSCAD

overestimate the doubling effect under open circuit of the voltage wave. For phase B the

voltage at A09 (Figure 5-15-bottom) it can be seen that Power Factory overestimate the

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doubling effect under open circuit of the voltage wave. Where the voltage phase C at

A09, the overvoltage is higher in the measurements.

From the same comparison in the platform for phase A, B and C (Figure 5-14-top,

Figure 5-15- top, Figure 5-16-top) is possible to notice that only PSCAD can simulate

the reflections on the platform, or at least the wave seems less random.

Figure 5-15 Case 1. Phase B voltage for each location (4,3-5,5 ms)

Figure 5-16 Case 1. Phase C voltage for each location (4,3-5,5 ms)

If now the voltage at the platform is plotted until 10 ms, it‟s possible to see that the

oscillations in the voltage were not presented in any of the simulation programs.

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Figure 5-17 Case 1. Platform voltages (4-10 ms)

If the voltage is now plotted for the first 50 ms is possible to notice that there are small

differences between the measured and simulated voltages. On the lower part of the wave

the discrepancy is larger on phase A, where in the lower part of the wave the measured

voltage seems to have higher amplitude. For phase A is also visible some kind of phase

shift but only when the voltage varies from maximum to minimum value.


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These differences could be due to measurement errors, but also to the simplification in

the voltage source, where the source is assumed as balanced.

To continue with the comparison, the instantaneous current in the platform are shown in

Figure 5-19, for the first milliseconds corresponding to the time to charge the MV cable.

Here is possible to see that the measured current in all phases is interrupted after zero

crossing, where the simulated currents are not. Here the only comparison that can be

made is that the relative value of the charging currents for the first “half-waves” is

similar for both simulation programs and the measurements.

Figure 5-19 Case 1. Platform currents (4-5,5 ms)

A further comparison for the first 50 ms of the current in the platform (Figure 5-20)

illustrates the inrush current required by the nine transformers of the row. Here is

possible to visualize that the currents simulated in Power Factory are higher than the

ones in PSCAD. However both are higher than the actual measured current, this could

be explain by the fact that it was assumed that the saturation characteristic of the nine

transformers were the same. Maybe in reality the transformers in wind turbines A02,

A03, A04, A05, A06, A07 and A08 are not identical to the ones in A01 and A09.

Another reason for the different inrush currents is the voltage, since the magnetic flux in

the transformers is the integral of the voltage, an increased voltage would produce and

increased flux, and this, based on the saturation curve would demand higher current.

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Figure 5-20 Case 1. Platform currents (4-50 ms)

The current in A01 is shown in Figure 5-21, and again, a higher inrush current is

achieved from Power Factory. Here a high harmonic current is present on the three

phases in the measurements and simulations. However this is more accentuated in phase

B and C from PSCAD. The current on phases B and C from Power Factory fits better

the measurements after 20 ms, in comparison with PSCAD.

Figure 5-21 Case 1. A01 currents (0-50 ms)

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The Figure 5-22 presents the current at A01 for the entire simulation time. It‟s possible

to see from this figure that the first cycles present the highest instantaneous current, of

the entire period.


The FFT spectrum for each phase on each simulation program and the measurements on

A01, is shown in Figure 5-23. It‟s possible to see that in phase A and C the harmonic

content for 200 Hz is higher in Power Factory than in the measurements or the results

from PSCAD. Another important difference is that none of the simulation programs

could emulate the harmonic contents of the measurement around 211 Hz.

This same figure also shows that the harmonic content of the current on all the phases in

PSCAD has a component around 470 Hz. This is caused by an error when defining the

capacitor bank‟s inductance.

The Figure 5-24 presents the inrush current for each phase in A09, from the

measurements and the results from both simulation programs. It can be seen from this

figure that the inrush currents for the first cycle are overestimated in Power Factory and

PSCAD, however the currents are higher is Power Factory.

If the same currents are now plotted for the entire simulation period (Figure 5-25), it can

be seen that both simulation programs fits very well to the overall instantaneous current.

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Figure 5-23 Case 1. A01 currents FFT


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If the same currents are plotted only for the first milliseconds (Figure 5-26), is possible

to see the current spikes appearing due to the charging of the capacitances in the

transformer. However is not very clear the difference between each simulation program.


For this, the Figure 5-27 presents only the current for the phase B on A09 for the first

milliseconds. From here is possible to see that neither one of the simulation programs

can emulate the magnitude of the current spikes.

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Figure 5-27 Case 1. A09 current phase B (4-6 ms)

Once the instantaneous voltage and currents have been compared between simulation

results in both programs and measurements, a comparison of the rms values can be

done. First the rms currents at the platform from the measurements, Power Factory and

PSCAD are shown in Figure 5-28. It can be seen here that the inrush current in the real

system decays slower that in the simulations.

Figure 5-28 Case 1. Rms current at platform

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From the last figure is important to notice as well that two of the highest currents on the

first cycle are from Power Factory, as explained before in the instantaneous current.

Another important difference in the current is the final state of it; further discussion was

done in the next subsection for the currents in the three locations, with both simulation

programs and the measurements at steady state.

The Figure 5-29 presents the results from the calculated rms current at A01 and A09.

Here, the currents in A01 are higher than the ones at A09, due to the capacitor bank

connected at A01. It‟s also important to notice an increase in the current from Power

Factory in A01 between 10 and 20 cycles compared with the measured current and the

results from PSCAD.

Figure 5-29 Case 1. Rms current at A01 and A09

If the active power is calculated as mentioned in subsection 3.4.3 in page 50, is possible

to compare the results from the simulations and the measurements a little further. The

calculated active power in the platform is shown in Figure 5-30. Here the active power

calculated from the measurements is shown in blue, the active power calculated from

the Power Factory is shown in green and finally the active power calculated from the

PSCAD is shown in red. In this figure a discrepancy in the results from Power Factory

is clear. A difference of 3,7 MW at the end of the simulation period is present here, the

explanation of this discrepancy is explained in the next subsection.

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Figure 5-30 Case 1. Active power at platform

If the active power is now calculated for the wind turbines A01 and A09, the difference

between the equipment connected at the LV side of the transformer can be noticed

(Figure 5-31).

With respect to the active power consumption in A01 is possible to see that there are

differences between the real system and the simulations. There are considerable

variations in the active power consumption from the measurements; however the most

surprising variation is in the simulation results, where negative consumption is

calculated in both programs. Here the only explanation is the method to calculate the

active power from instantaneous values, and the addition of harmonic current to the

signal.

The active power consumption in A09 reach steady state after 5 cycles in both

simulation programs, however in reality the decay of the inrush current in the

transformer is decided by the internal and external losses to the transformer. If the

resistance (damping) in the system is very low, the inrush current will take several

seconds to decay. Hence the damping in the real system is lower than in the simulations.

Now, if the reactive power is calculated from the voltages and current at the platform,

the difference between the measurements, Power Factory and PSCAD can be seen

(Figure 5-32). Here, as explained before, the damping of the inrush current is lower in

the real system than in the simulations, however Power Factory presents the highest

damping, this fact is important for the following subsection where the steady state

comparison is made.

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Figure 5-31 Case 1. Active power at A01 and A09

From Figure 5-32 is not very clear the value of the reactive power at 25 cycles, however

additional remarks are done in the following subsection.

Figure 5-32 Case 1. Reactive power at platform

Then, the reactive power for A01 and A09 is shown in Figure 5-33. Here is possible to

see that at 25 cycles the reactive power consumption at A01 reach a negative state

(reactive power production) in both simulations, explained only by the capacitor bank of

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180 kVAr on the LV side of this transformer. However the measurement does not show

this negative excursion since the energizing of the transformer has not finished.

On the other hand, the reactive power never reaches a negative value on A09, for any

simulation program. It is clear from this figure as well, that the damping from Power

Factory is very different between A01 and A09, where the only physical difference is 4

km of cable.

Figure 5-33 Case 1. Reactive power at A01 and A09

The active and reactive power consumption during the first cycle in at the platform and

at A09 are shown in Table 5-5:

Table 5-5 Case 1. Active and reactive power during the first cycle.

Active Power [MW] Reactive Power [MVAr]

A09 9xA09 Platform Difference A09 9xA09 Platform Difference

Measurements 0,09 0,81 1,2 0,39 3,0 27,0 30 3,0

Power Factory 0,04 0,36 6,0 5,64 5,0 45,0 57 12,0

PSCAD 0,04 0,36 1,2 0,84 4,3 38,7 40 1,3

From the last table, it can be seen that there is a large difference during the first cycle in

the reactive and active power in Power Factory, between the values at the platform and

a simple addition on the active and reactive power consumption in A09. The only place

where this power can be consumed is the collection cables. Further discussion was done

in the following subsection.

The rms voltage at the platform, calculated each cycle is shown in Figure 5-34, for the

measurements and both simulation programs. Here is possible to see that the phase

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voltages from the measurements are not balanced and that they increase with the time,

as (Abdulahovic & Thiringer, 2007) reported. This is due to the charging of the

capacitance in the cable, which does not seem to be well replicated in any simulation

program.

Figure 5-34 Case 1. Rms voltage at platform

If only the calculated rms voltages from the measurements are plotted (Figure 5-35), is

possible to see that the voltage at A09 is higher that the voltage at A01. This could be

related to the charging of the cable capacitances.

However, if the calculated rms voltages from Power Factory are plotted (Figure 5-36) a

voltage drop in the cable between the platform and A01, and between A01 and A09 is

visible. This could be explained from the steady state current in the platform from

Power Factory (Figure 5-28) where a current of 70 A is flowing.

In the same way, if only the calculated rms voltages from PSCAD are plotted, shown in

Figure 5-37, the voltage drop in the cables is not visible. However all the voltages are

lower than in Power Factory. This could be due to the voltage drop in the HV cables and

the park transformers, since the p.u. value of both voltage sources was the same and

neither the park transformer nor the HV cables were compared between simulation

programs.

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Figure 5-35 Case 1. Rms voltage from measurements

Figure 5-36 Case 1. Rms voltage from Power Factory

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Figure 5-37 Case 1. Rms voltage from PSCAD

Once the transient comparison of the study case has been made, the steady state

comparison can be realized.

5.2.4 Steady state comparison

In the Table 5-6 the steady state values of the current and voltages for each phase, based

on the calculations done in Table 3-2 on page 56 and the results from the previous

subsection, are summarized.

Here is possible to see that the rms currents from the measurements and Power Factory

are extremely large in comparison with the ideal case (calculated). However the current

difference in the measurements is due to the low damping in the system, as explained

before. Nevertheless the disparity in Power Factory has not been yet clarified. For this,

four additional simulations were done where the method for solution was changed (rms

instead of emt), as well as the frequency for parameter approximation in the cables and

the core characteristic in the transformers were changed.

The four cases are shown in Figure 5-38, where the top plot is the real power and the

bottom plot the reactive power in the platform for the study case 1. The color

nomenclature is:

Red. Emt simulations, with 1950 Hz as frequency for parameter approximation

in cables and two slope representation of the core reactances.

Green. Emt simulations, with 1950 Hz as frequency for parameter approximation

in cables and polynomial representation of the core reactances with saturation

exponent 7.

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Blue. Emt simulations, with 50 Hz as frequency for parameter approximation in

cables and two slope representation of the core reactances.

Pink. Rms simulations.

Here, is important to notice that the model representation in Power Factory, for the same

equipment, is different depending on the type of simulation (rms or emt). Where the rms

results (pink), are closer to the calculated values.

In Figure 5-38 is possible to notice that the emt results using 1950 Hz as frequency for

parameter approximation, gives a active power consumption of 3,7 MW, where the rms

results as well as the emt using 50 Hz as frequency for parameter approximation are

closer to the calculated steady state value. This problem is easily explain since the

impedance value of the cable is frequency dependant as equation (4.15) presented, and

this value is fixed in Power Factory as the frequency for parameter approximation,

where in PSCAD is variable. A value of 1950 Hz as the frequency for parameter

approximation would increase the impedance largely in comparison with only 50 Hz.

If the reactive power is compared (bottom plot in Figure 5-38) is possible to see that the

only case where the reactive power is consumed in the network is with the polynomial

representation of the core reactances with saturation exponent 7. As Figure 4-10 in page

77 shows, around the knee flux the reactance varies largely from a two-slope

representation and a polynomial representation. And since the voltage in the platform in

Power Factory is higher than 19 kV (1 p.u.), the flux would also be higher than 1 p.u.,

near the knee flux value of 1,1 p.u.

0.5000.4800.4600.4400.4200.400 [s]

5.00

3.75

2.50

1.25

0.00

-1.25

RootA: P in MW (emt-1950 Hz-Tw o-slope)

RootA: P in MW (emt-1950 Hz-Polynomial)

RootA: P in MW (emt-50 Hz-Tw o-slope)

RootA: P in MW (rms)

0.5000.4800.4600.4400.4200.400 [s]

5.00

3.75

2.50

1.25

0.00

-1.25

RootA: Q in MVAr (emt-1950 Hz-Tw o-slope)

RootA: Q in MVAr (emt-1950 Hz-Polynomial)

RootA: Q in MVAr (emt-50 Hz-Tw o-slope)

RootA: Q in MVAr (rms)

DIg

SIL

EN

T

Figure 5-38 Case 1. Power Factory. Steady state

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Table 5-6 Steady state values (at 25 cycles) for current and voltages

Steady state comparison Phase A Phase A Phase A Average

Cu

rren

t [A

] Platform

Calculated 8,50 8,50

Measured 50,00 49,00 21,00 40,00

Power Factory 70,00 71,00 72,00 72,00

PSCAD 8,00 9,00 9,00 8,67

WT A09


Measured 5,00 1,40 5,00 3,80

Power Factory 0,50 0,30 0,40 0,40

PSCAD 0,40 0,20 0,40 0,33

Vo

ltag

e

[kV

]

Platform


Measured 19,84 19,67 19,98 19,83

Power Factory 19,47 19,47 19,47 19,47

PSCAD 19,11 19,11 19,11 19,11

In Table 5-7, the steady state values of the real and reactive power at A09 and the

platform are shown. Here is clear the difference mentioned before about the active

power consumption in Power Factory, due to defining the frequency for parameter

approximation to 1950 Hz.

Where the difference between the real system and the ideal one (calculated), is the

damping in the inrush currents. In both simulation programs the cables generate reactive

power close to the ideal system, where the difference is that in Power Factory the

reactive power generation is higher due to the increased voltage in the platform.

Table 5-7 Steady state values (at 25 cycles) for real and reactive power

Real Power [MW] Reactive Power [MVAr]

Platform WT A09 Platform WT A09

Calculated 0,050 0,005 -0,483 0,000

Measured 0,152 0,015 1,519 0,132

Power Factory 3,690 0,005 -0,625 0,030

PSCAD 0,048 0,005 -0,555 0,020

Once the study case 1 has been fully analyzed, the other study cases can be examined.

5.3 Study case 2: Connection of Row A-II

In essence the second study case and the first one are the same, only the switching

moment had changed. This time difference in the point-in-wave of the voltage caused

higher overvoltages and inrush currents. The main figures are presented next, where the

rest of them are attached in the appendix B.

5.3.1 Power Factory and PSCAD

The model for the first study case was used in both programs. However, the phase angle

and the magnitude in the voltage source had to be changed. Then the switching events

for each phase in the breaker were defined based on the measurements.

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5.3.2 Comparison

Figure 5-39 shows the platform voltages from the measurements and both simulation

programs. It is possible to see in phase A (blue) several overvoltages due to the

reflection of the voltage wave. These overvoltages are also visible in phase B (green)

and phase C (red), nonetheless these values are not as high in comparisson with phase

A.

From this same figure is possible to see, that none of the simulation programs can

emulate the overvoltages due to wave reflections.


If the current in the platform is plotted for the first 50 ms after the switching event

(Figure 5-40), is possible to see the inrush current from the nine transformers. As

explained before, the measurements present a flat top, due to measurement errors.

However is important to notice that the inrush current in both programs decay faster

than in the real system. This is due to a higher damping in the digital systems, as

explained in the previous subsection.

The difference in the current peak is caused by a lower voltage in the simulations, as

Figure 5-43 shows graphically. Here is possible to notice that the real system has an

initial higher voltage than both simulation models.

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When the currents at A01 are plotted (Figure 5-41), a high harmonic current in all

phases is visible. This is caused by the capacitor connected on the LV side of the

transformer. As well is important to mention, that the inductance in the capacitor bank

from PSCAD has the wrong value, and the system is tuned incorrectly.

Figure 5-42 shows the current at A09. In this turbine no capacitor bank is connected,

hence no harmonic currents are present.

Figure 5-41 Case 2. A01currents (10-70 ms)

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The rest of the plots from this study case are attached as appendix B, at the end of the

report. However no additional conclusion, different from the first study case, can be

made

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5.4 Study case 3: Switch A09

Just as a reminder the Figure 5-44 shows the simplified network of the third study case,

where seven wind turbine generators were under production, and the transformer in A09

is energized.

Figure 5-44 Simplified network for study case 3

It‟s important to notice that in this study case it was not necessary to model the cable as

in the previous two cases. Here the cables were modeled as PI sections in PSCAD and

as Lines in Power Factory. In Power Factory seven generators were connected on the

low voltage side of the wind turbine transformer with its capacitor bank. In PSCAD one

wind turbine was connected with seven coherent machines, with a larger capacitor bank

and larger transformer.

The capacitor bank in A01 was set to 180 kVAr as in the previous cases with the same

low voltage load. For A09 the low voltage load was increased to 0,08 MW.

5.4.1 Power Factory

As mentioned before, a new model of the collection grid was created in Power Factory.

Figure 5-45 shows the new MV network. Here, the cables in row A were modeled as

simple lines with positive and negative sequence resistance and reactance, to decrease

the time of simulation. This was done because in this switching event no transient

phenomena occurred in the collection cables.

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The transformers on each wind turbine were modeled as in the previous study cases.

Although the low voltage equipment connected on the wind turbines was changed. In

A01 the only equipment connected was the LV load and the capacitor bank. In the wind

turbines A02, A03, A04, A05, A06, A07 and A08 an induction generator and a

capacitor bank were connected. In A09 the LV load was increased to 0,08 MW.

C(7)

C(6)

C(5)

C(4)

C(3)

C(1)

C(2)

WTG(..

G~

WTG(..

G~

WTG(..

G~

WTG(..

G~

WTG(..

G~

WTG(..

G~

WTG

G~

LV load(8)

LV load

Sea cableSea cable

A8-A9A8-A9

A7-A8(1)A7-A8(1)

A6-A7A6-A7

A5-A6A5-A6

A4-A5A4-A5

A3

-A4

A3

-A4

132 kV network

V~

A2-A3A2-A3

A1-A2A1-A2

Shunt/Filter

Lin

eL

ine

A8(1)A8(1)

A7(1)A7(1)

A6A6

A5A5

A4(1)A4(1)

A3(1)A3(1)

A2(1)A2(1)

A1(1)A1(1)

A9(2)A9(2)

H1

-H9

H1

-H9

G1

-G9

G1

-G9

F1-F

9F

1-F

9

E1

-E9

E1

-E9

DDCCBB

Ro

otH

Ro

otH

Ro

otG

Ro

otG

Ro

otF

Ro

otF

Ro

otE

Ro

otE

Ro

otD

Ro

otD

Ro

otC

Ro

otC

Ro

otB

Ro

otB

Ro

otA

Ro

otA


Platform/Sea

Raadsand/B1

Radsted/Shore

H9G9F9E9

D9C9B9

A9(..A9

H1G1F1E1

D1C1B1


A8

A7

A6(1)

A5(1)

A4

A3

A2

A1


Figure 5-45 Case 3. Power Factory. MV network.

5.4.2 PSCAD

In PSCAD a new model of Nysted was created as well. However the cables between

A01 and A09 were joined in two equal π sections, to simplify calculations. As explained

in subsection 4.8, page 101, the generators in PSCAD had to be started in speed control

followed by torque control. The generator model used for this simulation is showed in

Figure 5-46, with an increased capacitor bank and step-up transformer.

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Figure 5-46 Case 3. PSCAD. Induction generator

Since the starting of the induction machine has to follow a control sequence, the

simulation time increase dramatically, as well as the output file. Due to computational

constrains, the sampling time for this study case in PSCAD had to be doubled. This

variation in the resolution of the results, caused the current spikes in the transformer

A09, due to switching operation, to disappear from the results.

Other differences between measurements and simulation results were mentioned in the

following subsections.

5.4.3 Wind turbine generator

The generators at Nysted offshore wind farm are induction machines, as previously

explained. However, the details of the slip characteristic of the machine have not been

mentioned so far. The aim of this subsection is to clarify the phenomena occurring in

the rotor of an induction machine, subjected to a voltage decrease on the stator.

The active power characteristic for different percentage of slip and voltage levels is

shown in Figure 5-47. At nominal power and voltage (blue line) the generator slip is

around -0,7%. If the power production remains the same during a voltage dip, e.g.

caused by the energization of a transformer, the machine would accelerate by shifting to

the 0,95 Vnom line (green). This would cause certain amount of oscillation in the

system depending on the inertia of the generators and the damping in the system.

Similar sequence of events would cause variations in the reactive power consumption in

the generator. The reactive power characteristic for different percentage of slip and

voltage levels is shown in Figure 5-48.

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Figure 5-47 Active power characteristic of induction generator

Figure 5-48 Reactive power characteristic of induction generator

Although the oscillating phenomena can be simplified, the dynamic response of wind

turbines is out of the scope for this project.

5.4.4 Comparison

To simplify the vizualization of the voltage variations in the platform and A01 due to

the switching in A09, each phase voltage has been separated. Figure 5-49 shows the

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phase voltage A for the three locations of the measurements, and both simulation

results. Figure 5-50 and Figure 5-51 show the voltage of phase B and C, respectivelly. It

is possible to see in these figures that there is no variation in the voltage on the platform

during the switching in A09, for any of the phases. On the other hand small changes in

the voltage at A01 are visible.

Figure 5-49 Case 3. Phase A voltage for each location (2-6 ms)

From Figure 5-49 is possible to see a voltage oscilation from the measurements, that

none of the simulators can emulate. This voltage variation could be due to the magnetic

coupling in the core transformer, since the primary side of the transformer is connected

in delta and the vectorial sum of the magnetic fluxes should be zero.

From Figure 5-50 and Figure 5-51 is possible to notice that in phase B and C no

oscilation is present, and that the simulation results follow very acurately the

measurements.

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143

Figure 5-50 Case 3. Phase B voltage for each location (2-6 ms)

Figure 5-51 Case 3. Phase C voltage for each location (2-6 ms)

If now the measurements, results from Power Factory and results from PSCAD at A01

are separated (Figure 5-52), is possible to notice that the voltage variation are only

present in Power Factory. The cause of this is not very clear, since the sequence

resistance and reactance for the cables between A01 and A09, are the same for both

models.

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Figure 5-52 Case 3. A01 voltages (2-6 ms)

Figure 5-53 is important to show that the initial conditions at A01, in both simulation

programs were very simlar to the real system. However, after certain time the results

from Power Factory differ largely from the measurements (Figure 5-54) in all phases.

The current of phase A and B, from PSCAD, follows the measurements more acuratetly,

without taking into acount the high frequency current due to the faulty sintonization of

the capacitor bank.


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The Figure 5-55, shows the current at A09 for the entire period, where only a small shift

around zero current is present after 100 ms in phase A and B. The Figure 5-56, shows

the same currents but only for the first 50 ms. Here is possible to see that both

simulation currents are higher that the measurements. This is due to a higher voltage in

the digital models, as Figure 5-66 shows futher in the report. However, is important to

see that the simulated currents fits very well the flat current measurements.


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146


The Figure 5-57 shows the same currents as Figure 5-56, but only for the first

miliseconds after the switching event. Here is possible to see that some current spikes

are present in the measurements every time a pole closes in the breaker. These current

spikes are relatively larger that the current spikes when the fast-front-voltage-wave

arrives to each transformer, as in study cases 1 and 2. The current spikes from the first

and second study cases hardly reach 20 A, where the current spikes in this study cases

surpases 50 A in phase B.


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147

Figure 5-58 Case 3. Phase B currents in A09 (2-7 ms)

Figure 5-58 shows only phase B at A09 for the first milliseconds after the first

switching. The simulated current spike in Power Factory due to the closing of phase B

at A09, is very similar to the measurements. Here is important to remember that the step

time in PSCAD is 800 ns, and not 400 ns as in Power Factory, due to computational

constrains.

Figure 5-59 Case 3. Rms currents at platform

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148

Figure 5-60 Case 3. Rms currents at A01 and A09

The calculated rms currents at the platform from the measurements, and both simulation

results are shown in Figure 5-59. Here is very clear an oscillation from Power Factory,

however further in the report the oscillation difference was treated. On the other hand is

important to notice that there is an initial difference of 20 A between phases for the

measured and simulated currents. This is due to the inrush current in the transformer

A09, as Figure 5-60 illustrate.

It‟s important to remember that the instantaneous current was not measured correctly at

A09, and a lower rms current is the result from this error (less than 10 A). However, the

current limit set in the platform was not reached (1,25 kA).

Another important difference between simulations and measurements is shown in

Figure 5-60, where the rms current in A01 from Power Factory increases from 3 A in

the first cycle to 12 A at the end of the simulation. This current variation is not present

in PSCAD or the measurements.

The current in phase A from the measurements presents a constant value of 6 A, this

could be due to a unsymmetrical load connected on the LV side of the transformer. No

additional simulations were repeated to achieve this value, since no information was

available to correctly identify the LV load.

The calculated active power in the platform and in the wind turbines A01 and A09 is

shown in Figure 5-61 and Figure 5-62, respectively.

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149


Figure 5-61 and Figure 5-62 are very important because clear differences between

digital and real systems are noticeable. First, the active power production in the

platform from PSCAD is lower than the real system. This is due to the fact that the

torque control in the induction machine was set to a value lower than the actual

production, however this difference is not relevant to the overall system characterization

for switching transient studies.


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150

On the other hand, the amplitude of the oscillation in the active power from Power

Factory is extremely large. The difference between the first four cycles is almost 2 MW,

only due to the voltage dip caused by a transformer energizing. Although the real

system presents a lower frequency oscillation, with a variation less than 0,5 MW in six

cycles, it can be concluded that Power Factory overestimates the oscillation in the

machines.

The active power consumption in A01, between measurements and PSCAD has a

relative offset of 3 kW, this could be due to:

Copper losses in the transformer for the increased current of phase A as Figure

5-60 shows.

Core losses in the transformer due to the different voltage in A01, as Figure 5-67

and Figure 5-69 indicates.

Unsymmetrical LV load

On the other hand, the parabolic variation in the active power consumption in A01,

between measurements and Power Factory, is more likely to be related to the active

power calculation with high harmonic current.

The Figure 5-63 shows the influence of the inertia of the induction generators and the

power production during switching of the transformer in A01. It‟s important to notice

that for this comparison four additional simulations were done, where the differences

are:

Pm. Active power from measurements

PPF-20-2,3. Active power from Power Factory, with 20 kg∙m2 of inertia and 2,3

MW of generation each machine





PPF-180-2,3. Active power from Power Factory, with 180 kg∙m2 of inertia and

2,3 MW of generation each machine

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Figure 5-63 Case 3. Influence of generators inertia in active power at platform

It is clear from the previous comparison, that the amplitude of the oscillation does not

depend on the inertia of the generators. However the inertia changes the oscillation

frequency.

No further simulations to fit the results from Power Factory to the measurements, were

done due to time limitations. However, the oscillation amplitude might be dependant in

the damping of the system.

The calculated reactive power in the platform and in the wind turbines A01 and A09 is

shown in Figure 5-64 and Figure 5-65, respectively.

In the platform, the oscilation of the generators in Power Facotry is visible. Where the

results from PSCAD shows a higher damping in the model than the actual system. This

results match the conclusion of the first and second study cases.

Figure 5-65 shows a difference in the reactive power consumption, between the

measurements and the simulations in A01. These differences could be due to the high

harmonic current in A01 and the voltage difference. However, it‟s important to notice

that the reactive power generation in A01 remains at 300 kVAr, and that no information

regarding the equipment connected in this wind turbine was available.

In Figure 5-65, the difference in reactive power in A09 due to the transformer

energizing, is very large. If a comparison for the first and last cycle is made for the

measurements and both simulations (Table 5-8), at the platform and at A09, some

important conclusions can be made:

During the first cycle from the measurements, there is higher reactive power

consumption at the platform than in A09 (∆Q=600 kVAr). This could is due to:

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152

o The reactive consumption of the transformers under nominal load

(200 kVAr x 7=1400 kVAr)

o The reactive power production of the cables at increased voltage

(-600 kVAr)

o The reactive power from the capacitor bank in A01 at increased voltage

(-200 kVAr)

During the first cycle from Power Factory, there is higher reactive power

consumption in A09 than in the platform. This is due to the high inrush current

in A09 (voltage dependant). Where the reactive power compensation could

come from the capacitor banks in the other wind turbines, or the oscillation in

the generators.

During the first cycle from PSCAD, there is higher reactive power consumption

in A09 than in the platform. This is due to the high inrush current in A09

(voltage dependant). Where the reactive power compensation come from the

large capacitor bank connected with the induction generator and the cables.

During the last cycle from the measurements, there is the same reactive power

consumption at the platform than in A09.

During the last cycle from Power Factory, there is almost the same reactive

power consumption at the platform than in A09. The difference could be due to

the reactive power consumption in the cables.

During the last cycle from PSCAD, the reactive power consumption in A09 is

the same as in Power Factory. This reactive consumption is due to the lower

damping in the simulated system for both programs. And the difference from

PSCAD between the reactive power in the platform and A09, is due to the

decreased reactive consumption in the generators, and the capacitor bank

connected to it.

Another important conclusion from here, is that the damping in the real and simulated

systems is very similar for this study case in comparison with the first two cases.

Table 5-8 Reactive power comparison in MVAr

Measurements Power Factory PSCAD

1 cycle Platform 5,1 7,9 3,7

A09 4,5 12 9

20 cycle Platform 1,7 3 -1

A09 1,7 2,5 2,5

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The calculated rms voltage at the platform from the measurements and both simulation

programs is shown in Figure 5-66. The rms voltage from the measurements seems

unbalanced, however this difference is less than 2%, hence this difference is due to

measurement uncertainty.

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154

Figure 5-67 shows the measured voltages at each location. As in the previous cases, the

voltage at A01 is lower than in A09 and the platform.



Figure 5-68 and Figure 5-69 shows the rms voltage from Power Factory and PSCAD,

respectively. It is possible to see an oscillation in the voltage from Power Factory,

caused by the generators, which is not present in PSCAD.

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155

On the other hand is important to notice that both simulation programs seem to be able

to increase the voltage, caused by the reactive power generation in the cables. This has

changed from the first two study cases, most likely because the Line model in Power

Factory and the π section in PSCAD are able to increase their voltage.



Finally, a remark should be made because in both simulations, the voltage in A09 is the

highest followed by the voltage in A01, where the voltage in the platform is the lowest.

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156

5.5 Worst case switching- voltage

In terms of transient overvoltage, the worst switching would appear when the breaker

energizes the cable during peak voltage. In the first study case the switching took place

before the voltage in one of the phases reached peak value, where in the second study

case the first pole closed after one of the phases reached peak voltage.

This theoretical switching event was simulated in the network model used for study

cases 1 and 2, with Power Factory as Figure 5-70 shows. Here, the voltage from the grid

is presented in back color for all phases (phase shift in the park transformer was not

included), and the voltage for each phase in the platform and A01 are shown in colors as

the legend shows.

8.337.336.335.33 [ms]

2.500

1.500

0.500

-0.500

-1.500

-2.500

RootA: Phase Voltage A/Terminal i in p.u.

RootA: Phase Voltage B/Terminal i in p.u.

RootA: Phase Voltage C/Terminal i in p.u.

A9(2): Phase Voltage A/HV-Side in p.u.

A9(2): Phase Voltage B/HV-Side in p.u.

A9(2): Phase Voltage C/HV-Side in p.u.

Sea cable: Line-Neutral Voltage A/Terminal i in p.u.

Sea cable: Line-Neutral Voltage B/Terminal i in p.u.

Sea cable: Line-Neutral Voltage C/Terminal i in p.u.

5.998 ms-2.291 p.u.

Figure 5-70 Worst case switching at peak voltage

From this figure it‟s important to notice that the highest voltage appears in the last

transformer due to the voltage reflection, with a value of 2,29 p.u. (43,5 kV), even

higher than the overvoltage in the second case (Figure 5-39 page 135).

5.6 Worst case switching -current

As it was revealed in subsection 4.4.4.2 page 80, the worst inrush current in a

transformer would appear if one of the phase voltages was zero. In this subsection, a

theoretical worst switching scenario for the inrush current, when the breaker in the

platform energizes row A (study case model 1 and 2), was simulated.

The same voltages as in Figure 5-70 are shown in Figure 5-71, with the same color

nomenclature, for the worst inrush current switching. Here, the switching event was

defined as simultaneous pole closing in the breaker with no residual flux in the

transformers. The highest instantaneous peak current in one of the phases, during the

first cycle in the platform was 4,30 p.u., however no additional simulation or analysis

was done in this subsection because in the next section (page 163), different amount and

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157

combination of transformers were energized in sequence in order to assess the voltage

dip at the PCC.

20.0016.0012.008.004.00 [ms]

2.00

1.00

0.00

-1.00

-2.00

RootA: Phase Voltage A/Terminal i in p.u.

RootA: Phase Voltage B/Terminal i in p.u.

RootA: Phase Voltage C/Terminal i in p.u.

A9(2): Phase Voltage A/HV-Side in p.u.

A9(2): Phase Voltage B/HV-Side in p.u.

A9(2): Phase Voltage C/HV-Side in p.u.

Sea cable: Line-Neutral Voltage A/Terminal i in p.u.

Sea cable: Line-Neutral Voltage B/Terminal i in p.u.

Sea cable: Line-Neutral Voltage C/Terminal i in p.u.

Figure 5-71 Worst case switching at zero voltage

5.7 Fit traveling time of the voltage wave

At this stage all the simulations have been done with the available information from the

cable manufacturers, yet the velocity of the voltage wave from the simulations was

found to be higher than in the real system. In this subsection the velocity of the voltage

wave was fitted to the measurements, in order to visualize better the reflections.

This was done in both simulation programs in the digital systems used for study case 2,

where only the relative permittivity of the cable was increased. This study case was

selected because here the overvoltages caused by the reflections were higher than in the

first study case.

The changes in permittivity were made first in Power Factory, as Figure 5-72 shows.

Here the relative permittivity was increased from 2,1 to 3,2 with a frequency for

parameter approximation of 1950 Hz. This figure is based on Figure 7-9 page 188,

where the top plot shows the phase A voltage in the platform, the middle plot shows the

phase A voltage in A01 and the bottom page shows the phase A voltage in A09.

In Figure 5-72 is clear that the velocity of the voltage wave is inversely proportional to

the relative permittivity, as explained in subsection 4.5 page 88. It is also visible from

this figure that the voltage wave that match the best with the measurements is the one

with relative permittivity of 3,2. This is a very high value for the relative permittivity

however, it‟s important to notice that no variation in the relative permeability of the

conductor was done in any simulation at this stage.

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158

20.5020.4220.3420.2620.1820.10 [ms]

10.00

0.00

-10.00

-20.00

-30.00

-40.00

20.5020.4220.3420.2620.1820.10 [ms]

10.00

0.00

-10.00

-20.00

-30.00

-40.00

2.1

2.3

2.8

3

3.2

20.5020.4220.3420.2620.1820.10 [ms]

10.00

0.00

-10.00

-20.00

-30.00

-40.00

20.275 ms-11.611 kV

20.280 ms-11.713 kV

20.292 ms-12.231 kV 20.297 ms

-12.149 kV

20.198 ms 0.000 kV

20.202 ms 0.000 kV

20.204 ms 0.000 kV

20.196 ms 0.000 kV

20.205 ms 0.000 kV

20.301 ms-12.558 kV

DIg

SIL

EN

T

Figure 5-72 Fit traveling time of voltage wave. Power Factory. Relative permittivity.

Next, the frequency for parameter approximation was changed in order to visualize the

effect of this parameter in the velocity of the wave. The results from this variation is

shown in Figure 5-73, where the relative permittivity was set to 3,2 and the frequency

for parameter approximation was increased to 10000 Hz.

20.5020.4220.3420.2620.1820.10 [ms]

10.00

0.00

-10.00

-20.00

-30.00

-40.00

-50.00

RootA: Voltage A in kV- 1950 Hz, 3.2

RootA: Voltage A in kV- 10000 Hz, 3.2

A1(1): Voltage A in kV- 1950 Hz, 3.2




DIg

SIL

EN

T

Figure 5-73 Fit traveling time of voltage wave. Power Factory. Frequency.

It‟s possible to see from Figure 5-73 that Power Factory calculates the traveling velocity

of the voltage wave using the frequency for parameter approximation, although in

theory the velocity of the wave depends only in the relative permittivity and relative

permeability of the cable.

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159

During the simulations in PSCAD, some problems appear when the relative permittivity

of the insulation was increased to 3,2. However these problems were solved by

changing the earth resistivity to the standard value of 100 Ω∙m and by simplifying the

network with only one cable between wind turbines A01 and A09, instead of eight short

sections.

The comparison between the measurements and both simulation results, for the voltage

of phase A, in the three different locations is shown in Figure 5-74. From this figure

several important conclusions can be made:

None of the simulation programs can emulate the measured overvoltage in the

platform, caused by the voltage wave reflection. The difference between Power

Factory and the measurements at 0,0203 s is 15 kV. The difference between

PSCAD and the measurements at 0,0203 s is 9 kV.

None of the simulation programs can emulate the measured overvoltage in A01,

caused by the voltage wave reflection. The difference between Power Factory

and the measurements at 0,02035 s is 20 kV. The difference between PSCAD

and the measurements at 0,02035 s is 10 kV.

None of the simulation programs can emulate the measured overvoltage in A09,

caused by the voltage wave reflection. The difference between Power Factory

and the measurements at 0,02027 s is 7 kV. The difference between PSCAD and

the measurements at 0,02027 s is 5 kV.

The round corners in the fast front of the voltage wave in all locations are only

simulated in PSCAD. As explained before this is caused by the skin effect in the

conductor.

The behavior of Power Factory after the first reflection period (90 μs) looks

fairly random in all locations. Where in PSCAD the voltage reduction seems

gradual, nonetheless the results are not similar to the measurements.

In Power Factory the voltage level surpasses -40 kV at 0,02041 s in A09, just as

in Figure 5-73. This could be due to the voltage reflection; however no

information regarding the model is available from DigSILENT.

The results from Power Factory before the wave reflected from A09 arrives to

the platform, is very similar to the actual measurements. Here is visible some

kind of step-wise decrease in the voltage from 0,02022 s to 0,02025 s. This

phenomena is not present in the results from PSCAD.

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Figure 5-74 Fit travelling time of voltage wave. Comparison

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161

5.8 Summary

In this section the general procedure followed to create the models of Nysted offshore

wind farm in Power Factory and PSCAD was presented. Then, the results from both

simulation programs and the measurements for each study case were compared. Next

two additional simulations were done to assess the worst switching angle for the voltage

and the current. Finally the relative permittivity in the cables was increased in both

simulation programs to fit the velocity of the voltage wave to the measurements. Some

of the most important conclusions from the first two study cases were:

None of the simulation programs can accurately account for the transient

overvoltages, due to voltage wave reflections.

The cable models in both simulation programs overestimate the damping in the

system.

The cable models in both simulation programs do not contribute to the voltage

increase in the system, due to the charging of the capacitances in the cable.

The cable model in Power Factory with high frequency for parameter

approximation, cannot be used to compare the system at steady state.

The saturation exponent in the transformer model from Power Factory could

result in errors if a high value is not used.

Some of the most important conclusions from the last study case were:

The voltage dip due to the energizing of a transformer caused power oscillations

from the induction generators connected in the same row. However these

oscillations were overestimated in the model from Power Factory.

The simulated switching event in A09 using Power Factory, caused voltage

transients in A01 not present in the measurements nor the results from PSCAD.

The simulated switching event in A09 using Power Factory, caused an increase

in the current in A01 not present in the measurements nor the results from

PSCAD.

The damping in the real and simulated systems is very similar for this study case

in comparison with the first two study cases.

The most important conclusion from the worst switching cases was:

None of the study cases happened at the worst possible moment for the transient

overvoltage or the inrush current.

The most important conclusion from fitting the traveling wave velocity was:

None of the simulation programs can emulate accurately the measured

overvoltage in the platform, A01 or A09 caused by the voltage wave reflections.

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162

Voltage dip at the PCC, due to the connection of different amount of transformers at the

same time

163

6 VOLTAGE DIP AT THE PCC, DUE TO THE CONNECTION OF DIFFERENT AMOUNT OF TRANSFORMERS AT THE SAME TIME

In this section the voltage dip at the point of common coupling with the grid, due to the

connection of different amount of transformers at the same time, was assessed with 20

simulations in Power Factory and 8 in PSCAD.

The Figure 6-1 shows the overview of the simulated network, where the equipment in

black represents the devices without voltage. It‟s clear from this figure that no transient

phenomena had to be simulated in the cables; hence a new model for each program had

to be created where the cables were modeled accurately for steady state conditions.

Since the network in both programs is essentially the same as the first study case, no

figures showing the network in any program were included.

Figure 6-1 Overview of sequential energization of transformers

On the other hand, after several preliminary simulations in Power Factory, it was found

that the saturation characteristic had to be simulated as a polynomial curve with a high

saturation exponent. Figure 6-2 shows the phase current A in the platform for five


same time

164

different cases where the saturation characteristic and the frequency for parameter

approximation in the cable models were changed.

The characteristics of the model for each case is shown in the legend; where the last

value in the legend is the frequency for parameter approximation in the cable and the

second-last value is the saturation representation in the core of the transformer.

10.0008.0006.0004.0002.0000.000 [s]

0.800

0.560

0.320

0.080

-0.160

-0.400

RootA: Phase Current A in p.u. Tw o slope, 100 Hz

10.0008.0006.0004.0002.0000.000 [s]

0.800

0.560

0.320

0.080

-0.160

-0.400

RootA: Phase Current A in p.u. Polynomial 15, 100 Hz

10.0008.0006.0004.0002.0000.000 [s]

0.800

0.560

0.320

0.080

-0.160

-0.400


10.0008.0006.0004.0002.0000.000 [s]

0.800

0.560

0.320

0.080

-0.160

-0.400

RootA: Phase Current A in p.u. Tw o slope, 50 Hz

10.0008.0006.0004.0002.0000.000 [s]

0.800

0.560

0.320

0.080

-0.160

-0.400


Figure 6-2 Sequencial energization. Power Factory. Saturation exponent.

It is clear from the last figure, that the current with the two slope representation, is

unstable at the voltage level used. Another important conclusion is that the cable with

high value of frequency for parameter approximation would give wrong steady state

current.

After these preliminary results, the cable models in Power Factory were defined as

“Line” models to avoid problems and reduce the simulation time; where the saturation

exponent for the polynomial curve representation in the core was set to 15.

6.1 Sequence energization

As a start, four main sequences were defined to compare the influence of the number of

transformers simultaneously energized. Here the transformers were divided in groups

for energization with 1, 2, 5, or 9 transformers corresponding to 1WT, 2WT, 5WT and

9WT respectively. The time when each transformer would be energized is shown in

Table 6-1.

After the characterization of the energizing sequences, the switching scenarios have to

be defined. Here the conclusions from previous sections are important, since the inrush

current depends on the switching angle, the residual flux and the rest of the system.

Hence five different switching scenarios were defined:


same time

165

1. Vzero A01-A09. With simultaneous pole switching when one of the phase

voltages was zero and all rows connected. Here the order to energize the

transformers starts from A01 and not from A09, however the time intervals

remain the same.

2. Vzero. With simultaneous pole switching when one of the phase voltages was

zero and all rows connected.

3. Vpeak. With simultaneous pole switching when one of the phase voltages had

peak value and all rows connected.

4. Row B. With simultaneous pole switching, zero voltage and only the Row B

connected.

5. Residual flux. With simultaneous pole switching, zero voltage, all rows

connected and residual flux in the same polarity to that to which the flux would

normally attain under equivalent normal conditions.

6. Reduced grid. With simultaneous pole switching, zero voltage, all rows

connected and increased grid impedance (lower grid capacity).

Table 6-1 Times for sequencial energization in seconds

9WTx0s 5WTx5s 2WTx2s 1WTx1s

A01 0,1 5,1 6,1 8,1

A02 0,1 5,1 6,1 7,1

A03 0,1 5,1 6,1 6,1

A04 0,1 5,1 4,1 5,1

A05 0,1 0,1 4,1 3,1

A06 0,1 0,1 2,1 3,1

A07 0,1 0,1 2,1 2,1

A08 0,1 0,1 0,1 1,1

A09 0,1 0,1 0,1 0,1

All this scenarios were simulated in Power Factory, however only the second and third

scenarios were repeated in PSCAD due to the reduced time for the thesis. It‟s important

to mention that the scenario with residual flux is not realistic in the case of Nysted

offshore wind farm, since there is a permanent LV load connected in the transformer,

which de-energizes the core.

The “Vzero A01-A09” and “Row B” scenarios were developed to create guidelines on

how to energize the step-up transformers in the collection grid of an offshore wind farm,

presented in the last section of the thesis.

The “Reduced grid” scenario was developed to compare the influence of the grid in the

voltage dip when a weaker grid is used.

The results from the simulations are shown in Table 6-2. However the results were

discussed in the following subsections.


same time

166

6.2 Simulation in PF

From Figure 6-3 to Figure 6-8 the left side plot are the calculated rms current each cycle

and in the right plot the calculated rms voltage each half cycle from Power Factory.

Figure 6-3 shows the results from the scenario “Vzero A01-A09”. In this scenario only

the 1WT and 2WT sequences were simulated.

From Figure 6-3-left it is possible to see that in the 1WTx1s sequence, the current

increases each time a transformer is energized. Moreover, in the 2WTx2s sequence the

current increases each time two transformers are energized.

From Figure 6-3-right it is possible to see that in the 1WTx1s sequence, the voltage

decreases each time a transformer is energized. In addition, in the 2WTx2s sequence the

voltage decreases each time two transformers are energized. A voltage unbalance in

both sequences is also visible, for the first half cycle after the switching has occurred.

Figure 6-3 Sequence energization. Power Factory. Vzero A01-A09

Figure 6-4 shows the results from the scenario “Vzero”. In this scenario all sequences

were simulated.

From Figure 6-4-left it‟s possible to see an increase in current, each time a switching

operation occurs. However is important to notice that the highest current appear when

all transformers are energized simultaneously (9WTx0s), followed by 5WTx5s,

2WTx2s and finally by 1WTx1s.

The Figure 6-4-right shows that for the sequences 2WTx2s and 1WTx1s each time a

switching operation occurs, the voltage decrease compared with the previous switching.

Nevertheless the lowest voltage is present in the sequence 9WTx0s, followed by

1WTx1s.


same time

167

Figure 6-4 Sequence energization. Power Factory. Vzero

Figure 6-5 shows the results from the scenario “Vpeak”. In this scenario only the

sequences 2WTx2s and 9WTx0s were simulated.


operation occurs. It is important to notice that the highest current appear when all

transformers are energized simultaneously (9WTx0s).

The Figure 6-5-right shows that for the sequences 2WTx2s each time a switching

operation occurs, the voltage decrease compared with the previous switching. Between

these sequences, the lowest voltage is present in 9WTx0s.

Figure 6-5 Sequence energization. Power Factory. Vpeak

Figure 6-6 shows the results from the scenario “Row B”. In this scenario all sequences

were simulated.



transformers are energized simultaneously (9WTx0s), followed by 5WTx5s, 2WTx2s

and finally by 1WTx1s.


same time

168



However the lowest voltage is present in the sequence 9WTx0s, followed by 1WTx1s.

Figure 6-6 Sequence energization. Power Factory. Row B

Figure 6-7 shows the results from the scenario “Residual flux”. In this scenario all

sequences were simulated.





The Figure 6-7-right shows that for the sequences 2WTx2s each time a switching

operation occurs, the voltage decrease compared with the previous switching, where this

phenomena is not present in the sequence 1WTx1s. In this scenario the lowest voltage is

present in the sequence 9WTx0s, followed by 5WTx5s.

Figure 6-7 Sequence energization. Power Factory. Residual flux

Finally Figure 6-8 presents the results from the scenario “Reduced grid”. In this

scenario all sequences were simulated.


same time

169

From Figure 6-8-left it‟s possible to visualize an increase in current, each time a

switching operation occurs. It is important to notice that the highest current appear when





However the lowest voltage is present in the sequence 9WTx0s, followed by 1WTx1s.

Figure 6-8 Sequence energization. Power Factory. Reduced grid

6.3 Simulation in PSCAD

Figure 6-9 and Figure 6-10 presents on the left side plot the calculated rms current each

cycle and in the right plot the calculated rms voltage each half cycle from PSCAD.

The Figure 6-9 presents the results from the scenario “Vzero”. In this scenario all


From Figure 6-9-left it‟s possible to visualize an increase in current, each time a

switching operation occurs. It is important to notice that the highest current appear when




switching operation occurs, the voltage decrease slightly compared with the previous

switching. However the lowest voltage is present in the sequence 9WTx0s, followed by

5WTx5s.


same time

170

Figure 6-9 Sequence energization. PSCAD. Vzero

The Figure 6-10 presents the results from the scenario “Vpeak”. In this scenario all







switching operation occurs, the voltage decrease slightly compared with the previous

switching. However the lowest voltage is present in the sequence 9WTx0s, followed by

5WTx5s.

Figure 6-10 Sequence energization. PSCAD. Vpeak

If now the rms current and voltages are calculated each cycle from the results from

PSCAD and plotted, some conclusions can be made.


same time

171

Figure 6-11 Sequence energization. PSCAD. Vzero. Rms each cycle

Figure 6-12 Sequence energization. PSCAD. Vpeak. Rms each cycle

In Figure 6-11 the results from the “Vzero” scenario were plotted, while the results from

the “Vpeak” scenario were plotted in Figure 6-12. It is possible to see from both figures

that:

The highest rms current appears during the 9WTx0s sequence and in the

“Vzero” scenario.

The lowest rms voltage turn up during the 9WTx0s sequence and in the “Vpeak”

scenario. This is a contradictory results if the voltage is compared with Figure

6-9 and Figure 6-10, however the period for the calculation of the rms voltage is

different.

The voltage unbalance seems more severe in the “Vzero” scenario.

The voltage-current characteristic is different depending on the switching angle,

however is not different depending on the energizing sequence.


same time

172

6.4 Results

Once the plots have been compared, the lowest rms voltage each half cycle, the highest

rms current each cycle and the largest peak current were summarized in Table 6-2. Here

the values were classified by colors to simplify the comparison.

Table 6-2 Sequence energization results

1 2 3 4 5 6

Zero Zero Peak Zero Zero Zero

Residual 0 0 0 0 1 0

Sgrid 1 1 1 1 1 0,8

Connected All All All B All All

Sequence A01-A09 A09-A01 A09-A01 A09-A01 A09-A01 A09-A01

Half c

ycle

rm

s v

olta

ge d

ip

Pow

er

Facto

ry 1WTx1s+LV -4,9% -5,0% -4,8% -5,4% -4,9%

2WTx2s+LV -3,0% -3,5% -1,7% -3,1% -7,0% -3,3%

5WTx5s+LV -2,2% -3,6% -9,2% -3,9%

9WTx0s+LV -5,4% -3,5% -5,7% -13,8% -6,0%

PS

CA

D 1WTx1s+LV -0,6% -0,6%

2WTx2s+LV -1,7% -1,5%

5WTx5s+LV -2,2% -1,9%

9WTx0s+LV -4,3% -3,7%

Rm

s c

urr

ent

[pu]

Pow

er

Facto

ry 1WTx1s+LV 0,38 0,40 0,40 0,83 0,37

2WTx2s+LV 0,88 0,93 0,88 0,99 1,93 0,90

5WTx5s+LV 1,33 1,41 2,88 1,26

9WTx0s+LV 1,78 2,16 1,94 4,50 1,71

PS

CA

D 1WTx1s+LV 0,26 0,24

2WTx2s+LV 0,69 0,65

5WTx5s+LV 0,90 0,84

9WTx0s+LV 1,72 1,65

Peak c

urr

ent

[pu

]

Pow

er

Facto

ry 1WTx1s+LV 0,73 0,77 0,77 1,47 0,70

2WTx2s+LV 1,83 1,95 1,71 2,05 3,97 1,86

5WTx5s+LV 2,93 3,11 6,03 2,81

9WTx0s+LV 4,32 4,14 4,66 9,03 4,17

PS

CA

D 1WTx1s+LV 0,51 0,47

2WTx2s+LV 1,44 1,33

5WTx5s+LV 2,19 2,06

9WTx0s+LV 3,58 3,44

It‟s important to state that the measurements from the study cases cannot be directly

compared to the sequential energization results. The measurements from the first two

study cases are located below the circuit breaker in the platform, this location is ideal to

measure the transient phenomena in the cable; however a better location to measure the

voltage dip would have been in the other side of the breaker.


same time

173

With the time series available for the third study case, is not possible to calculate the

rms voltage dip since the event happened at 2 ms. In this study case is important as well

to mention that it was assumed since the beginning of the thesis that no generation was

present; however it was found further on that the induction machines were almost at full

production.

Although the study cases and the results from the sequential energization cannot be

compared directly, the transient voltage, current and powers were compared in the

previous section with acceptable differences. Hence it can be concluded that both

simulation programs can be extrapolated to practical cases with caution.

The comparison was further separated depending on the variable being compared:

Half cycle rms voltage dip

o All sequences from the scenario “Vzero A01-A09” presents smaller

voltage dip than the scenario “Vzero”

o Vzero. Power Factory overestimates the voltage dip caused by the

sequence 1WTx1s and 2WTx2s compared with PSCAD

o Vzero. Power Factory and PSCAD reach similar results in the sequence

5WTx5s

o Vzero. Power Factory presents a higher voltage dip than PSCAD for the

sequence 9WTx0s

o Vpeak. Power Factory and PSCAD reach similar results in the sequence

9WTx0s, however in the sequence 2WTx2s PSCAD presents larger

voltage dip

o In PSCAD all sequences from the scenario “Vpeak” presents smaller

voltage dip than the scenario “Vzero”

o The sequence 5WTx5s and 9WTx0s from the scenario “Row B”

presents larger voltage dip than the scenario “Vzero”

o The largest voltage dip from Power Factory, for each sequence, is

present in the scenario “Residual flux”

o The sequence 5WTx5s and 9WTx0s from the scenario “Reduced grid”

presents larger voltage dip than the scenario “Vzero”

Rms current

o All sequences from the scenario “Vzero A01-A09” presents less current

than the scenario “Vzero”

o Vzero. Power Factory presents higher current in all sequences than

PSCAD

o Vpeak. Power Factory shows higher results in both sequences than

PSCAD

o In PSCAD all sequences from the scenario “Vpeak” presents lower

current than the scenario “Vzero”


same time

174


presents larger current than the scenario “Vzero”

o The largest current from Power Factory, for each sequence, is present in

the scenario “Residual flux”

o All sequences from the scenario “Reduced grid” presents less current


Peak current

o All sequences from the scenario “Vzero A01-A09” presents less current


o Vzero. Power Factory presents higher current in all sequences than

PSCAD

o Vpeak. Power Factory shows higher results in both sequences than

PSCAD

o In PSCAD all sequences from the scenario “Vpeak” presents lower

current than the scenario “Vzero”


presents larger current than the scenario “Vzero”

o The largest current from Power Factory, for each sequence, is present in

the scenario “Residual flux”

o All sequences from the scenario “Reduced grid” presents less current


In general, the results from Power Factory regarding the sequence 1WTx1s and

2WTx2s, are contradictory since a large voltage dip is present ever though the current

has not increase that much.

The previous results were used in the next section, to create recommendations regarding

the simultaneous energizing of different amount of transformers in large wind farms.

Conclusions

175

7 CONCLUSIONS

In this section, the comparison between simulation tools is presented; followed by a

summary of required information to realize switching transient studies. Then, the

guidelines for the simultaneous energizing of different amount of transformers were

stated. Finally, the perspectives and future work are presented.

7.1 Results- simulation tools

A comparison between the models of the electrical devices, present in the collection

grid of offshore wind farms, was done in Power Factory and PSCAD with similar

results from both simulation tools.

Once each digital device was validated, three study cases were realized based on

measurements to compare the transient behavior of both simulation tools. At this stage,

some differences were visible; however, a detail analysis was done in order to

understand the results and the causes of these discrepancies. From these disagreements

between the measurements and the simulations, some relevant conclusions can be made:

None of the simulation programs can emulate accurately the measured

overvoltage in the platform, A01 or A09 caused by the voltage wave reflections

The cable models in both simulation programs overestimate the damping in the

system.

The cable model in Power Factory with high frequency for parameter

approximation, cannot be used to compare the system at steady state.

The saturation exponent in the transformer model from Power Factory could

result in errors if a high value is not used.

The voltage dip due to the energizing of a transformer, caused power oscillations

from the induction generators connected in the same row. However these

oscillations were overestimated in the model from Power Factory.

The simulated switching event in A09 using Power Factory, caused voltage

transients in A01 not present in the measurements nor the results from PSCAD.

The simulated switching event in A09 using Power Factory, caused an increase

in the current in A01 not present in the measurements nor the results from

PSCAD.

Then, when Power Factory and PSCAD were used to assess the voltage dip due to the

sequential energization of different amount of transformers, there were some

contradictory results on certain sequences from Power Factory.

Conclusions

176

7.2 Results- required information

In general, it can be concluded that there are important differences between Power

Factory and PSCAD for switching transient studies:

The circuit breaker model in Power Factory is not fully developed to simulate

possible switching conditions in the collection grid of an offshore wind farm.

The magnitude of the highest overvoltage measured, due to voltage reflections,

was only achieved in Power Factory, while the shape of the voltage was similar

in PSCAD.

The cable model in Power Factory cannot be used to compare steady state

conditions, after a switching event. While the cable model in PSCAD works for

every stage of the event.

The results in Power Factory, from the voltage dip due to the sequential

energization of transformers, have to be treated without full confident.

As stated at the beginning of section 6, there is a large amount of information needed

for switching transient studies; however, some of the most important information that

the manufactures do not provide willingly to the system designer is:

Circuit breaker

o Rate of rise of re-striking voltage

o Rate of rise of dielectric strength

Transformer

o High frequency capacitances

o Characteristic impedance

o Open circuit characteristic

Cable

o Material properties

o Geometrical characteristics

This information is important to create digital models in the appropriate simulation tool,

to achieve results as close to reality as possible at the design stage of a project; since in

practical applications there are not many installed measurement systems with so high

definition to compare the simulations results with.

Another important constrain at the design stage of the collection grid of large offshore

wind farms, is the risk assessment and insulation coordination; these are based in

simulation results and as it has been proven in this thesis, the results from Power

Factory and PSCAD are vaguely analogous to the measurements in some situations.

7.3 Results- simultaneous energization of transformers

After the many sequences and scenarios from the last section, some recommendations

regarding the simultaneous energizing of different amount of transformers was done.

The idea is to apply the results to the voltage dip control in large offshore wind farms, in

Conclusions

177

order to energize the transformers and comply with the UK requirements. Some of the

recommendations are:

There is no need to use segregated point-in-wave closing methods in the circuit

breaker; since there is no large difference in the voltage dip for switching at

peak or zero voltage.

The smallest voltage dips occur if the wind turbine transformers are switched-in

independently. However, there cannot be a generalization because the voltage

dip depends on the system itself and its connection to the grid.

To avoid higher inrush current when the transformers have residual flux, its

recommended to connect a permanent low voltage load on the secondary side of

the transformers, to de-energize the transformer.

No conclusive results were achieved when the cables of the other rows were

disconnected, however the capacitance from the other rows are likely to reduce

the voltage dip.

No conclusive results were achieved when changing the sequence of

energization from A09-A01 to A01-A09.

7.4 Perspectives

Some of the results from this thesis could be used in other offshore wind farms under

development, where the projects are at the design stage. The protection system could be

upgraded; the control system could include additional components; supplementary

information could be asked to the manufacturer and in general the system designer

could become more aware of the imitations of the simulation tools.

7.5 Further work

This project reflects the interest of the large offshore wind farm developers, to predict

the possible risks and protection of the electrical devices in the collection grid prior to

its installation in the sea. In order to continue to understand the network and the

simulation tools, many switching events are left still to simulate from the measurements

performed within the project entitled “Voltage conditions and transient phenomena in

medium voltage grids of modern wind farms”, funded by Energinet.dk.

On the other hand, plenty of effort could be used to simulate each and every one of the

switching events, nevertheless, the accuracy of the results are limited by the accuracy of

the simulation tool. On this front, there is plenty of work to be done, in order to

correctly estimate the transient phenomena of the electrical devices and the collection

grid itself.

Important ongoing work by the IEEE, is the switching transients induced by

transformer-breaker interaction, since there are plenty of these components in the

Conclusions

178

collection grid. However, no significant results will be archived if the transformer and

circuit breakers manufacturers are not part of the development.

179

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183

A NON-SIMULTANEOUS POLE CLOSING DURING THREE-PHASE TRANSFROMER ENERGIZATION IN POWER FACTORY

In this appendix the simulation results for non-simultaneous pole closing during a three-

phase transformer energization in Power Factory are presented. These results are

attached for the explanation in subsection 4.4.4.2, page 80.

The nomenclature showed in Table 7-1was used for the all the following figures in this

appendix.

Table 7-1 Color nomenclature for appendix A

Left side Right side

Color Name Color Name Blue Voltage phase A Blue Voltage phase A Green Voltage phase B Green Voltage phase B

Red Voltage phase C Red Voltage phase C Light blue Magnetizing flux phase A Light blue Magnetizing flux phase A Dark green Magnetizing flux phase B Dark green Magnetizing flux phase B Pink Magnetizing flux phase C Pink Magnetizing flux phase C

Blue Current phase A Blue Current phase A Green Current phase B Green Current phase B Red Current phase C Red Current phase C

The simulated events are presented in Table 7-2:

Table 7-2 Non-simultaneous simulation cases

Figure Δt [ms] Left side Right side

φd φq φd φq Figure 7-1 0,02 0 0 -1 0 Figure 7-2 2 0 0 -1 0 Figure 7-3 3,33 0 0 -1 0 Figure 7-4 5 0 0 -1 0 Figure 7-5 6,66 0 0 -1 0

Where

Δt is the time between pole closing

Φd is the residual flux in the d-axis

Φq is the residual flux in the q-axis

Non-simultaneous pole closing during three-phase transfromer energization in Power

Factory

184

35.0028.0021.0014.007.0000.000 [ms]

6.00

4.00

2.00

0.00

-2.00

-4.00

-6.00

35.0028.0021.0014.007.0000.000 [ms]

3.00

2.00

1.00

0.00

-1.00

-2.00

-3.0035.0028.0021.0014.007.0000.000 [ms]

3.00

2.00

1.00

0.00

-1.00

-2.00

-3.00

35.0028.0021.0014.007.0000.000 [ms]

6.00

4.00

2.00

0.00

-2.00

-4.00

-6.00

Vpsi and I(0.02ms)vs flux

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Annex: /6

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Figure 7-1 Non-simultaneous pole closing with 0,02 ms apart

35.0028.0021.0014.007.0000.000 [ms]

6.00

4.00

2.00

0.00

-2.00

-4.00

-6.00

35.0028.0021.0014.007.0000.000 [ms]

3.00

2.00

1.00

0.00

-1.00

-2.00

-3.0035.0028.0021.0014.007.0000.000 [ms]

3.00

2.00

1.00

0.00

-1.00

-2.00

-3.00

35.0028.0021.0014.007.0000.000 [ms]

6.00

4.00

2.00

0.00

-2.00

-4.00

-6.00

Vpsi and I(2ms)vs flux

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Annex: /7

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Figure 7-2 Non-simultaneous pole closing with 2 ms apart


Factory

185

35.0028.0021.0014.007.0000.000 [ms]

6.00

4.00

2.00

0.00

-2.00

-4.00

-6.00

35.0028.0021.0014.007.0000.000 [ms]

3.00

2.00

1.00

0.00

-1.00

-2.00

-3.0035.0028.0021.0014.007.0000.000 [ms]

3.00

2.00

1.00

0.00

-1.00

-2.00

-3.00

35.0028.0021.0014.007.0000.000 [ms]

6.00

4.00

2.00

0.00

-2.00

-4.00

-6.00


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35.0028.0021.0014.007.0000.000 [ms]

6.00

4.00

2.00

0.00

-2.00

-4.00

-6.00

35.0028.0021.0014.007.0000.000 [ms]

3.00

2.00

1.00

0.00

-1.00

-2.00

-3.0035.0028.0021.0014.007.0000.000 [ms]

3.00

2.00

1.00

0.00

-1.00

-2.00

-3.00

35.0028.0021.0014.007.0000.000 [ms]

6.00

4.00

2.00

0.00

-2.00

-4.00

-6.00


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Figure 7-4 Non-simultaneous pole closing with 5 ms apart


Factory

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35.0028.0021.0014.007.0000.000 [ms]

6.00

4.00

2.00

0.00

-2.00

-4.00

-6.00

35.0028.0021.0014.007.0000.000 [ms]

3.00

2.00

1.00

0.00

-1.00

-2.00

-3.0035.0028.0021.0014.007.0000.000 [ms]

3.00

2.00

1.00

0.00

-1.00

-2.00

-3.00

35.0028.0021.0014.007.0000.000 [ms]

6.00

4.00

2.00

0.00

-2.00

-4.00

-6.00


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187

B SECOND STUDY CASE PLOTS

Figure 7-6 Case 2. Phase A voltage for each location (20-22 ms)

Figure 7-7 Case 2. Phase B voltage for each location (20-22 ms)

Second study case plots

188

Figure 7-8 Case 2. Phase C voltage for each location (20-22 ms)

Figure 7-9 Case 2. Phase A voltage for each location (20-20,5 ms)


189




190


Figure 7-13 Case 2. A01currents (0-500 ms)


191


Figure 7-15 Case 2. A09 currents (20-21,5 ms)


192

Figure 7-16 Case 2. A09 current phase A (20-21,5 ms)

Figure 7-17 Case 2. A09 current phase B (20-21,5 ms)


193

Figure 7-18 Case 2. Platform current (400-500 ms)

Figure 7-19 Case 2. Rms currents at platform


194

Figure 7-20 Case 2. Rms currents at A01 and A09



195




196




197




198

www.dtu.dk/centre/cet

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Technical University of Denmark

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DK-2800 Kgs. Lyngby

Denmark

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Fax: (+45) 45 88 61 11

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