Eliminating zero-missing phenomenon in long, high voltage ...1324288/FULLTEXT01.pdfDEGREE PROJECT IN...

IN DEGREE PROJECT ELECTRICAL ENGINEERING,SECOND CYCLE, 30 CREDITS

, STOCKHOLM SWEDEN 2019

Eliminating zero-missing phenomenon in long, high voltage, underground cables

A case study

AGNES LINNET

KTH ROYAL INSTITUTE OF TECHNOLOGYSCHOOL OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE

Abstract

The maximum length of an high voltage underground cable (HV UGC) cable is of-ten constrained by the criterion that the cable cannot have more than 50% reactivepower compensation. If this limit is exceeded the current in the circuit breaker maynot have a zero crossing after energization, which is referred to as the zero missingphenomenon. This is problematic if a fault occur shortly after energization. Inthe past 10 years, different methods have been proposed which would allow greaterreactive power compensation. These methods either prevent the zero missing phe-nomenon (preventive methods) or provide a way to open the circuit breaker if afault occurs (handling methods).

A new 200 km, 220 kV line has been proposed in Iceland referred to as Sprengisands-lína. One proposed option is to build it as an OHL-UGC-OHL line as the voltagecriteria is not fulfilled if Sprengisandslína is built as an UGC with a 50% reactivepower compensation. The aim of this thesis is to see whether the zero missing phe-nomenon can be avoided by implementing countermeasures - this gives a preliminaryresults whether Sprengisandslína can be built as an UGC. In this thesis the four dif-ferent preventive methods are analyzed with a transient study for Sprengisandslína:(1) Pre-insertion resistor, (2) simultaneous synchronized switching, (3) synchronizedswitching where the cable is energized before the shunt reactor, and (4) synchro-nized switching where the shunt reactor is energized before the cable.

Preliminary steady state studies were performed to determine the minimum num-ber of shunt reactors needed to fulfill the voltage criteria. The results showed thatthe minimum number needed were three assuming they are all of equal size locatedevenly along the cable (one at each end and one in the middle). Additionally, it isnecessary to see whether the generators would become underexcited if the cable is

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energized with 100% reactive power compensation as it can reduce the lifetime ofthe generators. The results showed that the generators did not become underexcited.

The countermeasure of synchronized switching where the shunt reactor is energizedbefore the cable and the countermeasure of simultaneous synchronized switchingwere shown to eliminate the zero-missing phenomenon when the cable was ener-gized with 100% reactive power compensation. Synchronized switching where theshunt reactor is energized before the cable was seen to have lower switching over-voltages, 21% higher than the nominal value, and the lower inrush current of 2.38kA. However, the method of simultaneous synchronized switching is cheaper andthe switching overvoltages and inrush current were within an acceptable margin(switching overvoltages were 35.9% higher than the nominal value and the inrushcurrent was 4.01 kA).

The results of the study indicate that Sprengisandslína can be energized as an UGCwith 100% reactive power compensation if either the countermeasure of simulta-neous synchronized switching or synchronized switching where the shunt reactor isenergized before the cable are used. However, a detailed frequency study must beperformed before either of the countermeasures can be recommended.

Keywords: Underground cable, zero-missing phenomenon, switching transients,shunt reactors, underexcited generators.

Sammanfattning

Högsta längden på en högspänning underjordisk kabel begränsas ofta av de kriteriersom kabeln inte kan ha mer än 50% reaktiv effektkompensation. Om denna gränsöverskrids kan strömmen i strömbrytaren inte ha noll genomgang efter aktivering,kallad noll saknad fenomen. Detta är problematiskt om ett fel inträffar strax efteraktivering. Under de senaste 10 åren har olika metoder föreslagits, vilket skullemöjliggöra större reaktiv effektkompensation. Dessa metoder hindrar antingen detnollbristande fenomenet (förebyggande metoder) eller ger ett sätt att öppna ström-brytaren om ett fel uppstår (hanteringsmetoder).

En ny 200 km, 220 kV linje har föreslagits på Island kallad Sprengisandslína. Ettföreslaget alternativ för att den här linjen ska byggas är att bygga den som en OHL-UGC-OHL-linje, eftersom spänningskriterierna inte är uppfyllda om Sprengisand-slína är byggt som en UGC med en 50% reaktiv effektkompensation. Syftet meddenna avhandling är att se huruvida det saknade fenomenet kan undvikas genomatt genomföra motåtgärder - detta ger ett preliminärt resultat om Sprengisandslínakan byggas som en UGC. I denna avhandling analyseras de fyra olika förebyggandemetoderna med en övergående studie för Sprengisandslína: (1) Förinsättningsresis-tor, (2) Synkroniserad samtidigkoppling, (3) Synkroniserad inkoppling där kabelnaktiveras före shuntreaktorn och (4) ) synkroniserad inkoppling där shuntreaktornaktiveras före kabeln.

Preliminära steady state studier utförs för att bestämma det minsta antalet shuntreak-torer som behövs för att uppfylla spänningskriterierna. Resultaten visade att detminsta antalet som behövdes var tre förutsatt att de alla är lika stora som liggerjämnt längs kabeln (en i varje ände och en i mitten). Dessutom är det nödvändigtatt se om generatorer skulle bli underexiterad om kabeln är energiserad med 100%

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reaktiva effektkompensation eftersom det kan minska generatorns livslängd. Resul-taten visade att generatorer inte blev underexiterad.

Motståndet för synkroniserad omkoppling där shuntreaktorn aktiveras före kabelnoch motmätningen av samtidig synkroniserad omkoppling visades för att elimineradet nollmissande fenomenet när kabeln aktiverades med 100% reaktiv effektkompen-sation. Synkroniserad omkoppling där shuntreaktorn aktiveras innan kabeln visadesig ha lägre omkopplingsvolymer, 21% högre än nominellt värde och den lägre in-brusningsströmmen på 2,38 kA. Metoden för samtidig synkroniserad omkopplingär emellertid billigare och omkopplingsvolymen och inströmmen var inom en ac-ceptabel marginal (omkopplingsvolymer var 35, 9% högre än nominellt värde ochinströmningsströmmen var 4,01 kA).

De resultaten av studien indikerar att Sprengisandslína kan energiseras som en UGCmed 100% reaktiv effektkompensation om antingen motspelet av samtidig synkronis-erad omkoppling eller synkroniserad omkoppling där shuntreaktorn aktiveras innankabeln installeras. En detaljerad frekvensstudie måste dock utföras innan någon avmotåtgärderna kan rekommenderas.

Nyckelord: Underjordisk kabel, nollbristande fenomen, växlingstransienter, shuntreak-torer, underexiterad generatorer.

Preface

This thesis was completed in the school of Electrical Engineering and ComputerScience at KTH, The Royal Institute of Technology as a partial fulfillment for Masterin Science in Electrical Engineering. This thesis was completed in collaboration withNorconsult ehf. and Landsnet, the Icelandic transmission system operator.

Acknowledgement

I would like to thank Jóhannes Þorleiksson at Norconsult ehf. for continuous sup-port throughout the thesis process and for the opportunities he has given me toaspire as an engineer.

Special thanks to Magni Þór Pálsson for great discussion and for the opportunityto make this thesis valid by allowing me to work on the Icelandic grid model. Iwould like to express my sincerest gratitude to my examiner Hans Edin and mysupervisor Nathaniel Taylor at KTH and Landsvirkjun Energy Research Fund fortheir generous support.

I owe Kristbjörg Anna Þórarinsdóttir and Arnór Bragi Elvarsson my sincerest grat-itude for spending countless of hours reading through my thesis and correcting myerrors.

Last but not least I would like to thank my sisters, Eyrún Linnet and Fríða RakelLinnet, for being great role models in the field of Electrical engineering and a bit ofunhealthy competition.

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Table of Contents

Abstract i

Sammanfattning iii

Preface v

Acknowledgement v

Table of Contents vi

List of Figures ix

List of Tables xii

Nomenclature xiii

1 Introduction 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Thesis objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Thesis disposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.4 The simulation programs . . . . . . . . . . . . . . . . . . . . . . . . . 5

PSS R©E . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5PSCAD-EMTDC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5E-Tran . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Literature review 72.1 Reactive power compensation . . . . . . . . . . . . . . . . . . . . . . 72.2 Waveform distortion . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Harmonics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

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TABLE OF CONTENTS vii

Switching overvoltages . . . . . . . . . . . . . . . . . . . . . . . . . . 10Ferro-resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.3 Zero-missing phenomenon . . . . . . . . . . . . . . . . . . . . . . . . 112.4 Countermeasures for the zero-missing phenomenon . . . . . . . . . . 13

Pre-insertion resistor . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Sequential switching . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Delayed opening of healthy phases . . . . . . . . . . . . . . . . . . . . 17Synchronized switching . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Cable and shunt reactor energized simultaneously . . . . . . . 18Shunt reactor energized after the cable . . . . . . . . . . . . . 18Shunt reactor energized before the cable . . . . . . . . . . . . 19

2.5 Reactive power output capability of generators . . . . . . . . . . . . . 20

3 Model implementation 233.1 Landsnet’s case study . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.2 Cable model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.3 Circuit model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.4 Model for long term steady state studies . . . . . . . . . . . . . . . . 27

4 Preliminary steady state studies 294.1 Voltage profile and location of shunt reactors . . . . . . . . . . . . . . 29

Before the connection to the north end . . . . . . . . . . . . . . . . . 30After the connection to the north end . . . . . . . . . . . . . . . . . . 30

4.2 Underexcited generators . . . . . . . . . . . . . . . . . . . . . . . . . 31

5 Verification of transient model 335.1 Verification of cable model . . . . . . . . . . . . . . . . . . . . . . . . 335.2 Verification of the grid model . . . . . . . . . . . . . . . . . . . . . . 34

6 Analysis of different countermeasures - ideal voltage source 376.1 No countermeasure installed . . . . . . . . . . . . . . . . . . . . . . . 376.2 Pre-insertion resistor . . . . . . . . . . . . . . . . . . . . . . . . . . . 386.3 Simultaneous synchronized switching . . . . . . . . . . . . . . . . . . 396.4 Synchronized switching where the cable is energized before the shunt

reactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406.5 Synchronized switching where the shunt reactor is energized before

the cable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

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7 Analysis of different countermeasures - voltage source at Langalda 437.1 No countermeasure installed . . . . . . . . . . . . . . . . . . . . . . . 437.2 Simultaneous synchronous switching . . . . . . . . . . . . . . . . . . . 447.3 Synchronous switching where the cable is energized before the shunt

reactor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 457.4 Synchronous switching where the shunt reactor is energized before

the cable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

8 Conclusions 498.1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498.2 Further studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

Bibliography 53

Appendix I 57Solution for pre-insertion resistor value . . . . . . . . . . . . . . . . . . . . 57

List of Figures

1.1 The Icelandic transmission grid with the proposed Sprengisandslína. Fig-ure received and published with permission from Landsnet. . . . . . . . 2

2.1 Thévenin circuit connected to a load . . . . . . . . . . . . . . . . . . . . 92.2 Schematics of simplified circuit of a cable and a shunt reactors . . . . . . 122.3 Zero-missing phenomenon at different compensation ratio. As we in-

crease the reactive power compensation ratio the DC offset of the breakercurrent increases. Above 50% compensation ratio it is not possible toopen the breaker if a fault occurs. . . . . . . . . . . . . . . . . . . . . . . 12

2.4 Schematic of a breaker with a pre-insertion resistor . . . . . . . . . . . . 132.5 Cable is energized with 100% reactive power compensation at t=0.2, at

t=0.5 a L-G fault occurs in phase A.A) Current through the breaker. The faulted phase has a zero crossing.B) Current in the shunt reactor. All phases have a zero crossing. . . . . 15

2.6 The procedure during a sequential switching. Figure adapted from [1]. . 162.7 Single line diagram when the shunt reactor is energized after the cable

in synchronized switching . . . . . . . . . . . . . . . . . . . . . . . . . . 192.8 Single line diagram when the shunt reactor is energized before the cable

in synchronized switching. . . . . . . . . . . . . . . . . . . . . . . . . . . 202.9 Equivalent circuit of a steady state synchronous machine. Figure adapted

from [2]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.10 Resulting phasor diagram for the equivalent steady state circuit of the

synchronous machine. Figure adapted from [2]. . . . . . . . . . . . . . . 212.11 Limits of reactive power output capability of generators in P-Q plane. . 22

3.1 Cross sectional view of a cable with marked parameters that needs to beentered in PSCAD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

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x List of Figures

4.1 Voltage profile of the cable with 100% compensated line when the northend is open for three different scenarios:(a) Two shunt reactors(b) Two shunt reactors. The following power plants with voltage controlat 90%: Búðarháls, Hrauneyjar, Sigalda, Sultartangi, and Vatnsfellsstöð(c) Three shunt reactorsOption (a) does not fulfill the voltage criteria while option (b) and (c)are both below 1.1 p.u. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.2 Voltage profile of the cable with 100% compensated line when the northend is connected for two different scenarios:(b) Two shunt reactors(c) Three shunt reactorsOption (b) does not fulfill the voltage criteria while option (c) is below1.1 p.u. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

6.1 Current waveform in the breaker during energization when no counter-measure is installed - an ideal voltage source. . . . . . . . . . . . . . . . 37

6.2 Switching overvoltages at the open end during energization when nocountermeasure is installed - an ideal voltage source. . . . . . . . . . . . 38

6.3 Current waveform in the breaker during energizaiton with pre-insertionresistor - an ideal voltage source. . . . . . . . . . . . . . . . . . . . . . . 38

6.4 Switching overvoltages at the open end during energization when thecable is energized with pre-insertion resistor - an ideal voltage source. . 39

6.5 Current waveform in the breaker during energization with simultaneoussynchronized switching - an ideal voltage source. . . . . . . . . . . . . . 39

6.6 Switching overvoltages at the open end during energization with simul-taneous synchronized switcing - an ideal voltage source. . . . . . . . . . 40

6.7 Current waveform in the breaker with synchronized switching where thecable is energized before the shunt reactor - an ideal voltage source. . . . 40

6.8 Switching overvoltages at the open end during energization with syn-chronized switching where the cable is energized before the shunt reactor- an ideal voltage source. . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

6.9 Current waveform in the breaker with synchronized switching where theshunt reactor is energized before the cable - an ideal voltage source. . . . 42

6.10 Switching overvoltages at the open end during energization with syn-chronized switching where the shunt reactor is energized before the cable- an ideal voltage source. . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

List of Figures xi

7.1 Current waveform in the breaker when no countermeasure is installedand the cable is connected to the Icelandic grid model. . . . . . . . . . . 44

7.2 Resulting voltage of the open end during energization when no counter-measure is installed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

7.3 Current waveform in the breaker when the cable is energized with si-multaneous synchronous switching and connected to the Icelandic gridmodel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

7.4 Resulting voltage of the open end during energization when the cable isenergized with synchronous switching. . . . . . . . . . . . . . . . . . . . 45

7.5 Current waveform in the breaker when the cable is energized at zerovoltage and the shunt reactors are energized 5 ms later at peak voltage. . 46

7.6 Resulting voltage of the open end during energization when the cable isenergized at zero voltage and the shunt reactors is energized 5 ms laterat peak voltage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

7.7 Current waveform in the breaker when the shunt reactor is energized atpeak voltage and the cable is energized 5 ms later at peak voltage. . . . . 47

7.8 Resulting voltage of the open end during energization when the shuntreactor is energized at peak voltage and the cable is energized 5 ms laterat zero voltage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

List of Tables

3.1 Cable route specification set by the Icelandic TSO Landsnet [3] . . . . . 233.2 Relevant information from the datasheet . . . . . . . . . . . . . . . . . . 253.3 Other settings for the cable model in PSCAD-EMTDC . . . . . . . . . . 263.4 Line parameters of the cable (long line corrected) . . . . . . . . . . . . . 26

4.1 Reactive output of generators in the area of Þjórsá . . . . . . . . . . . . 32

5.1 Comparison of cable parameters . . . . . . . . . . . . . . . . . . . . . . . 335.2 Comparison of the voltages in PSCAD and PSS R©E for the model without

voltage control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345.3 Comparison of three phase short circuit current in PSCAD and PSS R©E

for the model without voltage control . . . . . . . . . . . . . . . . . . . . 35

8.1 Results of different countermeasures for ideal voltage source . . . . . . . 508.2 Results of different countermeasures when the cable is energized at Lan-

galda . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

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Nomenclature

AC Alternating current

BIL Basic insulation level

CB Circuit breaker

DC Direct current

EHV Extra high voltage

HVAC High voltage alternating current

OHL Overhead transmission line

P.U. Per unit

RMS Root mean square

SCC Short circuit current

SOV Switching overvoltage

UGC Underground cable

Chapter 1

Introduction

1.1 Background

The Icelandic transmission grid is an isolated electricity system. The electrical gridis composed of three 220 kV grids. One is a strongly meshed grid which connectsReykjavík, where the main load is, with the production site in the south. The second220 kV grid connects industry to the production site in the east of Iceland and thethird connects industry to the production in the northeast of Iceland. These 220kV grids are connected by a 132 kV ring connection. The long path1 of the ringconnection makes the grid vulnerable to low power oscillations between the mainproduction in the south and east of Iceland. To strengthen the Icelandic transmissiongrid, the Icelandic transmission operator, Landsnet, is considering to build a 200 km220 kV transmission line. The line is referred to as Sprengisandslína and it shouldconnect Langalda in the south and Bárðardalur in the north. Figure 1.1 shows howSprengisandslína is considered to be connected in the Icelandic transmission system.

Sprengisandslína is not a new idea. In a report written by Landsvirkjun in 1981(former transmission operator) they expected that this line would be built and putinto operation by 1986. The aim was to strengthen the grid but overall to close thering connection [4]. As the current transmission grid has reached its tolerance limit,Sprengisandslína is back in the development plan. Sprengisandslína would make thegrid more meshed, less sensitive to failures in the ring connection and increase thedamping of the system [?].

The installation of Sprengisandslína as an overhead line has been met with publicresistance. As Sprengisandslína crosses wild nature, building the line as an OHL

1Approximately 1100 km

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2 CHAPTER 1. INTRODUCTION

Figure 1.1: The Icelandic transmission grid with the proposed Sprengisandslína.Figure received and published with permission from Landsnet.

is considered to have significant negative environmental impact [5]. It is thoughtthat the implementation of a cable would be more likely to be accepted. However,several technical limitations limit the maximum length of HVAC cables. Due to thelarge capacitive reactive power of HVAC cables, shunt reactors are needed to keepthe voltage below 1.1 p.u. which is the normal limit to ensure safe operation ofelectrical equipment. The maximum reactive power compensation without riskingzero-missing phenomenon2 is 50%. With those restrictions, Landsnet has conductedthat the maximum length of a cable is 50 km assuming that it is energized atLangalda, which has higher short circuit capacity. Thus, the current proposal forimplementation of Sprengisandslína is with a 85 km OHL, 50 km UGC, and 65 kmOHL, with shunt reactors on each side of the cable. No analysis has been performedon implementing countermeasures for the zero-missing phenomenon in the case ofSprengisandslína [3].

If Sprengisandslína would be solely implemented as UGC, measures needs to betaken towards ensuring zero crossing due to higher than 50% reactive power com-pensation. Additionally, long HVAC cables have low resonance frequencies whichmay lead to amplification on lower order of harmonics (5th, 7th, 11th, 13th etc.).When the resonance frequency is expected to be lower than 700 Hz, it is recom-mended that a detailed harmonic study is performed [6]. Another problem whichmay arise, especially if the reactive power compensation is low, is underexcited gen-

2Zero-missing phenomenon is when the DC offset in the inrush current exceeds the amplitudeof the AC current making it impossible to open the circuit breaker at zero crossing.

1.2. THESIS OBJECTIVES 3

erators. When a generator is operated continuously underexcited, the lifetime ofthe generator is reduced.

1.2 Thesis objectives

A valid model is created to analyze whether the countermeasures for the zero miss-ing phenomenon ensure zero crossing after energization. Additionally, early steadystate studies are performed to make sure that the circuit does not harm electricalequipments. In order to achieve that, the following objectives have been outlined:

• Create a valid frequency dependent model of Sprengisandslína and the sur-rounding network.

• Determine the number of shunt reactor needed for 100% reactive power com-pensation.

• Determine whether the generators will become underexcited if the cable isenergized with 100% reactive power compensation.

• Analyze whether any of the listed countermeasures for the zero-missing phe-nomenon eliminate the zero missing phenomenon during energization of Sprengi-sandslína.

1.3 Thesis disposition

The first chapter states the background regarding the Icelandic transmission gridas well as the proposed Sprengisandslína. The thesis objectives and disposition arestated and a description of the programs used in this thesis.

The second chapter gives the necessary background on problems which may ariseduring installation of HVAC into an electrical grid. It discusses why reactive powercompensation is needed, why there is a limit of 50% compensation and what hap-pens if the reactive power compensation is higher than 50%. Additionally it dis-cusses other unwanted phenomena which may happen, such as waveform distortionand underexcited generators.

The third chapter discusses the model implementation and briefly states what arethe design criteria used in this thesis. A detailed description is provided of how the

4 CHAPTER 1. INTRODUCTION

frequency dependent model of the cable was created in PSCAD.

The fourth chapter presents the results from the long term stability studies. Thevoltage profile, before and after the connection to the north end, is shown for differ-ent configuration of the reactive power compensation and consequently the numberof shunt reactors are determined. Additionally, analysis of whether the generatorswill become underexcited is presented.

The fifth chapter shows the verification of the transient model. The frequency de-pendent cable model is verified by comparing the resulting electrical parameters(resistance, capacitance, and inductance) to the electrical parameters given by thedatasheet. The transient grid model is verified by comparing the steady state volt-age and the short circuit current from the PSCAD model to the results from thePSS/E model provided and verified by Landsnet.

The sixth chapter presents the results of the inrush current through the breaker af-ter energization of Sprengisandslína when Sprengisandslína is connected to an idealvoltage source. Five different cases are shown: (1) No countermeasure is installed,(2) pre-insertion resistor, (3) simultaneous synchronized switching, (4) synchronizedswitching where the cable is energized before the shunt reactor, and (5) synchro-nized switching where the shunt reactor is energized before the cable.

The seventh chapter presents the results of the inrush current through the breakeras well as the switching overvoltages after energization of Sprengisandslína whenSprengisandslína is connected to the Icelandic grid model. All countermeasureswhich eliminated the zero missing phenomenon in chapter six are considered.

The eighth chapter discusses the conclusions of this thesis as well as future work.

1.4. THE SIMULATION PROGRAMS 5

1.4 The simulation programs

Norconsult ehf. provided all software licenses for this study.

PSS R©E

The simulation program PSS R©E (Power System Simulator for Engineering) bySiemens is used in this program for steady state studies. PSS/E is used in over140 countries and is one of the leading power transmission simulation and analysistools in the world.

PSCAD-EMTDC

The simulation program PSCAD-EMTDC (Power Systems Computer Aided design- Electromagnetic Transients including DC) by Manitoba Hydro is used in thisproject for transient studies of the cable during energization. PSCAD is consideredto be the most precise software to simulate transient behavior of cables and is usedin nearly 80 countries by 30000 users [7].

E-Tran

E-tran is the bridge between PSS R©E and PSCAD-EMTDC. Since most users keeptheir system data in PSS R©E .raw file formats creating the equivalent PSCAD-EMTDC model manually is both time consuming and prone to human error. E-tranwas built to directly translate power system data from PSS R©E .raw file to PSCAD-EMTDC format. Additionally, as electromagnetic transient programs are unable tosolve large networks, E-tran creates multi-port network equivalents of large systemswhich are outside the scope of the study.

Chapter 2

Literature review

In this chapter we discuss different challenges and phenomena that can appear dur-ing installation of high voltage AC underground cables. The chapter starts off bydiscussing reactive power in UGC and the need for reactive power compensation.Then we discuss the concept of waveform distortion, including harmonics, switch-ing overvoltages and ferro-resonance. Then the zero missing phenomenon and itscountermeasures are introduced. Lastly, the problem of underexcited generators arediscussed and why they need to be analyzed when installing UGC.

2.1 Reactive power compensation

Underground cables are capacitive and generate reactive power. This is problematicin long, unloaded EHV cables, since the capacitance of the line is linearly dependenton its length and the reactive power produced is proportional to the voltage squared.In sinusoidal steady state, the voltage at the sending end, V1, can be expressed asa function of the voltage at the open end, V2, the current, Ir, the characteristicimpedance, Zc, and the propagation constant, γ

V1 =V2 + ZcIr

2eγx +

V2 − ZcIr2

e−γx (2.1)

where the characteristic impedance Zc is

Zc =√z/y (2.2)

γ is the propagation constant

γ =√yz = α + jβ (2.3)

The real part of the propagation constant, α, is called the attenuation constant whilethe imaginary part, β, is called the phase constant. The parameters z and y are the

7

8 CHAPTER 2. LITERATURE REVIEW

series impedance and shunt admittance per unit length and phase respectively:

z = r + jωl (2.4)

y = g + jωc (2.5)

where r is the resistance, l is the inductance, g is the conductance, and c is thecapacitance.

For an unloaded line, the current Ir = 0, thus

V1 =V22eγx +

V22e−γx (2.6)

Additionally if the line is assumed to be lossless, then γ = jβ thus

V1 =V22ejβx +

V22e−jβx = V2 cos(βx) (2.7)

The voltage at the open end can be found by rearranging the equation and substi-tuting x for the length of the cable, represented by d:

V2 =V1

cos(βd)(2.8)

The parameter βd is often referred to as the electrical length of the line and has theunit radians. For lossless line it can be expressed as

βd = ω√lcd = ω

√LC (2.9)

Since unloaded UGC have high capacitance, c, and inductance l, the voltage at thereceiving end may exceed the tolerance limit of the equipment as well as violatingpower supply quality regulation.

To consume the reactive power produced by the cable a shunt reactor can be in-stalled. The definition of shunt reactors according to IEEE is:

"A reactor intended for connection in shunt to an electricsystem for the purpose of drawing inductive current." [8]

Shunt reactors are typically installed on either end of the cable. However, an in-creased number of shunt reactors evenly distributed along the cable leads to a bettervoltage profile. It is necessary to optimize the number of shunt reactors based oncost and voltage limits. As the external system impacts the voltage profile it isnecessary to perform such study for every cable before installation. [9].

2.1. REACTIVE POWER COMPENSATION 9

To see the relation between the voltage at the bus of connection and the reactivepower and the short circuit capacity we can look at figure 2.1. The figure shows aThévenin circuit with voltage source, VTH , a Thévenin impedance of ZTH 6 θTH anda load of ZL 6 φL. The short circuit capacity, SCCap, at the connection point, isdefined as

SCCap =V 2th

Zth(2.10)

Vth Zth

V1

ZL

Figure 2.1: Thévenin circuit connected to a load

The voltage at the connection point of the load, V1, can be mathematically derivedfrom the other circuit parameters as:

V1 =VthZL√

Z2th + Z2

L + 2ZthZL cos(θth − φL)(2.11)

Thus a bus with a higher short circuit capacity, thus lower Zth for a given voltagelevel, will experience less voltage variation.

The reactive power produced by the load, denoted QL, can be derived as

QL =V 2thZL sin(φL)√

Z2th + Z2


By rearranging the equation, it is possible to show the relation between the producedreactive power, QL, and the voltage at the connection point, V1, as well as the othercircuit parameters.

V1 =

√ZLQL√

sinφL4√Z2th + Z2


Thus, the voltage increase is proportional to the produced reactive power and ap-proximately inversely proportional to the short circuit capacity at the connectionpoint. Thus the higher the short circuit capacity is the less voltage variation willoccur for the same amount of reactive power. When there is a large difference inshort circuit capacity between the connection points of a cable, it can be necessaryto only allow energization from the connection point which has higher short circuitcapacity to fulfill the voltage criterion [9], [3].


2.2 Waveform distortion

Waveform distortion is a distortion in the 50 Hz sinusoidal waveform. Some dis-tortions are due to active causes, such as rectification loads and electric furnaces.Other distortions can be due to passive causes such as imbalance in loads, saturationor LC resonance under special conditions of power network.

Harmonics

When the voltage and current are distorted in its steady state it contains harmoniccomponents. The definition of a harmonic component according to IEEE is:

"A component of order greater than one of theFourier series of a periodic quantity." [10]

In a power system operating at 50 Hz the third harmonic has the frequency of 150Hz, the fifth has a frequency of 250 Hz and so forth.

Harmonics are a matter of power quality as they can cause negative effect in al-most all power system components. For example; in motors/generators, trans-formers, power cables, capacitors, power electronic equipment, metering and relays,switchgear and in communication. The most common effect of harmonics is in-creased losses resulting in unwanted heating. That occurs in motors/generators andtransformers where the harmonics increase iron and copper losses. In power cablesharmonics result in skin and proximity effect which results in heating. Harmonicscan also cause increased losses and heat in switchgear [11].

Switching overvoltages

Switching overvoltage (SOV) is an inevitable transient phenomenon in power sys-tems produced by the opening and closing of breakers and disconnectors. SOV haslower amplitude than lightning overvoltage but it has longer rise time and/or longerduration [12]. The resulting SOV depends on the moment of connection/disconnection.A cable energized at a peak voltage produces a traveling wave with full ampli-tude. This wave will then be reflected and refracted at points where the waveimpedance differs [13]. When analyzing different countermeasures for zero-missingphenomenon, especially those which take advantage of energizing at at peak voltage,

2.3. ZERO-MISSING PHENOMENON 11

it is important to analyze the resulting switching overvoltages. This is to make surethat they do not exceed the basic insulation level (BIL).

Ferro-resonance

Ferro-resonance is an unwanted phenomenon that can occur in an electric circuitwhich contains at least one of the following: Non-linear inductance, a capacitor, avoltage source and/or low losses. The term was originally defined in 1920 by PaulBoucherot to describe the phenomenon where there are two stable fundamental fre-quencies in a circuit [14]. Thus the steady state response of a circuit can suddenlychange from the frequency of the AC source to the ferro-resonant frequency. Thiscan result in sustained overvoltages which can, alongside the resulting harmonic,cause harm to the electrical equipment [14].

2.3 Zero-missing phenomenon

Zero-missing phenomenon is when the DC offset is larger than the AC amplitudethus the current does not cross zero for several cycles. This happens if a cable isenergized with a shunt reactor which compensates more than 50% of the reactivepower [9]. Most circuit breakers interrupt the current at the zero crossing and areunable to do so if a zero-missing phenomenon occurs without the risk of damagingthe CB [15, 16]. Thus the zero-missing phenomenon does not become a problemunless there is a fault during energization [13, 1].

To understand the problem we look at a simplified circuit. The shunt reactor isrepresented by a series connected resistance and inductor and the cable is repre-sented by capacitance. At time t=0 the switch closes and the cable is energized, asshown in figure 2.2. The current in the inductor is continuous and 90 out of phasein respect to the inductor voltage. If the circuit is energized at any other momentthan peak voltage, a DC component will be present to maintain the continuity ofthe current. The largest DC offset occurs if the voltage is zero at the moment ofenergization. Since the resistance in an unloaded cable is small it can take up tofew seconds to dampen the DC component [16, 17].


t=0

AC

R

LC

Figure 2.2: Schematics of simplified circuit of a cable and a shunt reactors

Figure 2.3 shows the effect of different reactive power compensation ratio on thezero-missing phenomenon during the energization of a 220 kV, 200 km, 2000 mm2

cable. As we increase the reactive power compensation ratio the DC offset in thebreaker current increases. For compensation ratios above 50% we can now see thatthere is no zero crossing, which makes it impossible to safely open a circuit breaker.

Figure 2.3: Zero-missing phenomenon at different compensation ratio. As we in-crease the reactive power compensation ratio the DC offset of the breaker currentincreases. Above 50% compensation ratio it is not possible to open the breaker if afault occurs.

2.4. COUNTERMEASURES FOR THE ZERO-MISSING PHENOMENON 13

2.4 Countermeasures for the zero-missing

phenomenon

Several countermeasures for the zero-missing phenomenon have been proposed [16],[18]. The countermeasures can be divided into subsections depending on the effectthey have: prevention countermeasures and handling countermeasures. Preven-tion countermeasures, if correctly installed, eliminate the zero-missing phenomenon.These methods include three variations of synchronize switching and pre-insertionresistor. Handling methods provide a way to safely open the circuit breakers dur-ing a zero-missing phenomenon. These methods include sequential switching anddelayed opening of healthy phases.

Pre-insertion resistor

The zero-missing phenomenon is a problem due to low resistance and high ca-pacitance of the circuit during energization which leads to a slow decaying DC-component. This method aims to increase the resistance sufficiently by using abreaker equipped with a pre-insertion resistor. The pre-insertion resistor consistsof a resistor block connected in parallel with a breaking chamber [19]. A schematicof the pre-insertion resistor is shown in figure 2.4. The closing time of the circuitbreaker via arcing contact depends on the design of each circuit breaker. For ABBcircuit breakers this time is approximately 8-12 ms [19]. No information was foundon the closing time from other manufactures.

Resistor block

The breaking chamber

Figure 2.4: Schematic of a breaker with a pre-insertion resistor

If this method is implemented correctly the DC component should decrease suffi-ciently that the zero-missing phenomenon is avoided. To do so the resistance mustbe chosen correctly. If the resistor value is too low the DC component will not besufficiently damped before the arcing contact of the breaker. While if the resistorvalue is too high it will simulate an open circuit and the zero missing phenomenonwill still appear after the arcing contact of the breaker [16]. Ref. [17, 16] propose


two methods to calculate the optimal value of the pre-insertion resistor: the energyequation or a differential equation. Both of these equations are derived from a π-model of the cable with a single shunt reactor installed closest to the voltage source.In this thesis the energy equation will be used.

The energy which needs to be dissipated before the closing of the breaking chamberwhich is here assumed to be 10 ms is

W =1

2Ls(IDCs

)2 (2.14)

where Ls is the inductance value of the shunt reactor and IDCs is the DC componentthat needs to be damped. The energy which is dissipated through the pre-insertionresistor is

W =

∫ 0.01

0

RpI21 (2.15)

where Rp is the pre-insertion resistor value, I1 is the current through the pre-insertion resistor.

The energy equation calculates the pre-insertion resistor value by equating the en-ergy that needs to be dissipated (equation 2.14) with the energy that is dissipated(equation 2.14) with the following assumptions:

• The reactive power compensation ratio is 100%. The I1 and IDCs will be equaland both currents should be zero after 10 ms.

• I1 decreases linearly.

• The resistive element of the shunt reactor, Rs, is neglected as the Rp Rs.

Now it is possible to rewrite equation 2.14 and 2.15 as

W =0.01

3RpI

21 (0) =

1

2Ls(I

DCs )2 (2.16)

from which the value of the pre-insertion resistor is found as

Rp =3Ls0.02

(2.17)

Note, here the same assumptions are made as in [17, 16]. Despite that, the samesolution was not obtained, thus a more detailed mathematical solution is in 8.2 tostrengthen my case.


Sequential switching

The zero-missing phenomenon is only a problem if there is a fault during the ener-gization of the cable. If there is none, it is possible to wait until the DC componenthas been sufficiently damped before opening the circuit breaker. The method ofsequential switching proposes a way to open the circuit breaker during a singlephase-to-ground fault. It takes advantage of two things: the fault current has a zerocrossing, and the currents in the shunt reactor of the healthy phases also have a zerocrossing. Figure 2.5 a) shows the current in the breaker when a cable is energized att = 0.2 s and a L-G fault occurs at t = 0.5 s. Figure 2.5 b) shows the current in theshunt reactor for the same case. This method requires single pole operated circuitbreakers for the lines and the shunt reactors [1].

Figure 2.5: Cable is energized with 100% reactive power compensation at t=0.2, att=0.5 a L-G fault occurs in phase A.A) Current through the breaker. The faulted phase has a zero crossing.B) Current in the shunt reactor. All phases have a zero crossing.


Figure 2.6 shows the procedure how to safely open the circuit breaker if the zero-missing phenomenon is present during a single line-to-ground fault.

Step1

Step2

Step3

Open

Triggered

Closed

Point

ofconn

ection

Point

ofconn

ection

Point

ofconn

ection

Ope

nendof

thecable

Ope

nendof

thecable

Ope

nendof

thecableCB1

CB2 CB3

CB4

CB1

CB2 CB3

CB4

CB1

CB2 CB3

CB4

Figure 2.6: The procedure during a sequential switching. Figure adapted from [1].


A procedure to safely open the circuit breaker if the zero-missing phenomenon ispresent during a single line-to-ground fault is as follows [1]:

Step 1: The circuit breaker of the faulted phase (Phase A) is opened at the firstzero crossing after the fault (CB1-A). The fault should be cleared within the first60 ms.

Step 2: The circuit breakers of the shunt reactors of the healthy phases are opened(CB2-B and CB2-C). As the current in the shunt reactor of the faulted phase doesnot have a zero crossing it should not be opened at this stage.

Step 3: After the shunt reactors of the healthy phases have been disconnected thecurrent in the healthy phases contains only an AC component at this point. Thus itis now possible to open the circuit breakers of the healthy phase (CB1-B and CB1-C).

When one phase is opened and others are left closed for some time, induced ferro-resonance may occur which is even more unwanted than the zero-missing phe-nomenon [15]. Thus an extensive analysis of the resulting ferro-resonance mustbe performed before the method of sequential switching is proposed. Additionallyit is necessary to confirm the leading current capability of the circuit breakers.

Delayed opening of healthy phases

The method of delaying the opening of the healthy phases is similar to sequentialswitching as it takes advantage of the fact that the fault current has a zero crossing.The circuit breaker of the faulty phase is tripped at the first zero crossing afterthe fault. The healthy phases are then left open until the DC component has beensufficiently damped [16].

The benefit of using this method compared to sequential switching is economical asit only requires one set of single pole operated circuit breakers. The severe drawbackof this method compared to sequential switching is the resulting ferro-resonance. Asthe healthy phases are kept connected for longer time while the faulted phase hasbeen disconnected the induced ferro-resonance poses a larger problem within thismethod [15].


Synchronized switching

The method of synchronized switching takes advantage of the fact that the zero-missing phenomenon can be avoided depending on the moment of connection. Thismethod can be divided into three subgroups [16, 18]:1. When the cable and the shunt reactors are energized simultaneously.2. When the shunt reactor is energized 5 ms (for a 50 Hz system) before the cable.3. When the shunt reactor is energized 5 ms after the cable.

Cable and shunt reactor energized simultaneously

The zero-missing phenomenon can be avoided if the circuit is energized at a peakvoltage. By using one set of single pole operated circuit breaker and one normal (i.e.three-pole operated) circuit breaker each phase can be energized at peak voltage.The main drawback of energizing the cable simultaneously with the shunt reactoris that it can result in high switching overvoltages and inrush current. Thus it isnecessary to perform an insulation co-ordination study of the system at the pointof connection. If it is supposed to be possible to energize the cable from both ends,both circuit breakers must be single pole circuit breakers [16, 18].

Shunt reactor energized after the cable

By using three sets of single pole operated circuit breakers and one normal (i.e.three-pole operated) circuit breaker, it is possible to reduce switching overvoltages.This is done by connecting each phase of the cable at zero voltage and connectthe shunt reactor 5 ms later at peak voltage [16]. Figure 2.7 shows the single linediagram of the set-up needed when the shunt reactor is energized after the cable.First circuit breaker CB1 is energized at a zero voltage. Quarter of a cycle later,circuit breakers CB2 and CB3 are energized at a peak voltage. If it is supposed tobe possible to energize the cable from both ends, CB4 also needs to be a single polecircuit breaker.


Ope

nendof

thecable

Point

ofconn

ection CB1 CB4

CB2 CB3

UGC

Normal CB

Single pole CB

Figure 2.7: Single line diagram when the shunt reactor is energized after the cablein synchronized switching

Shunt reactor energized before the cable

Similarly to the previous method, the method of energizing the shunt reactor beforethe cable requires three sets of single pole operated circuit breakers and one normal(i.e. three pole operated) circuit breaker. Figure 2.8 shows the single line diagramof the set up needed when the shunt reactor is energized before the cable. Note,the only difference between figures 2.7 and 2.8 is the location of CB1. First thecircuit breaker CB2 is energized at a peak voltage. Quarter of a cycle later, at azero voltage, CB1 is energized. Finally, CB3 is energized at peak voltage, half acycle after CB1 is energized. If it is supposed to be possible to energize the cablefrom both ends, an extra set of single pole circuit breaker is needed on the left sideof the cable as well as an additional normal circuit breaker is needed next to the"Point of connection". This method requires two extra single pole circuit breakersfor every additional shunt reactor. This method was shown to result in the lowestswitching overvoltages of all the synchronized switching methods in ref. [18].


Ope

nendof

thecable

Point

ofconn

ection

CB2 CB3

UGCCB1 CB4

Normal CB

Single pole CB

Figure 2.8: Single line diagram when the shunt reactor is energized before the cablein synchronized switching.

2.5 Reactive power output capability of generators

When installing an element which produces reactive power close to generators itis important to analyze whether the generators become permanently underexcited.The reason is that when generators are underexcited, meaning generators whichconsume reactive power, their lifetime is reduced [2]. This is due to the fact thatthe reactive power output capability of generators is limited by different factors de-pending on whether the generator is consuming or producing reactive power [2].

The armature current limit is limited by the heat dissipation in the armature. Thislimit applies for both over- and underexcited generators and is given by the ratedMVA of the generator, S, and the phase angle φ[2]. It can be expressed as:

S = P + jQ = |Et||It|(cosφ+ j sinφ) (2.18)

where P and Q are the active and reactive power respectively and |Et| and |It| arethe magnitude of the stator terminal voltage and current respectively. In the P-Qplane, the armature current limit is a circle with a radius of the rated MVA of thegenerator.

Similarly, the field current limit is a heating limit set by the maximum field current.This is a limit for the overexcitation of the generator. Figure 2.9 shows the equiva-lent circuit of a simple synchronous machine in steady state where the salience and

2.5. REACTIVE POWER OUTPUT CAPABILITY OF GENERATORS 21

the armature resistance is neglected.

Eq

Xs = Xd = Xq

EtIt

Xs

Eq = Et0 + jXsIt0|Eq| = Xadifd = EI

Figure 2.9: Equivalent circuit of a steady state synchronous machine. Figureadapted from [2].

In figure 2.9, Xad is the mutual reactance between the stator and the rotor, Xs isthe synchronous reactance, ifd is the field current and δi is the angle between theq-axis and Et .

Et

jXsItXsIt cosφ

XsIt sinφIt

δiφ

Eq = Xadifd

Figure 2.10: Resulting phasor diagram for the equivalent steady state circuit of thesynchronous machine. Figure adapted from [2].

From the resulting phasor diagram shown in figure 2.10 it is possible to derive thefollowing equations[2]:

(Xadifd) sin δi = XsIt cosφ (2.19)

(Xadifd) cos δi = Et +XsIt sinφ (2.20)

By rearranging the equation and multiplying through them with Et, one can derivethe constant field current locus

P = EtIt cosφ =Xad

XsEtifd sin δi (2.21)

andQ = EtIt sinφ =

Xad

XsEtifd cos δi −

E2t

Xs(2.22)


The end region heating limit is the localized heating limit of the end of the arma-ture. This is a severe limit when the generator is underexcited because when thegenerator is overexcited, it has a high field current which saturates the retainingring thus the armature end leakage flux is small. However, when the generator isunderexcited the field current is small, thus the retaining ring is not saturated whichresults in high armature end leakage flux. If a generator is operating continuouslyin the end heating region, the lifetime of the generator is reduced. [2].

All three limits in the P-Q plane are shown in figure 2.11.

Q

P

Field currentheating limit

Armature currentheating limit

End regionheating limit

φ

Srated

−E2t

Xs

Xad

XsEti fd

δ1

Figure 2.11: Limits of reactive power output capability of generators in P-Q plane.

Chapter 3

Model implementation

3.1 Landsnet’s case study

In February of 2015 Landsnet published the report: "High Voltage UndergroundCables in Iceland" [3] which included a case study of Sprengisandslína. This casestudy included a set of premises such as cable size, material, voltage, cable bonding,layout and trench. These specifications, shown in table 3.1, are used as premises inthis thesis.

Table 3.1: Cable route specification set by the Icelandic TSO Landsnet [3]

Voltage (V) 220 kV

Minimum voltage at Lan-galda during energization

1.02 p.u.

Maximum voltage 1.1 p.u.

Cable size 3× 1× 2000 mm2

Conductor material Segmental Aluminum

Cable bonding Cross bonded

Cable layout Flat formation

Trench depth 1.2 m

Trench width 1 m

Additionally, due to the vast difference in short circuit capacity between each endof the line (3700 MVA at Langalda, 800 MVA at Bárdardalur), this thesis onlyfocuses on energization from Langalda. During energization the generators in thevicinity of Langalda is assumed to be able to operate with a voltage control of 90%,

23

24 CHAPTER 3. MODEL IMPLEMENTATION

as needed[3].

3.2 Cable model

The 2000 mm2 single core cable from NKT type (A)2XS(FL)2Y1 127/220 kV withsegmental aluminum conductor – relevant information from the datasheet shown intable 3.2 - was modeled according to the specification set in table 3.1 in PSCAD-EMTDC [20]. In PSCAD the cable is divided up into four layers: Core, insulation,wire screen and sheath (see figure 3.1). Each layer has specified radius rn where nis the number of the layer, core being the first layer and sheath the fourth.

r1

r2

r3

r4

Sheathε2

Wire screenρs, µs

Insulationε1

Coreρc, µc

Figure 3.1: Cross sectional view of a cable with marked parameters that needs tobe entered in PSCAD.

The core of the cable is segmental aluminum conductor with radius r1 = 27.15 mm[20]. The value for the conductor’s relative permeability is assumed to be the sameas for aluminum µc = 1.000022. As PSCAD models the cable as a solid conductor,a conversion method is used to find the effective resistivity, ρc, of the core,

ρc = ρ′cπr21Ac

(3.1)

where Ac is the cross sectional area of the core and ρ′c =2.8264× 10−8 Ωm is theresistivity of hard drawn aluminum at 20C [21].

The insulation of the cable is XLPE (Cross-linked polyethylene) with a outer radiusof r2 = r1 + 19 = 46.15 mm. When the capacitance of the cable is known, itis recommended to ignore the semi-conducting layer in the model. Instead, therelative permittivity, ε1, is to be changed since most datasheets do not give explicit

1Aluminum XLPE cable with copper wire screen and APL sheath

3.2. CABLE MODEL 25

information regarding the semi-conducting layers. The relative permittivity of theinsulation layer is:

ε1 =C ln(r2/r1)

2πε0(3.2)

where C is the capacitance of the cable and ε0 is the permittivity of vacuum.

The wire screen conductor is made out of copper. Relative permeability of thescreen is assumed to be the same as of copper, µs = 0.999994. To calculate theouter radius of the wire screen, it is approximated to be tubular conductor withcross sectional area equal to the total wire area As which is given in the datasheet.The outer radius of the wire screen can then be calculated with 3.3.

r3 =

√Asπ

+ r22 (3.3)

The resistance of the wire screen is assumed to be the same as the resistance ofannealed copper at 20C, ρs =1.7241× 10−8 Ωm.

The sheath is made of polyethylene. The outer radius of the sheath is the overallradius of the cable, thus r4 = 58 mm. The relative permittivity of polyethylene isε2 = 2.3 [22].

Other settings for the cable model set up are shown in table 3.3.

Table 3.2: Relevant information from the datasheet

Dimensions/Cross sections 2000 mm2

Conductor, round, stranded, segmental, ø approx. 54.3 mm

XLPE insulation nom. 19 mm

Screen,copper wire, cross section nom. 110 mm2

Outer diameter approx. 116 mm2

Electrical Data

Al conductor DC resistance at 20C max. 0.0149 Ω/km

Al conductor AC resistance at 90C max. 0.0193 Ω/km

Capacitance per core approx 0.270 µF/km

Inductance approx 0.50 mH/km

26 CHAPTER 3. MODEL IMPLEMENTATION

Table 3.3: Other settings for the cable model in PSCAD-EMTDC

Configuration

Depth below ground surface 1.084

Axial distance between phases 0.416

Ideal crossbonding is enabled

Cross-bonding group 1

Conducting core is excluded

1st conducting layer is included

Frequency Dependent (Phase) Model Options

Travel Time Interpolation On

Curve Fitting Starting Frequency 0.5 [Hz]

Curve Fitting End Frequency 1× 106 [Hz]

Total Number of Frequency Increments 100

Maximum Order of Fitting for Yc 20

Maximum Fitting Error for Yc 0.2 [%]

Max. Order per Delay Grp. for Prop. Func. 0.2 [%]

DC Correction Enabled

Passivity Checking Disabled

The resulting positive sequence line parameters for the cable are shown in table 3.4.The base of the per unit quantities is 220 kV (line-to-line) and 100 MVA.

Table 3.4: Line parameters of the cable (long line corrected)

Positive sequence Zero sequence

Resistance 7.066× 10−3 [pu] 6.981× 10−2 [pu]

Reactance 8.012× 10−2 [pu] 2.720× 10−2 [pu]

Susceptance 8.328 [pu] 8.243 [pu]

Surge Impedance 1.961× 10−1 [pu] 1.149× 10−1 [pu]

3.3. CIRCUIT MODEL 27

3.3 Circuit model

The cable is 200 km long and is modeled with 100% reactive power compensation.The shunt reactors are of equal size and positioned at either end of the cable andregularly across the cable as needed until the voltage criteria has been fulfilled.One cable end is connected to a voltage source and the other to a large resistor(1× 106 Ω), this simulates an open circuit. Realistically the cable would be trans-posed every 1 km but here the cable is ideally transposed.

As the resulting transient overvoltages and inrush currents are dependent on howthe propagating wave reflects and refracts at the transition points - it is importantto perform a transient study for each system. Thus the model was connected tothe Icelandic grid model where the voltage source is substituted for connection tothe substation at Langalda. The Icelandic grid model was converted from PSS/Eto PSCAD format via E-tran. To strike a balance between minimizing computa-tional time and maximizing modeling accuracy, the electromagnetic model of theIcelandic transmission grid was created of the 24 busses in the vicinity of Langalda.An equivalent network was created for what had not yet been modeled. This allowsfor a simplification of the model for less relevant parts of the network, but retainingthe level of detail where needed as switching transients will only propagate shortdistances2 into the network [23].

3.4 Model for long term steady state studies

The PSS R©E model of the transmission system, provided by Landsnet, is the basisfor the model used in the long term stability studies. A cable was modeled withthe parameters given in table 3.4. The south end of the cable was connected toLangalda. As there is no substation in the current network for Bárðardalur, thenorth end in this study was connected to the closest substation which was Krafla 2via 220/132 kV transformer. No data has been specified for this transformer, so it isassumed that its parameters are the same as the 220/132 kV 200 MVA transformerat Krafla: transformer resistance and reactance are 0.5% and 12% respectively.

2Here short distance is defined as one or two busses

Chapter 4

Preliminary steady state studies

In this chapter we will perform two different steady state studies with the cablesystem in operation. First we will analyze how many shunt reactors are neededto fulfill the voltage criterion of 1.1 p.u. Secondly we will analyze whether thegenerators in the vicinity of Langalda, often referred to as the area of Þjórsá, willbe underexcited.

4.1 Voltage profile and location of shunt reactors

The voltage profile is flattest when the shunt reactors are installed with regularintervals across the cable. The shunt reactors are assumed all to be of equal sizeand evenly distributed along the cable. Due to economical reasons, it is necessaryto optimize the number of shunt reactors based on cost and the criteria that thevoltage must remain less than 1.1 per unit. According to the Landsnet’s case studyon Sprengisandslína it may be possible to operate the generators in the vicinity ofthe south end of the cable (Langalda) with voltage control at 90% during the ener-gization. The voltage profile is attained by steady state simulation of the Icelandicgrid model in the simulation program PSS R©E.

We use trial and error procedure to optimize the number of shunt reactors needed.The voltage profile was created by dividing the cable, parameters specified in table3.4, into (2n − 2) × k segments of equal length where n is the number of shuntreactors and k is any integer (k ≥ 1). The cable was simulated with the north enddisconnected from the grid and connected to a shunt reactor.

29

30 CHAPTER 4. PRELIMINARY STEADY STATE STUDIES

Before the connection to the north end

Figure 4.1 shows the voltage profile of the cable if there is 100% reactive powercompensation for total of three cases: (a) two shunt reactors, (b) two shunt reactorswith voltage control at 90% for Búðarháls , Hrauneyjar, Sigalda, Vatnsfellsstöð andSultartangi (power plants)1, and (c) three shunt reactors. The only method thatdoes not fulfill the voltage criterion of 1.1 p.u. is option (a) .

Figure 4.1: Voltage profile of the cable with 100% compensated line when the northend is open for three different scenarios:(a) Two shunt reactors(b) Two shunt reactors. The following power plants with voltage control at 90%:Búðarháls, Hrauneyjar, Sigalda, Sultartangi, and Vatnsfellsstöð(c) Three shunt reactorsOption (a) does not fulfill the voltage criteria while option (b) and (c) are bothbelow 1.1 p.u.

After the connection to the north end

The generators can only be temporarily operated with 90% voltage control duringthe energization. Thus it is necessary to verify that the voltage limit is still fulfilledafter the cable is connected to Krafla via 132/220 kV transformer and the voltagecontrol has been removed. Figure 4.2 shows that cable is connected to Krafla andthe voltage control has been removed only option (c) fulfills the voltage criteria of

1Location is shown figure 1.1 but the name listed for the power plants is the abbreviation. Forexample, Búðarháls is listed as BUD, Hrauneyjar is listed as HRA, Sigalda is listed as SIG etc.

4.2. UNDEREXCITED GENERATORS 31

1.1 p.u. Thus we will only analyze the energization when the cable has three shuntreactors and no additional voltage control is in place.

Figure 4.2: Voltage profile of the cable with 100% compensated line when the northend is connected for two different scenarios:(b) Two shunt reactors(c) Three shunt reactorsOption (b) does not fulfill the voltage criteria while option (c) is below 1.1 p.u.

4.2 Underexcited generators

The effect that the cable and the shunt reactor has on the reactive power output ofgenerators can be seen by running a load flow study of the system before and afterthey are installed. As explained in section 2.5, operating generators as underexcitedis harmful to the generators. Thus we are only concerned with how much reactivepower the generators consume, not how much they produce.

Table 4.1 shows the negative reactive power limit of the generators in vicinity ofLangalda and the actual reactive power produced or consumed by the generatorsbefore and after Sprengisandslína is in operation2. Only the powerplant Búðarhálsis operating their generators as underexcited before Sprengisandslína has been in-stalled. After Sprengisandslína is in operation, all generators produce more reactive

2BUR II-V1 is neglected as it had not been built when this thesis project started

32 CHAPTER 4. PRELIMINARY STEADY STATE STUDIES

power than before. Thus it can be assumed that the cable system with 100% reac-tive power compensation does not reduce the lifetime of the generators in the areaof Þjórsá.

Table 4.1: Reactive output of generators in the area of Þjórsá

Power plant Generator Qgen withoutcable [Mvar]

Qgen with 100%compensated cable

[Mvar]

Qmin

BURFE-12 (ID: 1) 15.8 16.0

BURFE-12 (ID: 2) 15.8 15.9

Búrfell BURFE-34 (ID: 1) 10.3 10.4 -10

BURFE-34 (ID: 2) 10.3 10.4

BURFE-56 (ID: 1) 9.5 9.7

BURFE-56 (ID: 2) 9.5 9.7

BUR II-V1 N/A N/A N/A

SIGALD12 14.8 15.0

Sigalda SIGALD22 14.8 15.0 -20

SIGALD32 14.8 15.0

HRAUNE12 30.6 30.9

Hrauneyjar HRAUNE22 30.6 30.9 -20

HRAUNE32 30.6 30.9

Sultartangi SULT-V1 5 5.2

SULT-V1 7 7.3 -20

Búðarháls BUD-V1 -2.9 -2.5

BUD-V2 -2.9 -2.5 -19.6

Vatnsfellsstöð VATN-V1 15.8 15.9

VATN-V2 15.8 15.9 -10

Chapter 5

Verification of transient model

In this chapter the model used in this thesis is verified. First, the line parametersof the cable model will be compared to the line parameters of the cable given in thedatasheet. Secondly, Landsnet’s PSS R©E model of the system is used to verify thegrid model in PSCAD.

5.1 Verification of cable model

To verify the cable model we use the same cable model as was described in section3.2. However, the location of the phases were changed, with burial depth 1.2 mand 0.2 m between each phase. Table 5.1 shows the line parameters given by thedatasheet and the corresponding line parameters of the cable modelled in PSCAD.

Table 5.1: Comparison of cable parameters

Datasheet PSCAD

Resistance 0.0193 Ω/km 0.0182 Ω/km

Capacitanceper core

0.270 µF/km 0.270 µF/km

Inductance 0.50 mH/km 0.49 mH/km

There is no error in the capacitance of the cable. The inductance of the modeledcable in PSCAD is 2.4% lower than specified in the datasheet. The resistance in thecable is 5.7% lower than the specified value in the datasheet. This is deemed to bewithin the margin of error since the datasheet states the approximated inductancevalue and maximum resistance value for 90 C.

33

34 CHAPTER 5. VERIFICATION OF TRANSIENT MODEL

5.2 Verification of the grid model

For verification of the model it is necessary to compare steady state voltages as wellas three phase short circuit current (SCC) at different busses in the system [23].Here, four busses in PSCAD will be compared to the PSS R©E model of the systemprovided and verified by Landsnet. Table 5.2 shows the comparison of the steadystate voltages between PSCAD and PSS R©E. The voltage magnitude and the phaseangle is 0.003 p.u. and 0.14− 0.16 lower in PSCAD than in PSS R©E, respectively.This is deemed to be within an acceptable error margin.

Table 5.2: Comparison of the voltages in PSCAD and PSS R©E for the model withoutvoltage control

PSS R©E PSCAD

Bus Bus no. Voltage in p.u. and degrees Voltage in p.u. and degrees

Langalda 1065 1.0546 − 7.35 1.0516 − 7.50

Hrauneyjar 1030 1.0636 − 6.36 1.0606 − 6.50

Sultartangi 1050 1.0466 − 8.76 1.0436 − 8.92

Búðarháls 1060 1.0546 − 6.69 1.0516 − 6.83

When comparing the SCC between PSCAD and PSS R©E, one compares the threephase symmetrical subtransient SCC, I ′′

k , calculated with PSS R©E to the short cir-cuit current calculated with PSCAD. The SCC in PSS R©E was calculated with IEC60909 which gives a maximum and minimum value. Table 5.3 shows the compar-ison of the SCC between PSCAD and PSS R©E for the model which does not havevoltage control. For all busses the SCC calculated with PSCAD is within the rangeof maximum and minimum SCC calculated with PSS R©E.

5.2. VERIFICATION OF THE GRID MODEL 35

Table 5.3: Comparison of three phase short circuit current in PSCAD and PSS R©Efor the model without voltage control

Three phase SCC [kA]

PSS R©E PSCAD

Bus Bus no. Minimum Maximum

Langalda 1065 10.19 10.60 10.25

Hrauneyjar 1030 10.01 10.36 10.11

Sultartangi 1050 11.12 11.49 11.14

Búðarháls 1060 7.02 7.39 7.06

Chapter 6

Analysis of different countermeasures -ideal voltage source

In the transmission industry, the thought of taking risks is generally frowned uponas the industry has been known to be rather conservative, making it less likely forhandling methods to be accepted. In this chapter the inrush current and switchingovervoltages during energization are analyzed for all countermeasures that eliminatethe zero-missing phenomenon.

6.1 No countermeasure installed

Figure 6.1 shows the current waveform in the breaker during energization when thecable is connected to an ideal voltage source but no countermeasure is installed.The peak value of the inrush current is 7.04 kA.

Figure 6.1: Current waveform in the breaker during energization when no counter-measure is installed - an ideal voltage source.

37

38CHAPTER 6. ANALYSIS OF DIFFERENT COUNTERMEASURES - IDEAL

VOLTAGE SOURCE

Figure 6.2 shows the resulting switching overvoltages at the open end during en-ergization when no countermeasure is installed. The peak value of the switchingovervoltages is 374 kV (2.09 p.u.).

Figure 6.2: Switching overvoltages at the open end during energization when nocountermeasure is installed - an ideal voltage source.

6.2 Pre-insertion resistor

Figure 6.3 shows the current waveform in the breaker when the cable is energizedwith pre-insertion resistor and is connected to an ideal voltage source. The peakvalue of the inrush current is 3.50 kA. Not enough energy is absorbed before thepre-insertion resistor is bypassed, thus the zero missing phenomenon has not beeneliminated.

Figure 6.3: Current waveform in the breaker during energizaiton with pre-insertionresistor - an ideal voltage source.

6.3. SIMULTANEOUS SYNCHRONIZED SWITCHING 39

Figure 6.4 shows the resulting switching overvoltages at the open end when the cableis energized with pre-insertion resistor. The peak value of the switching overvoltagesis 207 kV (1.15 p.u.).

Figure 6.4: Switching overvoltages at the open end during energization when thecable is energized with pre-insertion resistor - an ideal voltage source.

6.3 Simultaneous synchronized switching

Figure 6.5 shows current waveform in the breaker when the cable is energized withsimultaneous synchronized switching and is connected to an ideal voltage source.The peak value of the inrush current is 7.18 kA. The zero-missing phenomenon hasbeen eliminated

Figure 6.5: Current waveform in the breaker during energization with simultaneoussynchronized switching - an ideal voltage source.

Figure 6.6 shows the resulting switching overvoltages at the north end when thecable is energized with simultaneously synchronized switching. The peak value of


VOLTAGE SOURCE

the switching overvoltages is 392 kV (2.19 p.u).

Figure 6.6: Switching overvoltages at the open end during energization with simul-taneous synchronized switcing - an ideal voltage source.

6.4 Synchronized switching where the cable is

energized before the shunt reactor

Figure 6.7 shows the current waveform in the breaker when the cable is energizedat zero voltage and the shunt reactor is energized 5 ms later at peak voltage. Thecable is connected to an ideal voltage source. The peak value of the inrush currentis 6.80 kA. The zero missing phenomenon has been eliminated.

Figure 6.7: Current waveform in the breaker with synchronized switching where thecable is energized before the shunt reactor - an ideal voltage source.

6.5. SYNCHRONIZED SWITCHING WHERE THE SHUNT REACTOR ISENERGIZED BEFORE THE CABLE 41

Figure 6.8 shows the resulting switching overvoltages at the open end during ener-gization with synchronized switching where the cable is energized before the shuntreactor. The peak value of the switching overvoltages is 376 kV (2.10 p.u.).

Figure 6.8: Switching overvoltages at the open end during energization with syn-chronized switching where the cable is energized before the shunt reactor - an idealvoltage source.

6.5 Synchronized switching where the shunt

reactor is energized before the cable

Figure 6.9 shows the current waveform in breaker CB1 (see figure 2.8) when the firstshunt reactor is energized at peak voltage and the first cable segment is energized5 ms later at zero voltage. This chain continues until all shunt reactors and cablesegments have been energized.1 In total the energization takes 0.02 s. The cable isconnected to an ideal voltage source. The peak value of the inrush current is 2.91kA. The zero missing phenomenon has been eliminated.

1When there are 3 shunt reactors, the cable is divided into two 100 km long segments.


VOLTAGE SOURCE

Figure 6.9: Current waveform in the breaker with synchronized switching where theshunt reactor is energized before the cable - an ideal voltage source.

Figure 6.10 shows the resulting switching overvoltages at the north end when thecable is energized with synchronized switching where the shunt reactor is energizedbefore the cable. The peak value of the switching overvoltages is 258 kV (1.44 p.u.).

Figure 6.10: Switching overvoltages at the open end during energization with syn-chronized switching where the shunt reactor is energized before the cable - an idealvoltage source.

6.6 Summary

All countermeasures, with the exception of pre-insertion resistor, eliminated thezero-missing phenomenon, when the cable was connected to an ideal voltage sourceand the reactive power compensation ratio is 100%.

Chapter 7

Analysis of different countermeasures -voltage source at Langalda

In this chapter we analyze the resulting inrush current and switching overvoltageswhen Sprengisandslína is connected to the Icelandic grid model. The countermea-sures analyzed are those which eliminated the zero missing phenomenon in chapter6: Simultaneous synchronous switching, synchronous switching where the cable isenergized before the shunt reactor, and synchronous switching where the shunt re-actor is energized before the cable.

7.1 No countermeasure installed

Figure 7.1 shows the current waveform in the breaker during energization when thecable is connected to the Icelandic grid model with no countermeasure. The peakvalue of the inrush current is 4.60 kA. There is no zero crossing when the currentreaches equilibrium.

Figure 7.2 shows the voltage at the open end during energization when no counter-measure is installed. The peak value of the switching overvoltages is 335 kV (1.87p.u.).

43

44CHAPTER 7. ANALYSIS OF DIFFERENT COUNTERMEASURES -

VOLTAGE SOURCE AT LANGALDA

Figure 7.1: Current waveform in the breaker when no countermeasure is installedand the cable is connected to the Icelandic grid model.

Figure 7.2: Resulting voltage of the open end during energization when no counter-measure is installed.

7.2 Simultaneous synchronous switching

Figure 7.3 shows the current waveform in the breaker during energization when thecable is connected to the Icelandic grid model and the countermeasure of simulta-neous synchronous switching is installed. The peak value of the inrush current is4.02 kA. The zero missing phenomenon has been eliminated.

Figure 7.4 shows the voltage at the open end when the cable is energized withsimultaneous synchronous switching. The peak value of the switching overvoltagesis 371 kV (2.07 p.u.).

7.3. SYNCHRONOUS SWITCHING WHERE THE CABLE IS ENERGIZEDBEFORE THE SHUNT REACTOR 45

Figure 7.3: Current waveform in the breaker when the cable is energized with si-multaneous synchronous switching and connected to the Icelandic grid model.

Figure 7.4: Resulting voltage of the open end during energization when the cable isenergized with synchronous switching.

7.3 Synchronous switching where the cable is

energized before the shunt reactor

Figure 7.5 shows the current waveform in the circuit breaker during energizationwhen the cable is energized at zero voltage and the shunt reactors are energized5 ms later at peak voltage. The peak value of the inrush current is 3.62 kA. Thezero-missing phenomenon has not been eliminated, however, the current does havea regular zero crossing in all phases 800 ms after energization.



Figure 7.5: Current waveform in the breaker when the cable is energized at zerovoltage and the shunt reactors are energized 5 ms later at peak voltage.

Figure 7.6 shows the voltage at the open end when the cable is energized at zerovoltage and the shunt reactor is energized 5 ms later at peak voltage. The peakvalue of the switching overvoltages is 312 kV (1.74 p.u.).

Figure 7.6: Resulting voltage of the open end during energization when the cableis energized at zero voltage and the shunt reactors is energized 5 ms later at peakvoltage.

7.4 Synchronous switching where the shunt

reactor is energized before the cable

Figure 7.7 shows the current waveform in breaker CB1 (see figure 2.8) when theshunt reactor is energized at peak voltage and the first cable segment is energized 5ms later at zero voltage. This chain continues until all shunt reactors and cable seg-ments have been energized. In total, the energization takes 0.02 s. The peak value

7.4. SYNCHRONOUS SWITCHING WHERE THE SHUNT REACTOR ISENERGIZED BEFORE THE CABLE 47

of the inrush current is 2.47 kA. The zero missing phenomenon has been eliminated.

Figure 7.7: Current waveform in the breaker when the shunt reactor is energized atpeak voltage and the cable is energized 5 ms later at peak voltage.

Figure 7.8 shows voltage at the open end when the shunt reactor is energized atpeak voltage and the cable is energized 5 ms later at zero voltage. The peak valueof the switching overvoltages is 266 kV (1.48 p.u.).

Figure 7.8: Resulting voltage of the open end during energization when the shuntreactor is energized at peak voltage and the cable is energized 5 ms later at zerovoltage.



7.5 Summary

The countermeasure of synchronized switching where the shunt reactor is energizedbefore the cable and the countermeasure of simultaneous synchronized switchingwere shown to eliminate the zero-missing phenomenon when the cable is connectedto the Icelandic transmission grid.

Chapter 8

Conclusions

8.1 Results

Preliminary steady-state studies showed that three shunt reactors are needed ifSprengisandslína is built as a 200 km, 220 kV, underground AC cable with 100%

reactive power compensation from shunt reactors of equal size. Additionally, thegenerators in the vicinity of the connection point, Langalda, do not become un-derexcited. Though the cable has a high production of reactive power, most of itwill be consumed by the shunt reactors which explains why the generators do notbecome underexcited (all reactive power would be consumed by the shunt reactorsif the shunt reactors would be infinitely many evenly distributed along the cable).

A transient study of energizing Sprengisandslína with three shunt reactors whichprovide 100% reactive power showed that the methods of simultaneous synchronizedswitching, synchronized switching where the cable is energized before the shunt re-actor and synchronized switching where the shunt reactor is energized before thecable, eliminated the zero missing phenomenon when the voltage source was ideal.A pre-insertion resistor did not ensure zero-crossing within the first second after en-ergization and was thus disregarded in future analyzes as a possible countermeasurefor the zero missing phenomenon.

Furthermore, the energization of Sprengisandslína was simulated as if Sprengisand-slína was connected to the Icelandic grid model. The results showed that the meth-ods of simultaneous synchronized switching and synchronized switching where theshunt reactor is energized before the cable ensured zero crossing after energizationthus eliminating the zero missing phenomenon. Synchronized switching where theshunt reactor is energized before the cable resulted in both lower switching over-

49

50 CHAPTER 8. CONCLUSIONS

voltages and inrush currents.

Higher switching overvoltages and inrush currents can lead to higher constraint inthe design criteria of electric equipment, thus higher cost. However, simultaneoussynchronized switching (which has the higher SOV and inrush current) requiresfewer circuit breakers, which leads to lower cost in CBs.Table 8.1 summarizes the results of different countermeasures when the cable isenergized with an ideal voltage source while table 8.2 summarizes the results ofdifferent countermeasures when the cable is energized at Langalda.

Table 8.1: Results of different countermeasures for ideal voltage source

Ideal voltage source

Inrush current[kA]

Switchingovervoltages [p.u.]

Zero crossing?

No countermeasure 7.04 2.09 No

Pre-insertion resistor 3.50 1.15 No

Synchronized switching:Simultaneous

7.18 2.19 Yes

Synchronized switching:Cable is energizedbefore the shuntreactor

6.80 2.10 Yes

Synchronized switching:Shunt reactor isenergized beforethe cable

2.91 1.44 Yes

8.2. FURTHER STUDIES 51

Table 8.2: Results of different countermeasures when the cable is energized at Lan-galda

Voltage source at Langalda

Inrush current[kA]

Switchingovervoltages [p.u.]

Zero crossing?

No countermeasure 1.87 4.60 No

Pre-insertion resistor N/A N/A N/A

Synchronized switching:Simultaneous

2.07 4.02 Yes

Synchronized switching:Cable is energizedbefore the shuntreactor

1.74 3.62 No

Synchronized switching:Shunt reactor isenergized beforethe cable

1.48 2.47 Yes

Thus, the preliminary results of the study indicate that Sprengisandslína can beenergized as an UGC with 100% reactive power compensation if either the counter-measure of simultaneous synchronized switching or synchronized switching wherethe shunt reactor is energized before the cable are installed.

8.2 Further studies

Long HVAC cables, such as Sprengisandslína, have low resonance frequency whichmay lead to amplification of low order harmonics. A detailed harmonic study isneeded before recommending either simultaneous synchronized switching or syn-chronized switching where the shunt reactor is energized before the cable.

As discussed in section 8.1, the countermeasure of pre-insertion resistor did noteliminate the zero missing phenomenon. The equations which were proposed in theliterature for calculating the value of the pre-insertion resistor both assume there isonly one shunt reactor which is located at the point of connection. Further studyshould be performed on how the resistor value changes when the location and/ornumber of shunt reactors changes.

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Appendix I

Solution for pre-insertion resistor value

As given in section 2.4, the value for the pre-insertion resistor value is found byequating equation 8.1 and 8.2.

W =1

2Ls(I

DCs )2 (8.1)

W =

∫ 0.01

0

RP I21dt (8.2)

The following assumptions were made

• The reactive power compensation ratio is 100%. The I1 and IDCs will be equaland both currents should be zero after 10 ms.

• I1 decreases linearly.

• The resistive element of the shunt reactor, Rs, is neglected as the Rp Rs.

By assuming that I1 is linear and I1(0.01) = 0 it is possible to rewrite equation 8.2as

W =

∫ 0.01

0

RpI21dt = Rp

∫ 0.01

0

(−I1(0)t

0.01+ I1(0)

)2

dt

= Rp

∫ 0.01

0

(I21 (0)t2

0.012− 2I21 (0)t

0.01+ I21 (0)

)dt

= RpI21 (0)

∫ 0.01

0

(t2

0.012− 2t

0.01+ 1

)dt

57

58 BIBLIOGRAPHY

= RpI21 (0)

[t3

3 ∗ 0.012− 2t2

2 ∗ 0.01+ t

]0.010

= RpI21 (0)

(0.013

3 ∗ 0.012− 0.012

0.01+ 0.01

)= RpI

21 (0)

0.01

3

(8.3)

Now it is possible equate equations 8.1 and 8.3

RpI21 (0)

0.01

3=

1

2Ls(I

DCs )2 (8.4)

By assuming I1 = IDCs it is possible to solve for Rp

Rp =3

0.02Ls (8.5)

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