earth fault distance protection (documento)

Earth Fault Distance Protection

Dissertation

Institute for Electrical Power SystemsGraz University of Technology

Supervisor:Univ.-Prof. DI Dr.techn. Lothar Fickert

Author:DI Georg Achleitner

Reviewer: Univ.-Prof. DI Dr.techn. Lothar FickertGraz University of Technology

Reviewer: Professor Matti LehtonenHelsinki University of Technology

Head of Institute: Univ.-Prof. DI Dr.techn. Lothar Fickert

A - 8010 Graz, Inffeldgasse 18-IPhone: (+43 316) 873 - 7551

Fax: (+43 316) 873 - 7553http://www.ifea.tugraz.at

http://www.tugraz.at

Graz / July - 2008

Acknowledgement

This thesis was written as part of my work as an assistant at the Institute for ElectricPower Systems at Graz University of Technology.

Many people assisted me in doing the work and writing this thesis. I especially wouldlike to thank the following persons:Prof. Lothar Fickert has been my main supervisor and mentor. He gave me the firstidea about this topic. Over the years he helped me with ideas, worldly wisdoms and asa very humanly head of the institute. Very often he just listened to me, gave me an ideaand brought me back on track of my work. He inspired me to try new approaches andalso allowed me to do this, without interrupting and correcting all the time.

Many thanks to Prof. Matti Lethonen, who accepted to review my thesis. I had thechance to meet him on a conference in Estonia and he gave me some very important andessential hints for this thesis.

Prof. Manfred Sakulin helped me with my first papers, gave me the ideas and discussedthe topics for hours. He helped me to understand earth faults better and better. Prof.Herwig Renner, who often asked me only questions, which gave me new ideas to finishthis thesis.

Clemens Obkircher was a perfect colleague and a good friend. We worked together onthe same research areas and we visited a few conferences together. Discussing with himwas all the time very creative and productive. Together we made the first steps in thearea of patents and publications.Many thanks also to Beti Trajanoski who was the quiet pole of the institute. She helpedme a lot at the institute with her intuition and also to finish the work.

Many thanks to Jasmine, our secretary. She was all the time cheerful and happy. Shehelped me a lot in the first days at the institute and afterwards she was a real goodfriend.I want to thank the staff of the institute, specially Herbert for his assistance with elec-tronics and computers, Erich for his help with everything which has to do with handcraftwork, for the office, for teachings, for experiments. Many thanks to Ulrike Mayer forcorrecting my thesis.Many thanks to all the other scientific staff who helped me during the years in my re-search as well as in lectures.

Many thanks to my friends, who helped me to free my mind after some very busy days.Special thanks to Christian, Karli, Eniko, Elisabeth, Eva, Karin, Judith and the restfrom the sauna group. Without them it would have been very boring and lonesome inGraz. Thank you.

Thanks to Paul, one of my oldest and best friends in Linz. Every time at home we metit was great fun and diversified.

I also say thanks to my family for supporting me over the years and who gave me theopportunity to study and who encouraged me to go abroad to get to know also othercountries and people. They also gave me the necessary peace and help to write thisthesis during several weekends.

ii

Abstract

Earth fault compensated networks improve power reliability, due to the reason that mostof the earth faults extinguish without interferences to the grid operation, thus allowinguninterrupted power supply during the fault situation. However, this type of neutraltreatment implicates problems in the localization of earth faults. Finding the fault pointis from high interest also in combination with network expansion. Up to now, distanceprotection relays measuring the distance between the point of their installation and faultlocation are available only for direct grounded networks.In this thesis it is shown that the classic algorithm of the distance protection relaysprincipally can be used also for compensated networks, however, the accuracy of thedistance calculation strongly depends on the network conditions. The main influenceparameters are described and investigated.A new improved algorithm was developed and is shown in this thesis. To improve theclassic algorithm the fault transition impedance, the fault current and the groundingimpedance of the measurement station are included. For this purpose an exact 3-phasemathematical simulation model of the investigated network is used and provided herein.The simulations show, that this improved distance calculation provides good results upto earth fault transitions impedances of 1 kOhm.Furthermore, it is shown, that the classic algorithm can also be used in 2-phase networks.With the improvements the algorithm can again be used up to earth fault transitionsimpedances of 1 kOhm.At the end the simulation results are validated with real test data of high and mediumvoltage networks to verify the usability of this improved algorithm.

Keywords: Earth fault, distance protection, earth fault compensated networks, fault lo-cation, localization of earth faults, high ohmic earth faults

Kurzfassung

Geloschte Netze erhohen die Versorgungssicherheit weil ein Großteil der Erdschlusse ohneAuswirkungen auf den Netzbetrieb von selbst verloschen. Diese Art der Sternpunkts-behandlung birgt jedoch Schwierigkeiten bei der Erdschlusssuche. Die Fehlersuche istjedoch von großtem Interesse in Kombination mit Netzausbauten.Bisher wurden Distanzschutzrelais, welche die Entfernung zwischen dem Messpunkt unddem Fehlerort bestimmen nur in niederohmig oder starr geerdeten Netzen eingesetzt.In dieser Arbeit wird gezeigt, dass der klassische Distanzschutzalgorithmus prinzipiellauch fur geloschte Netze verwendet werden kann, jedoch ist die Genauigkeit der Dis-tanzberechnung stark von den Netzwerkparametern abhangig. In dieser Arbeit werdendie wichtigsten Einflussparameter beschrieben und untersucht.Eine Erweiterung des klassischen Algorithmus wird vorgestellt. Diese Erweiterung bein-haltet die Fehlerimpedanz, den Fehlerstrom und den Ubergangswiderstand der Messsta-tion. Fur die Simulation wurde ein exaktes dreiphasiges Modell des untersuchten Netzesaufgestellt.Die Simulationen zeigen, dass es moglich ist, die Fehlerdistanz bis zu Fehlerwiderstandenvon 1 kOhm zu ermitteln.Weiters wird die Anwendbarkeit des klassischen Algorithmus in zweiphasen Netzengezeigt. Mit den oben angefuhrten Erweiterungen konnen ebenfalls Fehlerentfernungenbei Fehlerwiderstanden bis zu 1 kOhm ermitteln werden.Am Ende dieser Arbeit werden die Simulationen durch Erdschlussversuche in Hoch- undMittelspannungsnetzen verifiziert und die Anwendbarkeit des erweiterten Algorithmusgezeigt.

Keywords: Erdschluss, Distanzschutz, geloschtes Netz, Fehlerlokalisierung, hochohmigeErdschlusse

Contents

List of Abbreviations xi

1 Introduction 11.1 Research Theses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Research Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 General 52.1 General Network Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1.1 Isolated Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1.2 Earth Fault Compensated Network . . . . . . . . . . . . . . . . . 72.1.3 Low Impedance Grounded Networks . . . . . . . . . . . . . . . . 92.1.4 Transient Middle Ohmic Compensated Network . . . . . . . . . . 11

2.2 Characteristic Parameters for Earth Faults . . . . . . . . . . . . . . . . . 152.2.1 Displacement Voltage . . . . . . . . . . . . . . . . . . . . . . . . . 152.2.2 Zero Sequence Current . . . . . . . . . . . . . . . . . . . . . . . . 152.2.3 Zero Sequence Admittance . . . . . . . . . . . . . . . . . . . . . . 162.2.4 Higher Harmonic for Detecting the faulty Line . . . . . . . . . . . 162.2.5 Transients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.3 Earth Fault Transition Impedances . . . . . . . . . . . . . . . . . . . . . 162.4 High ohmic earth faults . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3 Earth Fault Location Methods 193.1 Location Methods Based on Low Frequency Signals . . . . . . . . . . . . 19

3.1.1 Distance Calculation Based on Fundamental Frequency . . . . . . 193.1.2 Distance Calculation Using a Delta Calculation . . . . . . . . . . 203.1.3 Distance Calculation Using an ”Improved Distance Calculation”’ . 203.1.4 Distance Calculation Using Inter-Harmonic Frequency Signals . . 213.1.5 Distance Calculation in Isolated Networks . . . . . . . . . . . . . 213.1.6 Distance Calculation by Determining the Network Parameters . . 21

3.2 Location Methods Based on Transient Signals . . . . . . . . . . . . . . . 223.2.1 Differential Equation Method . . . . . . . . . . . . . . . . . . . . 223.2.2 Wavelet Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.3 Transition Fault Impedance Estimation . . . . . . . . . . . . . . . . . . . 243.3.1 Transition Fault Impedance Estimation Based on a Delta Method 243.3.2 Transition Fault Impedance Estimation . . . . . . . . . . . . . . . 24

4 Simulation of Earth Faults 25

Contents

4.1 Three Phase Symmetrical Networks . . . . . . . . . . . . . . . . . . . . . 254.1.1 Earth fault - Symmetrical Components . . . . . . . . . . . . . . . 254.1.2 Different Simulation Models . . . . . . . . . . . . . . . . . . . . . 264.1.3 Used Simulation Environment of the Earth Fault . . . . . . . . . 264.1.4 Reference Model 1 . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.2 Two Phase Symmetrical Networks . . . . . . . . . . . . . . . . . . . . . . 304.2.1 Earth Fault - Symmetrical Components . . . . . . . . . . . . . . . 304.2.2 Different Simulation Models . . . . . . . . . . . . . . . . . . . . . 314.2.3 Used Simulation Environment of the Earth Fault . . . . . . . . . 324.2.4 Reference Model 2 . . . . . . . . . . . . . . . . . . . . . . . . . . 33

5 Basis of Earth Fault Distance Protection 35

6 Classic Algorithm in Classic Distance Protection Relays 376.1 Laboratory Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406.2 Simulations Based on Laboratory Network Model . . . . . . . . . . . . . 41

7 Improved Distance Protection 437.1 Increasing the Accuracy of the Algorithm . . . . . . . . . . . . . . . . . . 43

7.1.1 Estimation of the Fault Impedance . . . . . . . . . . . . . . . . . 437.1.2 Estimation of the Fault Current . . . . . . . . . . . . . . . . . . . 467.1.3 Neutral Point Current of the Transformer and Grounding Impedance 47

7.2 Improved Earth Fault Distance Algorithm . . . . . . . . . . . . . . . . . 487.3 Distributed Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

7.3.1 Simulation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 497.3.2 Comparison of Networks with Other Neutral Point Treatment . . 497.3.3 Correction of the Influence of Distributed Loads . . . . . . . . . . 50

8 Comparison of the Classic and Improved Algorithm 558.1 Sensitivity Analysis of the Algorithm . . . . . . . . . . . . . . . . . . . . 55

8.1.1 Linearization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 558.1.2 Measurement Influences . . . . . . . . . . . . . . . . . . . . . . . 568.1.3 Influences of Wrong Settings . . . . . . . . . . . . . . . . . . . . . 578.1.4 Influences of Parameters of the Electrical Grid . . . . . . . . . . . 598.1.5 Comparison of Networks with Other Neutral Point Treatment . . 64

8.2 Fault Distance Variation . . . . . . . . . . . . . . . . . . . . . . . . . . . 678.3 Compensated Cable Networks . . . . . . . . . . . . . . . . . . . . . . . . 68

8.3.1 Increasing of the Installed Cable Proportion in a Network . . . . . 698.4 Solidly Grounded Networks . . . . . . . . . . . . . . . . . . . . . . . . . 70

9 Earth Fault Distance Protection in a Two-Phase Network 739.1 Considerations on Earth Fault Distance Calculation . . . . . . . . . . . . 739.2 Laboratory Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 759.3 Testing of Two-Phase Distance Protection Relays . . . . . . . . . . . . . 75

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Contents

9.4 Improved Algorithm for Two-Phase Networks . . . . . . . . . . . . . . . 779.4.1 Derivation of the Improved Algorithm . . . . . . . . . . . . . . . 77

9.5 Comparison of the Classic and Improved Algorithm . . . . . . . . . . . . 789.5.1 Sensitivity Analysis of the Algorithm . . . . . . . . . . . . . . . . 789.5.2 Fault Distance Variation . . . . . . . . . . . . . . . . . . . . . . . 84

10 Earth Fault Field Tests 8710.1 Tests in a 110-kV-Network . . . . . . . . . . . . . . . . . . . . . . . . . . 8710.2 Tests in a 20-kV-Network . . . . . . . . . . . . . . . . . . . . . . . . . . 89

10.2.1 Water Resistor for Test Purpose . . . . . . . . . . . . . . . . . . . 8910.2.2 Earth Fault Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . 9010.2.3 Test Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9410.2.4 Discussion of the Results . . . . . . . . . . . . . . . . . . . . . . . 94

10.3 Tests in a Two-Phase 110-kV-Network . . . . . . . . . . . . . . . . . . . 95

11 Analyses of Earth Fault Tests with the Improved Algorithm 9711.1 Earth Fault Test in a 30-kV Network . . . . . . . . . . . . . . . . . . . . 9711.2 Earth Fault Test in a 20-kV Network . . . . . . . . . . . . . . . . . . . . 9911.3 Earth Fault Tests in a 10-kV-Network . . . . . . . . . . . . . . . . . . . . 9911.4 Earth Fault Tests in a Low Impedance Grounded Network . . . . . . . . 10011.5 Discussion of the Earth Fault Tests . . . . . . . . . . . . . . . . . . . . . 101

12 Conclusion 103

Bibliography 107

A Simulation Environment 115

B Simulation Environment Two-Phase Network 121

C Comparison of the Classic and Improved Algorithm 127C.1 Simulation of Different Percentages of Cable/Overhead Lines . . . . . . . 127

C.1.1 Overhead Line Network . . . . . . . . . . . . . . . . . . . . . . . 127C.1.2 Cable Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128C.1.3 Mixed Network, Cable at Beginning of the Feeder . . . . . . . . . 129C.1.4 Mixed Network, Cable at the End of the Feeder . . . . . . . . . . 130

C.2 Simulation of a Network with Distributed Loads . . . . . . . . . . . . . . 132C.2.1 Compensated Network . . . . . . . . . . . . . . . . . . . . . . . . 132C.2.2 Solidly Grounded Network . . . . . . . . . . . . . . . . . . . . . . 133C.2.3 Middle Ohmic Grounded Network . . . . . . . . . . . . . . . . . . 134

ix

List of Abbreviations

µ . . . . . . . . . . . . . . . . . . . permeability constantω . . . . . . . . . . . . . . . . . . . angular frequencyI0ZE . . . . . . . . . . . . . . . . . zero current over the grounding impedanceI1P , I

2P , I

0P . . . . . . . . . . . positive, negative and zero sequence current at the measuring

pointIΣ . . . . . . . . . . . . . . . . . . residual current at the measuring pointIc1,c2,c3,c4 . . . . . . . . . . . . distributed line capacitive currentsIcap1,cap2,cap3,cap4,cap5 . capacitive current from feeder 1, 2, 3, 4, 5I ih . . . . . . . . . . . . . . . . . . current of the inter-harmonic signalIL1, IL2 . . . . . . . . . . . . . current in phase L1, L2ILoad . . . . . . . . . . . . . . . . load currentI1load, I

2load, I

0load . . . . . positive, negative and zero sequence load current

ITR . . . . . . . . . . . . . . . . . neutral point current of the transformerk0 . . . . . . . . . . . . . . . . . . earth return path factork0 2phase . . . . . . . . . . . . . earth return path factor for a two-phase network

U0measreal . . . . . . . . . . . . real measured displacement voltage

U1, U2, U0 . . . . . . . . . . positive, negative and zero sequence voltage at the measuringpoint

U0 . . . . . . . . . . . . . . . . . . displacement voltageU1F , U

2F , U

0F . . . . . . . . . positive, negative and zero sequence voltage at the fault point

U ih . . . . . . . . . . . . . . . . . voltage of the inter-harmonic signalUL1E, UL2E . . . . . . . . . line-to-earth voltage of phase L1, L2Unet . . . . . . . . . . . . . . . . network source voltageUNE . . . . . . . . . . . . . . . . displacement voltageU0ZE . . . . . . . . . . . . . . . . grounding impedance voltage

Z0sys . . . . . . . . . . . . . . . impedance of the zero sequence systemz1′ , z2′ , z0′ . . . . . . . . . . specific positive, negative and zero sequence impedance per kmZ1sys . . . . . . . . . . . . . . . impedance of the positive sequence systemZF . . . . . . . . . . . . . . . . . fault impedanceZL . . . . . . . . . . . . . . . . . line impedanceZ12 . . . . . . . . . . . . . . . . . coupling ImpedanceZadd . . . . . . . . . . . . . . . . additional impedanceZEarth . . . . . . . . . . . . . . alternate earth impedanceZE . . . . . . . . . . . . . . . . . grounding impedance of the measuring stationZFloop . . . . . . . . . . . . . . impedance of the failure loop

Z1line, Z

2line, Z

0line . . . . positive, negative and zero sequence line impedance

Contents

Z1TR, Z

2TR, Z

0TR . . . . . . positive, negative and zero sequence transformer impedance

Zxx . . . . . . . . . . . . . . . . . impedances of the networkAx, Bx, Cx, Dx . . . . . . loads in % of the total line loadAR . . . . . . . . . . . . . . . . . automatic reclosureCE . . . . . . . . . . . . . . . . . line-to-earth capacitancesC1line, C

2line, C

0line . . . . . positive, negative and zero sequence capacitance of the feeder

currentC1net, C

2net, C

0net . . . . . . positive, negative and zero sequence capacitance of the residual

networkcoeffxy . . . . . . . . . . . . . correction coefficients y at busbar xcoeffx . . . . . . . . . . . . . . correction coefficient at busbar xdistx . . . . . . . . . . . . . . . . aberration in % of the nominal distanceE . . . . . . . . . . . . . . . . . . . earthf . . . . . . . . . . . . . . . . . . . frequencyGIS . . . . . . . . . . . . . . . . global information systemsH . . . . . . . . . . . . . . . . . . magnetic field densityI . . . . . . . . . . . . . . . . . . . currenti(t) . . . . . . . . . . . . . . . . . current of the transientik . . . . . . . . . . . . . . . . . . . current sampleIw . . . . . . . . . . . . . . . . . . wavelet coefficient for currentIarc . . . . . . . . . . . . . . . . . arc current in AmpereICE . . . . . . . . . . . . . . . . . capacitive earth fault currentKX . . . . . . . . . . . . . . . . . smelting constantL . . . . . . . . . . . . . . . . . . . inductancel . . . . . . . . . . . . . . . . . . . . fault distancelarc . . . . . . . . . . . . . . . . . length in meter of the arclcalculated . . . . . . . . . . . . distance calculated by using the improved algorithmN . . . . . . . . . . . . . . . . . . neutral pointRf . . . . . . . . . . . . . . . . . . resistance of the ground return circuitRarc . . . . . . . . . . . . . . . . arc resistanceRStp . . . . . . . . . . . . . . . . grounding impedance of the neutral pointS . . . . . . . . . . . . . . . . . . . transformation matrixT . . . . . . . . . . . . . . . . . . . inverse transformation matrixt . . . . . . . . . . . . . . . . . . . . timeUw . . . . . . . . . . . . . . . . . . wavelet coefficient for voltageUL1Enominal . . . . . . . . . nominal line-to-earth voltageV . . . . . . . . . . . . . . . . . . . integration volumev(t) . . . . . . . . . . . . . . . . . voltage of the transientvk . . . . . . . . . . . . . . . . . . voltage sampleXT . . . . . . . . . . . . . . . . . reactance of a transformerXarc . . . . . . . . . . . . . . . . arc reactanceXcoil . . . . . . . . . . . . . . . . inductance of an arc suppressing coilXkON . . . . . . . . . . . . . . . real arc furnace oven short circuit reactance including the whole

network

xii

Contents

ZS . . . . . . . . . . . . . . . . . . symmetrical impedance matrixL1′ , L2′ , L0′ . . . . . . . . . specific positive, negative and zero sequence inductance per kmx1′ , x2′ , x0′ . . . . . . . . . specific positive, negative and zero sequence reactance per km

xiii

1 Introduction

Earth fault compensated networks are a commonly used technology for operating mediumand high voltage grids. This kind of network has the advantage that earth fault currentsare quite small and influence (ohmic, inductive) problems can be minimised and danger,especially for humans, can be reduced. Earth faults cause problems in networks withoverhead lines, such as faults like a broken line, trees falling into the line, because thefaults are sometimes difficult to locate. Due to the reason that the network mentionedabove can be operated during an earth fault without any interruption for customers,the fault point has to be cleared as soon as possible. Therefore earth fault detectionmethods are necessary and are being developed.In this thesis earth faults are single line-to-earth faults. No cross country faults or doubleline faults with ground contact are investigated.

In chapter 2 of the thesis in hand, general facts due to line-to-earth faults will be de-scribed and possible detection methods will be discussed.

In chapter 3 different earth fault localization methods will be presented. They arebased firstly on fundamental frequency and secondly on transients. Different existingmethods will be described.Furthermore different algorithms for calculating the fault transition impedance will beexplained.

In chapter 4 the necessary basis for the simulation will be described and the simula-tion model will be presented.

In chapter 5 the basis of the earth fault distance protection, based on the simulationmodel presented in chapter 4 will be explained and the algorithm for distance protectionis derived.

In chapter 6 the classic distance protection algorithm is derived and it will be shown thatthis algorithm can also be used in compensated networks. Simulations and laboratorytests, which have been done in the first stage of the investigations, will be presented anddescribed.

In chapter 7 a new improved distance protection algorithm which will be based onthe classic distance protection algorithm (see chapter 5), will be presented and it will beshown that an estimation of the fault current at the fault point and the fault impedanceis possible and with the use of these both the accuracy of the distance protection can be

1 Introduction

increased.

Furthermore load distribution along a line will be simulated and the results of the im-proved distance protection algorithm will be presented. From that a method for correct-ing the aberrations will be derived.

In chapter 8 a sensitivity analysis and an investigation on influencing parameters will bedemonstrated. Different parameters such as the grounding impedance at the measuringpoint, the fault transition impedance, the load factor, which are influencing the algo-rithm will be investigated and the results will be presented and the classic and improvedalgorithm will be compared to each other.

In chapter 9 the distance protection in a two-phase network will be presented. It willbe shown that the classic and the improved algorithm (see chapter 5, 7, 8) can be usedin this kind of network. Additionally a sensitivity analysis will be done as presented inchapter 8.

In chapter 10 the result of various earth fault tests will be presented. These tests havebeen carried out in a compensated 110-kV-network, in several compensated mediumvoltage networks (20-/30-kV-networks) and in a low ohmic grounded network.

In chapter 11 the results from applying the improved distance protection algorithmwill be presented. The results show that the algorithm gives very accurate and goodresults even in the case of high ohmic earth faults and show the usability of the presentedapproach.

1.1 Research Theses

Table 1.1: Research theses

Theorem 1 It is possible to use a classic distance protection relay for earth faultdistance protection in compensated networks.

Theorem 2 It is possible to estimate the fault impedance at the fault point.Theorem 3 It is possible to estimate the fault current at the fault point.Theorem 4 It is possible to reduce the influence of the grounding impedance at

the measuring stationTheorem 5 With Theorem 1 to 4 it is possible to get very high accurate results

even at high ohmic earth faults.

2

1.2 Research Questions

1.2 Research Questions

Table 1.2: Research questions

Question Chapter TitleIs it possible to calculate the fault impedancewith classic distance protection relays?

5 Basis of Earth Fault DistanceProtection

What are the influences on a classic distanceprotection relay?

8.1 Sensitivity Analysis of the Algo-rithm

Can the fault transition impedance be deter-mined?

7.1.1 Estimation of the FaultImpedance

Can the fault current be determined? 7.1.2 Estimation of the Fault CurrentCan the influence of the groundingimpedance of the measuring station beminimized?

7.2 Improved Earth Fault DistanceAlgorithm

Can the accuracy of the algorithm presentedin chapter 5 be increased?

7.2 Improved Earth Fault DistanceAlgorithm

What are the influences of loads along a line? 7.3 Distributed LoadsCan the accuracy still be high even if thereare loads along the line?

7.3.3 Correction of the Influence of Dis-tributed Loads

Can the algorithm also be used in a two-phase network (railway)?

9 Earth Fault Distance Protectionin a Two-Phase Network

3

2 General

In this chapter different network types with their advantages and disadvantages will bedescribed. Furthermore the basic earth fault detection methods and detection possibili-ties will be explained.At the end of the chapter a short essay about the influence of the fault impedance andthe neutral point treatment regarding earth fault with higher fault transition impedanceswill be added.

2.1 General Network Types

This section is based on [FAOT07] [Obk04].

2.1.1 Isolated Networks

Figure 2.1: Principle scheme of an isolated network

ZL line impedanceXT reactance of a transformerN neutral pointUNE displacement voltageCE line-to-earth capacitancesE earth

In figure 2.1 the principle scheme of an isolated network is presented. The neutral pointof the transformer is isolated from the earth. In an ideal network without asymmetry,

2 General

the neutral point does not have any voltage against earth (neutral point displacementvoltage). Isolated networks are used in medium voltage networks of small expansion,since a larger expansion of the networks causes higher capacitive fault currents. Thelimit is not determined by the length of the lines, but by their current contribution tothe residual (uncompensated) ground fault current. Overhead lines have ten times lowerearth fault currents than cables.In isolated networks the residual earth fault current depends on the phase-to-groundcapacities of the network. This means that networks with larger system lengths andthe use of cables instead of overhead lines lead to larger ground fault currents. Duringa continuous earth fault the voltage of the fault-free conductors increases by

√3. In

overhead line networks self extinction of the arc can be expected, if the capacitive earthfault current ICE is small([OVE76]).

Usage:

• In medium voltage overhead line networks with small expansion• In small cable systems (e.g. networks for own needs, self supply power

plants, industrial networks)

Advantages:

• Simple realization• Self-extinguishing of the lightning arc• Simple ground fault detection in the sin-phi-procedure in the zero se-

quence system is possible, if it can be guaranteed that sufficient zerosequence current for the current measurement of the protection device isavailable.

Disadvantages:

• Inclination to intermittent ground faults• Increased overvoltage danger, in particular in the context of intermittent

ground faults• Continuous ground faults and thus danger of double earth faults• Fast reaching of the expansion limit given by too high earth fault currents

Economic remarks:

• When exceeding the self extinguishing limits of the residual current thenetwork must be examined with regard to double earth faults and touchvoltages, and measures (network separation, rearrangement of the neutralpoint treatment,...) will become necessary.

6


2.1.2 Earth Fault Compensated Network

Figure 2.2: Principle scheme of an earth fault compensated network

ZL line impedanceXT reactance of a transformerN neutral pointUNE displacement voltageCE line-to-earth capacitancesE earthXcoil inductance of an arc suppressing coil

In 1916 Waldemar Petersen [Pet16] [Pet18] had the idea to connect a coil between thetransformer neutral point and the grounding system, to add an inductive component tocapacitive earth fault currents in case of a single line-to-earth fault.In compensated networks one or more transformer neutral points or earthing transform-ers are grounded via one of those earth fault compensation coils, which inductivity isadjustable. If the coil is perfectly adjusted to the line-to-earth capacitances of the net-work, the rest of the compensated current appears at the earth fault point (residualcurrent as ohmic, harmonics and detuning currents) [Obk04]. The fundamental har-monic earth fault current depends mainly on the size of the network, however a totalcompensation by passive components is not possible because of the ohmic component.The earth fault compensation reduces the fault current at the fault point to such adegree that an electric arc extinguishes by itself even if the network is large. Becauseof the slower recovering voltage of the faulty phase after the clearance of the fault inthe compensated network in contrast to an isolated network, the limit value of selfextinguishing current is set higher than in isolated networks [OVE76].The earth fault compensated network can be operated for a longer time adherent to thetechnical conditions with an existing ground fault. With a continuous ground fault thevoltage in the fault-free conductors increase by a factor of

√3.

The main advantage of a thus constituted neutral point treatment is the increased powersupply security, since ground faults do not lead directly to a disconnection of the faulty

7

2 General

sections, and over 95% (according to the statistical data of the network carriers) of theground faults extinguish automatically, whereas the remaining 5% are persisting groundfaults. In the consequence these continuous ground faults can lead to double groundfaults or short-circuits, because the increase of the line-to-earth voltages in the fault-freephases are a stress to the high-voltage equipment.

Usage:

• In medium and high-voltage transmission networks of larger expansion

Advantages (selection):

• During single phase faults the network can be temporarily further oper-ated (no necessity of forced interruption of customers power supply)• Over 95 % of all ground faults they extinguish automatically (according

to the statistical data of the network operators [VDE91][VDE99])• Ground fault residual currents are small compared to rated currents• The recurring voltage rises substantially slower than in isolated networks

Disadvantages:

• Increased insulation demand of the fault-free phases• Limitation of the network expansion by the residual ground fault current• Continuous ground faults and thus the danger of double earth faults• High demand concerning protection devices• Necessary insulation has to withstand up to phase voltage time a factor

of√

3

Protection and operation:

• Difficult selective ground fault localization• Continuous ground faults and thus the danger of double earth faults• Appropriate instrumentation is necessary

8


Economic remarks:

• Additional effort by installation and regulation of the arc suppressioncoils• Limitation of the network expansion by the ground fault residual current• Concerned transformer neutral points must be appropriate• When exceeding the self extinguishing limits of the residual current the

network must be examined with regard to double earth faults and touchvoltages, and measures (network separation, rearrangement of the neutralpoint treatment,...) will become necessary.

2.1.3 Low Impedance Grounded Networks

Figure 2.3: Principle scheme of a low impedance network

ZL line impedanceXT reactance of a transformerN neutral pointUNE displacement voltageCE line-to-earth capacitancesE earthRStp grounding impedance of the neutral point

A low impedance grounded network is a network in which the neutral point of one oremore transformers, neutral point builder or generators are grounded over current limitersor low impedances.With this kind of neutral point treatment the earth fault currents are limited essentiallythrough resistances. Thus the touch voltage and influences become smaller than duringsolidly grounding. Voltage drops with magnitudes as with the solid grounding (see below)cannot be observed. With low impedance grounding the earth fault currents are limited

9

2 General

to the range of 50 - 1000 A, and they can be switched off on the basis of a relativelysimple overcurrent time protection relay on zero sequence current bases [Pol88]. Voltagedrops, as they appear in solidly grounded networks will not be observed.A special kind of low impedance grounded networks is the solidly grounded network. Inthis case the neutral point of the transformer is solidly grounded. During an earth fault,the voltages in the fault-free phases do not increase, on the contrary, for customers thistype of neutral point treatment leads to a voltage dip. Furthermore the fault currentsare rising to several kA, depending on the network. These currents can be detected byprotection devices and ´thus the line will be switched off. With an automatic reclosurethe line can be reconnected after the clearance of the fault.

Usage:

• High-voltage transmission systems of larger expansion when the allowedmaximum residual earth fault currents are already exceeded.• Networks with predominant cables

Advantages:

• Simple construction• In low impedance grounded networks smaller earth fault currents than

with solidly grounding• Almost no net expansion limit; if there occur adjusting difficulties things

can be put right with coordinated overcurrent zero sequence protectionrelays• Slighter, but no significant voltage dips for the customers than with

solidly grounding• Transients in connection with a ground fault situation are damped• Touch voltages and influences are clearly smaller than with solidly

grounding, however they must be controlled.• Simple protection schemes

Disadvantages:

• No self extinguishing, therefore automatic reclosure (AR )• Brief current flow in a necessary magnitude over earth (influence)• Higher fault currents at the earth fault point than in earth fault compen-

sated networks and thus problems with the keeping of permissible touchvoltages, if the faulty line is not switched off fast enough.• Capacitive current contribution of long lines (cables), may require direc-

tional overcurrent zero sequence protection

10



• Simple selective ground fault detection by phase overcurrent relays orovercurrent indicators, if the fault current reaches a minimum level oftwo times the load current.• Through a defined ”earth fault current” earth fault detection is possible.• With correct adjusting of zero sequence overcurrent relays these relays are

triggered off and their information can be used for ground fault detectionor even if necessary for disconnecting of the faulty line.• If grading is necessary because of selectivity and line operation, then it is

to be considered that a first and a second grading stage may be possible.Grading with more stages can not be realized if keeping short switch offtimes is necessary.• Appropriate network control technology is necessary.

Economic remarks:

• Resistor or reactance is necessary• Necessary improvement of a large number of local grounding systems• Transformer neutral points must be able to carry the expected currents

2.1.4 Transient Middle Ohmic Compensated Network

Figure 2.4: Principle scheme of a middle ohmic grounded network

ZL line impedanceXT reactance of a transformerN neutral pointUNE displacement voltageCE line-to-earth capacitances

11

2 General

E earthXcoil inductance of an arc suppressing coilZadd additional impedance

Figure 2.4 shows the combination of earth fault compensated networks and middle ohmicgrounding. One has both the advantages of the earth fault extinction (the capacitivecurrents are compensated by the arc suppressing currents) and the advantage of animproved ground fault detection by an additionally (passive), short time injected earthfault current [FAO07][Neu04]. The additional current is in the same level as the loadcurrents and does not reachThis network will in the following only be called ”‘middle ohmic network”, instead of”Transient middle ohmic compensated network”.It must always be proven that the touch voltages are kept.If the residual currents are high then the maximum allowed touch voltages ([CEN99])can not be guaranteed. Therefor a permanent additional resistor in parallel to the arcsuppression coil is necessary. The advantages of this system are again smaller earthcurrents than with solidly or low impedance grounding and possible selective earth faultdetection. Due to possible short switch off times the allowed touch voltages can beguaranteed.

Advantages:

• In the transitional phase earth faults usually extinguish themselves.• Fault currents in the network are in the range of load currents.• When injecting an ”earth fault current” an improved ground fault detec-

tion is possible.• Touch voltages and influences are smaller than with low impedance neu-

tral point treatment.• With appropriate adjustments, zero sequence over current relays can be

used for ground fault detection (section or branch detection).• With the use of appropriate distance protection relays a fault location is

possible.• Transients at the beginning of earth faults are damped.

Disadvantages:

• An additional resistor is necessary.• Local grounding systems have to be examined and if necessary improved.• Higher earth fault currents than in earth fault compensated networks,

since additional earth fault currents will develop, which could result inpossible problems with the keeping of permissible touch voltages.

12



• With appropriate adjustments, zero sequence overcurrent relays can beused for ground fault detection (section or branch detection)• With the use of appropriate distance protection relays fault location is

possible.• Networks can be operated further.• With the injected ”earth fault current” an improved ground fault detec-

tion is possible .• It can be operated through the combination and scaling of remote pro-

tection devices and overcurrent protection improvement of the protectionof medium voltage networks.

Economic remarks:

• An additional resistor is necessary• An additional circuit breaker is necessary for transient adding to the

resistor.• Training courses for the operating personal are necessary• When exceeding the self extinguishing limits of the residual current the

network must be examined with regard to double earth faults and touchvoltages, and measures (network separation, rearrangement of the neu-tral point treatment, permanent additional resistor,...) will become nec-essary.

Technical remarks:

• It is generally assumed that the existing lightning protections andgroundings already satisfy the safety requirements.• The requirements to for common 50 Hz / lightning grounding resistance

do not deteriorate the requirements concerning lightning protection.• It is perhaps necessary due to 50 Hz considerations to reduce the 50 Hz

grounding resistance: This may improve the lightning protection.

Earth fault compensated grids are favoured by many European grid operators, becauseof their high reliability of supply. More than 90% of occurring faults in overhead linenetworks are line-to-earth faults, which have no influences on power supply in these grids.So the grid operators want to keep their hitherto existing reliability when changing theneutral point treatment. One solution could be the use of the middle ohmic groundednetwork. The idea is to be prepared for the future when the limits are exceeded throughupgrading the protective system in combination with additional resistances parallel tothe compensation coils. These resistances cause slightly higher earth fault currents whichcan be detected more easily. Then the earth faults have to be switched off within short

13

2 General

time (defined by standards and dependent on magnitude). As a result it is possible tofulfil safety standards and to avoid endangerments. To be able to clear the fault rapidlyit is necessary to establish reliable earth fault localization.

14

2.2 Characteristic Parameters for Earth Faults

2.2 Characteristic Parameters for Earth Faults

There exist different detection methods [Ebe04] 1 to detect an earth fault and to findthe faulty line.

2.2.1 Displacement Voltage

The zero sequence voltage influences the whole network, additional the displacementvoltage increases due to any unsymmetrical construction in the network. A three phasenetwork is never totally symmetrical. Therefore the line-to-earth capacitances are notequal in all three phases which leads to a natural displacement voltage. To reduce thisvoltage it is necessary to detune the of the arc suppression coil . ([OSFR08]). In somenetwork the displacement voltage is 10 or more percent of the line-to-earth voltage dueto a capacitive coupling of two neighbouring systems. If the capacitive coupling is sodominant that displacement voltage under normal operation condition already reachesa limit it makes it difficult to detect earth faults with high transition impedances.From a significant increase of the displacement voltage it can be deduced that an earthfault has occurred. The detection of this voltage can be carried out easily by using theopen broken delta winding arrangement of a voltage instrument transformer.As shown in [LH96] [Ebe04] the displacement voltage can be problematic in case of highohmic earth faults, because it decreases fast with the increase of the earth fault transitionimpedance.The displacement voltage can be used as a trigger for all other earth fault detectionalgorithms and methods. If the displacement voltage is below a certain limit it can beassumed that the network is devoid of an earth fault, or a fault has occurred which wouldbe signalised. To find the faulty line switching actions can be done in the network. Thisleads to short interruptions in the power supply.

2.2.2 Zero Sequence Current

The zero sequence current is the geometrical sum of the three phase currents to obtainthe zero sequence current. The comparison of the zero sequence current phasors indifferent substations can be used to detect a faulty line, however, it is necessary to havecommunication between the substations to compare the measured data [Fic04] [Dru95b].In the control centre, where all the data is collected, the fault path can be analyzed andthe faulty feeder can be switched off.Furthermore, if the earth fault still remains or the faulty line is not switched off, themethod of low impedance (chapter 2.1.3) or innovative impedance grounding (chapter2.1.4) can be used to detect this faulty line. The zero sequence current will be increased toreach a secure starter level for residual current overcurrent relay or even more advancedtechnologies, which can detect the fault and actions can be set.Advanced technologies are for example:

1[Ebe04]p. 13f

15

2 General

• based on the measurement of the magnetic field [nor08]

• based on optical current measurement sensors [ibm08]

• detecting the faulty phase by measuring the phase- and zero sequence currents[hor08].

2.2.3 Zero Sequence Admittance

Besides the comparison of the zero sequence phasors there are various methods to detecta faulty line by measuring the admittance of the zero sequence system [Dru95a]. Theadmittance of the network and each feeder is measured continuously and if an earth faultoccurs, the change of the admittance will be detected and the fault detection relay willsignal the faulty feeder.

2.2.4 Higher Harmonic for Detecting the faulty Line

During an earth fault, harmonics in the zero sequence current are increasing. In most ofthe cases, harmonics are dominant [OAFS06] [Obk08]. Therefore, harmonics of the zerosequence current can be used for detecting the faulty line, especially the 5th harmonicis commonly used [Gut70] [Dru02]. Such earth fault detection systems using harmonicsare already in use.

2.2.5 Transients

Fault transients of the voltage or current can be used to detect earth faults. As presentedin chapter 3, several detection algorithms, such as the differential equation method, thewavelet algorithm or an artificial neural networks methods can be used.Transients are used by transient earth-fault protection relays to detect transient or con-tinuous earth faults.

2.3 Earth Fault Transition Impedances

Earth fault transition impedances are the problematic influence on earth fault distancecomputation. There are several discussions up to which impedance an algorithm has towork correctly, however, it is important to know that a fault is existing, because evenvery high impedance earth faults can cause an arc and therefore are prone to damage(fire,...) [Elk07].The value of the earth fault transition impedance depends on the type of fault. A treewhich has fallen into a line can have impedances from 2 kΩ to 30 kΩ, whereas a brokenoverhead line touching the ground can reach values up to 200 kΩ, depending on thesurface [AJ96] [BM03]. However, it has to be said that investigations have shown thatthe majority of faults are in the range of either around 200 Ω or around 2 kΩ [HL98].Faults above 10 kΩ are rare.

16

2.4 High ohmic earth faults

From an operation point of view upon certain fault transition impedances the displace-ment voltage during an earth fault is under the starting level of the relays and the earthfault will never be recognized. By using other detection methods, higher ohmic earthfaults can be detected up to several kΩ [DB07] [Elk07].The neutral zero sequence currents diminish with higher earth fault transition impedances,therefore it is difficult to detect them, even if the transformer neutral point is solidlygrounded (see figure 2.5). Therefore solidly grounding is not the solution for all earthfault problems despite common opinion.For the simulation in figure 2.5 the simulation model in chapter 4.1.4 is used. Thenominal voltage for the simulation is 20-kV.

0 200 400 600 800 10000

100

200

300

400

500

600

700

800

transition impedance in Ohm

zero

seq

uenc

e cu

rren

t in

Am

pere

direct grounded networkmiddle ohmic grounded networkcompensated grounded network

Figure 2.5: Zero sequence current at different transition impedances

2.4 High ohmic earth faults

As shown in chapter 2.3 earth fault transition impedances can vary from few to somekΩ. The definition of high ohmic earth faults is done in different ways. In [BM03] highohmic earth faults are defined by the fault current in a solidly grounded network lowerthan 100 Ampere.Another possibility is the definition using the displacement voltage. In isolated or com-pensated networks the displacement voltage decreases with the increase the of the faultimpedance.

U0

UL1Enominal

> 0.3 (2.1)

U0 displacement voltageUL1Enominal nominal line-to-earth voltage

17

2 General

Common detection and alarm levels are set to 30% of the maximum displacement voltage.Voltage levels lower than 30% are seen as high ohmic fault.For the simulation in figure 2.6 the simulation model in chapter 4.1.4 is used. Thenominal voltage for the simulation is 20-kV.

0 100 200 300 400 500 600 700 800 9000

10

20

30

40

50

60

70

80

90

100

transitions impedance ZF in Ohm

disp

lace

men

t vol

tage

in %

of t

he n

omin

al v

olta

ge

compensated networkmiddle ohmic grounded network

Figure 2.6: Displacement voltage at different transition impedances

The following equation 2.2 describes a possible approach for high ohmic earth faults,independent of the network system.

UF

UL1Enominal

> 10% (2.2)

UF voltage of faulty phase at fault pointUL1Enominal nominal line-to-earth voltage

18

3 Earth Fault Location Methods

In this chapter different earth fault localization methods will be described. They arebased firstly on the fundamental frequency analysis and secondly on the analysis of thetransient phenomenon during an earth fault. Furthermore, different existing algorithmsfor fault impedance calculation will be presented.A classification of the earth fault methods can be done as described in [Imr06] 1:

• Fault locators using fault generated signals

– Conventional fault locators

– Transient fault locators

– Travelling wave fault locators

• Fault locators using external signal sources

In this chapter these methods will be divided into two groups:

• Fault locators based on low frequency signals

• Fault locators based on transient signals

3.1 Location Methods Based on Low Frequency Signals

In this section fault location methods based on low frequency signals will be described.

3.1.1 Distance Calculation Based on Fundamental Frequency

Earth fault distance calculation (equation (3.1)) based on fundamental frequency is usedin distance protection relays. [Sie03][ABB03][ALS02].

Z1Line =

UL1

IL1 + k0 · IΣ

(3.1)

Z1Line positive sequence line impedance, fault distance impedance

UL1 line-to-earth voltage of phase L1IL1 current in phase L1k0 earth return path factorIΣ residual current at the measuring point

1[Imr06] p. 9f


This algorithm is the classic algorithm for line-to-earth faults in low impedance groundedsystems [Tra02][Fog00]. In these networks and for fault transition impedances up toseveral 100 Ω this algorithm works well.

3.1.2 Distance Calculation Using a Delta Calculation

In [Ebe04] a method using a delta technique is described. By detuning the arc suppres-sion coil during an earth fault or adding a capacitance in parallel to the arc suppressioncoil, two measurements at different moments can be carried out. Using these differ-ent measurement points and calculating the difference, an exact earth fault distanceprotection can be achieved (delta-method) [SE03].

l =imag

(∆U1+∆U2+∆U0

∆IF

)imag

((∆I1+∆I2)

∆IF· Z1sys

)+ imag

((1 + ∆I0

2·∆IF

)· Z0sys

) (3.2)

U1, U2, U0 positive, negative and zero sequence voltage at the measuring pointI1, I2, I0 positive, negative and zero sequence current at the measuring pointZ1sys impedance of the positive sequence systemZ0sys impedance of the zero sequence systemIF fault currentl fault distance

The above algorithm can calculate the distance of earth faults up to fault transitionimpedances of 1000 Ω in networks with overhead lines, and up to 50 Ω in cable networks.The reason for this difference is that the algorithm does not consider the distributionof the capacitances. In cable networks this distribution is of importance because of thehigh capacitances in comparison to overhead lines.

3.1.3 Distance Calculation Using an ”Improved DistanceCalculation”’

In [Imr06] an adapted method for distance calculation based on the standard distancealgorithm is presented. This algorithm is more accurate than the normal distance calcu-lation as shown in chapter 3.1.1. It is important to mention that the ratio between theload and fault current has a strong influence on the accuracy of the calculated distance.The necessary load current can be estimated from prefault values.

l =imag

(UL1

IF−Rf

)imag

(13

(z0′ + z1′ + z2′) +ILoadIF

z1′) =

imag(UL1

IF

)13

(x0′ + x1′ + x2′) + imag(ILoadIF

z1′) (3.3)

UL1 line-to-earth voltage of phase L1IF fault currentRf resistance of the ground return circuit

20

3.1 Location Methods Based on Low Frequency Signals

z1′, z2′

, z0′specific positive, negative and zero sequence impedance per km

x1′, x2′

, x0′specific positive, negative and zero sequence reactance per km

ILoad load currentl fault distance

3.1.4 Distance Calculation Using Inter-Harmonic Frequency Signals

In [TP08] a method for calculating the fault distance by using a inter-harmonic signal isproposed. This method injected additional inter-harmonic signals via ancillary suppres-sion coils into the zero sequence system of the network. By measuring the inter-harmonicvoltages and the currents of the zero sequence system the fault loop impedance can becalculated.

ZFloop =U ih

I ih(3.4)

ZFloop impedance of the failure loop

U ih voltage of the inter-harmonic signalIih current of the inter-harmonic signal

If only the imaginary part of the calculated fault loop impedance, the influence of thefault impedance can be reduced. With the knowledge of the line parameters the faultdistance can be estimated. The influence of the line-to-earth capacitances is neglected.

3.1.5 Distance Calculation in Isolated Networks

In [AW07] a new algorithm for isolated networks is presented. Two assumptions arenecessary for this algorithm: On one hand the load is located behind the fault, and onthe other hand that the fault is located behind the load. So the algorithm calculatestwo fault distances By calculating a feasibility where the fault could be, based on themeasured values and including the voltage drop on the line and comparing the resultswith the precalculated values from the two cases, the fault point can be estimated.

However this method is still under investigation.

3.1.6 Distance Calculation by Determining the Network Parameters

In [LO07] a new method for earth fault distance calculation is described. This fingerprint method is based on a very detailed network model, which includes all networkparameters, such as exact line length, correct line, cable types, etc. After the occurrenceof an earth fault, the algorithm tries to recalculate the fault recordings by varying thefault in the network. If the calculated fault scenario matches the real fault, it can beassumed, that the fault point has been found. This method also works in cable networks.

21


3.2 Location Methods Based on Transient Signals

The following chapter will describe various fault detection methods based on fault tran-sients.In order to do that the fault path inductance L will be used for calculating the fault dis-tance. This inductance L is proportional to the fault distance according to the followingequation.

L =1

3(L1′ + L2′ + L0′) · l (3.5)

L1′, L2′

, L0′specific positive, negative and zero sequence inductance per km

L inductance of the fault pathl fault distance

In [Imr06] a fault location program is proposed which includes different fault locationtechniques as differential equation method, the wavelet algorithm and the extendedalgorithm for detecting the earth fault.For transient methods the transfer behaviour of the current and voltage transformershave to be considered. If the transformers can not transfer higher frequencies, transientmethods may get into trouble with calculating the correct distance.

3.2.1 Differential Equation Method

The differential equation algorithm calculates the fault distance by numerical solvingthe differential equation that describes the fault circuit2.

v(t) = RF · i+ Ldi(t)

dt(3.6)

v(t) voltage of the transienti(t) current of the transientRF fault resistanceL inductance of the fault patht time

The equation can be solved with a numerical integration and the inductance of the faultpath can be calculated if three equally spaced pairs of phase currents and voltage samplesare available3:

L =∆t

2

[(ik+1 + ik)(vk+2 + vk+1)− (ik+2 + ik+1)(vk+1 + vk)

(ik+1 + ik)(ik+2 − ik+1)− (ik+2 + ik+1)(ik+1 − ik)

](3.7)

L inductance of the fault pathik current samplevk voltage samplet time

2[Imr06] p. 143[Han01] p. 57

22

3.2 Location Methods Based on Transient Signals

3.2.2 Wavelet Algorithm

The algorithm presented in equation (3.8) uses the wavelet transformation to calculatethe fault distance. [Han01]

L =1

ωimag

[Uw(k∆t, f)

Iw(k∆t, f)

](3.8)

ω angular frequencyL inductance of the fault pathUw wavelet coefficient for voltageIw wavelet coefficient for currentl fault distancef frequency

The algorithm first determines the maximum wavelet coefficient of the current includ-ing the amplitude, frequency and location of the wavelet. Using this frequency withdifferent time translations, the equivalent fault inductances can be calculated. The 2ms inductance interval, corresponding to 10 subestimates, is then determined with thesmallest standard deviation. The mean value of the inductance, which is calculated inthis interval, is finally used to determine the fault distance.4

4[Han01] p. 59

23


3.3 Transition Fault Impedance Estimation

The transition fault impedance is the parameter which influences the rest of the net-work. Unfortunately, this impedance is an unknown factor in those networks. In thischapter two different estimation algorithms, which can be used for determining the faultimpedance will be described.

3.3.1 Transition Fault Impedance Estimation Based on a DeltaMethod

As described in [SE03][Ebe04] the fault transition impedance can be calculated as shownin equation (3.9). This method is based on the delta-method, presented in chapter 3.1.2.

RF =1

3

(real

(∆U1 + ∆U2 + ∆U0

∆IF

)− real

((∆I1 + ∆I2

)∆IF

· Z1sys

)· l

−real((

1 +∆I0

2 ·∆IF

)· Z0sys

)· l)

(3.9)

U1, U2, U0 positive, negative and zero sequence voltage at the measuring pointI1, I2, I0 positive, negative and zero sequence current at the measuring pointZ1sys impedance of the positive sequence systemZ0sys impedance of the zero sequence systemIF fault currentRF fault resistancel fault distance

For the calculation of the fault impedance it is necessary to know Z1sys and Z0sys fromthe faulty line, which can be taken from measurements. The fault distance l can becalculated by using equation (3.2).

3.3.2 Transition Fault Impedance Estimation

As stated in [HL99], the fault impedance can be calculated as presented in equation(3.10).

ZF =

(UL1

U0

− 1

)Z0sys (3.10)

ZF fault impedanceUL1 phase-to-ground voltageU0 displacement voltageZ0sys impedance of the zero sequence system

Therefore, it is necessary to know the zero impedance Z0sys which can be determined bycalculating the equivalent circuit. This algorithm can be used to detect earth faults upto 200 kΩ.

24

4 Simulation of Earth Faults

The mathematical simulation model is designed for simulating an earth fault in a radialnetwork. It is used for varying different parameters. The results are applied to differentearth fault distance algorithms, which are tested for their usability.

4.1 Three Phase Symmetrical Networks

4.1.1 Earth fault - Symmetrical Components

The symmetrical components are easy to use if the network is symmetrical [For18][And07] [OO04], because in that case the positive, negative and zero sequence systemsare independent from each other. Otherwise, if the network is not symmetrical, the ad-vantage of simplifying the matrices cannot be used and it is the same effort as calculatingdirectly with phase values.

In figure 4.1 an earth fault in symmetrical components is shown. The positive, negativeand zero sequence system have to be connected serially at the fault point [Fic06][Muc78].

Figure 4.1: Earth Fault in Symmetrical Components


4.1.2 Different Simulation Models

Different simulation models can be used for calculating single line-to-earth faults. Thesimulation environments can be divided into two groups:

• Static network matrices

• Differential equation

Programs which use the network matrices often convert the network into symmetricalcomponents. Simulation environments for symmetrical components are all load flowprograms such as NEPLAN, Integral, SIMULINK (if the settings are set in symmetricalcomponents).Other approaches are programs which use phase values, such as SIMULINK and EMTP.These programs are based on solving the differential equations of the system componentsin the time domain. These programs can be used for transient as well as for steady statesimulations.

4.1.3 Used Simulation Environment of the Earth Fault

For simulating earth faults a model based on symmetrical components is used. Thistype of simulation is chosen, because if an earth fault in a compensated network doesnot distinguish automatically, it is enough time to analyze the signal and it is alreadyin a steady state condition.

Figure 4.2: Simulation model

For the simulation of earth faults in a radial network, a detailed model (figure 4.3) basedon figure 4.2 is developed. This model is used for simulations and the algorithms in thefollowing chapters are applied to the results.The lines are modeled as a π-equivalent network. The residual network is set intothe simulation as capacitance in the positive, negative and zero system; the load is

26


simulated as impedances. The impedance of the feeding network can be included intothe transformer impedance.In figure 4.3 the simulation model is shown. ZE is the grounding impedance of themeasurement station. The reason for introducing this impedance ZE is that the line-to-earth voltages are measured to the grounding system of the measurement station.Normally influence of the grounding system is negligible. In case of an earth fault, theresidual current causes a voltage drop at this grounding impedance which may lead toinaccurate voltage measurement results (for example in mountain areas).ZF is the transition impedance at the fault location. In this impedance also the ground-ing impedance of the fault point is included, because in reality it cannot be separated[Fre07][Bre07].Zadd is the additional impedance, in parallel to the arc suppressing coil. The addi-tional current increases the line current which makes it easier to detect the fault, thetrigger level is increased and the influence of the fault current is reduced (see chapter2.1.4)[Imr06].The line is divided into three sections (line1, line2, line3) for simulation purposes.No loads were placed between the protection device and the fault in this simulationmodel. For simulations with distributed loads along the line another model presented inchapter 7.3 is used.

27


Figure 4.3 shows figure 4.2 in symmetrical components.

ZTR

2Zline1

2Zline3

2

Zload

2

U2

p

ZTR

0Zline1

0Zline3

0

U0

p3Zadd

ZTR

1Zline1

1Zline3

1

Zload

1

UP

1

3ZE

C /2line1

1C /2line1

1C /2line3

1C /2line3

1

C /2line1

2C /2line1

2C /2line3

2C /2line3

2

C /2line1

0C /2line1

0C /2line3

0C /2line3

0

IP1

I2

P

I0

P

3Zpet

Zline2

2

Zline2

0

Zline2

1

C /2line2

1C /2line2

1

C /2line2

2C /2line2

2

C /2line2

0C /2line2

0

UF

2

3ZF

UF

0

UF

1

IF0

UF

ILoad

1

I2

Load

I0

LoadI

0

TR

Unet

1

positive sequence system

negative sequence system

zero sequence system

station rest of thenetwork

fault line3 + load

Cnet

1 Znet

1

Cnet

2 Znet

2

Cnet

0

line2line1

Figure 4.3: Simulations model in symmetrical components

C1net, C

2net, C

0net positive, negative and zero sequence capacitance of the residual network

C1line, C

2line, C

0line positive, negative and zero sequence capacitance of the feeder current

Z1line, Z

2line, Z

0line positive, negative and zero sequence line impedance

Z1TR, Z

2TR, Z

0TR positive, negative and zero sequence transformer impedance

I1P , I

2P , I

0P positive, negative and zero sequence current at the measuring point

U1, U2, U0 positive, negative and zero sequence voltage at the measuring pointU1F , U

2F , U

0F positive, negative and zero sequence voltage at the fault point

I1load, I

2load, I

0load positive, negative and zero sequence load current

ITR neutral point current of the transformerIF fault currentZadd additional impedanceZpet arc suppressing coil

ZF fault impedanceZE grounding impedance of the measuring stationUnet network source voltage

The detailed description of the simulation model is described in appendix A.

28


4.1.4 Reference Model 1

In table 4.1 the values for the simulation model are presented.

Table 4.1: Simulation data

Network 20-kV / overhead linesFrequency 50 HzTransformer 15 Mvar, uk=10,8%, Z1=j0.96 Ω, Z0=j0.96 ΩLine length 20 km, ZLine1+ZLine2

Line Z1 / Z0 per km 0.306 Ω+j0.355 Ω / 1.071 Ω+j1.2425 ΩLine cap C1 / C0 per km 10 nF / 6 nFFault distance 15 km, ZLine1=10 km, ZLine2=5 kmLoad 4 MW / 100 Ω, 0 Mvararc suppression coil 5 Ω+ j 142 ΩAdditional resistance 100 ΩCapacitive current of the Network 80 ALoad of the of the Network 10 MW / 40 Ω

These values of this reference network are chosen to investigate earth faults in a typicalmedium voltage network. In middle ohmic networks earth faults are the most frequentlyfaults.The nominal voltage of typical networks is between 10 and 30 kV.Typical feeding transformers are assumed between 10 and 60 Mvar.Maximum line lengths are up to 30 km.A network with overhead lines is chosen because earth faults are problematic especiallyin these kinds of networks. The line impedances are taken from the tables [FMR+05].The additional resistance is chosen as 100 Ω. This resistance adds around 100 Ampereto the fault current during an earth fault. If the activation is kept sufficiently short,additional 100 Ampere are no problem due to the standard HD637 [CEN99] and offerthe possibility for more secure fault detection.The load is chosen with 100 Ω∠0 because the load can be assumed as ohmic.

29


4.2 Two Phase Symmetrical Networks

4.2.1 Earth Fault - Symmetrical Components

As described in chapter 4.1 the symmetrical components can be used for calculating anearth fault. The high voltage transmission grid for transaction purpose in Austria, Ger-many and Switzerland is a two-phase symmetrical network. In this case the symmetricalcomponents have to be adapted [OO04] [Bra97] [Ede56] [Wan36].

IL1

IL2

UL1E

UL2E

Z11

Z22

Z21

Z12

Figure 4.4: Two-phase network

The values in figure 4.4 can be described using the following equations:

[UL1E

UL2E

]=

[Z11 Z12

Z21 Z22

]·[IL1

IL2

](4.1)

UL1E , UL2E line-to-earth voltage of phase L1, L2IL1, IL2 current in phase L1, L2Zxx impedances of the network

The transformation matrix is:

S =1

2

[1 11 −1

]and T = S−1

[1 11 −1

](4.2)

S transformation matrixT inverse transformation matrix

[U0

U1

]=

[1 11 −1

]·[UL1E

UL2E

](4.3)

30


S transformation matrixU1, U0 positive and negative sequence system voltageUL1E , UL2E line-to-earth voltage of phase L1, L2

The derivation of the impedance matrix is shown in equation (4.4). A symmetricalnetwork is assumed (Z11 = Z22 and Z12 = Z21):

ZS = S ·ZP ·T =1

2

[1 11 −1

]·[Z11 Z12

Z21 Z22

]·[1 11 −1

]=

Z11 + Z12 00 Z11 − Z12

(4.4)

ZS symmetrical impedance matrix

Figure 4.5: Earth fault in symmetrical components

In figure 4.5 an earth fault in symmetrical components is shown. Therefore, the positiveand zero sequence system have to be connected in series at the fault point.

4.2.2 Different Simulation Models

For simulating this type of network the program µPAS [upa08] can use for load flow andshort circuit calculations. Network calculation programs for three phase networks canbe used, if all parameters of the two-phase network are recalculated.Transient programs as SIMULINK or EMTP can also be used for simulating transientphenomenon.

31


4.2.3 Used Simulation Environment of the Earth Fault

Similar to chapter 4.1.3 the simulation model is build based on the theory of symmetricalcomponents (4.2.1).For the simulation of earth faults in a radial network, a detailed model (figure 4.3) basedon figure 4.2 is developed. This model is used for simulations and the algorithms in thefollowing chapters are applied to the results.Zadd is the additional impedance, in parallel to the arc suppressing coil.Figure 4.6 shows figure 4.2 as a two-phase network in symmetrical components.

ZTR

0Zline1

0Zline3

0

U0

p2Zadd

ZTR

1Zline1

1Zline3

1

Zload

1

UP

1

2ZE

C /2line1

1C /2line1

1C /2line3

1C /2line3

1

C /2line1

0C /2line1

0C /2line3

0C /2line3

0

IP1

I0

P

2Zpet

Zline2

0

Zline2

1

C /2line2

1C /2line2

1

C /2line2

0C /2line2

0

2ZF

UF

0

UF

1

IF0

UF

ILoad

1

I0

LoadI

0

TR

Unet

1



station rest of the

network

fault line3 + load

Cnet

1 Znet

1

Cnet

0

line2line1

Figure 4.6: Simulations model in symmetrical components

C1net, C

0net positive and zero sequence capacitance of the residual network

C1line, C

0line positive and zero sequence capacitance of the feeder current

Z1line, Z

0line positive and zero sequence line impedance

Z1TR, Z

0TR positive and zero sequence transformer impedance

I1P , I

0P positive and zero sequence current at the measuring point

U1, U0 positive and zero sequence voltage at the measuring pointU1F , U

0F positive and zero sequence voltage at the fault point

I1load, I

0load positive and zero sequence load current

IF fault currentZadd additional resistorZpet arc suppressing coil

ZF fault impedanceZE grounding impedance of the measuring stationUnet network source voltage

The detailed description of the simulation model is described in appendix B.

32


4.2.4 Reference Model 2

Table 4.2: Simulation data

Network 110-kV / overhead linesFrequency 16.7 HzEquivalent network impedance Z1 / Z0 j12 Ω / j12 ΩLine length 60 km, ZLine1+ZLine2

Line Z1 / Z0 per km 0.12 Ω+j0.13 Ω / 0.16 Ω+j0.37 ΩLine cap C1 / C0 per km 2 nF / 2 nFFault distance 40 km, ZLine1=20 km, ZLine2=20 kmLoad 40 MW / 300 Ω, 0 Mvararc suppression coil 0.1 Ω+ j 109 ΩAdditional resistance 400 ΩCapacitive current of the Network 500 ALoad of the of the Network 100 MW / 121 Ω

These values of this reference network are chosen to investigate earth faults in a typicaltwo phase network.The nominal line-to-earth voltage is 55 kV.In this network 110-kV is the highest voltage level. Therefore, the equivalent networkimpedance is used instead a transformer impedance.Maximum line lengths are up to 60 km.A network with overhead lines is chosen because earth faults are problematic especiallyin these kinds of networks. The line impedances are taken from the tables [FMR+05].The additional resistance is 400 Ω. This resistance adds around 100 Ampere to the faultcurrent during an earth fault.Because of the dimensions of such networks 500 Ampere is a realistic value for thecapacitive network currents.

33

5 Basis of Earth Fault DistanceProtection

Earth fault distance protection is used distribution networks. Especially in low andsolidly grounded networks, there exist distance protection relays, which can calculatethe distance from the relay to the fault point.

In this chapter, the derivation of the fault impedance calculation algorithm will bepresented. This algorithm is a simplification because in the derivation the distributedline-to-earth capacitances have been neglected.

The algorithm will then again be simplified to the classic algorithm, which will be shownin chapter 6. Unfortunately this classic algorithm only provides good results up to faultimpedances around some 100 Ω.

Furthermore, it will be shown that the algorithm of classic distance protection devices,as they are already in use, can also be used for earth fault distance protection in com-pensated networks, however, for low impedance earth faults only.

This chapter is based on [AF07], [AOFS06a] and [AOFS06b].

In chapter 6 the classic algorithm will be derived and explained.

In chapter 7 the improvements of the classic algorithm will be presented.

These general considerations are based on the model (see figure 4.2) in chapter 4.1.3.The distributed line-to-earth capacitances are neglected and the faulty phase is assumedto be in phase L1.

At the fault point (see figure 4.3) the following equation has to be fulfilled:

U1F + U2

F + U0F = UF (5.1)

Z1Line is the sum of unZ1

Line1 and unZ1Line2, respective it is the same for the negative and

zero sequence system.

Inserting the measured voltages and the voltage drop along the line, equation (5.1) canbe written:

U1− I1P ·Z1

Line +U2− I2P ·Z2

Line +U0− I0P ·Z0

Line− 3 · I0TR ·ZE = 3 · I0

F ·ZF (5.2)

A symmetrical network (no phase preferences) is assumed, leading to:

Z1Line = Z2

Line (5.3)

5 Basis of Earth Fault Distance Protection

The measured voltages in symmetrical components can be summed up to the line voltageof the faulty phase,

UL1 = U1 +U2 +U0 = (I1P + I2

P ) ·Z1Line + I0

P ·Z0Line + 3 · I0

F ·ZF + 3 · I0TR ·ZE (5.4)

UL1 − 3 · I0F · ZF

Z1Line − 3 · I0

TR · ZE

= I1P + I2

P + I0P ·

Z0Line

Z1Line

(5.5)

With IL1 = I1P + I2

P + I0P

UL1 − 3 · I0F · ZF − 3 · I0

TR · ZE

Z1Line

= IL1 − I0 + I0 · Z0Line

Z1Line

(5.6)

UL1 − 3 · I0F · ZF − 3 · I0

TR · ZE

Z1Line

= IL1 + I0 ·(Z0Line

Z1Line

− 1

)(5.7)

with k0 = 13

(Z0Line

Z1Line− 1)

and 3 · I0 = IΣ and 3 · I0F = IF and 3 · I0

TR = ITR

UL1 − IF · ZF − ITR · ZE

Z1Line

= IL1 + IΣ · k0 (5.8)

Z1Line =

UL1 − IF · ZF − ITR · ZE

IL1 + IΣ · k0

= z1′ · l (5.9)

Z1line, Z

2line, Z

0line positive, negative and zero sequence line impedance

I1P , I

2P , I


U1, U2, U0 positive, negative and zero sequence voltage at the measuring pointU1F , U

2F , U

0F positive, negative and zero sequence voltage at the fault point

IF fault currentZF fault impedanceIΣ residual current at the measuring pointk0 earth return path factorUL1 measured line-to-earth voltage in phase L1IL1 measured current in phase L1

z1′specific positive sequence system line impedance

ZE grounding impedance of the measuring stationITR neutral point current of the transformerl fault distance

Equation (5.9) is the basis for an algorithm in a fault distance calculation of a line-to-earth fault. The influence of line-to-earth capacitances have been neglected, which leadsto partial deviations in cable networks. This algorithm also needs accurate setting of k0

because a wrong setting can lead to miscalculations (see chapter 8.1.3). In this algorithmthe fault impedance ZF and the fault current IF are included, but both are unknownand have to be calculated through separate algorithms (see chapter 7).Generally in common literature ZE = ZE are set equal zero and are neglected (seechapter 6)

36

6 Classic Algorithm in Classic DistanceProtection Relays

As has been described above, distance protection relays have the possibility to locateearth faults [Sie03], however, this system is only established in solid or low impedancegrounded networks.

This feature is blocked in classic distance protection devices for compensated networks,because the relays generally use the line current level as trigger. In low and solidlygrounded networks, the line current is high enough to get a secure trigger level. However,in compensated networks the current during an earth fault is just a little above the loadcurrent. Settings around the load current are too insecure; it is recommended to reachthe level under all operating conditions.

The reason for choosing this type of detection algorithm is that has already been built inmodern distance protection relays. With some changes in the parameters or firmware thistechnology can also used for earth fault detection in earth fault compensated networks.An improved version could be easily set up on this platform, because the measurementtechnique and logic have already been implemented.

The model for earth fault distance protection can be simplified as shown in figure 6.1[AOFS06b].

6 Classic Algorithm in Classic Distance Protection Relays

ZTR

2Zline1

2Zline2

2

Zload

2

Up

2UF

2

ZTR

0Zline1

0Zline2

0

Up

0

3Zadd

UF

0

ZTR

1Zline1

1Zline2

1

Zload

1

Up

1UF

1

IP1

I2

P

I0

P

3Zpet

Unet

1

Figure 6.1: Simulation model in symmetrical components

For this model the following assumptions are made:

• Only fundamental harmonics

One idea behind this thesis is, to use a classic distance protection relay as plat-form for the new algorithm. Fundamental harmonics are chosen because distanceprotection relays use them for their algorithm. Therefore, fundamental harmonicsare chosen, even if theoretically higher harmonics could possibly be used for thedetection algorithm.

• Steady state conditions

For these investigations permanent earth faults are interesting. If such a faultoccurs, there is enough time for search actions. After some periods the transientconditions disappear and steady state conditions can be used.

• Capacitances are neglected

An overhead line or a cable has distributed line-to-earth capacitances which areresponsible for the earth fault current. In the classic algorithm, theses capacitancesare neglected because in low ohmic or solidly grounded networks the earth faultcurrent at the fault point is similar to the sum current at the measuring point.

• Low ohmic earth faults

The classic algorithm does not consider the fault impedance. This is acceptablefor low ohmic earth faults or networks, in which higher ohmic earth faults are rare.Furthermore, the algorithm reduces the influence of the ohmic parts by using only

38

the reactive part of the calculated impedance. The fault transitions impedance isdominantly ohmic and the influence can be reduced.

• Low ohmic station grounding impedances

Stations or substations have grounding systems with impedances around 0.05 to0.5 Ω. These values can be neglected because the influence on the measured volt-ages is small.

With the assumptions above, equation (5.9) can be simplified to equation (6.1).

Z1Line =

UL1

IL1 + IΣ · k0

= z1′ · l (6.1)


UL1 line-to-earth voltage of phase L1IL1 current in phase L1k0 earth return path factorIΣ residual current at the measuring point


l fault distance

ZF is seen as predominantly ohmic [Fre07]. If only the imaginary part of the equation(6.1) is used, the ohmic influences can be reduced.

l =1

x1′imag

(UL1

IL1 + IΣ · k0

)(6.2)


x1′specific positive sequence system line inductance

l fault distance

Equation (6.1) is already used in solid or low ohmic grounded networks with low ohmicearth faults when the capacitive currents can be neglected.

With the classic algorithm the location of earth faults up to some 100 Ω can be detectedin reality. Above these limit the deviation increases and the calculation results cannotbe used for an exact distance determination. Another problem is that higher ohmicearth faults are often not detected at all, because the displacement voltage or the zerosequence current are too small to reach any detectable starting limit for the protectiondevices (see chapter 2.2).In the following sections, the results of the classic algorithm will be presented.

39

6 Classic Algorithm in Classic Distance Protection Relays

6.1 Laboratory Tests

First tests were carried out in the laboratory. Therefore an analogical three phasenetwork model was used. Low ohmic earth faults were carried out at different faultpoints. For measurements and tests, a distance protection relay was installed in thisnetwork. The laboratory setup is presented in table 6.1.

Table 6.1: Data of the laboratory tests

Power supply 110 V, 3, 50 HzTransformer 1350 VA, uk 12%, YY0Line (100%) 3+j30 Ω, equivalent to 100km @ 0,3 Ω /kmLoad 120Ω

For more tests, which should be independent from the network model, the data wasrecorded and the fault recordings were saved. Afterwards, it was possible to replay theserecordings by using an OMICRON CMC 256-6[omi08]. This signal generator can replayfiles in comtrade format [com99]. Different distance protection relays could be testedwith one and the same test file (see figure 6.2).

Comtrade file

Comtrade file

Comtrade file

Comtrade file

Comtrade file

PC CMC Protection device

Comtrade file

Comtrade file

Comtrade file

Figure 6.2: Simulation system for protection relays

Due to the reason that the network model has only two possibilities to change the linelength, two different tests could be done: One at 0.5 Ω and the other one at 30 Ω. Theresults are presented in table 6.2.

Table 6.2: Result of the laboratory tests

Distance X in Ω Result of the protection device in Ω0.5 Ω 1 Ω30 Ω 30.5 Ω

These laboratory tests have been the very first tests in autumn 2004 and have proventhe principle usability of the classic distance algorithm for earth fault location in acompensated network.

40

6.2 Simulations Based on Laboratory Network Model

6.2 Simulations Based on Laboratory Network Model

For the first simulations and tests of the distance protection relays, a three phase net-works model has been developed by using MATLAB/SIMULINK R© [mat08]. This tran-sient model is an exact simulation model of the analogue laboratory network model asused for the first tests (see chapter 6.1). The transient results of the simulation model areconverted to the comtrade format and directly replayed with the OMICRCON CMC-256as input for the distance protection relays.The results of the variation of the fault distance are presented in figure 6.3.

0

5

10

15

20

25

30

35

0 5 10 15 20 25 30 35

X varied in Ohm

calc

ulat

ed re

acta

nce

in O

hm

X

Figure 6.3: Results distance variation of the laboratory tests

In figure 6.3, it can be seen that the calculated fault impedance increases linear to theincreasing real model fault distance in the simulation. These simulations and tests withclassic distance protection show that the classic algorithm is valid for earth faults incompensated networks with low ohmic earth faults.

41

7 Improved Earth Fault DistanceProtection in CompensatedNetworks

Distance protection based on the algorithm presented in chapter 5 is accurate for lowohmic earth fault; however, the deviation gets high for high ohmic earth faults.The classic algorithm can be used in radial networks as well as in meshed networks, whichare mostly 110-kV-networks. In meshed 110-kV-networks, this algorithm can be usedbecause most of the faults are low ohmic earth faults (arc surge arresters are damagedand good grounding of the pylons). Another improvement in these networks can be doneby using a two-sided fault locator [LSW07] which eliminates the concerning effects andreduces calculation errors.In radial medium voltage networks the number of earth faults is higher, fault impedancesare higher and in view of more branching points without protection devices the topologyis more complex.In the following chapter improvements for distance protection in radial distribution sys-tems will be presented. The influence of the distributed line-to-earth capacitances hasnot been included.This chapter is based on [AF07].

7.1 Increasing the Accuracy of the Algorithm

As presented in chapter 5 the fault current IF and the fault impedance ZF have to beconsidered when calculating the fault distance. In the next chapters a new approach toderive an estimation for the fault impedance ZF and the fault current IF will be shown.

7.1.1 Estimation of the Fault Impedance

The fault transition impedance is the parameter which influences the fault scenariostrongly. The line-to-earth voltages and the fault current depend on this impedance (seechapter 2.3). Faults with high impedance can cause problems in locating the fault point.If ZE is neglected and the zero sequence current is set equal to the fault current at thefault point equation (5.4) can be written :

UL1 = U1 + U2 + U0 = (I1P + I2

P ) · Z1Line + I0

P · Z0Line + 3 · I0

P · ZF (7.1)

7 Improved Distance Protection

3ZF · I0F = UL1 − IL1 · Z1

Line − I0P · Z0

Line + I0P · Z1

Line (7.2)

Inserting Z1Line = Z11−Z12 and Z0

Line = Z11 + 2Z12 in equation (7.2) it can be written:

ZF =UL1

IΣ

− IL1

IΣ

· Z1Line − Z12 (7.3)

Z1line, Z


I1P , I

2P , I


ZF fault impedanceIΣ residual current at the measuring pointUL1 measured line-to-earth voltage in phase L1IL1 measured current in phase L1Z12 coupling Impedance

Figure 7.1 shows the common used model for the fault loop impedance. The loopimpedance is divided into three parts, one is assigned to the lines (”overhead”) (Z1

Line),the second to the fault impedance (ZF ) and the third part to the earth return path(”underground”) (ZEarth).

Figure 7.1: Estimation of the Fault Impedance

As presented in [AOF+07] ZEarth is equal to the coupling impedance Z12. Equation (7.3)can be written as:

ZF =UL1

IΣ

− IL1

IΣ

· Z1Line − ZEarth (7.4)

Z1line positive sequence line impedance

I1, I2, I0 positive, negative and zero sequence current at the measuring pointZF fault impedanceIΣ residual current at the measuring pointUL1 measured line-to-earth voltage in phase L1IL1 measured current in phase L1ZEarth alternate earth impedance

44


The fault impedance can be calculated under the above mentioned restrictions by di-viding the phase-to-earth voltage UL1E from the faulty phase at the measured residualcurrent IΣ (figure 7.1). This estimation is acceptable because the fault impedance isthe dominant part of the faulted circuit impedance. If the fault impedance has a valuein the same amount as the line impedance, there is an aberration in the calculation,because the influence of the line impedance is the same or even higher. In that casethe fault transition impedance is not dominating the faulted circuit impedance and theaberration is caused by the dominant influence of the line impedance.In addition, load currents in the same range as the fault current cause an aberration,if the line and the fault impedance are the same. Therefore, an increase of the faultcurrent by use of an additional resistance is recommended [Imr06].This estimation can be used if the calculated fault impedance is higher than 2 to 3 timesthe line impedance.Due to experiences, the fault impedance is approximated ohmic (see chapter 8.1.4)[Fre07].It is also required, that the zero sequence current source is ”behind” the measuring point(”Bauch´sches paradox”’). [HAB+93a][HAB+93b]

RF = real

(UL1

IΣ

)(7.5)

UL1 line-to-earth voltageIΣ residual current at the measuring pointRF fault resistance

45


7.1.2 Estimation of the Fault Current

As shown in figure 7.2, the fault current IF consists of the inductive current of theneutral point impedance and the capacitive currents of the faulty line and of the otherfeeders.

Figure 7.2: Fault current

The fault current IF can be estimated with the following equations:

IF = IL + Icap2 + Icap3 + Icap4 + Icap5 + Ic1 + Ic2 + Ic3 + Ic4 (7.6)

IF = IΣ + Icap1 (7.7)

Ic1,c2,c3,c4 distributed line capacitive currents

Icap1,cap2,cap3,cap4,cap5 capacitive current from feeder 1, 2, 3, 4, 5

IΣ residual current at the measuring pointIF fault current

The residual current plus the capacitive current of the other feeders equals the currentIΣ which is measured through the protection relay equation (7.7. The missing capacitivecurrent is the capacitive current of the faulty line.For the determination of the fault current, the capacitive current of the faulty line isnecessary in conjunction with the measured residual current. The needed data for thiscan be achieved by measuring the residual current during network operation or can be

46


taken from tables. As it is shown in equation (7.7), the capacitive current from theline depends on the displacement voltage and the capacitive currents from the line.These currents depend on the switching state of the network. For estimation it can beassumed that the displacement voltage is the same in the whole network. If the capacitivecurrent from the faulty line is known, the current has to be multiplied with the ratiofrom displacement voltage to nominal voltage, because with smaller displacement voltagethe capacitive currents get smaller. If the capacitive current of the observed section isknown, equation (7.7) can be extended by the measured displacement voltage and thenominal line to earth voltage:

IF = IΣ + Icap1 ·∣∣∣∣ U0

meas

UL1Enominal

∣∣∣∣ (7.8)

IF fault currentIcap1 capacitive current from feeder 1

IΣ residual current at the measuring pointUL1Enominal nominal line-to-earth voltageU0meas measured displacement voltage

Equation (7.8) the fault current at the earth fault point. This equation can only be usedin radial networks.

7.1.3 Neutral Point Current of the Transformer and GroundingImpedance

The neutral point current of the transformer ITR depends on the current of the arcsuppressing coil and the additional resistance. These currents depend on the networkenlargement and the additional resistance and can reach values around some hundredAmpere.The knowledge of these currents can be achieved by measurements.The influence of ZE is described in chapter 8.1.4.1.

47


7.2 Improved Earth Fault Distance Algorithm

For higher impedance fault the classic algorithm presented in equation (6.1) is not sat-isfying. Above some 100Ω the algorithm cannot be used. In this case, that improvedalgorithm, presented in equation (5.9)has to be used to reduce the influences of the faulttransition impedance.Inserting equation (7.5) and equation 7.8 into equation 5.9 reads

Z1Line =

UL1 − real(UL1

IΣ

)·(IΣ + Icap ·

U0meas

UL1Enominal

)− ITR · ZE

IL1 + IΣ · k0

= z1′ · l (7.9)

k0 earth return path factorIcap capacitive current from faulty feeder

IΣ residual current at the measuring pointU0meas measured displacement voltage

UL1 measured line-to-earth voltage in phase L1UL1Enominal nominal line-to-earth voltageIL1 measured current in phase L1


Z1Line positive sequence system line impedance

ZE grounding impedance of the measuring stationITR neutral point current of the transformerl fault distance

The fault distance is calculated by using the imaginary part of the calculated impedanceZ1Line.

l =1

x1′imag

UL1 − real(UL1

IΣ

)·(IΣ + Icap ·

(U0meas)

UL1Enominal

)− ITR · ZE

IL1 + IΣ · k0

(7.10)

With equation (7.10) the fault distance can be calculated. The sensitivity analysis ofdifferent influence parameters will be explained in chapter 8.

48

7.3 Distributed Loads

7.3 Influence of load distribution on the distancecalculation

In the simulations above, the load is always set at the end of the line. In reality, the loadsare distributed along the line, sometimes split up in a more equal way, sometimes thereare load spots. This chapter shows the influence of distributed loads on the improvedalgorithm

7.3.1 Simulation Model

The following model is implemented in MATLAB/SIMULINK R©. The data used, is thesame as described in table 4.1.

Figure 7.3: Simulation model of load distribution

The fault point is varied from busbar 1 to busbar 5. The improved algorithm is againapplied to the simulation results.

7.3.2 Comparison of Compensated, Middle Ohmic and SolidlyGrounded Networks

In the following, different network types (compensated, middle ohmic and solidly grounded)are compared to each other. In figure 7.4a the distance calculation of a middle ohmicand in figure 7.4b of a solidly grounded network is shown.

49


0 100 200 300 400 500 600 700 800 900 10000

5

10

15

20

25

30


Cal

cula

ted

dist

ance

in k

m

fault at busbar 1fault at busbar 2fault at busbar 3fault at busbar 4fault at busbar 5

(a) Middle ohmic grounded network

0 100 200 300 400 500 600 700 800 900 10000

5

10

15

20

25

30


Cal

cula

ted

dist

ance

in k

m


(b) Solidly grounded network

Figure 7.4: Distance calculation with distributed loads

As it can be seen, at low ohmic earth faults in the solidly grounded network the faultdetection is more accurate. At higher ohmic earth faults, solidly and middle ohmicgrounded networks become more and more similar. The reason is, that in solidlygrounded networks the fault current is higher than the load current and therefor theload is negligible.

As experiences have shown in real networks the results of these simulations are thesame: With distributed load the calculated distance using the classic algorithm is alwaysdecreasing at higher ohmic earth faults.

With the improved algorithm it is possible to locate a fault area.

7.3.3 Correction of the Influence of Distributed Loads

In this chapter an idea for correcting the influence of distributed loads is presented.

As shown in the simulations in figure 7.4, a correlation between the distribution of loadalong a line and measured impedance up to fault location can be recognized. The moreloads there are before the absence place, the smaller the measured fault impedance gets.

50


0 200 400 600 800 10000

5

10

15

20

25

30

ZF in Ohm

cacl

ulat

ed fa

ult d

ista

nce

in k

m

fault at busbar 1fault at busbar 2fault at busbar 3

(a) Fault at busbar 1, 2 and 3

0 200 400 600 800 10000

5

10

15

20

25

30

ZF in Ohm

cacl

ulat

ed fa

ult d

ista

nce

in k

m

fault at busbar 4fault at busbar 5

(b) Fault at busbar 4 and 5

Figure 7.5: Simulations with random varied fault point and load distribution

In figure 7.5 the results of different load distributions are presented. The load distributionis varied whereas the total line load is unchanged. It can be seen that different loaddistribution offers several fault distances. For the first busbar the calculation works fine,for the others the information about calculated area is not possible.

7.3.3.1 Correction coefficients

The idea is to use correction coefficients to improve the computed fault distance. Equa-tion (7.11) tries to include these loads into this factor in order to correct the faultimpedance.The loads (load1 - load4) are filled in percentage of the total load. The coefficients arecomputed from several simulations/tests. The coefficients try to include the aberrationof the distance algorithm and combine it with the load factors.

A1 B1 C1 D1

A2 B2 C2 D2

A3 B3 C3 D3

A4 B4 C4 D4

·coeff11

coeff12

coeff13

coeff14

=

dist1dist2dist3dist4

(7.11)

Ax, Bx, Cx, Dx loads in % of the total line loaddistx aberration in % of the nominal distancecoeffxy correction coefficients y at busbar x

The coefficients coeffx are median values of coeffxy for the load at busbar x.

The coefficients matrix can be written: coeffT =[coeff1 coeff2 coeff3 coeff4

]The load matrix can be written as: loadsT =

[load1 load2 load3 load4

].

51


In this matrix the loads are inserted in percentage of the total line load.

0 200 400 600 800 10000

0.5

1

1.5

2

2.5

3

3.5

4

ZF fault transition impedance

corr

ectio

n fa

ctor

coeff1coeff2coeff3coeff4

Figure 7.6: Correction curves

It is shown that it is possible to determine coefficients, which are able to correct and toreduce the deviations (see figure 7.6).

The coefficients are likely to determine, however, only for one fault transition resistancevalue and for one area between the measurement and the load. Therefore, coefficientmatrices must be determined which are nearly independent of load.Best results can be achieved if the correction curves are calculated for faults at the endof the line. A similar approach for including the loads can be found in [AW07].

7.3.3.2 Distance Calculation with Correction Coefficients

The matrix is dependent on the neutral point treatment. Therefore, it has to be esti-mated for separately for these networks.Example:For a compensated network and approximately 100 A additional resistance in parallelto the arc suppressing coil, the coefficient matrix is presented at 50 Ω fault resistance :

coeff =

1.961.41.240.99

The fault distance can be corrected using equation (7.12).

l = lcalculated · coeffT · loads (7.12)

52


l fault distancelcalculated distance calculated by using the improved algorithmcoeffx correction coefficient at busbar x

The fault impedance can be estimated as presented in chapter 7.1.1. With the knowledgeof the fault impedance, the correcting coefficients are known and the calculated faultdistance can be corrected using equation (7.12).

0 200 400 600 800 10000

5

10

15

20

25

30

ZF fault transition impedance

cacl

ulat

ed fa

ult d

ista

nce

in k

m


Figure 7.7: Distributed loads with corrected values

.In figure 7.7 the curves at all 5 error locations (see chapter 7.3.1) are shown, wherebythe distribution of load is varied accidentally as presented in chapter 7.3.3.1.A practical realization could take place to that extent that the correction coefficients inthe relay are deposited and, depending on the neutral point treatment, are applied. Asuggestion for correcting the calculated distances is that only distance results which areat the third or fourth busbar, are corrected, and the rest remains as it is. For shorterdistances the algorithm already works well.Then the distribution of the load and the neutral point treatment has to be filled inincluding the neutral point resistance. A higher accuracy could be attained via additionalcurves, dependent on the line lengths between the loads.

53

8 Comparison of the Classic andImproved Algorithm

8.1 Sensitivity Analysis of the Algorithm

In this chapter the influences on the classic and improved algorithm will be discussedand, based on the sensitivity analysis, the most critical parameters are identified.In this chapter the influences of separate parameters will be investigated. The investi-gations are carried out by using reference model 1 (see chapter 4.1.4).These parameters can be divided into three groups:

• aberrations due to wrong measurements

• aberrations due to wrong settings (k0)

• aberrations due to physical influences (ZE, ZF )

The simulations in the following chapters will work on the basis of a compensated net-work. In chapter 8.1.5, different networks types (compensated, solidly grounded, isolatedand middle ohmic grounded) will be compared to each other.

8.1.1 Linearization

In this chapter the influences of separate parameters will be investigated. In one workingpoint the algorithm can be linearized. The classic algorithm (equation (6.1)) and theimproved algorithm (equation (7.10)) are linearized. The maximum aberration of eachparameter can be calculated using equation (8.4) and (8.2) and will conclude in anaberration of the calculated fault distance smaller than 10% (0.1 p.u.).

• Classic Algorithm

l = f(x1′ , UL1, IΣ, k0, IL1) (8.1)

∣∣∣∣ dldai ∆ail

∣∣∣∣ =

∣∣∣∣ ddxi ∆xil

1

x1′imag

[UL1

IL1 + IΣ · k0

]∣∣∣∣ ≤ 0.1p.u. (8.2)

with ai are the setting and measured parameters:

ai ∈ (x1′ , UL1, IΣ, k0, IL1)

8 Comparison of the Classic and Improved Algorithm

• Improved Algorithm

l = f(x1′ , UL1, Icap, IΣ, k0, ITR, ZE, IL1, U0meas, UL1Enominal) (8.3)

∣∣∣∣ dldxi ∆xil

∣∣∣∣ =∣∣∣∣∣∣ ddai ∆ail

1

x1′imag

UL1 − real(UL1

IΣ

)·(IΣ + Icap ·

(U0meas)

UL1Enominal

)− ITR · ZE

IL1 + IΣ · k0

∣∣∣∣∣∣≤ 0.1p.u. (8.4)


ai ∈ (x1′ , UL1, Icap, IΣ, k0, ITR, ZE, IL1, U0meas, UL1Enominal)

If the differential equation is solved, the following maximum aberrations of the param-eters can be calculated for the reference model (see chapter 4.1) with the fault point at15 km and a fault transition impedance of 1 Ω:

Table 8.1: Result of the linearization of some parameters

simulation result classic algorithm improved algorithmUL1 2432+j1092 V |∆UL1|= 270 V |∆UL1|= 266 VIL1 196-j29 A |∆IL1|= 27 A |∆IL1|= 27 AIΣ 93.89 -j17.65 A |∆IΣ|=34 A |∆IΣ|= 35 Ak0 0.833 |∆k0| = 0.3 |∆k0| =0.29

It can be seen that the influences on both algorithm are similar: 10 % aberration ofeach parameter causes around 10 % aberrations in the calculated line length. The sameresults will be seen in chapter 8.1.2.

8.1.2 Measurement Influences

Measurement influences can result from measurement transformers or the protection de-vices itself. The measurement transformers have specifications with aberrations lowerthan 0.5%. This accuracy does not lead to significant aberrations of the simulationalgorithm. Protection devices have A/D-converters which have to cover the whole mea-surement range. In case of an earth fault, the voltage of the faulty phase is low. As a

56


result the quantization can lead to wrong calculation results due to granularity.

In this simulation the parameters UL1, IL1 and IΣ = 3I0 are varied ± 10% from thesimulation result. This shows the influence of each parameter on the calculation result.

−10 −8 −6 −4 −2 0 2 4 6 8 1013.5

14

14.5

15

15.5

16

16.5

17

Variation in %

calc

ulat

ed fa

ult d

ista

nce

in k

m

Sensitivity at 1 Ohm fault transition impedance

U

L1

I0

IL1

nominal distance

(a) Classic algorithm

−10 −8 −6 −4 −2 0 2 4 6 8 1013.5

14

14.5

15

15.5

16

16.5

17

Variation in %

calc

ulat

ed fa

ult d

ista

nce

in k

m


U

L1

I0

U0

IL1

nominal distance

(b) Improved algorithm

Figure 8.1: Sensitivity analysis at 1 Ω fault impedance

Figure 8.1 shows that the line current and the line-to-earth voltage have the biggestinfluence, however, in a complementary direction. The influence of I0 is smaller thanthe line current, because the residual current is smaller compared to the line currentwhich xxx the line current and wrong measured values can reach an aberration around± 10%.

8.1.3 Influences of Wrong Settings

The appropriate setting of k0 can be measured or read off parameters tables, if avail-able. This earth return path factor k0 describes the ratio of the zero sequence systemimpedance to the positive sequence system impedance. This ratio independent of theline length and can be used for earth fault distance calculation.As published in [AOF+07] and [KF07] different ways of describing and writing this factork0 exist and are described in the following:

• with symmetrical components from protection point of view

This thesis uses equation (8.5).

k0 =1

3

(Z0Line

Z1Line

− 1

)(8.5)

57



Z0Line zero sequence system line impedance

k0 earth return path factor

• with complex earth and complex line impedance

kE =ZEearth

Z1Line

(8.6)

• with symmetrical components

k0k =Z0

Z1 (8.7)

Conversions between the different k0-factor in equation (8.5) and equation (8.7)are also possible using equation (8.8).

k0k = 1 + 3 · k0 (8.8)

• with separated earth and line impedance

kE =RE

RL

1

1 + jXLRL

+XE

XL

1

1− j RLXL

(8.9)

Equation (8.6) can be converted into equation (8.9) by using the line angle (equa-tion(8.10)).

tanφ =XL

RL

(8.10)

In network practice the exact line parameters of the positive and zero sequence systemare very obvious known, however, the exact factor k0 of a line can be achieved throughmeasurements[AOF+07].

A common practice is the setting of k0 to 0.8..1..1.5 with an angle of 0 [FMR+05].

In the simulation k0 is 0.83∠0.

58


(a) Classic algorithm (b) Improved algorithm

Figure 8.2: Variaton of k0

Figure 8.2 shows the effect of a wrong setting of k0. The black plane in figure 8.2 showsthe area which covers the result of the ideal line length ± 10% error tolerance. If thevalue of k0 is chosen smaller than its real value, the measured fault impedance is higher,because the earth return path is rated too low, and if k0 is set higher, the measuredimpedance is lower.The angle has a smaller influence in overhead line networks than the value, as it is thesetup for the simulations.

8.1.4 Influences of Parameters of the Electrical Grid

To test the conventional algorithm, the following influences have been selected for asensitivity analysis [Bre07]. These parameters are varied in the simulation environment(see chapter 4.1.4) and the algorithm is applied to the results:

• the grounding impedance at the measuring station ZE

• the fault impedance ZF

• the load factor cosϕ

8.1.4.1 Variation of ZE

Normally the voltages are line-to-earth voltages which are measured from line to thestation grounding, assuming that it is measured to the far earth (see figure 4.3). If thegrounding impedance is too high (for example at substations in mountains) and thereexists current over the grounding system (arc suppressing coil placed in this substation),the voltage rise of the grounding system of the station leads to measurement errors ofthe line-to-earth voltage and therefore to a miscalculation of the fault distance. The

59


miscalculation term is I0ZE · 3ZE. In equation (5.9) I0

ZE is named ITR, because in mostcases it is the neutral point current of the transformer.

U0ZE = I0

ZE · 3ZE (8.11)

U0meas = U0

measreal + U0ZE (8.12)

UL1 = U1meas + U2

meas + U0meas (8.13)

UL1 = U1meas + U2

meas + U0measreal + U0

ZE (8.14)

U1, U2, U0 positive, negative and zero sequence voltage at the measuring pointU0measreal real measured displacement voltage

I0ZE zero current over the grounding impedanceUL1 Line-to-earth voltage of phase L1U0ZE grounding impedance voltage

Figure 8.3 shows the influence of the impedance ZE.

The values are chosen at 0.01+j0.5 Ω for the starting point, the resistant part is varied,and the inductive part is chosen at 0.5 Ω due to practical experiences [Fre07]. Thegrounding system of a station has an inductive part because the grounding system coversa certain area. The current over the grounding system creates a magnetic field.

µ

∮H2dV =

1

2LI2 (8.15)

µ permeability constantH magnetic field densityL inductanceI currentV integration volume

Equation (8.15) shows that the grounding system at area V is inductive. The valuearound 0.5 Ω is proved by measurements [Fre07].

60


0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

2

4

6

8

10

12

14

16

18

20

grounding impedance ZE in Ohm

calc

ulat

ed d

ista

nce

in k

m

classic algorithm without resistanceclassic algorithm with resistanceextended algorithmnominal distance

Figure 8.3: Variation of ZE

In figure 8.3 it can bee seen that the aberration is smaller using an additional resistancein parallel to the arc suppressing coil the aberration is smaller. The reason is that ZE

is ohmic and the current is also more ohmic using an additional resistance. Therefore,the voltage drop is more ohmic than inductive. In the algorithm, only the imaginarypart of the calculated impedance is used for the distance calculation and therefore ohmicinfluences as ZE are reduced if the voltage drop is dominantly ohmic.

The improved algorithm reduces the influence of ZE and therefor the simulation resultis more accurate than in the classic algorithm.


Figure 8.4: Variation of ZE over the variation of ZF

61


Figure 8.4 shows a variation of ZE when the value of ZF is increased, and its reducedinfluence. The black plane in figure 8.4 shows the area which covers the result of the idealline length ± 10% error tolerance. The simulations show that the aberration decreaseswith the increase of ZF because the current over the grounding system decreases andtherefore the voltage drop along the grounding system decreases.

8.1.4.2 Variation of ZF

This impedance ZF is not known in reality and varies from 1 Ω (solid and very lowohmic earth fault), several 100 Ω up to several kΩ (trees, broken lines and dry ground).

For the simulation ZF is the sum of RF and j0.5Ω (see chapter 8.1.4.1). In the followingsimulations the variation of ZF will be reduced to the variation of RF .

• Impedance of the grounding at the fault point

In the simulation, this impedance is varied from 1 to 1000 Ω. The grounding impedanceat the fault point is included into the fault transition impedance because, in reality, it isalso seen as one single impedance. The grounding impedance is taken into the transitionimpedance by adding an inductive part of j0.5 Ω (see chapter 8.1.4.1).The fault impedance is often seen as purely ohmic. The reason is that, if the faulttransition impedance increases, the inductive part is so small that it can be neglectedbecause the ohmic part dominates the impedance.

• Impedance of the arc resistance

Arcs are one of the most common fault types in electrical networks. The grounding sys-tem can be seen as predominantly ohmic, however, the arc has an inductive componentwhich might influence the distance calculation.An estimation for the resistance of an arc can be done by using the Warrington formula[War68]:

Rarc =28688

I1.4arc

larc (8.16)

Rarc arc resistancelarc length in meter of the arcIarc arc current in Ampere

• Impedance of the arc reactance

In international scientific literature and publications there exists no general model forcalculating the reactance of an arc. In order to get at least an estimation of the range ofarc reactance the well funded and proved algorithm (see equation (8.17) for arc furnaceovens is taken as an indication.

62


The arc‘s reactance which is valid for arc furnace ovens can be estimated as described in[Ren02] (see equation (8.17))1. (The reason is that the arc current shows a small phaseshift and therefore it can be seen as a reactance). Also, in [Mah85], it is shown that thearc reactance is proportional to the arc resistance.

Xarc = 0.08 ·Rarc +KX

(0.12 ·Rarc + 0.08 · R

2arc

XkON

)(8.17)

Rarc arc resistanceXarc arc reactanceXkON real arc furnace oven short circuit reactance including the whole networkKX smelting constant

KX depends on the smelting. It varies from 0.9 at the beginning of the process to 0 atthe end. If a conservative approach is chosen, the KX factor is set to 0.9. The reactancewill reach values up to 10% of the arc resistance; however, the reactance of the arc isin the same range of magnitude as the grounding impedance. Both are so small thatthey can be neglected because they will not influence the distance calculation result. In[SAA00], the fault reactance is small in comparison to the fault resistance.

0 100 200 300 400 500 600 700 800 9000

2

4

6

8

10

12

14

16

18

20

ZF in Ohm

calc

ulat

ed d

ista

nce

in k

m

classic without additional resistanceclassis with additional resistanceimproved algorithmnominal distance

Figure 8.5: Variation of RF

In figure 8.5, the fault resistance is varied. It seems that the fault impedance has a smallinfluence on the calculated result of the classic algorithm. It can be seen that with theadditional resistor in parallel to the arc suppressing coil, the results are more accurate,which compares to [Imr06].The improved algorithm reduces the influences of the fault transition impedance, evenat high ohmic faults (see figure 8.5).

1[Ren02], page 8-9

63


8.1.4.3 Variation of the Load Factor (cosϕ)

In previous simulations the load factor is always set to 1 a cosϕ = 1 (see chapter 4.1.4).In medium voltage networks it is the aim to reduce line losses and therefore the loadsshould be as near as possible to cosϕ = 1, but also values of cosϕ = 0.95 are common.It is assumed that different load factors might have an influence on the fault calculation.In this chapter the load factor is varied from 0.95 to 1.05. The absolute value of the loadis still 100 Ω.


Figure 8.6: Variation of cos ϕ of the load over the variation of ZF

Figure 8.6 and also described in [Imr06] shows that the load has a significant influenceon the calculated result. The black plane in figure 8.6 shows again the area which coversthe result of the ideal line length ± 10% error tolerance.

8.1.5 Comparison of the Different Influences on the Earth FaultDistance Algorithm in Networks with Other Neutral PointTreatments

In this chapter networks with other neutral point treatments will be investigated andcompared. The simulations are the same as described in chapter 8.1.4.1 and 8.1.4.2.

The usability of the algorithm in different network types is interesting, because a generalsolution would be useful. In the following figure, the algorithm is applied to differentnetwork types.

8.1.5.1 Influence of k0

• Value of k0

64


0 0.5 1 1.5 20

5

10

15

20

25

30

value of k0

calc

ulat

ed d

ista

nce

in k

m

isolated networkcompensated networkmiddle ohmic grounded networksolidly grounded networknominal distance


0 0.5 1 1.5 20

5

10

15

20

25

30

value of k0

calc

ulat

ed d

ista

nce

in k

m



Figure 8.7: Influence of the value of k0 in different grounded networks

• Angle of k0

0 10 20 30 40 50 60 70 80 900

2

4

6

8

10

12

14

16

18

20

angle of k0 in °

calc

ulat

ed d

ista

nce

in k

m



0 10 20 30 40 50 60 70 80 900

2

4

6

8

10

12

14

16

18

20

angle of k0 in °

calc

ulat

ed d

ista

nce

in k

m



Figure 8.8: Influence of the angle of k0 in different grounded networks

If the factor k0 is varied, the results certainly differ from each other. The reason isthat the zero sequence current is different from network to network. In solidly groundednetworks the zero sequence current has more influence because the amplitude is higherthan in networks with another neutral point treatment. In compensated networks thecurrent is low and therefore the influence of k0 is low. In isolated networks the currentdepends only on the capacitances and does not flow over the whole line length. For thisnetwork type the simplified algorithm is not usable.

65


8.1.5.2 Influence of ZE

0 1 2 3 4 50

2

4

6

8

10

12

14

16

18

20


calc

ulat

ed d

ista

nce

in k

m



0 1 2 3 4 50

2

4

6

8

10

12

14

16

18

20


calc

ulat

ed d

ista

nce

in k

m



Figure 8.9: Influence of ZE in different grounded networks

ZE has more influence if the current over the grounding station is increased. In a solidlygrounded network the measurement error is higher than in a middle ohmic or an earthfault compensated network.

8.1.5.3 Influence of ZF

0 200 400 600 800 10000

5

10

15

20

25

30

transition impedance ZF in Ohm

calc

ulat

ed d

ista

nce

in k

m



0 200 400 600 800 10000

2

4

6

8

10

12

14

16

18

20

transition impedance ZF in Ohm

calc

ulat

ed d

ista

nce

in k

m



Figure 8.10: Influence of ZF in different grounded networks

Figure 8.10 shows that the classic algorithm provides similar results as the improvedalgorithm.

66

8.2 Fault Distance Variation

The obtained results in this chapter show that an increase of the zero sequence currentis necessary to achieve more accurate measurement results, independent from the pa-rameter k0, ZE and ZF . It should be kept in mind that higher earth fault currents leadto problems concerning the influence of a wrong k0, touch voltages [CEN99][OVE76] orother interferences.The simulations show that the improved algorithm could principally be used in all net-works, except the isolated one. The reason for this is that the algorithm neglects thecapacitive currents distribution along the line. However, in an isolated network, thesecurrents are the dominant parameter in case of an earth fault and must not be neglected.

8.2 Fault Distance Variation

For the simulation of the distance variation the simulation model presented in chapter4.1.4 is used. The simulations are carried out using a middle ohmic grounded simulationmodel. The model data represent a overhead line network (see table 4.1).


Figure 8.11: Fault distance variation

In figure 8.11 the fault distance is varied from 0.1 km (close fault point) to 20 km. Thetotal line length is 20 km. As above the classic and the improved algorithm are appliedto this simulation. It can be seen that with higher fault impedance the classic algorithmgets imprecise, whereas, the improved version keeps the calculated fault distance. It getseven better due to the fact that the influence of the line impedance on the estimation ofthe fault impedance decreases. Therefore, the calculation can be seen as more accurate.

67


8.3 Compensated Cable Networks

Former simulations have always been done through simulating an overhead line network.

Nowadays, especially in medium voltage networks, the percentage of cables is growing.

Figure 8.12 shows the distance calculation in a pure cable network. For the simulation ofthis network, the simulation model presented in chapter 4 is used. The line parametersare changed, however, the line lengths are unvaried. Again a middle ohmic groundednetwork is used for the simulations. The fault distance is varied from 0.1 km to 20 km.

Table 8.2: Simulation data for the cable network

Network 20-kV / overhead linesLine length 20 kmLine Z1 / Z0 per km 0.0256 Ω+j0.127 Ω / 0.103 Ω+j0.172 ΩLine cap C1 / C0 per km 0.3 µF / 0.3 µFarc suppression coil 4 Ω+ j 81 ΩAdditional resistance 100 Ω

Taking into account, typical values for earth faults in cable networks are a few ohms,limited to 10 Ω. Using the Warrington formula (equation (8.16)), assuming a faultcurrent of 200 A and a arc length of 10 cm the resistance can be calculated:

Rarc =28688

2001.4· 0.1 = 1.7Ω



68

8.3 Compensated Cable Networks

8.3.1 Increasing of the Installed Cable Proportion in a Network

These simulations show the usability of the algorithm in networks with different linetypes and different percentages of cable and overhead lines.In these simulations the fault point is varied along the line. Line 1 and line 2 are beforethe fault and line 3 is behind (see figure 4.2).In figure 8.13 the lines before the fault are cables and behind the fault the line is anoverhead line. Due to the reason that the fault point is varied in the simulation, thelength of the cable between the measuring point and the fault is increased and the lengthof the overhead line behind the fault is decreased. The whole line length remains 20 km.

(a) Middle ohmic grounding with additional 100 A (b) Middle ohmic grounding with additional 200 A


As it can be seen in figure 8.13 it might be recommended to increase the residual currentup to 200 A for a short time [?]. The fault detection is higher even in mixed networksand no problems due to interferences and touch voltages are expected.

69


8.4 Solidly Grounded Networks

In solidly grounded network the classic algorithm is commonly used. In this chapter, acomparison of the classic and improved algorithm will be presented.For the simulation figure 8.14 is used. The exact simulation model and the model datacan be found in chapter 4.1.4.

protection device

line3

transformer

loadnetwork

rest of the network

ZF

ZE

busbar

line1+2

station

Figure 8.14: Simulation model

As described in chapter 8.1.4.2 the fault resistance is varied.

0 100 200 300 400 500 600 700 800 9000

2

4

6

8

10

12

14

16

18

20

ZF in Ohm

calc

ulat

ed d

ista

nce

in k

m

classic algorithmimproved algorithmnominal distance

Figure 8.15: Simulation of the improved algorithm and comparison with the classic distance protectionalgorithm in case of high ohmic fault impedances in low ohmic grounded networks

Figure 8.15 shows that the improved algorithm can also be used for high ohmic earthfaults in solid or low ohmic grounded networks. The algorithm for estimating the faultimpedance is still valid. Due to the reason, that the capacitances can be neglected in

70

8.4 Solidly Grounded Networks

low and solidly ground networks, it can be supposed that the fault current is the sameas the residual current at the measuring point

71

9 Earth Fault Distance Protection in aTwo-Phase Network

As presented in chapter 4.2.1 a two-phase network can also be described in symmetricalcomponents.In this chapter the derivation of the fault impedance calculation algorithm for a two-phase compensated network will be presented. This algorithm is a simplification becausein the derivation the distributed line-to-earth capacitances have been neglected.The used classic algorithm will then again be simplified. Unfortunately this classic algo-rithm only provides good results up to fault impedances around some 100 Ω. However,this is adequate for these kinds of networks, because the majority of the earth faults arelow ohmic faults.

9.1 Considerations on Earth Fault Distance Calculation

For the general considerations the model in chapter 4.2 is used. The capacitances areneglected and the faulty phase is phase L1.The fault point can be described as:

U1F + U0

F = UF (9.1)

Z1Line is the sum of unZ1

Line1 and unZ1Line2, respective it is the same for the zero sequence

system.Inserting the measured voltages and the voltage drop along the line, equation (9.1) canbe written:

U1 − I1P · Z1

Line + U0 − I0P · Z0

Line − 2 · I0TStp · ZE = 2 · I0

F · ZF (9.2)

The measured voltages in symmetrical components can be summed up to the line voltageof the phase,

UL1 = U1 + U0 = I1P · Z1

Line + I0P · Z0

Line + 2 · I0F · ZF + 2 · I0

TStp · ZE (9.3)

UL1 − 2 · I0F · ZF − 2 · I0

TStp · ZE

Z1Line

= I1P + I0

P ·Z0Line

Z1Line

(9.4)

9 Earth Fault Distance Protection in a Two-Phase Network

with IL1 = I1P + I0

P

UL1 − 2 · I0F · ZF − 2 · I0

TStp · ZE

Z1Line

= IL1 − I0 + I0 · Z0Line

Z1Line

(9.5)

UL1 − 2 · I0F · ZF − 2 · I0

TStp · ZE

Z1Line

= IL1 + I0 ·(Z0Line

Z1Line

− 1

)(9.6)

with k0 2phase = 12

(Z0Line

Z1Line− 1)

and 2 · I0 = IΣ and 2 · I0F = IF

UL1 − IF · ZF − ITStp · ZE

Z1Line

= IL1 + IΣ · k0 2phase (9.7)

Z1Line =

UL1 − IF · ZF − ITStp · ZE

IL1 + IΣ · k0 2phase

= z1′ · l (9.8)

Z1line, Z


I1P , I

0P positive and zero sequence current at the measuring point

U1, U0 positive and zero sequence voltage at the measuring pointU1F , U

0F positive and zero sequence voltage at the fault point

IF fault currentZF fault impedanceIΣ residual current at the measuring pointk0 2phase earth return path factor for a two-phase network

UL1 measured line-to-earth voltage in phase L1IL1 measured current in phase L1


ZE grounding impedance of the measuring stationITStp neutral point current of the transformer

l fault distance

From equation (9.8) an algorithm for fault distance calculation of a line-to-earth faultcan be derived. This algorithm also needs accurate setting of k0 2phase because a wrongsetting can lead also to miscalculations (chapter 9.5.1.3).

As described before distance protection relays have the ability to locate earth faults[Sie00] [Sie93], however, this technology is only used if the second phase during an earthfault is solidly grounded.

With the assumption that high ohmic faults are not in the centre of attention, equation(9.8) can be simplified to equation (9.9).

74


Z1Line =

UL1


= z1′ · l (9.9)


UL1 line-to-earth voltage of phase L1IL1 current in phase L1k0 2phase earth return path factor

IΣ residual current at the measuring point


l fault distance

If only the imaginary part of equation (9.9)is used, the ohmic influences can be reduced.

l =imag(Z1

Line)

x1′(9.10)


x1′specific positive sequence system line inductance

l fault distance


First tests of the classic algorithm in a two-phase network were carried out in the lab-oratory. Therefore an analogical network model was used as described in chapter 6.1.Low ohmic earth faults were carried out at different fault points. For measurements andtests two distance protection relays, which will be referred to as Relay 1 and Relay 2 inthis and the next section, were installed in this network. These tests showed that it ispossible to use the existing relays, by changing the settings of the relay.

Due to saturation effects of the network model, the fault scenarios were too different tomake a statement about the usability, but the tests gave a first idea about the principleuse of this algorithm. Another problem was that the two relays did not react in thesame way, which might be based on different trigger levels and internal algorithms.

9.3 Testing of Two-Phase Distance Protection Relays

For the first simulations and tests of the distance protection relays, a two phase networkmodel has been developed by using MATLAB/SIMULINK R© [mat08] as shown in figure9.1. The transient results of the simulation model are converted to the comtrade formatand directly used as input for distance protection relays.

75


Figure 9.1: Simulation for the testing of the relays

The setup of the simulation is described in table 9.1. The values are the same, as thoseinserted in the simulation model. The lines are modelled as Π-equivalents. All testsscenarios were low ohmic earth faults.

Table 9.1: List of the elements in the simulation

Nominal voltage 110 kVFrequency 16.7 HzLine 1 40 km / 3.2 Ω+j4.6 ΩLine 2 20 km / 1.6 Ω+j2.3 ΩFault point at 40 km, after the first lineCapacitive current of the network 150 AArc suppressing coil 120 A

The protection relays, which use the classic algorithm, were tested with different set-tings of the simulation environment. The load, the resistor Radd in parallel to the arcsuppressing coil and the earth return path (RE

RLand XE

XL) were varied. Table 9.2 presents

the settings and the results.

76

9.4 Improved Algorithm for Two-Phase Networks

Table 9.2: Simultion and test results

ResultTest: Load Radd

RERL

XEXL

Relay 1 Relay 2

1 20 MW 100 Ω 1 1 40 km 42.3 km2 60 MW 100 Ω 1 1 40.9 km 42.4 km3 0 MW 100 Ω 1 1 41.5 km 42.4 km4 0 MW 100 Ω 0.1 0.1 41.5 km 42.1 km5 0 MW 100 Ω 0.1 0.5 41.5 km 42.6 km6 0 MW 400 Ω 0.1 0.5 41.5 km 42.2 km7 60 MW 400 Ω 0.1 0.5 41.5 km 40.1 km

The tests (table 9.2) show that the distance protection relay can be used for detectingearth faults in a compensated two-phase network for low ohmic earth faults.

9.4 Improved Algorithm for Two-Phase Networks

As presented in chapter 7.1.1 and 7.1.2 the fault current and the fault impedance canbe estimated. It has to be mentioned that this algorithm difficult to use in a meshednetwork, because it is not easy to estimate the capacitive currents. They flow from bothline ends into the line instead of one and the distribution depends on the fault point.Therefore a distance protection which includes measurements from both sides is prefer-able [LSW07].

9.4.1 Derivation of the Improved Algorithm

Inserting equation (7.5) and equation (7.8) into equation (9.8) can be written:

Z1Line =

UL1 − real(UL1

IΣ

)·(IΣ + Icap ·

abs(U0meas)

UL1Enominal

)− ITStp · ZE


= z1′ · l (9.11)

k0 2phase earth return path factor

Icap1 capacitive current from feeder 1

IΣ residual current at the measuring pointU0meas measured displacement voltage

UL1 measured line-to-earth voltage in phase L1UL1Enominal nominal line-to-earth voltageIL1 measured current in phase L1



ZE grounding impedance of the measuring stationITStp neutral point current of the transformer

l fault distance

77


Equation (9.11) is similar to equation (7.9) in a 3-phase network.Using the imaginary part of equation (9.11), the fault distance can be calculated.

9.5 Comparison of the Classic and Improved Algorithm

As presented in chapter 8, the classic and the improved algorithm have been comparedto each other.

9.5.1 Sensitivity Analysis of the Algorithm

In this chapter the influences of separate parameters will be investigated, as presented inchapter 8.1. The investigations are carried out by using reference model 2 (see chapter4.2.4).These parameters can be divided into three groups:

• aberrations due to wrong measurements

• aberrations due to wrong setting

• aberrations due to physical influences

For the simulations in the following chapters a compensated network is assumed.

9.5.1.1 Linearization

In this chapter the influences of separate parameters will be investigated. In one workingpoint the algorithm can be linearized. The maximum aberration of each parameter canbe calculated using equation (9.13) and (9.15) and will conclude in an aberration of thecalculated fault distance smaller than 10% (0.1 p.u.).

• Classic Algorithm

l = f(x1′ , UL1, IΣ, k0, IL1) (9.12)


∣∣∣∣ =

∣∣∣∣ ddxi ∆xil

1

x1′imag

[UL1


]∣∣∣∣ ≤ 0.1p.u. (9.13)


ai ∈ (x1′ , UL1, IΣ, k0, IL1)

78


• Improved Algorithm

l = f(x1′ , UL1, Icap, IΣ, k0 2phase, ITR, ZE, IL1, U0meas, UL1Enominal) (9.14)


∣∣∣∣ =∣∣∣∣∣∣ ddxi ∆xil

1

x1′imag

UL1 − real(UL1

IΣ

)·(IΣ + Icap ·

(U0meas)

UL1Enominal

)− ITR · ZE


∣∣∣∣∣∣≤ 0.1p.u. (9.15)


ai ∈ (x1′ , UL1, Icap, IΣ, k0 2phase, ITR, ZE, IL1, U0meas, UL1Enominal)

If the differential equation is solved, the following maximum aberrations of the parame-ters can be calculated for the reference model (see chapter 4.2) which works with a faultpoint at 40 km and a fault transition impedance of 1 Ω:

Table 9.3: Result of the linearization of some parameters

simulation result classic algorithm improved algorithmUL1 2225+j1751 V |∆UL1|= 315 V |∆UL1|= 270 VIL1 302-j73 A |∆IL1|= 55 A |∆IL1|= 41 AIΣ 167 -j54 A |∆IΣ|=52 A |∆IΣ|= 59 Ak0 2phase 0.57+j0.37 |∆k0| = 0.2 |∆k0| =0.22

It can be seen that the influences on both algorithm are similar: The same results canbe seen in chapter 9.5.1.2.

9.5.1.2 Measurement Influences

As described in chapter 8.1.2 UL1, IL1 and IΣ = 3I0 will be varied.

79


−10 −8 −6 −4 −2 0 2 4 6 8 1036

37

38

39

40

41

42

43

44

45

Variation in %

calc

ulat

ed fa

ult d

ista

nce

in k

mSensitivity at 1 Ohm fault transition impedance

U

L1

I0

IL1

dist nominal


−10 −8 −6 −4 −2 0 2 4 6 8 1040

41

42

43

44

45

46

47

48

49

50

Variation in %

calc

ulat

ed fa

ult d

ista

nce

in k

m


U

L1

I0

U0

IL1

dist nominal


Figure 9.2: Sensitivity analysis at 1 Ω fault impedance

Figure 9.2 shows that the line current and the line-to-earth voltage have the biggestinfluence on the fault distance algorithm, however, in a complementary direction. Theinfluence of I0 is smaller than the line current, because the residual current is smallercompared to the line current, which the load current and wrong measured values canreach an aberration around ± 10%.

9.5.1.3 Influences of Wrong Settings

In contrast to the analysis in chapter 9.5.1.2 the simulations in this chapter and chapter9.5.1.4 are carried out through varying the input parameters of the simulation modeland re-simulating without varying the results of the simulations.

The simulations are the same as described in chapter 8.1.3, the k0 2phase is defined inanother way (see equation (9.16)). Equation (9.16) is used in this chapter.

k0 2phase =1

2

(Z0Line

Z1Line

− 1

)(9.16)


Z0Line zero sequence system line impedance

k0 2phase earth return path factor

In the simulation k0 2phase is 0.68∠33.

80



Figure 9.3: Variaton of k0 2phase

Figure 9.3 shows the effect of a wrong setting of k0 2phase. The black plane in figure 9.3shows the area which covers the result of the ideal line length ± 10% error tolerance. Ifthe value of k0 2phase is chosen smaller than its real value, the measured fault impedanceis higher, because the earth return path is rated to low, and if k0 2phase is set higher, themeasured impedance is lower.

9.5.1.4 Influences of Parameters of the Electrical Grid

These parameters are varied in the simulation environment and the algorithm is appliedto the results as described in chapter 8.1.4.

Variation of ZE

Figure 9.4 shows the influence of the impedance ZE. The values are chosen at 0.01+j0.5 Ωfor the starting point, the resistant part is varied and the inductive part is chosen at0.5 Ω due to practical experiences [Fre07].

81


0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

5

10

15

20

25

30

35

40

45

50


calc

ulat

ed d

ista

nce

in k

m

classic algorithm without resistanceclassic algorithm with resistanceextended algorithmnominal distance

Figure 9.4: Variation of ZE

In figure 9.4 it can bee seen that the aberration is smaller using an additional resistance inparallel to the arc suppressing coil. The reason is that ZE is ohmic and the current is alsomore ohmic using an additional resistance. Therefore, the voltage drop is more ohmicthan inductive. In the algorithm, only the imaginary part of the calculated impedanceis used for the distance calculation and therefore ohmic influences as ZE will be reducedif the voltage drop is dominantly ohmic.The improved algorithm reduces the influence of ZE and therefore the simulation resultis more accurate than in the classic algorithm.


Figure 9.5: Variation of ZE over the variation of ZF

Figure 9.5 shows a variation of ZE when the value of ZF is increased and its reduced

82


influence. The black plane in figure 9.5 shows the area which covers the result of the idealline length ± 10% error tolerance. The simulations show that the aberration decreaseswith the increase of ZF because the current over the grounding system decreases andtherefore the voltage drop along the grounding system decreases.

Variation of RF

As done in chapter 8.1.4.2 the resistance is varied from 1 to 1000 Ω.The grounding impedance at the fault point is included into the fault transition impedancebecause, in reality, it is also seen as one single impedance. The grounding impedance isadded to the transition impedance by adding an inductive part of j0.5 Ω (see chapter8.1.4.1).

0 100 200 300 400 500 600 700 800 9000

10

20

30

40

50

60


calc

ulat

ed d

ista

nce

in k

m


(a) Fault impedance varied from 1Ω to 1kΩ

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60


calc

ulat

ed d

ista

nce

in k

m


(b) Fault impedance varied from 1Ω to 100Ω

Figure 9.6: Variation of ZF

In figure 9.6 the fault transition impedance is varied. Without the additional resistance,the fault current is too small in comparison to the load current at higher fault impedancesand therefore the calculated fault distance is too high. It can be seen that with theadditional resistor in parallel to the arc suppressing coil, the results get better, whichcompares to [Imr06]Due to the reason that according to experiences in a 110-kV-network faults are mostlylow ohmic faults, figure 9.6b shows a zoom of the first sector of figure 9.6a which presentsfault impedances from 1 to 10 Ω.The improved algorithm reduces the influences of the fault transition impedance evenat high ohmic faults.

Variation of the Load Factor

In previous simulations the load has always been set to a cosϕ = 1. It is assumed thatdifferent load factors might have an influence on the fault calculation. In this chapter

83


the load factor is varied from 0.95 to 1.05.


Figure 9.7: Variation of cos ϕ of the load over the variation of ZF

Figure 9.7 shows that the load has a significant influence on the calculated result. Theblack plane in figure 9.7 shows the area which covers the result of the ideal line length± 10% error tolerance.

9.5.2 Fault Distance Variation

In these simulations an additional resistance of 100 Ω is put in parallel to the Petersencoil. The line length is set to 60 km. The fault point is 40km far away.



84


The improved algorithm reduces the influence of the fault impedance, independent fromthe fault distance. The classic algorithm works well for low ohmic earth faults, asdescribed in 6, however, it cannot be used for high impedance fault. The same problemhas already been presented in chapter 7.

85

10 Earth Fault Field Tests

To test the classic algorithm in compensated networks earth fault tests were carried out.One test series took place in a 110-kV-network, another one in a 20-kV-network anda third one in a 110-kV two-phase network. In these tests the classic algorithm wastested because at the time when the tests were carried out, the improved algorithm wasnot applied with the field tests, but the test data was used later to verify the improvedalgorithm, which is presented in chapter 11.

10.1 Tests in a 110-kV-Network

In January 2006, earth fault field tests were carried out in an Austrian 110-kV-network.The distance between the measurement point and the earth fault location was 4.4 kmcorresponding 0.57+j1.69 Ω. The station, where the measurement were placed, wasconnected through a double system line (see figure 10.1) with the fault point. The zeroimpedance was 1.73+j5.14 Ω. The impedances are measured values.The earth fault was a low ohmic earth fault (direct connection of one phase to ground).

Measurement

Fault point

~~~

Figure 10.1: Earth fault tests in a 110-kV-network


Various tests with different network situations (additional cables see figure 10.1) havebeen carried out. The reason for these tests was to find the influence of different capac-itances and detuning of the coils in the network on the earth fault current at the faultpoint as described in [OAFS06].

Table 10.1: Various field test 110 kV

Nr. Description of network switching states during the tests1 Network with all cables connected, over-compensated 60 A2 Network with one cable disconnected (IE=-53 A); over-compensated 60 A3 Network with all cables connected, over-compensated 140 A4 Network with all cables connected, over-compensated 50 A

The measurements were done using a two step procedure (for replay at any time) (seefigure 6.2):

The first step was to record the data. This was done with an OMICRON CMC 256-6with a sampling rate of 9 kHz.

The second step was to verify the classic algorithm. With the recorded data and thetest system, the distance protection device was tested in the laboratory.

The results from all four experiments are shown in table 10.2. The values are thefault impedances in Ohm calculated by the distance protection device using the classicalgorithm.

Table 10.2: Results of the calculation of the relay of the field test 110 kV

k0=0.68 ∠0

Fault Distance R X km1 4.4 km 0.3 Ω 1.8 Ω 4.72 4.4 km 0.3 Ω 1.6 Ω 4.23 4.4 km 0.1 Ω 1.9 Ω 4.94 4.4 km 0.2 Ω 1.9 Ω 4.9

Compared to the real distance of 4.4 km, the results of the tests with k0=0.68 gave faultdistances between 4.2 and 4.9 km. The relative error is -5% and +11% respectively.

These tests prove the usability of the classic algorithm for compensated 110-kV-networksfor low ohmic earth faults. Even it was a meshed network with decentralized arc sup-pressing coils, the classic algorithm was working very well in case of low ohmic earthfaults.

88



In October 2005 earth fault field tests were carried out in a 20-kV-network. These testswere done to prove the principle usability of the classic algorithm described in chapter5.

To get a secure trigger and for a better function of the algorithm, an additional resistorin parallel to the arc suppressing coil was installed. As the additional resistor a waterresistor was used.

10.2.1 Water Resistor for Test Purpose

A water resistor was chosen because of the costs which lay around 100 Euro and theeasy adjustment of the ohmic value. For the tank a plastic garden tank is used, the twoelectrodes are made of copper.

By using distilled water and adding salt in small amounts the ohmic value could bevaried from 5 kΩ to 5 Ω.For dimensioning the water resistor was simulated by using EleFAnT2D1 [IGT03]

(a) Electrode of the water resistor Ω (b) Simulated electrical field in the water tank

Figure 10.2: Water tank

The results showed possible zones of high electrical field in the area of the upper electrode,but no critical point.

1http://www.igte.tugraz.at/de/elefant/elefant.html

89

http://www.igte.tugraz.at/de/elefant/elefant.html


Figure 10.3: Test setup in the high voltage laboratory

Furthermore, high voltage tests were considered for the use in the test network. Theresistor was tested in the high voltage laboratory at the Institute of High Voltage Engi-neering and System Management 2. The insulation coordination level was tested due tothe recommendations [ABB99].

A measurement system according to IEC 60060-1 was used [IEC94].

The insulation level was tested according to EN 60071-1, table 2 [IEC06]. The standardimpulse withstand voltage tests was tested according to the highest pollution level. Thestandard short-duration power-frequency withstand voltage tests was tested accordingto EN 60071-1, paragraph 6.2 and 6.3.

All tests were successful.

10.2.2 Earth Fault Tests

The actual tests were carried out in a 20-kV-network. The area shown in figure 10.4shows this 20-kV-network where a substation supplies the whole region and is connectedto a 110-kV-line via two star-star-transformers with arc suppressing coils.

The measurement equipment was placed in this substation (named ”Measurement” infigure 10.4). The first fault point (Fault point 1) was 0.8 km apart from the substation,the second fault point (Fault point 2) was 14,7 km far away. The earth faults were low-ohmic earth faults and the substations were connected via a combination of overheadvoltage lines and cables forming a radial network.

The distance between the measurement point and the first earth fault location was0.8 km corresponding 0.2+j0.221 Ω.

The distance between the measurement point and the second earth fault location was14.7 km corresponding 4.42+j4.1 Ω.

2http://www.hspt.tugraz.at/

90

http://www.hspt.tugraz.at/


Table 10.3: Earth fault tests

Station Description of the stationMeasurement Substation 110/20-kVFault point 1 0.8 km, 0.2+j0.221 ΩFault point 1 14.7 km, 4.42+j4.1 Ω

Figure 10.4: Earth fault tests in a 20-kV-network

10.2.2.1 Test Setup

The water resistor was connected in parallel to the arc suppressing coil via a circuitbreaker and put outside the building (see figure 10.5). The resistor was switched onwith this circuit breaker and was only connected for 300ms during the earth fault. Thecircuit breaker of the resistor was trigger by the displacement voltage of the network.

91


Figure 10.5: Experiment setup at the substation

10.2.2.2 Test Procedure

The switching sequence is shown in figure 10.6. After the detection of the earth fault bya displacement voltage relay and a time delay of 200ms the circuit breaker of the waterresistor was closed. 500ms after the entrance of the earth fault, the circuit breaker wasopened. The earth fault was switched off manually after about 1 second. It was usefulthat the resistor was not put in parallel to the arc suppression coil during the wholeearth fault, because enough test data with and without the resistor had been collected.Afterward different test with the distance protection relays were done.

t=0

EF ON

t=200ms

Resistor ON

t=500ms

Resistor OFF

t=1s

EF OFF

Earth fault

Resistor

AUS

AUS

EIN

EIN

(a) Switching sequence

rest of networkrest of network

EFZadd

Zadd

Zcoil

Zcoil

(b) Test circuit

Figure 10.6: Test procedure of the earth fault tests

The tests, which have been carried out, will be described in 10.4.

92


Table 10.4: Various Field-test 20 kV

Test nr. Fault point Description of the system states1 Fault point 1 No load current on the faulty line, no network at the

same transformer, with an additional resistance2 Fault point 1 No load current on the faulty line, no network at the

same transformer, with an additional resistance3 Fault point 1 No load current on the faulty line, small network at the

same transformer (3 MVA load, IC=46A), with an ad-ditional resistance

4 Fault point 1 Load current on the faulty line, small network at thesame transformer (3 MVA load, IC=46A), with an ad-ditional resistance

5 Fault point 1 Load current on the faulty line, small network at thesame transformer (3 MVA load, IC=46A), without anadditional resistance

6 Fault point 2 Load current on the faulty line, small network at thesame transformer (1.5 MVA load, IC=42A), with an ad-ditional resistance

7 Fault point 2 Load current on the faulty line, small network at thesame transformer (1.5 MVA load, IC=42A), without anadditional resistance

8 Fault point 2 Load current on the faulty line, small network at thesame transformer (1.5 MVA load, IC=42A), with an ad-ditional resistance

93


10.2.3 Test Results

Due to the reason that the zero impedance of the line was not known, two differentrealistic k0-factor settings were chosen to test the classic algorithm. The procedure byreplaying the recorded data as described in chapter 6.2 was used to test the algorithm.The results presented in table 10.5 are the calculation results of the distance protectionrelay.

Table 10.5: Results of the calculation of the relay of the field test 20kV by using the classicalgorithm at fault point 1

k0=0.6 ∠ 0 k0=0.8 ∠ 0

Nr Fault Distance R X km ∆ km R X km ∆ km1 0.8 km 0.37 Ω 0.44 Ω 1.59 0.79 0.34 Ω 0.39 Ω 1.41 0.612 0.8 km 0.37 Ω 0.45 Ω 1.62 0.82 0.33 Ω 0.40 Ω 1.44 0.643 0.8 km 0.36 Ω 0.45 Ω 1.62 0.82 0.32 Ω 0.39 Ω 1.41 0.614 0.8 km 0.33 Ω 0.42 Ω 1.52 0.72 0.31 Ω 0.38 Ω 1.37 0.575 0.8 km 0.17 Ω 0.51 Ω 1.84 1.04 0.16 Ω 0.43 Ω 1.55 0.75

Table 10.6: Results of the calculation of the relay of the field test 20kV by using the classicalgorithm at fault point 2

k0=0.6 ∠ 0 k0=0.8 ∠ 0

Nr Fault Distance R X km ∆ km R X km ∆ km6 14.7 km 4.09 Ω 5.72 Ω 20.5 5.80 3.35 Ω 5.18 Ω 18.5 3.807 14.7 km 3.86 Ω 4.36 Ω 15.6 0.90 3.33 Ω 4.07 Ω 14.5 0.208 14.7 km 4.07 Ω 5.71 Ω 20.4 5.70 3.36 Ω 5.22 Ω 18.71 4.01

10.2.4 Discussion of the Results

The tests have shown that the accuracy increases with growing failure distance.An important fact is that with the additional current injection resistor in parallel to thearc suppressing coil the trigger level is higher and more accurate, however, higher accu-racy in distance calculation was not observed. The differences are caused by fault pointtransition impedances and grounding impedances in substations or switching stations.These resistances are not included in the classic algorithm and the influence of theseimpedances increase along higher earth fault currents.

94

10.3 Tests in a Two-Phase 110-kV-Network

10.3 Tests in a Two-Phase 110-kV-Network

The transmission networks of some railway companies in Europe are operated as two-phase 110-kV-networks. It was possible to get data from earth fault tests to evaluatethe classic algorithm for two-phase systems, presented in chapter 9.

The distance to the fault point was 3.33 Ω+j4.96 Ω. The k0 2phase factor was 0.4 ∠ 42.The faults were a low ohmic earth faults.

Table 10.7: Earth fault tests in a two-phase network

k0 2phase = 0.4 ∠ 42

Fault Distance R X1 3.33 Ω+j4.96 Ω 3.86 Ω 4.96 Ω2 3.33 Ω+j4.96 Ω 5.00 Ω 4.60 Ω3 3.33 Ω+j4.96 Ω 3.90 Ω 4.82 Ω4 3.33 Ω+j4.96 Ω 4.61 Ω 5.10 Ω

In table 10.7 the data of the earth faults are presented.It can be seen, that the classic algorithm provides accurate results in case of low ohmicearth faults in a two-phase network.

95

11 Analyses of Earth Fault Tests withthe Improved Algorithm

For evaluating the improved algorithm results from various earth fault tests have beenanalyzed. For the analysis the improved algorithm was applied to the real test data andthe results were observed. The data were recorded from different network operators inAustria.

11.1 Earth Fault Test in a 30-kV Network

In three different 30-kV-networks earth fault tests were carried out. In all 4 networksan additional resistor was put in parallel to the arc suppressing coil. This resistor added600 A neutral current during an earth fault.

• network 1

This network was a network with mainly overhead lines. The fault distance was 12,19 Ω+j6.81 Ω.The capacitive current of this feeder was 11 A.

Table 11.1: Results of earth fault tests in network 1

Nr: Xdistance Xclassic Ximproved RFnom RFcalculated Icap Iadditional

1 6.81 Ω 7.95 Ω 7.49 Ω 40 Ω 52.79 Ω 11 A 600 A2 6.81 Ω 8 Ω 7.45 Ω 60 Ω 65.91 Ω 11 A 600 A3 6.81 Ω 7.95 Ω 6.91 Ω 100 Ω 93.79 Ω 11 A 600 A

• network 2

This network was a network with mainly overhead lines. The fault distance was 5.59 Ω+j4.7 Ω.The capacitive current of this feeder was 30 A.

11 Analyses of Earth Fault Tests with the Improved Algorithm



1 4.7 Ω 4.91 Ω 4.62 Ω 11 Ω 19.53 Ω 30 A 600 A2 4.7 Ω 4.60 Ω 4.50 Ω 11 Ω 16.95 Ω 30 A 600 A3 4.7 Ω 4.94 Ω 4.80 Ω 11 Ω 19.7 Ω 30 A 600 A4 4.7 Ω 4.84 Ω 4.74 Ω 11 Ω 12.21 Ω 30 A 600 A5 4.7 Ω 4.84 Ω 4.76 Ω 11 Ω 12.22 Ω 30 A 600 A6 4.7 Ω 3.86 Ω 3.84 Ω 11 Ω 12.21 Ω 30 A 600 A7 4.7 Ω 5.34 Ω 5.33 Ω 11 Ω 15.44 Ω 30 A 600 A8 4.7 Ω 6.25 Ω 4.73 Ω 100 Ω 62.53 Ω 30 A 600 A9 4.7 Ω 6.47 Ω 5.11 Ω 100 Ω 75.46 Ω 30 A 600 A10 4.7 Ω 6.77 Ω 5.66 Ω 100 Ω 72.43 Ω 30 A 600 A

• network 3




1 0.13 Ω 0.13 Ω 0.13 Ω 0.4 Ω 0.44 Ω 27 A 600 A2 0.13 Ω 0.10 Ω 0.10 Ω 0.4 Ω 0.37 Ω 27 A 600 A3 0.13 Ω 0.68 Ω 0.33 Ω 17 Ω 17.09 Ω 27 A 600 A4 0.13 Ω 1.59 Ω 1.07 Ω 80 Ω 35.39 Ω 27 A 600 A5 0.13 Ω 1.67 Ω 0.40 Ω 80 Ω 39.01 Ω 27 A 600 A

• network 4




1 0.89 Ω 1.03 Ω 1.02 Ω 2 Ω 2.4 Ω 11 A 600 A2 0.89 Ω 1.25 Ω 0.82 Ω 35 Ω 35.05 Ω 11 A 600 A3 0.89 Ω 2.25 Ω 1.19 Ω 100 Ω 67.37 Ω 11 A 600 A

98


The results of the tests in the 30-kV-networks show that the improved algorithm increasesthe accuracy significantly. Especially at high ohmic earth faults the improved algorithmprovides good results.


This network is already described in chapter 10.2. In this chapter the improved algorithmwill be applied to the results and compared to the classic algorithm.

In table 11.5 the results of the earth fault tests at fault point 1 are presented.

Table 11.5: Results of earth fault tests at fault point 1


1 0.221 Ω 0.3 Ω 0.3 Ω 0.9 Ω 0.95 Ω 0.5 A 100 A2 0.221 Ω 0.4 Ω 0.4 Ω 0.9 Ω 0.94 Ω 0.5 A 100 A3 0.221 Ω 0.39 Ω 0.27 Ω 0.9 Ω 0.92 Ω 0.5 A 100 A4 0.221 Ω 0.4 Ω 0.33 Ω 0.9 Ω 1.03 Ω 0.5 A 100 A

In table 11.6 the results of the earth fault tests at fault point 2 are presented.

Table 11.6: Results of earth fault tests at fault point 2


1 4.109 Ω 5.42 Ω 5.07 Ω 2 Ω 14.72 Ω 36 A 100 A2 4.109 Ω 5.39 Ω 4.44 Ω 2 Ω 13.71 Ω 36 A 100 A

The result of the simulation show, that the improved algorithm provides good results incomparison to the classic algorithm.

11.3 Earth Fault Tests in a 10-kV-Network

Tests were carried out in an urban 10-kV-network in Austria. This network is a cablenetwork.

For these tests the water resistance (see chapter 10.2.1) was used to vary the additionalresidual current.

The distance between the measurement point and the fault location was 2 km, corre-sponding 0.236 Ω+j0.178 Ω. The k0 factor was 0.5 ∠-30.

99


Table 11.7: Results of earth fault tests in a 10-kV-network

Nr: Xdistance Xclassic Ximproved Icap Iadditional

1 0.17 Ω 22 Ω 0.8 Ω 8 A 100 A2 0.17 Ω 2.11 Ω 0.4 Ω 8 A 100 A3 0.17 Ω 1.79 Ω 0.4 Ω 8 A 800 A4 0.17 Ω 0.12 Ω 0.1 Ω 8 A 500 A

In table 11.7 it can be seen, that the improved algorithm provides better results thanthe classic algorithm, however, the aberration in a cable network is higher than in anoverhead line network which is according to chapter 8.3.

Another problem in this network is the short fault distance. Even with 800 A additionalcurrent, the voltage in the faulty phase is only 160 V. This level is in the lowest rangeof the voltage measurement system of the relays and causes inaccuracy of the A/Dconverter.

11.4 Earth Fault Tests in a Low Impedance GroundedNetwork

The classic distance location of earth faults in low or solid ohmic grounded network isworking quite well (see chapter 8.1.5) but at high impedance earth faults the classicalgorithm does not work any more.

As presented in chapter 8.4 the improved algorithm can also be used for a more accuratedistance calculation in low impedance grounded networks.

It was also possible to get data from earth fault tests in a low impedance groundednetwork (table 11.8 and table 11.9). In the first table the results of the fault point 1are shown. This point was in a distance of 0.6 Ω. In the second table fault point 2 ispresented which is in a distance of 6.6 Ω.

The fault impedances were not known, but the type of the fault was noticed. Thecalculated fault impedances RF calculated are in the expected range.

100

11.5 Discussion of the Earth Fault Tests

Table 11.8: Results of earth fault tests in a low impedance grounded network at measurementpoint 1


1 0.6 Ω 10.2 Ω 0.63 Ω tree 3823.37 Ω 8 A 300 A2 0.6 Ω 3.22 Ω 0.5 Ω tree 4099.69 Ω 8 A 300 A3 0.6 Ω 2.01 Ω 0.79 Ω wire on earth 120.22 Ω 8 A 300 A4 0.6 Ω 0.73 Ω 0.55 Ω low fault point impedance 19.24 Ω 8 A 300 A5 0.6 Ω 0.35 Ω 0.22 Ω low fault point impedance 14.64 Ω 8 A 300 A6 0.6 Ω 0.2 Ω 0.24 Ω low fault point impedance 70.87 Ω 8 A 300 A

In table 11.9 the fault point 2, which was in a distance of 6.6 Ω is presented.

Table 11.9: Results of earth fault tests in a low impedance grounded network at measurementpoint 2


1 6.6 Ω 6.6 Ω 7.38 Ω low fault point impedance 30.01 Ω 8 A 300 A2 6.6 Ω 5.74 Ω 6.08 Ω low fault point impedance 35.72 Ω 8 A 300 A3 6.6 Ω 6.07 Ω 6.63 Ω low fault point impedance 23.56 Ω 8 A 300 A

The classic distance algorithm gave good results when the fault impedances were lowbut the results were of no use if the fault impedance was too high. Some of the earthfault tests, when the fault impedance was much higher (a fresh tree), did not trigger therelay and no fault data was recorded.

The results show that also in low impedance grounded networks the improved algorithmincreases the accuracy and offers the ability for earth fault distance location at higherohmic earth faults.

11.5 Discussion of the Earth Fault Tests

The tests show that the improved algorithm can be used to detect earth faults in com-pensated as well as in solidly or low ohmic grounded networks. The accuracy for higherohmic earth faults increases along higher additional earth fault currents as well as theaccuracy increases with increased fault distance. Although, there were load distributedalong the line, the improved algorithm provides accurate results.

101


-300,00

-200,00

-100,00

0,00

100,00

200,00

300,00

400,00

500,00

0 1 2 3 4 5 6 7 8

Fault distance in Ohm

Abb

erat

ion

in %

Classic AlgorithmImproved Algorithm

Figure 11.1: Accuracy depending on the fault distance

-200,00

-100,00

0,00

100,00

200,00

300,00

400,00

500,00

0,00 20,00 40,00 60,00 80,00 100,00 120,00 140,00

Transition impedance in Ohm

Abe

rrat

ion

in %

Classic AlgorithmImproved Algorithm

Figure 11.2: Accuracy depending on the fault impedance

Figure 11.1 and 11.2 show the comparison of the classic and the improved algorithm.It can be seen that the accuracy increases with the increase of the fault distance. Theaccuracy, if the improved algorithm is used, is constant in comparison to the classicalgorithm.The accuracy of faults close to the measurement point is widely ranged because smallaberrations in the calculation combined with the short fault distance give high aberra-tions in the fault distance.

102

12 Conclusion

Earth fault compensated networks are a common used technology for operating highand medium voltage grids. These kinds of networks have the advantage that earth faultcurrents are quite small, influence (ohmic, inductive) problems can be minimised anddanger for human body can be reduced. Earth faults cause problems in networks withoverhead line, for example a broken line or trees falling into the line. Due to the rea-son that this network can be operated during an earth fault without interruption forcustomers, the fault point has to be cleared as soon as possible. Therefore earth faultdetection methods are necessary and are being developed.

It is shown that it is possible, in principle, also to locate ground faults in compensatednetworks using the classic distance protection algorithm.The reason for choosing this type of detection algorithm is that it has already beenbuilt into modern distance protection relays. So it would be easy to use this technologyalso for earth fault detection in earth fault compensated networks. An improved versioncould be easily set up on this platform because the measurement technique and logic isalready implemented.Nowadays, this function is deactivated for compensated networks in protection devicesbecause the setting of the trigger level is difficult.For low impedance faults (up to approx. 100 Ω) this algorithm is applicable in lowimpedance or solidly grounded networks as well as in compensated networks.In cable networks it is problematic, since this algorithm neglects the cable capacitancescompletely, which would not be problematic in solidly grounded networks, however, incompensated networks it would lead to large deviations in the computation.

More accurate distance localization can be achieved by the parallel connection of aresistance to the arc suppressing coi., Thereby an additional zero sequence current isadded, which not only increases the accuracy but also the response threshold.

An improvement of the algorithm can be obtained by the inclusion of the fault resistanceand the knowledge of the fault current at fault location. The classic algorithm can beextended and thus its accuracy improvement, also at high impedance ground faults canbe obtained by the estimation of IF and RF .This improvement increases the accuracy of the calculated fault distance significantly.Independent of the variation of the fault impedance, the load factor or the influence ofthe grounding impedance, the improved algorithm gives results with deviations aroundapprox. ±10 %.

12 Conclusion

With distributed loads along the line the detection accuracy decreases, since the current”gets lost”. An idea for the improvement would be the inclusion of the distribution ofload to reach better results; additional data must be deposited in the relay.In networks with various branches it can be difficult to detect the fault location becausethere is no explicit solution. But this problem does not only exist in case of an earthfault but also in case of a short circuit. This problem can be solved by using globalinformation systems (GIS) to detect the fault location and reliability methods to findthe possible fault point.

Earth fault tests proved the usability and obtained good results even with high impedanceground faults.Attempts in solidly grounded networks also showed, particularly in the case of highimpedance fault that, the improved algorithm also in these networks gives a relativelyexact result.

Further research is necessary regarding:

• kE-factor

The knowledge of this factor is little, however, it is essential for a precise faultlocation to know the value of the earth return path factor. The only and exactway to get this value is to measure it [KF07] [AOF+07].

Further research is necessary regarding the variation of the factor k0 over the yearand the influence of weather and environment.

• Use of higher harmonics

During an earth fault higher harmonics can be very dominant [Obk08]. Investi-gations are necessary, if higher harmonics can provide additional informations forthe earth fault distance calculation.

• Influence of the distributed loads

As shown in chapter 7.3, the influence of distributed loads have to be taken intoaccount because theses loads lead to a too short value of the fault impedance.Including theses distribution in the algorithm can increase the accuracy of thefault estimation.

• Influence of distributed capacitances

In cable networks the line-to-earth capacitances are 10 to 20 times higher than innetworks with overhead lines [FMR+05]. These distributed capacitances can leadto miscalculations [Ebe04]. Additional simulations are necessary to identify theinfluence of these capacitances on the distance algorithm.

• Practical implementation

To get real measurement and experience, this kind of distance protection relaysshould be installed as additional devices. With these relays not only tests about

104

the usability of the algorithm under different conditions could be done but also theimplementation in the control system can be tested.

The goal is that relays which are already on the market are used and that theextended algorithm is included to get much better and exactly results.

105

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[OVE76] OVE ; OVE (Hrsg.): Beeinflussung von Fernmeldeanlagen durch Wechsel-stromanlagen mit Nennspannungen uber 1kV. Vienna, Austria: OVE, 1976.– Fachausschuss B ”Beeinflussungsfragen”

[Wan36] Wanger, Willi: Symmetrische Komponenten fur Mehrphasensysteme. In:Archiv der Elektrotechnik 29 (1936), Nr. 10, S. 683–688

[War68] Warrington, Albert R.: Protective Relays, Their Theory and Practise.Bd. 1. London : Chapman & Hall Ltd., 1968. – ISBN 0–412–09060–0

[WG098] WG03, CIRED Working G.: Fault Management in Electrical DistributionSystems / CIRED. 1998. – Forschungsbericht. – Final report

[Wil36] Willheim, R. ; Springer (Hrsg.): Das Erdschlußproblem in Hochspan-nungsnetzen. Berlin, Germany : Julius Springer, 1936

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http://homepage.hispeed.ch/proleitec/

A Simulation Environment

In chapter 4 the simulation model, which is mainly used, is presented. In this appendixthe detailed description is explained.

The detailed test data is presented in table A.1.

Table A.1: List of the values of the elements in the simulation

SourceUSource 20000 VYn j1.375 Ω

TransformerZ1 j0.96 ΩZ2 j0.96 ΩZ0 j0.96 Ω

Line parameters per km

Z1 0.306+j0.355 ΩZ2 0.306+j0.355 ΩZ0 1.071+j1.2425 ΩC1 10 nFC2 10 nFC0 6 nF

Line lengthline 1 10 kmline 2 5 kmline 3 5 km

Arc suppressing coilZpet j142 ΩPlosses 100 kW

Additional resistor Rwater 100 Ω

Rest of the network

C1 4.4 µFC2 4.4 µFC0 7.4 µFZ1 40 ΩZ2 40 Ω

Grounding impedance ZE 0.5+j0.5 Ω

In figure A.1 the detailed simulation model in symmetrical components is presented.


ZTR

2Zline1

2Zline3

2

Zload

2

U2

p

ZTR

0Zline1

0Zline3

0

U0

p3Zadd

ZTR

1Zline1

1Zline3

1

Zload

1

UP

1

3ZE

C /2line1

1C /2line1

1C /2line3

1C /2line3

1

C /2line1

2C /2line1

2C /2line3

2C /2line3

2

C /2line1

0C /2line1

0C /2line3

0C /2line3

0

IP1

I2

P

I0

P

3Zpet

Zline2

2

Zline2

0

Zline2

1

C /2line2

1C /2line2

1

C /2line2

2C /2line2

2

C /2line2

0C /2line2

0

UF

2

3ZF

UF

0

UF

1

IF0

UF

ILoad

1

I2

Load

I0

LoadI

0

TR

Unet

1


negative sequence system


station rest of thenetwork

fault line3 + load

Cnet

1 Znet

1

Cnet

2 Znet

2

Cnet

0

line2line1

Figure A.1: Simulations model in symmetrical components

In figure A.2 the detailed model is presented, which is used for building up the matrices(see matrix A.2) of the simulation environment.

116

Figure A.2: Simulations model in symmetrical components

In the following table the elements of the simulation model are described.

Table A.2: List of the elements in the simulation

Nr. Element Nr. Element Nr. Element Nr. Element1 Yn 11 ω · C7 21 Y2 31 ω · C9

2 ω · C1net + Y 1

net 12 Y8 22 Y3 32 ω · C10

3 ω · C1 13 Y 2load 23 Y4 33 ω · C11

4 ω · C2 14 1Zpd+Z9

24 ω · C3 34 13ZF+3ZE2

5 ω · C4 15 Ymess 25 ω · C2net + Y 2

net

6 Y 1load 16 Y10 26 ω · C5

7 Y5 17 Y11 27 ω · C6

8 Ymess 18 1ω·C12+Z12

28 ω · C8

9 Y6 19 Y 1 29 ω · C0net

10 Y7 20 Ymess 30 1ZE

Matrix A.1 is the element matrix. In this matrix all elements are number with 1 to 34.Only the main diagonal is used, the rest of the matrix is zero.

117


Y =

1 0 0 0 0 · · · · · · · · · 0 0 0 0 00 2 0 0 0 · · · · · · · · · 0 0 0 0 00 0 3 0 0 · · · · · · · · · 0 0 0 0 00 0 0 4 0 · · · · · · · · · 0 0 0 0 00 0 0 0 5 · · · · · · · · · 0 0 0 0 0...

......

......

. . ....

......

......

......

......

.... . .

......

......

......

......

......

. . ....

......

......

0 0 0 0 0 · · · · · · · · · 30 0 0 0 00 0 0 0 0 · · · · · · · · · 0 31 0 0 00 0 0 0 0 · · · · · · · · · 0 0 32 0 00 0 0 0 0 · · · · · · · · · 0 0 0 33 00 0 0 0 0 · · · · · · · · · 0 0 0 0 34

(A.1)

Matrix A.2 is the description of the network as a tree-incidence matrix.

C =

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1−1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0−1 −1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0−1 −1 −1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0−1 −1 −1 −1 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0−1 −1 −1 −1 −1 −1 0 0 0 −1 1 1 0 0 0 0 0 00 0 0 0 0 0 1 −1 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 1 −1 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 1 −1 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 1 −1 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 1 −1 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 1 −1 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 −1 00 0 0 0 0 0 0 0 0 −1 1 1 0 0 0 0 1 −10 0 0 0 0 0 0 0 0 −1 1 1 0 0 0 0 0 0

(A.2)

118

The voltage source is element 1 and therefore in the voltage vector as position 1, therest is 0, because no other sources are in the model.

U0 =[Usource 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

](A.3)

In the following the algorithm, which is used for the network simulation is presented[Muc78].

Z = inv(Y ) (A.4)

Z [] = CT · Z · C (A.5)

U[]0 = CT · U0 (A.6)

I [] = inv(Z []) ∗ U []0 (A.7)

I = C · I [] (A.8)

U = U0 − Z · I (A.9)

a = e2i·π

3 (A.10)

T =

1 1 11 a2 a1 a a2

(A.11)

The voltages Usym are taken at the elements 14(zero sequence system), 2(positive se-quence system) and 25(negative sequence system). The current Isymis measured atthe elements 15(zero sequence system), 20(positive sequence system) and 8(negativesequence system).

U = T · Usym and I = T · Isym

119

B Simulation Environment Two-PhaseNetwork

In chapter 4.2 the simulation model, which is used for the simulation of the two-phasenetwork, is presented. In this appendix the detailed description is explained.

The detailed test data is presented in table B.1.

Table B.1: List of the values of the elements in the simulation

SourceUSource 110000 VYn j1.375 Ω

Equivalent networkimpedance

Z1 j12 ΩZ0 j12 Ω

Line parameters per km

Z1 0.12+j0.13 ΩZ0 0.16+j0.37 ΩC1 2.2 nFC0 2.2 nF

Line lengthline 1 20 kmline 2 20 kmline 3 20 km

Arc suppressing coilZpet 0.1 Ω+j109 ΩPlosses 100 kW

Additional resistor Rwater 400 Ω

Rest of the networkC1 43 µFC0 43 µFZ1 121 Ω

Grounding impedance ZE 0.5+j0.5 Ω

In figure B.1 the detailed simulation model in symmetrical components is presented.

B Simulation Environment Two-Phase Network

ZTR

0Zline1

0Zline3

0

U0

p2Zadd

ZTR

1Zline1

1Zline3

1

Zload

1

UP

1

2ZE

C /2line1

1C /2line1

1C /2line3

1C /2line3

1

C /2line1

0C /2line1

0C /2line3

0C /2line3

0

IP1

I0

P

2Zpet

Zline2

0

Zline2

1

C /2line2

1C /2line2

1

C /2line2

0C /2line2

0

2ZF

UF

0

UF

1

IF0

UF

ILoad

1

I0

LoadI

0

TR

Unet

1



station rest of the

network

fault line3 + load

Cnet

1 Znet

1

Cnet

0

line2line1

Figure B.1: Simulations model in symmetrical components

In figure B.2 the detailed model is presented, which is used for building up the matrices(see matrix B.2) of the simulation environment.

Figure B.2: Simulations model in symmetrical components

In the following table the elements of the simulation model are described.

122

Table B.2: List of the elements in the simulation

Nr. Element Nr. Element Nr. Element Nr. Element1 Yn 7 1

Zpd+Z913 Y1 19 1

2ZE1

2 ω · C1net + Y 1

net 8 Ymess 14 Ymess 20 ω · Cnet3 ω · C1 9 Y10 15 Y2 21 ω · C9

4 ω · C2 10 Y11 16 Y3 22 ω · C10

5 ω · C4 11 1ω·C12+Z12

17 Y4 23 ω · C11

6 Y 1load 12 1

2ZF+2ZE218 ω · C3

Matrix B.1 is the element matrix. In this matrix all elements are number with 1 to 23.Only the main diagonal is used, the rest of the matrix is zero.

Y =

1 0 0 0 0 · · · · · · · · · 0 0 0 0 00 2 0 0 0 · · · · · · · · · 0 0 0 0 00 0 3 0 0 · · · · · · · · · 0 0 0 0 00 0 0 4 0 · · · · · · · · · 0 0 0 0 00 0 0 0 5 · · · · · · · · · 0 0 0 0 0...

......

......

. . ....

......

......

......

......

.... . .

......

......

......

......

......

. . ....

......

......

0 0 0 0 0 · · · · · · · · · 19 0 0 0 00 0 0 0 0 · · · · · · · · · 0 20 0 0 00 0 0 0 0 · · · · · · · · · 0 0 21 0 00 0 0 0 0 · · · · · · · · · 0 0 0 22 00 0 0 0 0 · · · · · · · · · 0 0 0 0 23

(B.1)

Matrix B.2 is the description of the network as a tree-incidence matrix.

123

B Simulation Environment Two-Phase Network

C =

1 0 0 0 0 0 0 0 0 0 0 00 1 0 0 0 0 0 0 0 0 0 00 0 1 0 0 0 0 0 0 0 0 00 0 0 1 0 0 0 0 0 0 0 00 0 0 0 1 0 0 0 0 0 0 00 0 0 0 0 1 0 0 0 0 0 00 0 0 0 0 0 1 0 0 0 0 00 0 0 0 0 0 0 1 0 0 0 00 0 0 0 0 0 0 0 1 0 0 00 0 0 0 0 0 0 0 0 1 0 00 0 0 0 0 0 0 0 0 0 1 00 0 0 0 0 0 0 0 0 0 0 1−1 0 0 0 0 0 0 0 0 0 0 0−1 −1 0 0 0 0 0 0 0 0 0 0−1 −1 −1 0 0 0 0 0 0 0 0 0−1 −1 −1 −1 0 0 0 0 0 0 0 00 0 0 0 1 1 0 0 0 0 0 0−1 −1 −1 −1 −1 −1 0 0 0 0 0 10 0 0 0 0 0 1 0 0 0 0 00 0 0 0 0 0 1 −1 0 0 0 00 0 0 0 0 0 0 1 −1 0 0 00 0 0 0 0 0 0 0 1 −1 0 00 0 0 0 0 0 0 0 0 1 −1 1

(B.2)

The voltage source is element 1 and therefore in the voltage vector as position 1, therest is 0, because no other sources are in the model.

U0 =[Usource 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

](B.3)

In the following the algorithm, which is used for the network simulation is presented[Muc78].

Z = inv(Y ) (B.4)

Z [] = CT · Z · C (B.5)

U[]0 = CT · U0 (B.6)

I [] = inv(Z []) ∗ U []0 (B.7)

I = C · I [] (B.8)

U = U0 − Z · I (B.9)

124

T =

[1 11 1

](B.10)

The voltages Usym are taken at the elements 7(zero sequence system) and 2(positivesequence system). The current Isymis measured at the elements 8(zero sequence system)and 14(positive sequence system).

U = T · Usym and I = T · Isym

125

C Comparison of the Classic andImproved Algorithm

In this chapter are the complete simulation results of chapter 8.

C.1 Simulation of Different Percentages ofCable/Overhead Lines

As described in chapter 8.3.1 the percentage of the cable/overhead lines is changed andthe usability of the improved algorithm is investigated. In the following sections the fullset of the simulations are presented.

C.1.1 Overhead Line Network

In these simulations a pure cable network is investigated.


Figure C.1: Middle ohmic grounded overhead line network

C Comparison of the Classic and Improved Algorithm


Figure C.2: Solidly grounded overhead line network

C.1.2 Cable Network

In these simulations a pure cable network is investigated.


Figure C.3: Middle ohmic grounded cable network

128

C.1 Simulation of Different Percentages of Cable/Overhead Lines


Figure C.4: Solidly grounded cable network

C.1.3 Mixed Network, Cable at Beginning of the Feeder

These figures show the result of the improved distance algorithm in a mixed (cables andoverhead lines) network, where the cables are located between the substation and thefault.


Figure C.5: Middle ohmic grounded mixed network

129



Figure C.6: Solidly grounded mixed network

C.1.4 Mixed Network, Cable at the End of the Feeder

These figures show the result of the improved distance algorithm in a mixed (cables andoverhead lines) network, where the overhead line are located between the substation andthe fault.


Figure C.7: Middle ohmic grounded mixed network

130

C.1 Simulation of Different Percentages of Cable/Overhead Lines


Figure C.8: Solidly grounded mixed network

131


C.2 Simulation of a Network with Distributed Loads

In this chapter is the full set of simulation results from chapter 7.3. Different networktypes are simulated and presented in the next pages.

C.2.1 Compensated Network

In this simulation a compensated network is assumed. It can be seen that the improvedalgorithm is more accurate than the classic algorithm.

Distance calculation with classic algorithm(see equation (6.1))

0 100 200 300 400 500 600 700 800 900 1000

0

50

100

150

200

250

300


Cal

cula

ted

dist

ance

in %

of t

he n

omin

al d

ista

nce


Figure C.9: Aberration of distancecalculation with classic algorithm

0 100 200 300 400 500 600 700 800 900 10000

5

10

15

20

25

30


Cal

cula

ted

dist

ance

in k

m


Figure C.10: Distance calculationwith classic algorithm

Distance calculation with improvedalgorithm (see equation (7.9))

0 100 200 300 400 500 600 700 800 900 10000

20

40

60

80

100

120


Cal

cula

ted

dist

ance

in %

of t

he n

omin

al d

ista

nce


Figure C.11: Aberration of dis-tance calculation with improvedalgorithm

0 100 200 300 400 500 600 700 800 900 10000

5

10

15

20

25

30


Cal

cula

ted

dist

ance

in k

m


Figure C.12: Distance calculationwith improved algorithm

Figure C.10 and C.12 show that the the influence of the loads along the line leads to atoo short calculated distance. The reason for this is that the current at the measuringpoint is too high in relation to the voltage at the measuring point.

132

C.2 Simulation of a Network with Distributed Loads

C.2.2 Solidly Grounded Network

This section shows the result of the two algorithms in a solidly grounded network.


0 100 200 300 400 500 600 700 800 900 1000

0

50

100

150

200

250

300


Cal

cula

ted

dist

ance

in %

of t

he n

omin

al d

ista

nce


Figure C.13: Aberration of dis-tance calculation with classicalgorithm

0 100 200 300 400 500 600 700 800 900 10000

5

10

15

20

25

30


Cal

cula

ted

dist

ance

in k

m




0 100 200 300 400 500 600 700 800 900 10000

20

40

60

80

100

120


Cal

cula

ted

dist

ance

in %

of t

he n

omin

al d

ista

nce



0 100 200 300 400 500 600 700 800 900 10000

5

10

15

20

25

30


Cal

cula

ted

dist

ance

in k

m



The results in a solidly grounded network show that the common algorithm can be used.It will not measure with that accuracy than the improved algorithm. The calculatedfault distance is always lower than fault distance (which is according to experiencesin real networks). The improved algorithm is more accurate, however it has the sameproblem with distributed loads as in the compensated network.

133


C.2.3 Middle Ohmic Grounded Network

Middle ohmic network are presented as a possibility for future network enhancement [?].Therefore this network type is simulated and the results are presented in the followingfigures.


0 100 200 300 400 500 600 700 800 900 1000

0

50

100

150

200

250

300


Cal

cula

ted

dist

ance

in %

of t

he n

omin

al d

ista

nce


Figure C.17: Aberration of dis-tance calculation with classicalgorithm

0 100 200 300 400 500 600 700 800 900 10000

5

10

15

20

25

30


Cal

cula

ted

dist

ance

in k

m




0 100 200 300 400 500 600 700 800 900 10000

20

40

60

80

100

120


Cal

cula

ted

dist

ance

in %

of t

he n

omin

al d

ista

nce



0 100 200 300 400 500 600 700 800 900 10000

5

10

15

20

25

30


Cal

cula

ted

dist

ance

in k

m



The result is very similar to the solidly grounded network. The accuracy of the commonalgorithm is worse. The measured distance will always decrease higher fault impedances.The improved algorithm is more accurate, however the calculated distances are smallerthan the real fault distance.

134

earth fault distance protection (documento)

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