Insulation Measurement and Supervision in Live AC and DC Unearthed Systems

Lecture Notes in Electrical Engineering 314

Piotr Olszowiec

Insulation Measurement and Supervision in Live AC and DC Unearthed Systems Second Edition

Lecture Notes in Electrical Engineering

For further volumes: http://www.springer.com/series/7818

Volume 314

Board of Series Editors

Leopoldo Angrisani, Napoli, ItalyMarco Arteaga, Coyoacán, MéxicoSamarjit Chakraborty, München, GermanyJiming Chen, Hangzhou, P.R. China Tan Kay Chen, Singapore, SingaporeRüdiger Dillmann, Karlsruhe, GermanyGianluigi Ferrari, Parma, ItalyManuel Ferre, Madrid, SpainSandra Hirche, München, GermanyFaryar Jabbari, Irvine, USAJanusz Kacprzyk, Warsaw, PolandAlaa Khamis, New Cairo City, EgyptTorsten Kroeger, Stanford, USATan Cher Ming, Singapore, SingaporeWolfgang Minker, Ulm, GermanyPradeep Misra, Dayton, USASebastian Möller, Berlin, GermanySubhas Mukhopadyay, Palmerston, New ZealandCun-Zheng Ning, Tempe, USAToyoaki Nishida, Sakyo-ku, JapanFederica Pascucci, Roma, ItalyTariq Samad, Minneapolis, USAGan Woon Seng, Nanyang Avenue, SingaporeGermano Veiga, Porto, PortugalJunjie James Zhang, Charlotte, USA

http://www.springer.com/series/7818

About this Series

“Lecture Notes in Electrical Engineering (LNEE)” is a book series which reports the latest research and developments in Electrical Engineering, namely:

• Communication, Networks, and Information Theory• Computer Engineering• Signal, Image, Speech and Information Processing• Circuits and Systems• Bioengineering

LNEE publishes authored monographs and contributed volumes which present cutting edge research information as well as new perspectives on classical fields, while maintaining Springer’s high standards of academic excellence. Also considered for publication are lecture materials, proceedings, and other related materials of exceptionally high quality and interest. The subject matter should be original and timely, reporting the latest research and developments in all areas of electrical engineering.

The audience for the books in LNEE consists of advanced level students, researchers, and industry professionals working at the forefront of their fields. Much like Springer’s other Lecture Notes series, LNEE will be distributed through Springer’s print and electronic publishing channels.

Piotr Olszowiec

1 3

Insulation Measurement and Supervision in Live AC and DC Unearthed Systems

Second Edition

Piotr OlszowiecElpoautomatyka Polaniec Staszow Poland

Library of Congress Control Number: 2014939050

1st edition: © Springer-Verlag Berlin Heidelberg 2013

© Springer International Publishing Switzerland 2014This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law.The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein.

Printed on acid-free paper

Springer is part of Springer Science+Business Media (www.springer.com)

ISSN 1876-1100 ISSN 1876-1119 (electronic)ISBN 978-3-319-07009-4 ISBN 978-3-319-07010-0 (eBook)DOI 10.1007/978-3-319-07010-0Springer Cham Heidelberg New York Dordrecht London

v

Low voltage unearthed AC and DC networks have been for long commonly applied for supply of power and control circuits in industry, transportation, medical objects, etc. The main reasons for their use are high reliability and numerous advantages offered by isolating the networks against ground.

Similar to other electrical systems, also in unearthed (IT) networks insulation level, is a decisive factor for operational reliability and safety. Electrical networks insulation fulfills the following main functions:

• establishing path for current flow,• elimination of various hazards including electric shock and fire risks.

The basic technical parameter determining condition and quality of electrical insulation is its resistance. Insufficient level of this parameter can cause various disturbances. According to statistic data ground faults are the most frequent type of failures in AC and DC networks. Other common defects include line-to-line faults, breaks (broken wires), voltage loss, or its abnormal deflections. Ground faults in IT systems do not make networks operation impossible, however, they may cause severe problems with their safe functioning. Therefore, special atten-tion should be paid to these abnormal conditions, possible threats created by them, and ways for their detection and elimination.

It has been proved that many insulation breakdown cases do not happen suddenly but are the final stage of a long degradation process. This fact is a strong argument for conducting continuous supervision over insulation condition to ensure timely detection of possible problems. The main causes of electrical insulation deterioration are aging, mechanical and thermal stresses, overvoltages, humidity, chemical factors, oil, radiation, etc. Continuous monitoring is an indispensable tool for preventive maintenance, which allows to avoid possible faults caused by insula-tion condition deterioration. Information about current insulation level helps users to achieve high reliability and safety of electrical systems.

AC and DC IT systems, as isolated against ground under normal operation, allow—in distinction from TN and TT systems—to fulfill continuous insula-tion monitoring. As a result, substantial qualities offered by these systems can be

Preface

Prefacevi

exploited. Compared to TN and TT systems, electrical unearthed networks are featured by:

1. high safety and reliability of operation, namely

• insulation-to-ground monitoring is possible only in networks isolated against ground,

•networks can operate with a single ground fault,• it is possible to conduct preventive maintenance due to on-line insulation

monitoring in live network,• insulation breakdowns can be detected without delay,• insulation monitoring can be fulfilled both in live and in de-energized

networks,

2. smaller fire and explosion hazards,3. lower shock currents and touch voltages,4. higher permissible resistance of devices protective earthing.

Utilization of these advantages is dependent on conducting correct insulation monitoring. Importance of electrical networks insulation monitoring has been known for long, but only rapid development of electronic and microprocessor technologies has led to implementation of sophisticated methods and systems. However, for their proper application adequate knowledge of electrical systems operation is indispensable. Therefore, in this book there are described most impor-tant issues concerning normal operation and ground fault phenomena occurring there. Theoretical basis of these subjects is delivered in concise form. Numerous methods of insulation parameters measurement in live circuits are presented. Few other procedures of the parameters determination based on measurement and cal-culation are explained. Some of them were proposed by the author. Practically all formulas are derived. For the text understanding merely a basic knowledge of electrical circuits theory is required. Overview of selected insulation measurement devices as well as fault locating systems is included. This book is addressed to electrical engineers, technicians, and students of this specialty. The author hopes that its extended second edition will supplement scant information about the sub-ject available in existing publications.

vii

Part I AC IT Systems

1 General Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.1 AC IT Systems Circuit Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Phase-to-Ground Voltages Determination in AC IT Systems . . . . . . . 4

1.2.1 Single-Phase Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2.2 Three-Phase Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.3 Ground Fault and Leakage Currents Calculation . . . . . . . . . . . . . . . . 81.3.1 Single-Phase Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.3.2 Three-Phase Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2 Ground Insulation Measurement in AC IT Systems . . . . . . . . . . . . . . . 152.1 General Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.1.1 Spatial Distribution of Insulation Resistance: Network’s Insulation Equivalent Circuit . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.2 Insulation Parameters Determination in Single-Phase Networks . . . . 162.2.1 De-energized Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.2.2 Live Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.3 Insulation Parameters Determination in Live Three-Phase Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.3.1 Insulation Equivalent Resistance and Capacitance

Values Determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.3.2 Insulation Resistance and Capacitance Determination

for Single Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.4 Unconventional Measurement Methods . . . . . . . . . . . . . . . . . . . . . . . 29

2.4.1 Periodical Measurement of Insulation Parameters . . . . . . . . . 292.4.2 Devices and Systems for Ground Fault, Earth Leakage

and Shock Currents Measurement . . . . . . . . . . . . . . . . . . . . . 322.5 Influence of Insulation Parameters on Possible Ground Fault,

Electric Shock and Ground Leakage Currents Levels . . . . . . . . . . . . 352.5.1 Assessment of Ground Fault and Ground

Leakage Currents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352.5.2 Assessment of Power Losses in Insulation . . . . . . . . . . . . . . . 36

Contents

http://dx.doi.org/10.1007/978-3-319-07010-0_1

http://dx.doi.org/10.1007/978-3-319-07010-0_1#Sec1







http://dx.doi.org/10.1007/978-3-319-07010-0_2






















Contentsviii

2.5.3 Electric Shock Hazard Assessment . . . . . . . . . . . . . . . . . . . . 372.6 Ground Fault Current Compensation . . . . . . . . . . . . . . . . . . . . . . . . . 38References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

3 Insulation Monitoring Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433.1 Visual Signalization Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433.2 Other Systems of Continuous Insulation Monitoring . . . . . . . . . . . . 45

3.2.1 Phase Voltages Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . 453.2.2 Zero-Sequence Voltage Component Monitoring . . . . . . . . . . 463.2.3 Residual Current Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . 483.2.4 Underimpedance System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4 Systems of Insulation Resistance Continuous Measurement . . . . . . . . 574.1 Measurement Circuits with Test Direct Current . . . . . . . . . . . . . . . . . 574.2 Measuring Circuits with Diode Rectifier . . . . . . . . . . . . . . . . . . . . . . 58

4.2.1 Star Connected Diode Rectifier . . . . . . . . . . . . . . . . . . . . . . . 584.2.2 Diode Bridge Rectifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 624.2.3 Other Rectifier Based Measuring Circuits . . . . . . . . . . . . . . . 64

4.3 Measurement Method with an Auxiliary Rectangular Voltage Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 674.3.1 Examples of Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

4.4 Measurement with Use of Auxiliary AC Voltage . . . . . . . . . . . . . . . . 694.4.1 Application Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

Part II DC IT Systems

5 Equivalent Circuit Diagrams of DC Networks . . . . . . . . . . . . . . . . . . . . 755.1 DC Network Simplified Circuit Diagram . . . . . . . . . . . . . . . . . . . . . . 755.2 Equivalent Circuit Diagrams of Batteries . . . . . . . . . . . . . . . . . . . . . . 77Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

6 Insulation Resistance Measurement Methods . . . . . . . . . . . . . . . . . . . . 836.1 Traditional Methods of Periodical Measurement of Insulation

Resistance in Live Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 836.2 Other Analytical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 866.3 Unconventional Methods of Insulation Resistance Measurement . . . 876.4 Evaluation of Errors of Analytical Methods . . . . . . . . . . . . . . . . . . . . 90

7 Devices and Systems for Insulation Deterioration Alarming . . . . . . . . 937.1 Visual Signaling of Insulation Resistance Level . . . . . . . . . . . . . . . . 937.2 Simple Systems of Continuous Insulation Monitoring . . . . . . . . . . . 94Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98



http://dx.doi.org/10.1007/978-3-319-07010-0_2#Bib1

http://dx.doi.org/10.1007/978-3-319-07010-0_3







http://dx.doi.org/10.1007/978-3-319-07010-0_4












http://dx.doi.org/10.1007/978-3-319-07010-0_5




http://dx.doi.org/10.1007/978-3-319-07010-0_6






http://dx.doi.org/10.1007/978-3-319-07010-0_7




Contents ix

8 Modern Methods of Continuous Insulation Measurement . . . . . . . . 998.1 Measurements with Superimposed AC Test Voltage . . . . . . . . . . . 998.2 Commutation Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

8.2.1 Example of Application . . . . . . . . . . . . . . . . . . . . . . . . . . 1018.2.2 Determination of Insulation Equivalent Resistance

of DC Network and Its Single Lines . . . . . . . . . . . . . . . . 1028.2.3 Example of Application . . . . . . . . . . . . . . . . . . . . . . . . . . 104

8.3 “Pulse” Test Voltage Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1058.3.1 An Example of Application . . . . . . . . . . . . . . . . . . . . . . . 106

8.4 Unconventional Methods of Insulation Resistance Monitoring . . . 1088.4.1 Insulation Supervision with Insulation Leakage

Resistance Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1088.4.2 Method of Auxiliary Voltage “Triangle” Pulses . . . . . . . . 1098.4.3 System of Automatic Insulation-to-Ground

Capacitance Compensation . . . . . . . . . . . . . . . . . . . . . . . 109References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

9 Ground Fault, Leakage and Electric Shock Currents in DC IT Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1139.1 Time Function of Ground Fault Current . . . . . . . . . . . . . . . . . . . . 1139.2 Measurements of Maximum and Steady-State Magnitudes

of Earth Fault Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1159.3 Earth Leakage Currents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

9.3.1 Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1189.3.2 Electric Shock Hazard Assessment . . . . . . . . . . . . . . . . . 120

9.4 Leakage Current Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . 1229.4.1 Periodic Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . 1229.4.2 Continuous Measurements . . . . . . . . . . . . . . . . . . . . . . . . 123

9.5 Earth Fault and Shock Currents Measurement . . . . . . . . . . . . . . . . 1249.5.1 Earth Fault and Shock Currents Measurements

in Network Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1249.5.2 Earth Fault and Shock Currents Measurements

in Live Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1259.6 Network-to-Ground Capacitance Determination . . . . . . . . . . . . . . 126References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

Part III AC and DC IT Systems

10 Effects of Insulation Failures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13110.1 Reasons of Insulation Failures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13110.2 Effects of Network Insulation Failures . . . . . . . . . . . . . . . . . . . . . 13210.3 Misoperation of Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13310.4 Prevention of Devices Misoperation . . . . . . . . . . . . . . . . . . . . . . . 139

10.4.1 Device Coil Shunted by Resistor . . . . . . . . . . . . . . . . . . . 139

http://dx.doi.org/10.1007/978-3-319-07010-0_8
















http://dx.doi.org/10.1007/978-3-319-07010-0_9

http://dx.doi.org/10.1007/978-3-319-07010-0_9

















http://dx.doi.org/10.1007/978-3-319-07010-0_10






Contentsx

10.4.2 Device Coil Shunted by Other Elements . . . . . . . . . . . . . 14010.4.3 Disconnection of Both Terminals of Device Coil . . . . . . 14110.4.4 Coil Shorting by NC Contact . . . . . . . . . . . . . . . . . . . . . . 14110.4.5 Limitation of Total Conductor-to-Conductor

and Conductor-to-Ground Capacitances . . . . . . . . . . . . . 14210.4.6 Insulation Resistance Control by Grounding

Through Resistors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143Reference. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

11 Insulation Monitors Settings Selection. . . . . . . . . . . . . . . . . . . . . . . . . 14511.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14511.2 Regulations Requirements for DC Systems . . . . . . . . . . . . . . . . . . 14611.3 Modified Approach for DC IT Networks . . . . . . . . . . . . . . . . . . . . 147

11.3.1 Shock and Fire Hazard Assessment . . . . . . . . . . . . . . . . . 14711.3.2 Misoperation of Devices in DC Circuits . . . . . . . . . . . . . 14811.3.3 Examples of Practical Checking of Insulation

Condition Assessment Criteria . . . . . . . . . . . . . . . . . . . . . 15011.3.4 Graphical Illustration of Insulation Conditions

in DC IT Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15211.4 AC Insulation Monitors Settings Selection . . . . . . . . . . . . . . . . . . 153

11.4.1 Simplified Approach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15311.4.2 Electric Shock and Fire Hazard Assessment . . . . . . . . . . 15411.4.3 Misoperation Risk for Devices in AC IT Auxiliary

Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15611.4.4 Insulation Monitors Application for Devices

Misoperation Risk Detection . . . . . . . . . . . . . . . . . . . . . . 157References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

12 AC/DC IT Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15912.1 Conductor-to-Ground Voltages . . . . . . . . . . . . . . . . . . . . . . . . . . . 15912.2 Earth Fault and Leakage Currents . . . . . . . . . . . . . . . . . . . . . . . . . 16112.3 Misoperation of Devices in “Mixed” Systems . . . . . . . . . . . . . . . . 16312.4 Insulation Resistance Measurement in AC/DC IT Systems . . . . . . 166

12.4.1 Method of “Three Readings of a Voltmeter” . . . . . . . . . . 16612.4.2 Utilization of Mean Value of Phase Voltage . . . . . . . . . . . 16712.4.3 Pulse Voltage Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17012.4.4 Auxiliary AC Voltage Method . . . . . . . . . . . . . . . . . . . . . 170

12.5 Insulation Resistance Measurement in IT Systems with Frequency Converters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172

13 Earth Fault Location in IT AC/DC Systems . . . . . . . . . . . . . . . . . . . . 17313.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17313.2 Test Current Measurement in Fault Locating Systems . . . . . . . . . 17513.3 Traditional Earth Fault Location Systems . . . . . . . . . . . . . . . . . . . 176









http://dx.doi.org/10.1007/978-3-319-07010-0_11


















http://dx.doi.org/10.1007/978-3-319-07010-0_12












http://dx.doi.org/10.1007/978-3-319-07010-0_13




Contents xi

13.4 Modern Insulation Fault Location Systems . . . . . . . . . . . . . . . . . . 17713.4.1 Pulse Voltage Test Signal: EDS470 (Bender) . . . . . . . . . 17713.4.2 Sinusoidal Test Current: Vigilohm (Schneider) . . . . . . . . 17813.4.3 Saw-Like Test Voltage Pulses: IPI-1M (Elterm) . . . . . . . 17813.4.4 Periodical Current Pulses: AT-3000 (Amprobe) . . . . . . . . 179

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180







Part IAC IT Systems

3

Abstract In the chapter there is presented general information on AC IT low voltage systems. Graphical and analytical methods of phase-to-ground voltages determination are described. There are also discussed methods of ground fault and leakage currents calculation in both single-phase and three-phase networks. Formulas for these currents determination in steady-state and transient condition are derived. Calculation of ground fault and leakage currents with use of symmet-rical components in three-phase systems is explained. Application of Thevenin’s theorem for these currents determination is underlined.

1.1 AC IT Systems Circuit Diagrams

Low voltage alternating (sinusoidal) current (AC) and direct current (DC) networks insulated from ground (IT) belong to electrical systems commonly applied in com-mercial and industrial objects. In AC IT systems all active parts are insulated from ground or one point of a network is connected to ground through a high imped-ance. This connection is made either between ground and the neutral point or between ground and the artificial neutral point.

There are several types of AC IT systems. The most commonly used are:

• single-phase two-wire systems,• single-phase three-wire systems,• two-phase three-wire systems,• three-phase three-wire systems,• three-phase four-wire systems.

A simplified circuit diagram of a single-phase AC IT system is shown in Fig. 1.1. Further examples, namely simplified circuit diagrams of three-phase three-wire and three-phase four-wire systems are shown in Fig. 1.2a, b.

Circuit diagrams of AC IT systems make it possible to perform calculations of basic electric parameters such as voltages and currents in single network elements.

Chapter 1General Characteristics

P. Olszowiec, Insulation Measurement and Supervision in Live AC and DC Unearthed Systems, Lecture Notes in Electrical Engineering 314, DOI: 10.1007/978-3-319-07010-0_1, © Springer International Publishing Switzerland 2014

4 1 General Characteristics

In these circuit diagrams there are shown elements representing parameters of sin-gle wires-to-ground insulation. These parameters are decisive for analysis of ground fault phenomena. Internal impedances of voltage sources, longitudinal impedances of phase and neutral conductors, wire-to-wire insulation impedances and networks load impedances are not taken into account as these parameters exert in practice no (sub-stantial) influence on voltages and currents between network elements and ground.

1.2 Phase-to-Ground Voltages Determination in AC IT Systems

Calculus with complex numbers is a convenient tool for analysis of AC IT systems. Complex values of phase-to-ground voltages prove useful for calculation of network electrical parameters including ground fault and leakage currents as well as insula-tion parameters. These complex voltages (phasors) can be determined graphically or analytically with use of their measured RMS (root mean square) values. Both methods are presented below separately for single- and three-phase AC IT systems.

1.2.1 Single-Phase Systems

On the basis of AC IT network circuit diagram (Fig. 1.1) vector diagram of volt-ages (Fig. 1.3) can be drawn with a ruler and a compass. Length of vectors E, Ua and Ub corresponds to RMS values E, Ua and Ub of these voltages.

Fig. 1.1 A simplified circuit diagram of a single-phase AC IT system

5

It is convenient to determine real and imaginary parts of complex quantities of phase voltages assuming zero argument (phase angle) of the source voltage E. Both parts of these voltages can be directly measured with a ruler on the diagram drawn according to Kirchhoff’s 2nd law E = Ua + Ub. Based on this diagram the following equations can be written:

From these equations unknown parts of the complex Ua voltage can be determined as:

(1.1)U2

a= (Re Ua)

2+ (Im Ua)

2

(1.2)U2

b= (E − Re Ua)

2+ (Im Ua)

2

(1.3)Re Ua =E

2+ U

2a

− U2

b

2 · E, Im Ua =

√

U2a

− (E2 + U2

a− U

2

b

2 · E)2

Fig. 1.2 a A simplified circuit diagram of a three-phase three-wire AC IT system. b A simplified circuit diagram of a three-phase four-wire AC IT system



These components of Ua voltage can also be calculated if impedances of both con-ductors-to-ground insulation are known. It follows from the network circuit diagram

where Za and Zb are complex impedances of a and b conductor-to-ground insulation

1.2.2 Three-Phase Systems

Network circuit diagram (Fig. 1.2a) and vector diagram (Fig. 1.4) prove useful for determination of real and imaginary parts of complex phase voltages. Both methods—graphical and analytical—are based on knowledge of RMS values and phase angles values of the source voltages. RMS values of network phase voltages must also be known.

The problem is solved graphically by means of a construction shown in Fig. 1.4, where radii of arcs correspond to measured RMS values Ua, Ub and Uc. The crossing point of the arcs is the end point of a vector of the network neu-tral point displacement voltage UN . Its real and imaginary components, marked respectively as x, y, can also be determined analytically from the following system of equations describing RMS values of phase voltages. For simplicity, symmetry of source voltages with RMS value E and phase angle of source voltage in phase a equal to zero were assumed.

(1.4)Ua = E ·Za

Za + Zb

, Ub = E ·Zb

Za + Zb

(1.5)Za =

Ra ·1

jωCa

Ra +1

jωCa

, Zb =

Rb ·1

jωCb

Rb +1

jωCb

Fig. 1.3 Vector diagram of conductor-to-ground voltages of AC IT network

7

From these equations formula for UN voltage is obtained

Complex phase voltages are calculated as follows

where a = ej 2π

3 . Complex phase voltages can be determined also if single conductors-to-ground insulation parameters are known e.g. admittances Ya, Yb, Yc. In this case UN

is determined by a well-known formula derived from circuit diagram shown in Fig. 1.2a

(1.6)U2a = (E − x)2

+ y2

(1.7)U2b = (x +

E

2)2+ (y +

√

3 · E

2)2

(1.8)U2c = (x +

E

2)2+ (y −

√

3 · E

2)2

(1.9)UN = x + j · y =U2

b + U2c − 2 · U2

a

6 · E+ j ·

U2b − U2

c

2√

3 · E

(1.10)Ua = E − UN

(1.11)Ub = a2· E − UN

(1.12)Uc = a · E − UN

(1.13)UN = E ·

Ya + a2· Yb + a · Yc

Ya + Yb + Yc

Fig. 1.4 Vector diagram of phase-to-ground voltages of AC IT three-phase network



This expression may be substituted into formulas (1.10), (1.11) and (1.12). As a result the following formulas are obtained:

(1.14)Ua = E ·(1 − a2

) · Yb + (1 − a) · Yc

Ya + Yb + Yc

(1.15)Ub = E ·(a2

− 1) · Ya + (a2− a) · Yc

Ya + Yb + Yc

(1.16)Uc = E ·(a − 1) · Ya + (a − a2

) · Yb

Ya + Yb + Yc

1.3 Ground Fault and Leakage Currents Calculation

1.3.1 Single-Phase Networks

1.3.1.1 Steady-State Condition

Steady-state single phase-to-ground short circuit (ground fault) currents can be calculated using formulas given in Sect. 1.2. Steady-state ground fault current Ifa of conductor for example a through resistance r can be calculated in the following way. Voltage between this conductor and ground Ufa in short circuit condition is expressed by formula

Ground fault current Ifa through a resistor r equals to

For a dead ground fault (r = 0) this current is given by a simpler formula

Formula (1.18a) can also be obtained with help of Thevenin’s theorem. For this purpose impedance seen from the ground fault terminals, i.e. between phase a and ground, with voltage source shorted should be determined. Therefore this

(1.17)Ufa = E ·

Za·r

Za+r

Za·r

Za+r+ Zb

(1.18a)Ifa =

Ufa

r= E ·

Za

Za+r

Za·r

Za+r+ Zb

= E ·Za

Za · r + Zb · (Za + r)

(1.18b)Ifa =E

Zb

9

substitute impedance consists of parallelly connected impedances Za and Zb. It is called network insulation-to-ground equivalent impedance Zi (shortly: insulation impedance) and is equal to

Voltage present between terminals of possible ground fault (in pre-fault condition) is given by formula (1.4). According to Thevenin’s theorem steady-state ground fault current Ifa equals to

Another problem is determination of leakage current from any conductor to ground. In a single phase AC IT system total earth leakage current Ila from con-ductor a, comprising currents flowing through insulation conductances and capaci-tances, is equal to

and of course is equal to total leakage current Ilb from conductor b.

1.3.1.2 Transient Condition

With use of Thevenin’s theorem transient phase-to-ground voltages and ground fault current through resistance r can be determined. In general all these electrical quantities, except of steady-state sinusoidal component, contain also an aperiodic exponentially decaying component. If a short circuit occurs at the moment t = 0 with a phase angle of voltage source α, then the initial value of a conductor– to-ground voltage ua is

where β = argZa

Za + Zb

.

The instantaneous voltage (function of time) ua(t) is a solution of a differential equation, which describes Kirchhoff’s first law for leakage currents valid for this ground fault condition for t >= 0 :

(1.19)Zi =Za · Zb

Za + Zb

(1.20)Ifa =Ua

r + Zi

= E ·

Za

Za+Zb

r +Za·Zb

Za+Zb

= E ·Za

r · (Za + Zb) + Za · Zb

(1.21)Ila =Ua

Za

=E

Za + Zb

(1.22)ua(0) =

√

2 · E ·

∣

∣

∣

∣

Za

Za + Zb

∣

∣

∣

∣

· sin(α + β)

(1.23)ua(t)

r+

ua(t)

Ra

+ Ca ·dua(t)

dt=

e(t) − ua(t)

Rb

+ Cb ·d[e(t) − ua(t)]

dt



Its solution—voltage ua(t)—is given by the following function

Amplitude of steady-state periodic component is ua(∞) =

√

2 · E ·

∣

∣

∣

∣

∣

r·Zar+Za

r·Zar+Za

+Zb

∣

∣

∣

∣

∣

and

its phase angle γ = arg

Za·r

Za+r

Za·r

Za+r+ Zb

. The initial value of aperiodic component calculated

from the initial condition is given by formula A = ua(0) − ua(∞) · sin(α + γ ), whereas its time constant is T = (Ca + Cb) ·

11

Ra+

1Rb

+1r

.

Instantaneous values of the short circuit current ifa (t) can be calculated from the formula

In case of a “dead” ground fault (r = 0) another formula is used

where γ = arg Zb.Single phase-to-ground voltages as well as ground fault current are therefore

described by the following function:

Parameters of phase voltages and short circuit current in a ground fault condition are dependent on the network insulation resistances and capacitances to ground,

(1.24)ua(t) = A · e−t/T+ ua(∞) · sin(ωt + α + γ )

(1.25)ifa(t) =ua(t)

rfor t > 0

(1.26)ifa(t) =E · sin(ωt + α + γ )

∣

∣Zb

∣

∣

for t > 0

(1.27)f (t) = A · e−t/T+ B · sin(ωt + φ)

Fig. 1.5 Ground fault current waveform in AC IT system—an example (here current is measured as voltage across fault resistance inserted into the circuit at t = 0)

11

fault resistance r and phase angle of voltage of the shorted conductor at the moment of a fault occurrence. An example of a ground fault current waveform through a fault resistance recorded in AC IT network is shown in Fig. 1.5. A grounded phase voltage for t > 0 is of course proportional to the ground fault current according to formula (1.25).

1.3.2 Three-Phase Networks

1.3.2.1 Steady-State Condition

Steady-state values of ground fault currents can be determined using formulas given in Sect. 1.2. Steady-state ground fault current Ifa of phase for example a through a fault resistance can be calculated in the following way. Voltage between this con-ductor and ground Ufa under this ground fault condition is given by the formula

Ground fault current Ifa through resistor r is equal to

In similar way steady-state leakage currents from any conductor can be calcu-lated. For example total leakage current Ila from phase a under normal condition (r = ∞) is

In general this current consists of an active component (current flowing through insulation resistances to ground) and reactive one (current flowing through insula-tion capacitances to ground). These components are determined in relation to vec-tor of the given phase-to-ground voltage.

Formula (1.30) can also be derived using Thevenin’s theorem. For this purpose impedance seen from the ground fault terminals, i.e. between phase a and ground with voltage sources shorted, should be determined. This impedance is a so called network-to-ground insulation equivalent impedance Zi and is equal to

(1.28)Ufa = E ·(1 − a2

) · Yb + (1 − a) · Yc

(1r

+ Ya) + Yb + Yc

(1.29)Ifa =

Ufa

r=

E

r·(1 − a2

) · Yb + (1 − a) · Yc

(1r

+ Ya) + Yb + Yc

(1.30)Ila = Ua · Ya = E ·(1 − a2

) · Yb + (1 − a) · Yc

Ya + Yb + Yc

· Ya

(1.31)Zi =

1

Ya + Yb + Yc



Voltage across terminals of a possible short circuit (i.e. prior to an earth fault occurrence) is given by (1.14). According to Thevenin’s theorem steady-state ground fault current Ifa equals to

(1.32)

Ifa =Ua

r + Zi

= E ·(1 − a

2) · Yb + (1 − a) · Yc

(Ya + Yb + Yc) · (r +1

Ya+Yb+Yc)

=E

r·(1 − a

2) · Yb + (1 − a) · Yc

1r

+ Ya + Yb + Yc

1.3.2.2 Transient Condition

With use of Thevenin’s theorem transient phase-to-ground voltages and ground fault current through resistance r can be determined. In general all these electri-cal parameters consist of both steady-state sinusoidal component and an aperiodic exponentially decaying component. Thus instantaneous values of any phase-to-ground voltage and ground fault current are given by the following function:

Values of voltages and current under a ground fault condition are therefore dependent on network insulation-to-ground resistances and capacitances, fault resistance and phase angle of voltage of the shorted conductor at the moment of a fault.

1.3.2.3 Zero Sequence Current Calculation

For design of a network and its electrical protections as well as for its effective operation and monitoring it is necessary to know zero sequence symmetrical component of phase currents both in a faulted and in healthy lines. This com-ponent is useful for analysis of ground fault phenomena and assessment of the network insulation condition. Its value for a given line can be determined from the definition using formulas (1.14)–(1.16) describing phase voltages. Let Ya, Yb, Yc be single phases insulation admittances to ground of the entire network (including the faulted line) and ya, yb, yc the same parameters of phases a, b, c of the faulted line.

(1.33)f (t) = A · e−t/T+ B · sin(ωt + ϕ)

(1.34)

I0 =1

3· (Ia + Ib + Ic) =

1

3· (Ua · ya + Ub · yb + Uc · yc) =

1

3·

E

Ya + Yb + Yc

·

ya ·

[

(1 − a2) · Yb + (1 − a) · Yc

]

+ yb ·

[

(a2− 1) · Ya + (a2

− a) · Yc

]

+ yc ·

[

(a − 1) · Ya + (a − a2) · Yb

]

13

Zero sequence component of phase currents I0 in the given line can also be expressed using zero sequence component of phase voltages

where U0, U1 and U2 are symmetrical components of phase voltages. In practice ya = yb = yc = y. Therefore, taking into account this assumption and identity 1 + a + a2

= 0, formula (1.35) can be simplified as follows:

Zero sequence component of phase currents of any line is often described by the following formula

where Yi is an equivalent (total) ground insulation admittance of all phases of the given line. With use of (1.35) it can be proved that formula (1.37) is valid only for lines with equal (symmetrical) admittances of single phases-to-ground insula-tion i.e. for ya = yb = yc. In order to calculate zero sequence component of phase currents in lines with asymmetrical phase-to-ground insulation admittances it is necessary to use formula (1.34) or (1.35). If the above mentioned asymmetry of admittances exists only in one line, then zero sequence component of phase cur-rents in this line can be calculated in a way that is simpler than using (1.34) or (1.35). It is namely equal to the sum of zero sequence components of phase cur-rents in all remaining n lines (connected to the same busbars) with symmetrical phase insulation admittances taken with opposite sign:

where Yki is an equivalent insulation admittance of the k-th line with symmetrical phase insulation admittances.

(1.35)

I0 =1

3·

(

Ia + Ib + Ic

)

=1

3·(

Ua · ya + Ub · yb + Uc · yc

)

=1

3·(

U0 + U1 + U2

)

· ya +1

3·

(

U0 + a2· U1 + a · U2

)

· yb

+1

3·

(

U0 + a2· U1 + a · U2

)

· yc

(1.36)I0 = U0 · y

(1.37)3 · I0 = U0 · Yi

(1.38)3 · I0 = −U0 ·

n∑

1

Yki


15

Abstract In the chapter there is presented general information on physical nature of network-to-ground insulation. Sense of “insulation equivalent resistance” param-eter is explained. A method of insulation resistances-to-ground of single phases and insulation equivalent resistance determination is presented for de-energized AC IT systems. Procedures of insulation equivalent resistance and total capacitance deter-mination in live networks are described. Detailed description of few methods of sin-gle phases insulation parameters (i.e. resistances and capacitances) determination in both single- and three-phase systems is given. Several unconventional methods of insulation parameters measurement are presented. Attention is paid to ways of ground fault, ground leakage and possible electric shock currents analytical evalua-tion and practical measurement. Influence of insulation parameters on these currents levels is discussed. Ground fault current compensation problems are dealt with.

2.1 General Information

In AC IT systems phase voltages and ground fault currents depend on line-to-ground insulation parameters of single conductors, but are not influenced by wire-to-wire insu-lation. This conclusion can be easily explained for single-phase networks. Leakage current from phase wire to earth is of course equal to leakage current from earth to the neutral wire. Its value is given by formula (1.21), from which it follows that earth leak-age current depends only on line-to-ground insulation parameters of single conductors.

2.1.1 Spatial Distribution of Insulation Resistance: Network’s Insulation Equivalent Circuit

Most often AC IT systems are supplied from a transformer, sometimes they are fed by a generator. Modern AC IT supply systems are equipped with necessary measurement

Chapter 2Ground Insulation Measurement in AC IT Systems


http://dx.doi.org/10.1007/978-3-319-07010-0_1

16 2 Ground Insulation Measurement in AC IT Systems

devices (voltage, current, power, energy etc. meters), insulation monitor and some-times fault locating system (see Figs. 1.1 and 1.2a, b). The most extensive component of a network are wires supplying power to all its parts. Insulation between conductors and also between any of them and ground has spatial distribution. Electrical param-eters of network insulation are resistance and capacitance. Their values are important for network performance both in transient and steady-state conditions.

In order to simplify description of behaviour of spatially distributed physical systems it is convenient to transform them into a topology consisting of discrete elements. The lumped element model of electric circuit’s insulation makes the simplifying assumption that its attributes (parameters)—resistance and capaci-tance—are concentrated into idealized elements i.e. resistors and capacitors con-nected to the network conductors.

According to the simplified network circuit diagram these elements are resis-tors Ra, Rb etc. and capacitors Ca, Cb etc. However practical usefulness of this rep-resentation comprising respective conductors is quite limited. Commonly applied insulation monitors measure insulation equivalent resistance which is a substitute resistance of all elements existing between galvanically connected points of this electric circuit and ground. Meaning (sense) of this electrical parameter can be explained with use of Thevenin’s theorem. Equivalent network insulation-to-ground resistance is resistance between the point of possible fault and ground. It is calcu-lated as a substitute resistance of all parallelly connected elements existing between this network and ground with all voltage sources being shorted and all current sources being eliminated. The purpose of this substitute parameter follows directly from Thevenin’s theorem—its application simplifies ground fault current calcula-tion. If insulation capacitance to ground can be neglected, this current magnitude is inversely proportional to sum of fault resistance at the place of the fault and the aforementioned substitute insulation resistance. Due to this dependence as well as convenience to perform measurement, insulation equivalent resistance parameter is much more often used than resistances of single conductors insulation to ground. For the same reasons network insulation equivalent (total) capacitance to ground is more useful parameter than capacitances of single conductors to ground.

2.2 Insulation Parameters Determination in Single-Phase Networks

2.2.1 De-energized Networks

2.2.1.1 Measurements with Megohmmeters

In de-energized single-phase AC IT systems insulation-to-ground equivalent resist-ance Ri can be easily measured with an megohmmeter. This parameter is defined similarly to insulation-to-ground equivalent impedance (see formula 1.19):

http://dx.doi.org/10.1007/978-3-319-07010-0_1

http://dx.doi.org/10.1007/978-3-319-07010-0_1

http://dx.doi.org/10.1007/978-3-319-07010-0_1

17

Both conductors (phase “a” and neutral “b”) should be shorted together and insulation equivalent resistance measured between these wires and ground. If resistances of single wires insulation to ground are sought, more measurements should be executed (see Fig. 2.1).

This procedure comprises the following insulation resistance measurements between ground (g) and:

(1) shorted “a” and “b”—readout Rab − g = Ri,(2) “a” with grounded “b”—readout Ra − bg,(3) “b” with grounded “a”—readout Rb − ag .

As result three equations are obtained with three unknown parameters Ra, Rb, Rab

The sought Ra, Rb values are given by the following formulas

(2.1)Ri =Ra · Rb

Ra + Rb

(2.2)Ri =Ra · Rb

Ra + Rb

, Ra − bg =Ra · Rab

Ra + Rab

, Rb − ag =Rb · Rab

Rb + Rab

(2.3)Ra =

2 · Ri · Ra − bg · Rb − ag

Ra − bg · Rb − ag + Ri · (Rb − ag − Ra − bg),

Rb =2 · Ri · Ra − bg · Rb − ag

Ra − bg · Rb − ag + Ri · (Ra − bg − Rb − ag)

Fig. 2.1 Single phase AC IT network circuit diagram showing all insulation resistances. Note for insulation measurement all voltage sources and loads must be disconnected!



Similar approach can be adopted in three-phase AC IT systems, however more separate measurements with an megohmmeter are necessary as there are six unknown insulation parameters.

If insulation-to-ground capacitances of single conductors are sought, these quantities could be determined with an additional procedure using an AC auxil-iary source replacing network’s disconnected supply source(s). This method is presented in the next section as a procedure applied in live networks.

2.2.1.2 Indirect Methods of Insulation Parameters Determination

There are several so called “technical” methods of indirect determination of parameters of electrical elements or circuits supplied by an auxiliary (test) voltage source. These procedures are based on use of typical (multi)meters as voltmeters, ammeters or wattmeters. In fact none of them is specially addressed to measurement of electrical insulation parameters (resistance and capacitance). Nevertheless under some assumptions few procedures bring results with satisfac-tory accuracy. An example of a simple indirect method exploiting a voltmeter, an ammeter and an auxiliary resistor is presented in Fig. 2.2.

The measuring circuit fed by an auxiliary voltage source U includes a resistor R0 = 1/G0 connected in parallel to the tested two-terminal element (e.g. network-to-ground insulation) of unknown parameters Gi = 1/Ri, Bi = 1/Xi. This procedure consists of two steps.

These two steps are described by equations

from which formulas for Gi, Bi can be derived

This method requires constant RMS value U of auxiliary voltage and internal impedance of (micro)ammeter negligible in comparison to Ri, Xi and R0 which is practically always true. In some cases these procedures may also be applied in live circuits in normal working conditions.

(2.4)I2

1=

(

G2

i + B2

i

)

· U2

(2.5)I2

2=

[

(Gi + G0)2+ B2

i

]

· U2

(2.6)Gi = −G0

2+

I2

2− I2

1

2 · G0 · U2

(2.7)Bi =

√

(

I1

U

)2

− G2

i

19

2.2.2 Live Networks

In live single-phase AC IT systems (Fig. 1.1) insulation equivalent resistance and capacitance can be calculated using measured conductor-to-ground RMS volt-ages of one of the wires a or b. Conductor-to-ground voltage of this wire (e.g. a) is measured in three states: (1) U1 in normal working condition (2) U2 with resis-tor R1 = 1/G1 connected between this conductor and ground, (3) U3 with resistor R2 = 1/G2 connected instead of R1. These conditions are described by the following equations of (ground) leakage currents balances according to Kirchhoff’s first law:

By eliminating the source voltage E two equations containing two unknown parameters Gi, Bi, where Gi = Ga + Gb and Bi = Ba + Bb, are obtained.

Substituting

these equations are as follows

From Eqs. (2.12) and (2.13) the following formulas are derived

(2.8)U1 · (Ga + jBa) = (E − U1) · (Gb + jBb)

(2.9)U2 · (Ga + G1 + jBa) = (E − U2) · (Gb + jBb)

(2.10)U3 · (Ga + G2 + jBa) = (E − U3) · (Gb + jBb)

(2.11)

(

U1

U2

)2

= q1 + 1 and

(

U1

U3

)2

= q2 + 1

(2.12)

(∣

∣

∣

∣

Gi + G1 + jBi

Gi + jBi

∣

∣

∣

∣

)2

= q1 + 1

(2.13)

(∣

∣

∣

∣

Gi + G2 + jBi

Gi + jBi

∣

∣

∣

∣

)2

= q2 + 1

(2.14)Ri =1

Gi

= 2 ·

q2

R1−

q1

R2

q1

R2

2

−q2

R2

1

Fig. 2.2 Explanation of an indirect method with two steps


http://dx.doi.org/10.1007/978-3-319-07010-0_1


Modification of the method described above is possible. It consists in replacement of resistors R1 and R2 by capacitors C1 = B1/ω and C2 = B2/ω. In this case insula-tion equivalent parameters are given by the following formulas (their derivation has been omitted as similar to the method described above):

This approach may serve for calculation of not only insulation equivalent resist-ance and capacitance values, but also for determination of single conductors resist-ances Ra, Rb and capacitances Ca, Cb. The procedure requires connection of only one element between a selected conductor and ground, however knowledge of the source voltage E is necessary. According to formulas (1.3) given in Sect. 1.2, real x and imaginary y parts of vector Ua complex magnitude can be calculated:

Thus

Similarly with conductor a grounded by resistor R1 = 1/G1 phase-to-ground volt-ages U ′

a, U ′

b are given as follows:

where

(2.15)Bi =

√

G2

1

q1

+2 · G1

q1

· Gi − G2

i

(2.16)Bi =1

2·

B2

2· q1 − B2

1· q2

B1 · q2 − B2 · q1

(2.17)Ri =1

Gi

=1

√

B2

2

q2+

2·B2

q2· Bi − B2

i

(2.18)x = Re Ua =E2

+ U2a − U2

b

2 · E

(2.19)y = Im Ua =

√

U2a − x2

(2.20)Ua = x + j · y

(2.21)Ub = E − x − j · y

(2.22)U ′

a = v + j · w

(2.23)U ′

b = E − v − j · w

(2.24)v =E2

+ U ′2a − U ′2

b

2 · E

(2.25)w =

√

U ′2a − v2

http://dx.doi.org/10.1007/978-3-319-07010-0_1

http://dx.doi.org/10.1007/978-3-319-07010-0_1

21

Substituting these expressions to Eqs. (2.18), (2.19) the following is obtained:

In each of (2.26) and (2.27) equations real and imaginary parts of both sides must be equal. By comparing these parts four Eqs. (2.28)–(2.31) are obtained. From these equations the unknown parameters Ga, Gb, Ba, Bb can be determined. The final formulas have been omitted—these can be easily derived by readers.

2.3 Insulation Parameters Determination in Live Three-Phase Networks

2.3.1 Insulation Equivalent Resistance and Capacitance Values Determination

In live three-phase IT AC systems (Fig. 1.2a, b) insulation equivalent resistance and capacitance values can be determined on the basis of measured RMS voltages of a selected phase a, b or c [1]. Phase-to-ground voltage of this conductor (e.g. c) is measured in three states: (1) in normal working (healthy) condition (2) with resistor R1 = 1/G1 connected between this conductor and ground, (3) with resistor R2 = 1/G2 connected instead of R1. In these conditions zero-sequence component of phase voltages is as follows:

(2.26)(x + j · y) · (Ga + jBa) = (E − x − j · y) · (Gb + jBb)

(2.27)(v + j · w) · (Ga + G1 + jBa) = (E − v − j · w) · (Gb + jBb)

(2.28)x · Ga − y · Ba = (E − x) · Gb + y · Bb

(2.29)x · Ba + y · Ga = (E − x) · Bb − y · Gb

(2.30)v · (Ga + G1) − w · Ba = (E − v) · Gb + w · Bb

(2.31)v · Ba + w · (Ga + G1) = (E − v) · Bb − w · Gb

(2.32)U01 =Ea · Ya + Eb · Yb + Ec · Yc

Ya + Yb + Yc

=Ea · Ya + Eb · Yb + Ec · Yc

Gi + j · Bi

(2.33)

U02 =Ea · Ya + Eb · Yb + Ec · (Yc + G1)

Ya + Yb + Yc + G1

=Ea · Ya + Eb · Yb + Ec · Yc + Ec · G1

G1 + Gi + j · Bi

(2.34)

U03 =Ea · Ya + Eb · Yb + Ec · (Yc + G2)

Ya + Yb + Yc + G2

=Ea · Ya + Eb · Yb + Ec · Yc + Ec · G2

G2 + Gi + j · Bi


http://dx.doi.org/10.1007/978-3-319-07010-0_1


By substituting formulas (2.32), (2.33), (2.34) to (1.10), (1.11), (1.12), phase voltages of conductor c in these operating states are obtained:

Dividing Uc1 by Uc2 and Uc1 by Uc3, there are obtained two equations con-taining two unknown parameters Gi, Bi where Gi = Re(Ya + Yb + Yc) and Bi = Im(Ya + Yb + Yc). Substituting

the aforementioned equations assume the following form

It should be noticed that Eqs. (2.39) and (2.40) are identical to (2.12) and (2.13). Therefore their solutions are also identical and are given by formulas (2.24) and (2.15).

For three-phase networks modification of the method described above is also possible. It consists in replacement of resistors R1 and R2 by capacitors C1 = B1/ω and C2 = B2/ω. In this case insulation equivalent parameters are given by formulas (2.16) and (2.17).

This procedure can be also applied in AC IT systems with any number of phases. Its correctness for multi-phase networks may be proved in the following way. According to Thevenin’s theorem voltages of phase c in the second and the third step are equal respectively to (mind that Uc1 is a pre-fault value)

(2.35)Uc1 =−Ea · Ya − Eb · Yb + Ec · (Ya + Yb)

Gi + j · Bi


G1 + Gi + j · Bi


G2 + Gi + j · Bi

(2.38)

(

Uc1

Uc2

)2

= q1 + 1 and

(

Uc1

Uc3

)2

= q2 + 1

(2.39)

(∣

∣

∣

∣

G1 + Gi + j · Bi

Gi + jBi

∣

∣

∣

∣

)2

= q1 + 1

(2.40)

(∣

∣

∣

∣

G2 + Gi + j · Bi

Gi + jBi

∣

∣

∣

∣

)2

= q2 + 1

(2.41)Uc2 =Uc1

∣

∣

∣

1Gi + jBi

+1

G1

∣

∣

∣

·1

G1

= Uc1 ·|Gi + jBi|

|Gi + G1 + jBi|

(2.42)Uc3 =Uc1

∣

∣

∣

1Gi + jBi

+1

G2

∣

∣

∣

·1

G2

= Uc1 ·|Gi + jBi|

|Gi + G2 + jBi|

http://dx.doi.org/10.1007/978-3-319-07010-0_1

http://dx.doi.org/10.1007/978-3-319-07010-0_1

http://dx.doi.org/10.1007/978-3-319-07010-0_1

23

From both equations given above, applying (2.38), formulas (2.39) and (2.40) are obtained.

Another method of insulation equivalent resistance and capacitance values deter-mination can be applied in multi-phase (not necessarily 3-phase) AC IT systems. This procedure consists of two steps and requires connection of only one element [2]. In this network a selected phase voltage is measured in two operating states: (1) in normal working (healthy) condition (2) with the above mentioned element, for example capacitor C, connected between this selected phase e.g. a and ground. In both these conditions dead (fault resistance equal to zero) ground-fault current value Ifa is of course the same. According to Thevenin’s theorem it is equal to

where Ua1 and Ua2 are complex values of phase a voltage measured in these two operating states, Yi = Gi + jBi is network insulation equivalent admittance. From Eq. (2.43) formula (2.44) for determination of insulation admittance parameters Gi and Bi is obtained:

It should be emphasized that for application of this method it is necessary to meas-ure phase angles of voltages Ua1 and Ua2 (in relation to any reference phasor e.g. source voltage E).

In case of symmetrical source voltages and symmetrical phase-to-ground capacitances Cph (which however is not always true for low voltage networks) and negligible leakage conductances a simple procedure exists for determination of network-to-ground equivalent (total) capacitance [3]. After closing a switch

(2.43)Ifa = Ua1 · Yi = Ua2 · (Yi + j · ω · C)

(2.44)Yi = Gi + j · Bi =j · ω · C · Ua2

Ua1 − Ua2


Fig. 2.3 Determination of symmetrical phase-to-ground capacitances Cph in a three-phase AC IT network with negligible leakage conductances


(Fig. 2.3) currents I1 and I2 flowing through two additional capacitors of equal value Ck are measured. Total network-to-ground capacitance is calculated as

2.3.2 Insulation Resistance and Capacitance Determination for Single Phases

There are known several methods of single phases insulation parameters deter-mination in live three-phase networks (in general in multi-phase networks). Each procedure consists of series of measurements and analytical processing of their results. These procedures are aimed at obtaining a necessary number of inde-pendent equations with unknown insulation parameters. In the most general case values of respective insulation parameters may be different. As these parameters are spatially distributed along the wires, it is impossible to measure (accurately) currents flowing through them. Therefore only voltages across these elements are accessible for measurement. For practical application only these methods are useful which provide safe operation of the system and persons performing meas-urements. In particular any applied procedure may cause neither interruptions of power supply, nor excessive changes of voltages and currents levels. Below there are presented three selected methods based on measurements and calculation; the first and the third procedures were proposed by the author.

2.3.2.1 Method of an Additional Single-Phase Voltage Source

This method employing an additional single-phase voltage source is explained in Fig. 2.4. It consists of measurements of phase voltages in the following operating conditions of the network:

(1) normal network operation(2) intentional grounding of a selected phase (e.g. c) through an element with Yd

admittance(3) inclusion of an additional voltage source Ud of the network frequency in

series into a selected phase (phase b in Fig. 2.4).

Network operating conditions relating to steps 1, 2, 3 are described by the follow-ing system of equations expressing balance of earth-leakage currents:

(2.45)3 · Cph =

√

3 · Ck · I1

I2 −

√

3 · I1

(2.46a)Ua1 · Ya + Ub1 · Yb + Uc1 · Yc = 0

(2.46b)Ua2 · Ya + Ub2 · Yb + Uc2 · Yc = −Uc2 · Yd

(2.46c)Ua3 · Ya + Ub3 · Yb + Uc3 · Yc = 0

25

Phase voltages and insulation admittances are complex values. To calculate three unknown admittances Ya, Yb, Yc three leakage current balance equations written according to Kirchhoff’s first law are necessary. To get an univocal result (i.e. set of three admittance complex values) system of these equations should have one solution. This requirement is met if determinant of the equations system (2.46a, 2.46b, 2.46c) is not equal to zero. Its value can be calculated with help of the fol-lowing relationships between voltages of network sources:

where for simplicity it was assumed that source voltages remain constant during measurements and contain only positive sequence symmetrical component, a = e j120. Taking into account (2.47) determinant of the system of Eqs. (2.46a, 2.46b, 2.46c) is expressed by the following formula:

After performing calculation this determinant is equal to

(2.47)

Ua1 = E − UN1, Ub1 = a2E − UN1, Uc1 = aE − UN1


Ua3 = E − UN3, Ub3 = a2E + Ud − UN3, Uc3 = aE − UN3

(2.48)det M =

∣

∣

∣

∣

∣

∣

E − UN1 a2E − UN1 aE − UN1


E − UN3 a2E + Ud − UN3 aE − UN3

∣

∣

∣

∣

∣

∣

(2.49)det M = (1 − a) · E · (UN2 − UN1) · Ud

Fig. 2.4 Circuit diagram of a three-phase AC IT system for measurement procedure I. Designations: E—positive sequence symmetrical component of source voltages, Ud—additional voltage source, UN —network displacement voltage, Yd—admittance of grounding element, Ga, Gb, Gc—phase a, b, c insulation-to-ground conductances, Ca, Cb, Cc—phase a, b, c insulation-to-ground capacitances



This matrix M determinant value is obviously different from zero because displacement voltages in steps 1 and 2 are not equal due to additional grounding element’s admittance in step 2.

As it was assumed above, source voltages usually contain only positive compo-nent and its value is constant during the measurements. It can be proved however that for insulation parameters measurement it is necessary that phase voltages con-tain negative component in one step of the cycle and zero sequence component in another one.

Negative sequence component of phase voltages may appear as result of:

(1) series connection of an additional voltage source into one phase(2) swapping of two source (network) phases.

Voltage zero sequence component may appear when:

(1) an additional voltage source is connected in series with one or more phases (it may be both an active element and passive one e.g. a choke across which there is voltage drop due to load current)

(2) one or more phases are grounded through an element with specially chosen admittance (intentional asymmetry of insulation admittances of single phases).

To get a solution different from zero, the second method of providing voltage zero sequence component must be applied because only for a network with one phase grounded, system of Eqs. (2.46a, 2.46b and 2.46c) is not homogeneous.

2.3.2.2 Method of Two Phases Swapping

In this method [2] steps 1 and 2 are identical as in method I, but in step 3 voltage negative sequence component is introduced by swapping of two phases e.g. a and b with a switch S as shown in Fig. 2.5.

Due to this change—over (swapping) positive component of source voltages is transformed into negative one. As a result the following system of equations is obtained:

where

(2.50)Ua1 · Ya + Ub1 · Yb + Uc1 · Yc = 0

(2.51)Ua2 · Ya + Ub2 · Yb + Uc2 · Yc = −Uc2 · Yd

(2.52)Ua3 · Ya + Ub3 · Yb + Uc3 · Yc = 0

(2.53)



Ua3 = E − UN3, Ub3 = E − UN3, Uc3 = aE − UN3

27

Determinant of this system of equations is given by the following formula:

After performing calculation it is equal to

As in the previous method voltages UN1 and UN2 are again different complex quantities. Unfortunately this method requires to switch off network supply twice to swap phases. It should be noted that both methods (I and II) can be applied only if network insulation parameters and source voltages are constant during the whole measuring cycle. The next requirement is knowledge of complex values of phase voltages in each step. These complex quantities can be determined using formulas (1.9)–(1.12).

However instead of a troublesome execution of an additional voltage source inclusion (method I) or practically impermissible phase swapping (method II) another measurement procedure can be suggested. Step 3 of method I or II is modified to utilize an auxiliary voltage source with a different frequency. It is con-nected between one of phases and ground. This idea of an auxiliary voltage source with a different frequency application has been also successfully implemented for continuous insulation monitoring.

(2.54)det M =

∣

∣

∣

∣

∣

∣



a2E − UN3 E − UN3 aE − UN3

∣

∣

∣

∣

∣

∣

(2.55)det M = 3 · (1 − a) · E2· (UN2 − UN1)

Fig. 2.5 Illustration of phase swapping method


http://dx.doi.org/10.1007/978-3-319-07010-0_1

http://dx.doi.org/10.1007/978-3-319-07010-0_1


2.3.2.3 Application of an Auxiliary AC Voltage Source with a Different Frequency

This method also consists of three separate steps. The first (normal operation of a network) and the second (artificial grounding of a line phase) are identical to steps 1 and 2 described above.

Measurements executed in these two steps are usually sufficient in most applications if single phase-to-ground capacitances are approximately equal i.e. Ca = Cb = Cc = Cph. In this case four equations with four unknown parameters Ga, Gb, Gc, Cph are obtained.

In the third step of the proposed procedure an auxiliary AC voltage source with RMS value Uaux of a different frequency faux ≠ f is connected between ground and a selected phase e.g. a. The equivalent scheme of the network in step 3 is shown in Fig. 2.6.

The auxiliary AC voltage source is connected in series with a band-pass filter F for faux frequency. To get two independent equations at this step it is necessary to measure not only RMS values of Uaux voltage and Iaux current but also phase shift ϕ between them. In this way three equations with complex coefficients and six unknown insulation parameters Ga, Gb, Gc, Ca, Cb, Cc are obtained:

It should be noted that by measuring Uaux, Iaux, ϕ in step 3, insulation equivalent conductance and capacitance values can be calculated without need of steps 1 and 2 execution. Of course at this step a DC auxiliary source cannot be applied as it would produce only one equation without possibility to measure capacitance.

In order to avoid a troublesome determination of phase shift ϕ, step 3 can be modified to comprise two steps 3 and 4 with measurement of Iaux current driven by the same auxiliary voltage source Uuax in identical conditions as in steps 1 and 2. As result four equations with six unknown insulation parameters are obtained. However it should be reminded that each of Eqs. (2.57) and (2.58) consists of two separate equations for real and imaginary parts.

(2.56a)Ua1 · (Ga + j · 2π · f · Ca) + Ub1 · (Gb + j · 2π · f · Cb)

+ Uc1 · (Gc + j · 2π · f · Cc) = 0

(2.56b)Ua2 · (Ga + j · 2π · f · Ca) + Ub2 · (Gb + j · 2π · f · Cb)

+ Uc2 · (Gc + j · 2π · f · Cc) = −Ua2 · Yd

(2.56c)

|Uaux| · [(Ga + Gb + Gc) + j · 2π · faux · (Ca + Cb + Cc)] =

∣

∣Iaux

∣

∣ · ejϕ

(2.57)

Ua1 · (Ga + j · 2π · f · Ca) + Ub1 · (Gb + j · 2π · f · Cb)

+ Uc1 · (Gc + j · 2π · f · Cc) = 0

29

Steps 3 and 4 alone allow to determine insulation equivalent parameters Gi = Ga + Gb +Gc and Ci = Ca + Cb + Cc from Eqs. (2.59) and (2.60). In this case there is no need to execute steps 1 and 2.

2.4 Unconventional Measurement Methods

2.4.1 Periodical Measurement of Insulation Parameters

With help of Thevenin’s theorem few other methods of insulation equivalent resistance and capacitance determination in live AC IT networks can be proposed. In distinction from methods described in Sect. 2.3 these procedures do not require performance of any calculations.

(2.58)Ua2 · (Ga + j · 2π · f · Ca) + Ub2 · (Gb + j · 2π · f · Cb)

+ Uc2 · (Gc + j · 2π · f · Cc) = −Ua2 · Yd

(2.59)

|Uaux1| · |[(Ga + Gb + Gc) + j · 2π · faux · (Ca + Cb + Cc)]| =

∣

∣Iaux1

∣

∣

(2.60)

|Uaux2| ·

∣

∣[(Ga + Gb + Gc) + j · 2π · faux · (Ca + Cb + Cc) + Yd]

∣

∣ =

∣

∣Iaux2

∣

∣

Fig. 2.6 Circuit diagram of a three-phase AC IT network for method III. Symbols Iaux—measuring current with frequency faux imposed by the auxiliary source, F—band-pass filter. The remaining symbols are as in Fig. 2.4


http://dx.doi.org/10.1007/978-3-319-07010-0_2


2.4.1.1 Insulation Resistance Measurement with Megohmmeters

For insulation resistance determination in de-energized circuits some dedicated measuring instruments are applied—these include both traditional hand-driven and modern digital megohmmeters. According to manufacturer’s recommendation they are designed for use in circuits with no voltage. However their application is also possible in live systems under condition that the instrument is connected to termi-nals with no potential difference between them. If voltage superimposed by the network source on the measuring device terminals, e.g. ohmmeter, is equal to zero, then current flowing through the instrument measuring system will depend only on the device own (internal) source. If this network-to-ground voltage is not equal to zero, insulation equivalent resistance measurement is also possible. However voltage between network terminal and ground cannot be too high as it would force an impermissibly high current to flow through the instrument. Of course current driven by the tested network does not influence the instrument indication due to this device’s different frequency (in this case DC). It should be noted that the above described application of megohmmeter may pose a threat of sensitive devices (e.g. semiconductor elements) damage or risk of misoperation of appara-tuses installed in the tested circuit. For this reason insulation testing with megohm-meter in live auxiliary (control) circuits is not applied.

2.4.1.2 Measurement with Variable Elements

An unconventional method of AC IT single and multiple-phase networks insula-tion parameters determination was developed and tested by the author. It is based on application of variable (adjusted) resistors and capacitors. This approach makes it possible to set actual values of insulation equivalent resistance and capacitance on the above mentioned test elements. The idea of insulation resistance determina-tion shown in Fig. 2.7a can be explained with Thevenin’s theorem. The measure-ment result is independent from network-to-ground capacitance level due to use of DC test current.

The procedure is performed as follows. First with released switch S, output voltage U of rectifier is read out at with DC voltmeter. A variable test resistor r should be set to maximum resistance. Then S is pressed and resistance r gradually decreased while supervising growth of voltmeter indication to U′. When the meas-ured DC voltage increases to half of its initial value (i.e. U′ = 0.5U) the switch should be released. Resistance set at the resistor r is equal to insulation equivalent resistance Ri. This conclusion directly follows from the equivalent circuit for DC test voltage source seen from the terminals of resistor r (Fig. 2.7b). In this circuit with r = Ri DC voltage U′ is equal to half of rectifier output voltage U. Equivalent insulation resistance can be read at the resistor r scale or this resistor value can be measured with an ohmmeter.

In similar way insulation equivalent capacitance of AC IT network can be determined (Fig. 2.8a). In this case an auxiliary voltage source is not necessary but

31

a resistor r set to Ri in the procedure described above is used. A variable capaci-tor, set to the minimal value smaller than the network-to-ground capacitance Ci, is connected parallelly with resistor r. First with released switch S voltage U at the AC voltmeter is read out. Then switch S should be pressed and capacitance C gradually increased. As this capacitance grows, voltmeter indication drops from U to U″. When the measured AC voltage decreases to half of its initial value (i.e. U″ = 0.5U) the switch should be released. Capacitance set at the capacitor C is equal to insulation equivalent capacitance Ci. This conclusion directly follows from the equivalent circuit seen from the terminals of resistor r and capacitor C (Fig. 2.8b). It is obvious that with r = Ri and C = Ci conductor-to-ground AC

Fig. 2.7 a System of insulation equivalent resistance determination for a single phase AC IT network with use of a variable test resistor—designations in the text. b An equivalent circuit diagram of the tested network



voltage U″ is equal to half of AC voltage U without connected elements r and C. Equivalent insulation capacitance can be read out at the capacitor C scale or this element value can be measured with a meter.

2.4.2 Devices and Systems for Ground Fault, Earth Leakage and Shock Currents Measurement

Variable elements set to insulation equivalent resistance or capacitance as described in Sect. 2.4.1 can be used for measurement of ground fault current in AC IT systems.

Fig. 2.8 a System of insulation equivalent capacitance determination for a single phase AC IT network with use of a variable capacitor—designations in the text. b An equivalent circuit diagram of the tested network

33

The measurement is executed in an auxiliary test circuit isolated from ground. It is supplied from another source or from a transformer connected to the tested net-work as shown in Fig. 2.9. Supply voltage level of the test circuit should be equal to conductor-to-ground voltage of a selected wire and should not be influenced by execution of the test. In the test circuit there are used parallelly connected elements representing insulation equivalent parameters: resistor r = Ri and capacitor C = Ci. A selection switch S is connected in series with these elements to choose either ground fault current (position 1) or shock current (position 2) measurement. In the latter option resistor Rh is used to represent human body internal resistance.

Using elements r and C possible ground fault and shock currents can be meas-ured also in the live AC IT network. This method of measurement is based on Thevenin’s theorem. Both parallelly connected elements r and C should be con-nected with an ammeter between selected wire and ground (Fig. 2.10). The readout value of current is equal to half of the dead ground fault current of this conductor. In order to measure a possible electric shock current, resistor with double resistance of human body should be connected in series with insulation equivalent model con-sisting of r and C . In this case an ammeter indication is equal to half of an electric shock current flowing through a body of a man touching this conductor.

In 2-wire AC IT live systems the above mentioned currents can be determined also by execution of an artificial dead ground fault of a selected phase e.g. a, of course only with sufficiently high level of insulation equivalent impedance. Voltage of the second conductor b should be measured without (Ub1) and with (Ub2) conductor a grounded by an ammeter. An earth fault current of conductor a is equal to the ammeter readout I, whereas total earth leakage current from con-ductor b in normal operating conditions Ilb is given by formula

(2.61)Ilb =Ub1

Ub2

· I

Fig. 2.9 Isolated test circuit for evaluation of ground fault and shock current in AC IT networks



Residual (ground leakage) currents can be measured in live AC IT systems with use of clamp-on ammeters. There are several methods of ground leakage current determination (Fig. 2.11). When grounding conductor of a device with a conduct-ing housing is embraced with clamp-on meter (a) only ground leakage current flowing through this wire is measured. When phase and neutral conductors are embraced (b) total ground leakage current flowing from the network is measured. If all conductors (phase, neutral and earthing) are included (c), clamp-on meter measures the leakage current flowing exclusively through ground and not in the mentioned wires. Of course application of clamp-on ammeter does not enable to discriminate resistive (i.e. flowing through insulation leakage resistances) and capacitive (i.e. flowing through insulation capacitances to ground) components of the measured ground leakage current.

Fig. 2.10 Test circuit for evaluation of ground fault and shock current in live AC IT networks

Fig. 2.11 Various methods of ground leakage current measurement

35

2.5 Influence of Insulation Parameters on Possible Ground Fault, Electric Shock and Ground Leakage Currents Levels

2.5.1 Assessment of Ground Fault and Ground Leakage Currents

In AC IT systems earth leakage currents flow both through places with deterio-rated insulation level and through network-to-ground capacitances. Earth leakage current level is an indicator of insulation condition i.e. insulation resistance and capacitance levels. Earth leakage currents flow leads to heat losses in its path and possible risks of electric shock, fire, explosion and corrosion. Insulation leakage resistances may be distributed at random (non-uniformly) along the network con-ductors. In a single-phase system total earth leakage current (including resistive and capacitive components) from one conductor Il is of course equal to total earth leakage current from the other conductor. This conclusion directly follows from the 1st Kirchhoff ‘s law. This steady-state value is equal to

For assessment of fire risk only RMS value of earth leakage current’s resistive component is important. It should be noted that resistive components of leakage currents from conductors a and b in a single-phase network are not always equal. RMS value of resistive component Ilres of leakage current from any wire e.g. a in that network always meets the following conditions

It might be of practical interest to determine highest possible leakage currents from any conductor in a single-phase network with known levels of insulation equivalent conductance Gi and total susceptance Bi. It is obvious that the highest leakage current resistive component Ilres max is smaller than E · Gi. For negligible Bi values it assumes maximum when insulation conductance is divided equally between both conductors i.e. Ilres max = E ·

Gi

4.

Magnitude Ifa of a possible dead ground fault current fulfills conditions

where Uapref is prefault value of phase a voltage.In three-phase AC IT systems with Bi = 0, resistive component of leakage

current from phases b, c assumes its maximum for the following insulation parameters Gb = Gc = Gi/2, Ga = 0. This highest value is calculated with formula

Ilres max =E·

√

3

4· Gi.

(2.62)Il =E

Za + Zb

(2.63)Ilres =Ua

Ra

≤E

Ra

≤E

Ri

(2.64)Uapref

Ri

≤ Ifa =Uapref

|Zi|≤

E

|Zi|= E ·

√

1

R2

i

+ B2

i

2.5 Influence of Insulation Parameters


Magnitude Ifa of a dead ground fault current in three-phase networks can be assessed in similar way

where E is network nominal phase voltage. Geometric sum of phasors of earth leakage currents from all conductors (phases and neutral) is also equal to zero. Generally each of these currents contains both resistive and capacitive component. These components are determined in relation to line-to-ground voltage of a given conductor. For fire risk assessment knowledge of the highest value of leakage cur-rent’s resistive component Ilres can be very useful. This maximum value in any phase of three-phase system fulfills the following inequalities

A more difficult task is determination of leakage current in any part of network e.g. in an outgoing line (feeder). In this case leakage current is equal to geometric sum of currents flowing in all conductors of this line. Analytic determination of this value requires knowledge of admittances of these conductors-to-ground insulation including all galvanically connected elements of this line. However in practice this requirement is not fulfilled because insulation resistance (or impedance) measure-ment is performed for the entire network. Therefore for single lines or parts of a network it is more convenient to measure than to calculate leakage currents.

2.5.2 Assessment of Power Losses in Insulation

For evaluation of fire hazards in unearthed networks it is also useful to know high-est possible heat losses produced (dissipated) in its insulation by leakage currents. In single-phase systems total active power losses in network-to-ground insulation can be assessed by formula (2.67) and in three-phase systems by formula (2.68):

where Ri is network insulation equivalent resistance, E—source phase voltage.It can be easily checked that in AC IT systems total active power loss in net-

work-to-ground insulation may vary from zero to its maximum possible levels given by both formulas.

(2.65)Uapref

Ri

≤ Ifa =Uapref

|Zi|≤

√

3 · E

|Zi|=

√

3 · E ·

√

1

R2i

+ B2i

(2.66)Ilres max ≤Uphase max

Ri

≤

√

3 · E

Ri

(2.67)P =U2

a

Ra

+U2

b

Rb

<

U2a + U2

b

Ri

≤E2

Ri

(2.68)P =U2

a

Ra

+U2

b

Rb

+U2

c

Rc

<

(√

3 · E)2

·

(

1

Ra

+1

Rb

+1

Rc

)

=3 · E2

Ri

37

It can be also shown that when insulation susceptance can be neglected, total active power losses attain their highest possible level for equal insulation resist-ances of all network phases.

2.5.3 Electric Shock Hazard Assessment

An important issue for ensuring safe working conditions for persons is determination of maximum possible leakage and shock currents in electric devices. Grounding is an additional safety measure applied in AC IT systems to limit dangerous touch voltages on conducting parts not belonging to electric circuits. In case of a device insulation deterioration leakage current may flow to ground. Maximum value of this current flowing through the enclosure grounding wire can be assessed if network insulation parameters are known. An example of these abnormal conditions in single-phase networks is discussed below. Figure 2.12 shows a single-phase network circuit dia-gram with grounded conducting enclosure where x and y are resistances of insulation between conductors a, b and the enclosure, Rg is grounding resistance.

If insulation equivalent resistance Ri is known e.g. from insulation monitor indication, maximum possible touch voltage between the enclosure and ground can be determined. To simplify calculations the enclosure-to-ground capacitances were neglected as much smaller than capacitances of the network. It can be shown that the highest possible current in the grounding wire of the enclosure will be for Ra = y = ∞ and Ba = 0 (or Rb = x = ∞ and Bb = 0). For these values network insulation equivalent resistance Ri is

whereas the highest possible RMS voltage Ug between the enclosure and ground equals to

From (2.70) maximum grounding resistance Rg can be derived, for which voltage between the enclosure and ground does not exceed permissible limit value. It can be shown that condition (2.70) does not impose any substantial limit on the range of permissible resistances of protective groundings in AC IT systems. Much lower grounding resistance is required to limit touch voltages on conducting enclosures in case of a double ground fault of both conductors a and b (one wire grounded outside the device, the other one connected to its enclosure). The current of this

(2.69)Ri =1

1Rb

+1

x + Rg

(2.70)

Ug max = E ·

∣

∣

∣

∣

∣

∣

∣

11

Rg + x

11

Rg + x

+1

jBb +1

Rb

∣

∣

∣

∣

∣

∣

∣

·Rg

Rg + x

= E · Rg ·

∣

∣

∣

1

Rb+ jBb

∣

∣

∣

∣

∣

∣1 + (Rg + x) ·

(

1

Rb+ jBb

)∣

∣

∣

= Rg · Ig max

2.5 Influence of Insulation Parameters


double fault must be high enough to ensure adequately fast reaction of overcurrent protections installed in this circuit.

It is also important to know the highest possible voltage between ground and the enclosure in case of its grounding conductor interruption. Assuming in (2.70) Bb = Bi and Rg = ∞ the discussed parameter Ug attains its maximum possible value E. Thus in case of insulation deterioration (but not an earthfault!) in the most unfavourable condition (i.e. Ra = ∞, Ba = 0, Rg = ∞) even the total source volt-age E may be present on the conducting enclosure.

2.6 Ground Fault Current Compensation

Ground fault current levels in AC IT systems can be reduced by forcing an induc-tive current flow with help of an additional, parallel inductive element. This idea is explained in Fig. 2.13a, b for a three-phase network with symmetrical voltage source and any possible, in general case nonsymmetrical, ground insulation admit-tances. Two ways of compensating reactor connection are considered.

In the first case (Fig. 2.13a) reactors were connected between single phases and ground. Capacitors were included in series to reactors to eliminate galvanic connection to ground; this may be necessary to ensure network-to-ground insulation monitoring with DC test signal. With an equivalent inductive admittance BL of the reactor-capacitor circuit, ground fault current through fault resistance r in phase a (see formula 1.14) is

(2.71)Ifa =Ua

r=

E

r·(1 − a2

) · (Yb − jBL) + (1 − a) · (Yc − jBL)

(

1

r+ Ya

)

+ Yb + Yc − 3 · jBL

Fig. 2.12 Circuit diagram of a single-phase network with grounded conducting enclosure

http://dx.doi.org/10.1007/978-3-319-07010-0_1

39

In case of symmetry of single phases-to-ground capacitances and complete compensation in each phase i.e. BL = Ba = Bb = Bc ground fault current depends only on the single phases-to-ground insulation conductances and fault resistance r. Under these conditions this current assumes minimal value for equal insulation conductances of single phases. If these conductances are not identical, the ground fault current is lowest for incomplete compensation of ground capacitances by reactors.

Fig. 2.13 a Connection of compensating reactors between single phases and ground. b Compensating reactor connection between neutral point and ground



Fig. 2.14 An example of a simple compensation system of electric shock current in three-phase AC IT system

Fig. 2.15 System of continuous compensation of capacitive and resistive components of ground fault current with a controlled voltage source

41

If a reactor with admittance BL is connected between the network neutral point and ground as shown in Fig. 2.13b, ground fault current Ifa is given by formula

For symmetrical insulation admittances (i.e. symmetry of both conductances and capacitances) this current assumes zero value with complete compensation i.e. BL

3= Ba = Bb = Bc. Similarly to the previous method, for nonsymmetrical

insulation admittances the lowest ground fault current is obtained with incomplete (i.e. BL = Ba + Bb + Bc) compensation by the reactor.

For limiting fire and electric shock hazards in AC IT systems various meth-ods of ground fault current compensation have been applied. An example of these technologies is capacitive current compensation system designed for 3-phase net-works operated among others at ships [4]. A simplified circuit diagram of this con-cept is shown in Fig. 2.14.

Ground fault or shock current’s capacitive component is compensated here by a reactor connected between an artificial neutral point and ground. Its reactance is man-ually adjusted during test grounding of respective phases (in the drawing this proce-dure is shown only for phase c as an example) via an element modelling human body impedance Rh − Ch. During periodical testing the reactor reactance should be set to such value at which the lowest current in the human body model is obtained. To ensure optimal compensation of shock current’s capacitive component, network-to-ground capacitances should be kept symmetrical—this is achieved with help of an additional set of manually adjusted capacitors (not shown in the figure). The task of complete ground fault or shock current’s capacitive component compensation can be imple-mented also with use of additional voltage source connected between the network artificial neutral point and ground (Fig. 2.15). This voltage source, automatically con-trolled by the grounded phase detector, drives an inductive current to compensate the capacitive component of ground fault current. In this system continuous compensation of the resistive component of a possible ground fault current can also be executed.

This system makes it possible to achieve practically complete ground fault current compensation after approximately 20 ms.

References

1. Ivanov E „Кaк пpaвильнo измepить coпpoтивлeниe изoляции элeктpoycтaнoвoк”, Novosti Elektrotechniki 2/2002 (in Russian) (“How to measure correctly insulation resistance?”)

2. Tsapenko E „Зaмыкaния нa зeмлю в ceтяx 6-35 кB”, Energoatomizdat 1986 (in Russian) (“Ground faults in 6–35 kV networks”)

3. Grawe W „Элeктpoпoжapoбeзoпacнocть выcoкoвoльтныx cyдoвыx элeктpoэнepгeтичecкиx cиcтeм”, Элмop 2003, (in Russian) (“Fire hazard in MV power systems at sea ships”)

4. Telzas Sp. z o.o. „Dokumentacja techniczno-ruchowa I-207-160. Układ kompensacji prądów pojemnościowych UKPP-2” (in Polish) („Technical documentation no. I-207-160 of UKPP-2 system of capacitive currents compensation”)

(2.72)Ifa =Ua

r=

E

r·(1 − a2

) · Yb + (1 − a) · Yc − jBL(

1

r+ Ya

)

+ Yb + Yc − jBL


43

Abstract In this chapter there is presented general information on insulation deterioration signalization systems for AC IT networks. Few systems of continu-ous insulation supervision are described. The old concepts include phase voltages and zero-sequence voltage component monitoring. A newer idea is residual cur-rent monitoring. Limitations of their application are pointed out. Underimpedance system of insulation resistance continuous supervision with use of an auxiliary voltage source is analyzed. Its operation is independent from network ground capacitance level which is a distinguished feature. However the presented systems do not provide accurate insulation resistance measurement.

3.1 Visual Signalization Systems

The oldest system of insulation monitoring in AC IT networks was made of lamps connected between single phases and ground (Fig. 3.1a). In case of one phase-to-ground insulation deterioration its lamp was shining weaker or went off at all. However this simplest system didn’t detect symmetrical insulation level decline. The second shortcoming of this solution was galvanic connection of the network with ground by means of relatively low lamp resistance which in fact eliminated an isolated character of the network. Another idea was replacement of lamps by voltmeters with much higher internal impedance (Fig. 3.1b); however this con-cept maintained the first drawback. In three-phase networks insulation failure was indicated by one of respective voltmeters. Another version of the above mentioned design was a detection system with reduced number of voltmeters (Fig. 3.1d) suit-able for networks with neutral conductor.

Chapter 3Insulation Monitoring Systems


44 3 Insulation Monitoring Systems

Fig. 3.1 a System of insulation monitoring in AC IT single-phase systems based on lamps. b Voltmeter system of insulation monitoring in AC IT single-phase systems. c System of insulation monitoring in AC IT three-phase systems with three voltmeters. d System of insulation monitoring in AC IT three-phase systems with two voltmeters

45

3.2 Other Systems of Continuous Insulation Monitoring

3.2.1 Phase Voltages Monitoring

As electrical engineering developed, electricians started to use voltage relays for insulation monitoring. The first systems of continuous insulation-to-ground moni-toring were based on phase voltages measurement with undervoltage or overvolt-age relays (Fig. 3.2).

Thanks to overvoltage relays application risk of this alarm system misoperation (inadvertent operation) caused by measuring circuit failure (break, short circuit, loss of supply) has been eliminated. Each of relays signalled the other conduc-tor-to-ground insulation deterioration, when voltage at its terminals exceeded set pick-up value Up Taking into account the relays pick-up condition Ua > Up or Ub > Up the range of alarmed values of single wires insulation resistances for pos-sible changes of network-to-ground capacitances can be established. For total net-work-to-ground capacitance Ci = Ca + Cb the highest voltage, for example Ua, is obtained when both total insulation leakage conductance Gi and capacitance Ci are lumped at conductor b. Assuming that the relays coils impedance is much higher than the network insulation capacitive reactance or leakage resistance, voltage across RVa relay terminals is of course maximal and equal to E.

As such asymmetrical distribution of insulation capacitances and conductances can-not be in practice excluded, this method of insulation monitoring with voltage relays is in fact useless. This negative conclusion is also true for symmetrical distribution of

Fig. 3.2 System of continuous insulation-to-ground monitoring of AC IT single-phase network based on undervoltage/overvoltage relays RV



both capacitance and conductance—in this situation voltages of conductors a and b are equal. Even for negligible ground capacitances the situation is not any better. Only in some few cases application of voltage relays proves useful. For example, with roughly symmetrical distribution of ground capacitances i.e. Ca ≈ Cb, pick-up Up voltage is obtained with Ra = ∞ and Rb = Ri fulfilling the following condition

This formula gives the highest insulation equivalent resistance Ri signalled by overvoltage relays set to Up in case of symmetrical capacitance values Ca = Cb. With higher insulation capacitance maximum value of signalled insulation equiva-lent resistance for the same alarm setting Up decreases. Operating characteristic of this monitoring system (ratio Ri/Xi versus relative overvoltage pickup setpoint Up/E) plotted according to formula (3.1) is shown in Fig. 3.3.

3.2.2 Zero-Sequence Voltage Component Monitoring

Another method of three-phase AC IT systems insulation monitoring is measure-ment of phase voltages zero-sequence component U0. Similarly to voltage relays application this method, due to substantial sensitivity to ground capacitances, can provide only approximate information on insulation resistance level. Taking an overvoltage relay pick-up condition U0 > Up into account, a range of alarmed insulation resistance levels—assuming some simplifying limitations—can be

(3.1)Rb = Ri ≤1

ω · Cb

√

E2 − U2p

4 · U2p − E2

Fig. 3.3 Characteristic curve of the monitoring system operation based on overvoltage relays valid for symmetrical distribution of ground capacitances Ca ≈ Cb

47

determined. If Ca = Cb = Cc = C (which however is not always true in low volt-age circuits), then maximum value of U0 for a given equivalent insulation resist-ance level is obtained when total insulation leakage conductance Gi is lumped at one phase only. This conclusion can be easily proved by checking maximum of function (of two variable parameters Ga and Gb) described by formula (1.13) for given values of insulation equivalent conductance Gi and susceptance Bi:

If total insulation leakage conductance Gi is lumped at one phase, maximum RMS value of U0 is

Voltage U0 referred to E depends on ratio Ri

X=

Ri1

3·ω·C

. From (3.3) maximum

equivalent insulation resistance Ri, signalled by the zero-sequence component overvoltage relay set to Up can be calculated

This dependence is illustrated in Fig. 3.4.Similarly to the previous concept with voltage relays, sensitivity of the system

detection decreases with growth of insulation-to-ground capacitances.

(3.2)

∣

∣U0

∣

∣ = E ·

∣

∣

∣

∣

∣

Ya + a2· Yb + a · Yc

Ya + Yb + Yc

∣

∣

∣

∣

∣

= E ·

∣

∣

∣

∣

Ga + a2· Gb + a · (Gi − Ga − Gb)

Gi + jBi

∣

∣

∣

∣

(3.3)U0 = E ·

∣

∣

∣

∣

Gi

Gi + j · 3 · ω · C

∣

∣

∣

∣

=E

√

1 + (3 · ω · C · Ri)2

(3.4)Ri =

√

E2 − U2p

3 · ω · C · Up

Fig. 3.4 Characteristic of insulation monitoring system based on zero-sequence voltage meas-urement in three-phase network


http://dx.doi.org/10.1007/978-3-319-07010-0_1


However in a general case for any possible distribution of both insulation capacitances and leakage conductances between single phases (which unfor-tunately cannot be excluded in low voltage unearthed circuits), this method of insulation monitoring proves useless. For example with ground capacitances and leakage conductances lumped at one phase only, U0 is equal to source voltage E. In this situation zero-sequence voltage relay cannot be set at all. On the other hand, for symmetrical insulation capacitances and leakage conductances of all phases, no symmetrical deterioration can be detected. These drawbacks substan-tially limit scope of this method’s application.

The discussed method was sometimes in the past applied also for single-phase AC IT networks (Fig. 3.5). In this case the test voltage for insulation resistance monitoring was measured between the network artificial neutral point (center N of identical elements e.g. capacitors C connected in series) and ground. In healthy conditions this “displacement” voltage is zero for symmetrical insulation admit-tances of both conductors a and b. The quantity increases with asymmetrical insu-lation deterioration. However, similarly to three-phase networks, this voltage is also strongly influenced by insulation capacitances.

3.2.3 Residual Current Monitoring

In low voltage AC TT and TN systems residual current monitors (RCM) have gained broad application for insulation fault location. These devices detect resid-ual (differential) current, i.e. geometric sum of current phasors in all phase and

Fig. 3.5 Insulation monitoring based on “displacement” voltage UN measurement in AC IT single-phase network

49

neutral conductors, which flows in lines with ground insulation deterioration. In three-phase three-wire networks residual current is zero-sequence component of phase currents. RCM’s operation should be selective, i.e. the devices should sig-nal current flow from network to ground only through insulation leakage conduct-ances, but not through capacitances.

In AC IT systems this selectivity requirement fulfillment is possible only in cer-tain specific conditions. Figure 3.6 presents an example of correct operation of RCM. Figure 3.7a, b show cases of RCM incorrect operation. In Fig. 3.7a the monitor can-not detect insulation deterioration because it does not measure actual fault current at all. In Fig. 3.7b monitor A measures only capacitive current, so it issues a false alarm.

A necessary condition for RCM correct operation follows from the figures above: network-to-ground upstream capacitances (Ca, Cb in Fig. 3.6) must be high enough to ensure the required minimal fault current flow measured by the monitor.

Using the network circuit diagram shown in Fig. 3.8 it is possible to determine an approximate range of insulation resistances detected by a RCM with Ip setting. At first for simplicity ground capacitances are neglected and it is assumed that the total current measured by the monitor is equal to ground fault current.

From the condition of the RCM’s pick-up in case of a single phase ground fault through a fault resistance r

it is possible to determine maximal equivalent ground insulation resistance Ri of the whole network (measured in the pre-fault condition), for which the earth fault current is higher than Ip threshold

(3.5)Ip <

E

r + Ri

(3.6)Ri <

E

Ip

− r

Fig. 3.6 Example of RCM correct operation



Thus residual current monitors installed at single lines set to Ip cannot detect insu-lation equivalent resistances higher than E

Ip. For equivalent resistances

in networks with negligible ground capacitances these monitors cannot detect even dead earth faults (i.e. r = 0). This proves that RCM’s capabilities for insulation

(3.7)Ri >

E

Ip

Fig. 3.7 a Example of RCM missing operation. b Example of false alarm issued by RCM-A

51

monitoring in AC IT systems are very limited. When ground capacitances are taken into account the upper detection limit for Ri grows. Application of direc-tional RCM’s, capable of discrimination of earth fault current flow direction, ensures selectivity of fault location. These monitors determine the direction with help of signals of residual current and network voltage. Directional RCM opera-tion in single phase AC IT system is explained in Fig. 3.9a, b. When ground fault location changes from internal (a) to external (b), direction of residual cur-rent detected by the monitor turns to opposite in relation to network voltage E. In three-phase networks zero-sequence component of phase voltages is used as volt-age signal for directional RCM’s.

In three-phase networks application of RCM’s without directional option is jus-tified only in systems with specific distribution of ground capacitances between respective lines. Dead ground faults in a single k-th line are detected only when its monitor’s pick-up value is

where I0k is zero sequence current in a given k-th line, Eph—source phase volt-age, Cs—total network-to-ground capacitance (i.e. for zero sequence compo-nent), Ck—total ground capacitance of k-th feeder. In order to avoid inadvertent pick-up of RCM in any healthy m-th line, its setting must meet the following condition

These conclusions are well-known principles of design of zero-sequence current ground fault protections in three-phase unearthed networks (Fig. 3.10).

(3.8)Ip < 3 · I0k = Eph · ω · (Cs − Ck)

(3.9)Ip > 3 · I0m = Ef · ω · Cm

Fig. 3.8 Illustration of AC IT single-phase network for evaluation of RCM’s sensitivity



3.2.4 Underimpedance System

For ground fault detection in AC IT networks with any number of phases an underimpedance system can be applied too. In the signalization system (Fig. 3.11) there is used an auxiliary AC voltage U source of f0 frequency different from fre-quency f of the monitored network. This source is connected through bandpass F filter for f0 frequency and blocking for other frequencies, and series connected resistor R0 between ground and any conductor of the network (Fig. 3.11).

Fig. 3.9 a Discrimination of ground fault location with use of directional RCM—internal fault. b Discrimination of ground fault location with use of directional RCM–external fault

53

Fig. 3.10 Directional RCM application in AC IT three-phase systems

Fig. 3.11 An underimpedance alarm system for insulation monitoring



To the measuring unit based on rectified voltages comparator two voltages of test frequency f0 are fed: voltage across resistor R0 (UR) and network-to-ground insulation impedance Z (UZ).

Comparator’s pick-up condition is

where voltages UR and UZ are respectively UR = U ·R0

R0+Z, UZ = U ·

ZR0+Z

, coeffi-

cients kR and kZ depend on ratio of the device input transformers (not shown in the drawing). An equivalent impedance Z consisting of parallelly connected insulation equivalent resistance Ri and insulation capacitive reactance Xi is given by formula

By substituting expressions for UR and UZ to inequality (3.10) characteristic of underimpedance alarm element is obtained

The alarm element operation area is located inside the circle (Fig. 3.12) described by inequality (3.12).

The underimpedance alarm element picks up if complex value of insulation equivalent impedance Z is located inside this circle.

Substitution of Z by (3.11) gives the condition

(3.10)∣

∣kZ · UZ − kR · UR

∣

∣ ≤ kR ·

∣

∣UR

∣

∣

(3.11)Z =Ri · (−j · Xi)

Ri − j · Xi

=Ri · X2

i − j · R2i · Xi

R2i + X2

i

(3.12)

∣

∣

∣

∣

Z −kR

kZ

· R0

∣

∣

∣

∣

≤kR

kZ

· R0

(3.13)

∣

∣

∣

∣

∣

(

Ri · X2i

R2i + X2

i

−kR

kZ

· R0) − j ·R2

i · Xi

R2i + X2

i

∣

∣

∣

∣

∣

≤kR

kZ

· R0

Fig. 3.12 Characteristic of the underimpedance alarm system on R-X plane

55

which can be transformed to the following inequality

After transformation and simplification the final condition for alarm is obtained:

It follows from the last formula that the alarm threshold is independent from capacitive reactance level Xi which is a valuable feature of the presented system. Implementation of continuous determination of insulation parameters with use of the presented measuring system is described in Sect. 4.4.

(3.14)(

Ri · X2i

R2i + X2

i

−kR

kZ

· R0)2+ (

R2i · Xi

R2i + X2

i

)2

≤ (

kR

kZ

· R0)2

(3.15)Ri ≤ R0 ·2 · kR

kZ


http://dx.doi.org/10.1007/978-3-319-07010-0_4

57

Abstract In this chapter several methods of continuous measurement of insulation resistance in AC IT systems are described. Measuring circuits with use of test direct current supplied by an auxiliary DC source or diode rectifiers are presented. The most commonly applied measurement method with an auxiliary rectangular voltage source is explained. Another method of continuous insulation resistance measurement is imposition of an auxiliary sinusoidal voltage of a specific fre-quency different from voltage frequency of the monitored network. Examples of both techniques implementation in modern insulation meters are presented.

4.1 Measurement Circuits with Test Direct Current

The oldest and still commonly applied method of continuous measurement of AC IT network-to-ground insulation resistance has been imposition of an auxiliary DC current signal. As direct current flows only through leakage resistances and not through insulation capacitances, then by measuring its parameters (voltage and current) insulation resistance can be determined. This idea is explained in Fig. 4.1 where an auxiliary battery Eaux drives a test current Itest through a resistor R and series connected insulation-to-ground resistances Ra and Rb. An AC source offers a negligible resistance to direct current and therefore for DC test current conductors a and b are connected parallelly. The test current is equal to

and provides information on insulation-to-ground equivalent resistance Ri. This well known idea has been successfully applied in traditional ohmmeters. Though also an alternating current driven by the AC voltage source flows through the auxiliary source Eaux, this component has zero mean value and therefore it does not influence the test current measurement result.

This concept has also been successfully implemented in measuring circuits based on diode rectifiers.

(4.1)Itest =Eaux

R +Ra·Rb

Ra+Rb

=Eaux

R + Ri

Chapter 4Systems of Insulation Resistance Continuous Measurement


58 4 Systems of Insulation Resistance Continuous Measurement

4.2 Measuring Circuits with Diode Rectifier

In AC IT systems with any number of phases broad application was gained by measuring circuits with diode rectifiers. Main advantages of this concept are sim-ple construction, lack of an auxiliary supply source and operation unaffected by network-to-ground capacitances.

4.2.1 Star Connected Diode Rectifier

A commonly used rectifying circuit comprising star connected diodes is presented below at two examples. In the first one (in Fig. 4.2 presentation for three-phase networks) ground capacitances were neglected. This assumption enables a sim-ple derivation of a formula describing the sought parameter i.e. insulation equiva-lent resistance. However it can be proved that with non-zero ground capacitances the derived formula is still valid.

Here three diodes V1, V2, V3 are star connected to respective phase conductors through fuses F. All cathodes are connected to ground through an ammeter and cur-rent limiting resistor Rm. In the circuit only this diode is conducting whose anode has the highest potential as compared to connected cathodes. Anodes of two remaining diodes have negative potential because voltage across the conducting diode is practically equal to zero. Switchover from one conducting diode to another one takes place at the moment when their phase voltages get equal. In this circuit the measured quantity is cur-rent i flowing through Rm resistor. For phase-to-phase voltage Uab given by a function

(4.2)uab(t) =

√

3 ·

√

2 · E · sin(

2π

T· t)

Fig. 4.1 Insulation resistance measurement with DC test current injection

59

phase a diode conducts in time period 2·T

12< t < 6·T

12. According to Thevenin’s the-

orem test current i is within this time interval

where ea(t) is the source phase a voltage, u0(t)—zero sequence voltage. Within period 6·T

12< t < 10·T

12 phase b diode conducts, whereas for 10·T

12< t < 14·T

12—it is

phase c diode. Therefore mean value imean of the test current is

(4.3)i(t) =ua(t)

Rm + Ri

=ea(t) − u0(t)

Rm + Ri

(4.4)

imean =1

T·

6T/12

2T/12

ea(t) − u0(t)

Rm + Ri

dt +

10T/12

6T/12

eb(t) − u0(t)

Rm + Ri

dt

+

14T/12

10T/12

ec(t) − u0(t)

Rm + Ri

dt

=1

T·

1

Rm + Ri

·

6T/12

2T/12

ea(t)dt +

10T/12

6T/12

eb(t)dt

+

14T/12

10T/12

ec(t) −

14T/12

2T/12

u0(t)dt

Fig. 4.2 Insulation measuring circuit with three star-connected rectifiers



Taking into account the following formulas

and that mean value of sinusoidal voltage u0(t) is equal to zero, mean value of the test current imean is obtained from (4.4) as

Insulation equivalent resistance Ri is therefore equal to

The main drawback of this method of insulation equivalent resistance determination is dependence of its result on the network supply voltage level E. If not all source voltages of respective phases are equal as was assumed above (4.5, 4.6 and 4.7), then formula (4.9) is no longer valid at all.

The second example presents a simplest measuring circuit made of two star- connected diodes. In Fig. 4.3 it is used in a multi-phase AC IT network. The rectifying diodes can be connected to any two conductors with voltage source e between them. Voltage sources of the remaining phases were replaced by ux source.

(4.5)ea(t) =

√

2 · E · sin2π

T· (t −

T

12)

(4.6)eb(t) =

√

2 · E · sin2π

T· (t −

5 · T

12)

(4.7)ec(t) =

√

2 · E · sin2π

T· (t −

9 · T

12)

(4.8)imean =3 ·

√

3 ·

√

2

2π

·E

Rm + Ri

(4.9)Ri =3 ·

√

3 ·

√

2

2π

·E

imean

− Rm

Fig. 4.3 Insulation equivalent resistance determination with use of two star-connected diodes

61

If ground capacitances cannot be neglected, then a different approach to the system’s operation analysis may be used. For simplicity this idea is explained at the example of a single-phase AC IT system where e(t) = Em · sin ωt with ux(t) = Uxm · sin(ωt − α) representing the remaining part of a multi-phase network. Generally parameters Uxm and α may assume any possible values. In a circuit with two diodes their commutation takes place every half of a cycle when source voltage e(t) assumes zero level.

The whole procedure consists of measuring of a selected pole to ground voltage mean value with a voltmeter with internal conductance GV. Within time interval 0 < t < T/2 diode D1 conducts

Within the next time interval T/2 < t < T diode D2 conducts

Designating insulation equivalent parameters of the whole network as Gi = Ga + Gb + Gx and Ci = Ca + Cb + Cx, both equations can be written in simpler form

After integrating Eq. (4.12) over its time limits 0 < t < T/2 and (4.13) over T/2 < t < T these expressions should be added. As all components dependent on ground capaci-tances give zero sum (note that e(0) = e(T/2) = e(T) = 0, ux(0) = ux(T) and that ux mean value over T period is zero), the following equation is obtained

from which the final formula is derived

In this way it was shown that a two star-connected diodes circuit is useful for insulation resistance measurement of not only single-phase systems but also of networks with any (unlimited, not necessarily known) number of phases. Other advantages of the presented method are extreme simplicity and possibility of

(4.10)(Ga + GV ) · u + Ca ·

du

dt− Gb · (e − u) − Cb ·

d(e − u)

dt

+ Gx · (u + ux) + Cx ·d(u + ux)

dt= 0

(4.11)(Gb + GV ) · u + Cb ·

du

dt+ Ga · (e + u) + Ca ·

d(e + u)

dt

+ Gx · (e + u + ux) + Cx ·d(e + u + ux)

dt= 0

(4.12)(Gi + GV ) · u + Ci ·du

dt= Gb · e + Cb ·

de

dt− Gx · ux − Cx ·

dux

dt

(4.13)

(Gi + GV ) · u + Ci ·du

dt= −(Ga + Gx) · e − (Ca + Cx) ·

de

dt− Gx · ux − Cx ·

dux

dt

(4.14)(Gi + GV ) ·1

T

T∫

0

udt = (Gi + GV ) · Umean =Em

π

· Gi

(4.15)Ri =1

Gi

= RV ·

Em

π− Umean

Umean



continuous operation which can be implemented either with a voltmeter graduated in resistance units (k ohms) or in a way presented in Fig. 4.4. In the latter case input 2 of a logometric meter LM is fed with u voltage and input 1 with difference of half of rectified e voltage and u voltage. The operating principle of logometric meter (namely division of input voltages) permits to fulfill insulation resistance measurement insensitive to voltage E variation.

4.2.2 Diode Bridge Rectifier

Full-wave bridge rectifier is another commonly used circuit for insulation equiva-lent resistance measurement in AC IT systems. This idea is explained in a general case of a multi-phase network (Fig. 4.5). Voltage sources of the remaining phases were replaced by ux source. Just as in previous case the rectifying diodes can be connected to any two conductors with voltage source e between them.

The procedure comprises measurement of mean value of both poles-to-ground voltages u1 and u2 with a voltmeter with internal conductance GV. In the first step u1 mean value is measured. Within time interval 0 < t < T/2 diodes D1 and D4 conduct and leakage currents balance according to Kirchhoff’s 1st law is

Within the next time interval T/2 < t < T diodes D2 and D3 conduct, so leakage currents balance is

(4.16)(Ga + GV ) · u1 + Ca ·

du1

dt− Gb · (e − u1)

− Cb

d(e − u1)

dt+ Gx · (ux + u1) + Cx ·

d(ux + u1)

dt= 0

(4.17)

(Gb + GV ) · u1 + Cb ·du1

dt+ Ga · (e + u1) + Ca ·

d(e + u1)

dt

+ Gx · (u1 + e + ux) + Cx ·d(u1 + e + ux)

dt= 0

Fig. 4.4 Logometric meter of continuous insulation resistance measurement with use of diode rectifiers

63

In the second step u2 mean value is measured. Within time interval 0 < t < T/2 diodes D1 and D4 conduct

Within the next time interval T/2 < t < T diodes D2 and D3 conduct

From these equations the following formulas for mean values of u1 and u2 are obtained (Gi = Ga + Gb + Gx)

Solution of this system of equations is

For three-phase symmetrical networks the following formula applies

(4.18)Ga · (e − u2) + Ca ·

d(e − u2)

dt− (Gb + GV ) · u2

− Cb ·du2

dt+ Gx · (ux + e − u2) + Cx ·

d(ux + e − u2)

dt= 0

(4.19)−Gb · (e + u2) − Cb ·

d(e + u2)

dt− (Ga + GV ) · u2

− Ca ·du2

dt+ Gx · (ux − u2) + Cx ·

d(ux − u2)

dt= 0

(4.20)(Gi + GV ) · U1−mean =Em

π

· (Ga + Gb + Gx)

(4.21)(Gi + GV ) · U2−mean =Em

π

· (Ga + Gb + Gx)

(4.22)Gi =1

Ri

= GV ·U1−mean + U2−mean

2·Em

π− U1−mean − U2−mean

(4.23)Gi =1

Ri


3√

3·Em

π− U1−mean − U2−mean

Fig. 4.5 Insulation equivalent resistance measurement with full-wave bridge rectifier in a multi-phase network



It can be easily checked that formulas (4.22) and (4.23) are specific cases of a gen-eral expression

where U12–mean is mean value of output (rectified) voltage of the applied full-wave rectifier in a network with any number of phases. Though this method of periodical insulation equivalent resistance determination is based on voltages division, it may be affected by source voltages variation as U1–mean, U2–mean and U12–mean are meas-ured successively (not simultaneously).

4.2.3 Other Rectifier Based Measuring Circuits

A simple circuit consisting of rectifying diodes, capacitor and an ammeter can be used for measurement of insulation equivalent resistance (Fig. 4.6). A charged capacitor C serves as a DC test voltage source. It is charged through diodes which conduct every second semi-period. During the remaining semi-periods, when diodes are blocked, the capacitor is discharged in the test cir-cuit: an auxiliary resistor R—ammeter—ground—insulation resistances and the network. Indication of the meter depends directly on insulation equivalent resistance value and to some extent also on ground capacitances (not shown at the drawing).

(4.24)Gi =1

Ri


U12−mean − U1−mean − U2−mean

Fig. 4.6 Insulation monitoring by discharging capacitor through leakage resistances Ra, Rb, Rc of single phases insulation

65

A simpler measuring circuit based on a single-diode half-wave rectifier (Fig. 4.7) was also applied along with bridge rectifier systems.

This circuit was suitable also for multiple-phase AC IT systems. However mean value of half-wave rectified test current is subject to strong influence of ground capacitances. Each phase-to-ground capacitance is consecutively charged by rectifier and discharged through insulation leakage resistances. Measuring cir-cuit with full-wave rectifier shown in Fig. 4.8 can operate in multiple-phase AC IT systems too.

Test current is injected by an auxiliary sinusoidal voltage source, which can be connected to the monitored network directly (not shown here) or through an intermediary transformer (Fig. 4.8). Test current is limited by resistors X and Y. An overcurrent (O/C) relay for insulation level deterioration alarm is series connected with milliammeter. Test current mean value is proportional to the auxiliary source voltage and inversely proportional to sum of insulation equiv-alent resistance and limiting resistors values. In order to make measurement results less dependent on the network AC voltage, the rectifier is shunted by a capacitor C. It forms a by-pass for AC currents flowing through network-to-ground capacitances.

Another concept of insulation equivalent resistance supervision in multiple-phase AC IT networks was based on logometric measuring system. Its windings are supplied with rectified stabilizing and test currents injected by an auxiliary AC voltage source. This idea was implemented in MKN-380 type devices (Fig. 4.9) manufactured in the former USSR.

Fig. 4.7 Insulation measuring circuit with half-wave rectifier



This device operating principle is similar to that of typical meg-ohmmeter. A sensitive magneto-electric overcurrent relay is connected in series with the test cur-rent winding. This alarm relay picks up with test current increase due to network insulation deterioration.

Fig. 4.9 Insulation monitoring with help of logometric measuring system

Fig. 4.8 Insulation measuring circuit with full-wave rectifier

67

4.3 Measurement Method with an Auxiliary Rectangular Voltage Source

Application of an auxiliary periodical rectangular voltage source is another effec-tive method of continuous monitoring of network-to-ground insulation (Fig. 4.10).

An auxiliary source of periodical rectangular voltage with amplitudes equal to −Uaux and +Uaux is connected between one of network conductors and ground. As a result each phase-to-ground voltage as well as all leakage currents are sub-ject to periodic variations. Duration of single voltage pulse is sufficiently long to obtain a steady-state network response. Therefore it must be much longer than both AC sinusoidal supply voltage cycle and the network time constant deter-mined by ground insulation capacitances and leakage resistances. Steady-state mean value of voltage between any point of the network and ground in consecu-tive halves of the period is equal respectively to −U0 and +U0 (generally U0 may differ from Uaux). In these halves of the period a steady-state current superimposed by the auxiliary source, flowing exclusively through insulation leakage resistances, is respectively equal to −I0 and +I0. Network-to-ground insulation equivalent resistance is given by formula

This formula can be derived using superposition principle. According to this prin-ciple periodic, rectangular variations of steady- state leakage current values depend only on the rectangular test voltage. Thus with steady-state phase-to-ground aver-age voltage −U0 total leakage current driven by the rectangular voltage source is

(4.25)Ri =U0

I0

(4.26)I1 = −U0

Ri

Fig. 4.10 Continuous insulation monitoring with use of an auxiliary periodical rectangular volt-age source

4.3 Measurement Method with an Auxiliary Rectangular Voltage Source


where Ri is network insulation equivalent resistance equal to the equivalent resist-ance seen from terminals of the auxiliary voltage source. In the next half of the period leakage current forced by +U0 auxiliary voltage equals to

Difference of leakage currents in two consecutive halves of period is

Designating I2 − I1 = 2 · I0 formula (4.25) is obtained.

4.3.1 Examples of Application

Insulation monitor (isometer) IRDH375 type [1] manufactured by Bender belongs to most commonly applied devices in AC IT (and DC as well) systems. Its measuring circuit is connected between the network phases and ground. An auxiliary rectan-gular voltage controlled by microprocessor is imposed on the monitored network. Frequency of voltage pulses with amplitude up to 50 V is adjusted to actual insula-tion resistance and capacitance levels. The isometer operation produces phase-to-ground voltage oscillations.

In Fig. 4.11 there is shown phase-to-ground voltage waveform versus time during IRDH375 operation.

On the basis of measured test current, the isometer calculates insulation equivalent resistance. Network-to-ground capacitance (maximal permissible level 500 µF) does not influence calculations result, however it affects time of measurement exe-cution. Test current is limited to 0.28 mA by the monitor’s internal impedance. An error of alarm pick-up and of displayed measurement result is below 20 % within the whole range of measurement 1 kΩ–10 MΩ.

Microprocessor device for insulation monitoring MR627 type (former AREVA) [2] is designed for both AC and DC IT systems with maximum voltage 690 V and frequency up to 400 Hz as well as galvanically connected AC and DC networks (see Chap. 12). There are two independent time-delayed alarm elements with set-ting range 10–990 kΩ. Measured insulation equivalent resistance is displayed at the front panel. It can be also transmitted as mA signal through current output 0–1 mA. The monitor is equipped with few options of insulation measurement. The basic one is superimposition of voltage rectangular pulses ±30 V with fre-quency adjusted to ground capacitance. The alarm maximum error is ±25 %. For any insulation parameters current forced by the monitor voltage source with inter-nal resistance 1 MΩ (version B) does not exceed 0.035 mA which is a safe level for network devices.

(4.27)I2 =U0

Ri

(4.28)I2 − I1 = 2 ·U0

Ri

http://dx.doi.org/10.1007/978-3-319-07010-0_12

69

4.4 Measurement with Use of Auxiliary AC Voltage

Imposition of an auxiliary sinusoidal voltage of a specific frequency different from frequency f of the monitored network, is another method of continuous insula-tion parameters measurement. In AC IT systems this test current flows through all ground capacitances and leakage resistances. Measurement of this current makes it possible to determine insulation equivalent resistance and capacitance. Equivalent circuit of the measuring system with connected monitored network is shown in Fig. 4.12.

The equivalent circuit diagram of this system for test signal frequency f0 is pre-sented in Fig. 4.13. Of course it does not include the network supply voltage E source as it drives currents of the network f frequency.

Therefore sinusoidal test current I0 of f0 frequency is given by formula

In the circuit RMS values of test voltage U0 and current I0 as well as phase shift between them are measured. From comparison of real parts and separately of imaginary parts of both sides of Eq. (4.29) values of sought parameters Ri and Ci are calculated.

Another example of application of sinusoidal test signal for insula-tion parameters measurement is under-impedance alarm system presented in Sect. 3.2.4. In the measurement circuit (Fig. 3.11) a simple method of insulation

(4.29)I0 =

U0

R +1

1

Ri+j·2π ·f0·Ci

Fig. 4.11 Network phase voltage (rated parameters 60 V, 50 Hz) variation with IRDH375 isometer in operation

4.4 Measurement with Use of Auxiliary AC Voltage

http://dx.doi.org/10.1007/978-3-319-07010-0_3

http://dx.doi.org/10.1007/978-3-319-07010-0_3


Fig. 4.12 Circuit diagram of AC IT network with use of insulation monitoring system comprising an auxiliary sinusoidal voltage U0 source of f0 frequency. F—band-pass filter for f0 frequency, R—measuring circuit internal resistance

Fig. 4.13 Circuit diagram of AC IT network for f0 test signal frequency

parameters (equivalent resistance Ri and capacitive reactance Xi) determination can be implemented. The following formulas for both parameters can be derived

(4.30)Ri = R0 ·2 · U

20

U2 − U2R

− U20

71

where U, U0 and Ui are RMS values of sinusoidal voltages of the test source frequency.

4.4.1 Application Example

Insulation monitor XM200 type (Schneider-Electric) [3] is designed for AC IT systems (and for DC too) up to 500 V rated voltage. Its operation principle con-sists in use of an auxiliary AC voltage of 2.5 Hz frequency. Because of this low frequency this isometer cannot be applied in circuits with frequency converters which produce voltages of frequency below 5 Hz. The device measures both insu-lation equivalent parameters, i.e. resistance and capacitance. Actual current values of theses quantities are continuously displayed at the front panel. Internal imped-ance of the meter is 33 kΩ. Test current with maximum value of 3 mA is driven by the auxiliary internal voltage source with rated parameters 25 V, 2.5 Hz. Insulation resistance measurement range is 0.1–999 kΩ for ground capacitance up to 200 µF. The monitor has two settable alarm thresholds with delayed operation. This device can also be used for earth fault location as a test signal generator.

References

1. http://www.bender.org2. http://www.schneider-energy.pl3. http://www.schneider-electric.com

(4.31)

Xi = −R0 ·2 · U

20

√(U + UR + U0) · (UR + U0 − U) · (U + U0 − UR) · (U + UR − U0)

4.4 Measurement with use of Auxiliary AC Voltage

http://www.bender.org

http://www.schneider-energy.pl

http://www.schneider-electric.com

Part IIDC IT Systems

75

Abstract In the chapter general information on DC networks is given. Spatial distribution of insulation between the network poles as well as between each pole and ground is pointed out. Transformation of spatially distributed physi-cal systems into topology of discrete elements is described. Equivalent circuit dia-grams of batteries in steady-state condition are presented. Formulas for parameters of the equivalent circuits are derived for the most general condition of insulation leakage conductance distributed nonuniformly (at random) within the battery’s single cells. DC system representation in form of Π or T two-port network is proposed. Equivalent circuit diagram of a DC network with an AC voltage source is given.

5.1 DC Network Simplified Circuit Diagram

Typical DC (direct current) network consists of supply source, measurements and protections systems/devices, wiring and loads (Fig. 5.1).

Most often DC IT network is fed by a battery charged by a rectifier supply unit. In correctly designed and maintained DC system there are no AC components pre-sent in its voltages. However in practice DC voltage supplied from a rectifier may contain some harmonics.

These unnecessary components are caused by inductive or capacitive couplings or galvanic connection with other AC circuits. Modern DC IT supply systems are equipped with indispensable current and voltage measuring devices, insu-lation monitor (isometer) and possibly an automatic earth fault locating system. The most extensive element of DC system is conductors delivering power to all parts of the network. Insulation between the network poles as well as between each pole and ground has spatial distribution. As in AC IT systems electrical insu-lation parameters are its resistance and capacitance. Their values influence line-to-ground voltages and ground fault currents both in transient and steady-state conditions. In DC systems line-to-ground voltages and earth fault currents depend exclusively on line-to-ground insulation of single conductors. These magnitudes

Chapter 5Equivalent Circuit Diagrams of DC Networks


76 5 Equivalent Circuit Diagrams of DC Networks

are—similarly to AC IT networks—not dependent on line-to-line (pole-to-pole) insulation parameters levels.

In order to simplify description of the behaviour of spatially distributed physical systems it is convenient to transform them into a topology consisting of discrete elements. The lumped element model of electric circuit’s insulation makes the simplifying assumption that its attributes, i.e. resistance and capacitance, are concentrated into idealized elements, resistors and capacitors, connected to the network conductors.

According to the simplified DC network circuit diagram these elements are respectively resistors R1, R2 and capacitors C1, C2. However practical usefulness of this representation is quite limited. Commonly applied insulation monitors measure network insulation equivalent resistance to ground which is a substi-tute resistance of all elements existing between galvanically connected points of this electric circuit and ground. Meaning (sense) of this electrical parameter can be explained using thevenin’s theorem. Network insulation equivalent resist-ance to ground is resistance between the point of possible earth fault and ground. It is calculated as a substitute resistance of all parallelly connected resistive ele-ments existing between this network and ground with all voltage sources being shorted and all current sources being eliminated. The purpose of this parameter follows directly from Thevenin‘s theorem—its application simplifies earth fault current calculation, which is inversely proportional to sum of fault resistance in place of the fault and the aforementioned substitute insulation resistance. Due to this dependence as well as convenience to perform measurement, this parameter is much more often used than resistances of single poles-to-ground insulation. For the same reasons equivalent (total) insulation to ground capacitance is a more useful quantity than capacitances of single conductors-to-ground.

Fig. 5.1 Simplified circuit diagram of a DC network

77

5.2 Equivalent Circuit Diagrams of Batteries

Any battery constitutes a voltage source system with three (or four) terminals (two poles and ground) and spatial distribution of single cells-to-ground insulation. For these active four terminal networks equivalent circuit diagrams can be formed with lumped insulation parameters. These circuit diagrams are useful for calcula-tion of currents and voltages between respective poles and ground in DC IT net-works with any insulation parameters levels. In particular they are indispensable for accurate determination of electrical parameters of ground faults both in tran-sient and steady-state condition. These calculations may be necessary for analysis of control devices behaviour in case of insulation failure.

Therefore an important task is to determine parameters of the four terminal net-work, such that with any insulation earth leakage conductances and capacitances of the external network, at the terminals of this battery’s equivalent circuit there will appear the same voltages and currents as at the terminals of the actual battery. An additional requirement, which follows from Thevenin’s theorem, are equal values of insulation equivalent resistance of the battery in both representations. Below at the example of pi (Π) two-port network it is proved that this require-ment, with any insulation leakage conductances G1S and G2S of external network, is fulfilled only for some specific values of battery insulation conductances G′ and G″. It is also shown that these parameters values are dependent exclusively on the battery insulation properties. Below these characteristic values G′ and G″ are determined. Also it is proved that at the terminals of both compared battery circuit diagrams there are present equal pole-to-ground voltages i.e. U′ = V′. Considerations presented below are limited to steady-state condition of battery and DC IT network without any voltage sources other than direct current. In these con-ditions there is no need to take into account insulation capacitances.

According to the author’s proposal [1], substitute (total) insulation conductance Gi of the battery was split to actual insulation leakage conductances of respective cells Gi =

∑N1

Gk (N-number of all cells, k-number of a consecutive cell). For very high number of cells or when leakage conductance within a single cell has spatial distribution, this sum can be replaced by an integral of a so called “leak-age conductance density” function g(x). Leakage conductance “density” function g(x) can be defined as ratio of battery leakage conductance dG(x) of an elementary stretch to the length of this stretch dx, i.e. g(x) =

dG(x)dx

, where 0 < x < 1 is relative distance of a given point of battery from its negative pole. From this definition a formula for equivalent leakage conductance of the battery insulation is obtained

Based on the equivalent circuit diagram of the actual battery with nonuniformly distributed leakage conductance, characterized by the above defined density

(5.1)Gi =

1∫

0

g(x)dx



function g(x), balance of leakage currents can be given according to the Kirchhoff’s 1st law:

For the equivalent circuit diagram of the battery in the form of active four-terminal network this balance is expressed by the equation:

By comparison of left sides of (5.2) and (5.3) the following equation is obtained

Taking into account the requirement of maintaining insulation substitute conduct-ance value G′ + G′′ = Gi from (5.4) the Eq. (5.5) is obtained:

The required equality of U2 and V2 voltages is fulfilled only for the following characteristic value of G′:

With use of Gi definition given by formula (5.1) the second characteristic value of battery leakage conductance is obtained:

Therefore a Π four-terminal network with G′ and G′′ parameters, defined by for-mulas (5.6) and (5.7), represents the given battery for any possible parameters of external network insulation. In practice conductances G′ and G″ can be easily cal-culated after determination of insulation equivalent conductance Gi with one of accessible methods described in the next chapter. For this purpose pole-to-ground voltages U1 and U2 should be measured with a voltmeter (of internal resistance RV much higher than Ri) with disconnected external network. Then the equivalent

(5.2)−U2 · G2S +

1∫

0

(−U2 + E · x) · g(x)dx + (−U2 + E) · G1S = 0

(5.3)−V2 · (G2S + G′′) + (−V2 + E) · (G1S + G′) = 0

(5.4)

−U2 · G2S +

1∫

0

(−U2 + E · x) · g(x)dx + (−U2 + E) · G1S

= −V2 · (G2S + G′′) + (−V2 + E) · (G1S + G′)

(5.5)(V2 − U2) · (G1S + G2S + Gi) = E · (−

1∫

0

x · g(x)dx + G′)

(5.6)G′=

1∫

0

x · g(x)dx

(5.7)G′′= Gi − G′

=

1∫

0

g(x)dx −

1∫

0

x · g(x)dx =

1∫

0

(1 − x) · g(x)dx

79

conductance Gi is divided between respective poles according to formulas corre-sponding to the equivalent circuit diagram shown in Fig. 5.2

These formulas give approximate results due to finite voltmeter resistance RV, which affects accuracy of voltages U1 and U2 measurement.

Based on equivalent circuit diagram shown in Fig. 5.2b insulation resistance parameters can be defined:

• positive pole-to-ground insulation resistance R1

• negative pole-to-ground insulation resistance R2

(5.8)G′≈ Gi ·

U2

Eand G

′′≈ Gi ·

U1

E

(5.9)R1 =1

G1S + G′

(5.10)R2 =1

G2S + G′′

Fig. 5.2 a Physical battery circuit diagram without insulation capacitances. b Battery equivalent circuit diagram relating to scheme in Fig. 5.2a



Network-to-ground equivalent (substitute) insulation resistance Ri is

In some applications a more convenient form of equivalent circuit diagram may be a “T” four-terminal network (Fig. 5.3).

(5.11)Ri =R1 · R2

R1 + R2

=1

G1S + G2S + G′ + G′′

Fig. 5.3 “T” four-terminal network as a battery representation

Fig. 5.4 An equivalent circuit diagram of a DC network with an AC voltage source EAC

81

To ensure equivalency of both circuits (Figs. 5.2b and 5.3) an element repre-senting total insulation leakage conductance Gi (or resistance Ri) should be con-nected between ground and so called “zero point” of the battery (point of battery with zero i.e. no voltage to ground). This point divides the battery into two sources with voltages equal to the above given values U1 and U2.

When analyzing transient conditions in DC IT system, its ground capacitance should be taken into account. Equivalent circuit diagrams of these networks with AC voltages present must include also insulation-to-ground capacitances. An equivalent scheme of such network is presented in Fig. 5.4.

Reference

1. Olszowiec P (2011) Kontrola izolacji w sieciach pradu stałego. COSiW Warszawa 2011 (in Polish) (Insulation Monitoring in Live DC Networks)


83

Abstract A traditional method of periodical measurement of insulation resistance in live DC networks is a so called “three voltmeters” method. Similar procedure with use of an ammeter is described. Formulas for insulation equivalent resist-ance calculation are derived with help of Thevenin’s theorem. Few other methods as well as other unconventional ideas are presented. Evaluation of possible errors of respective measurement methods is given. This assessment may be useful for selection of adequate measurement procedures in practical applications.

6.1 Traditional Methods of Periodical Measurement of Insulation Resistance in Live Networks

The most commonly applied method of DC IT network-to-ground insulation resistance periodical measurement is a so called method of “three voltmeters”. For its use it is necessary to locate the above mentioned “zero point” of a battery. With the finite value of insulation resistance this point is located inside the voltage source. Only with ideal insulation level (i.e. infinite value of insulation resistance) voltage between all points of battery and ground is equal to zero, but in this case insulation measurement is useless. Then voltages Ua and Ub of any two points a, b of the battery (in particular its poles) located on both sides of zero point should be measured with a voltmeter with RV internal resistance as it is shown in Fig. 6.1.

Insulation resistance substitute value of the whole DC network (or the battery alone if it was disconnected from external circuits) is calculated from the formula:

It is quite easy to derive this formula for a network with ideal voltage source with earth leakage conductances G1 and G2 lumped at its terminals. In this case volt-ages measured at points 1 and 2 (battery poles) are as follows:

(6.1)Ri = RV ·Uab − Ua − Ub

Ua + Ub

Chapter 6Insulation Resistance Measurement Methods


84 6 Insulation Resistance Measurement Methods

and their sum is

By transforming (6.3) formula (6.1) is obtained. In Sect. 5.2 it was proved that a battery with any possible distribution of insulation earth leakage conductances can be replaced by a four-terminal network or T—type with lumped insulation con-ductances. Therefore formula (6.1) is valid also for batteries with any distribution of earth leakage conductances at single cells.

Another way of derivation of formula (6.1) is based on Thevenin’s theorem applied for any two measurement points a and b (i.e. cells terminals) located at both sides of “zero point”. According to this principle voltmeter indication Ua is

where Ua–no–load is voltage between point a and ground without connected volt-meter, Ri is substitute battery-to-ground insulation resistance with all cells short-circuited. Similarly Ub voltage equals to

where Ub−no–load is voltage between point b and ground without connected volt-meter. Taking into account the condition Ua−no–load + Ub−no–load = Uab (the 2nd Kirchhoff’s law) formula (6.1) is obtained from (6.4) and (6.5).

(6.2)U1 = E ·G2

G1 + G2 + GV

and U2 = E ·G1

G1 + G2 + GV

(6.3)U1 + U2 = E ·G1 + G2

G1 + G2 + GV

= E ·

1

Ri

1

Ri+

1

RV

= E ·RV

Ri + RV

(6.4)Ua = RV ·Ua−no−load

RV + Ri

(6.5)Ub = RV ·Ub−no−load

RV + Ri

Fig. 6.1 “Three voltmeters” procedure of insulation resistance measurement

http://dx.doi.org/10.1007/978-3-319-07010-0_5

85

Method of “three voltmeters” makes it possible to determine insulation resistances of single poles defined by formulas (5.9) and (5.10). If network poles were chosen for voltage measurements, then sought resistances R1 and R2 are given by formulas:

There are also known few other simple methods of insulation equivalent resistance measurement with use of an ammeter. One of them is shown in Fig. 6.2.

This method is similar to the previous procedure, however measurement of voltages Ua and Ub was replaced by measurement of respective currents Ia and Ib with an ammeter with internal resistance RA and series connected resistor R. In this case insulation equivalent resistance is given by formula

This formula is easily derived with help of Thevenin’s theorem in the following way. Currents Ia and Ib are equal respectively to

Taking into account the condition Ua−no–load + Ub−no–load = Uab (see above) formula (6.8) is obtained after a simple transformation. Another way to prove this formula is to take advantage of “three voltmeters” method by substituting voltmeter resistance RV by sum of resistances RA + R and expressing voltmeter indications as Ua = (RA + R)Ia and Ub = (RA + R)Ib.

(6.6)R1 = RV ·E − U1 − U2

U2

(6.7)R2 = RV ·E − U1 − U2

U1

(6.8)Ri =Uab

Ia + Ib

− (RA + R)

Ia =Ua−no−load

(RA + R) + Ri

and Ib =Ub−no−load

(RA + R) + Ri

.

Fig. 6.2 Procedure of insulation equivalent resistance measurement with help of an ammeter and voltmeter

6.1 Traditional Methods of Periodical Measurement

http://dx.doi.org/10.1007/978-3-319-07010-0_5

http://dx.doi.org/10.1007/978-3-319-07010-0_5


6.2 Other Analytical Methods

Methods presented in Sect. 6.1 belong to so called indirect measurements of insu-lation resistance in live DC networks. This means that insulation resistance is determined not by resistance measurement, but by measurement of other electri-cal quantities such as voltages and/or currents. When using indirect methods it is required to obtain as many independent equations as the number of unknown (sought) insulation parameters i.e. R1, R2 or Ri. These procedures are in fact com-binations of measurement and analytical methods because the sought insulation parameter value is not directly read out at a measuring instrument but calculated. Few examples of direct methods, which deliver the sought parameter value as a readout of the instrument indication, will be given in further chapters.

In order to illustrate, how application of equivalent circuit diagrams and Thevenin’s theorem enables elaboration of indirect methods of insulation resist-ance determination, two other procedures are presented below. A method explained in Fig. 6.3 consists of two consecutive measurements of a chosen pole-to-ground voltage (here negative one) with voltmeter RV—in the second measure-ment this pole is additionally grounded through a resistor of known value Rd.

Insulation resistance equivalent value is given by an expression:

To derive this formula it is sufficient to express voltages U2′ and U2

′′ with help of

Thevenin’s theorem as U ′

2= Rv ·

U2−no−load

Rv+Riand U

′′

2=

Rv·Rd

Rv+Rd·

U2−no−load

Rv ·RdRv+Rd

+Ri

. By elimi-

nating U2−no–load from these two equations formula (6.9) is obtained. For Rd = 0 (dead ground fault in the second step of the procedure) this formula is not valid. In this case instead of voltage U2

′′ current If of this dead ground fault should be meas-ured with an ammeter RA. The sought value of Ri is equal to

In practical applications sufficient accuracy should be ensured by a simplified for-mula (RA = 0 and RV = ∞) which follows directly from Thevenin’s theorem

Another method involving use of ammeter only, comprises also two steps. At first a resistor with known value Rx should be connected in series with an ammeter of known internal resistance RA between one of poles and ground. Let its indication be Ix. Then resistor Rx should be replaced by another resistor Ry and indication of the ammeter Iy should be read. The sought value of Ri is given by formula

(6.9)Ri =Rv · Rd ·

(

U ′

2− U ′′

2

)

U ′′

2· (Rd + Rv) − U ′

2· Rd

(6.10)Ri =U ′

2− RA · If

Rv · If − U ′

2

· Rv

(6.11)Ri =U

′

2

If

87

In the latter method resistances Rx and Ry must differ so much that the difference Ix − Iy is sufficiently high (Fig. 6.4).

It should be noted that all above given expressions are valid only for constant value of the network source voltage and of course constant magnitudes of insula-tion resistances.

6.3 Unconventional Methods of Insulation Resistance Measurement

Using Thevenin’s theorem few other measurement methods can be developed which do not require any calculations. For example quite simple procedure can be executed in the system shown in Fig. 6.5.

(6.12)Ri =Iy · (Ry + RA) − Ix · (Rx + RA)

Ix − Iy

≈Iy · Ry − Ix · Rx

Ix − Iy

Fig. 6.3 An example of procedure of insulation resistance measurement with voltmeter and resistor

Fig. 6.4 Procedure of insulation resistance measurement with an ammeter and two resistors

6.2 Other Analytical Methods


Insulation equivalent resistance measurement comprises two steps. In position 1 of the switch, slide S of voltage divider should be set so as to achieve zero indi-cation of a voltmeter. It is easy to notice that resistance seen from terminals of this meter with shorted voltage source is sum of divider substitute resistance R′//R′′ and insulation equivalent resistance Ri. In position 2 of the switch the ohmmeter measures the above mentioned sum of resistances plus series connected addi-tional resistor Rd. Neglecting divider resistors values as much smaller than Rd, this value (i.e. Rd) should be deducted from the ohmmeter indication—the result is the sought value of Ri. To achieve accurate measurement several conditions should be fulfilled. Divider resistance should be as low as possible and voltmeter indication before ohmmeter connection has to be zero. Only under these conditions the ohm-meter test current depends only on the ohmmeter internal voltage source and is not influenced by the monitored network supply source.

If the voltmeter indication is not zero, a sufficiently accurate result can be obtained in the following way. The ohmmeter indication should be read first. Then after swapping this meter’s leads a and b, resistance between ground and slider should be measured again.

Fig. 6.5 Two-step procedure of insulation resistance measurement

Fig. 6.6 Equivalent circuit diagram of the measuring system with switch in position 2 and non-zero voltage indication (in position 1)

89

An arithmetic mean value of these two readouts is a sufficiently accurate value of resistance seen from the ohmmeter terminals. This conclusion can be proved with help of circuit diagram shown in Fig. 6.6.

Currents flowing through the ohmmeter in respective steps are according to Thevenin’s theorem equal to

where Um is the ohmmeter source voltage, Rm—its internal resistance, US−g—slider-to-ground voltage without connected ohmmeter, R′

d—sum of divider substi-tute resistance (of parallelly connected resistors R′ and R′′) and series resistor Rd, Ri—insulation equivalent resistance. The ohmmeter indication α is described by a non-linear function α = f (I). An arithmetic mean value of both indications can be expressed as follows:

The latter expression is the ohmmeter indication during insulation measurement in a de-energized network. Thus using a linear interpolation method for relatively low “unbalance” voltages US−g, sufficiently accurate measurement results are obtained.

A more complicated measuring system (proposed by author as shown in Fig. 6.7) enables an accurate readout of Ri actual value at an ammeter graduated in kilo ohms. The measurement procedure consists of three steps. In position 1 of S switch divider D resistors should be adjusted so that voltmeter indication is equal to a fixed value e.g. 50 V. In position 2 ohmmeter measures sum of R resis-tor and the divider Rd substitute resistance of its parallelly connected elements.

(6.13)I1 =Um − Us−g

Ri + Rm + R′

d

and I2 =Um + Us−g

Ri + Rm + R′

d

(6.14)

α1 + α2

2=

1

2·

[

f (Um + US−g

Rm + Ri + R′

d

) + f (Um − US−g

Rm + Ri + R′

d

)

]

≈ f (Um

Rm + Ri + R′

d

)

Fig. 6.7 Circuit diagram of a three-step measuring system

6.3 Unconventional Methods of Insulation Resistance Measurement


R value should be adjusted so that ohmmeter indicates fixed substitute value of R + Rd (e.g. 100 kΩ). In position 3 ammeter graduated in kilo ohms according to the formula

gives actual level of insulation equivalent resistance Ri. Another unconventional way of insulation resistance measurement, which is based on readout of the adjusted resistor value, was described in Chap. 9.

6.4 Evaluation of Errors of Analytical Methods

Evaluation of possible errors of respective measurement methods enables to assess their usefulness for determination of insulation resistance in live DC networks. Below maximum errors of few methods were determined. In case of the “three voltmeters” method (formula 6.1) maximum error of Ri determination can be expressed as

where ΔU is an error of Ua, Ub and Uab voltages measurement with a voltmeter of RV internal resistance. It was assumed that RV is an accurately known value and therefore there is no need to take into account an error of this resistance deter-mination. To simplify expression (6.15) an approximate equality Uab ≈ Ua + Ub was used, which is valid for Ri < 0.1RV. Assuming technical parameters of typical multimeters RV = 107 Ω, ΔU ≤ 1 V (in range 0–1,000 VDC) this error for battery 230 V can be assessed as

This value is inadmissibly high for typical levels of insulation resistance. Method implemented according to formula (6.9) has not got this drawback. Absolute error of this procedure is for the above given measuring instrument’s data:

(6.15)IA =UV

Ri + (R + Rd)

(

in this case IA =50

Ri + 105[A]

)

(6.16)

Ri =

[∣

∣

∣

∣

δRi

δUab

∣

∣

∣

∣

+

∣

∣

∣

∣

δRi

δUa

∣

∣

∣

∣

+

∣

∣

∣

∣

δRi

δUb

∣

∣

∣

∣

]

· U

=2 · Uab + Ua + Ub

(Ua + Ub)2

· RV · U ≈3 · U

Ua + Ub

· RV

R ≈3 · U

Ua + Ub

· RV ≤3 · 1

230· 10

7= 0.13 · 10

6.

(6.17)Ri ≈Rd ·

(

U ′

2+ U ′′

2

)

(

U ′′

2

) · U ≈Rd · 2 · 10

2

(

102)2

· 1 = 0.02 · Rd

http://dx.doi.org/10.1007/978-3-319-07010-0_9

91

In this method shunt resistance Rd is in fact an approximate substitute resistance of the “voltmeter-shunt” set. Thus an absolute error of procedures based on voltage measurements is proportional to internal resistance of applied voltmeter. The error can be substantially lowered by using smaller Rd values.

For comparison it is worth to evaluate an absolute error of methods based on current measurements. For example in case of procedure described by formula (6.11) this error is expressed as

For typical measurement results (Ri − 106 Ω, U′1 − 102 V, If − 10−4 A) for simi-lar multimeter as above with voltage and current measurement errors 100 times smaller than the used range (in this case respectively 1 V and 10−6 A), maximum absolute error of 104 Ω is obtained. It can be proved that both for higher and smaller Ri values this error is always also 100 times smaller than the measured resistance. Thus relative error is equal to ammeter relative error. This property is a valuable feature of the analyzed method. Similar advantage possess also other pro-cedures based on current measurement. This conclusion is proved below in case of the method described by formula (6.11). For batteries with rated voltage of 102 V let insulation resistance Ri be 10n Ω. In this case ground fault current If is 102−n A. Voltage and current measurement errors are not higher than 1 % of their meas-uring range, i.e. respectively 1 V and 10−n A. For these data maximum absolute error is equal to

Some practical recommendations follow from the above analysis. Procedures uti-lizing voltage measurements such as the “three voltmeters” method, should be used only for insulation resistance levels higher or comparable to voltmeter sub-stitute internal resistance (i.e. including a possible additional shunt resistor as in a method described in Sect. 6.2). Methods based on measurement of an artificial ground fault current are more universal and recommended for practically the whole range of insulation resistances. Correctness of their results depends mainly on accuracy class of applied meters.

(6.18)

Ri =

∣

∣

∣

∣

∣

δRi

δU′

2

∣

∣

∣

∣

∣

· U +

∣

∣

∣

∣

δRi

δIf

∣

∣

∣

∣

· I =U

If

+U

′

2

I2f

· If

=If · U + Ri · If · If

I2f

=U + Ri · If

If

(6.19)Ri =U + Ri · If

If

≈1 + 10n

· 10−n

102−n=

2

102−n= 2 · 10

n−2

6.4 Evaluation of Errors of Analytical Methods

93

Abstract In the chapter few traditional methods of insulation monitoring in DC networks are presented. The simplest system of insulation condition visual super-vision consisted of two bulbs. System of insulation monitoring comprising two undervoltage relays RV is analyzed. Another system of signaling of insulation level deterioration based on voltage criteria is shown. Commonly applied monitor-ing systems based on a bridge circuit are described. An example of application of the bridge measuring method is presented.

7.1 Visual Signaling of Insulation Resistance Level

The oldest system of insulation monitoring in DC IT networks consisted of two bulbs connected between respective poles and ground as shown in Fig. 7.1. In case of one pole-to-ground insulation deterioration its lamp was shining weaker or went off at all. However this simplest system did not detect symmetrical insulation level lowering. The second shortcoming of this concept was galvanic connection of the network to ground by means of relatively low lamp resistance which in fact eliminated isolation of the network from ground. Another idea was replacement of lamps by voltmeters of much higher internal resistance; however this concept maintained the first drawback.

Later bridge circuits were introduced—an example of insulation failure signal-ing system based on a bridge circuit is presented in Fig. 7.2.

The bridge arms are formed by low-value resistors R3 and R4 (usually R3 = R4) as well as insulation resistances R1 and R2. Across the bridge a lamp for visual alarming or a voltmeter was connected. Then these elements were replaced by overvoltage relays. As long as insulation resistances were very high or decreased symmetrically, the bridge was balanced. Voltage across the bridge appeared in case of one pole insulation failure. Thus also this system detected only unsymmetrical deterioration of the network insulation level.

Chapter 7Devices and Systems for Insulation Deterioration Alarming


94 7 Devices and Systems for Insulation Deterioration Alarming

7.2 Simple Systems of Continuous Insulation Monitoring

As electrical engineering developed, voltage relays were used for insulation super-vision. One of the first systems for continuous insulation monitoring consisted of two undervoltage relays connected between respective poles and ground (Fig. 7.3).

Each relay (with internal resistance Rp) issued an alarm when voltage across its terminals decreased below the set pick-up value Up.

From condition of the relay pick-up U1 < Up (or U2 < Up) the range of insula-tion resistances detected by this relay can be determined

(7.1)U1 = E ·

R1·Rp

R1+Rp

R1·Rp

R1+Rp+

R2·Rp

R2+Rp

≤ Up

Fig. 7.1 Insulation monitoring in DC IT systems based on lamps or voltmeters

Fig. 7.2 Insulation failure signaling in a bridge circuit with voltmeter

95

The condition for signaling positive pole insulation resistance R1—as function of the negative pole insulation resistance R2—is obtained from (7.1)

For the negative pole insulation deterioration a similar formula is valid

It is convenient to illustrate conditions (7.2) and (7.3) in system of coordinates (R2, R1) (Fig. 7.4).

Also this system does not allow for detection of symmetrical deterioration of both poles insulation level though it occurs quite rarely. It should be noted that it is possible to use overvoltage relays instead of undervoltage devices. Characteristics of “overvoltage” alarm system are similar to those presented in Fig. 7.4.

Another system of signaling of insulation level deterioration based on voltage criteria is shown in Fig. 7.5.

(7.2)R1 ≤ Rp ·R2

R2 ·E−2·Up

Up+ Rp ·

E−Up

Up

(7.3)R2 ≤ Rp ·R1

R1 ·E−2·Up

Up+ Rp ·

E−Up

Up

Fig. 7.3 System of insulation monitoring comprising two undervoltage relays RV

Fig. 7.4 Graphical illustration of insulation resistances ranges signaled by the undervoltage alarm system for a relay with parameters Rp = 100 kΩ, Up = 0.2E, x1—curve corresponding to (7.2), x2—curve corresponding to (7.3) condition



It consists of two units comparing positive pole-to-ground voltage U1 with negative pole-to-ground voltage U2 multiplied by selected coefficients k1 and k2. Pick-up conditions of this alarm system are described by the following inequalities

In this way breakdown of any pole insulation to ground is detected. However its operation is featured by a large “dead” zone corresponding to symmetrical insula-tion levels including also symmetrical insulation deterioration.

Both zones of the signaling system operation and a zone of normal insulation level (between lines X1 and X2) are shown for parameter values k2 = 1/k1 = 3 in the coor-dinates system (R2, R1) in Fig. 7.6. Similarly to the previous detection system this detector does not provide a precise supervision of the actual insulation level but rather only detects possible asymmetry of insulation resistances R1 and R2. In particular it

(7.4)k1 <U1

U2

< k2

Fig. 7.5 Insulation deterioration alarm system based on voltage criteria

Fig. 7.6 Characteristics of insulation level deterioration alarm system based on voltage criteria (166); x1—characteristic for negative pole, x2—characteristic for positive pole

97

does not detect symmetrical lowering of these two parameters values whereas it may unnecessarily signal sufficiently high but asymmetrical insulation levels.

Broad application have gained insulation monitors based on bridge circuits. In the system shown in Fig. 7.7 an overvoltage relay RV connected across the bridge circuit is designed for detection of insulation level deterioration.

With help of an equivalent circuit diagram it is possible to determine voltage Urelay across the relay terminals as function of insulation resistances R1 and R2. For simplification voltage drop across the rectifying diodes has been neglected.

(7.5)

Urelay = E · RP ·

∣

∣

∣

∣

R1 · R4 − R2 · R3

[Rp · (R3 + R4) + R3 · R4] · (R1 + R2) + (R3 + R4) · R1 · R2

∣

∣

∣

∣

Fig. 7.7 Circuit diagram of DC network insulation monitoring system based on a bridge circuit

Fig. 7.8 Graphic illustration of operating range of a bridge circuit monitor in case of negative pole insulation deterioration. The curve corresponding to positive pole insulation deterioration was omitted as a reflection across the R1 = R2 straight line. The graph was plotted for the follow-ing parameters R = 10 kΩ, Rp = 100 kΩ, Up = 0.3 E



An alarm is issued when voltage Urelay exceeds the set pick-up value Up of the relay. From the condition Urelay > Up in case of R1 > R2 a range of insulation resistances R1 as function of insulation resistance R2 is obtained within which negative pole insula-tion level deterioration is signaled (for simplicity it was assumed R3 = R4 = R):

This condition establishes a vertical asymptote for the area of negative pole insula-tion deterioration. In similar way an operating range for the positive pole is deter-mined. Sum of both ranges forms an area of insulation condition described by a pair of parameters (R2, R1) (see Fig. 7.8), for which the detector issues an alarm.

An example of application of this bridge measuring method is insulation moni-tor IL/5881 type manufactured by DOLD (Germany) [1]. This device is designated for IT DC networks with voltage 12–280 V. Its alarm range is 5–200 kΩ with hys-teresis up to 15 %. The monitor does not detect symmetrical deterioration of the network insulation. It does not provide measurement of any insulation parameter R1, R2 or Ri. There are available this monitor’s versions with external auxiliary supply or with supply from the monitored network.

Reference

1. http://www.dold.com

(7.6)R1 >R2

[

Rp(2 +E

Up) + R

]

Rp(E

Up− 2) + R − 2R2

for R2 < Rp ·E − 2Up

2Up

+R

2

http://www.dold.com

99

Abstract In the chapter modern methods of insulation continuous measurement are presented. The simplest one is imposition of an auxiliary AC test signal between DC network and ground. Procedures based on connection of a resistor between ground and one or both DC network poles are simple methods of indirect (i.e. based on measurement and calculation) determination of insulation- to-ground resistances. This solution is also referred to as “commutation method”. Waveforms of a chosen pole-to-ground voltage recorded during commutation are shown. “Pulse” (rectangular) test voltage imposition is another commonly applied approach. Details of the method are explained and formulas necessary for insulation-to-ground equivalent resistance determination are derived. Few exam-ples of these methods implementation are presented and waveforms illustrating the devices operation are attached. Three other unconventional concepts of insu-lation continuous monitoring are described. These ideas include insulation leak-age resistance automatic control, insulation ground capacitance compensation for an auxiliary AC test signal as well as imposition of auxiliary voltage “triangle” pulses.

8.1 Measurements with Superimposed AC Test Voltage

Numerous insulation monitors utilize an auxiliary sinusoidal voltage source of adequately selected frequency, connected between any point of DC IT system and ground. Superimposition of AC test signal is an effective method of continu-ous insulation parameters measurement. This concept is shown in Fig. 8.1a. One of advantages of this solution is that DC battery offers negligible impedance to sinusoidal current. Test current driven by its source flows through all insulation leakage resistances and capacitances to ground. Measurement of this current per-formed in the circuit shown in Fig. 8.1b allows to determine insulation-to-ground parameters.

Chapter 8Modern Methods of Continuous Insulation Measurement


100 8 Modern Methods of Continuous Insulation Measurement

The same idea of insulation monitoring is utilized also in AC IT systems (see Chap. 4). Sinusoidal test current of f0 frequency is given in DC networks by the same formula (4.29). For application example see description of XM 200 insula-tion monitor presented in Chap. 4.

8.2 Commutation Method

Procedures based on connection of a resistor between ground and one or both DC IT network poles are simple methods of indirect (i.e. based on measure-ment and calculation) determination of insulation-to-ground resistances. This approach has been successfully employed in modern insulation monitors imple-mented in microprocessor technology. The measurement cycle usually con-sists of measurement of line-to-line voltage and single lines-to-ground voltages with a known resistor connected at first between one pole and ground, then between the second pole and ground. This element is connected for time suf-ficiently long to ensure transient component decay. Therefore the result is not influenced by capacitance-to-ground level. Voltage measurements are carried out in steady-state and results are processed by the microprocessor system. Those monitors operation brings about unavoidable changes of line-to-ground voltages. An example of line-to-ground voltage variation during commutation process is shown in Fig. 8.2a.

Application of this method should not evoke risk of disturbances in the circuit’s apparatuses operation (see Chap. 10). In case of commutation method—when resistor is connected to positive pole—there appears a risk of misoperation of a relay with grounded coil’s positive terminal. Of course an inad-vertent operation (misoperation) of any apparatus caused by insulation monitor is unadmissible.

Fig. 8.1 a Circuit diagram of DC network with an auxiliary sinusoidal U0 voltage source of f0 frequency. F—band-pass filter for f0 frequency, R0—internal resistance of the measuring circuit, b Equivalent circuit diagram of DC network and measurement circuit for frequency f0 of super-imposed sinusoidal test signal

http://dx.doi.org/10.1007/978-3-319-07010-0_4

http://dx.doi.org/10.1007/978-3-319-07010-0_4

http://dx.doi.org/10.1007/978-3-319-07010-0_4

http://dx.doi.org/10.1007/978-3-319-07010-0_10

101

8.2.1 Example of Application

An MD-04 isometer manufactured by C&T Elmech (Poland) [1] serves for insu-lation resistance measurement of DC circuits with rated voltage 24 to 220 V. The meter is supplied from the monitored network. Its operating principle is based on the “three voltmeter” method. The measurement is executed periodically by con-nection of an additional (test) resistor between ground and each pole in succession. Waveforms of negative pole-to-ground voltage recorded during MD-04 monitor operation in a network with different total capacitances-to-ground are shown in Fig. 8.2b, c. It should be noted that in both cases steady-state voltages are equal because insulation resistances are the same. After each measurement cycle of both poles-to-ground voltages, a microprocessor system calculates insulation resistances. These values are displayed at the front panel. The isometer executes the measure-ment automatically immediately after connection to the network, periodically or

Fig. 8.2 a An example of pole-to-ground voltage variation (from 50 to 170 V) during commu-tation process in DC network. Waveforms of negative pole-to-ground voltage recorded during MD-04 monitor operation in DC network with the following insulation equivalent parameters: b Ri = 43 kΩ, Ci = 0 μF, c Ri = 43 kΩ, Ci = 20 μF



after manual start. Measurement and calculation takes from 4 s to 2 min. In case of one or both poles insulation deterioration an alarm LED is lit, then the measure-ment is repeated twice. If this result is confirmed, an output relay closes its con-tact. Information on the isometer status and insulation condition is issued also by RS485. Measurement error of MD-04 monitor does not exceed ±10 %.

8.2.2 Determination of Insulation Equivalent Resistance of DC Network and Its Single Lines

Commutation method allows to determine insulation equivalent resistance not only of the entire DC network, but also of its single lines. For calculation of the network insulation equivalent resistance Ri formula (6.1) can be used with voltmeter’s inter-nal resistance RV replaced by the test resistor value. For commutation method also few other simple formulas for determination of this parameter can be derived.

Based on the equivalent circuit diagram (Fig. 8.3) steady-state voltages across the test resistor in both positions of the switch are equal respectively to

Mean value of sum of voltages U1R and U2R is

where Ri is given by (5.11). As URmean voltage is a decreasing function of the sought parameter Ri, voltmeter connected across resistor R can be graduated in resistance units i.e. kΩ. Further properties of the commutation method can be learned with help of Fig. 8.4 presenting an example of DC network with any num-ber of outgoing lines (in this case there are shown two of them).

Leakage currents through insulation-to-ground resistances of positive r1 and negative pole r2 of for example line 1 are given by the following formulas at respective positions of the switch:

at position 1 (U1R1—voltage across r1 at the switch position 1) and

at position 2 (U2R2—voltage across r2 at position 2).From (8.3) and (8.4) total leakage currents flowing from both conductors of this

line to ground can be determined. At the switch position 1 total leakage current of this line is

(8.1)U1R = E ·R · R1

R · (R1 + R2) + R1 · R2

and U2R = E ·R · R2

R · (R1 + R2) + R1 · R2

(8.2)URmean =U1R + U2R

2=

E

2·

R

R + Ri

(8.3)I1r1 =U1R1

r1

, I1r2 =E − U1R1

r2

(8.4)I2r1 =E − U2R2

r1

, I2r2 =U2R2

r2

http://dx.doi.org/10.1007/978-3-319-07010-0_6

http://dx.doi.org/10.1007/978-3-319-07010-0_5

103

whereas at position 2 it is equal to

Their difference can be expressed as

where 1

r1+

1

r2=

1

ri. From (8.7) the final formula for insulation-to-ground equiva-

lent resistance ri of a single line is obtained

(8.5)I1r12 = I1r1 − I1r2 =U1R1

r1

−E − U1R1

r2

(8.6)I2r12 = I2r1 − I2r2 =E − U2R2

r1

−U2R2

r2

(8.7)

I2r12 − I1r12 = I2r1 − I2r2 − I1r1 + I1r2 =E − U1R1 − U2R2

r1

+E − U1R1 − U2R2

r2

=E − U1R1 − U2R2

ri

(8.8)ri =E − U1R1 − U2R2

I2r12 − I1r12

Fig. 8.3 Commutation method utilizing test resistor R—an example

Fig. 8.4 Circuit diagram of DC network with two outgoing lines



It should be taken into account that leakage currents I1r12 and I2r12 flow in oppo-site directions. Therefore deduction should be in fact replaced by adding in denominator of this formula if measured absolute values of currents are used.

This expression can be derived in a simpler way using formula (6.1) for insu-lation equivalent resistance Ri of the entire network. For simplicity let the net-work comprise only one line—in this case ri = Ri. Line-to-ground voltages Ua and Ub, which are of course respectively equal to U1R1 and U2R2, can be pre-sented as Ua = U1R1 = RV · I1r12 and Ub = U2R2 = −RV · I2r12. Substituting these two expressions to (6.1) formula (8.8) is obtained. Obviously vice versa derivation of the “three voltmeters” method formula is also possible starting from formula (8.8).

8.2.3 Example of Application

Russian microprocessor system “EKRA-SKI” (Fig. 8.5) for insulation resistance measurement and ground fault location in DC networks is based on commuta-tion method. The device comprises current detector CD for measurement of the network total leakage current I0 = I01 + I02 in two semi-periods of its opera-tion: (1) with switch K4 closed and K5 open, (2) with switch K5 closed and K4 open. Resistors R4, R5 are successively connected and disconnected from respec-tive conductors whereas resistor divider 1, 2 with grounding resistor R3 serves to limit deflection of poles-to-ground voltages from their normal value E/2 (see Sect. 10.4.6). The network insulation equivalent resistance is cyclically calculated according to formula (8.8). If Ri value decreases below set level e.g. 50 k Ω, the device is automatically switched to fault location mode (see Chap. 13).

This formula can be replaced by another expression, commonly applied in insu-lation measurements techniques. Positive pole grounded by test resistor voltage U1R1 can be expressed as sum of its mean value U1mean (in both positions of the switch) and amplitude U0 of this voltage variation around its mean value U1mean. Similarly total leakage current of the considered line Ir12 can be represented as sum or difference of its mean value Imean in both positions of the switch and amplitude I0 of this current variation around its mean value Imean. The following equations

can be substituted to (8.8) which provides the second, more useful form of for-mula for any line insulation-to-ground equivalent resistance:

Use of (8.10) requires total leakage current of the given line to be measured (i.e. alge-braic sum of currents flowing in positive and negative conductors). This measurement is performed by adequate current transformers. The above described method of indirect

(8.9)

U1R1 = U1mean − U0, U2R2 = E − (U1mean + U0), I1r12 = Imean − I0, I2r12 = Imean + I0

(8.10)ri =U0

I0

http://dx.doi.org/10.1007/978-3-319-07010-0_6

http://dx.doi.org/10.1007/978-3-319-07010-0_6

http://dx.doi.org/10.1007/978-3-319-07010-0_10

http://dx.doi.org/10.1007/978-3-319-07010-0_13

105

determination of insulation equivalent resistance of single lines or parts of network was applied in numerous dedicated devices for insulation monitoring and fault location.

8.3 “Pulse” Test Voltage Method

Except of commutation method also application of test “pulse” voltage allows to utilize property (8.10) for insulation-to-ground equivalent resistance determina-tion. A train of rectangular voltage pulses with amplitudes −Uaux and +Uaux is connected between one pole and ground as shown in Fig. 8.6.

Duration of each pulse is equal and long enough to ensure decay of transient components. As result steady-state pole-to-ground voltages and network leakage cur-rents are subject to periodical variation according to (8.11) equations similar to (8.9):

where U11 and U21 are steady-state voltages of respective poles towards ground in the first half of each period, U12 and U22—in the second half of the period, U0—amplitude of these voltages variation (U0 may differ from Uaux).

This process is similar to line-to-ground voltage oscillations caused by commu-tation of test resistor. As formula (8.10) was derived taking no account to reasons of oscillations, so it must be valid also in this case, though voltage variations are caused by imposition of an auxiliary test voltage source.

Formula (8.10) for process caused by pulse test voltage superimposition can be derived also in another way (see Sect. 4.2). Based on superposition principle amplitude of periodical leakage current variations of any line or the entire network can be determined. It must be noted that this current variations are caused only by the test voltage as the network supply source with constant magnitude E cannot

(8.11)

U11 = U1mean − U0, U12 = U1mean + U0, U21 = U2mean + U0, U22 = U2mean − U0

Fig. 8.5 “EKRA-SKI” system for insulation resistance measurement in a DC network with n lines (designations in the text)


http://dx.doi.org/10.1007/978-3-319-07010-0_4


evoke any changes in single poles-to-ground voltages. Therefore with amplitude of these voltages variation U0 around their mean value, total leakage currents in any line are in successive halves of a period equal to

Their difference is

With designation I2r12 − I1r12 = 2 · I0 formula (8.10) is obtained.

8.3.1 An Example of Application

IRDH375 isometer [2] manufactured by Bender belongs to most commonly used insulation monitors in DC and AC IT systems. Rectangular test voltage con-trolled by a microprocessor is imposed between monitored network and ground. Frequency of voltage pulses with amplitude 50 V depends on insulation param-eters i.e. resistance and capacitance, as well as on disturbances in the network voltage. Isometer operation evokes oscillations of both line-to-ground voltages. Figure 8.7a, b show a selected pole-to-ground voltage recorded for the same insu-lation resistance but for different ground capacitances.

Based on the measured test current the isometer performs calculation of insulation equivalent resistance. Network capacitance does not influence accuracy of the result determination, however time of the measurement pro-cess is strongly dependent on its magnitude. Test current is limited to 0.28 mA

(8.12)

I1r12 = I1r1 + I1r2 = −U0

r1

−U0

r2

= −U0 · (1

r1

+1

r2

) = −U0

ri

and

I2r12 = I2r1 + I2r2 =U0

r1

+U0

r2

= U0 · (1

r1

+1

r2

) =U0

ri

(8.13)I2r12 − I1r12 = 2 ·U0

ri

Fig. 8.6 Imposition of rectangular voltage pulses on DC network

107

Fig. 8.7 Selected pole-to-ground voltage waveform under IRDH375 isometer operation for the network 230 V with the following insulation parameters: a Ri = 18 kΩ, Ci = 10 μF, b Ri = 18 kΩ, Ci = 20 μF

Fig. 8.8 Waveform of test current driven by IRDH375 isometer (amplitude 200 uA (1 mV = 1 uA)—an example)

8.3 “Pulse” Test Voltage Method

Fig. 8.9 IRDH375 isometer operation following insulation resistance deterioration from Ri = ∞ to Ri = 20 kΩ. Network capacitance is Ci = 20 μF, T = 0.4 s


by internal source resistance approximately 180 kΩ. Its typical waveform is shown in Fig. 8.8. Error of monitors’ operation (difference between the set alarms (2 stages) pick-up thresholds and actual response values) and of dis-played insulation equivalent resistance value is less than 20 % in the whole measuring range 1 kΩ–10 MΩ. Insulation deterioration alarm is issued with a delay dependent on the circuit time constant. Time delayed operation of the isometer is illustrated in Fig. 8.9.

8.4 Unconventional Methods of Insulation Resistance Monitoring

Except of the three main methods of insulation resistance continuous measure-ment described in (8.1)–(8.3), many other solutions have been designed, tested and applied. Below there are presented three selected methods elaborated and used in Poland and former USSR (Fig. 8.10).

8.4.1 Insulation Supervision with Insulation Leakage Resistance Control

In this supervision system an auxiliary AC voltage source of very low frequency is used. Thanks to low frequency (approx. 1 Hz) of injected test signal, influ-ence of ground capacitances is effectively minimized. This approach consists in continuous automatic regulation of one of additional resistors R3 and R4, which are connected parallelly to existing insulation leakage resistances R1 and R2 of respective poles. System of automatic control allows to continuously bring to zero “differential” AC voltage between ground and an artificial “neutral” point of the monitored network. Under this forced “balanced” condition equivalent resistances of respective poles to ground are equal i.e. the following equation is fulfilled

During regulation the greater of the two insulation resistances R1 or R2 is decreased to the lower one of them by parallelly connected photoresistor R3 or R4. The photoresistor, which is not regulated by a beam of light produced by a controller, has approximately an infinite value. Under these conditions test cur-rent driven by the G source through all four R1, R2, R3 and R4 parallelly connected resistors is inversely proportional to their equivalent resistance. Smaller resistance of R1 and R2 is two times higher than equivalent resistance measured by the A ammeter graduated in resistance units. This method was successfully applied in Polish insulation monitors REZ-2 and REX type.

(8.14)R1 · R3

R1 + R3

=R2 · R4

R2 + R4

109

8.4.2 Method of Auxiliary Voltage “Triangle” Pulses

This method utilizes an auxiliary source of triangle-shaped voltage pulses con-nected between any selected pole of DC network and ground. This periodical volt-age signal is superimposed on parallelly connected resistances and capacitances of insulation-to-ground. The source drives test current flow consisting of two com-ponents: triangle-like pulses (current through resistance Ri) and rectangular (Ci capacitance charging current). The latter component can be easily eliminated by differentiation eg. by a transformer. Only voltage pulses corresponding to “capaci-tive” current’s abrupt changes are obtained on the transformer secondary side. Triangle-like current pulses, transformed to the secondary side, produce rectangu-lar voltage pulses. Amplitude of these pulses is inversely proportional to insulation equivalent resistance (Fig. 8.11).

This insulation resistance measurement method has been applied also for ground fault location system (see Chap. 13). However implementation of this technique may encounter some difficulties such as nonlinearity of voltage pulses slope, voltage disturbances caused by a battery rectifier as well as sud-den, transient deformation of voltage pulses due to insulation resistance abrupt changes.

8.4.3 System of Automatic Insulation-to-Ground Capacitance Compensation

This method is based on insulation-to-ground capacitance compensation for AC test signal injected by an auxiliary voltage source. The idea presented in Fig. 8.12 utilizes a choke with reactance continuously adjusted by a system of automatic control.

Fig. 8.10 a Schematic circuit diagram of isometer REZ-2 type. b Equivalent circuit diagram of DC network monitored by REZ-2 isometer


http://dx.doi.org/10.1007/978-3-319-07010-0_13


Choke inductance L for fG frequency is adjusted by a phase-sensitive transducer PST which supervises phase shift between the source sinusoidal voltage UG and test current IG driven by this source through insulation leakage resistances and capacitances as well as through the choke. Another criterion of control can also

Fig. 8.12 Insulation resistance measurement in a system of automatic capacitance compensa-tion. Designations: G—auxiliary AC voltage source with UG magnitude and fG frequency, F—band-pass filter for fG frequency, R0—current limiting resistor, Uout—rectified output voltage of phase-sensitive transducer PST, L—inductance of the choke

Fig. 8.11 Illustration of triangle-like voltage pulses method

111

be minimizing of RMS value of the test current IG. Under full compensation of reactive component of current IG i.e. in parallel resonance of choke inductance L and insulation capacitance Ci, phase shift between voltage UG and current IG is equal to zero. In this condition the measurement circuit for AC test current signal becomes a single-loop circuit consisting of resistors R0 and Ri. Voltage U0 (RMS value) measured across resistor R0 is a declining function of Ri resistance

The sought value of Ri can be read as indication of voltmeter with scale graduated in kΩ according to the above given formula. Accuracy of the presented method is strongly influenced by compensation level of capacitive test current component. This undesired impact can be effectively limited by compensation of capacitive current in the primary winding of the current transformer instead of capacitive component compensation of current IG produced by the generator. To achieve this goal an additional wire with current of an adverse sign (direction) than capacitive component of current IG, is inserted through the current transformer window. This additional compensating current is adjusted by an automatic control system com-prising phase-sensitive transducer. Under complete compensation current flowing in the secondary winding of current transformer contains only an active compo-nent which is proportional to the test current component flowing through insula-tion leakage resistances (Fig. 8.13).

References

1. http://www.elmech.pl2. http://www.bender.org

(8.15)U0 = UG ·R0

R0 + Ri

Fig. 8.13 Compensation of capacitive component of AC test current on primary side of the measuring transformer


http://www.elmech.pl


113

Abstract In the chapter theoretical basis of ground fault phenomena in DC circuits is given. Ground fault transient voltages and current waveforms are shown. Measurements of earth fault current characteristic parameters such as initial value and steady-state value are described. Formulas for evaluation of earth fault and leakage currents are derived. Methods of analytical assessment of electric shock hazard as function of insulation parameters are given. Procedures and systems for earth fault and shock current evaluation by means of experimental measurements both in live networks and in network models are proposed. Network total capaci-tance to ground together with insulation equivalent resistance to ground determine time constant of currents and voltages transients under earth fault conditions. The last section of this chapter presents an overview of methods of ground capacitance determination with use of waveform recording and calculations.

9.1 Time Function of Ground Fault Current

Based on DC IT system circuit diagram shown in Fig. 9.1 time function of ground fault current of any pole (in this case—positive one) through fault resistance r can be determined.

The 1st Kirchhoff’s law for the node linked with ground gives the following equation

which can be transformed to the form

This differential equation has solution given by the time function

(9.1)U1

R1

+U1

r+ C1 ·

dU1

dt=

E − U1

R2

+ C2 ·d(E − U1)

dt

(9.2)(C1 + C2) ·dU1

dt+ U1 · (

1

R1

+1

R2

+1

r) =

E

R2

(9.3)U1(t) = U1(0) · e−t/T+ U1(∞) · (1 − e−t/T

)

Chapter 9Ground Fault, Leakage and Electric Shock Currents in DC IT Systems


114 9 Ground Fault, Leakage and Electric Shock Currents in DC IT Systems

whereas initial (t = 0) and steady-state (t = ∞) values of U1 are respectively U1(0) = E ·

R1

R1 + R2(U1(0−) = U1(0+) = U1(0) for Ci > 0) and

The third characteristic parameter of U1(t) time function is time constant T of its exponential component. This value is given by the formula

where Ci is equivalent (total) network to ground capacitance, R—network-to-ground insulation equivalent resistance Ri with parallelly connected fault resistance r.

Bearing in mind that at any moment t ≥ 0 an earth fault current If1 flowing from pole 1 through fault resistance r is equal to If 1(t) =

U1(t)r

, this quantity can be expressed as

It follows from the above formulas that time constant T is a characteristic parameter of both earth fault quantities i.e. current and voltage of the grounded pole. Of course time constant of exponential component of the other pole-to-ground voltage is the same magnitude because U2(t) = E − U1(t).

Earth fault current initial (t = 0) − I(0) and steady-state (t = ∞) − Ist−st values are respectively If 1(0) = E ·

R1

(R1 + R2)·r(for Ci > 0) and

An example of an earth fault current with its characteristic parameters is shown in Fig. 9.2.

(9.4)U1(∞) = E ·R1 · r

R1 · R2 + r · (R1 + R2)

(9.5)T =C1 + C2

1

R1+

1

R2+

1

r

= Ci · R

(9.6)If 1(t) = If 1(0) · e−t/T+ If 1(∞) · (1 − e−t/T

)

(9.7)If 1(∞) = E ·R1

R1 · R2 + r · (R1 + R2)

Fig. 9.1 DC IT system equivalent circuit diagram

115

From formulas (9.7) there follows dependence of both characteristic parameters of earth fault current, i.e. initial and steady-state values, on insulation resistances R1 and R2 as well as on fault resistance r. An interesting problem is evaluation of possible range of these earth fault currents magnitudes for a given network insulation equivalent resist-ance Ri . These values are important among others for assessment of risk of relays mis-operation as well as shock and fire hazards (see Chap. 11). Therefore minimum and maximum initial and steady- state earth fault current values should be found knowing Ri value measured in prefault condition. Substituting R2 as R2 =

R1·Ri

R1 − Ri to formulas (9.7)

two functions of variable parameter R1 (for set values of Ri and r) are obtained.

For Ri < R1 < ∞ minimum values If1min(0) = If1min(∞) = 0 and maximum values If 1max(0) =

Er, If 1max(∞) =

Er + Ri

are obtained.In particular case of dead earth fault (r = 0) maximum earth fault current is

limited only by resistances of the source and the circuit wires (omitted in the circuit diagram). The time constant of earth fault current function decreases to zero which means that the transient state is practically absent.

9.2 Measurements of Maximum and Steady-State Magnitudes of Earth Fault Current

Measurements of earth fault current characteristic parameters may be useful to establish these values experimentally and/or to verify their calculations. A simple method of earth fault current maximum (i.e. initial) value measurement is com-monly known. This task can be fulfilled in an additional circuit of two capacitors connected to respective poles as shown in Fig. 9.3.

Assuming that capacitances Cd1 and Cd2 are much greater than insulation capacitances C1 and C2 it can be analytically proved that initial value I(0) of current recorded in the grounding wire of additional capacitors is (approximately)

(9.8)If 1(0) = E ·R1 − Ri

R1 · rand If 1(∞) = E ·

R1 − Ri

R1 · (Ri + r)

Fig. 9.2 An earth fault current recorded in a DC network

9.1 Time Function of Ground Fault Current

http://dx.doi.org/10.1007/978-3-319-07010-0_11


equal to initial value If (0) of an earth fault current. This conclusion can also be explained in another way. As voltages across insulation capacitances C1 and C2 cannot change abruptly at the moment of earth fault (i.e. U1(t) and U2(t) are continuous functions of time), then currents in insulation resistances R1 and R2 must be continuous too. As result the emerging earth fault current at t = 0 can flow only through capacitors Cd1, Cd2, C1, C2 connected to ground. Under condi-tion Cd1 ≫ C1 and Cd2 ≫ C2 practically the whole earth fault current at the ini-tial moment flows through the wire connecting additional capacitors to ground. Figure 9.4a, b present recorded earth fault current If and current I flowing in the

Fig. 9.3 An auxiliary circuit for earth fault current initial value measurement/recording (REC)

Fig. 9.4 a Earth fault current If waveform recorded in DC network, b waveform of current I flowing in the grounding wire in DC network—examples

117

grounding wire. Small difference between their values at t = 0 was caused by insufficiently high values of Cd1, Cd2 in comparison to C1, C2.

Of course both currents If and I are equal only at the initial moment of an earth fault. The presented circuit can serve also for detection of an earth fault occur-rence and assessment of the earth fault current maximum value by means of a sensitive high-speed overcurrent relay. It should be noted that connection of addi-tional capacitors Cd1 and Cd2 leads to growth of the network capacitance to ground which is undesirable because of e.g. risk of relays misoperation (see Chap. 10). A simpler method of earth fault detection (however without its initial value meas-urement) utilizes current input of fault recorder connected through a capacitor between any pole and ground. In this system in case of an earth fault occurrence there will be recorded a pulse of current charging (or discharging) this capacitor.

Use of a recorder as shown in Fig. 9.5 allows also to determine insulation resistances R1 and R2 of the respective poles. For Cd1 ≫ C1 + C2 and negligible recorder’ current input impedance, R1 is approximately equal to R1 =

EI(0)

. This conclusion follows from the fact that at the moment t = 0 an uncharged capacitor Cd1 forms a dead grounding of the negative pole. Thus at this moment R1 resist-ance is connected directly to the voltage source E. If this capacitor is connected to the positive pole, R2 resistance can be obtained from similar formula R2 =

EI(0)

.Application of insulation monitor allows to determine the second characteristic

parameter of earth fault current, namely its steady-state value Ist−st = If(∞). According to Ohm’s law this value is equal to Ist−st =

Ust−st

r, where Ust−st is a

steady-state value of the grounded pole voltage. Taking into account relationship of fault resistance r and insulation resistance monitor’s indications Ri

′ (in prefault condition) and Ri

″ (with a fault) 1

R′′

i=

1

R′′

i+

1

r the following formula is obtained:

(9.9)Ist−st = Ust−st ·

(

1

R′′

i

−1

R′

i

)

Fig. 9.5 Detection of earth faults with help of a fault recorder (REC)

9.2 Measurements of Maximum and Steady-State Magnitudes of Earth Fault

http://dx.doi.org/10.1007/978-3-319-07010-0_10


Knowledge of If(0) and If(∞) as well as time constant of a circuit seen from earth fault terminals enables an exact determination of earth fault current time function.

There is a simple method of determination of steady-state dead (r = 0) earth fault current without such risky operation as a dead fault execution. For this pur-pose a given pole should be grounded through a resistor Rd. Without this resistor steady-state dead earth fault current of this pole would be Ist−st−f 1 = Ust−st1 ·

1

Ri,

whereas with this resistor it would be Ist−st−f 2 = Ust−st2 · (1

Ri+

1

Rd), where

Ust−st1 and Ust−st2 are this pole-to-ground steady-state prefault voltages without (1) and with (2) the resistor Rd connected. Of course currents Ist−st−f1 and Ist−st−f2 are equal because steady-state dead earth fault current is independent from insu-lation resistance to ground of the faulted pole. Insulation-to-ground equivalent resistance Ri is measured in prefault condition without resistor Rd connected. Comparing the right sides of both expressions the following formula is obtained

It should be noted that this simple procedure allows also to determine insulation resistance Ri which is equal to

9.3 Earth Leakage Currents

9.3.1 Calculations

Earth leakage current from DC IT network flows through places with defected insulation. Leakage current is an indication of insulation to ground resistance though dependence between these quantities is not univocal. Leakage currents cause heat losses and possibly fire, shock and corrosion hazards. Insulation defects may be distributed in any possible way along the circuit. Total leakage current Il from the positive pole is of course equal to the total leakage current to the negative pole. This fact is a conclusion from Kirchhoff’s Ist law. Il value can be calculated in steady-state condition from the following formula derived from DC network equivalent circuit diagram:

Most often insulation equivalent resistance Ri is known instead of single poles insulation resistances R1 and R2. Using formulas U1 =

E ·R1

R1 + R2, U2 =

E ·R2

R1 + R2, Ri =

R1·R2

R1 + R2, formula (9.12) can be transformed into the alternative

equation

(9.10)Ist−st−f =Ust−st1 · Ust−st2

(Ust−st1 − Ust−st2) · Rd

(9.11)Ri = Rd ·Ust−st1 − Ust−st2

Ust−st2

(9.12)Il =E

R1 + R2

(9.13)Il =

U1 · U2

E · Ri

119

where voltages U1 and U2 were measured with a voltmeter with infinite internal resistance. However if U1 and U2 were measured successively with one voltmeter with internal resistance RV, then leakage current is

Usually it may be sufficient to estimate possible maximum leakage current if insulation resistance Ri is known. Taking into account relationship between arith-metic and geometric mean values (

√R1 · R2 ≤

R1 + R2

2) the following inequality is

obtained from (9.13) :

Earth leakage current is a function of insulation resistances R1 and R2 but its dependence on network insulation equivalent resistance Ri is not univocal. In fact insulation equivalent resistance value does not determine univocally leakage cur-rent level and vice versa. Figure 9.6 presents maximum leakage currents for Ri determined from (9.15). The smallest leakage current for any Ri value is of course zero which occurs when one of resistances R1 or R2 is equal to infinity.

Using the curve shown in Fig. 9.6 range of possible leakage currents for a given Ri value can be read out. Another, more difficult task is to determine total leakage current in a part of a network, for example in a single line. Total leak-age current of this line is equal to the difference of currents flowing in both wires

(9.14)Il =E

RV

·U1 · U2

(U1 + U2) · (E − U1 − U2)

(9.15)Ii =E · Ri

Ri + R2

·E · R2

Ri + R2

·1

E · Ri

=E

Ri

·

(√

Ri · R2

Ri + R2

)

≤E

4 · Ri

Fig. 9.6 Maximum leakage current as function of insulation resistance Ri in 220 VDC network



(positive and negative pole conductors) of this line. In distinction from the whole network this parameter does not have to be zero. In order to calculate this value it is necessary to know insulation-to-ground resistances of both wires with con-nected devices. However this requirement is usually not met because insulation resistance measurements provide results relating to the whole network instead of its parts. Therefore for particular lines it is more convenient to measure than cal-culate leakage current. Some methods are described in further section of the book.

9.3.2 Electric Shock Hazard Assessment

An important issue for ensuring safe working conditions for persons is evaluation of maximum possible leakage and shock currents in electric devices. Direct cur-rent values leading to pathological effects to human organism are 3–4 times higher than for alternating current. This means that heart fibrillation is much less prob-able for DC than AC electric shock. Nevertheless direct current flowing through a human body for a long time may cause pathological effects, even if it is below threshold of perception which is about 2 mA.

Grounding is an additional safety measure applied in DC IT systems to limit dan-gerous touch voltages on conducting parts not belonging to electric circuits. In case of device insulation deterioration leakage current may flow to ground. Maximum value of this current flowing through the enclosure grounding wire can be assessed if network insulation parameters are known. Two examples of these abnormal cases are discussed below. Figure 9.7 shows a DC network circuit diagram with grounded conducting enclosure where x and y are resistances of insulation between respective poles and the enclosure, Rg is the enclosure grounding resistance.

If insulation equivalent resistance Ri is known, e.g. from insulation monitor indication, maximum possible touch voltage between the housing and ground can be determined. It can be shown that the highest possible current in the grounding wire of the enclosure will be with insulation resistances R1 = y = ∞ (or R2 = x = ∞). In these conditions maximum voltage to ground of the enclosure is

whereas insulation to ground equivalent resistance is

From (9.16) maximum grounding resistance Rg can be determined for which on the conducting enclosure there appears voltage to ground not higher than permis-sible level Uperm.

It should be noted that even with insulation relatively low level this requirement does not impose a substantial limit on allowable range of protective groundings resistances in DC networks. Much smaller value is required to limit touch voltages on conducting enclosures in case of double earth fault in various points (one pole

(9.16)Ugmax = E ·Rg

4 · Ri

(9.17)Ri =R1 · (y + Rg)

R1 + y + Rg

or Ri =R2 · (x + Rg)

R2 + x + Rg

121

grounded outside the device, the other pole connected to the enclosure). The cur-rent of this double fault must be high enough to ensure adequately fast reaction of overcurrent protections installed in this circuit.

Another case of electric shock hazard is shown in Fig. 9.8. Insulation resistance Ri was measured following a break in the enclosure grounding wire and therefore does not take into account insulation resistances x and y.

In these conditions the highest possible—for any unknown x and y values—magnitude of shock current Ih through human body resistance Rh is equal to

(9.18)Ihmax =E

Ri + Rh

Fig. 9.7 DC network circuit diagram with grounded conducting enclosure

Fig. 9.8 DC network circuit diagram with broken grounding wire of the conducting enclosure



This most dangerous condition occurs in one of two cases: (1) R1 = y = ∞, x = 0 and Ri = R2 or (2) R2 = x = ∞, y = 0 and Ri = R1. It should be noted that insula-tion resistance Ri in the latter formula is greater than this parameter value meas-ured in the former case of electric shock hazard (9.17). This is due to the fact that insulation leakages of single poles R1, R2 are no longer shunted by leakages x, y of the device itself. Formulas (9.16) and (9.18) prove useful for assessment of electric shock hazard in DC IT networks in the worst possible conditions.

9.4 Leakage Current Measurements

9.4.1 Periodic Measurements

There are many methods of DC IT leakage current measurement. In a de-energized network measurement can be performed with both poles galvanically separated e.g. by opening switches and disconnecting apparatuses. In this condition insulation resistance of single poles R1 and R2 can be measured and then with formula (9.12) leakage current can be calculated. In a network with separated poles, supplied from its own voltage source E or from any other source Ex, leakage current can be easily measured. It is simply current supplied from the source to the positive pole wire. If voltage source Ex is used, the result obtained should be multiplied by E/Ex . If net-work poles cannot be galvanically separated, two measurements with use of volt-age source Ex and an ammeter are necessary. Each pole of the network fed from this source should be grounded through the ammeter one after another. Of course this is permitted for sufficiently high insulation resistance level (i.e. there is no risk of shorting the source). Both measured currents I1 and I2 are put into formula

With proper insulation level this procedure can be executed also in normal operat-ing conditions when the network is supplied by its voltage source E. In this case (Ex = E) leakage current is

It is also possible to measure leakage current in live IT DC networks using modern clamp meters. These digital clamp-on ammeters with measuring range of few mA are applied among others in portable fault locating devices. In order to measure leakage current in any line, its both conductors (positive and negative) are embraced by the clamp jaws to measure difference of their currents. When using these instruments it should be borne in mind that algebraic sum of currents in all conductors (taking into account directions of currents flow) embraced by the clamp cannot exceed maximum value given by the manufacturer.

(9.19)Il =E

Ex

I1+

Ex

I2

(9.20)Il =I1 · I2

I1 + I2

123

9.4.2 Continuous Measurements

Continuous measurements are most often executed with help of direct current transformers. These devices are applied among others in stationary fault locating systems. Some of direct current sensors are in fact DC transmitters which pro-duce at the output milivolts proportional to miliamps measured. An example of those devices is a current sensor DCZTC-20M type manufactured by MMI Co. Its measuring range is 1–1000 mA DC with window diameter 20 mm. Measuring error does not exceed 1 % . The device requires auxiliary supply 5 V DC. Another device is earth leakage current monitor type DDCA manufactured by Thiim A/S [1]. It utilizes DC differential current transformer with window diameter of 14 or 29 mm. This monitor comprises an overcurrent relay which picks up when the set leakage current is exceeded. There are also available dedicated systems of leakage currents monitoring such as ISOPAK200 delivered by Megacon [2]. It is based on electronic current transmitters AG31 type of accuracy class 0.1. Their measuring range is 0–100 mA DC. Output analog signal as well as binary alarm are sent to central supervisory system.

Different solution is applied in leakage current monitoring systems based on a shunt resistor. This monitor is supplied with mV signal Um taken across resistor Rm connected in series with one of line conductors at its beginning in a switchgear (see Fig. 9.9).

This input signal is influenced also by current flowing through leakage resist-ance r12 between positive and negative conductors of the monitored line. Leakage current flowing only through r1 and returning through R2 is not taken into account at all. Therefore generally the monitor does not accurately evaluate insulation level

Fig. 9.9 Leakage current measurement based on voltage signal monitoring

9.4 Leakage Current Measurements


between single conductors and ground. When measured voltage signal exceeds set threshold value, it issues an alarm.

9.5 Earth Fault and Shock Currents Measurement

Earth fault, shock and leakage currents can be easily assessed knowing pole-to-ground voltages and insulation equivalent resistance Ri. There are also few meth-ods of these quantities measurement in live networks. Below there are described two examples of such procedures developed by the author.

9.5.1 Earth Fault and Shock Currents Measurements in Network Models

For measurement of earth fault and shock currents in the network model, a resis-tor with value equal to insulation equivalent resistance is used. System shown in Fig. 9.10 can be used for periodic determination of this parameter in live DC IT network.

The measurement is executed as follows. First with released switch S voltage U2 at DC voltmeter is read. Resistor r should be set to maximum resistance. Then

Fig. 9.10 System for periodic determination of insulation equivalent resistance with help of a variable resistor r

125

S is pressed and gradually resistance r is decreased supervising lowering of U2 voltmeter indication to U2′. When the measured voltage decreases to half of its initial value (i.e. U2

′ = 0.5U2), the switch is released. Resistance set at the resistor r is equal to network-to-ground insulation equivalent resistance Ri . This conclu-sion directly follows from the equivalent circuit seen from the terminals of resistor r . Insulation equivalent resistance can be read at the resistor r scale or it can be measured with ohmmeter.

Earth fault and shock current assessment can be performed in DC IT network model shown in Fig. 9.11. For simplicity only negative pole earth fault and shock currents measurements were illustrated.

Voltage divider D provides pole-to-ground voltages existing in prefault con-dition. In slider S position ensuring voltmeter zero indication, voltages across the divider arms are U1 and U2 . Due to the divider low resistance these voltages remain unchanged when resistors are connected during measurements. In position 1 of switch P the ammeter indicates earth fault current of the negative pole. In posi-tion 2 shock current of a man with body resistance Rh touching this pole is read out.

9.5.2 Earth Fault and Shock Currents Measurements in Live Networks

In distinction from the method described above this procedure does not require use of resistor divider delivering “frozen” network-to-ground voltages. The procedure shown in Fig. 9.12 is based on Thevenin’s theorem.

An adjusted resistor r is connected via a switch S with an ammeter between ground and the chosen pole—to avoid risk of relay misoperation it is advised to choose negative pole (see Chap. 10). First with released switch S voltage U2 at DC voltmeter is read. Resistor r should be set to maximum resistance. Then S is pressed and the resistor’s value is decreased to the moment when the negative pole-to-ground

Fig. 9.11 System for earth fault and shock current evaluation with voltage divider in balanced condition

9.5 Earth Fault And Shock Currents Measurement

http://dx.doi.org/10.1007/978-3-319-07010-0_10


voltage falls to half of the initial level. Double value of the read out current is equal to earth fault current of this pole whereas resistor r value is network insulation equiva-lent resistance. In order to measure electric shock current, resistor with double human body resistance should be connected in series with resistor r set to Ri . Ammeter indi-cation is half of electric shock current for a man’s contact with this pole.

9.6 Network-to-Ground Capacitance Determination

Network capacitance to ground exerts substantial influence on transient phenomena in DC IT systems. Network total capacitance to ground together with insulation equivalent resistance to ground determines time constant of currents and voltages transients under earth fault conditions. Charging or discharging of insu-lation capacitances may cause inadvertent operation of apparatuses. Therefore in various applications it may be necessary to determine network total capacitance to ground. In a deenergized network this parameter can be measured with use of so called technical method. It is based on use of auxiliary AC voltage source with frequency f connected between ground and short-circuited poles of the network.

Insulation impedance module Zi is calculated by dividing the auxiliary source voltage by current driven by it. Insulation equivalent resistance is indicated by an isometer or can be measured with a megohmmeter or by any other method. The sought capacitance value is given by the formula

(9.21)Ci =

√

1

Z2

i

−1

R2

i

2π f

Fig. 9.12 Procedure of earth fault and shock currents measurement in live network

127

This method can be used also in a live DC networks as battery is a short circuit for alternating current. Application of two auxiliary AC voltage sources with different frequencies f1 and f2 is another version of this concept. In this procedure currents forced by respective sources are measured. If these sources voltages are known, insulation conductances for both frequencies can be easily calculated. From two equations with two unknown parameters

insulation capacitance Ci can be calculated as

Another method for de-energized networks utilizes an auxiliary DC voltage source connected between ground and short circuited poles of the tested network. At the moment of this source disconnection, the network-to-ground voltage waveform should be recorded. From the oscillogram time constant T can be graphically determined.

Capacitance Ci is given as

There are numerous methods designated for live networks. One of them utilizes transient pole –to-ground voltage waveform recorded when an artificial earth fault of any of the poles through fault resistance Rd is executed. Also in this case Ri value must be known. From the oscillogram time constant T should be graphically determined. Capacitance Ci is given by formula

If Ri value is not known, two earth faults through fault resistances Rd1 and Rd2 can be executed. From the recorded oscillograms of any pole voltage transients, time constants T1 and T2 are graphically determined. Then set of two equations with two unknown parameters Ci and Ri should be solved:

Use of recorder as shown in Fig. 9.5 allows not only to determine insulation resistances R1 and R2 of the respective poles but also network-to-ground total capacitance C1 + C2 . For this purpose a discharged capacitor Cd1 is connected to a selected pole and ground. Maximum recorded current of its charging when con-nected to the negative pole is i1(0).

(9.22)Y2

i1=

1

R2

i

+ C2

i· (2π f1)

2and Y

2

i2=

1

R2

i

+ C2

i· (2π f2)

2

(9.23)Ci =1

2π

√

Y2

i1 − Y2

i2

f 2

1− f 2

2

(9.24)Ci =T

Ri

(9.25)Ci =T

Ri·Rd

Ri + Rd

(9.26)T1 = C1 ·Ri · Rd1

Ri + Rd1

and T2 = Ci ·Ri · Rd2

Ri + Rd2

(9.27)i1(0) =

E

R1 · (1 +C1 + C2

Cd1)

9.6 Network-to-Ground Capacitance Determination


From this formula sought value of C1 + C2 is calculated. If R1 value is not known, the same measurement should be repeated but with another capacitor Cd2. In this case maximum recorded current is

From formulas (9.27) and (9.28) value of C1 + C2 can be now calculated.For Ci determination there can also be used an oscillogram of any pole-to-

ground voltage recorded with isometer superimposing pulsed voltage +U0/−U0. Time constant read out from the oscillogram presenting exponential rise or decline of a selected pole-to-ground voltage is given by formula

where Rint is isometer internal resistance given in its technical data, Ri is isome-ter indication. This formula can be explained with network and isometer circuit diagrams (Fig. 9.13a, b) where pulsed voltage superimposed by the device on insulation-to-ground of positive pole is shown.

References

1. http://www.thiim.com2. http://www.megacon.com

(9.28)i11(0) =E

R1 · (1 +C1 + C2

Cd2)

(9.29)T = Ci ·Ri · Rint

Ri + Rint

Fig. 9.13 a DC network and isometer circuit diagram, b equivalent circuit diagram of DC network with isometer

http://www.thiim.com

http://www.megacon.com

Part IIIAC and DC IT Systems

131

Abstract In the chapter electrical, mechanical, thermal, chemical and other reasons of electric insulation failures are described. Consequences of network insulation failures are discussed. The most frequent problems are misoperation of control and protective devices installed in the circuits. Various cases of mis-operation of DC and AC devices caused by insulation faults are presented and explained. Few methods of prevention of devices malfunctioning are given, among others device’s coil shunting by a resistor or a damping filter. Some useful formu-las for resistor selection are derived.

10.1 Reasons of Insulation Failures

Main reasons of electric insulation failures are ageing, mechanic and thermal impacts, overvoltages, humidity, chemical factors, oil and radiation. Mechanic fac-tors include excessive strain, pressing, bending, cutting, vibration etc. Mechanic strain may cause breaks of insulation resulting in penetration of water or impuri-ties into the material. All this leads to lowering of electric strength. Vibration of elements can cause abrasion of insulation outer layer. Most frequent factors short-ening insulation lifetime are temperature and humidity. Heating leads to insulation drying, breaking or softening. These factors decrease electric insulation mechanic endurance. Temperature increase over permissible operating level by 10 °C cuts insulation lifetime approximately twice, by 20 °C—about 4 times etc. Protection of electric devices against overloads is sometimes difficult to implement because of low nominal currents of some elements. For example coils of relays usually have current carrying capacity below 1 A, whereas their supply circuits are pro-tected by fuses 6 or 10 A. Excessively low temperature leads to breaking of some insulating materials, especially under mechanic strain e.g. bending. Therefore dur-ing frosts it is not permitted to bend and lay cables with insulation made of sensi-tive materials such as polyethylene.

Chapter 10Effects of Insulation Failures


132 10 Effects of Insulation Failures

Overvoltages (excessive voltage rises) shorten insulation lifetime and sometimes cause its irreversible breakdown. Immunity to overvoltages of insulation material depends among others on insulation layer thickness, circuit make-up, overvoltage value and duration, temperature, humidity and surface contamination. Most fre-quent causes of overvoltages are:

(1) insulation breakdown from another circuit remaining under higher voltage,(2) insulation resistance measurement with megohmmeter using too high voltage,(3) voltage resonance,(4) voltage rise across open winding of a transformer,(5) commutation in a circuit with high inductance.

The greatest threat for insulation pose overvoltages supplying high energy e.g. caused by breaking currents of big electromagnets. In order to reduce overvolt-ages specially selected damping resistors or circuits as well as overvoltage protec-tors are connected across terminals of sensitive elements, especially coils. Electric insulation durability depends on keeping recommended parameters and work con-ditions, among others:

• rated voltage• type of current (direct or alternate), its value and frequency,• applied test voltage,• ambient air humidity and temperature,• air contamination,• type of operation (continuous, intermittent, etc.).

10.2 Effects of Network Insulation Failures

Earth faults in AC or DC IT systems can cause various threats, which may lead to failures with grave consequences. Few typical examples are presented below. Some cases of apparatuses misoperation risk are described in Sect. 10.3, whereas electric shock and fire hazards are discussed in Chap. 11.

Short circuiting of an element by double earth faults (Fig. 10.1) not only elimi-nates it from operation but also causes rise of current in this circuit.

If there is no additional, current limiting resistor connected in series with the coil as in the figure above, this fault may cause tripping of overcurrent protection result-ing in supply shutdown. In case of double earth fault at both poles, network sup-ply source gets shorted. Even a short duration flow of excessive current through a closed contact may rise its temperature. This temperature growth can weld contacts or they would loose resilience. In some cases double earth fault current may exceed current carrying capacity of the closed contact, but nevertheless it may not cause the overcurrent protection to switch off supply. Natural consequence of insulation breakdown is necessity to locate and correct it as soon as possible. However fault location in live system without specialistic equipment is not only laborious and time consuming, but also can cause some subsequent disturbances in network operation.

http://dx.doi.org/10.1007/978-3-319-07010-0_11

133

10.3 Misoperation of Devices

Insulation deterioration and high capacitances to ground or between conductors are the most common reasons of improper operation of devices (relays, contac-tors etc.) installed in AC or DC IT auxiliary circuits. These undesired events include lack of necessary pick-up, unnecessary pick-up and lack of dropout of a device. Circumstances of some of these failures are shown in subsequent figures. Figures 10.2 and 10.3 relate to both DC and AC circuits.

Lack of necessary pick-up of a device P may occur due to short circuiting of its coil by a branch formed by insulation leakages or simply two earth faults (Fig. 10.2). As result current flowing through the coil with series connected limiting resistor Rd may not reach pick-up value of the device. Without this resistor an overcurrent protection should switch off supply. This artificial branch shunting the coil increases dropout time of the device (if it picks up at all) because it enables gradual coil current decay after opening of the P1 contact.

In the circuit shown in Fig. 10.3 an inadvertent pick-up of the device P can occur due to grounding of the coil positive terminal inspite of an open contact P1. The energizing current flows to the coil through positive pole insulation leakage R1 and earth fault resistance R2

′ . Another type of misoperation is also possible: relay P was correctly energized by a P1 contact but after its opening the relay does not drop out because current flowing through resistors R1 and R2

′ exceeds its dropout threshold.Another case of a device misoperation is shown in Fig. 10.4—in DC circuit

grounding of the coil positive terminal forms a path for negative pole capacitance C2 discharge with simultaneous charging of positive pole capacitance C1. Both capacitive currents flow through the coil in the same direction i.e. they add alge-braically. Initial value of this total, exponentially decaying current may exceed the device pick-up threshold and cause its unnecessary pick-up.

Fig. 10.1 Shorting of a DC control device by insulation leakages



Too high conductor-to-ground capacitance in DC IT circuit can also cause another failure i.e. extension of a device dropout time as shown in Fig. 10.5. After opening of P1 contact, the device P does not de-energize immediately due to cur-rent flow through its coil. This is a discharging and then charging current of Cp capacitance of a conductor connecting P1 and P.

In this case—with open P1 contact—unnecessary energization of a device is also possible following grounding of network positive pole. Current that charges Cp capacitance to the full network source voltage, flows through the coil as shown in Fig. 10.6a. Similarly, device misoperation—i.e. inadvertent pickup or lack of dropout—is a typical risk in AC IT circuits with high Cp capacitance of a wire connected to the coil phase terminal. This failure caused by grounding of network

Fig. 10.3 An example of inadvertent pick-up or lack of dropout of the relay P due to its coil positive terminal grounding

Fig. 10.2 Shunting of a coil by a branch formed of insulation leakages

135

phase conductor is illustrated in Fig. 10.6b whereas device misoperation caused by grounding of the coil phase terminal is explained in Fig. 10.6c.

A separate group of disturbances are failures involving other electric networks. A DC device misoperation may occur as effect of insulation fault at any of three points indicated in Fig. 10.7. In this case current flow through the coil P is forced by an external voltage source Eext installed in another, galvanically isolated DC network. Magnitude and time function of this current depend on leakages and capacitances of insulation between both networks as well as between any one of them and ground.

Similar failure is shown in Fig. 10.8 where undesired current flow through a DC device P coil is forced by an external AC voltage source Eext. Possible paths of

Fig. 10.4 Inadvertent energization of a device due to capacitive currents flow—currents flow direction is marked with arrows indicating movement of positive charges

Fig. 10.5 Extension of drop out time of relay P caused by capacitive current



Fig. 10.6 a Inadvertent device energization caused by capacitive current flow. b AC device misoperation caused by current flow through the coil and conductor capacitance Cp following phase wire grounding. c AC device misoperation caused by grounding of the coil phase terminal

137

this current flow are the same as in Fig. 10.7. A superimposed AC voltage across the coil causes vibration of an armature and contacts as a result of periodic ener-gizing and deenergizing of the device with AC frequency. The relay’s unstable, intermittent operation under this condition, leading possibly to its damage, is illus-trated by a waveform in Fig. 10.9.

AC devices are subject to another kind of misoperation risk. It is possible because of series resonance of the conductor capacitance Cp1 with the coil induct-ance Lp (Fig. 10.10a, b). Under resonance condition there may appear voltage across the coil terminals exceeding the device pick-up threshold.

Fig. 10.7 Illustration of inadvertent device energization by an external DC network voltage source

Fig. 10.8 An example of inadvertent device energization by an external AC voltage source



Fig. 10.9 Oscillogram of periodic energization and de-energization of a DC relay (waveform A) and of its coil voltage (waveform B)

Fig. 10.10 a AC device misoperation due to series resonance—schematic circuit diagram. b AC device misoperation due to series resonance—equivalent circuit diagram

139

10.4 Prevention of Devices Misoperation

10.4.1 Device Coil Shunted by Resistor

Traditional method of preventing relays’ inadvertent pick-up is shunting its coil with an appropriate resistor. Parallel connection of this element decreases equiva-lent resistance of coil-resistor circuit. This leads to lower voltage across the coil terminals appearing in case of insulation failure or capacitive or magnetic cou-pling. With help of Fig. 10.11 it is possible to explain this simple remedy and determine its effectiveness in DC circuits.

For this purpose it is necessary for given values of resistances R1, R2, R2′ to

compare steady-state voltages across the coil without shunt resistor R

and with resistor R

From comparison of both formulas it follows that due to the shunt resistor connection, steady-state voltage across the coil is smaller in case of insulation deterioration. However this solution has got also few undesired effects. Protected device dropout time is extended because a loop comprising resistors Rp and R is formed to allow gradual decay of the coil current. Additionally heat power is gen-erated in the shunt resistor as soon as voltage is applied to it. Shunt resistors are a common remedy used also in AC IT circuits. This simple solution proves effective for DC devices in case of charging/discharging of capacitances C1 and C2, trig-gered by grounding of the coil positive terminal through fault resistance R2

′. Initial values of voltage across the coil Up are as follows:

• without shunt resistor

(10.1)

Up(∞) = E ·

(R′

2+ Rp)·R2

R′

2+ Rp + R2

R1 +(R

′

2+ Rp)·R2

R′

2+ Rp + R2

·Rp

R′

2+ Rp

= E ·R2

R1·R′

2+ R1·R2 + R2·R

′

2

Rp+ R1 + R2

(10.2)

UpR(∞) = E ·

(R′

2+

Rp·R

Rp + R)·R2

R′

2+

Rp·R

Rp + R+ R2

R1 +(R

′

2+

Rp·R

Rp + R)·R2

R′

2+

Rp·R

Rp + R+ R2

·

Rp·R

Rp + R

R′

2+

Rp·R

Rp + R

= E ·R2

R1·R′

2+ R1·R2 + R2·R

′

2Rp·R

Rp + R

+ R1 + R2

(10.3)Up(0) =

U2(0) · Rp

R′

2+ Rp



• with shunt resistor R connected

where U2(0) is negative pole-to-ground voltage at the moment of earth fault occur-rence. It should be reminded that both pole-to-ground voltages do not change at this instant due to presence of ground capacitances C1 and C2.

Also in this case of insulation deterioration, connection of shunt resistor leads to lower initial value of the coil voltage. Additionally time constant of the coil voltage decay decreases as well as steady-state coil voltage level. It should also be noted that this solution may decrease network insulation resistance to ground seen by an insulation monitor (shunt resistor does not influence the monitor indication only for R

′

2= ∞ or R1 = 0 or R2 = 0).

10.4.2 Device Coil Shunted by Other Elements

In DC circuits grounding of the device coil positive terminal forms a discharge path of the negative pole-to-ground capacitance. Simultaneously through this coil in the same direction flows current charging positive pole-to-ground capaci-tance. An effective method of avoiding inadvertent device pick-up by sum of these capacitive currents is shunting of the coil by an overvoltage protective circuit. There are numerous circuits composed of resistors and capacitors which ensure very fast damping of voltage emerging across the coil at the moment of insulation failure. An example of such device is RXTCB1 type filter (Fig. 10.12) manufac-tured by former ASEA [1]. These filters were designed for DC circuits with rated

(10.4)UpR(0) =

U2(0) ·R·Rp

R + Rp

R′

2+

R·Rp

R + Rp

=U2(0) · Rp

R′

2· (1 +

Rp

R) + Rp

≤ Ucoil(0)

Fig. 10.11 DC circuit diagram with the coil positive terminal grounded by fault resistance R2

′

141

voltage max.250 V and maximum capacitance to ground 10 μF. The circuit guar-antees much faster voltage decay across the coil and lower power losses than com-monly used shunt resistors. Fast voltage decay is achieved by forming a path for above mentioned capacitive currents flow through R1 − C1 branch. Voltage decay time constant is with this filter below 1 ms which is much shorter than pick-up time of any relay. Resistor R2 makes steady-state voltage across the coil lower and forms a discharge path for capacitor C1. Diode V1 prevents capacitor C1 discharge through the coil thanks to which the relay dropout time is not extended. Diode V2 opens path for discharge of magnetic energy stored in the coil after opening the contact P. In this way overvoltage at the coil terminals is substantially reduced though relay dropout time is slightly extended.

10.4.3 Disconnection of Both Terminals of Device Coil

Misoperation risk of devices in DC and AC IT networks can be reliably eliminated by disconnection of both terminals of their coils by NO (normally open) contacts of a triggering relay or switch (see Fig. 10.13). It is recommended to discon-nect both wires as close to the device as possible. In this way risk of ground fault occurrence within the coil wiring is diminished. Ground capacitances of these wires are also reduced. This simple solution breaks path of current flow through the coil in case of possible failures described above.

10.4.4 Coil Shorting by NC Contact

Shorting of an AC or DC device coil by NC (normally closed) contact of an ener-gizing relay or switch automatically eliminates any voltage on it (Fig. 10.14). As result no unintentional pickup of the device is possible.

Fig. 10.12 DC circuit diagram with RXTCB1 type damping filter



10.4.5 Limitation of Total Conductor-to-Conductor and Conductor-to-Ground Capacitances

Magnitude of capacitance between conductors or conductors and ground or between different networks exerts direct influence on transient phenomena trig-gered by insulation failure. Even though in DC circuits higher capacitance val-ues not always increase initial values of charge or discharge current, they extend time constant of current/voltage decay which raises risk of devices misoperation. Limiting these capacitances by reducing networks length, elimination of additional overvoltage (surge) capacitors (connected between coil terminal and ground) or screening of cables are some examples of effective means of lowering this hazard.

Fig. 10.13 Disconnection of both terminals of device coil—an example for an AC circuit

Fig. 10.14 Shorting of a device coil by NC contact of a triggering apparatus—an example for AC circuit

143

10.4.6 Insulation Resistance Control by Grounding Through Resistors

Some DC IT networks are equipped with resistive divider for symmetrization of respective poles-to-ground voltages. For this purpose an artificial grounding of both poles through resistors is implemented as shown in Fig. 10.15.

For Rd2 resistance appropriately set smaller than Rd1 resistance, in case of a coil positive terminal grounding, voltage across the coil is much below its pickup threshold. Also C2 capacitance discharge current flowing through the coil in this failure condition should not inadvertently energize the device due to both its lower maximum value and shorter time constant.

Resistances Rd1 and Rd2 must be high enough so that in case of any pole grounding, current supplied by the source does not trip the line protection. Unfortunately with this solution no insulation continuous measurement is possi-ble. For periodical testing of the insulation both additional resistors must be dis-connected from ground with a S switch. However during this procedure capacitive current (charging or discharging the coil wire capacitance Cp) may flow through the coil posing risk of inadvertent pickup of the device.

Thus the described idea ensures that voltage of the negative pole to ground is maintained below required level and all devices become immune to misoperation caused by their coil positive terminal grounding. However at the same time the main feature of DC IT circuits is lost i.e. their galvanic isolation from ground in normal operating conditions. Similar concept may be applied also in AC IT cir-cuits however with all above mentioned drawbacks.

DC network poles-to-ground voltages may be also adjusted automatically. An example of this idea implementation was presented in Chap. 8. Thanks to adjust-ment of additional resistors grounding both poles, required ratio of their voltages is achieved. This in turn eliminates risk of misoperation of devices with appropri-ately set pick-up threshold.

Fig. 10.15 Artificial grounding through resistors of DC network poles


http://dx.doi.org/10.1007/978-3-319-07010-0_8


Reference

1. ASEA RELAYS – Buyer’s Guide B03-0011, 1985–1986

145

Abstract In the chapter general requirements set to insulation monitors selection in AC and DC networks are given. Examples of regulations requirements for circuits insulation equivalent resistance are presented. Traditional method of setting isometers response values is described. Modified approach for settings selection of DC and AC networks isometers takes into account assessment of electric shock and fire hazards as well as devices misoperation risk. Novel criteria for setting iso meters are developed. Insulation monitors application for devices misoperation risk detection is discussed. Few examples of dedicated systems for these hazards detection are given.

11.1 General

AC and DC IT networks should ensure reliable and safe power supply to connected devices and loads. A particularly important task is an uninterruptible supply of auxiliary voltage to automation, control, measurement and protection systems. To meet these requirements it is necessary to eliminate such risks as shock and fire hazards as well as misoperation of devices in case of insulation deterioration. To achieve this goal it is necessary to detect all these operating conditions in which the above mentioned hazards arise. Only in correctly designed and maintained networks these risks are excluded even in case of a single (dead) earth fault.

An indispensable condition for effective insulation monitoring is knowledge of its minimum permissible level. Monitoring of insulation equivalent resistance or single conductors insulation resistances will not bring expected results if no appropriate criteria of this parameter assessment are adopted. Measured values of insulation resistance are sometimes used to plot its trends but this does not allow to precisely detect above mentioned risks. Recommended minimum values e.g. 100 Ω/1 V of insulation resistance in DC circuits ensure only limitation of earth leakage or shock current to a specified level—in this case to about 10 mA. This level may be safe for humans indeed but it does not guarantee failure-free

Chapter 11Insulation Monitors Settings Selection


146 11 Insulation Monitors Settings Selection

operation of most devices. Sometimes alarm threshold of insulation monitors is set below level prevailing under normal operating conditions so as to avoid too frequent alarms.

11.2 Regulations Requirements for DC Systems

According to regulations e.g. in EU insulation equivalent resistance of auxiliary DC circuits should be at least 200 Ω/1 V of rated voltage. If this value declines to 100 Ω/1 V level, an alarm is to be issued. One of criteria for insulation monitors threshold selection in networks equipped with fault location system is sensitivity of its current detectors. Monitors should signal only these insulation conditions in which earth fault currents exceed lower measuring threshold of installed detectors. Generally it is assumed that settings of DC auxiliary circuits insulation monitors should ensure detection of all those conditions in which a single dead earth fault could prevent dropout of any energized device (relay, contactor etc.). Alarm setting of 50 % higher than insulation resistance level causing this risk is recommended. For this condition the most unfavourable case (i.e. leading to the highest required insulation equivalent resistance) is unintentional maintaining the device energized (lack of required dropout, called also a device “holding”) through the positive pole insulation-to-ground leakage resistance with no leakage from the negative pole (see Fig. 11.1).

Under this assumption for the circuit voltage 5 % higher than rated level Un, current keeping the device in energized condition is not less than

(11.1)Idropout =Udropout

Rp

=1.05 · Un − Udropout

Ri

,

Fig. 11.1 Unintentional “holding” of an energized device in a DC circuit with the highest Ri value

147

where Udropout, Idropout—device dropout voltage and current, Rp—coil resistance. From (11.1) minimum permissible insulation equivalent resistance is obtained

This formula [1] can be used for insulation monitors alarm threshold selection in DC auxiliary circuits. However due to other hazards occurring in DC IT systems it is reasonable to modify this approach [2]. Criterion (11.2) can be extended in the way presented below.

11.3 Modified Approach for DC IT Networks

11.3.1 Shock and Fire Hazard Assessment

Shock hazard determination is possible with established criterion of this risk assessment. These criteria can be for example maximum permissible steady-state values of shock current or touch voltage. For further analysis there was assumed con-dition of exceeding the permissible, steady-state touch voltage to any network pole. Uh1 touch voltage of a man with body resistance Rh in contact with positive pole (i.e. voltage across human body is voltage between ground and the touched pole) is

whereas in contact with negative pole

where E is source voltage, R1, R2—single poles insulation-to-ground resistances.From formulas (11.3) and (11.4) conditions for both resistances R1, R2 can be

determined, for which touch voltages Uh1 or Uh2 exceed permissible safe level Uhsafe:

when touching negative pole or

when touching positive pole.

(11.2)Ri = Rp ·1.05 · Un − Udropout

Udropout

(11.3)Uh1 =

Rh·R1

Rh+R1

Rh·R1

Rh+R1+ R2

E

(11.4)Uh2 =

Rh·R2

Rh+R2

Rh·R2

Rh+R2+ R1

E

(11.5)R1 ≤Rh · R2

Rh + R2

·E − Uhsafe

Uhsafe

(11.6)R1 >

Rh · R2 · Uhsafe

Rh · (E − Uhsafe) − R2 · Uhsafe

11.2 Regulations Requirements for DC Systems


Examples of characteristics described by formulas derived above for DC IT network are shown in Fig. 11.2.

Research results [1] have proved that for initiation and maintaining combustion process it is necessary to deliver to the place of short circuit thermal power about 60 W. In 230 V DC network this would require earth fault current flow of at least 0.26 A. So high currents may occur only with insulation resistance level below 1 kΩ. Therefore fire prevention is not critical for assessment of minimum permissible insu-lation level in these networks and it will not be taken into account in further analysis.

11.3.2 Misoperation of Devices in DC Circuits

Another threat for safe DC IT networks operation is risk of devices malfunction caused by insulation-to-ground deterioration (see 10.3). Influence of these unrequired phenomena risk on permissible range of insulation resistance is discussed below.

Line-to-ground capacitances can cause inadvertent pickup of a device when its coil positive terminal is grounded. Following this earth fault occurrence, negative pole-to-ground voltage (which is also voltage across the device coil in case of a dead earth fault) decreases exponentially from initial value U2(0) to steady-state one U2(∞) according to the formula given below

where T is a time constant of a circuit seen from terminals of the earth fault. For simplicity of calculation and to obtain the highest required insulation levels, a dead fault was assumed. The device picks-up if this voltage after the device tp pickup time has elapsed, exceeds its pickup threshold Up. From this condition

(11.7)U2(t) = U2(0) · e−t/T+ U2(∞) · (1 − e−t/T

),

(11.8)U2

(

t = tp)

> Up

Fig. 11.2 Characteristics of electric shock hazard in DC IT networks for the following parameters E = 240 V, Rh = 2 kΩ and Uhsafe = 24 V: x1—curve described by (11.6), x2—by (11.5)

http://dx.doi.org/10.1007/978-3-319-07010-0_10

149

a range of insulation resistances (R1, R2) is obtained within which the device misoperation is possible. An accurate determination of this range is difficult because of dependence of momentary values of U2(t) voltage on the network insulation parameters i.e. insulation total capacitance and insulation resistances of single poles.

In steady-state condition another hazard is also possible. Following device P energizing by closing P1 contact its coil positive terminal earth fault may occur. If after this fault contact P1 opens, it may happen that the device P remains unnecessarily energized (“held” in energized position) by leakage current flow-ing through insulation resistance R1. From condition of lack of the device dropout U2 > Udropout, where U2 is voltage across its coil following P1 contact opening and Udropout—the device dropout voltage, a range of insulation resistances (R1, R2) can be determined within which this inadvertent phenomenon is possible:

It is worth noting that with infinite value of R2, condition (11.9) is tantamount to (11.2). The latest inequality, which is the second criterion of insulation level assessment following condition (11.5) or (11.6), can be also expressed with use of insulation equivalent resistance Ri:

This condition can be derived with help of the venin principle in the following way. Let U2 be negative pole i.e. coil positive terminal-to-ground pre fault volt-age. In this case an earth fault current If of this terminal is U2 = If · (Ri + Rp). Device dropout condition is If < Idropout = Udropout/Rp. From both formulas condi-tion (11.10) is obtained.

Another case of a device’s inadvertent holding in energized condition was shown in Fig. 10.3. It is described by completely different characteristic on the plane (R1, R2). In this circuit the only one insulation resistance to ground of the negative pole is R2

′ (shunt resistor R is omitted here). An inadvertent lack of the device dropout occurs if

from which the following condition is obtained for insulation resistances R1 and R2 (in this particular case R2 = Rp + R2

′):

Using formulas U1 =E·R1

R1+R2, U2 =

E·R2

R1+R2, Ri =

R1·R2

R1+R2 inequality (11.12) can be

expressed in another form

(11.9)R1 ≤E − Udropout

Udropout

·Rp · R2

Rp + R2

(11.10)U2 −Udropout

Rp

· Ri > Udropout

(11.11)Ucoil =E · Rp

R1 + R′

2+ Rp

≥ Udropout ,

(11.12)R1 + R2 ≤E

Udropout

· Rp

(11.13)Ri ≤U1 · U2

E · Udropout

· Rp


http://dx.doi.org/10.1007/978-3-319-07010-0_10


Taking into account that in this case R2 ≥ Rp solution of inequality (11.12) can be illustrated as an area under a section of a line with end points with coordinates (

Rp,E−Udropout

UdropoutRp

)

and (

EUdropout

Rp, 0

)

. Summing up, conditions describing the

above presented risks are as follows

The criteria listed above can be extended by a condition of detecting electric shock hazard of a man touching the positive pole expressed similarly to (11.15)

Presentation of the proposed criteria of insulation level assessment in the form of voltage conditions (11.14)–(11.17) makes their checking easier. Instead of troublesome consideration of the conditions in (R1, R2) plane it is much more convenient to process network voltages according to the respective formulas. Two examples of checking the criteria in dedicated electrical circuits suggested by the author are presented below.

11.3.3 Examples of Practical Checking of Insulation Condition Assessment Criteria

Criterion of lack of device dropout risk described by (11.15) can be checked both in electrical circuit and analytically e.g. by microprocessor iso meter. The pro-posed circuit of this risk detection is shown in Fig. 11.3. Overvoltage relay RU set to Udropout picks up in all insulation conditions determined by pair of parameters (R1, R2), for which there would be no required device dropout due to its coil posi-tive terminal grounding. If in the network there are installed various devices, this criterion should be checked for the most “sensitive” type.

Another system for detection of the same hazard is a simple measuring circuit applied in some oldest iso meters (see Fig. 11.4).

An over current relay issues an alarm if its current exceeds the set pickup value Ip. The relay picks up if any of the two following conditions is fulfilled

or

(11.14)U2(tp) > Up

(11.15)U2 −Udropout

Rp

· Ri > Udropout

(11.16)Ri ≤U1 · U2

E · Udropout

· Rp

(11.17)U1 −Uhsafe

Rc

· Ri > Uhsafe

(11.18)R1 ≤

EIp

− 2Rp + R

2R2 + R + 2Rp +EIp

· R2

(11.19)R1 ≥

E

Ip+ 2Rp + R

E

Ip− 2Rp + R − 2R2

· R2 for R2 ≤R

2− Rp +

E

2Ip

151

The first inequality has form similar to (11.9) condition, which determines insulation resistances area with risk of lack of device dropout. By an appropriate selection of R and Ip parameters, curve (11.18) can be adjusted to match the device characteristic (11.9).

Fig. 11.3 An electric circuit for detection of risk of device holding. Designations: IM—

insulation monitor, Uout—output DC voltage of the monitor equal to Udropout

Rp· Ri, RU—overvoltage

relay with pick-up threshold set to Udropout

Fig. 11.4 Detection of insulation deterioration with an overcurrent relay RI with coil resistance Rp



11.3.4 Graphical Illustration of Insulation Conditions in DC IT Networks

In Fig. 11.5 there are marked areas of insulation resistances for which all hazards described by (11.8), (11.9), (11.12) are possible as well as electric shock of a human. All the curves were plotted for a typical Polish auxiliary relay with rated data given in the Table 11.1.

If in the given network there are installed various types of devices, then for determination of “safe” (i.e. without any risks in case of ground fault) insulation resistances area, a joint part of “safe” areas of single devices should be found. In Fig. 11.5 hyperbola X3 corresponding to the minimum required insulation equiva-lent resistance 22 kΩ is plotted for comparison with characteristics of respective hazards. Divergence of the hyperbola location from the mentioned characteris-tics underlines little usefulness of the traditional approach to the problem of iso meter’s response values selection.

Fig. 11.5 Illustration of insulation resistances area within which relay R15 misoperation risks and human shock hazard are possible. Designation of curves: x1, x2—human shock, x3—insulation monitor set to Ri = 22 kΩ, x4—relay inadvertent “holding”, x5—relay inadvertent pickup due to coil positive terminal grounding, x6 and x7—relay inadvertent pickup according to (11.12)

Table 11.1 Technical parameters and data for Fig. 11.5

Relay type

Pickup voltageUr(V)

Droput voltage Up(V)

CoilresistanceRp(kΩ)

Relay pickup timetp(ms)

Relay inadvertent “holding” area —formula (11.9)

Inadvertent pickup area—formula (11.8) for network with Ci = 60 μF

R15220 VDC

135 50 35 60 R1 ≤122.5·R2

35+R2

R1 ≤ 0.65 · R2

153

11.4 AC Insulation Monitors Settings Selection

11.4.1 Simplified Approach

In AC IT auxiliary circuits the most unfavourable event (i.e. leading to the highest required value of insulation equivalent resistance) is “holding” (lack of dropout) of an energized device by earth leakage current of the phase conductor following dead grounding of the coil terminal with no leakage conductance of a neutral conductor (see Fig. 11.6).

Under these assumptions and neglecting network insulation capacitances, the device dropout current is exceeded if

From this inequality the sought condition is obtained:

where

Un network rated voltageUdropout device dropout voltageU2 neutral conductor-to-ground voltage in pre fault condition i.e. prior to the

coil terminal grounding

(11.20)Idropout =

Udropout

X=

Udropout

U2n

S

=U2

√

R2

i +

(

U2n

S

)2

≤Un

√

R2

i +U4

n

S2

(11.21)Rimax ≤U2

n

S·

√

U2n − U2

dropout

Udropout

Fig. 11.6 Inadvertent “holding” of a device by leakage current



Rimax maximum value of network insulation equivalent resistance for which this failure is possible

X coil reactance (approximately equal to impedance module)S coil apparent power consumption at rated voltage

Formula (11.21) enables to calculate the lowest permissible insulation equiva-lent resistance for which no inadvertent pickup or “holding” of the device occurs following its coil terminal dead grounding. If there are devices of various types in the circuit, the highest value of Ri calculated from (11.21) should be selected. This formula can be therefore used for determination of setting of iso meter in AC IT auxiliary circuits. However the approach described above should be modi-fied to account for presence of insulation capacitances as well as fire and shock hazards.

11.4.2 Electric Shock and Fire Hazard Assessment

Electric shock hazard determination is possible if a criterion of this risk assess-ment has been adopted. This criterion can be for example maximum permissible steady-state value of shock current or touch voltage. For further analysis there was assumed the condition of exceeding the permissible, steady-state shock current.

Based on AC IT network circuit diagram shown in Fig. 11.7 (for simplicity analysis is limited to single-phase systems) steady-state shock current Ih of a man with body resistance Rh touching for example neutral conductor is

where U2 is neutral wire-to-ground voltage in pre fault condition, Zi-insulation–to-ground equivalent impedance as seen from terminals of possible electric shock. From (11.22) shock current is obtained

As it was noted above, the most unfavourable case (i.e. leading to the highest required insulation equivalent resistance level) is when the whole leakage conduct-ance and capacitance are lumped at the phase wire G1 = Gi, G2 = 0, B1 = Bi, B2 = 0. With an additional assumption of Rh ≪ Ri, requirement for insulation resistance maximum level can be obtained from approximate formula (11.24) if shock current Ih is to exceed the permissible value of Ihpermis:

(11.22)

Ih =

∣

∣

∣

∣

U2

Zi + Rh

∣

∣

∣

∣

= Un

∣

∣

∣

∣

∣

1

G2+j·B2

1

G1+j·B1+

1

G2+j·B2

∣

∣

∣

∣

∣

·1

∣

∣

∣

1

G1+j·B1+G2+j·B2+ Rh

∣

∣

∣

(11.23)Ih = Un ·

√

G2

1+ B2

1

(1 + Rh · Gi)2+ (Rh · Bi)

2

(11.24)Rimax =

2 · Un√

4 · I2

hpermis − U2n · B2

i

155

Based on the above formula dependence of maximum permissible value of equiv-alent insulation resistance on network total capacitance is shown in Fig. 11.8.

According to this formula for Ci > Cimax =2·Ihpermis

ω·Un the shock current is greater

than Ihpermis for any Ri value.In AC IT low voltage networks, inspite of limited ground fault current levels,

fire hazard is also possible. Research results [1] revealed that for initiation and maintaining combustion process it is necessary to deliver to the place of short circuit thermal power about 60 W. To assess this risk earth fault power Pf gener-ated at fault resistance Rf can be calculated as follows (there were taken the same assumptions as for shock hazard assessment)

(11.25)Pf = I2

f · Rf = U2

n · Rf ·G2

i + B2

i

(1 + Rf · Gi)2 + (Rf · Bi)

2

Fig. 11.7 Circuit diagram of AC IT single-phase network for evaluation of electric shock hazard

Fig. 11.8 Dependence of maximum equivalent insulation resistance Ri on network total insulation capacitance Ci, for which the shock current Ih reaches its permissible level (for parameters Un = 230 V, Ihperm = 10 mA)



Dependence of insulation equivalent resistance Ri on network total capacitance Ci, for which thermal power Pf reaches its permissible level, is shown in Fig. 11.9.

Curves in Figs. 11.8 and 11.9 indicate that both shock and fire hazards are within broad range of network capacitance values critical for assessment of mini-mum permissible insulation resistance in AC IT systems. For capacitances greater than some defined threshold values both risks exist for all possible levels of insula-tion resistance if the most unfavourable distribution of these parameters (i.e. Ri, Ci lumped at one conductor only) cannot be excluded.

11.4.3 Misoperation Risk for Devices in AC IT Auxiliary Circuits

As was shown in Fig. 10.6 in case of the coil terminal grounding there is formed a path for current flow to energize the device or—if it was energized earlier by P1 con-tact—to hold it in energized position inspite of subsequent opening of this contact.

It is well known that to hold a device in energized condition lower current flow-ing through its coil is required than to pick it up. Therefore in further considerations parameters relating to the device dropout are applied (dropout voltage Udropout, coil reactance X of an energized apparatus). Dropout current Idropout = Udropout/X of a device held by insulation leakage conductance and capacitance fulfils the condition

Minimal value of network insulation equivalent conductance Gimin for this failure is obtained from (11.26) assuming (like in previous section) Gi = Gi and B1 = Bi.

(11.26)

Idropout ≤

∣

∣

∣

∣

U2

Zi + j · X

∣

∣

∣

∣

= Un

∣

∣

∣

∣

∣

1

G2+j·B2

1

G1+j·B1+

1

G2+j·B2

∣

∣

∣

∣

∣

·1

∣

∣

∣

1

G1+j·B1+G2+j·B2+ j · X

∣

∣

∣

Fig. 11.9 Maximum values of network insulation equivalent resistance Ri versus total capacitance Ci according to (11.25) for Un = 230 V, Pf = 60 W

http://dx.doi.org/10.1007/978-3-319-07010-0_10#Fig6

157

Maximum insulation equivalent resistance Rimax = 1/Gimin is this parameter’s highest value for which “holding” of the device is possible.

From this equation formula for Rimax is obtained

Maximum insulation resistance values Rimax, for which inadvertent “holding” of an energized apparatus is possible, are given in Fig. 11.10 as function of insulation total capacitance.

11.4.4 Insulation Monitors Application for Devices Misoperation Risk Detection

Application of insulation monitors for detection of control devices misoperation risk in AC IT (single-phase) auxiliary circuits depends on network-to-ground capaci-tance level. For assessment of these potential possibilities it is necessary to determine

(11.27)

Gimin =

√

√

√

√

√

−(U2n − U2

dropout) · B2

i −2U2

dropout

X· Bi +

U2

dropout

X2· (1 − X2

)

U2n − U2

dropout

Rimax =

√

√

√

√

√

U2n − U2

dropout

−(U2n − U2

dropout) · B2

i −2U2

dropout

X· Bi +

U2

dropout

X2· (1 − X2

)

(11.28)

for Bi <

Un · Udropout

(U2n − U2

dropout) · Xwhereas Rimax = ∞ for Bi >

Un · Udropout

(U2n − U2

dropout) · X


Fig. 11.10 Maximum values of insulation equivalent resistance of AC IT control circuit for which “holding” of an apparatus with rated data Un = 230 V, Udropout = 130 V, X = 6.5 kΩ is possible


maximum possible total capacitance of the network. Assuming the most unfavourable case, characteristic Rimax = f(Ci) according to formula (11.28) should be plotted for each device (curves “1” and “2” at Fig. 11.11). Then crossing points of these curves with vertical line “5” corresponding to maximum total capacitance value (for this net-work for example 0.05 µF) should be found. Ordinate Ri of the highest located cross-ing point is equal to maximum insulation equivalent resistance, for which “holding” of the corresponding apparatus is possible. This value (here 19 kΩ) increased if nec-essary by a safety factor can serve as insulation monitor’s alarm setting. The above described approach is illustrated in Fig. 11.11 for two typical relays.

From this drawing permissible values of insulation equivalent resistance can be read out for any insulation capacitance smaller than its critical values 0.15 and 0.07 μF for relays “1” and “2” respectively. For example for Cimax = 0.05 μF minimum permissible insulation resistance is 19 kΩ, whereas for Cimax > 0.07 μF it is infinite. For Ci > 0.07 μF “holding” of the relay “2” with its coil terminal grounded will occur even if there is no insulation leakage at all, but the whole capacitance is lumped at the phase conductor.

Ri values for both relays calculated from formula (11.21) are equal to magnitudes read out as ordinate of crossing points of characteristics with the ordinate axis. These ordinates (in this case 9 and 15 kΩ) are minimum permissible values of insulation equivalent resistance valid for circuits with negligible ground capaci-tance. Thus the simplified model of control circuits described by this formula leads to substantial lowering of permissible insulation resistance.

References

1. Hofheinz W (2000) Protective measures with insulation monitoring. VDE Verlag, Berlin2. Olszowiec P (2002) Prufsysteme fur isolationen. Bulletin SEV/AES, 21 2002

Fig. 11.11 Graphical illustration of minimum permissible insulation equivalent resistance for an auxiliary circuit equipped with two relays with following data: 1—Udropout = 130 V, X = 6.5 kΩ, 2—Udropout = 160 V, X = 15 kΩ, 3, 4–asymptotes of curves 1, 2

159

Abstract In the chapter general description of insulation monitoring in “mixed” unearthed networks is given. Formulas for wire-to-ground voltages and ground fault currents at both sides of AC/DC system are derived. Few examples of voltage and leakage currents waveforms recorded in a “mixed” network are presented. Problems of misoperation of control devices are dealt with. Several examples of such fail-ures are analyzed and required insulation resistance levels are evaluated. There are described most commonly used methods of insulation equivalent resistance meas-urement. A novel method based on analysis of mean value of phase voltage is presented. Adaptation of a well-known “three voltmeters” procedure is explained.

12.1 Conductor-to-Ground Voltages

In “mixed” unearthed networks comprising alternating and direct current circuits, AC part of system is connected with DC part through rectifying valves. Commutation of the valves causes cyclic variation of all AC side conductors-to-ground voltages. A distinct feature of AC/DC IT systems is that voltages between all points of AC side and ground may have mean value different from zero. Circuit diagram of a simplest “mixed” network i.e. single phase AC/DC IT system is shown in Fig. 12.1.

In distinction from “pure” AC or DC IT networks, analytical determination of voltages and currents in “mixed” networks encounters some difficulties due to presence of rectifiers. Operation of this nonlinear coupling device changes peri-odically the network configuration as valves are commuted in consecutive parts of supply voltage cycle. However in respective semi-periods (for a single-phase sys-tem), assuming ideal valves with no resistance and conducting for the whole semi-period, a “mixed” network can be considered as linear one. In this case respective laws of linear circuit analysis can be applied. Based on this property time function of any conductor-to-ground voltage can be determined at both AC and DC side. Below there is presented calculation of voltage momentary values at AC supply

Chapter 12AC/DC IT Systems


160 12 AC/DC IT Systems

source terminals a and b for any values of insulation resistances R1, R2, R3, R4. For simplicity network-to-ground capacitances were neglected. Under these assump-tions voltage between any conductor of AC side and ground can be calculated in two consecutive semi-periods. Circuit equivalent diagrams of the “mixed” network valid in these two halves of cycle are shown in Fig. 12.2a, b.

Let the source voltage time function be

In the first considered semi-period (Fig. 12.2a) momentary value of for example U4 is given as

In the next semi-period (Fig. 12.2b) U4 voltage is

(12.1)e(t) =

√

2 · E · sin2π

Tt

(12.2)u′

4(t) =

R2·R4

R2+R4

R2·R4

R2 + R4+

R1·R3

R1 + R3

· e(t) for 0 < t < T/2

(12.3)u′′

4(t) =

R1·R4

R1 + R4

R1·R4

R1 + R4+

R2·R3

R2 + R3

· e(t)k dla T/2 < t < T

Fig. 12.1 Circuit diagram of a single phase AC/DC IT system

Fig. 12.2 a, b Circuit equivalent diagrams of a “mixed” single-phase network valid in two con-secutive semi-periods

161

The same expressions (but without change of sign) describe ground voltages of DC side poles—this is due to the fact that each of the poles is connected alter-nately to both terminals of the AC source. Mean (average) value of U4 voltage over the whole T period is

It should be noted that any point of AC side of a “mixed” network has got the same mean value of voltage. In particular this concerns a conductor whose ground voltage u3(t) is sum of u4(t) voltage and the source voltage

√

2 · E · sin(2π

T· t). An average

value of the source voltage e(t) is of course equal to zero. From formula (12.4) it follows that in case of insulation leakage symmetry at DC side (i.e. R1 = R2) mean value of the AC side conductor-to-ground voltage is zero. Formulas (12.2) and (12.3) show that in respective semi-periods ground voltage of each conductor of AC side is given by a sinusoidal function. Generally amplitudes of these functions are differ-ent. Waveform of conductor-to-ground voltage at AC side recorded in a single-phase “mixed” system is shown in Fig. 12.3a, whereas waveform of ground voltage of a selected pole at DC side is presented in Fig. 12.3b.

12.2 Earth Fault and Leakage Currents

Analytical method used for determination of ground voltages at AC and DC sides of “mixed” networks is useful also for calculation of earth fault currents at any point of the system. For this purpose Thevenin’s theorem can be applied if network

(12.4)

U4mean =1

T·

T/2

0

u′

4(t)dt +

T

T/2

u′′

4(t)dt

=

√

2

2 · π

· E ·

R2·R4

R2 + R4

R2·R4

R2 + R4+

R1·R3

R1 + R3

−

R1·R4

R1 + R4

R1·R4

R1 + R4+

R2·R3

R2 + R3

Fig. 12.3 Waveform of voltage at AC (a), DC (b) side of a “mixed” single-phase system

12.1 Conductor-to-Ground Voltages


ground capacitances were neglected. Its use is permissible in any semi-period of voltage variation because the network is linear under the above adopted assump-tions, though its configuration changes. Application of this principle for calcula-tion of earth fault current at AC side is explained in Fig. 12.4.

Momentary value of a conductor earth fault current if3(t) through fault resist-ance r is given by formula:

where u3(t) is momentary value of U3 ground voltage at terminal a, Requiv3—resistance seen from the terminals of the possible earth fault (in this case terminal a and ground).

Resistance Requiv seen from any point of the “mixed” network (any terminal of voltage source or any DC side pole) and ground is the same at each semi-period. It is equal to insulation-to-ground equivalent resistance Ri of the whole AC/DC IT system

In the same way steady-state earth fault current at DC side is calculated. Formula (12.5) should be applied twice, separately for two consecutive semi-periods. In Fig. 12.5a, b there are shown waveforms of earth fault current at points of ground voltage recording (see Fig. 12.3a, b). It is obvious that steady-state earth fault current waveform has got the same shape as waveforms of those voltages to ground. This is a direct conclusion from Thevenin’s theorem [formula (12.5)].

Formula (12.5) gives time function of steady-state leakage current through a fault resistance r. Total momentary leakage current i4(t) from for example conductor

(12.5)if 3(t) =u3(t)

Requiv3 + r

(12.6)Requiv = Ri =1

1

R1+

1

R2+

1

R3+

1

R4

Fig. 12.4 A ground fault through resistance r at AC side

163

b, comprising both AC and DC sides, can be calculated in respective semi-periods as follows

and

where u′

4(t) voltage is given by (12.2) and u′′

4(t) by (12.3).Knowledge of time functions of leakage currents i4(t) (or i3(t)) over the whole

cycle allows to determine its RMS value I4 (or I3). This parameter is defined by the following formula

12.3 Misoperation of Devices in “Mixed” Systems

Similarly to AC or DC IT systems, insulation deterioration may lead to higher leakage and earth fault currents magnitudes in “mixed” networks too. Therefore it is interesting and useful to evaluate maximum possible levels of these currents for a given insulation equivalent conductance value Gi.

(12.7)i′

4(t) =

u′

4(t)

R4

+u′

4(t)

R2

for 0 < t < T/2

(12.8)i′′

4(t) =

u′′

4(t)

R4

+u′′

4(t)

R1

for T/2 < t < T

(12.9)I4 =

1

T·

T/2

0

i′24(t)dt +

T

T/2

i′′24

(t)dt

Fig. 12.5 Waveforms of currents at AC (a) and DC (b) side of a “mixed” single phase system corresponding to Fig. 12.3a, b respectively

12.2 Earth Fault and Leakage Currents


If network-to-ground capacitances are neglected the highest possible leak-age currents appear in two cases: (a) Ga = Gb = Gi/2 and G1 = G2 = 0, (b) Ga = Gb = 0 and G1 = G2 = Gi/2. This maximum value is given by formula

Earth fault current reaches its greatest possible level for a given insulation equiva-lent conductance value Gi also in two cases: (a) Ga = Gi and Gb = G1 = G2 = 0 (dead earth fault of conductor “b”), (b) Ga = Gb = G1 = 0 and G2 = Gi (dead earth fault of the positive pole). This highest value is

Misoperation of devices may be a serious hazard in “mixed” networks too. Insulation deterioration and/or excessive magnitude of ground capacitance can cause malfunction of relays, contactors or other control devices. Below there are presented few examples of inadvertent pickup or “holding” of energized appara-tuses caused by a single insulation ground fault.

Misoperation of a control device installed at AC side may occur among others as result of grounding of its coil terminal. Possible paths of current flow through the coil are shown in Fig. 12.6a–c.

(12.10)Ileak max =E

4· Gi

(12.11)Ie−f max = E · Gi

Fig. 12.6 a, b, c Examples of misoperation of an AC device caused by its coil grounding

165

These drawings explain that following a ground fault, an AC device misopera-tion may occur due to insulation deterioration at any side of the “mixed” system or even due to high capacitance at AC side only. Control devices installed at DC side are also subject to misoperation risk. Few examples of their incorrect operation are shown in Fig. 12.7a–c. There are indicated possible paths of ground fault current flow through the coil of a DC device.

Based on examples presented above it is possible to determine the required level of the whole “mixed” network’s insulation equivalent resistance. With this minimum value of insulation resistance, possibility of devices misoperation is excluded even in case of a dead ground fault. The most stringent condition i.e. leading to the highest value of permissible insulation equivalent resistance of the whole system for AC devices is shown in Fig. 12.6a. In this case “holding” of the respective device with rated dropout current Idropout and coil reactance Xp is pos-sible—neglecting insulation ground capacitances—if

From this formula the highest value of permissible level of insulation equivalent resistance Ri is obtained as

(12.12)Idropout ≤

∣

∣

∣

∣

U4

Zi + j · Xp

∣

∣

∣

∣

≤

∣

∣

∣

∣

E

Ri + jXp

∣

∣

∣

∣

(12.13)Ripermissible =

√

E2

I2

dropout

− X2p

Fig. 12.7 a, b, c Examples of misoperation of DC device caused by its coil grounding

12.3 Misoperation of Devices in “Mixed” Systems


Similarly for DC devices with rated dropout current Idropout and coil resistance Rp the highest permissible level of this parameter is obtained from the following condition

and is equal to

The highest of Ri values given by formulas (12.13) and (12.15), determined for each device (both AC and DC) installed in the “mixed” network, may serve as a setting of its insulation monitor.

12.4 Insulation Resistance Measurement in AC/DC IT Systems

As described above, conductor-to-ground voltages at AC side may contain a DC component of substantial value (see formula 12.4). This fact introduces a limita-tion to the range of possible methods of insulation-to-ground resistance meas-urement. When applying a traditional method based on use of an auxiliary DC voltage source e.g. megohmmeter, the above mentioned DC component adds to or deducts from that auxiliary DC voltage introducing an error of measurement. That is why measurement procedures insensitive to this disturbing factor are applied in “mixed” networks comprising any number of phases. The most popular is pulse voltage method distinctive for its immunity to presence of both AC voltage and DC component. The other method is based on imposition of AC auxiliary volt-age on the monitored network. It should be pointed out that insulation monitors should measure such insulation parameter which is useful not only for assessment of its condition but also for analysis of earth fault phenomena. These requirements are fulfilled by insulation-to-ground equivalent resistance of both galvanically con-nected AC and DC sides given by formula (12.6).

12.4.1 Method of “Three Readings of a Voltmeter”

Just as in DC circuits, also in “mixed” networks it is possible to use simple meth-ods comprising measurements and calculation for insulation equivalent resistance determination. The most popular is the method of “three readings of a voltmeter”

(12.14)Idropout ≤

√

2 · E

Ri + Rp

(12.15)Ripermissible =

√

2 · E

Idropout

− Rp

167

described in Chap. 6. With help of a voltmeter with internal resistance RV mean values of both poles (+) U1 and (−) U2 and rectified output voltage U12 of DC side should be measured. The sought value of the “mixed” network insulation equivalent resistance Ri is given by the formula

identical to the formula applied for DC circuits. This approach can be explained with help of Thevenin’s theorem valid for measurement of momentary values of each pole-to-ground voltage at any time instant within each semi-period (in a single-phase system). Of course this theorem is correct also with respect to mean values calculated over one chosen semi-period. Thus mean value of u1 over this semi-period is equal to

where U1 no–load is the mean value (over this semi-period) of the positive pole-to-ground voltage without connected voltmeter. In order to derive formula (12.17) it is necessary to consider momentary values of u1 and u1no–load voltages in the given semi-period. These values are linked by the above given relationship. Then both sides of this equation should be integrated over the considered semi-period. Similarly the mean value of u2 over the same semi-period is

where U2 no–load is mean value of the negative pole-to-ground voltage without voltmeter. Taking into account the equation U1no–load + U2no–load = U12 (2nd Kirchhoff’s law), formula (12.16) is obtained by “adding” Eqs. (12.17 and 12.18). Of course formula (12.16) is valid also for AC/DC IT systems comprising any number of AC source phases, in particular for three-phase systems.

12.4.2 Utilization of Mean Value of Phase Voltage

Another method (proposed by author) takes advantage of a bridge diode rectifier which delivers a criterial quantity useful for insulation equivalent resistance deter-mination. For determination of this quantity, i.e. mean value of phase voltage at AC side of a AC/DC IT system, an equivalent circuit diagram shown in Fig. 12.8 (an example for three-phase network) is helpful.

Let network source voltages be ea(t) = Em · sin ωt, eb(t) = Em · sin[

ω(t −T3)

]

,

ec(t) = Em · sin

[

ω(t −2T3

)

]

and phase voltages ua(t) = ea(t) − u0(t), ub (t) =

eb (t) − u0 (t), uc(t) = ec(t) − u0(t) where u0(t) is a so called displacement voltage equal to zero sequence component of phase voltages taken with reverse sign. Within time interval T/12 < t < 3T/12 diodes D1 and D5 conduct

(12.16)Ri = RV ·U12 − U1 − U2

U1 + U2

(12.17)U1 = RV ·U1no−load

RV + Ri

(12.18)U2 = RV ·U2no−load

RV + Ri


http://dx.doi.org/10.1007/978-3-319-07010-0_6


Similarly within consecutive time intervals the following diodes conduct: 3T/12 < t < 5T/12-D1and D6

5T/12 < t < 7T/12-D2 and D6

7T/12 < t < 9T/12-D2 and D4

(12.19)

(Ga + G1) · (ea − u0) + (Ca + C1) ·d(e

a− u0)

dt+ (Gb + G2) · (eb − u0)

+ (Cb + C2) ·d(eb − u0)

dt+ Gc · (ec − u0) + Cc ·

d(ec − u0)

dt= 0

(12.20)

(Ga + G1) · (ea − u0) + (Ca + C1) ·d(e

a− u0)

dt+ Gb · (eb − u0)

+ Cb ·d(eb − u0)

dt+ (Gc + G2) · (ec − u0) + (Cc + C2) ·

d(ec − u0)

dt= 0

(12.21)

Ga · (ea − u0) + Ca ·d(e

a− u0)

dt+ (Gb + G1) · (eb − u0)

+ (Cb + C1) ·d(eb − u0)

dt+ (Gc + G2) · (ec − u0) + (Cc + C2) ·

d(ec − u0)

dt= 0

(12.22)

(Ga + G2) · (ea − u0) + (Ca + C2) ·d(e

a− u0)

dt+ (Gb + G1) · (eb − u0)

+ (Cb + C1) ·d(eb − u0)

dt+ Gc · (ec − u0) + Cc ·

d(ec − u0)

dt= 0

Fig. 12.8 An equivalent circuit diagram of a three-phase AC/DC IT network

169

9T/12 < t < 11T/12-D3 and D4

11T/12 < t < 13T/12-D3 and D5

By adding Eqs. (12.19–12.24) integrated each one over its specified limits and after transformation formula for u0 mean value is obtained

where Gi is insulation-to-ground equivalent conductance Gi = Ga + Gb + Gc + G1 + G2 of the whole “mixed” network. Mean values of u0 voltage and of each phase voltage are of course equal.

In three-phase AC/DC IT networks with rectifiers phase voltages mean value exhibits similar properties as in single-phase systems. It does not depend on net-work-to-ground capacitances at both sides of rectifier. It also appears only in case of asymmetry of insulation conductances G1, G2 of single poles of DC circuit. Therefore this fact can be used for selective detection of earth faults (or even insu-lation deterioration) in these “mixed” networks. It can be also used for periodical determination of insulation-to-ground equivalent resistance of the whole “mixed” network.

The latter procedure developed by the author [1] consists of two steps. AC side conductor-to-ground mean voltage is measured in two states: (1) U01–mean in nor-mal working condition (2) U02–mean with an additional resistor Radd = 1/Gadd con-nected between any conductor at AC side and ground. The sought parameter Gi can be calculated from formula

which follows directly from (12.25).If AC side-to-ground voltage has zero mean value (due to G1 = G2), then one

of G1 or G2 conductances should be changed by grounding artificially any selected pole through a test conductance Gt. Then both steps of the procedure described above are executed, after which the test conductance Gt should be removed. The sought parameter Gi is given as

(12.23)

(Ga + G2) · (ea − u0) + (Ca + C2) ·d(e

a− u0)

dt+ Gb · (eb − u0)

+ Cb ·d(eb − u0)

dt+ (Gc + G1) · (ec − u0) + (Cc + C1) ·

d(ec − u0)

dt= 0

(12.24)

Ga · (ea − u0) + Ca ·d(e

a− u0)

dt+ (Gb + G2) · (eb − u0)

+ (Cb + C2) ·d(eb − u0)

dt+ (Gc + G1) · (ec − u0) + (Cc + C1) ·

d(ec − u0)

dt= 0

(12.25)U0−mean = Em ·3√

3

2π

·G1 − G2

Gi

(12.26)Gi = Gadd ·U02−mean

U01−mean − U02−mean



12.4.3 Pulse Voltage Method

DC rectangular voltage with amplitude U0, changing cyclically its polarity, is imposed between any terminal of AC side of the “mixed” network and ground. This test current flow through leakage resistances in two consecutive semi-periods of its variation is shown in Fig. 12.9a–d.

With positive polarity of U0 voltage, test current flows through parallelly con-nected resistors R1, R3, R4 and a parallel branch consisting of series connected resistors R2 and R0. With negative polarity of U0 test current flows through par-allelly connected resistors R2, R3, R4 and a parallel branch consisting of series connected resistors R1 and R0. A precondition for this method is that the rectifier valves must be kept open over the whole semi-period which requires sufficiently high load current through resistor R0. In practice resistance R0 can be neglected as much smaller than resistances R1, R2. Therefore with sufficient accuracy it can be assumed that pulse voltage method provides measurement of insulation equivalent resistance of the whole “mixed” network.

12.4.4 Auxiliary AC Voltage Method

In “mixed” networks application of this well-known method is similar to AC and DC IT systems. In AC/DC IT systems sinusoidal test current flows along the same

(12.27)Gi = Gadd ·U02−mean

U01−mean − U02−mean

− Gt

Fig. 12.9 Test current flow through leakage resistances for: a positive U0 and positive e(t), b positive U0 and negative e(t), c negative U0 and positive e(t), d negative U0 and negative e(t)

171

paths as in case of pulse voltage method (see Fig. 12.9a–d) including additionally insulation-to-ground capacitances. Therefore its frequency must be chosen as low as possible to minimize influence of ground capacitances. Under this condi-tion this method can with sufficient accuracy provide measurement of the whole “mixed” network’s insulation equivalent resistance.

12.5 Insulation Resistance Measurement in IT Systems with Frequency Converters

Another type of AC/DC IT systems are networks feeding frequency converters. Figure 12.10 presents a general example of such three-phase “mixed” system with a DC test current injection for insulation monitoring [2].

There are six stages of inverter operation in consecutive intervals of its output phase voltage, for example Ua2. In each of them different insulation conductances are connected to the poles of rectifier output. These combinations are given in the table below.

Stage number Phase angle of Ua2 Insulation conductances connected to pole (+)

Insulation conductances connected to pole (−)

1 0 − π/3 G1 + Ga2 + Gc2 G2 + Gb2

2 π/3 − 2π/3 G1 + Ga2 G2 + Gb2 + Gc2

3 2π/3 − π G1 + Ga2 + Gb2 G2 + Gc2

4 π − 4π/3 G1 + Gb2 G2 + Ga2 + Gc2

5 4π/3 − 5π/3 G1 + Gb2 + Gc2 G2 + Ga2

6 5π/3 − 2π G1 + Gc2 G2 + Ga2 + Gb2

It follows from the table that insulation equivalent resistance seen from DC side poles is subject to cyclical changes. If inverter’s thyristors are treated as ideal switches S1-S6, the whole system can be substituted by a circuit shown in Fig. 12.11 where each three-thyristor group (S1-S3 and S4-S6) is represented as DC voltage source of mean value E equal to half of rectifier output voltage E ≈ 1.17 · Ea · cos α, where α—firing angle of thyristors. An equivalent circuit of the network is shown in Fig. 12.11.

Based on this circuit mean value of test current I0mean driven by insulation monitor’s voltage source E0 can be calculated for each of six stages. Its mean value over the whole period (comprising six stages with variable configuration) is given by formula

where R0 = Rs +Rs1

3 is the test source’s equivalent internal resistance and

Re =1

(Ga1+Gb1+Gc1)+(G1+G2)+(Ga2+Gb2+Gc2) is the whole network-to-ground

(12.28)I0 =E0 + E · Re · (G1 − G2)

R0 + Re



insulation substitute resistance. The latter sought parameter can be determined from formula (12.28) only if DC pole-to-ground insulation conductances G1 and G2 are equal. Only in this case no DC bias voltage is imposed on insulation monitor.

References

1. Olszowiec P (2013) Application of network voltages to insulation monitoring in unearthed AC circuits with rectifiers. Pomiary Automatyka Kontrola, Gliwice

2. Szczucki V et al. (1997) Problems of insulation monitoring in a network with frequency con-verters. XI international conference “Electrical Safety”, Wrocław

Fig. 12.11 An equivalent circuit of an IT three-phase network with a frequency converter from Fig. 12.10

Fig. 12.10 IT three-phase network feeding a frequency converter

173

Abstract The chapter presents general information on requirements, the modern systems of insulation fault location in AC, DC and AC/DC networks must meet. Procedures of ground fault location in these networks with help of stationary sys-tems and portable locators are described. Test current measurement techniques in fault locating systems are indicated. Traditional earth fault location systems based on AC test signal imposition are presented. Measurement techniques that are com-monly applied for ground fault location in live AC and DC networks are described. These technologies are presented at the example of modern insulation fault loca-tion systems widely used all over the world.

13.1 General

One particularly valuable feature of unearthed electrical networks is possibility to detect and eliminate earth faults under their operation. In distinction from TT and TN systems a single earth fault (usually) does not lead to operation of pro-tection of the faulted part of the network. Even in case of double earth fault at points belonging to different poles or phases of IT system, one of them may not be switched off and the whole network, except of the eliminated circuit, will remain in operation. Thus following a single earth fault, an AC or DC IT system (as well as a “mixed” network) does not have to be deenergized. However existing regula-tions e.g. IEC 60364-4-41 require a possibly fast correction of the fault with main-taining power supply of loads. Modern earth fault locating systems (Fig. 13.1a, b) allow to indicate lines not only with insulation breakdowns (dead earth faults) but also with insulation deterioration. Similarly to insulation monitors operation, locating of insulation faults should not pose any hazards to safe operation (or read-iness to operation) of devices installed in the monitored network. Risk of inad-vertent device energization or “holding” is avoided usually by limiting maximum test current to level below the smallest dropout current of any of the apparatuses.

Chapter 13Earth Fault Location in IT AC/DC Systems


174 13 Earth Fault Location in IT AC/DC Systems

Fig. 13.1 Procedure of ground fault location in DC IT network with a stationary system, b portable locator

175

Connection of fault locators should not decrease insulation resistance to ground either. In some countries it is recommended that these systems be put into opera-tion only after insulation resistance decline below the set level.

When locating faults it is not allowed to connect the measurement sensor directly i.e. galvanically to the network points under voltage. It is recommended to introduce automatization of fault location in the main supply circuits of the network to speed up the process. Fault location in the remaining lines should be executed with a portable locating device. In both types of location no breaks or interruptions to power supply are permitted.

13.2 Test Current Measurement in Fault Locating Systems

Insulation monitoring devices based on auxiliary AC test voltage source utilize elec-tromagnetic current transformers for measurement of imposed test currents. When test signals contain low frequency or distorted components, these transformers operation is featured by impermissibly high transformation errors. For about two decades Hall current sensors have been widely applied in this field. Hall effect consists in voltage generation between surfaces of a conductor carrying polarizing current Ip, placed in a magnetic field. Hall sensors with current compensation shown in Fig. 13.2 offer higher accuracy than conventional CT’s, especially for low frequencies.

The compensating winding, fed with current proportional to the measured quantity, produces in the magnetic core the compensating flux opposite to flux generated by the measured current I1. In this way Hall effect sensor operates here

Fig. 13.2 Simplified system of a Hall sensor with current compensation

13.1 General


as a sensor of zero magnetic flux in the core gap. With complete compensation of measured current I1 by compensating current I2, output voltage Uout across resistor R0 is proportional to I1.

Current transformers based on Hall effect are suitable for measurement of any kind of current including alternating, direct or even heavily distorted one. These devices are used both in stationary applications and in portable clamp-on meters for measurement of test or leakage current. The lowest threshold of measurement may reach tens of microampers.

13.3 Traditional Earth Fault Location Systems

At the early stages of electrical engineering development only portable earth fault locators were used. There were no stationary automatic location systems put into operation by insulation monitors. In older location systems designed for DC IT net-works, principle of AC test signal superimposition was applied. An auxiliary AC volt-age source forced sinusoidal test current flow through not only insulation leakages but also through ground capacitances. Except of resistive currents the locating device measured also capacitive currents and any spurious signals which disturbed correct measurement process. To improve selectivity of operation test signal was modified—its frequency was set different from network frequency magnitude and therefore band-pass filters were used. Another solution was application of sinusoidal intermit-tent current signal which was easy to detect. This idea is shown in Fig. 13.3.

Fig. 13.3 Concept of imposition of intermittent sinusoidal current signal on the monitored network

177

Test pulses flow through the network wires to the place of insulation deteriora-tion and then return through ground to signal generator PG. The user locates test current flow path with help of clamp-on meter. It is equipped with an ammeter tuned to the generator signal frequency. Thanks to introduction of breaks in gen-erator operation it is easy to distinguish indication of this sensor caused by capaci-tive currents of network frequency or possible disturbing currents from actual earth fault signals. Generator produces a train of intermittent sinusoidal pulses which are superimposed on the monitored network. User can select time duration of the pulses and breaks between them. Test current is limited by capacitor Cbl which also blocks DC current flow from the monitored network to the test device. The main drawback of the method is its unnecessary reaction to the test current flowing through network-to-ground capacitances. This limits application of the locator to insulation failures with relatively small fault resistance r.

13.4 Modern Insulation Fault Location Systems

The following measurement techniques are the most commonly applied meth-ods of ground fault location in live AC and DC networks. These technologies are described below at the example of insulation fault location systems widely used all over the world.

13.4.1 Pulse Voltage Test Signal: EDS470 (Bender)

Insulation fault locating system of the EDS470 series [1] is designed to continu-ously monitor AC or DC IT networks insulation and to automatically locate insu-lation ground faults under normal operation. Basic elements of the system are the following devices: isometer IRDH575, evaluator EDS470-12 and measuring cur-rent transformers. An IRDH575 isometer is an insulation monitoring relay similar to IRDH375B (see Chap. 4) with additional functions of controlling fault location process. This isometer drives test current which is limited to safe level. It flows along wires to places of insulation-to-ground faults and then from ground via PE conductor back to the isometer. Test current pulses are detected by measur-ing current transformers installed at selected outgoing lines. All current-carrying conductors (except of PE conductor) of each line are passed through the CT win-dow, none of them can be shielded. Current transformers convert residual currents up to 100 A into signals transmitted to the evaluator. These signals are evaluated by EDS which determines faulted lines. Up to 12 measuring current transformers can be connected to one EDS. A total of 90 EDS evaluators can be linked via one RS-485 interface. Therefore up to 1080 circuits can be monitored. The maximum scanning time does not exceed 10 s. A ground fault alarm threshold depends on

13.3 Traditional Earth Fault Location Systems

http://dx.doi.org/10.1007/978-3-319-07010-0_4


the evaluator sensitivity and is equal to 5 mA for EDS470 and 0.5 mA for EDS473 designed for control circuits monitoring.

The manufacturer offers also a portable insulation fault locating system EDS3065 series. It consists of EDS165 evaluator and clamp-on meter for residual current measurement. This system can be used in AC or DC IT networks with or without installed EDS stationary system. When used with stationary system, test signal is generated by IRDH575 isometer. Under independent operation generat-ing function is fulfilled by test current injector PGH185 which executes periodical grounding through a test resistor. Residual current flow is measured by clamps and displayed by the evaluator.

13.4.2 Sinusoidal Test Current: Vigilohm (Schneider)

Insulation fault location system Vigilohm (Schneider) [2] is offered in two variants.Version for automatic fault location comprises stationary test signal genera-

tor integrated in XM200 isometer (see Chap. 4), fault detectors XD312 type con-nected to current transformers and portable XRM fault locating receiver with current clamps. System for manual localizing consists of portable XRG genera-tor and the above mentioned receiver with current probes. Ground fault detector XD312 type cooperates with up to 12 toroidal residual current transformers. The detector measures sinusoidal test current 2.5 Hz of at least 2.5 mA. Each of con-nected CT’s is scanned for 20 s. Portable XRM receiver supports process of auto-matic fault location in outgoing lines without stationary CT’s installed. In manual localizing this receiver with clamps is the only tool for fault detection. For easy evaluation of line insulation condition it displays numbers from 0 to 19 corre-sponding to insulation level.

13.4.3 Saw-Like Test Voltage Pulses: IPI-1M (Elterm)

Concept of saw-like test signal superimposition is implemented in IPI-1M type device (see Sect. 8.4) manufactured by OAO “Elterm” (Russia) [3]. This system is designed for application in DC auxiliary circuits. It comprises a stationary gen-erator of test voltage pulses and portable current clamps. Range of insulation dete-rioration detection is 0–40 kohms with practically unlimited ground capacitance. Clamp-on sensor is equipped with visual indication of insulation level. Amplitude of voltage signal imposed on the monitored network is 40 V and its frequency is 2 Hz. Linearity of voltage variation is kept with accuracy ± 5%. Output resistance of voltage pulses generator is 17 kΩ. Clamp-on sensor measures residual current’s derivative. Due to this property it evaluates only test current flowing through insu-lation leakage resistances to ground.

http://dx.doi.org/10.1007/978-3-319-07010-0_4

http://dx.doi.org/10.1007/978-3-319-07010-0_8

179

13.4.4 Periodical Current Pulses: AT-3000 (Amprobe)

The AT-2000 system (newer version AT-3000) manufactured by Amprobe (USA) [4] is commonly applied for wire tracing and insulation fault location in AC and DC electrical networks up to 300 V (or 600 V). The AT-2001 system used for ground fault localizing consists of the load signal generator S2300 (or S2600) and receiver R2000. When connected to the network between any of its energized phases (or poles) and ground the generator produces periodical train of current pulses. These pulses flow is traced with portable sensor- receiver R2000. Specific form and limited parameters of the pulses eliminate risk of inadvertent apparatuses operation. Current pulses are generated as result of cyclic connection and discon-nection of internal test resistor between the grounded wire and earth. This wire-to-ground voltage must be at least 9 V, otherwise an auxiliary voltage source must be connected in series with the generator. Procedure of the AT system application for location of ground faults is shown in Fig. 13.4.

The receiver R2000 is equipped with detectors tuned to frequency 32.768 kHz of the pulses. Every 0.5 s the generator produces 2 current pulses with peak value 35 or 70 mA and duration of 0.0625 s each. Sensitivity of the receiver can be adjusted in a large range. AT system is suitable for ground fault location in AC

Fig. 13.4 Application of AT system for ground fault location

13.4 Modern Insulation Fault Location Systems


or DC IT networks only with low insulation-to-ground capacitance. The receiver indication is practically the same when used for current pulses tracing in healthy lines with high capacitance and in grounded line. This is illustrated in Fig. 13.5.

References

1. http://www.bender.org2. http://www.schneider-electric.com3. http://www.elterm-pskov.ru/4. http://www.amprobe.com

Fig. 13.5 Waveform of test signal generated by S-2300. a in a wire grounded through resistor 1 kΩ, b in a healthy conductor with ground capacitance 20 µF


http://www.schneider-electric.com

http://www.elterm-pskov.ru/

http://www.amprobe.com

Documents

Insulation Measurement and Supervision in Live AC and DC Unearthed Systems