Lightning Interaction with Power Systems: Applications (Volume 2) (Energy Engineering) 1839530928, 9781839530920

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Table of contents :
Contents
About the editor
Preface
Acknowledgments
About the authors
1. Application of the Monte Carlo Method to Lightning Protection and Insulation Coordination Practices-Alberto Borghetti, Fabio Napolitano, Carlo Alberto Nucci and Fabio Tossani
1.1 Introduction
1.2 Description of the MC-based Procedure
1.3 Identification of the Lightning Current Functions
1.4 Stratified Sampling Technique
1.5 Application Results for a MV Overhead Line in Open Terrain
1.5.1 Influence of the Return Stroke Current Waveform
1.5.2 Application of the Recursive Stratified Sampling Technique
1.6 Conclusions
References
2. Lightning interaction with power substations-Shigemitsu Okabe
2.1 Fundamental Concepts
2.1.1 Definition and Procedure of Insulation Coordination
2.1.2 Lightning Overvoltage in Insulation Coordination
2.1.3 Lightning Surge Analysis
2.2 Simplified Statistical Approach of Lightning Surge Analysis
2.2.1 Basics
2.2.2 Calculation of the Limit Distance
2.2.3 Estimation of the Lightning Overvoltage Amplitude
2.2.4 Simplified Method
2.2.5 Assumed Maximum Value of the Representative Lightning Overvoltage
2.3 Detailed Deterministic Approach of Lightning Surge Analysis
2.3.1 Basic Analysis Conditions
2.3.2 Analysis Conditions and Models
2.4 Failure Rate Evaluation Considering Front Time of Lightning Current
2.4.1 Crest Value and Wavefront Time of Lightning Stroke Current
2.4.2 Wavefront Time of Lightning Stroke Current and Amplitude of Lightning Surge
2.4.3 Lightning Failure Rates in Substations in Consideration of Lightning Current Waveforms
References
3. Lightning Interaction with Power Transmission Lines-William A. Chisholm
3.1 Lightning Attachment to Overhead Transmission Lines
3.1.1 Overhead Line Attachment Rates using Ground Flash Density and Typical Dimensions
3.1.2 Local Voltage Rise from Lightning Attachment to Transmission Line Phase Conductor
3.1.3 Role of Span Length and Nearby Arresters on Peak Insulator Voltage
3.1.4 Shielding of Transmission Line Phase Conductors using Overhead Groundwires
3.2 Lightning Impulse Flashover of Power Transmission Line Insulation
3.2.1 Lightning Impulse Voltage Test Waveshapes
3.2.2 Single Gap Full-wave Flashover Strength for Dry Arc Distance of 0.5 to 10 m
3.2.3 Strength of Multiple Air Gaps in Parallel under Shielding Failure Conditions
3.2.4 Strength of Multiple Air Gaps in Series
3.2.5 Evolution of Surge Protective Devices for Insulation Coordination
3.2.6 Design and Performance of Unshielded Power Transmission Lines
3.3 Bonding, Earthing and Equalisation of Potential differences on Transmission Lines
3.3.1 Analysis of Transient Voltage Rise on Connections from OHGW to Earthing Electrodes
3.3.2 Analysis of Transient Voltage Rise on Earthing Electrodes
3.3.3 Analysis of Transient Voltage Reduction from Adjacent Phases
3.3.4 Analysis of Transient Voltage Rise on Insulated Phases from Surge Impedance Coupling
3.3.5 The Backflashover from OHGW to Phase
3.3.6 Design and Performance of Shielded Power Transmission Lines
3.3.7 Methods for Increasing the Backflashover Critical Current
3.3.8 Methods for Improving the Equalisation of Potential Differences
3.4 Considerations in the Design Trade-off: Arresters versus Earthing
References
4. Lightning Interaction with Medium-Voltage Overhead Power Distribution Systems-Alexandre Piantini, Alberto Borghetti and Carlo Alberto Nucci
4.1 Flash Collection Rate
4.2 Effects of Various Parameters on Lightning Overvoltages
4.2.1 Direct Strokes
4.2.2 Indirect Strokes
4.3 Lightning Protection of MV Systems
4.3.1 Increase of the Line Withstand Capability
4.3.2 Use of Shield Wires
4.3.3 Application of Surge Arresters
4.4 Lightning Performance of Overhead Distribution Lines
4.4.1 Influence of the Environment around the Line
4.4.2 Lines Located above open Ground
4.4.3 Lines Surrounded by Buildings
4.4.4 Hybrid Configuration (MV and HV Lines Mounted on the Same Poles)
4.5 Concluding Remarks
References
5. Lightning Interaction with Low-voltage Overhead Power Distribution Networks-Alexandre Piantini
5.1 Typical Configurations of LV Networks
5.2 Lightning Surges on LV Power Systems
5.2.1 Cloud Discharges
5.2.2 Direct Strikes
5.2.3 Indirect Strikes
5.2.4 Transference from the MV Line
5.3 Lightning Protection of LV Networks
5.3.1 Distribution Transformers
5.3.2 LV Power Installations
5.4 Concluding Remarks
References
6. Lightning Protection of Structures and Electrical Systems Inside of Buildings-Fridolin Heidler
6.1 Lightning Currents
6.1.1 Current Components
6.1.2 Lightning Protection Level
6.1.3 Simulation of the Lightning Currents for Analytical Purpose
6.2 Lightning Protection of Buildings
6.2.1 Lightning Protection Zone
6.2.2 Lightning Protection System
6.2.3 Surge Protection Measure (SPM) System
6.3 Volume Protected against Direct Lightning Strike
6.3.1 Striking Distance
6.3.2 Rolling Sphere Method
6.3.3 Simplifications of the Rolling Sphere Method
6.4 Air-termination and Down-conductor System
6.4.1 Air-termination System
6.4.2 Down-conductor System
6.4.3 Materials and Dimensions
6.5 Earth-termination System
6.5.1 Earth-termination System for the Lightning Protection System (LPS)
6.5.2 Improved Earth-termination System for the Surge Protection Measure (SPM) System
6.6 Lightning Equipotential Bonding
6.6.1 Lightning Equipotential Bonding Required for LPS
6.6.2 Lightning Equipotential Bonding According to thE Surge Protection Measure (SPM) System
6.7 Separation Distance
6.7.1 Material Coefficient km
6.7.2 Current Steepness Coefficient ki
6.7.3 Configuration Coefficient kc
6.8 Currents and Voltages on Lines
6.8.1 Protection of Connection Lines at the Entrance into LPZ
6.8.2 Shielded Connection Lines
6.8.3 Lines in Reinforced Concrete Cable Duct
6.8.4 Current Share on Lines in Case of Direct Lightning
6.8.5 Reduction of the Induced Over-voltage on Internal Lines by Line Routing
6.9 Grid-like Spatial Shield
6.9.1 Magnetic Field inside LPZ 1 in the Case of a Direct Lightning Strike
6.9.2 Magnetic Field inside LPZ 1 in the Case of a Nearby Lightning Strike
6.9.3 Magnetic Field Inside LPZ 2 and Higher
References
7. Lightning Protection of Smart Grids-William A. Chisholm and Kenneth L. Cummins
7.1 Introduction: History of Power System Technologies
7.1.1 Electric Power Systems and Mathematics
7.1.2 Electric Power Systems and Communication
7.1.3 Electric power systems and Lightning Measurements
7.2 Smart Grid Functions and Technologies
7.2.1 Wide-area Monitoring and Visualization
7.2.2 Flow Control
7.2.3 Enhanced Fault Identification
7.2.4 Adaptive Protection and Automated Feeder Switching
7.2.5 Automated Islanding and Reconnection
7.2.6 Diagnosis and Notification of Equipment Condition
7.2.7 Dynamic Thermal Rating Capabilities
7.3 Lightning and Digital Recording Technology
7.3.1 Digital Recording Systems for Lightning Overvoltages
7.3.2 Voltage Sensors for Lightning Overvoltages
7.3.3 Combined Current and Voltage Sensor for Lightning Measurements
7.3.4 Non-contact Sensors for Impulse Voltage and Current
7.3.5 Commercial Current Sensors for Equipment Monitoring
7.4 Lightning Protection of Smart Grid Sensors
7.4.1 Reliability Requirements for Smart Grid sensors and Systems
7.4.2 Candidate Wiring Configurations for Smart Grid Sensors
7.4.3 Industry Standards for Lightning Protection of Smart Grid sensors
7.4.4 Industry Standards for Lightning Protection of Smart Grid Communication Systems
7.4.5 Case Study: EMC and Residential Smart Grid Interoperability
7.5 Conclusions
References
8. Lightning Protection of Wind Power Systems-Masaru Ishii and Joan Montanya
8.1 Wind Turbine Components and Overview of the Lightning Protection System
8.2 Lightning Phenomenology and Wind Turbines
8.2.1 Interaction with Downward Lightning
8.2.2 Upward Lightning
8.3 Lightning Damage to Wind Turbines due to Direct Impacts
8.3.1 Lightning Damage Mechanisms
8.3.2 Overview of Types of Lightning Damage to Wind Turbines
8.3.3 Statistics on Lightning Damage to Wind Turbines
8.4 Lightning Protection of Wind Turbine Components
8.4.1 Blades
8.4.2 Consideration of CFRP in Blades and Other Components
8.4.3 Other Components: Hub, Bearings and Nacelle
8.4.4 Overvoltages caused by Direct Lightning
8.5 Overvoltages in Wind Farms
8.5.1 Structure of Wind Farms
8.5.2 Sources of Lightning Overvoltages in Wind Farms: The Back-flow Surge
References
9. Renewable energy systems—photovoltaic systems-Kazuo Yamamoto and Yaru Mendez
9.1 Solar Energy: Solar Radiation, Parameters, Hourly and Daily Parameters
9.1.1 Daily Parameters
9.1.2 Second, Minute or Hourly based Parameters
9.1.3 Extraterrestrial and Terrestrial Solar Radiation
9.2 Photovoltaics: PV Cells, PV Modules, Partial Shading and its Effects
9.3 PV Systems: Off-grid and Grid-connected, Considerations of the Grid Connection
9.4 Earthing (Grounding) of PV-systems
9.4.1 The Importance of Earthing Characteristics
9.4.2 The Earthing Characteristics of Photovoltaic Systems
9.4.3 The Earthing Characteristics for Optimal Selection of SPDs
9.5 Internal and Overvoltage Lightning Protection
9.5.1 Protection at the PV Generator’s Side or DC Side
9.5.2 Protection at the AC Side
9.6 External Lightning Protection
9.6.1 Internal Lightning Protection
9.7 Mounting (Racking) Systems as Air-termination Systems
9.8 External Dedicated Mounting Systems (Non-isolated, Isolated)
9.9 Concluding Remarks
References
10. Measurement of Lightning Currents and Voltages-Ruy Alberto Correa Altafim, Wenxia Sima and Qing Yang
10.1 Historical Introduction
10.2 Lightning Current Measurements
10.2.1 Lightning Current Measurement Methodology on Transmission Lines
10.2.2 Lightning Current Measurement Methodology on High Towers
10.3 Measurement Method of Lightning Voltage
10.3.1 Voltage Divider
10.3.2 Capacitive Sensor Connected to Bushings
10.3.3 Noncontact Capacitive Voltage Divider
10.3.4 Integrated Optical Waveguide Voltage (Electric Field) Sensor
10.3.5 Crystal-based Batteryless and Contactless Optical Transient Overvoltage Sensor
10.3.6 Optical Voltage (Electric Field) Sensor based on Converse Piezoelectric Effect
10.4 Application of Various Lightning Overvoltage Sensors in Power Systems
References
11. Application of the FDTD Method to Lightning Studies-Yoshihiro Baba and Vladimir A. Rakov
11.1 Introduction
11.2 FDTD Method
11.2.1 Fundamentals
11.2.2 Advantages and Disadvantages
11.3 Representations of Lightning Source
11.3.1 Lightning Return-stroke Channel
11.3.2 Excitation Methods
11.4 Applications
11.4.1 Surges on grounding electrodes
11.4.2 Lightning Surges on Overhead Power Transmission Lines and Towers
11.4.3 Lightning Surges on Overhead Power Distribution and Telecommunication Lines
11.4.4 Lightning Electromagnetic Environment and Surges in Power Substation
11.4.5 Lightning Surges on Underground Distribution and Telecommunication Lines
11.4.6 Lightning Surges in Wind-turbine-generator Towers
11.4.7 Lightning Surges in Photovoltaic Arrays
11.4.8 Lightning Surges and Electromagnetic Environment in Buildings
11.4.9 Lightning Electromagnetic Fields at Close and Far Distances
11.4.10 Other Applications
11.5 Summary
References
12. Software Tools for the Lightning Performance Assessment-Alberto Borghetti, William A. Chisholm, Fabio Napolitano, Carlo Alberto Nucci, Farhad Rachidi and Fabio Tossani
12.1 Introduction
12.2 FLASH Program
12.2.1 Simplified Modelling of Shielding and Backflashover Calculations
12.2.2 Adoption of ‘Red book’ Method by IEEE, 1982–85
12.2.3 Adjustments of IEEE FLASH Program, 1985–93
12.2.4 Standardizing the IEEE FLASH Program, 1993–97
12.2.5 Maintaining the IEEE FLASH Program, 1997–2007
12.2.6 Developing the IEEE FLASH V2.0 program, 2007–19
12.3 Lightning-induced Overvoltages–electromagnetic Transients Program
12.3.1 Interfacing LIOV with EMTP
12.3.2 LIOV–EMTP Input Parameters
12.3.3 Application Examples
12.4 Application to a Real Distribution Network
References
Index
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IET ENERGY ENGINEERING 172

Lightning Interaction with Power Systems

Other volumes in this series: Volume 1 Volume 4 Volume 7 Volume 8 Volume 10 Volume 11 Volume 13 Volume 14 Volume 15 Volume 16 Volume 18 Volume 19 Volume 21 Volume 22 Volume 24 Volume 25 Volume 26 Volume 27 Volume 29 Volume 30 Volume 31 Volume 32 Volume 33 Volume 36 Volume 37 Volume 38 Volume 39 Volume 40 Volume 41 Volume 43 Volume 44 Volume 45 Volume 46 Volume 47 Volume 48 Volume 49 Volume 50 Volume 51 Volume 52 Volume 53 Volume 55 Volume 56 Volume 57 Volume 58 Volume 59

Power Circuit Breaker Theory and Design C.H. Flurscheim (Editor) Industrial Microwave Heating A.C. Metaxas and R.J. Meredith Insulators for High Voltages J.S.T. Looms Variable Frequency AC Motor Drive Systems D. Finney SF6 Switchgear H.M. Ryan and G.R. Jones Conduction and Induction Heating E.J. Davies Statistical Techniques for High Voltage Engineering W. Hauschild and W. Mosch Uninterruptible Power Supplies J. Platts and J.D. St Aubyn (Editors) Digital Protection for Power Systems A.T. Johns and S.K. Salman Electricity Economics and Planning T.W. Berrie Vacuum Switchgear A. Greenwood Electrical Safety: A guide to causes and prevention of hazards J. Maxwell Adams Electricity Distribution Network Design, 2nd Edition E. Lakervi and E.J. Holmes Artificial Intelligence Techniques in Power Systems K. Warwick, A.O. Ekwue and R. Aggarwal (Editors) Power System Commissioning and Maintenance Practice K. Harker Engineers’ Handbook of Industrial Microwave Heating R.J. Meredith Small Electric Motors H. Moczala et al. AC–DC Power System Analysis J. Arrillaga and B.C. Smith High Voltage Direct Current Transmission, 2nd Edition J. Arrillaga Flexible AC Transmission Systems (FACTS) Y.-H. Song (Editor) Embedded generation N. Jenkins et al. High Voltage Engineering and Testing, 2nd Edition H.M. Ryan (Editor) Overvoltage Protection of Low-Voltage Systems, Revised Edition P. Hasse Voltage Quality in Electrical Power Systems J. Schlabbach et al. Electrical Steels for Rotating Machines P. Beckley The Electric Car: Development and future of battery, hybrid and fuel-cell cars M. Westbrook Power Systems Electromagnetic Transients Simulation J. Arrillaga and N. Watson Advances in High Voltage Engineering M. Haddad and D. Warne Electrical Operation of Electrostatic Precipitators K. Parker Thermal Power Plant Simulation and Control D. Flynn Economic Evaluation of Projects in the Electricity Supply Industry H. Khatib Propulsion Systems for Hybrid Vehicles J. Miller Distribution Switchgear S. Stewart Protection of Electricity Distribution Networks, 2nd Edition J. Gers and E. Holmes Wood Pole Overhead Lines B. Wareing Electric Fuses, 3rd Edition A. Wright and G. Newbery Wind Power Integration: Connection and system operational aspects B. Fox et al. Short Circuit Currents J. Schlabbach Nuclear Power J. Wood Condition Assessment of High Voltage Insulation in Power System Equipment R.E. James and Q. Su Local Energy: Distributed generation of heat and power J. Wood Condition Monitoring of Rotating Electrical Machines P. Tavner, L. Ran, J. Penman and H. Sedding The Control Techniques Drives and Controls Handbook, 2nd Edition B. Drury Lightning Protection V. Cooray (Editor) Ultracapacitor Applications J.M. Miller

Volume 62 Volume 63 Volume 65 Volume 66 Volume 67 Volume 68 Volume 69 Volume 70 Volume 72 Volume 73 Volume 74 Volume 75 Volume 76 Volume 78 Volume 79 Volume 81 Volume 82 Volume 86 Volume 87 Volume 88 Volume 89 Volume 90 Volume 91 Volume 92 Volume 93 Volume 94 Volume 95 Volume 96 Volume 97 Volume 98 Volume 100 Volume 101 Volume 104 Volume 106 Volume 107

Lightning Electromagnetics V. Cooray Energy Storage for Power Systems, 2nd Edition A. Ter-Gazarian Protection of Electricity Distribution Networks, 3rd Edition J. Gers High Voltage Engineering Testing, 3rd Edition H. Ryan (Editor) Multicore Simulation of Power System Transients F.M. Uriate Distribution System Analysis and Automation J. Gers The Lightening Flash, 2nd Edition V. Cooray (Editor) Economic Evaluation of Projects in the Electricity Supply Industry, 3rd Edition H. Khatib Control Circuits in Power Electronics: Practical issues in design and implementation M. Castilla (Editor) Wide Area Monitoring, Protection and Control Systems: The enabler for smarter grids A. Vaccaro and A. Zobaa (Editors) Power Electronic Converters and Systems: Frontiers and applications A.M. Trzynadlowski (Editor) Power Distribution Automation B. Das (Editor) Power System Stability: Modelling, analysis and control B. Om P. Malik Numerical Analysis of Power System Transients and Dynamics A. Ametani (Editor) Vehicle-to-Grid: Linking electric vehicles to the smart grid J. Lu and J. Hossain (Editors) Cyber-Physical-Social Systems and Constructs in Electric Power Engineering S. Suryanarayanan, R. Roche and T.M. Hansen (Editors) Periodic Control of Power Electronic Converters F. Blaabjerg, K.Zhou, D. Wang and Y. Yang Advances in Power System Modelling, Control and Stability Analysis F. Milano (Editor) Cogeneration: Technologies, optimisation and implementation C.A. Frangopoulos (Editor) Smarter Energy: From smart metering to the smart grid H. Sun, N. Hatziargyriou, H.V. Poor, L. Carpanini and M.A. Sa´nchez Fornie´ (Editors) Hydrogen Production, Separation and Purification for Energy A. Basile, F. Dalena, J. Tong and T.N.Vezirog˘lu (Editors) Clean Energy Microgrids S. Obara and J. Morel (Editors) Fuzzy Logic Control in Energy Systems with Design Applications in MATLAB‡/Simulink‡ ˙I.H. Altas¸ Power Quality in Future Electrical Power Systems A.F. Zobaa and S.H.E.A. Aleem (Editors) Cogeneration and District Energy Systems: Modelling, analysis and optimization M.A. Rosen and S. Koohi-Fayegh Introduction to the Smart Grid: Concepts, technologies and evolution S.K. Salman Communication, Control and Security Challenges for the Smart Grid S.M. Muyeen and S. Rahman (Editors) Industrial Power Systems with Distributed and Embedded Generation R Belu Synchronized Phasor Measurements for Smart Grids M.J.B. Reddy and D.K. Mohanta (Editors) Large Scale Grid Integration of Renewable Energy Sources A. MorenoMunoz (Editor) Modeling and Dynamic Behaviour of Hydropower Plants N. Kishor and J. Fraile-Ardanuy (Editors) Methane and Hydrogen for Energy Storage R. Carriveau and D.S.-K. Ting Power Transformer Condition Monitoring and Diagnosis A. Abu-Siada (Editor) Surface Passivation of Industrial Crystalline Silicon Solar Cells J. John (Editor) Bifacial Photovoltaics: Technology, applications and economics J. Libal and R. Kopecek (Editors)

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Fault Diagnosis of Induction Motors J. Faiz, V. Ghorbanian and G. Joksimovic´ High Voltage Power Network Construction K. Harker Energy Storage at Different Voltage Levels: Technology, integration, and market aspects A.F. Zobaa, P.F. Ribeiro, S.H.A. Aleem and S.N. Afifi (Editors) Wireless Power Transfer: theory, technology and application N.Shinohara DC Distribution Systems and Microgrids T. Dragicˇ evic´ , F.Blaabjerg and P. Wheeler Structural Control and Fault Detection of Wind Turbine Systems H.R. Karimi Thermal Power Plant Control and Instrumentation: The control of boilers and HRSGs, 2nd Edition D. Lindsley, J. Grist and D. Parker Fault Diagnosis for Robust Inverter Power Drives A. Ginart (Editor) Power Systems Electromagnetic Transients Simulation, 2nd Edition N. Watson and J. Arrillaga Power Market Transformation B. Murray Wind Energy Modeling and Simulation, Volume 1: Atmosphere and plant P.Veers (Editor) Diagnosis and Fault Tolerance of Electrical Machines, Power Electronics and Drives A.J.M. Cardoso Characterization of Wide Bandgap Power Semiconductor Devices F. Wang, Z. Zhang and E.A. Jones Renewable Energy from the Oceans: From wave, tidal and gradient systems to offshore wind and solar D. Coiro and T. Sant (Editors) Wind and Solar Based Energy Systems for Communities R. Carriveau and D.S.-K. Ting (Editors) Metaheuristic Optimization in Power Engineering J. Radosavljevic´ Power Line Communication Systems for Smart Grids I.R.S. Casella and A. Anpalagan Variability, Scalability and Stability of Microgrids S.M. Muyeen, S.M. Islam and F. Blaabjerg (Editors) Energy Generation and Efficiency Technologies for Green Residential Buildings D. Ting and R. Carriveau (Editors) Electrical Steels, 2 Volumes A. Moses, K. Jenkins, Philip Anderson and H. Stanbury Power System Protection, 4 Volumes

Lightning Interaction with Power Systems Volume 2: Applications Edited by Alexandre Piantini

The Institution of Engineering and Technology

Published by The Institution of Engineering and Technology, London, United Kingdom The Institution of Engineering and Technology is registered as a Charity in England & Wales (no. 211014) and Scotland (no. SC038698). † The Institution of Engineering and Technology 2020 First published 2020 This publication is copyright under the Berne Convention and the Universal Copyright Convention. All rights reserved. Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may be reproduced, stored or transmitted, in any form or by any means, only with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publisher at the undermentioned address: The Institution of Engineering and Technology Michael Faraday House Six Hills Way, Stevenage Herts, SG1 2AY, United Kingdom www.theiet.org While the authors and publisher believe that the information and guidance given in this work are correct, all parties must rely upon their own skill and judgement when making use of them. Neither the authors nor publisher assumes any liability to anyone for any loss or damage caused by any error or omission in the work, whether such an error or omission is the result of negligence or any other cause. Any and all such liability is disclaimed. The moral rights of the authors to be identified as authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.

British Library Cataloguing in Publication Data A catalogue record for this product is available from the British Library ISBN 978-1-83953-092-0 (Hardback Volume 2) ISBN 978-1-83953-093-7 (PDF Volume 2) ISBN 978-1-83953-090-6 (Hardback Volume 1) ISBN 978-1-83953-091-3 (PDF Volume 1) ISBN 978-1-83953-094-4 (Hardback Volumes 1 and 2)

Typeset in India by MPS Limited Printed in the UK by CPI Group (UK) Ltd, Croydon

Contents

About the editor Preface Acknowledgments About the authors

1 Application of the Monte Carlo method to lightning protection and insulation coordination practices Alberto Borghetti, Fabio Napolitano, Carlo Alberto Nucci and Fabio Tossani 1.1 1.2 1.3 1.4 1.5

Introduction Description of the MC-based procedure Identification of the lightning current functions Stratified sampling technique Application results for a MV overhead line in open terrain 1.5.1 Influence of the return stroke current waveform 1.5.2 Application of the recursive stratified sampling technique 1.6 Conclusions References 2 Lightning interaction with power substations Shigemitsu Okabe 2.1

Fundamental concepts 2.1.1 Definition and procedure of insulation coordination 2.1.2 Lightning overvoltage in insulation coordination 2.1.3 Lightning surge analysis 2.2 Simplified statistical approach of lightning surge analysis 2.2.1 Basics 2.2.2 Calculation of the limit distance 2.2.3 Estimation of the lightning overvoltage amplitude 2.2.4 Simplified method 2.2.5 Assumed maximum value of the representative lightning overvoltage 2.3 Detailed deterministic approach of lightning surge analysis 2.3.1 Basic analysis conditions 2.3.2 Analysis conditions and models

xv xvii xxi xxiii

1

1 4 7 9 11 11 16 21 21 27 27 27 28 31 33 33 33 35 38 40 40 40 44

viii

Lightning interaction with power systems, volume 2 2.4

Failure rate evaluation considering front time of lightning current 2.4.1 Crest value and wavefront time of lightning stroke current 2.4.2 Wavefront time of lightning stroke current and amplitude of lightning surge 2.4.3 Lightning failure rates in substations in consideration of lightning current waveforms References 3

46 46 48 50 53

Lightning interaction with power transmission lines William A. Chisholm

57

3.1

59

3.2

3.3

Lightning attachment to overhead transmission lines 3.1.1 Overhead line attachment rates using ground flash density and typical dimensions 3.1.2 Local voltage rise from lightning attachment to transmission line phase conductor 3.1.3 Role of span length and nearby arresters on peak insulator voltage 3.1.4 Shielding of transmission line phase conductors using overhead groundwires Lightning impulse flashover of power transmission line insulation 3.2.1 Lightning impulse voltage test waveshapes 3.2.2 Single gap full-wave flashover strength for dry arc distance of 0.5 to 10 m 3.2.3 Strength of multiple air gaps in parallel under shielding failure conditions 3.2.4 Strength of multiple air gaps in series 3.2.5 Evolution of surge protective devices for insulation coordination 3.2.6 Design and performance of unshielded power transmission lines Bonding, earthing and equalisation of potential differences on transmission lines 3.3.1 Analysis of transient voltage rise on connections from OHGW to earthing electrodes 3.3.2 Analysis of transient voltage rise on earthing electrodes 3.3.3 Analysis of transient voltage reduction from adjacent phases 3.3.4 Analysis of transient voltage rise on insulated phases from surge impedance coupling 3.3.5 The backflashover from OHGW to phase 3.3.6 Design and performance of shielded power transmission lines 3.3.7 Methods for increasing the backflashover critical current 3.3.8 Methods for improving the equalisation of potential differences

60 64 70 72 73 74 76 80 81 81 82 85 85 89 98 99 102 103 104 106

Contents 3.4 Considerations in the design trade-off: arresters versus earthing References 4 Lightning interaction with medium-voltage overhead power distribution systems Alexandre Piantini, Alberto Borghetti and Carlo Alberto Nucci 4.1 4.2

Flash collection rate Effects of various parameters on lightning overvoltages 4.2.1 Direct strokes 4.2.2 Indirect strokes 4.3 Lightning protection of MV systems 4.3.1 Increase of the line withstand capability 4.3.2 Use of shield wires 4.3.3 Application of surge arresters 4.4 Lightning performance of overhead distribution lines 4.4.1 Influence of the environment around the line 4.4.2 Lines located above open ground 4.4.3 Lines surrounded by buildings 4.4.4 Hybrid configuration (MV and HV lines mounted on the same poles) 4.5 Concluding remarks References

5 Lightning interaction with low-voltage overhead power distribution networks Alexandre Piantini 5.1 5.2

Typical configurations of LV networks Lightning surges on LV power systems 5.2.1 Cloud discharges 5.2.2 Direct strikes 5.2.3 Indirect strikes 5.2.4 Transference from the MV line 5.3 Lightning protection of LV networks 5.3.1 Distribution transformers 5.3.2 LV power installations 5.4 Concluding remarks References

6 Lightning protection of structures and electrical systems inside of buildings Fridolin Heidler 6.1

Lightning currents 6.1.1 Current components

ix 107 108

113 114 115 115 117 132 132 133 146 153 153 154 158 160 164 164

173 174 176 176 177 178 201 207 208 212 217 218

227 228 230

x

Lightning interaction with power systems, volume 2 6.1.2 Lightning protection level 6.1.3 Simulation of the lightning currents for analytical purpose 6.2 Lightning protection of buildings 6.2.1 Lightning protection zone 6.2.2 Lightning protection system 6.2.3 Surge protection measure (SPM) system 6.3 Volume protected against direct lightning strike 6.3.1 Striking distance 6.3.2 Rolling sphere method 6.3.3 Simplifications of the rolling sphere method 6.4 Air-termination and down-conductor system 6.4.1 Air-termination system 6.4.2 Down-conductor system 6.4.3 Materials and dimensions 6.5 Earth-termination system 6.5.1 Earth-termination system for the lightning protection system (LPS) 6.5.2 Improved earth-termination system for the surge protection measure (SPM) system 6.6 Lightning equipotential bonding 6.6.1 Lightning equipotential bonding required for LPS 6.6.2 Lightning equipotential bonding according to the surge protection measure (SPM) system 6.7 Separation distance 6.7.1 Material coefficient km 6.7.2 Current steepness coefficient ki 6.7.3 Configuration coefficient kc 6.8 Currents and voltages on lines 6.8.1 Protection of connection lines at the entrance into LPZ 6.8.2 Shielded connection lines 6.8.3 Lines in reinforced concrete cable duct 6.8.4 Current share on lines in case of direct lightning 6.8.5 Reduction of the induced over-voltage on internal lines by line routing 6.9 Grid-like spatial shield 6.9.1 Magnetic field inside LPZ 1 in the case of a direct lightning strike 6.9.2 Magnetic field inside LPZ 1 in the case of a nearby lightning strike 6.9.3 Magnetic field inside LPZ 2 and higher References

230 233 233 234 236 238 241 241 241 242 244 244 245 245 247 247 249 250 250 251 255 256 256 256 260 260 261 262 263 264 265 265 266 267 268

Contents 7 Lightning protection of Smart Grids William A. Chisholm and Kenneth L. Cummins 7.1

Introduction: history of power system technologies 7.1.1 Electric power systems and mathematics 7.1.2 Electric power systems and communication 7.1.3 Electric power systems and lightning measurements 7.2 Smart Grid functions and technologies 7.2.1 Wide-area monitoring and visualization 7.2.2 Flow control 7.2.3 Enhanced fault identification 7.2.4 Adaptive protection and automated feeder switching 7.2.5 Automated islanding and reconnection 7.2.6 Diagnosis and notification of equipment condition 7.2.7 Dynamic thermal rating capabilities 7.3 Lightning and digital recording technology 7.3.1 Digital recording systems for lightning overvoltages 7.3.2 Voltage sensors for lightning overvoltages 7.3.3 Combined current and voltage sensor for lightning measurements 7.3.4 Non-contact sensors for impulse voltage and current 7.3.5 Commercial current sensors for equipment monitoring 7.4 Lightning protection of Smart Grid sensors 7.4.1 Reliability requirements for Smart Grid sensors and systems 7.4.2 Candidate wiring configurations for Smart Grid sensors 7.4.3 Industry standards for lightning protection of Smart Grid sensors 7.4.4 Industry standards for lightning protection of Smart Grid communication systems 7.4.5 Case study: EMC and residential Smart Grid interoperability 7.5 Conclusions References

8 Lightning protection of wind power systems Masaru Ishii and Joan Montanya` Wind turbine components and overview of the lightning protection system 8.2 Lightning phenomenology and wind turbines 8.2.1 Interaction with downward lightning 8.2.2 Upward lightning

xi 271 272 272 273 276 278 278 281 282 284 286 286 287 288 288 291 292 293 294 295 295 297 298 298 301 302 303 309

8.1

310 311 311 312

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9

Lightning damage to wind turbines due to direct impacts 8.3.1 Lightning damage mechanisms 8.3.2 Overview of types of lightning damage to wind turbines 8.3.3 Statistics on lightning damage to wind turbines 8.4 Lightning protection of wind turbine components 8.4.1 Blades 8.4.2 Consideration of CFRP in blades and other components 8.4.3 Other components: hub, bearings and nacelle 8.4.4 Overvoltages caused by direct lightning 8.5 Overvoltages in wind farms 8.5.1 Structure of wind farms 8.5.2 Sources of lightning overvoltages in wind farms: the back-flow surge References

317 317 318 324 324 324 327 329 330 335 336

Renewable energy systems—photovoltaic systems Kazuo Yamamoto and Yaru´ Me´ndez

343

Solar energy: solar radiation, parameters, hourly and daily parameters 9.1.1 Daily parameters 9.1.2 Second, minute or hourly based parameters 9.1.3 Extraterrestrial and terrestrial solar radiation 9.2 Photovoltaics: PV cells, PV modules, partial shading and its effects 9.3 PV systems: off-grid and grid-connected, considerations of the grid connection 9.4 Earthing (grounding) of PV-systems 9.4.1 The importance of earthing characteristics 9.4.2 The earthing characteristics of photovoltaic systems 9.4.3 The earthing characteristics for optimal selection of SPDs 9.5 Internal and overvoltage lightning protection 9.5.1 Protection at the PV generator’s side or DC side 9.5.2 Protection at the AC side 9.6 External lightning protection 9.6.1 Internal lightning protection 9.7 Mounting (racking) systems as air-termination systems 9.8 External dedicated mounting systems (non-isolated, isolated) 9.9 Concluding remarks References

336 339

9.1

10 Measurement of lightning currents and voltages Ruy Alberto Correˆa Altafim, Wenxia Sima and Qing Yang 10.1 Historical introduction 10.2 Lightning current measurements

343 344 345 346 346 349 351 351 354 359 363 363 364 364 366 368 369 369 369 371 371 372

Contents 10.2.1 Lightning current measurement methodology on transmission lines 10.2.2 Lightning current measurement methodology on high towers 10.3 Measurement method of lightning voltage 10.3.1 Voltage divider 10.3.2 Capacitive sensor connected to bushings 10.3.3 Noncontact capacitive voltage divider 10.3.4 Integrated optical waveguide voltage (electric field) sensor 10.3.5 Crystal-based batteryless and contactless optical transient overvoltage sensor 10.3.6 Optical voltage (electric field) sensor based on converse piezoelectric effect 10.4 Application of various lightning overvoltage sensors in power systems References 11 Application of the FDTD method to lightning studies Yoshihiro Baba and Vladimir A. Rakov 11.1 Introduction 11.2 FDTD method 11.2.1 Fundamentals 11.2.2 Advantages and disadvantages 11.3 Representations of lightning source 11.3.1 Lightning return-stroke channel 11.3.2 Excitation methods 11.4 Applications 11.4.1 Surges on grounding electrodes 11.4.2 Lightning surges on overhead power transmission lines and towers 11.4.3 Lightning surges on overhead power distribution and telecommunication lines 11.4.4 Lightning electromagnetic environment and surges in power substation 11.4.5 Lightning surges on underground distribution and telecommunication lines 11.4.6 Lightning surges in wind-turbine-generator towers 11.4.7 Lightning surges in photovoltaic arrays 11.4.8 Lightning surges and electromagnetic environment in buildings 11.4.9 Lightning electromagnetic fields at close and far distances 11.4.10 Other applications

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372 378 380 380 383 384 385 386 388 389 390 393 393 396 396 398 399 399 402 403 403 404 405 407 408 408 409 409 410 412

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12 Software tools for the lightning performance assessment Alberto Borghetti, William A. Chisholm, Fabio Napolitano, Carlo Alberto Nucci, Farhad Rachidi and Fabio Tossani 12.1 Introduction 12.2 FLASH program 12.2.1 Simplified modelling of shielding and backflashover calculations 12.2.2 Adoption of ‘red book’ method by IEEE, 1982–85 12.2.3 Adjustments of IEEE FLASH program, 1985–93 12.2.4 Standardizing the IEEE FLASH program, 1993–97 12.2.5 Maintaining the IEEE FLASH program, 1997–2007 12.2.6 Developing the IEEE FLASH V2.0 program, 2007–19 12.3 Lightning-induced overvoltages–electromagnetic transients program 12.3.1 Interfacing LIOV with EMTP 12.3.2 LIOV–EMTP input parameters 12.3.3 Application examples 12.4 Application to a real distribution network References Index

413 413 425

425 426 427 428 429 430 430 430 431 432 436 442 444 448 453

About the editor

Alexandre Piantini graduated in electrical engineering from the Federal University of Parana´ in 1985 and got his masters and doctoral degrees from the Polytechnic School of the University of Sa˜o Paulo in 1991 and 1997, respectively. He joined the University of Sa˜o Paulo in 1986 and served as the director of Technological Development of the Institute of Energy and Environment (1998–2011), where he is Associate Professor and the head of the Lightning and High Voltage Research Centre. He has participated in 26 research projects related mainly to lightning and electromagnetic compatibility (EMC). He coordinated 21 of these projects, of which 15 funded mainly by power companies and national agencies for research support. IEEE Senior Member since 2004, he was the Convener of the CIGRE´ WG C4.408 “Lightning Protection of Low-Voltage Networks” and member of various IEEE and CIGRE´ working groups. He is Associate Editor of the IEEE Trans. Electromagnetic Compatibility, High Voltage (IET), Electrical Engineering (Springer), and member of the Editorial Advisory Panel of the Electric Power Systems Research (Elsevier). He is member of the Steering Committee of the Int. Project on Electromagnetic Radiation from Lightning to Tall Structures. He was deputy editor-in-chief of the Journal of Lightning Research (2005–15) and associate editor of The Open Atmospheric Science Journal (2008–13). He has given various invited lectures and courses related to lightning in universities and international conferences organized in Brazil, Sweden, Spain, Colombia, Russia, and China. Prof. Piantini is the chairman of the Int. Symposium on Lightning Protection (SIPDA), vice-chairman of the Int. Conf. Grounding and Earthing & Int. Conf. Lightning Physics and Effects, and member of scientific committees of various conferences such as the Int. Conf. Lightning Protection (ICLP). He is a founder member of the Institute for Lightning Protection and Safety (ILPS), guest professor of the Chongqing University, China, and member of the IEEE Award Committee of the Sun & Grzybowski Award. In 2018, he was the recipient of the ICLP Rudolf Heinrich Golde Award, “for extraordinary theoretical and experimental achievements in lightning protection of power systems.” He is author or coauthor of four book chapters and over 150 scientific papers published in prestigious peer-reviewed journals or presented at international conferences with review board. He has given over 190 interviews to national and regional TV stations, radios, newspapers, etc. in topics related mainly to lightning.

Preface

The importance of improving the reliability and robustness of power systems makes protection of transmission and distribution lines against lightning-related effects a primary concern. This situation stems mainly from the increasing emphasis on overall power system efficiency, the continuous proliferation of equipment sensitive to short duration voltage disturbances, the increasing level of consumer demand for power quality, and the high economic losses associated with power-quality issues. Numerous studies have been carried out in this area with a view to a better understanding of the phenomena involved and the identification of technically and economically viable solutions that provide effective improvement of the quality of energy supplied to consumers. Lightning is particularly noteworthy in this context, as it is often responsible for a significant number of unscheduled outages of power transmission lines and distribution networks even in regions with relatively moderate ground flash densities. Besides, renewable electricity generation capacity has been increasing rapidly all over the world. Wind turbines are growing not only in number but also in size, leading to an increasing concern for lightning protection of wind power plants. Lightning is a major source of damages to wind turbines and can cause failures either hitting the turbines directly or inducing transients on the control systems that lead to equipment failure, malfunction or degradation. Photovoltaic (PV) systems may be vulnerable to lightning transients associated with both direct and nearby strikes, which can damage sensitive electronics or weaken the dielectric strength of the PV module insulation. Lightning is a multidisciplinary subject and the importance of understanding the physics of the phenomenon and its interaction with various objects and materials, as well as the need to effectively protect structures, systems, people, and animals against its deleterious effects, has led to the existence of several books involving different lightning-related aspects. However, the current literature lacks a comprehensive work with specific focus on the interaction between lightning and electrical power systems that addresses in depth the lightning protection of transmission and distribution networks, including smart grids and renewable energy systems. This is the aim of this book, which contains well-established information and includes the most recent advancements in the field. This book is intended primarily for a two-semester course for undergraduate and graduate students in energy and electrical engineering, but it can be used also for a one-semester or even shorter courses. It is also useful as reference for academic scientists, researchers, and engineers in the areas of electrical engineering

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and physics, power systems consultants, and professionals from electric power companies involved in the fields of lightning protection, electromagnetic compatibility, renewable energy systems, and smart grids. The secondary readership consists of professionals from telecommunication companies and manufacturers of power equipment. This book is divided into two volumes. The chapters in Volume 1 describe and discuss the main concepts, fundamentals, and models necessary to understand and evaluate the interaction between lightning and electrical systems. The first chapter is concerned with an assessment of how global lightning may respond to global climate change. In Chapter 2, basic lightning terminology is introduced and the main lightning processes are described. The “classical” distributions of lightning parameters needed in engineering applications are reviewed along with the distributions based on more recent direct current measurements. Correlations between the parameters are discussed and mathematical expressions used to represent lightning current waveforms are reviewed. Chapter 3 introduces the reader to the various concepts used to construct engineering return stroke models. After describing the most important models, it provides a review of the basic features of lightning electromagnetic fields and presents methods for their calculation, including the horizontal electric field associated with return stroke over finitely conducting ground. Chapter 4 provides the basis for calculating ground flash densities, details of techniques used by modern lightning location systems (LLSs), examples of well-established LLSs in different parts of the world, and methods used to validate the performance characteristics of LLSs. In Chapter 5, the physical process and engineering models of lightning attachment to overhead power lines are described in detail and a general procedure for the estimation of lightning incidence to overhead power lines is presented. Chapter 6 presents the coupling of lightning electromagnetic fields to overhead and underground lines based on the transmission line approximation, whereas Chapter 7 addresses the lightning response of grounding electrodes. Chapter 8, which deals with surge protective devices, presents the most common definitions, characteristics, operating mechanisms, classifications, and applications of devices used in transmission and distribution networks, including low-voltage (LV) systems. Chapters 9 and 10 present and discuss models of the most important power transmission and distribution (medium and LV) system components for simulations of lightning electromagnetic transients. The second volume, devoted to the applications, contains Chapters 1–12, which cover lightning protection of various systems, including structures and buildings, transmission and distribution networks, renewable energy systems, and smart grids. Chapter 1 is devoted to the application of the Monte Carlo method to lightning protection and insulation coordination practices and describes also the application of the stratified sampling technique to reduce the computational effort usually required. The effect of lightning on the insulation performance of substation equipment is dealt with in Chapter 2, which includes also the evaluation of the failure rates of gas-insulated switchgear and transformers. Chapter 3 organizes the lightning interactions with power transmission lines from the simple consequences of a direct stroke attachment to an unshielded line to the complex consequences of a

Preface

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stroke attachment to a shielded line with multiple ground wires, including the effects from phases protected with line arresters. It builds on the information in previous chapters to develop important measures in transmission line lightning performance. Chapter 4 deals with the lightning impacts on medium-voltage power distribution systems and discusses the effects of the most important parameters on the overvoltages, as well as the effectivenesses of the main protective measures that can be applied to improve the line lightning performance. A procedure for estimating the mean annual number of line flashovers of overhead lines is presented and the lightning performances of lines with different protective measures are compared. In Chapter 5, devoted to the lightning interaction with LV power distribution networks, the major mechanisms by which lightning overvoltages can be produced are explained and the general surge characteristics are evaluated. The effectiveness of the installation of secondary arresters along the network in protecting the LV side of transformers and consumers’ entrances is also discussed. Chapter 6 is dedicated to the lightning protection of common structures, including their installations and content, and persons as well. Such protection requires the combination of external and internal countermeasures, which are also discussed in the chapter. A broad view of “lightning protection” finds many smart grid applications of real-time lightning information in proactive protection strategies. After presenting the history of power system technologies and describing the roles that lightning research plays in successful integration of digital technologies into electric power systems, Chapter 7 discusses lightning-related digital recording technologies and addresses the lightning protection of smart grid sensors. Chapters 8 and 9 focus on the lightning protection of renewable energy systems. Chapter 8 gives an introduction to wind power generators and their components from the perspective of lightning protection, as well as an overview of lightning occurrence in relation to wind turbines. It presents the mechanisms of lightning damage to wind turbines, their classification and statistics, discusses the protection of the most sensitive components, and describes the mechanisms whereby lightning surges invade a wind farm through a lightning-struck wind turbine. Chapter 9 deals with PV systems and gives a brief introduction to solar radiation, PV cells, modules, and the associated effects of shading. Off-grid and gridconnected PV systems are described and the common configurations of external and internal lightning protection systems are discussed. Chapter 10, which is about measurements of lightning currents and voltages, describes various types of sensors and discusses their application in power systems. Chapter 11 presents the fundamentals of the finite-difference time-domain method and reviews the application of the method to the analysis of lightning electromagnetic fields and lightning-caused surges in various systems. Chapter 12 describes two of the most adopted software tools for the evaluation of the lightning performance of transmission and distribution lines, namely, FLASH and LIOVEMTP, together with some application examples. The chapters follow a logical order and ideally should be read sequentially by a beginner reader, but they are self-contained and can be read independently, so that a reader interested in a specific topic can go directly to the relevant chapter. Alexandre Piantini

Acknowledgments

I would like to express my sincere thanks to my colleagues and friends, authors of the chapters, for their dedication and esteemed contributions. My special thanks go to Prof. Carlo Alberto Nucci, Prof. Farhad Rachidi, Prof. Marcos Rubinstein, Prof. Vernon Cooray, Prof. Vladimir A. Rakov, and Prof. William A. Chisholm, for the valuable discussions and continuous support. I am also grateful to Dr. Christoph von Friedeburg, Senior Books Commissioning Editor at the IET, for the interesting discussions, and to Ms. Olivia Wilkins, assistant editor at the IET, for her kindness, sincerity, and patience to deal with submission delays. Working with her was indeed a great pleasure. I am indebted to all my former and current students, postdocs, and colleagues, and specially thank Miss Michele N.N. Santos, Ph.D. student, for her precious help during the organization of the book. Finally, I would like to thank my parents, Farley and Elza, my 102-year-old grandmother Nair, my sisters Andrea and Barbara, and my nieces Angel, Farly, and Isabella, for their unlimited love and support and for always bringing joy to my life. Alexandre Piantini

About the authors

Ruy Alberto Correˆa Altafim was born in Agudos, Brazil, on January 4, 1957. He received his Ph.D. degree in electrical engineering from the University of Sa˜o Paulo, Brazil, in 1991. In 1994, He worked as a guest researcher for the National Institute of Standards and Technology-NIST in USA, with liquid dielectrics. In 1995, he was promoted to associate professor and, in 1997, he had got a university position as full professor of electrical engineering in the University of Sa˜o Paulo. In 2001, he was nominated as a member of CEIDP/IEEE board and, in 2013, as an AdCom member of DEIS-IEEE society. He is a member of SIPDA scientific board. He is a member of Editorial Board Associate Editor of IEEE Transactions on Dielectric and Electrical Insulation, and until 2018, at IEEE Electrical Insulation Magazine— regional editor. In 2010, He worked as a guest professor at the University of Potsdam—Germany, with PROBRAL/CAPES financial support in the piezoelectret research area. He is a senior member of IEEE and his special fields of interest are solid and liquid dielectrics, liquid crystal, electrets, piezoelectric sensors, and high-voltage engineering. Dr. Altafim was also head of the Electrical and Computer Department of EESC-USP for 10 years, vice-dean at Engineering School of Sa˜o Carlos-USP and Pro-Rector at the University of Sa˜o Paulo. He has also worked as leader of the Applied Electrical Metrology and High Voltage Group and leaded many research projects in areas such as reforestation wood cross-arm, lightning-induced voltages on distribution power systems, piezoelectret sensors, and impulse impedance of grounding systems. He is Senior Professor of the Electrical Engineering Department of EESC/USP and Visiting Professor at the Federal University of Paraı´ba. He has continually published in these areas in many journals such as IEEE Transactions on Dielectric and Electrical Insulation, IEEE Transactions on Industry Application, Molecular Crystals, Applied Physics, Journal of Applied Physics and Liquid Crystals, and on many international conferences.

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Yoshihiro Baba received the B.Sc., M.Sc., and Ph.D. degrees from the University of Tokyo in 1994, 1996, and 1999, respectively. In 1999, he joined Doshisha University, Kyoto, Japan, where since 2012 he has been a professor. From April 2003 to August 2004, he was a visiting scholar at the University of Florida. He received the Technical Achievement Award from the IEEE EMC Society in 2014. He is the Chairperson of Technical Program Committee of the 2015 AsiaPacific International Conference on Lightning (APL), Nagoya, Japan. He has been the vice chairperson of the APL Steering Committee since 2017. He has been the convener of CIGRE´ C4.37 Working Group since 2014. He had been an editor of the IEEE Trans. Power Delivery from 2009 until 2018. He has been an editor of the IEEE Power Engineering Letters since 2009, a guest associate editor of the IEEE Trans. EMC since 2018, and an associate editor of Electric Engineering (Springer Journal) since 2019. He is a fellow of both IET and IEEE. Alberto Borghetti was born in Cesena, Italy, in 1967. He graduated (with honors) in electrical engineering from the University of Bologna, Italy, in 1992. Since then, he has been working with the power system group of the same university, where he is now a professor of electrical power systems. His research and teaching activities are in the areas of power system analysis, power system restoration after blackout, electromagnetic transients, optimal generation scheduling, and distribution system operation. He is the author or coauthor of over 150 scientific papers published in peer-reviewed journals or presented at international conferences. He has served as Technical Program Committee chairperson of the 2010 30th Int. Conf. on Lightning Protection and chair of the 2016 Bologna CIGRE´ Colloquium on Lightning and Power systems. He was special reporter for the Study Committee C4 (System technical performance) of CIGRE´ 2018, recipient of the Int. Conf. on Lightning Protection Scientific Committee Award in 2016, and of the 2018 CIGRE´ Technical Council Award. He is a fellow of the Institute of Electrical and Electronics Engineers (class 2015) for contributions to modeling of power distribution systems under transient conditions. From 2010 to 2017, he has served as an editor of IEEE Trans. on Smart Grid. Since 2018, he is serving as an editor of IEEE Trans. on Power Systems and as an associate editor of Journal of Modern Power Systems and Clean Energy (MPCE), SGEPRI Press and Springer. Since 2019, he serves as editor in chief of

About the authors

xxv

Electrical Engineering—Archiv fu¨r Elektrotechnik, Springer. Since 2008, he is as editorial board member of Electric Power Systems Research, Elsevier. William A. Chisholm (IEEE M’79–SM’90– F’07) was born in New York, USA, in 1955. He received the B.A.Sc. degree in engineering science and the M.Eng. degree in electrical engineering from the University of Toronto, Toronto, ON, Canada, in 1977 and 1979, respectively, and the Ph.D. degree in electrical engineering from the University of Waterloo, Waterloo, ON, Canada, in 1983. He was with Kinectrics, the former Ontario Hydro Research Division, from 1977 to 2007. He continues to serve as a consultant to industry, professor at UQAC, Chicoutimi, QC, Canada, and the University of Toronto and mentor at METSCO, Mississauga, ON, Canada. He has coauthored reference books on icing for IEEE/Wiley, a textbook for Mc-Graw-Hill, and chapters in the Electric Power Research Institute Red, Blue and Gray books and the CRC/IEEE Electric Power Engineering Handbook. Dr. Chisholm was a chair of the IEEE Power and Energy Society Transmission and Distribution Committee, with many contributions to IEEE and CIGRE´ literature and standards related to the effects of adverse weather, including lightning, earthing, icing, and low wind on overhead lines. In addition to IEEE fellow in 2007, he received an IEEE “Best Standard” award for Std. 1243-1997 (‘99), Masters Swim Canada #1 Rank (‘98, ‘00, ‘01, ‘05, ‘06, ‘10, ‘11) and national record (‘15), the Masoud Farzaneh Prize (2014) and the INMR Claude de Tourreil Award (2017). Kenneth L. Cummins (IEEE S’73–M’78– SM’99) received the B.S. degree in electrical engineering from the University of California, Irvine, in 1973, and the M.S. and Ph.D. degrees in electrical engineering from Stanford University, Stanford, CA, in 1974 and 1978, respectively. Until 1989, he was involved in the field of neurosciences as a Research Scientist at Stanford Medical Center and the Veterans’ Administration, and then, as a Staff Scientist at Nicolet Instrument. From 1989 to 2005, he was the R&D Manager and the chief scientist for the Thunderstorm Business Unit, Vaisala (formally Global Atmospherics, Inc.) in Tucson, AZ. He is currently a research professor in the Department of Hydrology and Atmospheric Sciences at the University of Arizona. He is the author or coauthor of more than 85 scientific papers and holds 9 US patents.

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Dr. Cummins is a member of NASA’s Science Team for the space-based Geostationary Lightning Mappers on the GOES weather satellites. He has served in various IEEE and CIGRE´ Working Groups related to lightning. Over the last 5 years, he received three NASA awards for his research activities and for his service on NASA’s Lightning Advisory Panel. Fridolin H. Heidler received the B.Eng. and the M.Eng. degrees in electrical engineering with special emphasis on high-voltage engineering from the Technical University Munich, Munich, Germany, in 1978 and 1982, respectively, and the Ph.D. and Dr.-Ing. habilitation degrees in the high-voltage engineering, in 1987 and 1999, respectively. From 1987 to 1991, he was with Industrial Engineering Company (IABG), where he was engaged in the field of electro-dynamic calculations in the frequency and time domains. In 1991, he joined the Institute of High Voltage Engineering, University of the Federal Armed Forces, where he is currently a professor of highvoltage engineering. His current research interests include the fields of lightning research, lightning protection, and electromagnetic compatibility (EMC) with main emphasis on numerical calculations of lightning discharge process, and the measurement of the currents and electric or magnetic fields from lightning striking the Peissenberg telecommunication tower nearby Munich, Germany. He has authored or coauthored more than 180 scientific papers on lightning protection, lightning research, and electromagnetic compatibility. Masaru Ishii received the B.S., M.S., and Ph.D. degrees in electrical engineering from the University of Tokyo, Tokyo, Japan, in 1971, 1973, and 1976, respectively. In 1976, he joined the Institute of Industrial Science, the University of Tokyo, where he was a professor during 1992–2013. He became an emeritus professor of the University of Tokyo and an Advisor of Central Research Institute of Power Industry (CRIEPI) in 2013. He became an honorary research advisor of CRIEPI in 2019. He was the vice president of the Institute of Electrical Engineers of Japan from 2007 to 2008 and is the president of the Institute of Electrical Installation Engineers of Japan since 2015. Prof. Ishii is a fellow of IEEE, a fellow of IEE of Japan, and a distinguished member of CIGRE´.

About the authors

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Since 2015, Dr. Yaru´ Me´ndez works as a lecturer in electrical engineering (EE) at the Universidad Simo´n Bolı´var (USB) and entrepreneur at the company Murayh in Caracas, Venezuela. Main focus of the professional and academic activity is on power systems and renewable energy-based power generation. Previously, he was “Director of Engineering” at the company Raycap GmbH in Munich, Germany, and “Research Engineer” at the company General Electric Global Research (GEGR) in Munich, Germany, working on topics of renewable energy (wind and solar) and their interaction to the grid in terms of lightning and transients. Concerning education, he owns a degree in electrical engineering in power systems from the Universidad Simo´n Bolı´var (USB), a Dr.-Ing. degree from the University of Kassel (UNIK) in Germany, and a MBA degree from the University of Applied Sciences Munich (HM) in Germany. Currently, Mr. Me´ndez owns 17 patents and has published 54 scientific publications as author and coauthor. Joan Montanya` was born in Su´ria (Barcelona), Spain, in 1975. He received the B.S. degree in industrial engineering and M.S. and Ph.D. degrees in electrical engineering from the Polytechnic University of Catalonia, Barcelona, Spain, in 2000 and 2004, respectively. He joined the Department of Electrical Engineering of the Polytechnic University of Catalonia as adjunct lecturer in 1997. In 2003, he became assistant professor, in 2011 associated professor, and in 2017 obtained a full professor position. He did several short stays at the University of Arizona (Tucson, AZ, US), the Laboratoire d’Ae´rologie (Toulosue, France), and the Massachusetts Institute of Technology (Cambridge, MA, US). He is author and coauthor of more than 150 publications related to atmospheric electricity including lightning protection, transient luminous events, terrestrial gamma ray flashes (TGF), lightning warning, high energy radiation from lightning and laboratory sparks, thunderstorm electrification, severe weather, and Schumann resonance. He has special interest in lightning protection of wind turbine blades with composite materials. He is currently the head of the UPC Lightning Research Group. He participated in more than 15 research projects related to lightning research being principal investigator of 10 projects. Five of these projects are

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related to the Atmosphere-Space Interactions Monitor (ASIM) an ESA mission in order to investigate the origin of the TGF. Since 2014, he is member of the International Commission on Atmospheric Electricity. He is also member of several international standardization groups for lightning protection. He is convener of the EU CENELEC TC81X/WG5 for the standard EN 50536 “Protection against lightning—Thunderstorm warning systems.” He is an active member of the IEC TC 88 PT 24 about lightning protection of wind turbines. He is also active in several CIGRE´ SC C4 committees including the committee WG C4.409 related to lightning protection of wind turbine blades, the WG C4.410 about lightning to very tall objects, and the WG C4.36 related to winter lightning. Fabio Napolitano received the M.S. degree (with honors) in electrical engineering and the Ph.D. degree in electrical engineering from the University of Bologna, Italy, in 2003 and 2009, respectively. He is an assistant professor at the Department of Electrical, Electronic, and Information Engineering of the University of Bologna, Italy. Since his graduation, he collaborated with the Power Systems group of the University of Bologna on the analysis of power systems transients, in particular those due to indirect lightning strokes, and lightning protection systems. He is senior member of IEEE and member of CEI Technical Committee 81. He is currently associate editor of the journal Electrical Engineering. Carlo Alberto Nucci graduated with honors in electrical engineering from the University of Bologna, Bologna, Italy, in 1982. He is a full professor and head of the Power Systems Laboratory of the Department of Electrical, Electronic, and Information Engineering “Guglielmo Marconi,” University of Bologna. He has authored or coauthored over 370 scientific papers published in peer-reviewed journals or in proceedings of international conferences. Prof. Nucci is a fellow of the IEEE and of the International Council on Large Electric Systems (CIGRE´), of which he is also an honorary member, and has received some of the best paper/technical international awards, including the CIGRE´ Technical Committee Award and the ICLP Golde Award. From January 2006 to September 2012, he served as chairman of the CIGRE´ Study Committee C4 ªSystem Technical Performance. He has served as IEEE PES Region 8 Rep in 2009 and 2010. Since January 2010, he has served as editor-in-chief of the Electric Power Systems Research journal (Elsevier). He has served as the president

About the authors

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of the Italian Group of the University Professors of Electrical Power Systems (GUSEE) from 2012 to 2015. He is an advisor of the Global Resource Management Program of Doshisha University, Kyoto, Japan, supported by the Japanese Ministry of Education and Science and has represented PES in the IEEE Smart City Initiatives Program since 2014. Prof. Nucci is doctor Honoris Causa of the University Politehnica of Bucharest and a member of the Academy of Science of the Institute of Bologna. Shigemitsu Okabe received the B.S., M.S., and Ph.D. degrees in electrical engineering from the University of Tokyo in 1981, 1983, and 1986, respectively. Since 1986, he has been with Tokyo Electric Power Company and presently is the chief researcher at the R&D Department. He was a visiting scientist at the Technical University of Munich in 1992. He has been an adjunct professor of Doshisha University since 2005 and of Nagoya University since 2006. He is also the visiting lecturer of the University of Tokyo. He has served as the secretary and or member of several WG/MT in CIGRE´ and IEC. He is an associate editor of the IEEE Transactions on Dielectrics and Electrical Insulation. Alexandre Piantini graduated in electrical engineering from the Federal University of Parana´ in 1985 and got his masters and doctoral degrees from the Polytechnic School of the University of Sa˜o Paulo in 1991 and 1997, respectively. He joined the University of Sa˜o Paulo in 1986 and served as the director of Technological Development of the Institute of Energy and Environment (1998–2011), where he is Associate Professor and the head of the Lightning and High Voltage Research Centre. He has participated in 26 research projects related mainly to lightning and EMC. He coordinated 21 of these projects, of which 15 funded mainly by power companies and national agencies for research support. IEEE Senior Member since 2004, he was the Convener of the CIGRE´ WG C4.408 “Lightning Protection of Low-Voltage Networks” and member of various IEEE and CIGRE´ working groups. He is Associate Editor of the IEEE Trans. Electromagnetic Compatibility, High Voltage (IET), Electrical Engineering (Springer), and member of the Editorial Advisory Panel of the Electric Power Systems Research (Elsevier). He is member of the Steering Committee of the Int. Project on Electromagnetic Radiation from Lightning to Tall Structures. He was Deputy Editor-in-Chief of the Journal of Lightning Research (2005–15) and Associate Editor of The Open Atmospheric Science Journal (2008–13). He has given various invited lectures and courses related to lightning in universities and

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international conferences organized in Brazil, Sweden, Spain, Colombia, Russia, and China. Prof. Piantini is the chairman of the Int. Symposium on Lightning Protection (SIPDA), vice-chairman of the Int. Conf. Grounding and Earthing & Int. Conf. Lightning Physics and Effects, and member of scientific committees of various conferences such as the Int. Conf. Lightning Protection (ICLP). He is a founder member of the Institute for Lightning Protection and Safety (ILPS), guest professor of the Chongqing University, China, and member of the IEEE Award Committee of the Sun & Grzybowski Award. In 2018, he was the recipient of the ICLP Rudolf Heinrich Golde Award, “for extraordinary theoretical and experimental achievements in lightning protection of power systems.” He is author or coauthor of four book chapters and over 150 scientific papers published in prestigious peerreviewed journals or presented at international conferences with review board. He has given over 190 interviews to national and regional TV stations, radios, newspapers, etc. in topics related mainly to lightning. Farhad Rachidi (M’93–SM’02–F’10) received the M.S. degree in electrical engineering and the Ph.D. degree from the Swiss Federal Institute of Technology, Lausanne, Switzerland, in 1986 and 1991, respectively. He was with the Power Systems Laboratory, Swiss Federal Institute of Technology, until 1996. In 1997, he joined the Lightning Research Laboratory, University of Toronto, Toronto, ON, Canada. From 1998 to 1999, he was with Montena EMC, Rossens, Switzerland. He is currently a Titular Professor and the head of the EMC Laboratory with the Swiss Federal Institute of Technology, Lausanne, Switzerland. He has authored or coauthored over 190 scientific papers published in peer-reviewed journals and over 400 papers presented at international conferences. Dr. Rachidi is currently a member of the Advisory Board of the IEEE Transactions on Electromagnetic Compatibility and the president of the Swiss National Committee of the International Union of Radio Science. He has received numerous awards including the 2005 IEEE EMC Technical Achievement Award, the 2005 CIGRE´ Technical Committee Award, the 2006 Blondel Medal from the French Association of Electrical Engineering, Electronics, Information Technology and Communication (SEE), the 2016 Berger Award from the International Conference on Lightning Protection, the 2016 Best Paper Award of the IEEE Transactions on EMC, and the 2017 Motohisa Kanda Award for the most cited paper of the IEEE Transactions on EMC (2012–16). In 2014, he was conferred the title of honorary professor of the Xi’an Jiaotong University in China. He served as the vice-chair of the European COST Action on the Physics of Lightning Flash and its Effects from 2005 to 2009, the chairman of the 2008 European Electromagnetics International Symposium, the president of the International Conference on Lightning Protection from 2008 to 2014, the editor-in-chief of the Open Atmospheric Science Journal (2010–12), and the editor-in-chief of the IEEE Transactions on

About the authors

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Electromagnetic Compatibility from 2013 to 2015. He is a fellow of the IEEE and of the SUMMA Foundation, and a member of the Swiss Academy of Sciences. Vladimir A. Rakov received the M.S. and Ph.D. degrees in electrical engineering from the Tomsk Polytechnical University, Russia, in 1977 and 1983, respectively. He is currently a professor in the Department of Electrical and Computer Engineering, University of Florida, Gainesville, and co-director of the International Center for Lightning Research and Testing (ICLRT). He is the author or coauthor of 4 books and over 700 other publications on various aspects of lightning, with about 300 papers being published in peerreviewed journals. Dr. Rakov is a fellow of four major professional societies, the IEEE, the American Meteorological Society, the American Geophysical Union, and the Institution of Engineering and Technology (formerly IEE). He is also a recipient of Karl Berger Award for distinguished achievements in lightning research, developing new fields in theory and practice, modeling and measurements (2012), and Toshio Takeuti Award for outstanding contribution to worldwide recognition of winter lightning (2017). In 2015, he was awarded honorary doctoral degree by the Institute of Applied Physics of the Russian Academy of Sciences (IAP RAS). Wenxia Sima received the B.S. and Ph.D. degrees in electrical engineering from the Chongqing University, Chongqing, China, in 1988 and 1994, respectively. In 1988, she was involved in high-voltage research at the High Voltage Research Institute (a division of Chongqing University), where from 1996 to 2014, she held the position of the vice director of High Voltage and Insulation Technology Department. From 1994 to 1997, she was an assistant professor of Electrical Engineering at Chongqing University. From 1997 to 2001, she was an associate professor. In 2001, she became a professor at Chongqing University. She is currently the director of High Voltage and Insulation Technology Department, and a professor of the State Key Laboratory of Power Transmission Equipment & System Security and New Technology. She is the author or coauthor of 1 book, 6 patents, and more than 100 papers. She has been in charge of more than 30 scientific research projects, including 3 projects supported by National Science Foundation of China (NSFC) and 2 National Basic Research Program of China. Her research interests are in mechanism of long air gap discharge, lightning shield model and lightning protection theory, space charge measurement in liquids and discharge mechanism, overvoltage monitoring, grounding, and grounding grid diagnosis.

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Lightning interaction with power systems, volume 2 Fabio Tossani (S’15–M’16) received the B.S. (Hons.), M.S. (Hons.), and Ph.D. degree in electrical engineering from the University of Bologna, Italy, in 2010, 2012, and 2016, respectively. He is currently a junior assistant professor of the Electrical Power Systems group of the University of Bologna. His research interests are power system transients, with particular reference to lightning electromagnetic pulse interaction with electrical networks, power systems protection, and the integration of renewables in power distribution networks. He is assistant editor of the journal Electric Power Systems Research.

Kazuo Yamamoto was born in Osaka, Japan, in 1974. He received the B.E., M.E., and Ph.D. degrees in engineering from Doshisha University, Kyoto, Japan, in 1997, 2000, and 2007, respectively. From 1998 to 1999, he was a visiting researcher with Manitoba HVDC Research Centre, Winnipeg, MB, Canada. From 2000 to 2006, he was with Nara National College of Technology, Nara, Japan, and from 2007 to 2012, he was with Kobe City College of Technology, Kobe, Japan. In 2012, he was a visiting researcher with Electro Magnetic Applications, Inc., Lakewood, CO, USA. He is currently an associate professor with the Department of Electrical and Electronic Engineering, College of Engineering, Chubu University, Kasugai, Japan. His research interests include lightning protection for renewable energy systems and automobiles. Qing Yang received the B.S and Ph.D. degrees in electrical engineering, respectively, in 2002 from North China Electrical Power University and in 2006 from Chongqing University, China. He is now a professor in the State Key Laboratory of Power Transmission Equipment & System Security and New Technology, Chongqing University. His research interests include lightning protection, overvoltage protection, electric-field measurement, and space charge dynamics. He is the author and coauthor of more than 60 journal and international conference papers.

Chapter 1

Application of the Monte Carlo method to lightning protection and insulation coordination practices Alberto Borghetti1, Fabio Napolitano1, Carlo Alberto Nucci1 and Fabio Tossani1

Lightning insulation coordination is based on statistical approaches. This allows to correlate the electrical stress caused by lightning and the electrical strength of the insulations, both having probabilistic nature. This chapter provides an example of lightning insulation coordination. Specifically, it deals with the statistical appraisal of the so-called lightning performance of distribution systems, carried out by means of Monte Carlo (MC) simulations. The relevant application to both the cases of direct and indirect lightning events, considering the correlation between the probability distributions of the lightning current parameters, is described and discussed. In particular, the application to the indirect events is based on the definition of a surface around the power line and on the calculation of the induced voltages along the line caused by indirect events having stroke location uniformly distributed within such a surface. The result obtained through the MC simulations is finally scaled taking into account the annual number of flashes per square kilometer expected in the region of interest. In order to obtain significant results, two aspects need to be considered: the surface around the power line should be large enough in order to collect all the events that may endanger the insulation, and the density of the stroke locations should be sufficiently high. Therefore, for medium voltage systems, or even more for the case of low voltage ones, the area can reach a large value indeed, and the number of events to be considered can be consequently huge. The chapter also describes the application of the stratified sampling technique able to reduce the computation effort typical to this type of calculation.

1.1 Introduction The basic question for the purposes of insulation and protection coordination of distribution lines is how many lightning originated flashovers per year a certain 1

Department of Electrical, Electronic and Information Engineering, University of Bologna, Italy

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Lightning interaction with power systems, volume 2

distribution line may experience, as a function of its insulation. The attention is mostly focused on the number and intensity of lightning-induced voltages, either because distribution lines are surrounded by elevated objects or because direct strikes protection is uneconomical. The issue has been the object of several studies in the past and it is still of interest due to the stringent power quality requirements of modern distribution networks, especially nowadays, given the increasing amount of distributed generation that is connected to them [1–5]. In [1,2], the frequency of overvoltages exceeding a given insulation level is evaluated by means of analytical methods for the case of an infinite long line over a perfect conducting plane. The amplitude of the lightning current at the channel base is considered as a random variable considering its probability distribution, while the front time of the lightning current and the return stroke velocity are assumed fixed. In [3], a statistical method is employed. Both the probability distribution of amplitude and that of front time of the lightning current are considered, along with the correlation coefficient between the two above-mentioned parameters. The positive value of that coefficient indicates that the higher the current amplitude, the longer the front time of the impulse. The striking distance of the indirect stroke from the line (lightning strokes occurring within a certain critical distance from the line will directly strike the line) is evaluated as a function of the return stroke peak current (while in [1], it is considered as independent of the current). The return stroke velocity is fixed and the ground is assumed as a perfectly conductive plane. In [4], the Monte Carlo (MC) method has been employed to solve the problem. The induced voltages are calculated at the termination of a 2 km line matched at both ends. The MC simulation involves 10,000 events taking place over a surface covering the line and 1 km away from it. The same striking distance equation from the line as in [3] is adopted. The correlation between peak value and front time of lightning current distributions is disregarded. Lightning originated overvoltages in overhead lines are due to both direct strikes and the coupling between the conductors and the electromagnetic pulse generated by nearby strikes to ground (see, e.g., [6,7]). For power distribution overhead lines, characterized by lower insulation and height with respect to transmission lines, most of the lightning related flashovers are caused by strikes to the ground or structures located in proximity of the line [8]. As a consequence, the influence of these events on the lightning performance of the line needs to be appropriately assessed to grant the adequate protection. It is also worth adding that while for distribution lines all direct strikes are expected to cause flashovers (unless a large amount of surge arresters and shield wires are installed, ideally one per phase and per pole), only a fraction of nearby strikes to ground are expected to induce voltages larger than the line withstand insulation level. Different is the case for those lightning strokes that, although not hitting directly the line conductor, hit those elevated objects that are located close to the line and therefore can be able to cause flashovers. As described in [5], the standard MC approach for the lightning performance assessment of power distribution lines consists in generating a large number of

Application of the Monte Carlo method to lightning protection

3

events, each characterized by different values of lightning current waveshape parameters and different coordinates of the perspective stroke location (i.e., the stroke location in absence of the line). The values of the lightning current parameters are generated in agreement with the relevant probability distributions available in the literature or provided by lightning location systems (see, e.g., [9,10]). The coordinates of the stroke location are assumed uniformly distributed within a region around the line wide enough to include all the events that may cause a flashover. In several papers (e.g., [11,12]), the calculation of the lightning-induced overvoltages is performed by using simplified formulas in order to reduce the computational effort. However, as the accurate appraisal of the induced voltages can be achieved only by a time-domain electromagnetic transient simulation (in this chapter, performed by using the LIOV–EMTP-RV code described in [6,13,14] and validated by the comparison of the results with several experimental results [15,16]), the lightning performance of distribution networks by means of standard MC simulations involves a significant amount of computational resources. Some recent papers have dealt with the lightning performance assessment by means of electromagnetic transients simulations (e.g., [17–19]), which are quite time consuming. Nearby strikes to ground are often referred as indirect strokes in the relevant literature; this term is also used to indicate other indirect lightning events that are not considered in this chapter, such as side flashes and the line interaction with a ground current (e.g., [20,21]). In [22], a method to reduce the computational effort is presented. It is based on the application of the so-called Mean Square Pure Error (MSPE) algorithm to determine the optimal number of MC extractions and on a 3D interpolation that bypasses the necessity of the timedomain simulation of each MC event. In order to reduce the number of LIOV–EMTP-RV simulations, in [23] a heuristic technique has been proposed for the case of an unprotected network, which has been adapted in [24] to the case of distribution networks with surge arresters. The heuristic technique is conceived to avoid the time-domain computation of events expected to be less harmful than the previously calculated ones. This requires to fix a priori conditions so to discard the upcoming events which, in general, have characteristics (e.g., amplitude) that depend on the particular network configuration, especially in presence of nonlinearities [25]. An improved estimation accuracy can be achieved by two approaches: by increasing the number of replications or reducing the variance of the estimator. A typical variance reduction technique adopted in MC methods is the stratified sampling (e.g., [26,27]) and the application of this technique for the lightning performance assessment of distribution lines has been presented in [28]. The structure of the chapter is the following. Section 1.2 is devoted to the description of the MC approach with particular reference to the random generation of the values of the lightning parameters from a multivariate probability distribution. Section 1.3 describes the identification of the functions that describes the lightning current waveforms. Section 1.4 describes the stratified sampling technique. Section 1.5 illustrates the application of the MC method to the case of a

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Lightning interaction with power systems, volume 2

medium voltage (MV) overheard line in open terrain. As mentioned in the conclusions of the chapter (Section 1.6), the application of the MC method for the lightning performance assessment of lines and networks with realistic configuration will be presented in Chapter 4 of this volume.

1.2 Description of the MC-based procedure As described in detail in what follows, the proposed procedure is based on the application of the MC method and on the calculation of the induced voltages by using the LIOV code. From now on, this procedure will be called LIOV-MC. Such a procedure is defined by the following steps. 1.

2.

A large number of lightning events ntot is randomly generated. Each event is characterized by the parameters that describe the current waveform at the channel base and the coordinates of the stroke location. Only negative downward first strokes are taken into account; the effects of the presence of positive flashes and subsequent strokes in negative flashes on the line lightning performance are assumed negligible.* The stroke locations are assumed to be uniformly distributed within striking area A, having a size large enough to contain the entire line and all the lightning events that could cause voltages larger than the minimum voltage value of interest for the analysis. Typical lightning channel base current waveforms are defined by the following parameters: peak Ip, front time tf, maximum front steepness Sm and wavetail time to half value th. The relevant probability distributions are provided in [29,30].† The correlation between these parameters has been recently reviewed by Rakov et al. in [9]. In particular, in direct current measurements relatively strong correlation is observed between the current rate-of-rise characteristics and current peak. The MC random generation of lightning current parameters is described hereafter. From the total set of events, those relevant to indirect lightning are selected by adopting a lightning incidence model for the line. In [5], it is analyzed the influence of the adoption of different incidence models. For the calculations of this chapter, we have adopted the electro-geometric model suggested in [8].

* Further investigations are needed to include the effects of subsequent return strokes, solving several open issues, such as (i) relationship between the subsequent stroke’s path and that of the first stroke, (ii) correlation between first and subsequent stroke current parameters, and (iii) number of subsequent strokes. † Note that the simpler Anderson equation for the peak current distribution adopted by IEEE Std. [8], follows the trend of the Cigre´ two-line distributions comparatively well [29]. These statistical distributions have been inferred mostly from measurements obtained by using instrumented towers. The measurements at the towers are affected by reflections [56]. Moreover, the current amplitude distributions of the lightning events collected by the towers are biased toward values higher than those of the distributions of the flashes to ground, as analyzed in, e.g., [31,32] and references therein. These aspects will be deliberately disregarded in this chapter.

Application of the Monte Carlo method to lightning protection 3.

4.

5

For each lightning event, the maximum induced voltage value on the line is calculated – as earlier mentioned – by means of the using the LIOV–EMTPRV code [6,13] that is described in Chapter 12 of this volume. For the entire line, the expected annual numbers of events Fp that causes overvoltages with amplitude larger than a given value V is: n ANg (1.1) Fp ¼ ntot where n ¼ ni þ nd , being ni and nd the number of indirect events and direct events, respectively, that generate overvoltages larger than V and Ng is the annual ground flash density. In this study, we assume Ng ¼ 1 flash/km2/yr. The estimation of the mean time between failures (MTBF) expected at specific poles of the line, generally of interest for the protection of the transformers connected to those poles, is calculated as the inverse of the Fp value given by (1.1) with ni and nd evaluated by comparing the overvoltage at the pole with the withstand voltage of the connected transformer.

The application of the MC method requires the knowledge of the multivariate distribution of the lightning current parameters. We reasonably assume that every parameter follows the log-normal probability distribution, as generally done in the literature on the subject. Let x1 ; . . .; xn be n jointly Gaussian random variable. In our case, they are the four natural logarithms of peak amplitude Ip, equivalent front times tf ¼ t30 =0:6 (t30 is the interval from 30% to 90% amplitude intercepts on the wavefront), maximum front steepness Sm, and wavetail time to half value th. The multivariate normal distribution is said to be non-degenerate when the symmetric covariance matrix K is positive definite. In this case, the probability density function is   1 1 T 1 ffi exp  ðx  mÞ K ðx  mÞ f ðx1 ; . . .; xn Þ ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (1.2) 2 ð2pÞn jKj where x is a real n-dimensional column vector, m is the corresponding mean vector, and jKj is the determinant of K. The ijth off-diagonal element of K is given by correlation coefficient rij between xi and xj multiplied by the product of their two corresponding standard deviations (i.e., sxi and sxj), while the iith diagonal element is equal to variance s2xi of random variable xi. Let be Q ¼ K1 , the conditional variance of xn is ðsxn Þ2 ¼ Varðxn jx1 ; . . . ; xn1 Þ ¼

1 Qnn

(1.3)

n1 1 X Qnj ðxj  mj Þ Qnn j¼1

(1.4)

and the conditional mean of xn is mxn ¼ Eðxn jx1 ; . . . ; xn1 Þ ¼ mn 

where Qnj is the njth element of matrix Q.

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Lightning interaction with power systems, volume 2

The MC random generation of a quadruple of lightning current parameters values is obtained by applying the following steps, where Zk ; Zkþ1 ; Zkþ2 ; Zkþ3 are four standard normal variates. Step (1) for the calculation of an Ip value: (1.1) Ip ¼ expðmln Ip þ sln Ip  Zk Þ; Step (2) for the calculation of a tf value: (2.1) sln tf , sln Sm , sln th are calculated by using (1.3); (2.2) mln tf is calculated by using (1.4); (2.3) tf ¼ expðmln tf þ sln tf  Zkþ1 Þ; Step (3) for the calculation of a Sm value: (3.1) mln Sm is calculated by using (1.4); (3.2) Sm ¼ expðmln Sm þ sln Sm  Zkþ2 Þ; Step (4) for the calculation of a th value: (4.1) mln th is calculated by using (1.4); (4.2) th ¼ expðmln th þ sln th  Zkþ3 Þ. A complete set of the data required for the MC generation procedure is provided by Berger and Garbagnati in [30] and is reported in Tables 1.1 and 1.2. For each parameter y, Table 1.1 provides median value y ðmln y ¼ ln y Þ and sln y . Table 1.2 provides correlation coefficients rln y1 ln y2 between parameters y1 and y2. Since these statistical distributions have been inferred mostly from measurements obtained by using instrumented towers, the current amplitude distributions of the lightning events collected by the towers are biased toward values higher than those of the distributions of the flashes to ground, as analyzed in, for example, [31,32] and references therein. This aspect will be deliberately disregarded in this analysis, as earlier mentioned at note.† Table 1.1 Statistical parameters of the log-normal distributions for negative downward first strokes [30] Parameter

Median value

Standard deviation of the parameter logarithm (base 10)

Ip Tcr Sm th

30 kA 5.5 ms 12 kA/ms 75 ms

0.26 0.31 0.26 0.26

Table 1.2 Correlation coefficients between parameters [30] Parameter

Ip

Tcr

Sm

th

Tcr Sm th

0.37 0.36 0.56

1 –0.21 0.33

1 0.1

1

Application of the Monte Carlo method to lightning protection

7

The parameters of the distribution relevant to the front duration Tcr is given instead of the ones relevant to tf. Since [29] provides both the parameters of Tcr (the same as Table 1.1) and of tf (t f ¼ 3:8 ms, sln tf ¼ 0:55) obtained from almost the same set of experimental measurements used in [30], the implemented MC procedure generates the values of Tcr according to step (2). The values relevant to tf are obtained by multiplying each value of Tcr by the ratio between t f and T cr provided by [29]. If a simple current function, that is, a step waveform, a linearly rising current, linearly rising with flat top (trapezoidal) or with drooping tail, is used for the calculation of the maximum overvoltages along the line, the values generated for Ip, tf, and th are directly used. However, for more complex current functions, a specific identification procedure is needed as described in Section 1.3.

1.3 Identification of the lightning current functions As known, the waveform of the return stroke current at the channel base as well at its peak value have a significant influence on the lightning originated overvoltages along the lines. Different functions have been proposed in order to represent the typical lightning current waveform. The most commonly used are: the one adopted by CIGRE WG [29] and the one proposed by Heidler in [33]. Other functions that can be found in the literature are the classical double exponential [34], others derived from it (e.g., [35]), the combination of multiple Heidler functions (e.g., [36]) and more recent ones (e.g., [37]). Functions for multi-peaked waveforms have been also proposed in [38,39]. For a given quadruple of values for Ip, tf, Sm, and th, we describe here the procedures to identify the parameters of the Cigre´ function and of the Heidler function, as presented in [40] that analyzes the effects of different current waveforms on the lightning performance of distribution lines for both direct and indirect strokes. Cigre´ function The current waveform is [29]: iðtÞ ¼ At þ Btn ; t  tn iðtÞ ¼ I1 eðttn Þ=t1  I2 eðttn Þ=t2 ; t > tn

(1.5)

where SN ¼ Sm tf =Ip n ¼ 1 þ 2ðSN  1Þð2 þ 1=SN Þ    tn ¼ 0:6tf 3SN 2 = 1 þ SN 2

  Ip 1 1 0:9 n  Sm Sm tn  0:9Ip A¼ B¼ n n1 tn ðn  1Þ tn t1 ¼ ðth  tn Þ=ln 2 t2 ¼ 0:1Ip =Sm



Ip Ip t1 t2 t1 t2 I1 ¼ Sm þ 0:9 Sm þ 0:9 I2 ¼ t1  t2 t2 t1  t2 t1

(1.6)

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Lightning interaction with power systems, volume 2

This formulation presents some numerical issues if n < 1 or n > 55. In case a MC event presents a value of n out of these bounds, the value of Sm is adjusted as Sm ¼ 1:01Ip =tf

if n < 1

Sm ¼ 12Ip =tf

if n > 55

(1.7)

As this procedure can lead to small errors on the resulting current peak, the current is normalized to the desired peak value. Heidler function The Heidler function is [33]: I0 ðt=t1 ÞN expðt=t2 Þ h 1 þ ðt=t1 ÞN "   # t1 t2 N 1=N h ¼ exp  t1 t2

iðtÞ ¼

(1.8)

It is completely defined by four parameters, that is, I0 ; t1 ; t2 and N , which cannot be fully obtained from the values Ip  , tf  , Sm  , and th  by analytical equations. In [41], an iterative graphical method is presented to identify the parameters as a function of a waveform, while the use of a genetic algorithm (GA) is adopted in, for example, [42,43]. The following procedure based on MATLAB GA function has been developed. The objective of the algorithm determines a set of values I0 ; t1 ; t2 and N such to minimize the following fitness function   Ipc  Ip  þ c2 tfc  tf þ c3 thc  th (1.9) f ¼ c1 t t  Ip  f h where Ipc , tfc , and thc are the peak value, the equivalent front time, and the time to half value of the current calculated at every iteration of the algorithm, respectively. Parameters c1, c2, and c3 are the weights ascribed to the relative errors of the three parameters Ip  , tf  , and th  , respectively. The algorithm is stopped if the relative errors on the three parameters satisfy all the three following conditions   Ipc  Ip  < 0:5%; tfc  tf < 0:5%; thc  th < 1% (1.10) I t t  p f h The possible values of N are limited to the integer values 2, 3, or 4. At first, the values of c1, c2, and c3 are equal to each other. The initial population size and the maximum number of generations are set to 50 and 100, respectively, and they are subsequently enlarged in case any of the conditions of (1.10) is not satisfied. If after some tens of attempts, conditions (1.10) are still not satisfied, the time to half value is penalized by means of a reduction of c3 with respect to c1 and c2. At the end of this procedure, only for 10 out of 20,000 events the constraint on th is not satisfied, while the constraints relevant to peak and equivalent front time are always fulfilled. Table 1.3 compares the expected median value of the parameters with those obtained by 20,000 current waveforms calculated by using Cigre´ function (1.5).

Application of the Monte Carlo method to lightning protection

9

Table 1.3 Median values of the parameters obtained from (1.5) and from the GA compared to the expected values given in [30]

Expected Cigre´ Heidler

Ip (kA)

tf (ms)

Sm (kA/ms)

th (ms)

30.0 30.0 30.0

3.80 3.89 3.81

12.0 13.1 12.0

75.0 74.7 75.4

The small deviations in the Cigre´ model are due to the corrections previously mentioned. Table 1.3 also compares the expected median value of the parameters with those obtained by 20,000 current waveforms calculated by using Heidler function (1.8) with the parameter given by the GA. The mean errors resulting on 20,000 Heidler waveforms are: 0.004% for Ip, 0.17% for tf, and 0.21% for th. Although the Sm is not taken directly into account by the GA, also the relevant median value is in close agreement with the expected one.

1.4 Stratified sampling technique As mentioned in the Introduction, the calculation of the lightning performance of distribution lines considering also indirect strokes is a typical rare event calculation. Indeed, the endpoints of the 95% confidence interval of the estimate b p ¼ n=ntot of (2.1) p where Cp is the relative error that can be evaluated as [26]: are b p  Cp  b sffiffiffiffiffiffiffiffiffiffiffi 1p Cp ¼ 1:96 (1.11) ntot p under the assumption that the estimator b p is a normal random variable with mean value p and variance equal to pð1  pÞ=ntot . As area A needs to be quite wide and the density of events that cause a flashover decreases with the distance from the feeder, p is generally small. Therefore, in a standard MC approach, ntot needs to be large so to achieve the desired level of accuracy (i.e., a predefined value of Cp). As shown in [28], several advantages with respect to the standard MC method are obtained by the use of the stratified sampling technique: ●





it allows a significant computational time reduction (up to more than 75% for the cases analyzed in [28]) while maintaining the accuracy of the solution; it reduces the importance of the choice of the smallest area A that includes the perspective stroke locations of all the events inducing voltages exceeding the insulation withstand capability; it is directly applicable to the case of networks with complex configuration, with surge arresters and with the adoption of detailed flashover models, while heuristic rules need to be adapted for each specific case.

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Lightning interaction with power systems, volume 2

According to this technique, area A is divided in subdomains. The number of events generated in each subdomain is proportional to the variance of the local estimator that is recursively updated. Therefore, the larger the distance to the lines or the shorter the distance to surge arresters, the lower the number of events in the specific subdomain. Let us define X as a random variable such that Xk ¼ 1 if MC event k causes an overvoltage greater than W, 0 if not. As in standard MC methods, the probability p of observing an overvoltage greater than W is estimated by b p¼

ntot n 1 X ¼ Xk ntot ntot k¼1

(1.12)

and the perspective stroke locations of the events in the absence of the power lines and other structures are assumed to be uniformly distributed over area A. As already mentioned, for the application of stratified sampling, total area A is divided in m subdomains and probability p is estimated by ! Nj m X aj 1 X b (1.13) Xjk J¼ A Nj k¼1 j¼1 where aj is the area of Psubdomain j, Nj is the number of MC events allocated in subdomain j such that m j¼1 Nj ¼ ntot , and Xjk is the k-th observation of X in domain j. b is given by As shown in [27], the variance of estimator J b ¼ VarðJÞ

m 2 s2 X aj j j¼1

A

Nj

(1.14)

b is always smaller or where s2j is conditional variance of X in domain j. VarðJÞ equal to VarðX Þ=ntot . Since the values of s2j are not known a priori, they are initially estimated by a certain number of pilot runs, that is, by the simulation of some MC events. For this purpose, the same number Njs of starting events is generated in each sub-domain, with Njs chosen large enough to estimate s2j even with a very small probability p, for example, in presence of surge arresters (SAs). In order to obtain a near-random sample distribution for both the parameters of the lightning current waveshape and the stroke location with a limited Njs , the starting events in each subdomain j are generated by using the Latin hypercube sampling (LHS) [44]. The use of LHS allows an improved accuracy on the initial estimation of s2j with respect to the usual random sampling. b are J b  CJ  J b The endpoints of the 95% confidence interval of the estimate J where CJ is the relative error provided by vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uX m 2 s2 aj 1:96u j t CJ ¼ (1.15) b A N j J j¼1

Application of the Monte Carlo method to lightning protection

11

Starting from the initial value of s2j , the procedure adds new MC events until CJ becomes lower than the desired estimation error. Each new MC event is allocated in the area A according to a weighted uniform distribution with different weights for each subdomain. The weight of each subdomain j is proportional to the corresponding conditional variance s2j and the sum of the weights of all the m subdomains is equal to 1. Indeed, the minimum variance value given by (1.14) is obtained when the events are allocated proportionally to the conditional variance s2j of each subdomain, provided that all subdomains have the same area [27]. If a too small Njs is adopted, a null value can be obtained in the first estimate of 2 sj , in this case the initial guess of the weight of the subdomain can be set according to the mean values of the variances of the adjacent subdomains. The values of s2j are updated recursively after each MC run, so that their estimation is progressively improved as the number of simulated events increases.

1.5 Application results for a MV overhead line in open terrain 1.5.1 Influence of the return stroke current waveform In order to illustrate the application of the MC method, we consider here a simple three-phase overhead line, straight in shape. The conductors are assumed horizontally placed at 9.3 m above ground, with diameter equal to 1 cm. The distances between the lateral conductors and the central one are 1.5 and 0.7 m. In all the calculations of this section, we have assumed the soil conductivity equal to 1 mS/m. The striking area A is chosen as a 1-km band from the line. The number of lightning events n is 20,000. Direct events nd are 1,208. Indirect events nd are 18,792. Figure 1.1 shows the annual number of overvoltages of the line with length equal to 2 km for the three different current waveforms adopted caused by indirect events only. Such a result is here denoted as the perspective lightning performance of the distribution line, as the calculations are run in absence of surge arresters and by neglecting the flashovers along the line. The steady state voltage at the utility frequency is not taken into account in the calculations. Figure 1.1 shows that the choice of different current waveforms has a limited impact on the estimation of the perspective lightning performance. It is worth mentioning that the lowest curve is obtained by using the Heidler function. Without surge arresters and flashovers, all direct events result in overvoltages larger than the maximum value in abscissa (i.e., 0.24 events/year for the case of the 2-km long line), as expected, since all the Ip of the MC generated events are greater than 2 kA. Indeed, the peak current values included in the Berger-Garbagnati distribution are all above 2 kA (i.e., 2 or 3 kA was the triggering level of the Italian measuring stations, while the minimum peak current value included in Berger’s distribution is 2 kA).

Lightning interaction with power systems, volume 2

Number of events having amplitude larger than the abscissa/yr

12

Trapz Cigré Heidler 100

10–1

100

150

200 250 Voltage (kV)

300

350

Figure 1.1 Comparison of the perspective indirect lightning performances calculated by using three different current waveforms. Length of the line equal to 2 km. Adapted from [40]

Let us now consider the same three-conductor line but with sets of three surge arresters installed at different distance intervals. The voltage–current characteristic of the adopted 15-kV class surge arresters is the one reported in [45]. The considered rated voltage at the utility frequency is 13.8 kV. The distance between subsequent poles is 50 m. The parameters of the disruptive effect criterion (adopted for the representation of the flashovers in the line insulators) are reported in Table 1.4. These parameters have been obtained in [46] from the results of laboratory tests performed on a 15 kV pin-type ceramic insulator. We assume the presence of a transformer at the middle point of the line. The withstand voltage of the transformer is assumed to be constant and equal to 110 kV, as suggested in [47].‡ In [48], a procedure able to take into account the withstand probability distribution of transformer insulation is described. Figure 1.2 shows the top view of the line; the position of the transformer is denoted by the cross in the middle of the line while the circles indicate the surge arrester locations. Distance d defines the interval between consecutive surge arresters. The length of the line is 2 km and the number of generated events in the MC procedure is again 20,000. Tables 1.5 and 1.6 show the MTBF values relevant to a transformer connected to the middle of the line for the two different insulators described in Table 1.4, corresponding to a critical flashover voltage (CFO) of

‡ In the computation of the MTBF values, the transformer failure is expected to occur if the voltage amplitude exceeds the withstand voltage of the transformers even for a very short time interval.

Application of the Monte Carlo method to lightning protection

13

Table 1.4 Parameters assumed for the disruptive effect model DE model parameters CFO (kV)

V0 (kV)

k

DE (kVms)

100 165

90 132

1 1

60.9 255

d

2,000 m

Figure 1.2 Top view of the line with the indication of the observation point in the middle of the line and the position of the SAs 165 and 100 kV, respectively. The results are reported for the three different current waveforms and for different distances d between consecutive SAs, namely 100, 200, 300, and 400 m. The comparison between Tables 1.5 and 1.6 shows that with SAs at d ¼ 200 m and above, the MTBF values calculated for insulator CFO ¼ 165 kV are higher than those calculated for CFO ¼ 100 kV, while the opposite happens without SAs or with d ¼ 100 m. Such a difference is due to additional flashovers near the transformer for the case of 100 kV CFO insulators with respect to the case with 165 kV CFO insulators. The oscillatory transients originated by these flashovers and by the associated reflections at the surrounding SAs may cause voltages, at the transformer location, with peak value higher than without flashovers. These overvoltages are not limited by the nearby SAs if the distance between them is significant, namely d ¼ 200 m and above. A similar unfavorable effect of large separating distances between SAs has been already observed and discussed in [49]. The adoption of a different current waveform generally results in slight differences between the MTBF values. The larger differences – concerning the direct events only – appear to be those relevant to the case with d ¼ 100 m and CFO ¼ 165 kV, for which the adoption of the Heidler and the Cigre´ turn out in an 8% increase of the MTBF. By increasing the distance between SAs, these differences tend to be negligible. Concerning the indirect events only, the differences are negligible for the cases of d ¼ 100 m and d ¼ 200 m due to the very low probability of exceeding the withstand voltage of the transformer. The differences turn out to be appreciable, instead, by increasing d, while again they are negligible if the line is unprotected. These variations in the results are ascribed to the effect of nonlinearity introduced by SAs and flashover model that enhance the effect of the difference among the chosen current waveforms and in particular of their front. The computational cost due to the assumption of more realistic current waveforms rather than the trapezoidal one is quite heavy. The time required to obtain the results of both Tables 1.5 and 1.6 of this volume relevant to indirect

Trapezoidal Cigre´ Heidler

Current waveform d ¼ 100 m

d ¼ 200 m

With SA d ¼ 300 m

d ¼ 400 m

4.3 4.3 4.3

2.8 2.9 2.9

1.7 1.7 1.7

22.3 23.9 23.9

Inf Inf Inf

22.3 23.9 23.9

11.5 12.1 11.8

333 294 263

11.1 11.6 11.3

7.7 8.4 8.2

89.3 82.0 86.2

7.1 7.6 7.5

5.7 6.1 6.0

41.3 36.5 38.5

5.0 5.2 5.2

Direct Indirect Both Direct Indirect Both Direct Indirect Both Direct Indirect Both Direct Indirect Both

Without SA

Table 1.5 MTBF (in years) at midpoint of the line for different distances between consecutive surge arresters, withstand voltage of 110 kV. CFO of the insulators ¼ 165 kV

Trapezoidal Cigre´ Heidler

Current waveform d ¼ 100 m

d ¼ 200 m

With SA d ¼ 300 m

d ¼ 400 m

4.3 4.3 4.3

3.2 3.2 3.3

1.8 1.8 1.9

25.3 25.8 26.9

Inf Inf Inf

25.3 25.8 26.9

9.9 10.8 10.5

250 238 227

9.6 10.4 10.0

6.9 7.2 7.1

87.7 79.4 80.6

6.4 6.6 6.5

5.2 5.5 5.4

39.7 35.5 36.5

4.6 4.7 4.7

Direct Indirect Both Direct Indirect Both Direct Indirect Both Direct Indirect Both Direct Indirect Both

Without SA

Table 1.6 MTBF (in years) at midpoint of the line for different distances between consecutive surge arresters, withstand voltage of 110 kV. CFO of the insulators ¼ 100 kV

16

Lightning interaction with power systems, volume 2

strikes for the case of trapezoidal current waveform is about 8 h and about twice the time for the two other currents waveforms (almost all the computational effort is required by the calculation of the lightning electromagnetic pulse (LEMP), which is performed only once for each MC event and then used for all the different SA configurations and insulator types).

1.5.2

Application of the recursive stratified sampling technique

In this section, the earlier illustrated recursive stratified sampling procedure is applied to the case of a single-conductor straight line, assuming a withstand voltage value W equal to 150 kV. The line is 2 km long, 10 m high, and is matched at both terminations with the matrix of surge impedances to render more straightforward the interpretation of the results. In the simulations of this section, a linearly rising current with flat top is assumed for the representation of the channel base lightning-current waveform, with peak amplitude Ip and equivalent front time tf . The return-stroke propagation speed is set to 1.5  108 m/s. The lightning performance is evaluated for overhead lines above a soil with conductivity equal to 0.001 S/m and relative permittivity equal to 10. In Figure 1.3, the top view of one half of the considered area A is reported (the line is located on the x-axis and the distribution of the stroke locations is 2,000 1,800 1,600 1,400

m

1,200 1,000 800 600 400 200 0 –1,000 –800 –600 –400 –200

0 m

200

400

600

800 1,000

Figure 1.3 Position of the events generated by the stratified sampling procedure for the case of an unprotected line (direct strikes in red, nearby strikes to ground in blue). Adapted from [28]

Application of the Monte Carlo method to lightning protection

17

obviously symmetric with respect to the line). The figure shows also the stroke locations of all the simulated events, that is, the initial pilot events and those generated by the stratified sampling procedure. The red dots represent direct strikes to the line while the nearby strikes to ground are indicated in blue. For the considered case, the semi-area is a 2  2 km2, divided in m ¼ 400 subdomains of area 0.1  0.1 km. The number of pilot events simulated before starting the stratification procedure is 5,200. The stratified sampling calculation is stopped when relative error CJ reaches the same value of Cp calculated with the standard MC method with 100,000 events for W ¼ 150 kV. The total number of events generated by the stratified sampling procedure are 3,464 direct strikes and 23,093 nearby strikes, as reported in Table 1.7 of this volume. Since only the evaluation of the voltages induced by nearby strikes needs time domain LIOV–EMTP-RV simulations, the computational time reduction   indicated in Table 1.7 of this volume is estimated as 100 nind;p  nind;J =nind;p , where nind,J is the number of events required by the stratified sampling and nind,p is the corresponding number calculated in the standard MC. As shown by Figure 1.3, the procedure allocates the majority of the events in the subdomains closest to the line. A very few events are allocated farther than 1.2 km from the line, since the initial variance in those subdomains is null. In order to limit the computational time of the standard MC procedure, the smallest area A that includes all the dangerous events is to be chosen, as discussed in [5]. The capability of the stratified sampling to recursively allocate the events in the subdomains with the largest variance value reduces the importance of an accurate choice of the smallest area A. Figure 1.3 also shows that fewer events are allocated near the matched terminations with respect to the subdomains close to the internal part of the line, due to the risers effect that reduce the induced overvoltages [50]. The above-described assessment has been repeated for the case of a line protected with SAs. Two cases are considered with SAs placed every d ¼ 500 m and d ¼ 200 m, respectively, starting from the line terminations. The line terminations are open. The voltage–current characteristic of the considered SAs is the same used in [51]. Table 1.7 Comparison between number of direct and nearby strikes in the standard MC and stratified sampling. Computational time reduction due to stratified sampling

Unprotected With SAs d ¼ 500 m With SAs d ¼ 200 m

Relative error %

Direct strikes Standard/ stratified

Nearby strikes Standard/ stratified

Time saved %

2.4 2.8 10.7

3,103/3,464 12,166/12,095 24,665/18,687

96,897/23,093 187,834/42,455 175,335/50,163

76 77 71

18

Lightning interaction with power systems, volume 2

For the case of SAs placed every d ¼ 500 m, the semi-area is a 2  1 km rectangle, divided in m ¼ 20  10 subdomains of area 0.1  0.1 km. For the case of d ¼ 200 m, the semi-area is a 2  0.5 km rectangle, divided in m ¼ 20  20 subdomains of area 0.1  0.025 km. In both cases, the number of pilot runs before starting the stratified sampling procedure is 20,000. The stratified sampling procedure is stopped when the relative error reaches that achieved by the standard MC with 200,000 events for W ¼ 150 kV. As shown in Table 1.7, the accurate assessment of the performance of a line with SAs requires a very large value of ntot since, with respect to the case of an unprotected line, the overvoltage becomes a rare event. Indeed, even with 200,000 events the standard MC procedure does not reach a relative error below 10% in the case of SAs installed every 200 m. Figure 1.4 shows the position of the simulated lightning events shown for the case of SAs placed every 500 m. In subdomains close to a SA, the values of s2j are very small; therefore, the procedure tends to allocate few events in such subdomains while a large number of events is generated in subdomains between two consecutive SAs, where the values of s2j are higher. The presence of SAs considerably reduces the number of dangerous events at distances larger than few hundred meters, as confirmed by Figure 1.4. This justifies the choice of a smaller area with respect to the case of an unprotected line. The reduction of the considered area, however, results in an increase of the fraction of direct events, as it can be noticed from the results shown in Figure 1.4 and in Table 1.7, particularly for the case with SAs placed at d ¼ 200 m. Figure 1.5 shows the lightning performance for the case of the unprotected line and of the line protected by SAs placed at d ¼ 500 m and d ¼ 200 m. For each curve, the results are obtained for the same MC event population generated assuming W ¼ 150 kV. By using both the standard MC and the stratified sampling

1,000 800

m

600 400 200 0 0

200

400

600

800 1,000 1,200 1,400 1,600 1,800 2,000 m

Figure 1.4 Position of the events generated by the stratified sampling procedure for the case of a line with consecutive SAs at distance d ¼ 500 m (direct strikes in red, nearby events to ground in blue). Adapted from [28]

Application of the Monte Carlo method to lightning protection

19

101

Number of events having amplitude larger than the abscissa/yr

Standard MC Stratified sampling

100 Unprotected

10–1

With SAs d = 500 m

10–2

10–3 50

With SAs d = 200 m

100

150

200

250

300

Voltage (kV)

Figure 1.5 Comparison of the lightning performance of a line without SAs and with SAs calculated by the standard MC and stratified sampling. Adapted from [28] procedure, the Fp values at 150 kV are: 0.489 (unprotected), 0.100 (with SAs at d ¼ 500 m), and 0.003 (with SAs at d ¼ 200 m). Figure 1.5 shows that the curves resulting from the application of the stratified sampling are all in close agreement with the results of the standard MC method, for all the withstand values considered in the abscissa. Figure 1.6 compares the values of Cp and CJ for different values of ntot (which accounts for both indirect and direct events). As expected, the value of CJ is always lower or equal than Cp for the same value of ntot. Moreover, the figure shows that the use of the stratified sampling allows a fast reduction of the relative error as the number of MC events increases. As already shown in Table 1.7 of this volume, the same value of relative error achieved with the standard MC with ntot ¼ 100,000 for the unprotected line and ntot ¼ 200,000 with SAs are obtained by the stratified sampling with ntot ¼ 26,557 (unprotected line), ntot ¼ 54,550 (with SAs located every 500 m), and ntot ¼ 68,850 (with SAs located every 200 m). Figure 1.7 compares the values of Cp and CJ as a function of the considered withstand voltage level for the case without SAs for the case of the unprotected line. As the stratified sampling event population is generated assuming W ¼ 150 kV, CJ is higher than Cp for voltages lower than W and its value practically remains constant. This provides a criterion for the choice of W, unless the withstand voltage of the line is already defined. For all the voltages equal to or higher than 150 kV, instead, the relative error CJ is always very similar (and even smaller) than Cp. Additionally, as expected, it is significantly lower than the relative error values obtained by using the 5,200 pilot runs only.

20

Lightning interaction with power systems, volume 2 100

Standard MC Stratified sampling

Relative error

With SAs d = 200 m

10–1

With SAs d = 500 m

Unprotected

10–2 103

104

26,557 Number of events

105 54,550 68,850

2 × 105

Figure 1.6 Comparison of the relative errors calculated for a straight line by the standard MC and stratified sampling as a function of the number of MC events for W ¼ 150 kV. Adapted from [28]

100

Relative error

Standard MC Stratified sampling Standard MC (pilot runs) 10–1

10–2

10–3 50

100

150

200

250

300

Voltage (kV)

Figure 1.7 Comparison of the relative errors of an unprotected straight line calculated by the standard MC (full and limited to the pilot runs only) and the stratified sampling as a function of the withstand voltage. Adapted from [28]

Application of the Monte Carlo method to lightning protection

21

Also in presence of SAs and for the configuration with laterals illustrated in [28], results similar to those of Figure 1.7 have been obtained. The proposed stratified sampling method can be easily extended to the case in which the insulation breakdown is represented by means of a specific model, for example, the disruptive effect criterion [46,52,53]. The method is applicable also to more complex coupling models, for example, the approach proposed in [54], based on the use of the finite element method model presented in [55] that allows accounting the shielding and LEMP attenuation effects provided by surrounding buildings.

1.6 Conclusions This chapter has described the use of the MC method for the lightning performance assessment of MV distribution lines. For this type of lines, it is important to take into account both direct and indirect strikes (while for transmission lines, the induced effects can be in general disregarded). In order to take into account the effect of indirect lightning, we need to consider all the events with a stroke location in an area around the line wide enough to include all the strikes that could provide dangerous-induced voltages. Therefore, the chapter illustrated also the application of the stratified sampling method able to reduce the computational effort without scarifying the accuracy. The application to more complex and realistic line configurations will be presented in Chapter 4 of this volume.

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devices due to nearby lightning flashes’. IEEE Trans Power Deliv. 2016; 31(2):596–604. Bendato I., Brignone M., Delfino F., Procopio R., and Rachidi F. ‘A methodology to reduce the computational effort in the evaluation of the lightning performance of distribution networks’. Atmosphere (Basel). 2016;7(11):147. Borghetti A., Nucci CA., and Paolone M. ‘Indirect-lightning performance of overhead distribution networks with complex topology’. IEEE Trans Power Deliv. 2009;24(4):2206–2213. Borghetti A., Dos Santos GJG., Fagundes DR., et al. ‘Indirect lightning performance of a real distribution network with focus on transformer protection’. 32nd International Conference on Lightning Protection. Shanghai, China; 2014. Napolitano F., Tossani F., Borghetti A., et al. ‘Lightning performance of a real distribution network with focus on transformer protection’. Electr Power Syst Res. 2016;139:60–67. Rubino G., and Tuffin B. Rare Event Simulation Using Monte Carlo Methods. Wiley; 2009. Brandimarte P. Handbook in Monte Carlo Simulation: Applications in Financial Engineering, Risk Management, and Economics. Wiley; 2014. Napolitano F., Tossani F., Borghetti A., and Nucci CA. ‘Lightning performance assessment of power distribution lines by means of stratified sampling Monte Carlo method’. IEEE Trans Power Deliv. 2018;33(5):2571–2577. Cigre´ Working Group 33.01. Guide to Procedures for Estimating the Lightning Performance of Transmission Lines (TB 63). Paris: CIGRE; 1991. Berger K., and Garbagnati E. ‘Lightning current parameters. Results obtained in Switzerland and in Italy’. Proc. URSI Conference. Florence, Italy; 1984. Mousa AM., and Srivastava KD. ‘The implications of the electrogeometric model regarding effect of height of structure on the median amplitude of collected lightning strokes’. IEEE Trans Power Deliv. 1989;4(2):1450–1460. Borghetti A., Nucci CA., and Paolone M. ‘Estimation of the statistical distributions of lightning current parameters at ground level from the data recorded by instrumented towers’. IEEE Trans Power Deliv. 2004;19(3): 1400–1409. Heidler F. ‘Analytische blitzstromfunktion zur LEMP-berechnung’. Proc. 18th Int. Conf. Lightning Protection. Munich, Germany; 1985. Bruce CER., and Golde RH. ‘The lightning discharge’. J Inst Electr Eng. 1941;88:487–505. Jones RD. ‘On the use of tailored return-stroke current representations to simplify the analysis of lightning effects on systems’. IEEE Trans Electromagn Compat. 1977;EMC-19(2):95–96. Nucci CA., and Rachidi F. ‘Experimental validation of a modification to the transmission line model for LEMP calculations’. Proc. 8th International Symposium on Electromagnetic Compatibility. Zurich, Switzerland; 1989: 389–394.

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Javor V., and Rancic PD. ‘A channel-base current function for lightning returnstroke modeling’. IEEE Trans Electromagn Compat. 2011;53(1):245–249. De Conti A., and Visacro S. ‘Analytical representation of single- and doublepeaked lightning current waveforms’. IEEE Trans Electromagn Compat. 2007;49(2):448–451. Javor V. ‘Multi-peaked functions for representation of lightning channelbase currents’. Proc. 31st International Conference on Lightning Protection. ICLP; 2012. Borghetti A., Napolitano F., Nucci CA., and Tossani F. ‘Influence of the return stroke current waveform on the lightning performance of distribution lines’. IEEE Trans Power Deliv. 2017;32(4). Heidler F., Cvetic JM., and Stanic BV. ‘Calculation of lightning current parameters’. IEEE Trans Power Deliv. 1999;14(2):399–404. Chandrasekaran K., and Punekar GS. ‘Use of genetic algorithm to determine lightning channel-base current-function parameters’. IEEE Trans Electromagn Compat. 2014;56(1):235–238. Bermudez JL., Pena-Reyes CA., Rachidi F., and Heidler F. ‘Use of genetic algorithms to extract primary lightning current parameters’. Proc. of EMC Europe 2002. International Symposium on Electromagnetic Compatibility; 2002. Zio E. The Monte Carlo Simulation Method for System Reliability and Risk Analysis. Springer; 2014. Borghetti A., Napolitano F., Nucci CA., and Tossani F. ‘Influence of the return stroke current waveform on the lightning performance of distribution lines’. IEEE Trans Power Deliv. 2016;32(4):1. De Conti A., Perez E., Soto E., Silveira FH., Visacro SS., and Torres H. ‘Calculation of lightning-induced voltages on overhead distribution lines including insulation breakdown’. IEEE Trans Power Deliv. 2010;25(4): 3078–3084. ‘IEEE standard for insulation coordination - Definitions, principles, and rules’. IEEE Std C62821-2010 (Revision IEEE Std 13131-1996). April 2011:1–22. Lopes GP., Martinez MLB., Borghetti A., et al. ‘A procedure to evaluate the risk of failure of distribution transformers insulation due to lightning induced voltages’. Proc. 22nd International Conference and Exhibition on Electricity Distribution (CIRED); 2013:1484–1484. Paolone M., Nucci CA., Petrache E., and Rachidi F. ‘Mitigation of lightninginduced overvoltages in medium voltage distribution lines by means of periodical grounding of shielding wires and of surge arresters: modeling and experimental validation’. IEEE Trans Power Deliv. 2004;19(1):423–431. Nucci CA., Rachidi F., Ianoz M., and Mazzetti C. ‘Lightning-induced voltages on overhead lines’. IEEE Trans Electromagn Compat. 1993;35(1):75–86. Tossani F., Napolitano F., Borghetti A., et al. ‘Estimation of the influence of direct strokes on the lightning performance of overhead distribution lines’. 2015 IEEE PowerTech Conference. Eindhoven; 2015.

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Application of the Monte Carlo method to lightning protection

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[52] Darveniza M., and Vlastos AE. ‘The generalized integration method for predicting impulse volt-time characteristics for non-standard wave shapes A theoretical basis’. IEEE Trans Electr Insul. 1988;23(3):373–381. [53] Borghetti A., Napolitano F., Nucci CA., and Tossani F. ‘Response of distribution networks to direct and indirect lightning: Influence of surge arresters location, flashover occurrence and environmental shielding’. Electr Power Syst Res. 2017;153:73–81. [54] Tossani F., Borghetti A., Napolitano F., Piantini A., and Nucci CA. ‘Lightning performance of overhead power distribution lines in urban areas’. IEEE Trans Power Deliv. 2017;33(2):581–588. [55] Borghetti A., Napolitano F., Nucci CA., and Paolone M. ‘Effects of nearby buildings on lightning induced voltages on overhead power distribution lines’. Electr Power Syst Res. 2013;94:38–45. [56] Guerrieri S., Nucci CA., Rachidi F., and Rubinstein M. ‘On the influence of elevated strike objects on directly measured and indirectly estimated lightning currents’. IEEE Trans Power Deliv. 1998;13(4):1543–1551.

Chapter 2

Lightning interaction with power substations Shigemitsu Okabe1

This chapter presents the influence of lightning on the insulation performance of substation equipment. First, in Section 2.1, the lightning surge analysis including reliability evaluation is positioned in the insulation coordination procedure. As an introductory section of the following ones, the lightning surge analyses are classified in terms of treatment of statistics and calculation tools. Next, in Section 2.2, as a representative example of a simplified statistical approach, the International Electrotechnical Commission (IEC) method is introduced, which calculates simply a lightning surge overvoltage in shielding failure and in back flashovers based on the limit distance, the distance between a surge arrester and protected equipment, the number of connected overhead lines and damping by corona effects. Then, Section 2.3 refers to a detailed lightning surge analysis, taking the ultra-high-voltage (UHV) case carried out by Tokyo Electric Power Company, Inc., Japan, as a decisive approach. Lightning surge analyses for back flashover are dealt with especially from the viewpoint of insulation design of electric power facilities considering the special conditions peculiar to the UHV class. Finally, Section 2.4 evaluates the failure rates of gas insulated switchgear and transformers with changing parameter values of the lightning current crest value and the front time. Together with the probability distribution of the lightning current, failure rates caused by back flashover are comprehensively evaluated.

2.1 Fundamental concepts 2.1.1 Definition and procedure of insulation coordination Studies have been conducted on the insulation coordination of power facilities, such as power transmission lines and substations since electric power systems were initially built, and it is more than 70 years since the basic concept of insulation coordination and the original form of study procedures thereof were established [1]. During this period, insulation coordination techniques have continually progressed, alongside significant progress in relevant technologies and other aspects, such as overvoltage analysis [2], field observation data accumulation and analysis [3],

1

Tokyo Electric Power Company Holdings, Yokohama, Kanagawa, Japan

28

Lightning interaction with power systems, volume 2

equipment insulating characteristics data [4,5] and reliability evaluation and equipment design. As ultra-high-voltage (UHV) systems have increasingly been planned and constructed in recent years, more rationalized insulation coordination is required [6]. To this end, making large-scale field observations and introducing new analysis techniques have enabled the development of advanced technologies capable of transforming conventional techniques. Back to the original concept of insulation coordination, IEC [7] defines it as ‘selection of the dielectric strength of equipment in relation to the operating voltages and overvoltages which can appear on the system for which the equipment is intended and taking into account the service environment and the characteristics of the available preventing and protective devices’, and gives the procedure for insulation coordination. The final objects of insulation coordination consist of the selection of the standard rated withstand voltages (Uw) together with a corresponding set of highest voltage for the equipment (Um), which characterize the insulation of the equipment needed for the application. This procedure is outlined in Figure 2.1. The optimization of the selected set of Uw may require repetition of part of the procedure with careful re-examination of some input data. The rated withstand voltages shall be selected from the lists of standard rated withstand voltages. The set of selected standard voltages constitutes a rated insulation level. For reference, ‘lightning impulse withstand voltage (LIWV)’ is summarized by voltage class in Table 2.1 [7].

2.1.2

Lightning overvoltage in insulation coordination

As can be seen in Figure 2.1, a lightning overvoltage, and consequently lightning surge analysis, hold an important position in the insulation coordination procedure. Lightning overvoltages are primarily caused by back flashovers, and then by direct strokes to the phase conductors. The representative shape of the lightning overvoltage is the standard lightning impulse (1.2/50 ms) [8]. The representative amplitude is either given deterministically as an assumed maximum or statically by a probability distribution of peak values.

2.1.2.1

Lightning overvoltages in substations

The lightning overvoltages and their rates of occurrence in substations are dependent on ●

● ● ●

the lightning performance and the number of lines of the overhead lines connected to them the substation layout and size the number, layout and performance of surge arresters the instantaneous value of the operating voltage

The severity of lightning overvoltages for the substation equipment is determined from the combination of these factors above, and several steps are necessary to assure adequate protection. The amplitudes of the overvoltages are usually higher to base insulation coordination on these values, particularly on the cases without enough limitation of surge arresters. In another case, however, in particular with cable-connected

Lightning interaction with power substations Origin and classification of stressing voltages Protective level of overvoltage limiting devices Insulation characteristics

29

System analysis

Representative voltages and overvoltages Urp

Insulation characteristics Performance criterion Statistical distribution Inaccuracy of input data

Selection of the insulation meeting the performance criterion

Coordination withstand voltages Ucw Altitude correction factors Ka (or atmospheric correction factors Kt) Effects combined in a safety factor Ks Equipment test assembly Dispersion in production Quality of installation Ageing in service

Application of factors to account for the differences between type test conditions and actual service conditions

Required withstand voltages Urw

Test conditions Test conversion factor Ktc Standard withstand voltages Ranges of Um

Selection of rated withstand voltages or standard rated withstand voltages Uw from the lists

Rated or standard insulation level: set of Uw NOTE: In brackets the subclauses reporting the definition of the term or the description of the action. Sided boxes refer to required input Sided boxes refer to performed actions Sided boxes refer to obtained results

Figure 2.1 Procedure for insulation coordination

substations, the self-protection provided by the low surge impedance of the cables may reduce the amplitudes of the lightning overvoltages to suitably low values. For the phase-to-phase and the longitudinal insulation, the instantaneous power frequency voltage value on the opposite terminals shall be considered. Lightning overvoltages caused by back flashovers are dominant among lightning overvoltages and back flashovers are most likely to occur on the phase which has the highest instantaneous power-frequency voltage value of opposite polarity. This means that the representative longitudinal lightning overvoltage shall be equal to the sum of the representative lightning overvoltage to earth at one terminal and of the

30

Lightning interaction with power systems, volume 2 Table 2.1 Standard rated lightning impulse withstand voltage Highest voltage for equipment Um [kV (rms value)]

Standard rated lightning impulse withstand voltage [kV (peak value)]

3.6 7.2 12 17.5 24 36 52 72.5 100 123 145 170 245 300 362 420 550 800 1,100 1,200

20, 40 40, 60 60, 75, 95 75, 95 95, 125, 145 145, 170 250 325 (380), 450 (450), 550 (450), 550, 650 (550), 650, 750 (650), (750), 850, 950, 1,050 850, 950, 1,050 950, 1,050, 1,175 1,050, 1,175, 1,300, 1,425 1,175, 1,300, 1,425, 1,550 1,675, 1,800, 1,950, 2,100 1,950, 2,100, 2,250, 2,400, 2,550 2,100, 2,250, 2,400, 2,550, 2,700

operating voltage peak at the other. Regarding direct lightning overvoltages, shielding failures occur randomly on the power-frequency wave. The effect of the power-frequency at the opposite terminal of a longitudinal insulation has to be taken into account.

2.1.2.2

Protection by surge arrester towards lightning overvoltages

The protection performance given by surge arresters towards lightning overvoltages depends on ● ● ● ●



the amplitude and wave shape of the overvoltage the protection characteristic of the surge arrester the surge impedance and/or capacitance of the protected equipment the distance between arrester and protected equipment including grounding connections the number and surge impedance of the connected lines

When currents through the arrester are expected to be higher than its nominal discharge current (e.g. 5–10 kA in lower voltage classes and 10–20 kA in higher voltage classes), it shall be verified that the corresponding residual voltages still provide a suitable overvoltage limitation.

Lightning interaction with power substations

31

For the determination of the energy absorption of surge arresters installed in a substation, it may be normally sufficient to suppose that the representative amplitude of the prospective lightning overvoltage may be equal to the negative 50% LIWV of the overhead line. However, for the total energy absorption, one should consider the possibility that a lightning flash may be formed by multiple strokes. The protection characteristics of a surge arrester work as they do only at its location. Therefore, corresponding overvoltage limitation at the equipment location should consider the separation between the two locations. As the separation distance of the surge arrester from the protected equipment becomes larger, its protection efficient for this equipment is less and, in fact, the overvoltage applied to the equipment can increase above the protection level of the arrester with increasing separation distance. Furthermore, if the determination of its protection characteristics neglects the effect due to the length of the arrester, this length shall be added to the length of the connecting leads. For metal-oxide arresters without gaps, the reaction time of the material itself may be neglected and the arrester length can be added to the connection leads [9].

2.1.2.3 Limitation by design of overhead lines Lightning overvoltage occurrences can be limited by appropriate design of the overhead lines [10–12]. Effective possible countermeasures in designing for the limitation of lightning overvoltage occurrences are as follows: ●





for direct lightning strokes to conductors (shielding failure): appropriate earthwire shielding design for back flashovers: reduction of the tower footing grounding impedance or addition of insulation usage of line surge arresters

In some cases, earthed crossarms or spark gaps have been used close to substations in an attempt to limit the amplitude of incoming lightning overvoltages. Such countermeasures, however, tend to increase the likelihood of flashovers near the station. Furthermore, especially near the station, special attention should be given to shielding and tower grounding to lower the probability of back flashovers. Since transmission towers in higher voltage classes are taller and interphase distances are longer, direct lightning strokes to phase conductors should be a matter of some concern even though a grounding wire is equipped, especially equal to and above 550 kV systems [10].

2.1.3 Lightning surge analysis Approaches to perform lightning surge analysis may be classified according to the following two criteria: ●



use or not of digital simulation techniques with an electromagnetic transient programme (‘detailed’ or ‘simplified’) application or not of a statistical approach (‘statistical’ or ‘deterministic’)

32

Lightning interaction with power systems, volume 2 The following is a brief description of these approaches.

1.

2.

3.

4.

5.

Statistical method This method presents an estimation of the risk of failure of equipment in a system taking into account all the possible configurations and other conditions of the system including line diagram, layout, surge arrester, lightning stroke current conditions and so on. Semi-statistical method This method gives an estimation of the risk of failure of equipment in a system with only a specifically predetermined configuration. An electrogeometric model is used to evaluate the lightning incidence on the aerial part of the system, and an electromagnetic transient programme is used to evaluate the overvoltages generated by the lightning strokes on substation equipment. Deterministic approach From experience, the minimum value of lightning current at a specific point of impact has been determined, which produces (minimum) overvoltages that the equipment has to withstand. This is called the representative lightning stroke current and it usually depends on the system voltage and the type of equipment considered. In this regard, the deterministic method substantially includes statistical concept through reliability evaluation. Simplified statistical approach The method consists in: i. calculating a lightning current with the supposed return rate using lightning data and the shielding failure rate and/or the back flashover rate within the limit distance, whether shielding failure or back flashovers are considered ii. calculating the amplitude of the invading lightning surge at substation based on several simplified assumptions iii. using the invading surge voltage evaluated previously to perform a travelling wave circuit calculation within the substation IEC proposes a complete analytical approach with the assumption that the configuration of the substation is very simple, a surge arrester is installed only at the substation entrance and the overvoltage at a tower is generated by the tower footing resistance, neglecting further increase due to the tower surge impedance. This IEC method [1] is as a typical example of ‘a simplified statistical approach’ introduced just below in Section 2.2. Detailed deterministic approach With progress of computer capability, the use of an electromagnetic transient programme allows a more accurate estimation of the overvoltages. For this reason, the methods will be based on the use of such a programme represented by electromagnetic transients program (EMTP). Applications of this type of approach are used at present especially in Japan [13] and in many other countries. An example of ‘a detailed deterministic approach’ is presented in Section 2.3.

Lightning interaction with power substations

33

2.2 Simplified statistical approach of lightning surge analysis A representative example of a simplified statistical approach is introduced in IEC [1], which calculates simply a lightning surge overvoltage in shielding failure and in back flashovers based on the limit distance, the distance between a surge arrester and protected equipment, the number of connected overhead lines and damping by corona effects. In this section, its essence is presented.

2.2.1 Basics The overvoltages in substations are featured by amplitude and shape of the overvoltage impinging on the substation from the overhead line conductor, and affected by the travelling wave behaviour of the substation itself. The occurrence frequency of such impinging overvoltages is given by the lightning performance of the overhead line connected to the substation. For substations without surge arresters, the amplitude of the impinging overvoltage is the most important parameter. Meanwhile, for substations protected by surge arresters, those parameters are its steepness and the separation distance between surge arrester and the equipment under consideration. The steepness of an impinging overvoltage surge is reduced mainly by corona damping effects on the overhead line [14]. Consequently, only the lightning stroke hitting the overhead line within a certain distance from the substation can cause the sufficient steepness of the impinging surge to cause certain overvoltage amplitude. For strokes hitting further, the steepness will be too low for certain overvoltage amplitude, irrespective of the amplitude of the surge. The knowledge of this limit distance is of primary importance. In detailed digital overvoltage calculations using transient programs a part of which is described in Section 2.3, the overhead line should be carefully simulated over this distance. Recommendations for the necessary parameters to be included in such calculations are given in [14]. Furthermore, all simplifications which take into account the frequency of occurrence of the overvoltage amplitudes are based on similar considerations.

2.2.2 Calculation of the limit distance 2.2.2.1 Protection by arresters When plural number of an overhead line is connected to the substation, the original steepness (S) of the impinging surge can be divided by the number of lines (n). However, the number of lines should correspond to the minimum one which reasonably remains in service taking into account possible outages during lightning activities. Supposing the fact that the steepness of the impinging surge reduces inversely with the travel distance on the overhead line, the steepness S of the impinging surge is approximately to be S ¼ 1=ðnKco X Þ

(2.1)

34

Lightning interaction with power systems, volume 2

where n: the number of overhead lines connected to the substation Kco: the corona damping constant according to Table 2.2 (ms/(kVm)) X: the distance between struck point of lightning and substation (m) Equation (2.1) has been derived with the assumption that the distances between the protected object and the connection points of the overhead lines result in travel times of less than half the front time of the impinging surge. The use of this steepness value in (2.1) does not give sufficiently accurate results for the calculation of overvoltage at the equipment. It is, however, conservatively enough to estimate the limit distance Xp by    Xp ¼ 2ts = nKco U  Upl (2.2) where U: the lowest considered overvoltage amplitude ts: the longest travel time between any point in the substation to be protected and the closest arrester (ms) Upl: the lightning impulse protection level of the arrester For distances larger than Xp, the steepness will be reduced such that the overvoltage at the equipment will in general be smaller than the assumed value U.

2.2.2.2

Self-protection of substation

Self-protection of the substation exists when the lightning overvoltage impinging the substation from the overhead line is decreased below the certain withstand voltage by the reflections within the substation itself without any action of arresters. The fundamental requirement is that the number of lines connected to the substation is sufficiently large. The necessary number of lines can be estimated by    =U c  1 (2.3) n  4b U50 where n: the number of overhead lines  U50 : the 50% lightning impulse flashover voltage of the line insulation, negative polarity U: the overvoltage amplitude considered Table 2.2 Corona damping constant Kco Conductor configuration

Kco [ms/(kVm)]

Single conductor Plural

1.5 1.0 0.6 0.4

Double conductor bundle Three or four conductor bundle Six or eight conductor bundle

   

10–6 10–6 10–6 10–6

Lightning interaction with power substations

35

The impinging surges are not to cause too high overvoltages before the reflections from the additional lines act to decrease them. This requirement is fulfilled if the steepness of the impinging surge is so small due to corona damping effects on the line that the substation can be considered as a lumped element. This can be considered as valid when the lightning struck-point is beyond the limit distance: Xp > 4ðts =Kco U Þ

(2.4)

where ts: the travel time to the most distant point from the substation busbar (ms) An appreciable self-protection effect can work in the case of gas insulated switchgear (GIS) or cable-connected substations, since the reflections at the line entrance already decrease greatly the overvoltages below the permitted values. This can be estimated as valid if:  U > ð6Zs =ðZs þ ZL ÞÞU50

(2.5)

where Zs: the surge impedance of the substation ZL: the surge impedance of the overhead line However, the distance between the lightning struck-point and the substation entrance is not necessarily to be so small that the reflection from the substation interferes with the lightning. For this reason, the following minimum limit distance is applicable: ● ●

for shielding failures: Xp ¼ 1 span for back flashovers: Xp ¼ 2 towers

2.2.3 Estimation of the lightning overvoltage amplitude 2.2.3.1 General Since the full travelling wave calculation including the simulation of the overhead line performance is extremely difficult in a simple approach, a simplified procedure has been proposed in [14]. This procedure consists in calculating a lightning current with the desired return rate and calculating the overvoltage by travelling wave calculations in the substation including a short-line section equivalent circuit.

2.2.3.2 Shielding failure in transmission lines The lightning current leading in the impinging surge is determined from the shielding failure rate within the limit distance Xp and its probability to be exceeded:   F ðI Þ ¼ F ðIm Þ þ Rt =Rp (2.6) where F(Im): the lightning current probability corresponding to the maximum shielding current Rt: the considered return rate Rp: the shielding penetration rate within the limit distance

36

Lightning interaction with power systems, volume 2

The shielding penetration rate can be obtained from the shielding failure flashover rate by Rp ¼

Rsf F ðIcr Þ  F ðIm Þ

(2.7)

where Rsf: the shielding failure flashover rate F(Icr): the probability corresponding to the current causing line insulation flashover at negative polarity The currents corresponding to the probabilities can be obtained from the lightning stroke current probability distribution in the shielding failure range. The amplitude of the impinging overvoltage surge and its steepness may be given by (2.8) and (2.9), respectively: Ul ¼ ZL I=2

(2.8)

S ¼ 1=ðKco XT Þ

(2.9)

where XT ¼ XP/4. Its time to half-value should be 140 ms. If peak values higher than 1.6 times the negative flashover voltage of the line insulation are obtained, an impinging surge with this peak value should be used. The impinging voltage surge is applied to conduct a travelling wave calculation within the substation and the overvoltages are obtained for this return rate for the various locations.

2.2.3.3

Back flashovers

The lightning current determining the design impinging surge in the case of back flashovers is determined from the number of flashes to the overhead line tower and grounding wires within the limit distance, and its probability to be exceeded is F ðI Þ ¼ Rt =Rf

(2.10)

where Rt: the considered return rate Rf: the flashing rate within the limit distance The voltage generated at the tower footing impedance by this current is determined by its time response and current dependence characteristics. When the extension of the tower footing is within a radius of 30 m, the time response could be neglected and the tower footing impedance is Rlc Rhc ¼ qffiffiffiffiffiffiffiffiffiffiffi 1 þ llg

(2.11)

Lightning interaction with power substations

37

where Rlc: the low current resistance Ig: the limit current (kA) The limit current Ig represents the soil ionization and is evaluated by Ig ¼

1 E0 r 2p R2lc

(2.12)

where r: the soil resistivity (Wm) E0: the soil ionization gradient (recommended value: 400 kV/m) The amplitude of the design impinging surge is then given as   1  cf Rlc l Ul ¼ qffiffiffiffiffiffiffiffiffiffiffi 1 þ llg

(2.13)

where cf: the coupling factor between grounding wire and phase conductor Typical values of cf are ● ●

cf ¼ 0.15 for single earth-wire lines cf ¼ 0.35 for double earth-wire lines

If amplitudes higher than 1.6 times the negative flashover voltage of the line insulation are obtained, an impinging surge with this amplitude should be used. The design impinging surge has an exponentially decreasing tail with a time constant t given by (2.14) and a linear increasing front whose steepness S is given by (2.15): t¼

Ze Lsp Rlc c

(2.14)

where Ze: the grounding wire surge impedance (typical values are 500 W for single earth-wire lines and 270 W for double earth-wire lines) Lsp: the span length (m) c: the light velocity (recommended value: 300 m/ms) S ¼ 1=ðKco XT Þ where Kco: given by (2.1) XT: given by (2.9)

(2.15)

38

Lightning interaction with power systems, volume 2

A single conductor of the length XT and surge impedance equal to that of the phase conductors are connected to the substation for travelling wave calculations in the considered substation. A voltage source with the internal impedance of the low current footing resistance Rlc is placed at the end of the conductor. It produces a voltage with the shape parameters of the impinging surge. If the impinging surge amplitude is higher than 1.6 times the positive 50% lightning impulse flashover voltage, the simplifications are no longer applicable and more careful studies may be recommendable. The same applies for tower footing extensions larger than 30 m in radius. The overvoltage amplitude is dependent on two kinds of the return rate: one for shielding failures and the other for back flashovers. The overall dependency is obtained by adding the return rates for a constant amplitude.

2.2.4

Simplified method

A further simplification is achieved with applying the basic principles given in Sections 2.2.2 and 2.2.3 and adopting the following assumptions: ●



all lightning events within a certain distance from the substation cause higher overvoltages at the protected equipment than an assumed value, while all events outside this distance lower values the overvoltage at the equipment can be calculated according to (2.1)

With regard to the distance X to be applied in (2.1), it has been shown that back flashovers do not occur at a tower close to the substation owing to the low substation grounding. The minimum value of X is one overhead line span length. The representative steepness Srp to be applied in (2.1), therefore, is equal to    Srp ¼ 1= Kco Lsp þ Lt (2.16) And the overhead line section in which the lightning flashover rate is equal to the desired return rate [15] is equal to Lt ¼ (Rt/Rkm) where Rt: the adopted overvoltage return rate (1/year) Rkm: the overhead line outage rate per year for a design corresponding to the first kilometre in front of the station (see (2.16)) [usual unit: 1/(100 kmyear); recommended unit: 1/(myear)] Thus, introducing Srp and putting A ¼ 2/(Kcoc) for transmission lines, the dependence of the representative lightning overvoltage on the return rate is obtained by Urp ¼ Upl þ

A L n Lsp þ Lt

(2.17)

where Urp: the representative lightning overvoltage amplitude (kV) A: a factor given in Table 2.3 describing the lightning performance of the overhead line connected to the station

Lightning interaction with power substations

39

Table 2.3 Factor A for various overhead lines Type of line

A (kV)

Distribution lines (phase-phase)

• with earthed crossarms (flashover to ground at

Transmission lines (single-phase to ground)

• • • • •

low voltage) wood-pole lines (flashover to ground at high voltage) single conductor double conductor bundle four conductor bundle six and eight conductor bundle

900 2,700 4,500 7,000 11,000 17,000

Note: Values in this table are applicable in (2.17) and (2.19).

Upl: the lightning impulse protection level of the surge arrester (kV) n: the minimum of lines connected to the substation (n ¼ 1 or n ¼ 2) L: the separation distance Lsp: the span length (m) Lt: the overhead line length with outage rate equal to adopted return rate (m) The coordination withstand voltage is obtained by replacing Lt by the line length La, which yields an outage rate equal to the acceptable failure rate Ra: La ¼ Ra =Rkm

(2.18)

where La: the overhead line section with outage rate equal to acceptable failure rate Ra: the acceptable failure rate for equipment And the coordination lightning impulse withstands voltage (Ucw) is equal to Ucw ¼ Upl þ

A L n Lsp þ La

(2.19)

The factors A are obtained from Table 2.3 and the corona damping constants Kco from Table 2.2 for transmission lines. As for distribution systems, lightning overvoltages are usually multiphase and current division of the phase conductors may be considered. Regarding steel towers, the flashovers of more than one tower during one lightning stroke lead to a further reduction of the lightning overvoltages. For these lines, the factor A has been matched with the service practice. GISs are, in general, better protected than open-air substations owing to a surge impedance much lower than that of the overhead lines as described in Section 2.1. A generally valid recommendation for the estimation for GIS as compared to openair substations cannot be made, but the use of (2.19) for the open-air substation results in conservative estimates of the LIWV or the protection range.

40

Lightning interaction with power systems, volume 2

2.2.5

Assumed maximum value of the representative lightning overvoltage

The assumed maximum value of the representative overvoltage at new stations, where lightning insulation performance of existing stations is known, may be estimated by  

Urp2 n1 L2 Upl1 Urp1 ¼1þ 1 (2.20) Upl2 n2 L1 Upl2 Upl1 where Urp: the assumed maximum representative overvoltage Upl: the lightning impulse protection level of the surge arrester N: the minimum number of in-service overhead lines connected to the station L: a1 þ a2 þ a3 þ a4 The index 1 refers to the situation for which service experience has been satisfactory, and the index 2 to the new station situation. Alternatively, the assumed maximum value can be obtained by supposing the return rate in (2.16) equal to zero, thus leading to Lt ¼ 0, and: Urp ¼ Upl þ

A L n Lsp

(2.21)

2.3 Detailed deterministic approach of lightning surge analysis As an example of a detailed deterministic approach, this section presents the lightning surge analysis method with ‘electromagnetic transients program’ (EMTP) conducted in Japan regarding UHV substations.

2.3.1

Basic analysis conditions

The UHV substations, together with the UHV designed transmission lines, were analysed. Figures 2.2 and 2.3 show the circuit for analysing UHV designed transmission lines and UHV substations, respectively, while Table 2.4 lists the analysis conditions [16]. The locations of the lightning strokes and back flashovers were determined based on the assumption of lightning strokes hitting the first transmission tower nearest the substation and a flashover occurring at the arcing horn of the same tower. A multistory model was used for the transmission tower, and each constant was set based on testing of the surge characteristics at UHV transmission towers [17]. For the surge-arrester model, which has a significant impact on the calculated result, the model proposed by the IEEE [9] was used. For other equipment models, each constant was reviewed in accordance with the basic characteristics of UHV equipment, following the means [18] used to determine the LIWV according to the standard for test voltage in the Japanese domestic standard [19].

(a)

1C

1B

1A

1G

2A

2B

2C

2G

(c)

10 Ω

Phase conductor 2 ACSR 810 mm × 8 Outer diameter: 38.4 mm St outer diameter: 9.6 mm Resistance: 0.0356 Ω/km Wire conductor distance: 40 cm

Overhead ground wire

Earth resistance 50 Ω.m

33 m

32 m

31 m

38 m

10 Ω

650 m

(8 phases)

model

Semlyen

No. 3

L1

L4

L3

L2

R4

Zt2

R3

Zt1

R2

Zt1

R1

650 m

650 m

11.26 Ω 15.77 Ω 15.77 Ω 8.25 μH 11.56 μH

R1 R2 R3 L1 L2 L3

300 m/μs 42.81 Ω

vt2 R4 L4

31.38 μH

120 Ω

Zt2

11.56 μH

300 m/μs

Zt1 vt1

Multistory model 120 Ω

(8 phases)

(8 phases)

Zt1

model

model

10 Ω

Semlyen

Semlyen

No. 2

iL

10 Ω

BFO

No. 1

(d)

L2

L1

120 m

(8 phases)

model

Semlyen

R2

Zt2

R1

Zt1

L2

6.69 μH

20.08 Ω

300 m/μs

90 Ω R2

9.67 μH Zt2 vt2

29.01 Ω L1

300 m/μs R1

Multistory model 130 Ω

Substation bushing

Zt1 vt1



Gantry

Figure 2.2 Circuit for analysing lightning surge to transmission lines. (a) The transmission line configuration and the direct lightning stroke model; (b) average conductor configuration; (c) transmission tower (for a strain tower); and (d) gantry

(b)

109.0 m

No. 10

110.0 m

Zb = 400 Ω

50.0 m

Matching resistor RC

17.5 m 17.5 m

62.5 m

12.5 m 17.5 m 17.5 m 62.5 m

25.0 m 25.0 m

6

6

13 6

6

13 13 6

13 6

13

6

6

6

Tr.

6

25

25

25

25

4

6

8

5

13

6

Le C Rz Lz a R

Lz aR

Nonlinear resistor

1.0 μH 0.17 pF 31 Ω 7.4 μH 11 (constant)

C

Le

(b)

Note: The factor of ‘a’ is determined by the characteristics of the equipment.

R a–1

a

Rz

Figure 2.3 Circuit for analysing lightning surge at a substation. (a) Substation configuration and (b) surge arrester equivalent circuit

(a)

6

6

13

6

Numbers in the drawing indicate the length (m)

Primary side terminal of the transformer

Circuit breaker at the service line entrance

13

9

3

11.5

6

11.5

11.5

11.5

11.5

11.5

11.5

11.5

4

Bushing: 300 pF

Single-phase GIS

Midpoint of the service line

Service entrance of the transmission line

Lightning interaction with power substations

43

Table 2.4 Analysis conditions

Lightning stroke phenomena

Back flashover location

Upper phase back flashover due to a lightning stroke to the first transmission tower

Lightning stroke current

Ramp waveform Current amplitude: 200 kA Front time: 0.6–2.0 ms in 0.2 ms increments Time to half-value: 70 ms 400 W

Lightning path impedance AC phase Flashover

Transmission lines

Transmission line Transmission tower

Substation Circuit

AC voltage (1,100 kV) superimposed Nonlinear inductance model based on the leader progression method 8 phase Semlyen model

Four story transmission tower model (constant determined by actual measurement) Grounding resistance: 10 W Anchor steel Two story model wire Grounding resistance: 4 W Corona effect Not considered All GIS double bus – 4 bus tie – 4 transmission lines – 4 banks Configuration I Open circuit breaker at the service line entrance Configuration II 1 line – 1/4 bus – 1 transformer GIS Single phase distributed constant circuit Loss-less line Surge impedance: 91 W, 270 ms/m Circuit breaker Same as the GIS in closing p-type capacitance simulation in opening Transformer Capacitance simulation 16,600 pF (Core-type) 5,800 pF (Shell-type) Bushing Capacitance simulation: 300 pF Surge arrester Model taking fast transient current characteristics into account (V20kA ¼ 1,620 kV)

The assumed lightning stroke current waveform was simulated by a ramp wave [2,20,21] with current amplitude of 200 kA and a time to half-value of 70 ms. As the phenomena and measurement data are analysed in a detail [3], the observed wavefront is generally concave; but, the front ramp of the waveform used in the simulation of this study was a straight line with a slope equal to the maximum steepness of the lightning stroke current front [21,22]. In reference to the investigation results in International Council on Large Electric Systems (CIGRE) [3], the front time varied within the range 0.6 to 2.0 ms in 0.2 ms increments, including the 1.7 ms proposed in reference [22]. A current of 200 kA is the value exceeded in the field, with a cumulative probability of 0.3% [23].

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Lightning interaction with power systems, volume 2

As shown in Table 2.4, configuration I was used as the circuit configuration of a substation in the GIS overvoltage analysis, which opens the circuit breaker at the service line entrance in order to impose a high surge voltage on the GIS. Configuration II was used for the transformer overvoltage analysis, which allows only a small surge current diversion in the substation to impose a high surge voltage on transformer terminals. Core- and shell-type transformers were used. The analysis used ATP-EMTP [24].

2.3.2

Analysis conditions and models

Lightning surge analysis using EMTP can accurately determine overvoltages with detail system models, as clearly seen in the latest technical report of IEC [2] and the special publication compiled by the Institute of Electrical and Electronics Engineers (IEEE) WG [20]. Japan started comparatively early to try to establish a highly accurate simulation technique using EMTP, which has since been used as the present standard for test voltage [19] and the design of UHV power transmission and transformer equipment; however, the analysis conditions and analysis models differ compared with the methods used by the IEC and IEEE. For example, transmission tower models are simulated in detail in Japan, while the IEC and IEEE models are relatively simple. In contrast, the grounding resistance of transmission towers and corona effect are modelled in detail by the IEC and IEEE. Whereas the standard method and model for lightning surge analysis in Japan is reported in [18], the present section presents, in detail, how to set up the variable conditions of lightning stroke locations, the corona effect, the grounding resistance of transmission towers and the surge arresters, including a description of the characteristics of UHV equipment.

2.3.2.1

Location of lightning strokes

If a lightning strike occurs far from a substation, the surge voltage/current generated by the lightning stroke is attenuated before reaching the substation and the waveform also varies due to the different propagation speeds of different propagation modes. With a surge in high voltage, a corona is generated and the waveform is deformed. Therefore, the wavefront of the surge encroaching the substation becomes less steep and the surge overvoltage can easily be suppressed by the surge arrester. In contrast, if a lightning strike occurs adjacent to a substation, a steep surge caused by flashover intrudes into the substation barely attenuated, resulting in a significant overvoltage. Therefore, analysis of lightning surge at a substation for the purposes of UHV insulation design is based on the condition that the lightning stroke hits the first or second transmission tower nearest the substation and that flashover occurs at the arcing horn of the same tower. Figure 2.4 summarizes the overvoltage generated at the open end of the GIS from lightning strokes hitting the first to the fifth transmission tower with a current amplitude of 200 kA, a front duration of 1.0 ms and a tail time of 70 ms, with no consideration of the line corona effect. The highest overvoltage is generated from a lightning stroke to the first transmission tower; hence, this analysis has used a lightning stroke to the first transmission tower as the basic condition.

Lightning interaction with power substations

45

3,000

Voltage (kV)

2,800 2,600 2,400 2,200 2,000 No. 1

No. 2

No. 3

No. 4

No. 5

Tower hit by lightning strokes

Figure 2.4 Relationships between the GIS terminal voltage amplitude and the lightning location without including line corona effect

2.3.2.2 Grounding resistance of transmission towers The grounding resistance of a transmission tower has a significant impact on the back flashover analysis. Lightning protection design in Japan uses a constant resistance model, although the IEEE and CIGRE recommend a current-dependent model [25–28]. If current-dependent resistance is used, it tends to reduce the voltage increase at the top of the transmission tower. Therefore, the overvoltage at a substation during back flashover analysis is expected to be reduced. In order to use the frequency-dependent resistance model, it is necessary but difficult to determine appropriate impedance because the physical constants of the soil that determine the model constant are significantly affected by the weather and other conditions. The validity of the grounding impedance characteristics of a large-scale tower like a UHV transmission tower within the high-current range is also not well established. For these reasons, this analysis uses a constant resistance for the grounding resistance of a transmission tower. Similarly, a constant resistance was used for the ground resistance of the gantry, which is tied to the grounding grid of the substation and thus requires a smaller resistance compared with the transmission tower. The value selected for analysis was, however, stricter than the value typically employed.

2.3.2.3 Surge arrester in substations When a current with a steep wavefront flows, such as a lightning surge with a front duration of several microseconds, the discharge voltage level of a surge arrester increases momentarily. This phenomenon is part of what is referred to as fast transient current characteristics, for which several surge-arrester models have been proposed. The present study uses the model recommended by the IEEE [9], among them. The equivalent circuit in Figure 2.3(b) has nonlinear resistors at two locations, which are separated by an Resistance–Inductance (RL) filter. This latter provides varying impedance for fast and slow surges, respectively. The procedures

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Lightning interaction with power systems, volume 2

used to determine the model constant are available in [9] and the model constant can be calculated based on the overall length of the surge arrester elements, the parallel number of elements and the discharge voltage.

2.3.2.4

Corona effects in transmission lines

As mentioned in Section 2.3.2.1, the present study assumes lightning strokes striking the first transmission tower; hence, the presumed effect of the corona is small due to the short distance to the substation. In addition, UHV designed transmission lines use eight-phase conductors, the equivalent diameter of which is as large as 0.9 m, making corona discharge unlikely. For these reasons, this analysis does not simulate the corona effect. For an additional reason, though, a sophisticated corona model reflecting a physical process is proposed [29,30], although neither its accuracy nor its stability have been established yet. In particular, since no measured data concerning phase-to-phase corona are available, it is difficult at present to perform analysis reliable enough to contribute to insulation design.

2.4 Failure rate evaluation considering front time of lightning current 2.4.1

Crest value and wavefront time of lightning stroke current

The lightning stroke current waveform is an essential parameter for the design of lightning protection for electric power facilities, which includes the current amplitude, the front duration, and the front steepness. Accordingly, it was an urgent issue to evaluate lightning stroke current waveforms associated with lightning overvoltages based on actual data in extra-high-voltage systems including UHV. The current waveforms of lightning strokes had been measured on 60 transmission towers for 500 kV transmission lines (including towers designed for UHV) from 1994 to 2004, and lightning parameters were quantitatively evaluated from the engineering viewpoint [23]. 120 waveforms of negative first return strokes were observed, of which there were three records as large as exceeding 100 kA. Figure 2.5 shows the cumulative frequency distribution of peak current of lightning strokes. The maximum peak current observed was 130.2 kA, and the 50% value at the regression line was 29.3 kA. The distribution of the present data showed almost no characteristic difference from previous data including Berger’s data [31] which are described in detail in Chapter 2 of Volume 1 on the basis of [3]. In this section, taking notice of dependence of peak current of lightning strokes on front duration, investigation will be deepened from one variable function to two variable function in the following as a new attempt. Figure 2.6 extracts the relationship between the first peak amplitude and the front duration, and the front duration tends to be longer particularly in the highcurrent area. The relationship is expressed by (2.22): x

y ¼ 1:31e230

r ¼ 0:983 ðfor the first peakÞ

(2.22)

Lightning interaction with power substations

47

99.9

Cumulative probability (%)

(1) Berger [6] (2) CIGRE [5] (3) CRIEPI [3]

(3) (1) (2)

99 95 90 80 70 60 50 40 30 20 10 5 1 0.1 1

10

100

Peak amplitude (kA)

Figure 2.5 Cumulative frequency distribution of peak current of lightning strokes 1

First peak amplitude Maximum rate-of-rise

(μs)

10

1

95% confidence interval of data –1

10

1

101

102

First peak amplitude (kA)

Figure 2.6 Relationship between first peak current and front duration defined by ‘first peak amplitude/maximum rate of rise’ The probability density of the occurrence P(i,tf) as a function of the two variables of the current amplitude i and the front duration tf of the lightning stroke current waveform is derived as the following (2.23), and is exhibited in 3D way in Figure 2.7, which means significance for lightning protection design:  

9 8 i > > > logðm2 Þ >

> 2psi sf 2s2f 2s2i > > : ; (2.23)

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Lightning interaction with power systems, volume 2 0.007–0.008 0.006–0.007 0.005–0.006 0.004–0.005 0.003–0.004 0.002–0.003 0.001–0.002 0–0.001

180 150 120 90 Current 60 amplitude (kA) 30

0.008 0.007 0.006 0.005 0.004 0.003 0.002 0.001 0 0

5

4

3

2

1

Normalized probability (%)

0

Front duration (μs)

Figure 2.7 Occurrence probability of lightning stroke current waveforms as a function of the amplitude and the front duration

The results above indicate that ‘the front duration to be considered for lightning protection design’ is positively correlated with the current amplitude, the relationship of which are to be adapted to the insulation design [22].

2.4.2

Wavefront time of lightning stroke current and amplitude of lightning surge

The relationship between the current amplitude and the front duration was clarified, and it emerged that an assumed lightning stroke current waveform with a front duration of 1.7 ms is appropriate for a current amplitude of 200 kA in the UHV system [22]. This section analyses the lightning surge overvoltages generated at the GIS and transformer in a UHV substation at the time of back flashovers [16].

2.4.2.1

Overvoltages at GIS

Overvoltage waveforms generated at the open circuit breaker terminal of the entrance line are shown in Figure 2.8. All the waveforms reach their peak voltages in a spike of the wavefront, and as a whole, as the front duration of the lightning stroke current becomes longer, the generated surge voltage amplitudes are lower. The maximum voltage was 2,667 kV with a front duration of 0.8 ms. The spike waveform was caused by a delay of around 0.2 ms of the surge arrester operation, that is, the fast transient current characteristics [9]. The peak values become higher with the steepness of the wavefront of the intruding lightning surge current. Excluding the spike, the value is almost constant at the level of the surge arrester discharge voltage of 1,620 kV.

Lightning interaction with power substations

49

3,000

Voltage (kV)

2,000

0.6 μs

0.8 μs

1.0 μs

1.2 μs

1.4 μs

1.6 μs

1.7 μs

1.8 μs

2.0 μs

1,000

0 0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

–1,000 Time (μs)

Figure 2.8 Overvoltage waveforms generated at the GIS terminal

3,000

Voltage (kV)

2,000

0.6 μs

0.8 μs

1.0 μs

1.2 μs

1.4 μs

1.6 μs

1.7 μs

1.8 μs

2.0 μs

1,000

0 0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

–1,000 Time (μs)

Figure 2.9 Overvoltage waveforms generated at a shell-type transformer

2.4.2.2 Overvoltage at transformer The waveforms of overvoltages generated at the primary terminal of the shell-type transformer (C ¼ 5,800 pF) are displayed in Figure 2.9. Similar to the voltage waveform at the GIS, a spike waveform due to the increase of the discharge voltage of the surge arrester is observed during the wavefront, and then the voltage converges at the discharge voltage V20kA of about 1,620 kV. However, in contrast to the voltage at the GIS, with an increase in the front duration of the lightning stroke current, the peak voltage of the spike waveform decreases, although once the front duration goes beyond 1.0 ms, the peak voltage increases again. If the front duration is shorter than 1.0 ms, two peaks are observed at the wavefront; however, if the front duration is longer than 1.2 ms, the peak points overlap each other and the voltage

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Lightning interaction with power systems, volume 2

amplitude is greater. The maximum voltage of 1,844 kV was generated when the front duration of the lightning stroke current was 0.6 ms.

2.4.3

Lightning failure rates in substations in consideration of lightning current waveforms

Since it is difficult to evaluate the probability of insulation breakdown of equipment at present, this study defines the failure rate as the frequency of occurrence of overvoltages exceeding the LIWV [32].

2.4.3.1

Distribution of overvoltages generated at GIS

Figure 2.10 shows the distribution of overvoltages in 3D displays generated at the GIS terminals with changing lightning stroke current waveform parameters of the amplitude and the wavefront. The negative part in the distribution of overvoltages generated is the area where back flashovers do not occur. According to the distribution of generated voltages and the contour lines of overvoltages, in the area where the front duration is about 0.5 ms or longer, as the current amplitude becomes higher, and the front duration becomes shorter, the lightning surge voltages generated tend to be higher. While the area of occurrence of overvoltages between 1,500 and 2,000 kV is wide, the area between 1,500 and 1,600 kV was found to be the widest of all after detailed checking. This was due to the suppression of generated overvoltages by surge arresters.

3,500–4,000 3,000–3,500 2,500–3,000 2,000–2,500 4,000 3,500 3,000 2,500 2,000 Voltage (kV) 1,500 1,000 500 0 –500 –1,000 270 240 210 180 150 120

1,500–2,000 1,000–1,500 500–1,000 0 or below

0 2

90

Current amplitude (kA)

60

3 30 0

5

Front duration (μs)

Figure 2.10 Distribution of overvoltages generated at the terminal of GIS’s with changes in current amplitude and front duration of lightning stroke current waveforms

Lightning interaction with power substations

51

2.4.3.2 Distribution of overvoltages generated at transformer Figure 2.11 shows the distribution of overvoltages generated at the primary terminal of shell-type transformers. The way back flashovers occur is strongly affected by the front duration. However, the overvoltage distribution after back flashovers occur is different to that of GIS’s. The contour line of overvoltages at transformers is closer to being in parallel with the front duration axis than in the case of GIS’s. Overvoltage waveforms are steep during the wavefront due to the effect of the front duration of lightning stroke current and the maximum voltage appearing at the peak during the wavefront of waveforms. However, if a large capacitance, such as a transformer, is connected to the line, the impedance to steep surge voltage is reduced and the influence of the front duration of lightning stroke current decreases. The generated voltage at transformers increases as if charging the entire substation, so the overvoltage is regarded as being determined by the charge quantity from a lightning surge.

2.4.3.3 Evaluation of lightning failure rate of GIS In the UHV field-test equipment, the failure rate is very low at 8.41  106 [times/ route/year] (MTBF: 1.19  105 years per route). If the LIWV is reduced to 2,100, 1,950 and 1,800 kV, the failure rate is increased to 2.5, 6.5 and 18.9 times, respectively. Evaluating the failure rate conventionally, based only on the frequency of occurrence of the assumed lightning stroke current amplitude of 200 kA (the cumulative frequency of occurrence of 0.3% of the current amplitude

2,000–2,500 1,500–2,000 1,000–1,500 500–1,000 0 or below 2,500 2,000 1,500 270 240 210 180 150 120

1,000 500 Voltage (kV) 0 –500 –1,000 0

90

Current amplitude (kA)

1

60

2

30 0

3 4

Front duration (μs)

Figure 2.11 Distribution of overvoltages generated at primary terminal of shelltype transformers with changes in current amplitude and front duration of lightning stroke current waveforms

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Lightning interaction with power systems, volume 2

exceeding 200 kA), would mean that failures occur once in about 700 to 1,000 years [6]. The failure rate mentioned above is considerably lower than this. A high assumed failure rate with the conventional method is mainly due to not taking into consideration the frequency of occurrence of the front duration of the assumed lightning stroke current. Figure 2.12 shows the overvoltage distribution overlaid with the density distribution of occurrence of lightning stroke current. The failure rate conventionally used was evaluated using only the current amplitude, regardless of the front duration. Consequently, overvoltages generated under the condition of 200 kA or higher are assumed to result in failure in all cases. On the other hand, in the case of evaluation using overvoltages, these overvoltages depend on the influence of the current amplitude and the front duration. The area surrounded by a light red line in Figure 2.12 is determined by overvoltages of 2,622 kV contour line, whose area is smaller. The evaluation of the failure rate with overvoltages is more essential, and the front duration has a large impact on overvoltages. Therefore, evaluations of failure rates with the overvoltage level using two parameters, the current amplitude and the front duration of lightning stroke current, are more rigorous.

2.4.3.4

Evaluation of lightning failure rate of transformer

The relationship between the failure rate and the LIWV is shown by the solid line in Figure 2.13. The failure rate at the test voltage of 1,950 kV [6] for transformers in the UHV field-test equipment was 7.94  105 [times/route/year] (MTBF: 1.26  104 years per route). In comparison with the case of GIS’s in Figure 2.12, if a comparison is made based on the test voltages of the UHV field-test equipment for transformers (LIWV: 1,950 kV) and GIS’s (LIWV: 2,250 kV), the failure rate of transformers is about nine times that of GIS’s.

0 200 kA, 1.0 μs

1 2

200 kA, 1.7 μs

Front duration (μs)

3 4

270

240

210

180

150

120

90

60

30

0

Current amplitude (kA)

Figure 2.12 Distribution of overvoltages at GIS with respect to the current amplitude and the front duration of lightning stroke current, and density distribution of occurrence of lightning stroke current waveforms

Lightning interaction with power substations

53

0 200 kA, 1.0 μs

1 2

200 kA, 1.7 μs

Front duration (μs)

3 4 270

240

210

180

150

120

90

60

30

0

Current amplitude (kA)

Figure 2.13 Distribution of overvoltages at shell-type transformer with respect to the current amplitude and the front duration of lightning stroke current, and density distribution of occurrence of lightning current waveforms

References [1] [2] [3] [4]

[5]

[6] [7] [8] [9] [10]

IEC 60071–2. ‘Insulation co-ordination - Part 2: Application guideline’. 2018 IEC 60071–4. ‘Insulation co-ordination - Part 4: Computational guide to insulation co-ordination and modelling of electrical networks’. 2004 CIGRE WG C4.407. ‘Lightning parameters for engineering applications’. CIGRE Technical Brochure, No. 549, 2013 CIGRE WG C4.302. ‘Insulation co-ordination related to internal insulation of gas insulated systems with SF6 and N2/SF6 gas mixtures under AC condition’. CIGRE Technical Brochure, No. 360, 2008 CIGRE JWG.A2/C4.39. ‘Electrical transient interaction between transformers and the power system part 1: Expertise’. CIGRE Technical Brochure, No.577-A, 2014, ‘Electrical transient interaction between transformers and the power system part 2: Case studies’. CIGRE Technical Brochure, No. 577-B, 2014 CIGRE WG C4.306. ‘Insulation coordination of UHV AC systems’. CIGRE Technical Brochure, No. 542, 2013 IEC 60071–1. ‘Insulation co-ordination - Part 1: Definitions, principles and rules’. 2006 IEC 60060–1. ‘High-voltage test techniques – Part 1: General definitions and test requirements’. 2010 IEEE Working Group 3.4.11. ‘Modeling of metal oxide surge arresters’. IEEE Trans. PD, Vol. 7, No. 1, pp. 302–309, 1992 Okabe S., Tsuboi T., and Takami J. ‘Analysis of aspects of lightning strokes to large-sized transmission lines’. IEEE Trans. DEI. Vol. 18, No. 1, pp. 182– 191, 2011

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[11]

Taniguchi S., Tsuboi T., Okabe S., Nagaraki Y., Takami J., and Ota H. ‘Improved method of calculating lightning stroke rate to large-sized transmission lines based on electric geometry model’. IEEE Trans. DEI. Vol. 17, No. 1, pp. 53–62, 2010 Taniguchi S., Tsuboi T., Okabe S., Nagaraki Y., Takami J., and Ota H. ‘Study on the method of calculating the lightning outage rate of large-sized transmission lines’. IEEE Trans. DEI. Vol. 17, No. 4, pp. 1276–1283, 2010 Kawamura T., Sasaki S., Ueda T., Kouno T., Zaima E., and Kato Y. ‘Principles and recent practices of insulation coordination in Japan’. CIGRE Session 2000, 33–109 Eriksson A.J., and Weck K.-H. ‘Simplified procedures for determining representative substation impinging lightning overvoltages’. CIGRE report 33–16, 1988 CIGRE WG 33.01. ‘Guide to procedures for estimating the lightning performance of transmission lines’. CIGRE Technical brochure, No. 63, 1991 Takami J., Okabe S., and Zaima E. ‘Lightning surge overvoltages at substations due to back flashover with assumed lightning current waveforms based on observations’. IEEE Trans. PD. Vol. 25, No. 4, pp. 2958–2969, 2010 Yamada T., Mochizuki A., Sawada J., et al. ‘Experimental evaluation of a UHV tower model for lightning surge analysis’. IEEE Trans. PD, Vol.10, No.1, pp. 393–402, 1995 Ametani A., and Kawamura T. ‘A method of a lightning surge analysis recommended in Japan using EMTP’. IEEE Trans. PD, Vol. 20, No. 2, pp. 867–875, 2005 The Japanese Electrotechnical Committee. ‘Standard for test voltage’. JEC-0102–1994, 1994 (in Japanese) IEEE WG 15.08.09. ‘Modeling guidelines for fast front transients. Chapter 5 of modeling and analysis of system transients using digital programs’. IEEE PES Special Publication, TP-133–0, 1999 Anderson J. G. ‘Lightning performance of transmission lines. Chapter 12 of transmission line reference book 345kV and above. 2nd ed. (EPRI)’. California: Sep. 1982 Okabe S., and Takami J. ‘Evaluation of improved lightning stroke current waveform using advanced statistical method’. IEEE Trans. PD, Vol. 24, No. 4, pp. 2197–2205, 2009 Takami J., and Okabe S. ‘Observational results of lightning current on transmission towers’. IEEE Trans. PD, Vol. 22, pp. 547–556, Jan. 2007 Canadian/American EMTP User Group. Alternative transients program (ATP) rule book. 1987 IEEE Working Group on Lightning Performance of Transmission Line, ‘A simplified method for estimating lightning performance of transmission lines’. IEEE Trans. PAS, Vol. 104, No. 4, pp. 919–927, 1985 IEEE Working Group on Estimating the Lightning Performance of Transmission Lines. ‘Estimating lightning performance of transmission

[12]

[13]

[14]

[15] [16]

[17]

[18]

[19] [20]

[21]

[22]

[23] [24] [25]

[26]

Lightning interaction with power substations

[27] [28] [29] [30]

[31] [32]

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lines, II - update to analytical models’. IEEE Trans. PD, Vol. 8, No. 3, pp. 1254–1267, 1993 IEEE Guide for Improving the Lightning Performance of Transmission Lines. IEEE standard, pp. 1243–1997, 1997 CIGRE SC33-WG01. ‘Guide to procedures for estimating lightning performance of transmission lines’. CIGRE Technical brochure, No. 61, 1991 Jesus C., and Barros M. T. C. ‘Modeling of corona dynamics for surge propagation studies’. IEEE Trans. PD, Vol. 9, No. 3, pp. 1564–1569, 1994. Guiller J. F., Poloujadoff M., and Rioual M. ‘Damping model of traveling waves by corona effect along extra high voltage three phase line’. IEEE Trans. PD, Vol. 10, No. 4, pp. 1851–1861, 1995 Berger K., Anderson R. B., and Kroeninger H. ‘Parameters of lightning flashes’. CIGRE Electra, No. 41, pp. 23–27, 1975 Okabe S., and Takami J. ‘Occurrence probability of lightning stroke current waveforms and lightning failure rates of substations’. IEEE Trans. DEI, Vol. 18, No. 1, pp. 221–231, 2011

Chapter 3

Lightning interaction with power transmission lines William A. Chisholm1

The modern electrical infrastructure is the largest machine ever constructed. In real time, it balances generation and load over continental distances, with a minimum of inertia, using voltages that transform to the consumer level from medium-voltage (MV) distribution systems up to 69 kV AC line to line. Distribution stations are energised in turn by transmission networks, with voltages that can reach ultra-high voltage (UHV) levels of 1,000 kV AC or 800 kV DC. Each transmission line component has specific vulnerabilities to lightning stress. The simplest interaction of a direct stroke to a phase conductor leads to a flashover through air around nearby line insulation to ground. The resulting arc forms a phase-to-ground fault that must be detected and cleared by automatic circuit breakers, leading to a momentary outage and widespread voltage dip that lasts a few power frequency cycles. The measure of overhead transmission line lightning performance is given by the annual number of these tripouts, normalised to a reference line length of 100 km. Unshielded transmission lines in areas of low ground flash density may have an outage rate expressed as 3–10 tripouts per 100 km-year (100 km)–1 year–1. Each tripout on a transmission line affects all the connected distribution lines and represents a damage threat to several types of customer equipment. It is feasible to divert the lightning stroke current away from phase conductors to ground in ways that prevent faults. The most common lightning protection system (LPS) for a transmission line is an overhead groundwire (OHGW), positioned above the phases. As is true for structure protection, the OHGW system’s performance is imperfect. The threat levels considered by IEC in structure protection for negative-polarity first return stroke current peak amplitude (IˆF) are also relevant to lightning interaction with power transmission lines. Flashes with IˆF in the range of 3 kA < IˆF < 16 kA have small striking distance (SD) of 20 m < SD < 60 m that may cause shielding failures as shown in Figure 3.1. Chapter 7 of Volume 1 was devoted to calculating transient ground potential rise (GPR) with a concise representation of soil properties, electrode shape and size, giving a low-frequency resistance (RLF) and factors to estimate the corresponding impulse impedance (ZP) that relates peak GPR to IˆF or negative-polarity subsequent return stroke current peak amplitude (IˆS). As flashes with 50 kA < IˆF < 200 kA 1

Consultant, Toronto, Ontario, Canada

58

Lightning interaction with power systems, volume 2 Stroke to tower top

Stroke to overhead groundwire at midspan

θ: Negative shielding angle at tower

θ: Positive shielding angle at midspan θ Stroke to middle phase at midspan: Shielding failure and line-to-ground fault

Stroke to ground

Stroke to ground

Sag of OHGW Sag of phase

(a)

(b)

Figure 3.1 Nomenclature for transmission line shielding failures. (a) End view of line with large positive shielding angle, prone to shielding failures. (b) End view of line with small negative shielding angle, resistant to shielding failures

Stroke to tower with typical peak current Impulse overvoltage from tower to phase does not cause flashover of 1-m air gap

Stroke to tower with high peak current

Impulse overvoltage from tower to phase does not cause flashover of 1-m air gap Backflashover: Arc from tower to phase through air gap

Impulse overvoltage from tower to phase does not cause flashover of 1-m air gap

Transient ground potential rise: Peak current times footing impedance Adverse: 80 kA × 30 Ω = 2,400 kV

Transient ground potential rise: Peak current times footing impedance Typical: 30 kA × 20 Ω = 600 kV

(a)

(b)

Figure 3.2 Nomenclature for transmission line backflashover failures. (a) Normal interception of lightning by OHGW: GPR is less than line insulation strength. (b) Interception of high-magnitude lightning surge: GPR exceeds line insulation strength flow through the earthing of transmission-line towers (pylons) into the soil, significant GPR appears at the ground end of all insulators connected to that structure. If this GPR exceeds than the critical lightning flashover strength of an insulator, considering any system voltage bias and surge impedance coupling from OHGW to that phase, a backflashover will occur from ground to phase as shown in Figure 3.2. OHGW protection in Figure 3.2 improves when ZP is low (ZP < 20 W) at the base of every tower, but insulation strength, flash-to-flash log-normal distribution

Lightning interaction with power transmission lines

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of IˆF and tower-to-tower log-normal variation of soil resistivity are three important factors in this risk calculation. The efficiency of OHGW protection can be high, especially on UHV lines with critical impulse flashover (CFO) insulation levels exceeding 2 MV. Further improvements in the OHGW efficiency can also be achieved when they are combined with properly placed underbuilt groundwires (UBGW), which are sometimes disguised as HVDC line insulated earth return wires, as optical fibre cables (OPGW) installed in metal sheaths below the HV phases or as phase and neutral wires of MV circuits on the same towers. Backflashover outage rates (BFR) of 0.1 tripouts (100 km)–1 year–1 have been demonstrated in some regions. A total lightning outage rate of 0.5 tripouts (100 km)–1 year–1 is often achieved for Class-A reliability requirements, considering both shielding failures and backflashovers when using OHGW protection. Applications of transmission line surge arresters (TLSA) across insulators have proved to be less sensitive to earthing issues than OHGW and should be considered for HV line protection when median ZP > 50 W. In areas of high soil resistivity, new lines have been protected with a combination of OHGW and TLSA across all insulators. Older lines, either unshielded or using large positive shielding angles, have also been upgraded by protecting insulators on all exposed phases with TLSA. While the field experience is limited, ‘perfect’ lightning performance with no outages on lines using TLSA on all phases is a reasonable expectation during the arrester service life. This chapter organises the lightning interactions with power transmission lines from the simple consequences of a direct stroke attachment to an unshielded line, to the complex consequences of a stroke attachment to shielded line with multiple groundwires, including the UBGW effects from phases with TLSA protection. It builds on the information in Chapters 1 and 2 of this volume to develop important measures in transmission line lightning performance: NL, the number of flashes (100 km)–1 year–1 of line length per year, and the number of those flashes that bypass an OHGW, giving a Shielding Failure Flashover Rate (SFFOR) with the same units. Simplified models from industrial standards are then used to illustrate important principles and concepts such as the ‘critical current’ that just causes backflashover from a normally earthed component to a phase conductor. Matrix methods are used to manage the self and mutual surge impedance, with sample calculations shown using Microsoft ExcelTM as a common language. Specialised computer programs to calculate BFR on lines with OHGW and full or partial application of TLSA are described further in Chapter 12 of this volume.

3.1 Lightning attachment to overhead transmission lines Lightning location systems (LLS) were described in Chapter 4 of Volume 1 as modern tools to measure ground flash density Ng and infer peak current ˆI for individual strokes of either polarity. Comparisons of LLS observations with operating records demonstrate that lightning is a significant cause of line-to-earth faults on

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electrical systems. Nearly every attachment to an overhead distribution line, operating at system line-to-line voltage below 69 kV, causes a fault because OHGW protection above the phases is not used, the insulation strength is low and the surge impedance of the phases is high. Most high voltage (HV) transmission lines at system voltage from 69 to 230 kV do use one or two OHGW along with insulation that can withstand at least 500 kV for a short time. Lightning attachment remains a problem even for overhead transmission lines operating at the highest extra-high voltage (EHV) 315–765 kV and UHV levels, all using bundles of multiple phase conductors for each phase.

3.1.1

Overhead line attachment rates using ground flash density and typical dimensions

In 1947, Cuffe [1] reported construction details of 10-, 38- and 110-kV overhead lines in Ireland, along with 10 years of operating history. The 10-kV lines were operated individually, and thus it was possible to aggregate their individual performances in Figure 3.3 along with a country-wide average performance of 6.6 faults (100 km)–1 year–1(4.1 (100 mi)–1 year–1). This seems good compared to

Layer 1 Ng (Sum) 0 or less

(a)

0.50 or more

(b)

Figure 3.3 Incidence of lightning outages on 10-kV distribution lines and lightning ground flash density in Ireland. (a) Observed lightning outage rate, per 100 miles of distribution line per year, for 10 kV lines in Ireland, reproduced from [1] with permission from The Institution of Engineering and Technology, 1947. (b) Observed lightning ground flash density of Ireland, Ng, flashes km–2 year–1 based on optical transient density data [2] and Ng ffi OTD/3. A redrawn detail of Figure 4.1 of Volume 1

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61

‘Class C’ requirements of better than four faults (100 km)–1 year–1 for transmission lines with much higher insulation levels. However, this performance was achieved in a country that has one of the lowest values of Ng in the world. Figure 3.3 includes estimates of Ng from optical transient density (OTD) data [2]. The highest value of Ng for Ireland in Figure 3.3 does not exceed 0.6 flashes km–2 year–1. Modern standards for evaluating lightning protection of overhead lines [3–5] normalise the model for the number of lightning flashes to a line using Ng, and they introduce an attractive width of a conductor based on its height at the tower ht (m) such as NL ¼

 Ng  28h0:6 t þW 10

(3.1)

where NL is the number of flashes (100 km)–1 year–1, Ng is the ground flash density in flashes km–1 year–1 and W is the width of the line (m). The value of 10 in the denominator of (3.1) converts units of exposed width (m) and length (100 km) to km2. The value of Ng in (3.1) is established with a CIGRE lightning flash counter, with 1-s lockout time and uncorrected for multiple ground point terminations. For a single conductor or lines with vertical orientation, W ¼ 0 and for horizontal threephase AC wire configurations, W is twice the phase-to-phase spacing. In 1985, Anderson [6] consolidated the sustained lightning outage performance of 92 overhead power lines in the voltage range from 10 to 800 kV. Overall, sustained faults from lightning represented about 40 per cent of the total fault rate. This trend persists in the most recent on-line statistics posted by the National Electric Reliability Council (NERC) for North America. The sustained outage rates, NS in [6] were normalised by the expected number of flashes to the line, NL, considering individual line heights and local flash density in an exposure model like (3.1). Figure 3.4 shows an industry-wide trend to provide more effective lightning protection in areas where Ng exceeds five flashes km–1 year–1. It was concluded that utilities could, and did, make improvements to overhead line design features as adaptations to Ng. Anderson also plotted the trend of improved sustained-tripout performance with increased system voltage. This is overlaid in Figure 3.5 with standard design probability levels [7] recommended for shielding failures from low-amplitude first return strokes that terminate directly on energised phase conductors. Figure 3.6 shows the corresponding overlay of design probability levels for large-amplitude first return strokes, leading to backflashovers from portions of the electric power system that are normally at earth potential. Anderson’s focus on sustained outage rate NS from lightning reflected the electrical industry concerns of the 1980s, in a customer environment that tolerated any number of momentary disturbances if there was no loss of service lasting more than about 5 min. Automatic circuit breakers restore electrical service after a lightning fault by reclosing the circuit breaker terminals after a programmed time interval after a fault has been recognised. Transmission system breakers usually attempt to reclose every line-to-ground fault at least once, unless the feature is blocked for safety purposes, inhibited by system conditions or disabled from faults

Lightning interaction with power systems, volume 2 Fraction: sustained lightning outages/number of flashes to the line

62

No protection

100%

90%

10%

99%

1%

0.1%

99.9%

0

2 4 6 10 8 Lightning flash density Ng (flashes km–1 year–1)

12

Figure 3.4 Correlation of lightning protection efficiency, sustained outages divided by total number of flashes, with ground flash density. Redrawn from [6] with permission from The Institution of Engineering and Technology, 1985

Fraction: sustained lightning outages/number of flashes to the line

100%

No protection

10%

Backflashover (high current regime)

90%

95%, IEC 62305 LPL IV, III (100 kA) 98%, IEC 62305 LPL II (150 kA) 1%

99%, IEC 62305 LPL I (200 kA)

99.9%

0.1%

0.01%

0

100

200

300 400 500 System voltage (kV)

600

700

800

Figure 3.5 Correlation of lightning protection efficiency, sustained outages divided by total number of flashes, overlaid by shielding (low-current) design requirements in IEC 62305 [7]. Adapted from [6] with permission from The Institution of Engineering and Technology, 1985

Lightning interaction with power transmission lines

Fraction: sustained lightning outages/number of flashes to the line

100%

63

No protection Shielding (low current regime)

10%

84%, IEC 62305 LPL IV (16 kA) 91%, IEC 62305 LPL III (10 kA)

90%

97%, IEC 62305 LPL II (5 kA) 1%

99%, IEC 62305 LPL I (3 kA)

99.9%

0.1%

0.01%

0

100

200

300 400 500 System voltage (kV)

600

700

800

Figure 3.6 Correlation of lightning protection efficiency, sustained outages divided by total number of flashes, overlaid by backflashover (highcurrent) design requirements in IEC 62305 [7]. Adapted from [6] with permission from The Institution of Engineering and Technology, 1985 in communication systems. The performance of automatic reclosing was measured by a reclose success rate (RSR): RSR ¼ 100% 

NM  NS NM

(3.2)

where NM is the momentary outage rate, outages (100 km)–1 year–1, and NS is the sustained outage rate in the same units. The RSR for transmission systems is typically 90 per cent for the first attempt, 94 per cent with second attempt and 95 per cent with third attempt. With the pervasive adoption of computers and digital technology since the 1980s, and a shift from manufacturing to knowledge-based economy, the costs of momentary outages to advanced economies such as the USA and Japan have been assessed as two-thirds of the overall cost of imperfect electric system reliability [8]. Regulatory standards for reliability of electric power distribution lines such as [9] now define a momentary average interruption frequency index (MAIFI). The recognition of power quality problems from automatic reclosing also drives development of standards for improving equipment performance for short-duration voltage sags [10]. Thus, the interaction of lightning with power lines today calls on utilities to reduce NM as well as ensure that protection systems maintain adequate RSR and low NS.

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3.1.2 3.1.2.1

Local voltage rise from lightning attachment to transmission line phase conductor Surge impedance of single conductor over earth

Lightning impulse currents establish travelling waves on overhead conductors. An 1889 treatment of lightning conductor surge impedance [11] exploits the Telegrapher’s Equations, used again in Chapter 9 of Volume 1 to relate voltage and current through a scalar surge impedance, Z (W): rffiffiffiffi   L 2h ¼ 60 ln (3.3) Z¼ C r where h is the height above earth (m) of the round wire and r is its radius (m). Table 9.1 of Volume 1 introduced corrections to per-unit impedance for lossy wires and earth. At a high frequency, the surge impedance in (3.3) converges to a scalar ratio of per-unit length inductance L and per-unit length capacitance, C, with units of W. The parallel capacitance to ground and series inductance of a section of transmission line, length l (m) can be established from Z and the travel time t (s) ¼ l/c with speed of light, c ¼ 3  108 m/s: C¼

t l ¼ Z Zc

L ¼ Zt ¼

Zl c

(3.4)

In digital travelling wave calculations [12,13], (3.4) can model lumped capacitance as an open-circuit transmission line stub, and lumped inductance appears as a stub line that is earthed at its remote end.

3.1.2.2

Surge impedance response of short conductor over earth

Short lengths of conductor over earth, with t less than the rise time of the applied source, will behave as lumped capacitance C if open-circuited at both ends. If the conductor leads to a low-impedance termination to earth, it will present an inductance L in series with the impedance at the remote point. A 100-m section of substation bus, with r ¼ 0.1 m and h ¼ 10 m, will have Z ¼ 318 W from (3.3) and t ¼ 0.33 ms. The bus travel time t is small compared to the typical lightning surge equivalent front time TC of 2 ms. The substation bus can thus be modelled as parallel C ¼ 1.05 nF from (3.4) if unterminated, or as series L ¼ 106 mH if excited at one end and earthed at the other. The flow of current from lightning into the bus capacitance will cause a rate of voltage rise of dV/dt ¼ I/C. In practical cases, with Iˆ > 10 kA, this will exceed the flashover strength of the station insulators within a few ms. If the ramp current flows into a protective device such as a voltage-limiting surge arrester, the voltage rise at current peak, for a linear 2 ms front, will add LdI/dt ¼ 106 mH  Iˆ/(2 ms) ¼ (53 V/A) at the sending end to any arrester or resistive voltage at the remote termination at the wave crest, 2 ms. The inductive voltage rise will cause a flashover on 3-m insulation rated at a critical flashover (CFO) strength of 1,620 kV for any surge with IˆF that exceeds the median value of 31 kA, even if the remote end of the bus is earthed.

Lightning interaction with power transmission lines

65

A termination of a lightning stroke on a part of the electric power system that is normally energised is described as a shielding failure. In the case of substations, and normally for transmission line phase conductors too, any shielding failure normally causes an impulse flashover from line to earth. Once the arc is formed, power system fault current will flow through the same path. The arc from line to earth will be hot enough to reignite every time the fault current passes through zero. Most shielding failures result in shielding failure flashovers. The resulting overload must be detected and cleared by power system protection systems such as relays, breakers or fuses. The rate of shielding failures is expressed either as a mean time between failures (MTBF), failures year–1 for substations, or as an SFFOR on transmission lines.

3.1.2.3 Surge impedance response of long conductor over earth with no corona On long transmission line spans, a travelling wave behaviour, relating voltage and current by the self-surge impedance, Z11, will persist until there is a change in geometry. At an interface such as a line entrance to a substation, with different impedance Z22, there will be a reflection, governed for voltage waves by a reflection coefficient Gv: Gv ¼

Z22  Z11 Z22 þ Z11

(3.5)

The refraction coefficient (1  Gv) relates the forward-directed voltage wave in Z11 to the forward-directed voltage wave in Z22, the new geometry. The reflected voltage Gv will travel in the reverse direction in the medium with impedance Z11, back towards the source. If Z22  Z11, Gv ¼ –1, the transmitted wave will be 0, and the reflected wave will exactly cancel the incoming wave. Thus, a wave of zero potential will travel from the earthed object back along the medium Z11 towards the source. At the termination point, the current into Z22 will double, as the reflection coefficient for current Gc ¼ Gv. Extension of this travelling-wave model to cases with multiple conductors is found in Table 9.4 of Volume 1.

3.1.2.4 Interaction of lightning channels with long conductors Thin, vertical lightning channels have inherently high surge impedance, on the order of several hundred to a few kW [14]. The travelling wave ‘transmission line’ (TL) model for lightning [15] describes a wave of zero potential that sweeps up the pre-charged channel at constant speed. For many purposes, this average propagation velocity is about c/3 for negative return strokes. The TL model then relates the remote radiated fields from lightning to the source current and has other uses for predicting electromagnetic fields near the source as described in Chapter 4 of Volume 1 (Equation (4.6)). Researchers have exploited the reflection coefficients observed between tall towers and stroke channels to estimate the impedance of subsequent return-stroke channels. Impedance of first return stroke channels can be can be derived from any proposed relation between the leader potential VLP (kV) and IˆF (kA). Cooray [16]

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Lightning interaction with power systems, volume 2

‘Impedance’ of stroke channel: leader potential divided by peak current (Ω)

12,000

10,000 Observations: Mazur and Ruhnke, 2001 8,000

Estimate: Cooray, IET 2014, power law Estimate: Cooray, IET 2014, quadratic

6,000

4,000

2,000

0

0

20

40

60

80

100

Peak negative first return stroke current (kA)

Figure 3.7 Comparison of modelling and observations of first negative lightning return stroke impedance, based on ratio of leader potential VLP to peak negative first return stroke current IˆF offers a pair of estimates for VLP using quadratic and power-law fits to numerical modelling of the attachment process: 2 0:767 VLP ffi 5; 860 þ 1; 569  bI F  3:279bI F ffi 3; 760bI F

(3.6)

Numerical estimates of first return stroke channel impedance can be confirmed from field tests that infer VLP and IˆF using multiple measurements of remote electric and electromagnetic fields. The relations in (3.6) are overlaid with one dataset from [17] in Figure 3.7. An electrical power system conductor with 10-mm radius and clearance of 10 m above ground, has a surge impedance Zphase of 456 W using (3.3). When lightning terminates on a single conductor, the resulting surge current I will divide equally and flow into each branch away from the point of attachment, presenting a surge impedance of Z22 ¼ Zphase/2 ¼ 228 W. The voltage reflection coefficient Gv from (3.5) will be about –0.8 if the channel surge impedance Z11 ¼ 2 kW from Figure 3.7 modelling, or Gv ¼ –0.95 if Z11 of 9 kW is selected from the observations. VLP from (3.6) exceeds 20 MV for a weak flash with IˆF ¼ 10 kA. The voltage on the conductor relative to earth will be 5 to 20 per cent of VLP using this simplified surge impedance model. The voltage reflection coefficient of Gv ¼ –0.8 to –0.95 also suggests that the current flowing into the phase conductor in two directions would be about 80 to 95 per cent of the reference current IˆF that would flow into a low-impedance earth

Lightning interaction with power transmission lines

67

electrode. Lightning parameters for IˆF are normally measured on well-earthed instrumented towers. The minor interaction of lightning with the phase conductor impedance can be treated with this small adjustment, but it is usually ignored in engineering calculations [3–5] to yield (3.7): Vphase to earth ffi

Zphase  bI F 2

(3.7)

3.1.2.5 Surge impedance response of long, single conductor over earth including corona Partial discharges will develop when Vphase to earth (kV) in (3.7) causes an electric field gradient on the surface of the conductor Eo (kV/m) to exceed a level called the corona threshold. Corona can be visualised as a network of thin radial streamers that extends outward from the metal conductor. The ends of the streamers form a luminous envelope. The electric field gradient at the edge of this envelope under lightning transient conditions will be Eo ¼ 1,500 kV/m for negative polarity. The corresponding gradient for positive polarity corona around conductors over ground is about Eo ¼ 500 kV/m, so the luminous envelope is larger and more energetic. Chapter 7 of Volume 1 suggested a critical electric field in soil of Eo ¼ 400 kV/m for IˆF ionization. Corona discharges dissipate energy from the line and effectively increase the capacitance of the wire to earth. Modelling of impulse corona generally establishes an equivalent, increased radius of the corona envelope Rcorona (m) using the following recursive relation: Rcorona ¼

Vphase to earth   2h Eo ln Rcorona

(3.8)

Figure 3.8 illustrates the rapid convergence of the recursive equation using Excel. Fixed parameters are entered in cells B1, B2 and B3. The calculation is initialised with the physical radius of the conductor in cell B5. For novice users of Excel, the formula in cell B10, ¼B$3/($B$2*LN(2*$B$1/B9)), uses: ●

● ●

A relative reference to the cell just above, B9, containing the previous value of Rcorona; Absolute references to cells $B$1 and $B$2; and A mixed reference to the cell with peak voltage in row 3, B$3.

This allows the formula to be copied into multiple columns to explore the influence of impulse peak voltage, as shown in Figure 3.9. The corona radius affects the distributed capacitance C of the conductor over earth in (3.3) but not the distributed inductance L. The effective radius of the conductor becomes the geometric mean of physical radius r and Rcorona, giving a surge impedance in corona Zcorona (W) of   2h Zcorona ¼ 60 ln pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (3.9) r  Rcorona

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Lightning interaction with power systems, volume 2

Figure 3.8 ExcelTM calculation of corona radius for 10-mm radius conductor at height of 20 m with 1,000 kV lightning impulse voltage

Figure 3.9 ExcelTM calculation of conductor surge impedance in corona for 10-mm radius conductor at height of 20 m as a function of impulse peak voltage where Rcorona  r. For 100 kV peak impulse voltage in Figure 3.9, the corona radius converges to a value less than the physical radius, and thus no corona effect will occur. The surge impedance should be unchanged, and this is ensured by forcing a condition that Rcorona  r in (3.9).

3.1.2.6

Surge impedance response of bundle of conductors over earth with no corona

Extra-high voltage transmission lines make use of bundles of similar subconductors to reduce the surface electric field gradient from line voltage to acceptable levels. If the subconductor surface gradient from line-to-earth voltage exceeds about 1,800 kV/m, there may be corona discharges from the surface to air nearby,

Lightning interaction with power transmission lines

69

Vertical distance y (m)

20

10 Bundle conductor 0

Ground level

Bundle image conductors

–10

–20 –10

(a)

–5 0 5 Horizontal distance x (m)

10

(b)

Figure 3.10 ExcelTM calculation of distance matrix and surge impedance matrix for 10-mm radius subconductors in square bundle with spacing 0.457 m at upper subconductor height of 20 m. (a) Locations of conductors and images. (b) ExcelTM spreadsheet computing [Zii] especially when the conductor is wet. These discharges produce audible noise as well as electromagnetic interference. Modelling of the surge impedance of bundle conductors normally makes use of an equivalent bundle radius, which is given by the geometric mean of the subconductor radius and its centre-to-centre distance to every other subconductor in the bundle. Limitations of this approach were suggested in Section 9.1.2.2 of Volume 1. The general approach in ExcelTM is introduced for this simple case to calculate the self and mutual impedance of conductors over earth, and then to solve the impedance matrix over perfect ground. The bundle spacing is usually 1800 (0.457 m). Self-surge impedance of each subconductor in Figure 3.10 is given by r ¼ 0.01 m and h ¼ 20.0 or (20 – 0.457) ¼ 19.543 m in (3.3). These give values that are slightly different for Z11, Z22, Z33 and Z44 along the diagonal of the impedance matrix Zab in Figure 3.10. The mutual impedance between subconductors, Zab, is given by   d 0 Zab ¼ 60 ln ab (3.10) dab where dab0 is the distance from subconductor a to the image of subconductor b, and dab is the direct centre-to-centre distance. The matrices of dab and dab0 are developed using the subconductor locations, the subconductor image locations (with negative values of height y) and the distance calculations in Figure 3.10. The expression in cell F23, ¼SQRT(($D23-F$16)^2þ($E23-F$17)^2), in Figure 3.10 shows how mixed references to data in the top two rows and two left-hand columns are formed to calculate distances between subconductors and their images. The surge impedance matrix [Zab] is developed from (3.3) for the diagonal elements and (3.10) using the distance matrices dab and dab0 for the off-diagonal mutual impedances. The symmetrical matrix is inverted using the MINVERSE

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Figure 3.11 ExcelTM calculation of bundle conductor surge impedance for 10-mm radius subconductors in square bundle with spacing 0.457 m at upper subconductor height of 20 m function in Figure 3.11. The entire 4  4 area where the inverse [Zab]–1 will be placed is highlighted, the expression ¼MINVERSE(A2:D5) is typed into the upper left corner, then the F2 button is pressed, then will populate every cell and place the curly braces {} around the expression. The same process, using the MMULT function with F2 and then is used to multiply [Zab]–1 by a vector of potentials, set to 1,000 kV in cells E7 to E10 in Figure 3.11. The resulting currents in cells G7 to G10 are nearly the same, 778 A in the upper two subconductors and 786 A in the lower two. They are slightly different because the subconductors are at different heights and have slightly different surge impedance, respectively, 497.6 and 496.3 W. The applied potential, divided by the sum of currents in all four subconductors, yields the surge impedance of the bundle of four conductors, 319.8 W. This is the surge impedance in each direction; a low-amplitude surge to the middle of a long bundle of four phase conductors will thus encounter a surge impedance of 320 W/2 ¼ 160 W because the impressed current divides equally into each branch.

3.1.3

Role of span length and nearby arresters on peak insulator voltage

Figure 3.12 shows lightning intercepting an unshielded phase conductor near its attachment to a tower. Two identical voltage and current waves will travel away from the source, to the left and right.

Lightning interaction with power transmission lines

71

I

S

S Vpk

VIR(I/2)

VIR(I/2) Vfooting = 0

Vfooting = Rf I/2 Rf

Rf

Vfooting = Rf I/2 Rf

Figure 3.12 Schematic of current flow and overvoltage across insulation point, considering surge arresters at distance S Low-voltage waves travel along a phase conductor over perfect earth at the speed of light, 300 m ms–1. Radial corona streamers increase the mean path length and thus tend to retard the propagation velocity and increase the rise time of the portion of any overvoltage above the corona threshold. The peak voltage Vpk from line to earth at the point of lightning termination I in Figure 3.12 is a sum of three components, related to the flow of current I/2 in each branch. The flow of current I/2 into an earthing impedance Rf generates a resistive rise, Vfooting relative to earth. Figure 3.12 also shows the passage of I/2 through a pair of surge arresters. These components were introduced in Section 9.5 of Volume 1. The flow of I/2 through each arrester leads to a voltage rise VIR across its terminals. TLSA are applied only to protect against lightning impulse insulator flashover across line insulators, to distinguish them from station-class surge arresters applied across terminals of equipment to limit both slow and fast-front overvoltages at substations. Finally, at the point where the lightning enters the line in Figure 3.12, an inductive or travelling wave response will add to Vpk, computed using the connection of length S from lightning stroke attachment to the remote, protected points on each side. Simplified modelling converts the surge impedance of the phase conductor in Figure 3.12 and its length to an equivalent inductance, and then divides this value by the equivalent front time of the surge. This summation synchronises the peak current and maximum dI/dt in time, which matches the observations of lightning waveshapes [14] for both first and subsequent strokes. Some typical line parameters for this calculation are: I ¼ 10 kA; equivalent (linear ramp) front time 2 ms; spans S ¼100 m; Rf ¼ 20 W; arresters rated at 96 kVrms line-to-earth maximum continuous operating voltage (MCOV) with

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Lightning interaction with power systems, volume 2

maximum discharge voltage of VIR ¼ 206 kV peak for 5 kA 8/20 current wave; conductor radius of 10 mm and average height 20 m. A review of Figure 3.9 suggests that 5 kA in each branch would reduce the surge impedance from 498 to 399 W, and cause a peak transient voltage rise of 2,000 kV, if the span length is long. However, the surge will only reach this overvoltage level at 2 ms. With S ¼ 100 m and v ¼ 0.9c, the protection from adjacent arresters will arrive at 0.74 ms, well before the corona develops to its full extent. Also, as mentioned, the corona only affects the parallel capacitance, not the series inductance. Thus, we use the impedance unmodified by corona (498 W), the 0.37-ms one-way travel time at speed of light and (3.4) to obtain an equivalent series inductance of LS ¼ 184 mH. The voltage Vpk in Figure 3.12 will rise linearly to 5 kA  (184 mH/2 ms) þ 5 kA  20 W þ 206 kV ¼ (461 kV þ 100 kV þ 206 kV) ¼ 767 kV. This overvoltage can cause a flashover from attachment point to earth if the gap distance between conductor and earth at Vpk is less than 1 m. The dominance of inductive voltage rise in this calculation also illustrates why arresters need to be close to a protected asset to be effective.

3.1.4

Shielding of transmission line phase conductors using overhead groundwires

Lightning may cause direct damage to phase conductors by introducing heat energy at the point of attachment. The flow of charge through the arc can melt several strands of the aluminium conductor, steel reinforced (ACSR) in use around the world. The broken strands from lightning attachment are more of a concern when the core that supports the wire mechanically is not steel. Lightning also initiates indirect damage. The short circuit formed by any phase-to-earth flashover arc from overvoltage Vpk in Figure 3.12 is kept alive with every half cycle of power system fault current that flows through the same path. If the arc root of power system current remains in one location, for example, at a pinhole formed in a phase conductor coated with a dielectric, then the energised conductor will melt, break and fall to the ground. An OHGW can be located to divert lightning away from phase conductors, and thus protect them from charge ablation damage. This often means that the OHGW have a short service life, compared to most transmission line components. In North America, some OHGW made of steel or aluminium-clad steel are worn out after 25 to 45 years of service, while ceramic insulators sometimes retain most of their electrical and mechanical integrity after 100 years. In simplified travelling wave modelling, a propagation velocity of v ¼ 0.9c is often assumed for span length S in Figure 3.12 of 70 < S < 500 m [4]. This considers the horizontal distance, as well as the propagation down and up the tower at the speed of light. Table 3.1 shows the limitation of this fixed factor for short spans of tall double-circuit transmission lines. An extra 6 m of electrical clearance from the top phase conductor to an OHGW above is added from the sum of midspan clearance (10 m) and conductor sag.

Lightning interaction with power transmission lines

73

Table 3.1 Typical tower height from span length, midspan clearance 10 m, electrical clearance 6 m for shielded lines Span length (m) Sag of ACSR (m)* OHGW height of horizontal circuit (m) Effective propagation velocity, % of c OHGW height of vertical circuit (m) Effective propagation velocity, % of c

70 0.34 16.3 81 28.3 71

100 0.70 16.7 86 28.7 78

150 1.6 17.6 90 29.6 84

200 2.8 18.8 91 30.8 87

300 6.3 22.3 93 34.3 90

400 11.2 27.2 94 39.2 91

500 17.5 33.5 94 45.5 92

* Using ACSR sag ¼ 0.0014span2/(%RTS) and tension of 20% of rated tensile stress [4]

New transmission lines, and many existing lines, have been fitted with special OPGW with hollow interior cores that hold and protect a bundle of optical fibres. There are specialised tests that simulate the charge damage to these OPGW in IEC and IEEE standards. These switch a DC source to introduce charge of 50 to 200 C over a duration of 0.5 s. Imperfect OHGW shielding can be addressed by applying TLSA to exposed phases. TLSA can generally dissipate impulse charge in the range of 1.2 to 3.6 C, according to IEC 60099–4 Ed. 3 classes SL to SH and IEEE C62.11–2012 energy classes C to J. A single arrester with these ratings cannot survive the charge in a typical negative lightning flash, which is about 7 C considering a first stroke and two subsequent strokes [14]. Figure 3.12 shows that arresters are placed in parallel, but any TLSA near an attachment point will heat up and absorb more charge than those at remote points. In this application, the role of the OHGW is to attract largeamplitude flashes and can reduce the number of times that a TLSA must dissipate energy from the charge, thus improving its service life.

3.2 Lightning impulse flashover of power transmission line insulation Section 3.1 established the main features of the lightning interaction with power transmission lines, including the calculation of the local overvoltage from conductor to earth based on its surge impedance in corona. The consequence of this attachment is a unipolar surge voltage, usually negative in polarity, across the terminals of an insulator that is dimensioned to withstand the ac line voltage. Section 9.4 of Volume 1 set out several models for the electrical strength of insulators under fast-front overvoltage. The lightning impulse insulation strength (kV), divided by the surge impedance (W), gives a critical current (kA). A lightning flash with any stroke that exceeds its corresponding critical current will cause a line-toearth fault. There will be different critical currents for first and subsequent strokes, and for lightning of positive and negative polarity and for different attachments to phase conductors, towers and OHGW.

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Lightning interaction with power systems, volume 2

3.2.1

Lightning impulse voltage test waveshapes

Observations of lightning overvoltages on overhead transmission lines were made using some of the first cathode ray oscilloscopes. Field results provided a mixed set of induced overvoltages, with relatively low, positive amplitude of less than 300 kV peak, and a few negative overvoltages from direct strokes, with peak voltages sometimes exceeding 1 MV. By 1931, the AIEE (which merged with IRE to form IEEE in 1963) recommended three double-exponential test waves to be used in coordination of rod–rod gap protection, through assured disruptive discharge (ADD), with the basic impulse level (BIL) withstand strength of transformer and equipment insulation. The waveforms were designated 0.5/5, 1/10 and 1.5/40. The first number in each designation gives the front time in ms, and the second number indicates the time to half value measured from the start of the wave, also in ms. It proved difficult to generate 0.5/5 waves in HV laboratories of the 1930s for transmission line insulator tests, even though the 0.5 ms front time matches the median equivalent front time tm ¼ 0.308 ms from observations in [14]. A 1/5 wave was adopted by the IEEE Lightning and Insulator (L&I) Subcommittee in 1933. The 1.5/40 wave became the 1/40 wave after adoption of the definition of 10–90 per cent rise time rather than using a zero-to-peak measure. Cross-adoption of the lightning impulse voltage test in both insulation and transformer testing occurred in the USA in the early 1940s. In the UK, voltage doubling at transformer bushings was recognised in 1932 [18]: Travelling waves originating in the transmission line arrive at the transformer terminals, and the voltage associated with a travelling wave may be greater than the normal line voltage. . . . A transformer terminal is a point of discontinuity, and, since the surge impedance of a transformer is greater than that of an overhead line, the voltage produced at the transformer terminals is greater than the voltage E associated with the incoming wave. In the limit, regarding the transformer as constituting a break in the circuit, the voltage at the terminals becomes 2E. Transformer bushing and transformer winding insulation must therefore, in the absence of protective devices, be capable of withstanding an impulse voltage which is definitely greater than that of the incoming wave. The BSS testing standards at that time made use of one-minute AC tests in wet and dry conditions, but no specific impulse test. The UK used 12 standard (146 mm  254 mm) discs in a normal string at 220 kV, giving a dry AC flashover of 580 kV. It was recommended [18] to use a ‘safety string’ of 10 discs with 510 kV dry AC flashover, located close to the transformer terminals, to limit overvoltage magnitude. However, this protection leads to a steep collapse of voltage, resulting in the need for ‘chopped wave’ tests with gaps that flashover at 2 or 3 ms as shown in Figure 3.13 [19]. In Europe, around the same time, a tail time of 50 ms was adopted for all lightning impulse voltage waveshapes. A global lightning voltage impulse waveshape was standardised as 1.2/50 in the early 1960s. To solve problems with oscillations, the rise time specification TC in Figure 3.14 is defined to be 1.67 times

Lightning interaction with power transmission lines

Figure 3.13 Voltages applied across transformers in 1950. Calibrating oscillation: 1 MHz. Reproduced from [19] with permission from The Institution of Engineering and Technology, 1950

Um 0.9Um

0.5Um 0.3Um T0.3

0

A Tc

T0.9 T0.5

Tm t Tg

(a)

Uu

0.7Uu

T0.1 0.1Uu

T0.7

0 (b)

Tw

0 t

ΔTu

Figure 3.14 Definitions of lightning impulse waveshape features. Reproduced from [21] with permission from The Institution of Engineering and Technology, 1987. (a) Full lightning impulse wave. (b) Chopped lightning impulse wave

75

76

Lightning interaction with power systems, volume 2

the time difference (T0.9 – T0.3) between 30 and 90 per cent points. Monitoring of the 10, 30 and 90 per cent levels of lightning current wavefront and the 50 per cent level on the wavetail T0.5 remains a standard reporting practice today [14,20]. A lightning impulse voltage wave of sufficient magnitude Um will cause a disruptive discharge through an air gap. The flashover causes a steep collapse in voltage, called a chop, with chopping time DTu defined in Figure 3.14. The voltage at the time of chop Uu may be on the rising part of the waveshape, called a front-ofwave flashover, or may occur after the peak, making it a tail-of-wave flashover. The time to chopping is defined as the duration from virtual origin A to the start of the chop, based on extrapolation of T0.1 and T0.7 to Uu. The CFO of an insulation system is the peak voltage, using the waveshape in Figure 3.14, that causes a disruptive discharge in 50 per cent of the applications. If a peak voltage that exceeds the CFO is applied, self-restoring insulation such as air tends to flashover faster with decreasing time to chopping. For flashover on the tail of wave, the peak voltage Um is reported even though the voltage at the time of flashover Uu was lower. For front-of-wave flashover, Um ¼ Uu. The peak values Um are plotted against the corresponding time to chopping to form a volt–time curve, introduced in Section 9.4.2.2 of Volume 1.

3.2.2

Single gap full-wave flashover strength for dry arc distance of 0.5 to 10 m

3.2.2.1

Full lightning impulse waveshape for first stroke

A standardised waveshape was established in the 1930s, based on observations of overvoltages corresponding to first return strokes that struck long overhead conductors. Then, many electrical utilities and manufacturers carried out standard impulse tests on chains of suspension insulators, with cap-to-pin spacing of 146 mm (5¾00 ) and 254 mm (1000 ) diameter. For strings exceeding 0.6 m length (four discs), Figures 3.15 and 3.16 show that the flashover gradient of test results, flashover voltage divided by the dry arc distance from the edge of the top cap to the bottom pin, is nearly constant for each waveshape. Points of reference are given in Figure 3.15 by the flashover strength at peak of AC wave, þ500 kV/m, compared to þ600 kV/m for the 1.5/40 wave and þ730 kV/m for the 1/5 wave. Thus, it takes a higher voltage to cause a flashover with a faster wave that has only a limited time to deliver energy into streamer and leader development compared to a slower wave. Figures 3.15 and 3.16 also show impulse flashover gradients measured on station post insulators with overall length up to 4.6 m [22]. Despite the differences in geometry, these show nearly the same 1.5/40 strength as suspension discs and rod–rod gaps. Positive lightning impulse strength in Figure 3.15 is relevant for the case where the normally earthed tower is struck by a negative lightning flash, bringing the earthed end of the insulator to a lower potential than the phase. The tests are carried out by applying a positive impulse to the phase conductor, giving the same electric fields, streamer and leader development if the earthed end of the chain remains at zero potential. In contrast, negative lightning impulse strength in Figure 3.16 is

Lightning interaction with power transmission lines

77

X = 192 mm S = 146 mm

1,000 900 Minimum impulse flashover gradient (kV/m)

800 s 700 181"

600 500 400 1/5 positive, discs 1.5/40 positive, discs 1.2/50 positive, discs 1.5/40 positive, posts Crest of 60 Hz, discs

300 200 100

~ 4,600 mm D=

0 0

1,000

2,000

3,000

4,000

5,000

2100 BIL

Dry arc distance D (mm)

Figure 3.15 Positive lightning impulse flashover gradients for ceramic posts and ceramic disc insulator strings. 1.5/40 string data: AIEE 1934. Post data: [22]

Minimum impulse flashover gradient (kV/m)

1,000

≥700 >1,000

900

250 ≤ d ≤ 2,500 >1,000

300 ≥4000

800

Insulator

700 181"

600 500 1.2/5 negative, rod gap

400

1.2/50 negative, rod gap 300 1.5/40 negative, posts 200

~ 4,600 mm D=

1.2/50 negative, disc insulators

100

Crest of 60 Hz, rod gap

0 0

1,000

2,000

3,000

4,000

5,000

2100 BIL

Dry arc distance D (mm)

Figure 3.16 Negative lightning impulse flashover gradients for rod–rod gaps, ceramic posts and ceramic discs. Gap data: IEEE Std. 4. Post data: [22]

78

Lightning interaction with power systems, volume 2

relevant for the calculation of shielding failure critical currents for lines and stations.

3.2.2.2

Volt–time curve for standard lightning impulse waveshape

There is a dependence in the flashover strength on the tail time of the wave, comparing the 1.2/5 and 1.2/50 curves in Figure 3.16. It is reasonable to infer that applying a super-critical peak impulse voltage will lead to flashover in a shorterthan-normal time, because the high-amplitude surge delivers enough energy to develop the arc in a shorter time. Integration methods in Section 9.4.2.3 of Volume 1 and leader-progression models for flashover in Section 9.4.2.4 of Volume 1 attempt to capture this physics. The effect is illustrated in Figure 3.17 from [23] comparing the volt–time curves for ceramic insulators with 500 (127 mm) spacing against the volt-time curves of rod gaps with the same dry arc distance. Both show similar upturn in strength for the air gap as time to chopping reduces. For example, with a 7000 gap 1,800 Units in string 16

14

1,600

12

Rod-gap spacing, in.

1,400

80 10

Applied voltage (kV)

1,200

70

8

1,000

60 6

800

50 40

600

4 30

400 2 200 0

0

2

4

6 Time (μs)

8

10

12

Figure 3.17 Volt–time curves for 1/50 lightning impulse: rod-gap (broken line) and ceramic disc strings (solid line). Discs had 254 mm diameter and 127 mm spacing, without arcing horns. Horizontal axis: time to chopping. Reproduced from [23] with permission from The Institution of Engineering and Technology, 1957

Lightning interaction with power transmission lines

79

(1.778 m) the strength at 2 ms is 1,580 kV, giving a gradient of 889 kV/m. The strength of the 14-unit string with flashover at 2 ms is 1,440 kV, or 810 kV/m. The corresponding gradients at 6 ms time to chopping are 703 and 645 kV/m. The volt–time curve for strings of ceramic discs was generalised in 1975 [24] for dry arc distance, measured from live part of bottom insulator to earthed part of top insulator, up to 11.2 m. The median flashover gradient E50 for strings of ceramic insulators as a function of time to chopping tc is given from (9.18) as E50 ¼ 400

kV 710 kV þ 0:75m m tc

(3.11)

where tc is in ms and E50 is in kV/m. Equation 3.11 provides a gradient of E50 ¼ 822 kV/m at 2 ms and 585 kV/m at 6 ms, similar to the values of 810 and 645 kV/m for the 14-unit string in Figure 3.17.

3.2.2.3 Full lightning impulse waveshape for subsequent strokes The median duration of a subsequent stroke in [14], measured from 2 kA to the half-peak value on the tail, is given as 32 ms compared to 75 ms for negative first return strokes. The adjustment of impulse flashover gradient for an 8:1 decrease in tail time Tg under positive polarity in Figure 3.15 is about 22 per cent. There are no corresponding data in standards for 1/5 negative impulses. As median first and subsequent stroke waveshapes are both close to the 1.2/50 standard, the negativepolarity 1.2/50 impulse flashover level is recommended for computing the rate of subsequent-stroke flashover failures.

3.2.2.4 Effects of nonstandard voltage waves There are several different reasons of why lightning overvoltages deviate from waveshape of the impressed current. The most important relates to the transmission line span length [25]. A typical transmission span length is 200–400 m, with corresponding two-way travel time of 1.5 to 3 ms. This means that a surge current impressed at a tower will reach its peak, and start to fall, before reflections from the two adjacent towers arrive. A second source of nonstandard overvoltage waveshape relates to the V ¼ LdI/dt transient associated with the inductance of the connection from OHGW to earthing system through pole bond or tower. The peak voltage at tower top is the sum of the full inductive rise and the resistive rise of the earthing system because the peak of the lightning surge current and its maximum steepness occur at the same time [14]. Finally, lightning surge currents are observed to have concave fronts, rather than rising linearly from a low level as in Figure 3.14. Gary et al. [26] noted several of these causes of nonstandard voltage waves in lightning backflashover and made some estimates of the effects on wavetail time Tg on flashover voltage. They measured the influence of these short wave-tail times on insulator strings with 0.53 to 2.7 m distance between arcing horns. Figure 3.18 shows these accessories, which are recommended in CIGRE Technical Brochure 365 [27] to divert power system arcs away from fragile silicone-rubber surfaces and interfaces.

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Lightning interaction with power systems, volume 2

2,000 d

d = 2.70 m

d

110 kV b

U50 (kV)

1,500

d = 1.62 m

1,000

220–400 kV a

d = 1.05 m d = 0.79 m d = 0.53 m

HV insulator strings with arcing horns or arcing rings h   i   þ logd U50 Tg ¼ CFO  log T33:6 0:31 Tg g

Empirical expression fitted to experimental data

0 4 8 13

50

25 Tg (μs)

50% probability withstand voltage of disc insulator strings as a function of time to half value Tg (Figure 3.14)

Figure 3.18 Variation in flashover voltage with wavetail time for strings of ceramic disc insulators with arcing horns. Reproduced from [26] with permission from The Institution of Engineering and Technology, 1986. Most insulator models described in Section 9.4 of Volume 1 capture certain portions of the increase in strength with decreasing time to chop tc and decreasing tail time Tg. For example, the LPM constants proposed by Motoyama [28] provide a close match to volt–time gradient (3.11) for 0.5 < tc < 3 ms with dry arc distance of 1 to 3 m, both typically of greatest interest for transmission backflashover calculations.

3.2.3

Strength of multiple air gaps in parallel under shielding failure conditions

The probability of flashover of any one insulator, given that there are n insulators in parallel and exposed to the same conditions, is PðanyofnÞ ¼ 1  ð1  Pð1ÞÞn

(3.12)

For continuous AC line voltage and switching surge overvoltages, the number of insulators with the same stress could be 50 or 300 on each phase. A large value

Lightning interaction with power transmission lines

81

of n in (3.12) shifts the CFO downward, and at the same time reduces the standard deviation. For switching surges with 8 per cent relative standard deviation, the CFO is reduced by 20 per cent if there are 100 insulators in parallel on a phase. Under lightning surge conditions, it is no longer true that all insulators are exposed to the same voltage, and the relative standard deviation drops to about 3 per cent. In the case of direct stroke to phase here, the heavy corona on the phase distorts the voltage as it propagates along a conductor. At adjacent insulators, the voltage peaks will be attenuated, and the rise times will be longer than at the attachment point.

3.2.4 Strength of multiple air gaps in series Some transmission lines are constructed with wood poles and crossarms. Wood cannot provide good long-term power frequency electrical insulation in outdoor conditions. However, wood does provide considerable lightning impulse strength [29]. Methods in [5] combine the strength of individual porcelain, polymer, wood or fibreglass components, taking the electrical insulator as the base and adding CFO for every meter of additional component dry-arc length. The CFO-Added method in [5] has a library of second- and third-gap components. It is missing a listing for covered conductor (cross-linked polyethylene, XPLE of 1.5-mm thickness) that includes covered tie-wrap. Covered conductor systems add about 120 kV to the CFO of porcelain post insulators. This is important in countries such as Japan and Korea that mandate some use of covered conductor on overhead lines. An alternative to the CFO-added method describes the combined strength of wood crossarm insulation in series with porcelain discs, where both individual values of CFO are known [29], using: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 (3.13) CFOCombined ¼ CFO3Wood þ CFO3Porcelain

3.2.5 Evolution of surge protective devices for insulation coordination A TLSA is selected to limit fast-front overvoltages to levels significantly below the insulator and air gap CFO. A general description of the voltage–current characteristic of metallic oxide varistor (MOV) arresters breaks down into low-current, normal and high-current regimes. The high-current upturn often occurs for surge currents more than 10 kA, as illustrated previously in Figure 9.4 of Volume 1, and can be modelled as a series resistance. In some arrester configurations, a series air gap is introduced between the phase conductor and the arrester. This externally gapped line arrester (EGLA) configuration has some important benefits, as noted in CIGRE TB 440 [30]. The housing of the arrester will not degrade as quickly if it is not energized by line voltage in normal operation. The EGLA configuration also eliminates troubleprone flexible mechanical connections, and there is no need for dangerous

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Lightning interaction with power systems, volume 2

100% 90% 70% 50% 30% 10% 0%

CH1 tension 0

50.0 μs

100 μs

150 μs

200 μs

250 μs

300 μs

Figure 3.19 Typical tail-of-wave flashover on EGLA with 50-cm series air gap and 240 kV clipping level of series varistor unit explosive-disconnect devices, which must be rendered secure during transport and safe during disposal. Impulse testing of an EGLA leads to a result that is the sum of the air gap flashover level and the arrester protective level. The testing also tends to give flashover late on the tail of the impulse wave, as seen in Figure 3.19.

3.2.6 3.2.6.1

Design and performance of unshielded power transmission lines Critical current for first return stroke to phase

The critical current IˆFCritical that just causes the CFO to appear across an insulator placed across the gap in Figure 3.12 is 2  CFOLI bI FCritical ¼ ZCorona

(3.14)

where CFOLI is given by dry arc distance, multiplied by a flashover gradient E50 of –605 kV/m from Figure 3.16 and ZCorona is calculated for single or bundle conductor, using VPhase to Earth ¼ CFOLI in (3.8). The probability of exceeding IˆFCritical is given approximately by [4,5,14]: PðI > bI FCritical Þ ¼ ð1  LOGNORM:DIST ðbI FCritical ; LN ð31:1Þ; 0:484; TRUEÞ

ffi"

1   # bI FCritical 2:6 1þ

(3.15)

31 kA

where the values 31.1 kA and slnI ¼ 0.484 for the natural lognormal distribution are from [14] and the LOGNORM.DIST function in Excel computes the required integral. For a typical bundle conductor surge impedance of 320 W, and CFOLI of 2,210 kV for 25 standard discs with 3.65 m of dry arc distance, (3.14)

Lightning interaction with power transmission lines

83

yields- IˆFCritical ¼ 3.8 kA. The probability of exceeding this current, using (3.15), is 89 per cent.

3.2.6.2 Critical current for subsequent return stroke to phase The example in Section 3.2.6.1 computed that 11 per cent of the first return strokes to a phase conductor bundle would not have enough current to cause a flashover across a string of 25 disc insulators normally used on 500-kV system voltage. However, this calculation of flashover risk is incomplete [4]. There will be an 82 per cent chance that one or more subsequent strokes will follow through the same channel, and a median 2.4 subsequent strokes per flash [14]. The median tail time of subsequent return strokes is about half of the median tail time for first return strokes. However, the difference between 1.5/40 and 1.2/50 strength of disc insulation in Figures 3.15 and 3.16 is small. Thus, IˆSCritical ffi IˆFCritical. The probability of exceeding IˆSCritical is given approximately by [4,5,14]: PðI > bI SCritical Þ ¼ ð1  LOGNORM:DIST ðbI SCritical ; LN ð12:3Þ; 0:53; TRUEÞ ffi"

1   # bI SCritical 2:7 1þ

(3.16)

12 kA

In this case, with IˆSCritical ¼ 13.8 kA, there is a 41% chance that the first subsequent stroke will flashover, 41% that the second will flashover and so on. The probability of subsequent-stroke flashover is PS ¼

1 X

PN  ð1  ½1  PðI > bI SCritical ÞN 1 Þ

(3.17)

N ¼2

In close comparison with LLS observations, subsequent-stroke flashovers on transmission lines and stations have sometimes been seen to be the sequence of a low-amplitude first return stroke, IˆF < 10 kA that caused a shielding failure, forming a channel that was re-illuminated by a subsequent stroke IˆS with larger peak current that was time-matched to the power system fault.

3.2.6.3 Probability of exceeding critical current with any stroke in a flash The total probability of flashover from lightning attachment, considering both IˆF and IˆS, makes use of the median number of return strokes, (3.4), and the natural log standard deviation slnN ¼ 0.96 [14] to compute PN, the probability of exactly N subsequent strokes in Table 3.2. There is about 7 per cent chance of N > 10 and the infinite sum in (3.17) converges to PS ¼ 56 per cent when these terms are included. The overall probability of flashover on an exposed 500-kV phase becomes 95 per cent, rather than unity in [4] or 89 per cent based only on IˆF.

84

Lightning interaction with power systems, volume 2

Table 3.2 Calculation of probability of exceeding critical current for direct stroke to bundle conductor with ICritical ¼ 13.8 kA # of strokes N

1

2

3

4

5

6

7

8

9

10

Sum

PN, % with exactly N* 18% 24% 17% 11% 8% 5% 4% 3% 2% 2% 93% 89% 41% 66% 80% 88% 93% 96% 98% 99% 99% Probability of any exceeding IˆCritical Product in (3.17) n/a 10% 11% 9% 7% 5% 4% 3% 2% 2% 51% * Based on PN ¼ 1 – LOGNORM.DIST(N,LN(3.4),0.96,TRUE)

Table 3.3 Distribution and transmission line tripout criteria and performance in Australia [29] Line voltage (kV)

11,22 33 66 110 132

3.2.6.4

Total outage rate, (100 km)–1 year–1

Lightning outage rate, (100 km)–1 year–1

Acceptable

Very Good

Unshielded

Shielded

10 7 5 1.5 1.5

5 3 2 0.5 0.5

6.6 9 3.9

0.46 0.48 0.7

Predicted and observed flashover rates of unshielded lines

If it is accepted that nearly every lightning flash to a phase conductor will cause a line-to-earth fault, then the observed tripout rate of a transmission line with no OHGW provides a good estimate of the number of flashes to the line. Observations can be validated against models for the average number of flashes to a horizontal conductor at average height h [31]: NSF ffi

 Ng  0:45 38hc þ W 10

(3.18)

where Ng is the ground flash density (flashes /(km2-year)), W is the width of the line (m, twice the phase to phase separation), hc is the average conductor height (m, height at the tower minus 2/3 of the sag) and the shielding failure flashover rate NSF in flashovers (100 km)–1 year–1. Unshielded 66-kV and 110-kV transmission lines in Australia had lightning outage rates of 7 and 9 tripouts (100 km)–1 year–1 [29], respectively. Table 3.3 lists thresholds for ‘Acceptable’ and ‘Very Good’ total outage rates as a function of system voltage. Unshielded lines did not achieve acceptable outage rates. Similar lightning tripout rates of 6 to 9 outages (100 km)–1 year–1, normalised to a ground flash density of 1.0 flash/(km2-year), were reported for several 500 kV

Lightning interaction with power transmission lines

85

unshielded lines in British Columbia, Canada [32]. The computed critical currents for these 500-kV lines were in the range of 13 to 20 kA.

3.3 Bonding, earthing and equalisation of potential differences on transmission lines The concept of shielding using OHGW was introduced in Section 3.1.4. The OHGW divert lightning away from phase conductors and protect them from charge ablation damage. The OHGW will rise in potential, and the overvoltage on a normally earthed component bonded to the OHGW may cause a backflashover. Earthing of the OHGW, through metallic connections to electrodes buried in the soil, raises the critical current. This is the main reason for the improved lightning outage rate for shielded lines in Table 3.3. The OHGW protection is less effective if the earthing electrodes are laid on the surface of rock, resulting in high earthing impedance, but there are still some benefits related to the mutual surge impedance from OHGW to protected phases. Generally, the greatest threat to a shielded transmission line is from backflashover resulting from large-amplitude first strokes, with IˆF > 40 kA for 115-kV systems and IˆF > 100 kA for EHV systems. Most shielded transmission lines have critical currents that greatly exceed the median value of IˆS ¼ 12 kA [14] for subsequent strokes. Lines constructed with tall, thin towers or wire downleads may be vulnerable to backflashovers or insulator punctures related to the fast rate of rise of subsequent strokes.

3.3.1 Analysis of transient voltage rise on connections from OHGW to earthing electrodes 3.3.1.1 Conical antenna surge impedance If the wire radius r and height h are fixed in (3.3), the surge impedance of the horizontal wire over earth is constant. Consider a case where their ratio, h/r, is fixed instead. If the radius of the wire is reduced as the height is decreased, the surge impedance of the system should remain constant. Taken to the extreme, if the ratio h/r is fixed, the tapered conductor can be brought down to a point on the earth without causing a reflection that would be analysed using (3.5). The geometrical object formed by holding a constant ratio h/r is a cone. The conical antenna, fed from the apex over an earth plane, looks like a capacitor at low frequencies, but forms an efficient radiator for wavelengths that are short compared to the cone length. The characteristic impedance of a cone with flare angle qo is constant under these conditions and given approximately by [33,34]:    qo r Zo ¼ 60 ln cot (3.19) where qo ¼ tan1 h 2

3.3.1.2 Surge impedance from capacitance The surge impedance of a cone can also be derived by considering its static capacitance per unit length. For this calculation, a simple approach based on surface

86

Lightning interaction with power systems, volume 2

area A [35] gives important insights that can be generalised to the non-conical towers discussed in Table 9.2. The capacitance of any object (box, cylinder, cone, disc, prism, etc.) in free space is estimated by pffiffiffiffiffi pffiffiffiffiffiffiffiffiffi 2g C ¼ eo Cf 4pA where Cf ¼ (3.20) ln 4g With g being the aspect ratio, height divided by width. The shape factor Cf is defined as unity for a sphere. In the case of a cone, g ¼ h/(2r) varies with qo. Theffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffi one-way travel time t along the cone is given by the path length a ¼ h2 þ r2 , divided by c. The cone surface area is A ¼ pra. Table 3.4 shows that the surge impedance Z ¼ t/C calculated from capacitance in free space [35] from (3.20) and t is an excellent approximation to the reference value of Zo from electromagnetic theory in (3.19). Table 3.4 shows that performance of the general capacitance model in (3.20) is excellent for thin cones and acceptable even for a wide cone angle of 45 . Timedomain reflectometry (TDR) is a useful way to verify the constant reflection coefficient between a cone and a feed cable with 50 W surge impedance. The measured reflection coefficient in the test of Figure 3.20 can be manipulated with (3.5) to establish the impedance of a cone or tower, using the known impedance of the feed cable.

3.3.1.3

Surge impedance of prisms, triangular plates and bow-tie antennas

The capacitance model, based on the object surface area A and a variational shape factor [35], can provide some important insights into the surge response of a transmission tower. Most important is that about 90 per cent of the surface area can be removed from a convex object before there is a significant effect on its capacitance. This means that there should be a little difference measured between the surge impedance of a solid tower, a tower of identical shape constructed of thin lattice elements or wire segments. It is common to use rigid wire segments to approximate the shape of a cone in portable reference antenna systems. A surge impedance model based on capacitance also facilitates the accurate calculation of impedance of square or flat towers. A square tower will have 4/p times more surface area than a round tower inscribed inside it, and thus its capacitance will be (4/p)0.5 times larger, giving an impedance that is 13 per cent lower. Pressing the cone to a flat triangular plate, the surface area counting both sides will be A ¼ 2hr. For small flare angles, the plate area is 2/p times the cone area and the plate impedance with the same angle qo will be (p/2)0.5 ¼ 25 per cent times higher. Triangular plate impedances are easily verified with TDR experiments. The degenerate case for these simplifications, using both flattening and wireframe substitution for a round cone, is the common bow-tie antenna used for UHF television reception. Wire segments approximate the outline of a pair of triangular plates, meeting at an apex. Each arm has a length of about 120 mm, width of 80 mm and included angle of 37 . The surge impedance of each arm of a UHF bow tie, fed

0.05 0.14 401.1 3.14 200 2.99 166.4 66.7 400.5 –0.14%

0.1 0.29 359.5 6.28 100 2.36 185.7 66.7 359.0 –0.14%

0.2 0.57 317.9 12.57 50 1.89 210.0 66.7 317.5 –0.13%

0.5 1.43 262.9 31.43 20 1.44 253.9 66.7 262.6 –0.12%

1 2.86 221.4 62.91 10 1.21 301.8 66.7 221.2 –0.09%

20

Impedance values in bold font from surge impedance and capacitance models are directly comparable.

r (m) qo ( ) Zo (W) A (m2) g ¼ h/(2r) Cf C (pF) t (ns) Z ¼ t/C (W) Error in Z

h (m)

Table 3.4 Comparison of surge impedance models for 20-m cone excited at apex

2 5.71 179.9 126.3 5 1.06 372.3 67.0 179.9 0.03%

5 14.04 125.7 323.8 2 0.96 543.2 68.7 126.5 0.65%

10 26.57 86.6 702.5 1 1.02 848.6 74.5 87.8 1.4%

20 45 52.9 1,777 0.5 1.44 1,909 94.3 49.4 –6.6%

88

Lightning interaction with power systems, volume 2 Spherical cap θ θo a

Conical antenna r

Mathematical hemisphere Infinite plane

Z=0 Junction

Zo Zo Coaxial line

Z ρ

(a)

2

(b)

Figure 3.20 Surge impedance of cone over earth plane. Reproduced from [33] with permission from The Institution of Engineering and Technology, 1949. (a) Spherically capped conical antenna fed by coaxial cable. (b) Full equation for Zin with ka ¼ 2p/l. hn(2) is spherical Hankel function of second kind; Pn(cos q) is Legendre polynomial of order n from the centre, is 150 W, constant over a broad range of reception frequencies. The impedances of each arm add to present 300 W to the receiver terminals. The surge impedance of a round cone with qo ¼ 18 is 109 W from (3.19). Impedance of a flat plate with the same angle is 137 W. Thus, the two-wire approximation to the outline adds about 10 per cent to the surge impedance of a flat plate.

3.3.1.4

Surge impedance of antennas of arbitrary shape

The average impedance of an antenna of arbitrary shape is given by integrating Zo from base to height. This does not matter for conical antennas of constant qo and Zo, but a cylinder of constant radius r has a continuously changing value of q0 hc. It is convenient to segment the cylinder into a set of stacked discs, each with an impedance Zo(h) established from (3.3) if r  H. The average impedance of a single, thin cylindrical tower becomes:    

ð ð 1 H 1 H 2h 2H dh ¼ 60 ln 1 (3.21) Zo ðhÞdh ¼ 60 ln Zo ðavÞ ¼ H 0 H 0 r r The 60-W difference between average and tower-top impedance of cylinders was also noted by other researchers. Table 9.2 of Volume 1 gives formulas for vertical cylinders and cones. Effect of orientation, vertical for stroke to tower top versus horizontal for a stroke to midspan, has also been discussed in Table 9.3 of Volume 1.

Lightning interaction with power transmission lines

89

θ1

θ2

The infinite earth plane in Figure 3.20 provides a special case of the general expression for the characteristic impedance of an unsymmetrical bicone antenna:



    q1 q2 tan Zo ¼ 60 ln cot 2 2

(3.22)

where q1 is half the upper cone angle and q2 is (180 – half the lower cone angle), as shown in (3.22). With infinite earth plane below, q2 is 90 and tan(45 ) ¼ 1, defaulting to (3.19). In the case of a thin vertical lightning channel to tower top, exited from above as in Figure 3.21, the impedance of the tower is unchanged from (3.19). However, as q2 approaches 180 , the surge impedance of the channel above the tower increases and approximates a current source.

3.3.2 Analysis of transient voltage rise on earthing electrodes Chapter 7 of Volume 1 (Section 7.3 of Volume 1) defined some ratios to relate footing voltage rise to impressed current, including: ● ●





RT ¼ VT / IT, grounding resistance at low frequency (f < 100 Hz or w < 628 rad s–1) Z(w) ¼ VT(w)/IT(w), harmonic impedance for frequency range (628 rad s–1 < w < 6,280 krad s–1) ZP, the impulse impedance relating the non-simultaneous voltage peak VP to peak p current IP ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi pffiffiffiffiffiffiffiffiffi Z ¼ ðR þ jwLÞ=ðG þ jwC Þ ffi L=C for high frequency (f > 1 MHz or w > 6,280 krad s–1)

The time-domain analogue to harmonic impedance Z(w) is a time-dependent dynamic impedance Z(t) ¼ VT(t)/IT(t). This is derived from field tests with step or impulse excitation using samples at each time interval t of measured tower base voltage rise (V) and impressed current (A). This section develops a related definition for time-dependent resistivity r(t) (Wm), using Z(t) measured at two or more distances from an electrode. The r(t) has a dual relation via Fourier transform to the frequency-dependent resistivity r( f) described in Section 7.3 of Volume 1. The transient voltage rise discussions in this section are organized from early to late time. Earth-plane surge response to a fast-rising step is found first, and longtime effects for RT appear last.

90

Lightning interaction with power systems, volume 2 Zch

i(t) Zgw

Ut

Uarm

Uarm

ht

ha

L

Ua

harm

it

øoc

øt

R

Figure 3.21 Equivalent inductance model for lightning surge response of single tower and stroke to tower top. Reproduced from [26] with permission from The Institution of Engineering and Technology, 1986

3.3.2.1

Surge impedance of earth plane

The question about what happens when the travelling wave in Figure 3.21 arrives at the tower base, and encounters an earth plane, can be treated through analogy, numerically or with image methods. In an appealing analogy, the tower cone angle measured from the junction of lightning and tower top is fixed for the period that it is moving downward. When the wave reaches the earth, the cone angle starts to increase. Initially, the impedance match from tower to earth plane will be rather good. A set of diffuse reflections will be established as the cone angle increases, with a different impedance in each annulus along the earth surface. At one tower travel time, for a thin tower, q1 in (3.22) will be 45 and the effective surge impedance of the earth plane at that radial distance will be 53 W, dropping to 29 W at two travel times and so on. The half-angle q1 will eventually reach 90 . When it does, the computed impedance from (3.22) will be 0 W. Many digital travelling wave methods [12,13] can accommodate changing impedance in each section of a line, provided that the impedance is the same in each direction of propagation, and these can be used to model the so-called earth plane surge impedance. Experimentally, the widening-cone model proved to be a disappointment [36], and numerical modelling confirmed that the experiments in closed geometries were correct [37,38]. In the current measured at tower top, there is a rather crisp initial reflection from the tower base, corresponding to an impedance of 60 W, and the reflections follow the impedance model for a cylindrical waveguide, Zo ¼ 60 h/r when r is the radius of the wavefront and h is the tower height. The imperfect reflection appears at the time corresponding to speed-of-light propagation. The cylindrical waveguide impedance model can populate the values in the nonuniform transmission line modelling with different impedance values in each

Lightning interaction with power transmission lines

91

section, such as [13] to match experimental results. Many field measurements of footing impedance also show a tendency to initiate at 60 W impedance at the wavefront, when the surges are still propagating in towers or surge injection wires. Present thinking about this problem [37–39] suggests that the reflection at an earth plane is perfect, but changing impedance values on the return trip up a conical tower attenuate and distort the reflected wave. Re-defining the tower radius and height from tower base, rather than from tower top, provides an appropriate distortion of the reflected wave. This line of thinking matches the computed pulse currents nicely but has the disadvantage that it cannot be modelled using fixed impedance values in each segment, independent of propagation direction. Fixed impedance values in each segment is an inherent requirement of normal travelling wave methods in Section 9.1.4 of Volume 1, simplified EMTP p-section models and cascades of uniform transmission lines in Section 9.2.3.2 of Volume 1 to model nonuniform geometries. Experimentally, lightning subsequent-stroke currents observed on tall structures can be processed to yield frequency-dependent reflection coefficients [40] at tower base that are unity, as expected, for DC and drop smoothly to G ¼ 0.7  j0.1 for frequencies between 100 and 900 kHz. For a tower with ZT ¼ 340 W surge impedance, the tower base impedance from (1G)/(1 þ G)ZT works out to 60 W. The fictitious transient impedance of an earth plane, approximated by Zo ¼ 60 h/r, can be integrated to develop a lumped inductance element to be used at the peak of a linearly rising waveshape. The ‘earth plane inductance’ adds to the tower inductance in this simplified model. The resulting voltage rise will increase with decreasing equivalent front time.

3.3.2.2 Surge impedance of counterpoise Section 7.3.2 describes the attenuation and distortion of current and voltage along buried horizontal (counterpoise) wires. Field studies of the transient impedance of counterpoise below confirm the predicted response in the time domain. Examples in [41] and [42] show dynamic impedance Z(t) with decay time constants of 2 ms for length of 282 m in Figure 3.23 and 0.5–1 ms for short lengths of counterpoise in Figure 3.24. The effective length LEF described in Section 7.3.2 of Volume 1 and the impulse coefficient IC in Section 7.3.3 of Volume 1 link the early-time impulse impedance and its smooth decay to the low frequency resistance RLF. In Figure 3.24, Case 1 and Case 3 have the shortest length, 6 or 5 m, respectively, and have the fastest decay to constant late-time response, corresponding to RLF in Figure 7.10 of Volume 1. Dynamic impedance for Case 2 with 34-m length, still less than LEF in Figure 7.10, has not quite reached its RLF at 5 ms. In Figure 3.23, with 282-m length that is much greater than LEF, the dynamic impedance Z(t) at 5 ms was found to be twice the low-frequency value indicated as ‘leakage resistance’.

3.3.2.3 Soil resistivity and low-frequency, low-current resistance There is an important dual relationship between calculations of capacitance and resistance. Any accurate model of the capacitance in free space with permittivity e (F/m) can be converted to resistance in an infinite medium with resistivity

92

Lightning interaction with power systems, volume 2 3,368 ft (14–30 ft poles)

3,077 ft (16–30 ft poles)

e2 – line wire

Initiating circuit (6)5¾ in. × 10 in. insul. NO. 6 Cu. wire Surge gen.

e1 – ground wire 23-kV pedestal insul. 30 ft

CRO 3 – counterpoise

Driven grounds 0.4 Ω

(¼ in. steel wire) 925 ft

50 Ω

Figure 3.22 Test circuit for measuring impedance of counterpoise in 1934. Reproduced from [41] with permission of IEEE 130

110

Am p

1,000 100

100

900

90

90

800

80

80

700

70

70

600

60

500

50

400

40

300

30

200

20

100 0

10 0

60 Z

50

kV

30 20

Leakage resistance

10 0

0

(a)

40 Z

Z = counterpoise impedance

kV

Amp

120 Z

1

2 3 Microseconds

4

5

(b)

Figure 3.23 Measured impedance of counterpoise in 1934. Reproduced from [41] with permission of IEEE. (a) Photo of test setup. (b) Test result for 9250 (282 m) counterpoise r (Wm) using RC ¼ er. Since soil occurs in a half-space, the resistance of half of an electrode is twice the free-space value. Soil resistivity is a geological feature that varies from region to region [43] and from tower to tower. Figure 3.25 shows a wide range, 16 Wm r 500 Wm, within many 50-mile (80 km) square regions of the UK [44]. The resistivity r in geological surveys is established using power-frequency electrical tests. As soil is typically layered, surveys consolidate average, nearsurface or ‘bulk’ values and couple them to soil-parent material maps. According to [44], Figure 3.25 shows ‘the first geological unit encountered beneath the base of pedological soil’. For transmission lines, the tower-to-tower variation in resistivity

Lightning interaction with power transmission lines

93

70 Impedance (Ω)

60 PG I

h

50 40 20 10

I (a)

Case 1 Case 2 Case 3 Case 4 Case 5

30

0 (b)

0

2

4 Time (μs)

6

8

Figure 3.24 Measured impedance of counterpoise in 2006. Redrawn from [42] with permission from The Institution of Engineering and Technology, 2006. (a) Case 1: h ¼ 0.2, l ¼ 6 m; Case 2: h ¼ 1, l ¼ 34 m; Case 3: h ¼ 1, l ¼ 5 m; Case 4: h ¼ 1, l ¼ 15 m; Case 5: h ¼ 1, l ¼ 30 m. (b) Soil resistivity: 100 < r < 400 Wm

over 200–400 m span length should be treated as a variable with a log-normal distribution, having a typical slnr of 0.9 [45,46]. Resistivity directly affects the resistance of an earthing electrode. For an electrical substation, the low-frequency resistance RT of a grid of wires Rgrid is approximated using: rffiffiffi r p r þ (3.23) RT ¼ Rgrid ffi 4 A L where A is the surface area of the grid (m2) and L (m) is the total length of wire in the wireframe approximation to the solid. The first term is named a geometric resistance and is related to the overall shape and size of the electrode, in this case a disc at the earth surface. The second, correction term is a contact resistance, representing the difference in resistance between a solid disc and a wireframe approximation. Many individual earthing elements on transmission lines are long and thin, rather than disc-like. In some cases, a few vertical rods are driven in a line, and connected below grade with horizontal counterpoise wires to approximate a vertical plate or large cylinder. Formulas are derived for several simple geometrical configurations, such as rods in a circle, buried rings, vertical and horizontal plates. It is convenient to represent the resistance of all these electrode shapes using a single expression, based on the form of (3.23) but using updated capacitance calculation methods [35,36] to yield [47]: pffiffi !  2  r 2pe 3 g 2 r N A ln ln RT ¼ RGeometric þ RContact ¼ þ 2pg 2pL 8 Awire A qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (3.24) where g ¼ rx2 þ ry2 þ rz2

94

Lightning interaction with power systems, volume 2

Resistivity range (Ωm) 0–16 16–32 32–64 64–125 125–250 250–500 >500

0

25 50

100 Miles

Figure 3.25 Typical soil resistivity in the United Kingdom [44]. Reproduced with permission of the British Geological Survey where N is the integer number of radial wires that meet at the injection point, for example N ¼ 2 for injection into the centre of a buried horizontal counterpoise wire, and Awire is the surface area (m2) of the wireframe with total segment length L (m), given by Awire ¼ 2prwire L. The factor 2peH3 ¼ 11.8 makes the

Lightning interaction with power transmission lines

95

geometric resistance term match the resistance of a hemisphere or radius r, R ¼ r/(2pr). The area A in (3.24) is the concave envelope of the electrode, including bottom and sides, but not the top surface that is exposed to air. Best results for rectangular electrodes are obtained by taking rx as the distance from centre to corner and adjusting ry to give an ellipse with the same perimeter as the box [47]. The depth gives rz.

3.3.2.4 Soil ionisation and effect on high-current lightning impulse impedance In the same way that HV causes an envelope of corona to form around phase conductors, lightning will cause ionisation in the soil. The simplified modelling uses a similar concept, calculating the extent of a corona envelope, with reduced gradient of Eo ¼ 400 kV/m for negative lightning impulse behaviour in lowresistivity soil. There is some evidence [48] that Eo varies with soil resistivity, and Eo ¼ 241r0.215 with Eo in kV/m and r in Wm serves as an important benchmark in recent studies. The Korsuncev similarity method describes the onset and high-current behaviour of electrodes by defining two dimensionless variables: P1 ¼

gRI rI ; P2 ¼ ; P1 ffi 0:24 P20:3 Eo g 2 r

(3.25)

where g is the geometric radius (m) and I is the impulse current (kA). A relation between P1 and P2 in (3.25) [48] is valid for values of P2 that cause P1 to fall below its low-current value P1o, computed using (3.24). This basic approach also underlies the simplified Weck model [3] described in Section 7.3.4 of Volume 1. For single electrodes, ionisation provides a large increase in surface area A in (3.24) and a corresponding decrease in RT. The model in (3.25) predicts that a rod with rx ¼ ry ¼ 0.01 m and length rz ¼ 3 m will start to ionise with a surge current of 0.5 kA in 100 Wm soil, and its resistance will drop from 34 W at low current to RI ¼ 10 W with Iˆ ¼ 31 kA. In contrast, the Weck model [3] predicts IPI ¼ 5.6 kA from (7.12) and RI ¼ 5.2 W for the same conditions from (7.11). Ionisation is less important for larger electrodes, such as the foundations of transmission towers. If rx and ry are set to 3 m, forming a hemisphere, then RT from (3.24) drops to 5.3 W in 100 Wm soil for low currents. It now requires I > 111 kA to initiate the ionisation process. An impressed current of I ¼ 200 kA will add 0.6 m of corona envelope to the outside of the hemisphere, reducing resistance to RI ¼ 4.4 W. For a pair of rods, A becomes a function of the overall wireframe, in this case a two-sided vertical plate, rather than the rod radius. The computed increase in radius from ionisation will increase Awire and thus reduce Rcontact, but it will have a limited effect on RGeometric. Thus, one useful simplification in computing high-current ionisation effects for arrays of rods is to set Rcontact to zero and use I Rgeometric to estimate the tower base voltage rise.

96

Lightning interaction with power systems, volume 2

Table 3.5 Effect of frequency on soil resistivity for first and subsequent negative return strokes Stroke type

IˆF IˆS

Low frequency resistivity ro (Wm)

f (MHz)

0.124 0.516

100

300

1,000

3,000

10,000

93 85

259 214

730 510

1,620 960

3,290 1,620

Table 3.6 Comparison of ZP1st from Table 7.2 with terms in (3.24) r

(Wm)

Counterpoise length L (m)*

100 300 600 1,000 2,000 4,000

5 15 25 40 50 60

o

*

Table 7.2

Equation (3.24)

ZP1st for 3.8 ms front time (W)

Rgeometric (W)

Rcontact (W)

RT (W)

22.4 28.9 37.5 40.9 63.3 96.4

16.9 24.0 32.7 37.8 63.4 109.5

7.6 7.6 9.1 9.5 15.2 25.3

24.5 31.5 41.8 47.3 78.5 134.6

Conductor diameter 15 mm, depth of burial 0.5 m

3.3.2.5

Frequency dependence of soil resistivity and effect on lightning impulse impedance

Soil resistivity has proved to have an inherent variation with frequency r(f), independent of the role of relative permittivity er that affects skin depth. The dominant frequencies of interest in lightning calculations relate the peak current and maximum derivative of the stroke waveshape [5]. For median lightning parameters these are 124 kHz for IˆF and 516 kHz for IˆS. A suitable model for mean frequency dependence of soil resistivity r( f) and relative permittivity er(f) is found in (7.7) and (7.8) of Section 7.2.5 of Volume 1. This model can be converted to time domain r(t) using an inverse Fourier transform, where it yields a slowly rising resistivity in the time from 100 ns to 3 ms. As was the case for ionisation, Table 3.5 shows that the effects of frequency are stronger for soils with higher resistivity. The sine-wave frequencies in Table 3.5 relate median peak current and median rate of current rise [5], and are representative for calculations of peak GPR in backflashover calculations.

3.3.2.6

Combined effects: simplified modelling of transient impedance

For transmission lines, the simplified prescription in Section 7.5 of Volume 1 can be updated to use low-frequency resistance RT from (3.24), ignoring ionization effects, to approximate ZP1st. Table 3.6 confirms that the estimates of RT from

Lightning interaction with power transmission lines

97

(3.24) are rather good for low-resistivity soil with short lengths of counterpoise. The table also suggests that the contact resistance term can be ignored in highresistivity soil, so that ZP1st ffi Rgeometric for ro  1,000 Wm. The physical rationale for this frequency-dependent soil resistivity effect is similar to the argument that Rcontact would vanish for significant soil ionisation.

3.3.2.7 Combined effects: measuring transient impedance and resistivity The inductive response of a counterpoise should give a decaying dynamic impedance with an L/R time constant, related to the wire surge impedance and its lowfrequency leakage resistance RT. Examples of this response are seen in Figures 3.23 and 3.24. At the same time, the frequency-dependent nature of soil resistivity in Table 3.5 should give a dynamic impedance that is rising with time. Both effects occur in the same time scale. It is feasible to separate the effects by carrying out simultaneous measurements of footing impedance and soil resistivity. The basic technique was described in Section 8.5.4 of Volume 1, using GPR waves associated with IˆF and IˆS to calculate ZP1st and ZPsub. Many results have been obtained using a ‘Zed Method’ [45], where a fast-rising flat-top surge is impressed between an electrode and a long, insulated cable of constant surge impedance, laid on the earth surface. Potential rise is measured from electrode to nearby points on the earth. The instantaneous impedances Z1(t) and Z2(t), measured at distances D1 and D2 from the centre of the electrode, yield: rðtÞ ¼ 2p

Z1 ðtÞ  Z2 ðtÞ rðtÞ rðtÞ ; Z1 ðtÞ ¼ Z1 ðtÞ þ ¼ Z2 ðtÞ þ 1 1 2pD1 2pD2 D1  D2

(3.26)

where r(t) is the time-varying resistivity of the soil volume (Wm) and Z?(t) is the impedance of the earthing electrode, extrapolated to infinite distance (W). The ratio of r(t)/Z?(t) gives the dynamic perimeter P(t) of the equivalent hemispherical electrode that could replace the tower under test. This will be a constant value for compact electrodes with L  LEF and should theoretically increase with time for distributed earthing systems with L > LEF as defined in Section 7.3.2 of Volume 1. However, experimentally, long electrodes do not obey the inverse-distance fall of potential model for a hemisphere used in (3.26) so additional corrections are needed to derive r(t) and P(t) accurately. For dynamic earthing impedance tests carried out at the base of a tower with OHGW, the measured impedance Z?(t) will be the earthing impedance of the footing under test Ze(t) in parallel with half of the surge impedance of the OHGW. It is feasible to un-parallel this effect using: Ze ðtÞ ¼

1 Z1 ðtÞ

1 2  ZOHGW

(3.27)

where ZOHGW has been computed using (3.3) and (3.10). This expression is valid after the ring-down time of tower transients (typically, t > 400 ns) and before the arrival of reflections from adjacent towers (typically, t < 2 ms).

98

Lightning interaction with power systems, volume 2

Inversion of touch and step potentials with Fourier transforms was used to establish frequency-dependent soil parameters, leading to the models in [49]. Measurement of transient step potentials as a function of distance from tower base has also been demonstrated [50] to map areas of electrocution risk.

3.3.3

Analysis of transient voltage reduction from adjacent phases

Anderson [51] evaluated several aspects of the travelling wave problem for stroke to tower top, with a focus on accurate calculation of the peak tower-voltage VT(t) in response to a ramp current rising to maximum at time to. This approach was adopted in IEEE Std. 1243 [4] using to ¼ 2 ms. For three towers and footings, all the same and separated by span travel time ts, the voltage from adjacent towers V0 T(s) at the central tower is governed by a span reflection factor Gs: 0

VT ðtÞ ¼ Gs VT ðt  2ts Þ where Gs ¼ Ks Z ðt o Þ ¼

V T ðt o Þ IT ðto Þ

4Z ðto ÞðZOHGW  2Z ðto ÞÞ and 2 ZOHGW

(3.28) where Ks is an attenuation factor, defaulting to 0.85 but adjusted to match observations. Ignoring travelling wave contributions from the tower, at an evaluation time of more than three times tower travel time tt, the reflected voltage for footing impedance Ze simplifies to 0

VT ðtÞ ffi 4Ks



Ze ZOHGW þ 2Ze

2 1

2Ze I ZOHGW þ 2Ze

(3.29)

The expression (3.29) was validated by measuring the impedance Z?(t) at tower base on transmission lines with short span lengths using ramp waves with to < 100 ns. Two cases were studied: ●



36 towers with single OHGW, ZOHGW ¼ 511 W, 92 m average span length and 21 m poles 39 towers with double OHGW, ZOHGW ¼ 317 W, 116 m average span length and 21 m poles

A typical observation of Z?(t) in Figure 3.26 shows stabilization to 73 W in the period 500–700 ns. A strong cancelling voltage reflection from adjacent towers, expected at (2ts þ 4tt) ¼ 900 ns, stabilises to Z? ¼ 50 W in the period 1,200–1,400 ns. The time at which Z?(t) drops in Figure 3.26 can be used in two ways. First, it represents the time of deviation away from a standard impulse and can be substituted as tc in the volt–time curve expression, (3.11). Alternately, the entire voltage waveshape can be used as input to the disruptive-effect or leader progression flashover models described in Section 9.4.2 of Volume 1.

Lightning interaction with power transmission lines Z at infinity (left scale)

Resistivity (right scale)

120

2,400 Isolated tower response: median 500–700 ns Z infinity (Ω) = 72.6 Stdev 2 Resistivity (Ω m) = 692 Stdev 47

100

2,000

80

1,600 Median w/adjacent twrs, 1,200–1,400 ns: 50 Ω

60

1,200

40

800

20

400

Dynamic resistivity ρ(t) (Ωm)

Dynamic impedance Z∞(t) (Ωm)

99

0

0 0

500

1,000

1,500

2,000

Time (ns)

Figure 3.26 Impedance Z?(t) at base of steel monopole tower with single OHGW and 92 m span length

Figure 3.26 also shows the evolution of r(t) using (3.26). This rises to a constant value of 700 Wm in the period before reflections return from adjacent towers. A ratio Z?(1,200:1,400 ns)/Z?(500:700 ns) is defined as G1300. In Figure 3.26, G1300 ¼ 50/72.6 ¼ 0.69. This value and those for many other tested towers are plotted as a function of Z?(500:700 ns) in Figure 3.27. The predicted reflections from adjacent towers using (3.29) are weak if Z? is low (since fraction of current in OHGW is low); strongest for Z? ¼ 80 W with double OHGW; and curving back to a weak reflection in the case that Zg ZOHGW. The scatter in the results relates mainly to wide tower-to-tower variation in soil resistivity and Ze, as the model in (3.29) assumes that Ze is the same at every tower.

3.3.4 Analysis of transient voltage rise on insulated phases from surge impedance coupling The GPR in Figure 3.26 appears on the OHGW, and a reduced-magnitude copy of the voltage will be measured on nearby insulated conductors. A mathematical treatment of this surge impedance coupling from OHGW to phase conductors in [52] is more than 100 years old. For lines with two or more OHGW, the matrix method used to compute the surge impedance matrix of a bundle conductor in Figure 3.11 is expanded to include both driven and undriven conductors. The voltages on OHGW and under-built wires carrying lightning surge current are set to the same, arbitrary value. Any voltages on phase conductors protected by surge

Lightning interaction with power systems, volume 2 Relative change in wave impedance after reflections from adjacent towers (ratio)

100

1.25

1 0.75

0.5 Γ1300 for monopole line with single OHGW, 92 m spans

0.25

Predicted change from IEEE Std. 1243 with Ks = 1

0 0

Relative change in wave impedance after reflections from adjacent towers (ratio)

(a)

(b)

20 40 60 80 100 Measured wave impedance, 500 to 700 ns (Ω)

120

1.25 1

0.75 0.5 Γ1300 for H-frame line with twin OHGW, 116 m spans

0.25

Predicted change from IEEE Std. 1243 with Ks = 1

0

0

20 40 60 80 100 Measured wave impedance, 500 to 700 ns (Ω)

120

Figure 3.27 Observed reduction in tower base voltage from adjacent-span reflections, overlaid with (3.29). (a) Single OHGW. (b) Double OHGW

arresters are fixed at this value, plus or minus the constant voltage drop across the arrester for modest current flow in the range 0.5 to 10 kA. The arrester voltage drop adds to the conductor voltage if lightning terminates on the energised conductor (shielding failure) and subtracts from the conductor voltage under backflashover conditions. If the tower voltage is less than the arrester conduction voltage, then the protected phase is treated as insulated. Voltages on insulated phases are initially set to zero, and the currents in each conductor are computed from [Z]–1  [V] ¼ [I] as shown in Figure 3.11. The voltages on insulated phases are then adjusted, using the ExcelTM SOLVER, to force the currents in those phases to zero.

Lightning interaction with power transmission lines

101

40

Vertical distance y (m)

30

20

OHGW

10

Bundle conductor Underbuilt MV circuit Ground level

0 –15

–10

–5 0 5 10 Horizontal distance x (m)

15

Figure 3.28 Locations of OHGW, EHV phase conductor bundles and HV circuit for coupling calculations

Typically, the voltages on insulated phases will be a significant fraction of the voltage on the OHGW. The voltage ratios, coupling factors (Cn), are dimensionless. As the voltages on OHGW and arrester-protected phases rise, corona will cause a reduction in Zcorona that will increase the values of Cn from their lowvoltage geometric values. The voltage on an unprotected insulator will be roughly (1 – Cn) times the tower voltage. Thus, the underbuilt MV circuit in Figure 3.28 raises the critical current by up to (1 – 0.26)/(1 – 0.52) or 54 per cent on the outer phase, compared to the case when the MV circuit is not present.

Tower top voltage (kV) Low* OHGW

Rcorona (m) 0.007 553 Zcorona (W) 0.014 MV circuit** Rcorona (m) 460 Zcorona (W) Outer phase Coupled voltage (kV) 0.26 Cn Middle phase Coupled voltage (kV) 0.28 Cn *

600

1,000

2,000

3,000

0.056 490 0.053 421 266 0.44 315 0.52

0.102 0.234 0.384 472 447 432 0.106 0.267 0.464 399 372 355 472 1,007 1,559 0.47 0.50 0.52 562 1,203 1,867 0.56 0.60 0.62

Treating MV circuit as insulated (no arrester conduction) Arrester voltage drop 100 kV on underbuilt MV circuit (or flashover for unprotected insulators)

**

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Lightning interaction with power systems, volume 2

3.3.5

The backflashover from OHGW to phase

Anderson [51] evaluated the substitution of a tower inductance and resistance model for the tower and footing in place of a travelling wave model for tower impedance ZT and travel time tT with the variables listed in Figure 3.29. If RT < ZT, the usual case, then the distributed inductance L is convenient for calculating insulator voltage as a linear fraction of the tower top voltage V0 T(t). Both circuits have the same response at the peak of a ramp current when:  0  2ZOHGW ZT RT ZT ZOHGW þ 2R0 2 2Zwave tT 0 0 ZOHGW ¼ ; R ¼ ; L¼ (3.30) 0 ZOHGW þ 2ZT ZT  RT ZOHGW ð1  YÞ2 With: " #





2 2ZOHGW ZT ZT  RT 2ZT  ZOHGW ZT  RT ZWave ¼ ; Y ¼ (3.31) 2ZT þ ZOHGW ZT þ RT ðZOHGW þ 2ZT Þ2 ZT þ RT For a ramp current I(t) ¼ At, rising to Io at time to, the tower top voltage simplifies to   0 0 AZ OHGW LZ OHGW 0 to VT ðto Þ ffi 0 þR (3.32) 2R þ Z 0 OHGW 2R0 þ Z 0 OHGW The ramp rises to a maximum at to ¼ 2 ms in [4], so A ¼ 15.5 kA/ms for median IˆF of 31 kA. If R  ZT, then the tower surge response can be ignored, and peak VT(to) ffi VR(t): VR ðto Þ ffi

1 RT

Ato 2 þ ZOHGW

(3.33)

I(t) = 1 if t ≥ 0, 0 if t < 0

I(t) = 1 if t ≥ 0, 0 if t < 0

ZOHGW/2

ZT

R

Z′OHGW/2

L

VT(t)

V′T(t)

R′

Figure 3.29 Equivalent travelling-wave and tower inductance models for lightning surge response

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For the cases where the travelling wave response of the tower is important, the number of two-way reflections N is defined as the largest whole number (to/(2 tT)). The tower-top voltage VT(t) then becomes [51]: " #  

1  YN 1  YN N YN VT ðtÞ ffi At ZI  Zwave þ 2AtT Zwave (3.34)  1Y ð1  YÞ2 1  Y With: ZI ¼

ZOHGW ZT ZOHGW þ 2ZT

(3.35)

The tower base voltage VR at t þ tT was used by Anderson [51] to interpolate peak insulator voltage: " !! # 2ARZI 1  YðN þ1Þ 1  YN NYN VR ðt þ tT Þ ffi t  2YtT (3.36)  ZT þ R 1Y ð1  YÞ2 1  Y The difference between VT and VR is scaled by the position of the insulator, divided by the total length of the propagation path, harm /ht in Figure 3.21. For most towers, the denominator includes the height of the OHGW ht as well as the distance from OHGW to centre axis. Earth plane inductance is placed between the tower inductance and footing resistance and raises the effective arm height harm. Effects of adjacent spans from (3.29), as observed in Figure 3.26, are considered in the calculation of VT if the two-way span travel time is less than 2 ms [4,51]. Voltages on phases protected by arresters will be equal to the voltage on the tower at attachment point, less the voltage drop across the arrester. The voltage across each insulator is adjusted for instantaneous AC voltage bias. There will be at least one phase that has line voltage that adds to the negative stress from IˆF. This can be integrated numerically for phase angle from 0 to 359 to establish the fraction of time that each phase has the lowest value of IˆFCritical and will be the first to flashover. The voltages across each unprotected insulator are then adjusted for coupling coefficients. This makes an iterative process to compute the backflashover critical currents, IˆFCritical, as the coupled voltages depend on VT(t). The iteration objective is to adjust the impressed current to a level that just causes peak insulator voltage, plus or minus the system voltage bias, to reach the strength from the volt-time curve (3.11) at the time when voltage starts to deviate below a nonstandard wave. The IˆFCritical value is normally evaluated [4] using peak voltage at 2 ms and the insulator strength at the span reflection time, using two times the span length and about 0.9c based on Table 3.1, for tC in (3.11). Advanced software for this calculation, including Monte Carlo variation of relevant parameters, is discussed in Chapter 12 of this volume.

3.3.6 Design and performance of shielded power transmission lines The backflashover reliability in Figure 3.30 is defined as the number of negative first return strokes that do not exceed IˆFCritical, divided by to the total number of

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Lightning backflashover reliability (%)

90 80 70 60 500 kV

50

230 kV

40

115 kV

30

69 kV

20 10 0 0

10

20 30 Footing resistance (Ω)

40

50

Figure 3.30 Effect of footing resistance on lightning backflashover performance

negative flashes to the OHGW on shielded lines with typical construction features. The calculation for probability of exceeding IˆFCritical uses (3.15). The backflashover reliability is a strong function of the footing resistance for 69-kV systems with relatively low dry arc distance and insulation strength of about 0.6 m. For 500 kV lines with 3.65 m of dry arc distance from 25 standard discs, the reliability is excellent even for average footing resistance of R ¼ 50 W. The backflashover lightning outage rate will be given by (1 – reliability) times the number of flashes to the line, in units of (100 km)–1 year–1. The BFR will be added to the shielding failure rate SFR to obtain the total lightning outage rate in the same units.

3.3.7

Methods for increasing the backflashover critical current

If the anticipated lightning performance of an overhead line is unsatisfactory, or the observed MAIFI is after construction too high, then a traditional range of options can be used to improve the line [4].

3.3.7.1

Improvements to earthing impedance

The most common modification is to make improvements to the earthing resistance, through installation of supplementary electrodes. These may take the form of a single treatment, such as an array of radial counterpoise wires, to be installed at every tower. It is feasible to measure the footing impedance Z? and estimate local soil resistivity r. These two inputs can be used to customise a plan to treat only the towers that do not meet a target value, such as 20 W to achieve 80% reliability on a

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115-kV line in Figure 3.30. Tower-by-tower measurements are much more useful than programmes based on regional reconnaissance of resistivity. Many lines share a right-of-way (servitude) with others that may be at the same system voltage or originate at the same substation. It is feasible to interconnect towers with short, below-grade connections. This will increase the critical current for each tower, but does expose both circuits to more overvoltages, and largecurrent events may cause more multiple-circuit outages. Since the original purpose of constructing multiple lines or multi-circuit lines on the same tower is often to improve the double-circuit outage rate, interconnection is often rejected. In these cases, guy wires from one circuit, anchored near another, may be fitted with long in-line guy strain insulators. If interconnection of circuits is rejected, and high reliability is paramount, then the possibility of fitting ground wires on separate structures on both sides of highdensity, critical transmission corridors should be evaluated.

3.3.7.2 Improvements to insulation Some utilities have a policy to over-insulate certain transmission systems, for example, using 138-kV class insulators on lines operated at 69 kV. Figure 3.30 illustrates the anticipated benefits, which are significant provided that the footing impedance can be maintained at a relatively low value for all towers. Many utilities make use of the impulse strength of wood crossarms and poles, in series with conventional ceramic insulators. In areas where this may lead to wood pole fires, problems can be addressed by switching to polymer insulators with lower leakage current under normal, wet and polluted conditions. Isolated bonding of OHGW downleads, using fibreglass wands to route the down-conductors away from the base of insulators, is also a recommended practice for improving lightning performance. At one point, it was believed that the use of weak-link insulators on one circuit of a double-circuit line would improve the performance of the other circuit. The thinking was that the coupling coefficients would improve as soon as the first phase faulted to earth. It is feasible to reduce the insulation strength by adjusting the distance between arcing horns, which also protect the insulators from power-arc damage. There is a limited change in CFO when corona rings are fitted, as the flashover strength improves but the dry-arc distance is reduced in most treatments. These days, fitting TLSA achieves the same benefits without the penalty of degraded performance of a reduced-insulation circuit.

3.3.7.3 Improvements to tower surge impedance The modern tendency to thin, narrow-base monopole towers of improved visual aspect accepts a penalty in degraded lightning performance, in comparison with wood structures where the impulse strength adds to insulator strength or with steel lattice structures having much larger outside diameter. The surge impedance of a narrow steel pole can exceed 300 W. Tower impedance can be reduced using guywires, each with its own rock or soil anchor that provides an additional earthing electrode. An array of four typical guy wires give a beneficial, wide cone flare angle. Four guywires and their anchors can reduce the surge impedance and footing

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impedance of a tower by a factor of two – provided that the utility does not interrupt the parallel paths by indiscriminate use of guy-strain insulators that are considerably longer than the insulator dry arc distance.

3.3.7.4

Improvements to overhead groundwire systems

Many European lines were originally designed with a single OHGW. In some cases, the reduced shielding failure rate of a double OHGW system can be achieved by reconfiguration of circuits. There are other practical changes that can achieve reduced surge impedance and improved electromagnetic coupling. Projects to install new communications capability, through OPGW, have been successfully completed by placing the new, metallic wire below the phase conductors. This works best on compact transmission line designs with restrained horizontal motion of insulators. Under-built ground wires (UBGW) below the phases can also be optimized to reduce ground-level electric and magnetic fields. In some areas, considerations of high flash density and fault current management led to choices of three or four OHGW rather than two on EHV circuits, all located above the phases. These provide improved shielding protection but are not as helpful as UBGW in raising critical currents for backflashover. Based on the most recent experiences on UHV systems, utilities should focus on obtaining improved shielding performance, especially in cases where separation from OHGW to phase exceeds 20 m.

3.3.8

Methods for improving the equalisation of potential differences

Development of reliable TLSA led to pilot projects [30], for example, widespread use of EGLA configurations at 77 and 90 kV in France and applications at higher voltages in Japan.

3.3.8.1

Transmission line surge arresters on selected conductors, direct and indirect aspects

Improved lightning performance can be obtained by fitting TLSA to some, but not all, phases of a transmission line. Calculations in [30] stress the benefits in improved critical current for backflashover when the TLSA are fitted the bottom phase conductor, at greatest distance from OHGW.

3.3.8.2

Under-built ground wires including OPGW retrofit projects, aerial and buried counterpoise

The benefits of partial treatment using TLSA are due mainly to the improved coupling coefficient, raising the transient voltage on unprotected phases and thus reducing the potential difference from tower to those phases. These benefits are also achieved when groundwires are placed in the air, below the phase conductors. There was a limited improvement in coupling even when the counterpoise was buried [41]. The use of UBGW is not new; some lines from the 1930s had a fourth set of crossarms located below the phases, supporting a pair of aerial counterpoise wires. UBGW in the form of distribution-system neutral conductors are common on lines

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with shared HV and MV circuits. Recently, projects to retrofit optical fibre groundwires (OPGW) on existing 220 kV/380 kV lines placed them below the phases and existing OHGW, where they were protected from charge ablation damage [25] and accessible to fibre technicians who can respect general limits for safe approach to energised phases while making repairs.

3.3.8.3 Co-located infrastructure with reduced insulation strength Joint use of transmission structures, allowing internal or external clients to string additional conductors on the same towers, often provides benefits to the transmission utility while delivering lower-than-expected reliability to the shared infrastructure. The dry arc distance and impulse insulation strength of the infrastructure will be much lower than the transmission circuit. Under lightning surge conditions, backflashover will occur first across the weakest insulation, which will divert a fraction of current into the surge impedance of the infrastructure cables heading away from a tower. This flow of current after insulation failure will reduce the impedance of the OHGW and earthing system and raise the coupling coefficients to other conductors nearby. Any surge protective devices fitted to shared infrastructure must be capable of carrying their shares of the total charge in a severe flash.

3.3.8.4 Co-located infrastructure with arrester protection The calculation of coupling coefficients in Figure 3.28 showed the benefits of treating an under-built medium voltage (MV) circuit with arresters on every insulator. This treatment essentially converted the phases to UBGW under lightning conditions, as the voltage drop on each MV TLSA is low. The cost of MV arresters is also quite low compared to those that withstand transmission voltages, and utility experience is more extensive. For example, 230-kV TLSA were introduced as commercial products in 1999, about 12 years after polymer-housed arresters were introduced for MV systems.

3.4 Considerations in the design trade-off: arresters versus earthing The engineer challenged to improve the lightning performance of an existing transmission line makes an economic and technical evaluation that should be quantitative. A budget for improvement should be based on the number of customer loads affected by each momentary outage. Provision of OHGW on transmission lines places an inherent value of about $US 0.1 to $1 per avoided customer momentary dip, based on the combined cost of construction cost (additional 8% compared to unshielded), peak power loss ($2/W) and a small amount for energy loss ($0.1/ kWh) from induced currents. A single customer with a sensitive process controlled by equipment with insufficient immunity to voltage sags may encounter >$1M of clean-up costs per momentary outage. In some cases, customers have reimbursed utilities to make improvements to transmission lines under performance

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improvement contracts with defined follow-up observation periods to verify improved lightning outage rates. The first priority should be to study the correlation between recent tripout dates and times with records of an LLS. If most of the tripouts are associated with flashes that have estimated IˆF < 20 kA or are time-matched to IˆS strokes, then the problems are related to inadequate shielding. It is difficult to make minor adjustments to OHGW placement on an operating line to rectify this. If shielding failures are the dominant problem, then the affected phases should be retro-fitted with TLSA that have sufficiently high rating for stroke charge. If the estimated IˆF from LLS that match times of breaker operations are high, for example IˆF > 50 kA, then backflashovers are suspected. These can be treated either with improved earthing, or with TLSA having modest energy rating. In most areas, earthing conductors are vulnerable to theft after installation, especially if they use copper for long service life. New installations of TLSA also demonstrate a series of challenges related to mechanical vibration of flexible leads. Thus, both treatments should be considered as having a short service life of perhaps 10 years, compared to much longer life for other components such as ceramic insulators, steel towers or aluminium/steel conductors. The engineer should always be open to selecting niche solutions, such as improving end-to-end communication security by retrofitting underbuilt OPGW. Aerial counterpoise below phases also provides improved physical security compared to buried wires. Aerial counterpoise can be inspected by helicopter and delivers most of the benefits of counterpoise laid on the surface of rock in difficult terrain.

References [1] [2]

[3] [4]

[5]

[6]

R. Cuffe, “Lightning surges on transmission lines in Ireland,” Journal of the IEE – Part II: Power Engineering, vol. 94, no. 40, pp. 270–282, 1947. D. Cecil, D. Buechler and R. Blakeslee, “LIS/OTD gridded lightning climatology data collection,” 2014 [Online]. Available: http://dx.doi.org/ 10.5067/LIS/LIS-OTD/DATA311 [Accessed 30 10 2017]. CIGRE WG 33.01, Guide to procedures for estimating the lightning performance of transmission lines, Paris: CIGRE Technical Brochure 63, 1991. IEEE, IEEE guide for improving the lightning performance of transmission lines, Piscataway, NJ: IEEE Standard 1243–1997, Reaffirmed 2008, September 2008. IEEE, IEEE guide for improving the lightning performance of electric power overhead distribution lines, Piscataway, NJ: IEEE Standard 1410–2010, January 2010. R. Anderson, “Lightning performance criteria for electric power systems,” IEEE Proceedings C – Generation, Transmission and Distribution, vol. 132, no. 6, pp. 298–306, 1985.

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IEC, Protection against lightning – Part 1: General principles, Geneva: IEC Standard 62305–1 Edition 2.0, December 2010. J. H. Eto, “The national cost of power interruptions to electricity customers,” in IEE PES General Meeting, Distribution Reliability Working Group, Boston, MA, July 19, 2016. IEEE, IEEE guide for electric power distribution reliability indices, Piscataway, NJ: IEEE Standard 1366–2012, 2012. IEEE, IEEE trial-use recommended practice for voltage sag and short interruption ride-through testing for end-use electrical equipment rated less than 1000 V, Piscataway, NJ: IEEE Standard 1668–2014, 2014. O. Lodge, “On lightning, lightning conductors, and lightning protectors,” Journal of the Institution of Electrical Engineers, vol. 18, no. 80, pp. 386– 430, 1889. L. Barthold and G. Carter, “Digital travelling-wave solutions I – singlephase equivalents,” AIEE Transactions Part III: Power Apparatus and Systems, vol. 80, no. 3, pp. 812–818, 1961. A. Ametani, “Modified travelling-wave techniques to solve electrical transients on lumped and distributed constant circuits. Refraction-coefficient method,” IEE Proceedings, vol. 120, no. 4, pp. 497–504, 1973. CIGRE WG C4.407, Lightning parameters for engineering applications, Paris: CIGRE Technical Brochure 549, August 2013. M. Uman and D. McLain, “Magnetic field of the lightning return stroke,” Journal of Geophysical Research, vol. 74, pp. 6899–6910, 1969. V. Cooray, Attachment of lightning flashes to grounded structures, in The Lightning Flash, 2nd edn, London: IET Publishers, 2014. V. Mazur and L. Ruhnke, “Evaluation of the lightning protection system at the WSR-88D radar sites,” National Oceanic and Atmospheric Administration (NOAA), National Severe Storms Laboratory, Norman, OK, 2001. W. John, “Bushing insulators for outdoor transformers,” Journal of the Institution of Electrical Engineers, vol. 70, no. 423, pp. 297–333, 1932. A. Chadwick, J. Ferguson, D. Ryder and G. Stearn, “Design of power transformers to withstand surges due to lightning, with special reference to a new type of winding,” IEE Proceedings Part II: Power Engineering, vol. 97, no. 60, pp. 737–744, 1950. IEEE, IEEE standard for high-voltage testing techniques, Piscataway, NJ: IEEE Standard 4–2013, May 2013. R. Sobocki, “Function representation of lightning impulse wave,” IEE Proceedings Part A, vol. 134, no. 9, pp. 721–726, 1987. S. Killian and J. Moran, “Characteristics of EHV station post insulators,” IEEE Transactions on Power Apparatus and Systems, vol. 83, no. 3, pp. 280–285, 1964. A. Thomas and D. Oakeshott, “Choice of insulation and surge protection of overhead transmission lines of 33 kV and above,” Proceedings of the IEE – Part A, vol. 104, no. 15, pp. 229–239, 1957.

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Lightning interaction with power systems, volume 2 M. Darveniza, F. Popolansky and E. Whitehead, “Lightning protection of UHV transmission lines,” Electra, vol. 41, pp. 39–69, 1975. W. Chisholm, J. Andersion, A. Phillips and J. Chan, “Lightning performance of compact lines,” in X International Symposium on Lightning Protection (SIPDA), Invited Lecture, Curitiba, Brazil, November 2009. C. Gary, Z. Garabedian, Z. Zhang, D. Critescu and R. Enache, “Breakdown characteristics of insulator strings stressed by short tail waves,” IEE Proceedings A – Reviews, vol. 133, no. 8, pp. 552–561, 1986. CIGRE WG B2.21, On the use of power arc protection devices for composite insulators on transmission lines, Paris: CIGRE Technical Brochure 365, December 2008. H. Motoyama, “Experimental study and analysis of breakdown characteristics of long air gaps with short tail lightning impulse,” IEEE Transactions on Power Delivery, vol. 11, no. 2, pp. 972–979, 1996. M. Darveniza, Electrical properties of wood and line design, St. Lucia, Queensland, Australia: University of Queensland Press, 1980. CIGRE WG C4.301, Use of surge arresters for lightning protection of transmission lines, Paris: CIGRE Technical Brochure 440, December, 2010. F. A. Rizk, “Modeling of transmission line exposure to direct lightning strokes,” IEEE Transactions on Power Delivery, vol. 5, no. 4, pp. 1983–1997, 1990. A. M. Mousa and K. Srivastava, “The lightning performance of unshielded steel-structure transmission lines,” IEEE Transactions on Power Delivery, vol. 4, no. 1, pp. 437–445, 1989. C. H. Papas and R. King, “Input impedance of wide-angle conical antennas,” Proceedings of the I.R.E., vol. 37, no. 11, pp. 1269–1271, 1949. E. C. Jordan and K. G. Balmain, Electromagnetic waves and radiating systems, Englewood Cliffs, N.J.: Prentice Hall, 1968. Y. Chow and M. Yovanovich, “The shape factor of the capacitance of a conductor,” Journal of Applied Physics, vol. 53, no. 12, pp. 8470–8475, 1982. W. Chisholm and W. Janischewskyj, “Lightning surge response of ground electrodes,” IEEE Transactions on Power Delivery, vol. 4, no. 2, pp. 1329– 1337, 1989. Y. Baba and V. Rakov, “On the interpretation of ground reflections observed in small-scale experiments simulating lightning strikes to towers,” IEEE Transactions on Electromagnetic Compatibility, vol. 47, no. 3, pp. 533–542, 2005. A. Shoory, F. Vega, P. Yutthagowith, et al., “On the mechanism of current pulse propagation along conical structures: Application to tall towers struck by lightning,” IEEE Transactions on Electromagnetic Compatibility, vol. 54, no. 2, pp. 332–342, 2012. Y. Baba and V. A. Rakov, “On the mechanism of attenuation of current waves propagating along a vertical perfectly conducting wire above ground: Application to lightning,” IEEE Transactions on Electromagnetic Compatibility, vol. 47, no. 3, pp. 521–532, 2005.

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[40] J. Bermudez, M. Rubinstein, F. Rachidi, F. Heidler and M. Paolone, “Determination of reflection coefficients at the top and bottom of elevated strike objects struck by lightning,” Journal of Geophysical Research, vol. 108, no. D14, pp. 4413–4425, 2003. [41] L. Bewley, “Theory and tests of the counterpoise,” AIEE Transactions, vol. 53, no. 8, pp. 1163–1172, 1934. [42] A. K. Mishra, N. Nagaoka and A. Ametani, “Frequency-dependent distributed parameter modelling of counterpoise by time-domain fitting,” IEE Proceedings on Generation, Transmission and Distribution, vol. 153, no. 4, pp. 485–492, 2006. [43] ITU (International Telecommunications Union), “Recommendation ITU-R P832–3, World atlas of ground conductivities,” ITU, Geneva, February 2012. [44] D. Entwisle, J. White, J. Busby, R. Lawley and I. Cooke, Electrical resistivity model of Great Britain: User guide, Keyworth, Nottingham, UK: British Geological Survey Report OR/14/030, 2014. [45] W. Chisholm, E. Petrache and F. Bologna, “Grounding of overhead transmission lines for improved lightning protection,” in Proceedings of IEEE Transmission & Distribution Exposition, New Orleans, LA, April 2010. [46] W. A. Chisholm and S. de Almeida de Graaff, “Adapting the statistics of soil properties into existing and future lightning protection standards and guides,” in 2015 International Symposium on Lightning Protection (XIII SIPDA), Balneario Camboriu, Brazil, 28 September–2 October 2015. [47] W. Chisholm, “Evaluation of simple models for the resistance of solid and wire-frame electrodes,” IEEE Transactions on Industry Applications, vol. 51, no. 6, pp. 5123–5129, 2015. [48] E. Oettle´, “A new general estimation curve for predicting the impulse impedance of concentrated earth electrodes,” IEEE Transactions on Power Delivery, vol. 3, no. 4, pp. 2020–2029, 1998. [49] R. Alipio and S. Visacro, “Modeling the frequency dependence of electrical parameters of soil,” IEEE Transactions on Electromagnetic Compatibility, vol. 56, no. 5, pp. 1163–1171, 2014. [50] CIGRE WG B2.56, Ground potential rise at overhead AC transmission line structures during power frequency faults, Paris: CIGRE Technical Brochure 694, July 2017. [51] J. G. Anderson, “Chapter 12, lightning protection,” in Transmission Line Reference Book, 345 kV and Above, 2nd edn, Palo Alto, CA, EPRI, 1982. [52] E. Creighton, “Theory of parallel grounded wires and production of high frequencies in transmission lines,” AIEE Transactions, vol. 35, no. 6, pp. 945–988, 1916.

Chapter 4

Lightning interaction with medium-voltage overhead power distribution systems Alexandre Piantini1, Alberto Borghetti2 and Carlo Alberto Nucci2

Distribution lines located in areas with high ground flash densities are prone to lightning-caused power interruptions. Lightning overvoltages can be produced on medium-voltage (MV) systems when lightning hits either the line conductors (direct strokes) or a point in the vicinity of the distribution network (indirect strokes). The evaluation of the lightning electromagnetic environment is essential to mitigate its effects and improve the power system quality. This chapter presents initially, using the concepts given in Chapter 5 of Volume 1, a procedure for the estimation of the mean annual number of direct lightning strikes to a given overhead distribution line. Then, the basic features of the lightning overvoltages are discussed. Although some typical characteristics can be identified, the analysis of the overvoltages depends on various parameters relevant to the adopted model of the lightning return stroke, soil and power network. The influences of the most important ones are discussed in this chapter, with examples of measured and calculated voltage waveshapes. Then, the main protective measures that can be applied to improve the lightning performance of MV distribution lines, namely the increase of the line insulation withstand capability, the use of periodically grounded shield wires and the installation of surge arresters along the line, are addressed. The analysis of the effectiveness of each measure as a function of the type of phenomenon (direct or indirect strikes) and of various parameters, such as the soil resistivity, ground resistance and grounding spacing, is performed. After that, the procedure presented in Chapter 1 of this volume for estimating the mean annual number of line flashovers that an overhead MV line can experience, is applied to the case of lines with different protective measures and the relevant performances are compared. The case of urban lines, whose performance is affected by the presence of buildings in 1

Institute of Energy and Environment, Lightning and High Voltage Research Center, University of Sa˜o Paulo, Sa˜o Paulo, Brazil 2 Department of Electrical, Electronic and Information Engineering, University of Bologna, Bologna, Italy

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their vicinity, is also dealt with, as well as the case of hybrid configurations, in which MV and high voltage (HV) lines share the same structures.

4.1 Flash collection rate The number of direct lightning strikes to a distribution line is commonly estimated – for example, IEEE Std. 1410 [1] – considering the average attractive radius presented by structures as a function of height proposed by Eriksson [2]: Ram ¼ 14h0:6 ðmÞ;

(4.1)

where h is the height of the uppermost conductor at the pole (m). If the line is in open ground, that is, without significant trees or buildings in its vicinity, the flash collection rate (flashes per year) or the mean annual number of direct strokes (N) can be estimated by N ¼ Ng Aa;

(4.2)

where Ng is the ground flash density (number of flashes per km2 per year) and Aa (km2) is the attraction area of the line, given by: Aa ¼ ð2  Ram þ bÞl;

(4.3)

where b corresponds to the horizontal distance between the outer conductors and l is the length of the line. For a 100-km long line, substituting (4.1) and (4.3) into (4.2) yields   (4.4) N ¼ 0:1Ng 28h0:6 þ b ; with h and b in meters. If the distribution line is surrounded by elevated objects, such as trees or buildings, the flash collection rate may decrease, as such objects may intercept many lightning flashes which otherwise would hit the line. The shielding provided by nearby objects can be taken into account by means of the shielding factor, SF, which is defined as the per-unit portion of the distribution line shielded by nearby objects. Thus, the general expression for the number of direct strikes to the line, taking into account the influence of nearby objects, is Ns ¼ N ð1  SF Þ

(4.5)

If the line is surrounded by tall objects on its both sides, the shielding factors for the left and right sides should be summed. SF ¼ 0 represents a line in open ground and SF ¼ 1 represents a line surrounded by taller objects, so that it is completely shielded from direct flashes. Figure 4.1, adapted from [1], gives a means for approximating the shielding factors for objects of various heights for a 10-m tall distribution line. The objects

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1.00

Shielding factor (SF)

Ho = 20 m 0.80 Ho = 15 m

0.60 0.40

Ho = 10 m

0.20 Ho = 7.5 m 0.00 0

20 40 60 Distance of the object from the line (m)

80

Figure 4.1 Shielding factors (SF) due to nearby objects of different heights (Ho) for a 10-m high distribution line. Adapted from [1] are assumed to be in a uniform row parallel to the line and located on one side of it, which could represent a continuous row of trees or buildings paralleling the line.

4.2 Effects of various parameters on lightning overvoltages Lightning overvoltages, especially those associated with nearby strokes, are affected by numerous parameters and may vary substantially depending on the soil characteristics and the network configuration. Some of their basic features are presented in this subsection, which deals with unprotected lines. As a direct strike to an unprotected distribution line provokes flashovers in virtually all the cases, emphasis is given on the surges induced by indirect strokes. The analysis of the protection measures and their impacts on the improvement of the line performance are discussed in Sections 4.3 and 4.4.

4.2.1 Direct strokes If a flash hits an overhead line, the current injected into the conductor is divided at the strike point, giving rise to two voltage waves that propagate in opposite directions. The prospective magnitude of these voltages can be estimated by multiplying the current that flows in each direction (half of the stroke current) by the characteristic impedance of the line, which is normally in the range of 400–500 W. Therefore, for a line characteristic impedance of 400 W and a stroke current of 10 kA, whose probability of being exceeded is larger than 90%, the corresponding overvoltage is 2 MV, which is far beyond the line insulation level. As a consequence, multiple flashovers occur between the conductors and also to ground in different points of the line. Customers around the fault location experience both a voltage sag during the short-circuit and a momentary interruption when the breaker opens to clear the fault.

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Overvoltages caused by direct strikes to MV lines are characterised by a few short spikes, produced by multiple line insulation breakdowns [3–7], followed usually – especially in the case of high ground resistance values – by a slower front component whose amplitude is somewhat lower than the insulation level of the line. Figure 4.2 presents overvoltages caused by direct strikes to an unprotected, three-phase MV line for stroke currents with triangular waveshapes and different magnitudes (10 and 30 kA) and front times (2 and 6 ms). The height of the conductors is 10 m, the distance between adjacent concrete poles is 70 m, the soil resistivity is 100 Wm and the ground resistance of the poles is 10 W. Insulators are modelled according to the Disruptive Effect Model described in Chapter 10 of Volume 1 assuming U0 ¼ 120 kV, K ¼ 1 and DEc ¼ 0.043 kVms. Soil ionization is disregarded. The voltages are calculated at the struck point using the electromagnetic transient program EMTP-RV. [8]. In Figure 4.3, the voltages refer to the same conditions, except for the soil resistivity and the ground resistance of the poles, whose values are 1,000 Wm and 100 W, respectively. 800

600 I = 30 kA

I = 30 kA

600

400 Voltage (kV)

Voltage (kV)

I = 10 kA 400 200 0

I = 10 kA 200 0

0

1

2

3

4

5

6

7

8

–200

0

1

2

3

4

5

6

7

8

–200

(a)

(b)

Time (μs)

Time (μs)

Figure 4.2 Phase-to-ground overvoltages due to a direct strike to an unprotected MV line for stroke currents with different magnitudes (I). Soil resistivity and ground resistance are 100 Wm and 10 W, respectively. (a) tf ¼ 2 ms. (b) tf ¼ 6 ms

1,200

800

800 I = 10 kA 400

0

(a)

Voltage (kV)

Voltage (kV)

I = 30 kA I = 30 kA

0

1

2

3

5 4 Time (μs)

6

7

600 400 I = 10 kA 200 0

8

(b)

0

1

2

3

4 5 Time (μs)

6

7

8

Figure 4.3 Phase-to-ground overvoltages due to a direct strike to an unprotected MV line for stroke currents with different magnitudes (I). Soil resistivity and ground resistance are 1,000 Wm and 100 W, respectively. (a) tf ¼ 2 ms. (b) tf ¼ 6 ms

Lightning interaction with MV overhead power distribution systems

117

The magnitude of the first peak (U), which corresponds to the voltage immediately before the insulator flashover, depends on the characteristics of the insulator and the stroke current steepness (S). For the cases considered in Figures 4.2 and 4.3, for which K ¼ 1 and the currents rise linearly, the relationship between the voltages at which insulator flashover occurs, considering two situations which differ only in terms of the current amplitude, is given by rffiffiffiffiffiffiffi S1  (4.6) U1 ¼ U0 þ ðU2  U0 Þ S2 For the case of Figure 4.2(a), U0 ¼ 120 kV, S1 (30 kA) ¼ 15 kA/ms, S2 (10 kA) ¼ 5 kA/ms and U2 ¼ 452 kV. Substituting these values into (4.6) yields U1 ¼ 695 kV. After the insulator flashover, the voltage at the struck point is given basically by the product of the ground resistance and the current that flows to ground, which is in general much higher than the voltage drop associated with the inductance of the reinforced concrete pole. Therefore, the higher the current, the higher the voltage. For low values of ground resistance, the total voltage is lower than the voltage U that caused insulator flashover, as shown in Figure 4.2. The opposite occurs in the case of high ground resistance values, as illustrated in Figure 4.3. Currents with longer front times – and, therefore, with lower steepness – lead to voltages with smaller magnitudes. Direct strikes usually do not cause permanent damages to lines with bare conductors as long as the fault duration is limited by a short-circuit protection device. On the other hand, in the case of lines with covered conductors, the coating prevents the footpoint of the power frequency arcing current from moving along the line, and therefore a flashover between phases for such lines may cause a mechanical breakdown of the conductors [7].

4.2.2 Indirect strokes Due to the impacts of the lightning-induced overvoltages on the performance and power quality of distribution systems, several theoretical and experimental studies have been conducted in order to better understand their characteristics or to assess the effectiveness of the methods that can be used for their mitigation [9–34]. The induced voltage magnitudes and waveforms vary widely and depend on the soil characteristics and many lightning parameters. They are also substantially affected by the network configuration. In the case of a strike to an elevated object in the vicinity of the line, the induced voltage also depends on the height, surge impedance and ground impedance of the structure, as well as on the equivalent surge impedance of the lightning channel [4,13]. An example of a typical lightning-induced voltage waveform, recorded by the system described in [20] and [21] on a 2.7-km long, un-energized line matched at both terminations, is presented in Figure 4.4. Despite the large variation of the induced voltage waveforms, they are usually characterised by shorter tail times in comparison with overvoltages caused by direct strokes.

118

Lightning interaction with power systems, volume 2 20

Voltage (kV)

15 10 5 0 –5 0

10

20 30 Time (μs)

40

50

Figure 4.4 Example of a typical lightning-induced voltage [10]

In this section, the influences of the most important parameters on the induced voltages on a three-phase line without neutral and connected equipment are analysed by means of computational simulations run with the Extended Rusck Model (ERM) [22,35–37]. Comparisons between measured and calculated lightninginduced surges, which illustrate the validity of the model, can be found also in Chapter 6 of Volume 1 and Chapter 5 of this volume. Unless otherwise indicated, in the simulations presented in this subsection, the stroke current is assumed to have a triangular waveshape with amplitude I ¼ 50 kA, front time tf ¼ 3 ms, time to half-value of 50 ms, and propagation velocity equal to a fraction b ¼ 0.3 (30%) of the velocity of light in free space (c). The channel length is 3-km long, the line has horizontal configuration, and the conductors’ height (h) and diameter are equal to 10 m and 1 cm, respectively. The distance from the strike point to the line (d) is 50 m and the stroke location is equidistant from the line terminations. The observation point is at x ¼ 0 m, where x represents the distance between the observation point and the point of the line just in front of the stroke location (i.e., x ¼ 0 m corresponds to the point closest to the lightning strike point). The transmission line (TL) model [38] is adopted for the simulation of the lightning channel. The line is 3.6-km long and matched at both ends. The lightning impulse withstand capability of the insulators is supposed to be very high, so that the occurrence of flashovers is not considered. The soil resistivity (r) is 500 Wm and the relative permittivity (eR) is equal to 10.

4.2.2.1

Lightning channel

The length of the lightning channel, generally in the range of 1–6 km, has just a small, usually negligible, influence on the induced voltages, which is restricted to the wavetail. This is due to the fact that, in the great majority of the cases, the return stroke current reaches the upper end of the channel only after the induced voltage has reached its crest value [22].

Lightning interaction with MV overhead power distribution systems

119

In [39], Matsubara and Sekioka propose analytical formulas for calculating induced surges on an overhead line of infinite length considering inclined lightning channels with arbitrary angles. The formulas, derived from the Rusck model [40], are very simple, and comparisons with results obtained using the finite-difference time-domain (FDTD) method show a very good agreement. As shown by Andreotti et al., the channel tortuosity can have a significant influence on the lightning voltages induced on lines with both simple [12] and complex [9] topologies.

4.2.2.2 Stroke current magnitude and waveform If non-linear phenomena such as corona and soil ionization are not considered and non-linear devices such as surge arresters are not present, the induced voltages are directly proportional to the stroke current magnitude. The time to half-value of the stroke current, which is of the order of tens of microseconds, has usually a negligible effect on the induced voltage amplitude and affects only the voltage wavetail [41]. Current front times present statistical distributions with median values of about 3.8 ms for the first and 0.7 ms for subsequent strokes (Tf30 [42,43]). For this reason, although the median amplitude of subsequent stroke currents is approximately 40% of that of first strokes [42], in some situations, depending on the combination of the values of the various parameters that affect the induced voltages, subsequent strokes may induce surges with higher magnitudes than those associated with first strokes [36,44]. Figure 4.5 presents lightning-induced voltages for stroke currents with different front times and two values for the soil resistivity. The stroke current front time has a strong influence on the induced voltage amplitude and waveform, being this influence more important in the case of lower values of the soil resistivity. Induced voltages associated with stroke currents with short front times are steeper and have larger magnitudes than those associated with slow front currents. The effect of the stroke current front time is more important for short distances between the line and the stroke location. 360

600

tf = 1 μs

tf = 1 μs 480 Voltage (kV)

Voltage (kV)

300 240

tf = 3 μs

180

tf = 9 μs

120

tf = 9 μs 240 120

60 0

0 2

(a)

tf = 3 μs

360

4

6

8

Time (μs)

10

12

14

2

(b)

4

6

8

10

12

Time (μs)

Figure 4.5 Lightning-induced voltages for stroke currents with different front times (tf) [10]. I ¼ 50 kA; b ¼ 0.3; h ¼ 10 m; d ¼ 50 m; x ¼ 0 m. (a) r ¼ 0 Wm. (b) r ¼ 500 Wm

14

120

Lightning interaction with power systems, volume 2

4.2.2.3

Stroke current propagation velocity

As mentioned in [45], the return stroke current propagation velocity along the channel falls in the range of about 6 to over 90% of that of light in free space and tends to decrease with height. This range includes both first and subsequent strokes and measurements made at different portions of the lightning channel. As pointed out in [46], the existence of a relationship between the velocity and the peak current is not generally supported by experimental data. Figure 4.6 shows the induced voltages corresponding to currents with propagation velocities of 10%, 30% and 60% of that of light in free space for two values of the soil resistivity. For both situations considered, it can be seen that the amplitudes of the induced voltages diminish as the propagation velocity increases, but the influence of the propagation velocity tends to be more significant in the case of soil with lower resistivity. However, the effect of the propagation velocity depends on the stroke current front time tf. In general, for stroke currents with steep fronts, as is usually the case of subsequent strokes, the induced voltage magnitude tends to increase as the propagation velocity increases; whereas for currents with slow fronts, the opposite behaviour is observed. This is illustrated in Figure 4.7, for which the calculations refer to a stroke current front time tf ¼ 1 ms. Unlike in the previous case, for this condition the influence of the propagation velocity is more prominent for the soil with higher resistivity. This is a consequence of the behaviour of the horizontal component of the electric field, whose effect on the lightning-induced voltages increases with the increase of the soil resistivity.

4.2.2.4

Conductor height

In practical cases, for which both the length of the stroke channel and the distance between the stroke location and the distribution line conductors are much greater than the line height, scale model experiments [31] have confirmed theoretical predictions that, for the case of perfectly conducting ground, induced voltages are directly proportional to the height of the line. 360

480 b = 0.3

b = 0.1

360 240

120

Voltage (kV)

Voltage (kV)

b = 0.1

b = 0.3

240

b = 0.6

120 b = 0.6 0 (a)

2

4

6

8

Time (μs)

10

12

0

14 (b)

2

4

6

8

10

12

14

Time (μs)

Figure 4.6 Lightning-induced voltages for stroke currents with different propagation velocities (b corresponds to the ratio of the return stroke velocity to that of light in free space) [10]. I ¼ 50 kA; tf ¼ 3 ms; h ¼ 10 m; d ¼ 50 m; x ¼ 0 m. (a) r ¼ 0 Wm. (b) r ¼ 500 Wm

Lightning interaction with MV overhead power distribution systems 360

121

600

240

Voltage (kV)

Voltage (kV)

b = 0.6 480

b = 0.1

120 b = 0.6

4

10

6 8 Time (μs)

(a)

b = 0.1

240 120

0 2

360

12

0

14

2

4

(b)

6 8 Time (μs)

10

12

14

Figure 4.7 Lightning-induced voltages for stroke currents with different propagation velocities (b corresponds to the ratio of the return stroke velocity to that of light in free space) [10]. I ¼ 50 kA; tf ¼ 1 ms; h ¼ 10 m; d ¼ 50 m; x ¼ 0 m. (a) r ¼ 0 Wm. (b) r ¼ 500 Wm

500 1

1, 4: h = 12 m 2, 5: h = 10 m 3, 6: h = 8 m

400 Voltage (kV)

2 300 4

ρ = 500 Ωm

3

200

5

100

ρ = 0 Ωm 6

0

2

4

6 8 Time (μs)

10

12

14

Figure 4.8 Lightning-induced voltages for lines with different heights (h) and soils with different resistivities [11]. I ¼ 50 kA; tf ¼ 3 ms; b ¼ 0.3; d ¼ 50 m; x ¼ 0 m; eR ¼ 10 However, when the soil cannot be assumed as perfectly conducting, the voltage increase with height is not linear and varies with the stroke location, observation point and soil resistivity, as shown by Nucci and Rachidi in [14]. Such a behaviour, which is associated with the horizontal component of the lightning electric field, is illustrated in Figure 4.8, which presents induced voltages calculated for different line heights (8, 10 and 12 m) and two values of soil resistivity. For r ¼ 0 Wm (perfectly conducting ground), the ratio between the peak values of the induced voltages corresponding to h ¼ 12 m and h ¼ 8 m is 1.50, whereas for r ¼ 500 Wm the ratio is approximately 1.26.

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Lightning interaction with power systems, volume 2

4.2.2.5

Distance between the line and the stroke location and position of the observation point

The influence of the distance d between the line and the lightning strike point is pronounced, as illustrated in Figure 4.9 for two conditions of the soil resistivity: r ¼ 0 Wm and r ¼ 500 Wm. In both cases the distance has a pronounced effect on the induced voltages. As expected, the shorter the distance, the higher the voltage magnitude. It can also be observed that the voltage front time tends to increase as the distance increases. The dependence of the induced voltage on the position along the line is illustrated in Figure 4.10 for the two values adopted for the soil resistivity (0 and 500 Wm), where x represents the distance between the observation point and the point of the line which is closest to the stroke location. The simulations show that, for the case of low-resistivity soils (Figure 4.10(a)), the induced voltage reaches its highest amplitude at the point of the line just in front of the stroke location, a result which is in agreement with measurements performed on a reduced scale model 300

500 d = 50 m

d = 50 m Voltage (kV)

Voltage (kV)

400 200 d = 100 m 100

300 d = 100 m 200 d = 200 m

100 d = 200 m 0

2

4

6 8 Time (μs)

(a)

10

12

0

14

2

4

(b)

6 8 Time (μs)

10

12

14

Figure 4.9 Lightning-induced voltages for different distances (d) between the line and the lightning strike point [10]. I ¼ 50 kA; tf ¼ 3 ms; b ¼ 0.3; h ¼ 10 m; x ¼ 0 m. (a) r ¼ 0 Wm. (b) r ¼ 500 Wm 300

500 x=0

x=0

400 Voltage (kV)

Voltage (kV)

x = 500 m 200 x = 1,000 m 100

300 x = 500 m

200 100

x = 1,000 m

0 0

(a)

2

4

8 6 Time (μs)

10

12

14

–100 2

(b)

4

6 8 Time (μs)

10

12

14

Figure 4.10 Lightning-induced voltages at different positions (x) along the line (x ¼ 0 corresponds to the point in front of the stroke location) [10]. I ¼ 50 kA; tf ¼ 3 ms; b ¼ 0.3; h ¼ 10 m; d ¼ 50 m. (a) r ¼ 0 Wm. (b) r ¼ 500 Wm

Lightning interaction with MV overhead power distribution systems

123

[31]. For the parameter values considered, in the case of r ¼ 500 Wm (Figure 4.10 (b)) the maximum value of the induced voltage occurs also at the point closest to the stroke location. However, as it will be shown in Section 4.2.2.6, in the case of finite ground conductivity the point corresponding to the maximum voltage is highly dependent on the position of the lightning strike point relative to the line.

4.2.2.6 Soil resistivity The soil resistivity is one of the parameters which most widely affects the horizontal electric field [30,47–51], which in turn has a great influence on the lightning-induced voltages. In general, the induced voltages tend to increase with the soil resistivity, although they may also decrease and/or change polarity depending on the stroke location and the observation point as shown, for example, in [10,47]. The influence of the soil resistivity on the voltages induced at the point closest to the stroke location (x ¼ 0 m) is illustrated in Figure 4.11 for stroke current front times of 3 and 1 ms. The voltages are unipolar and increase with the soil resistivity. The results shown in Figure 4.12 refer to the point x ¼ 1,000 m. It can clearly be seen that the voltages present a different behaviour in comparison to those calculated at x ¼ 0 m. For the situations considered, the voltage magnitudes tend to decrease as the soil resistivity increases. They also tend to be bipolar with an initial negative excursion, which tends to be more significant (in amplitude and duration) as the resistivity increases and the stroke current front time becomes shorter. The influence of the soil resistivity is even more significant when the lightning strike point is close to one of the line terminations. An example of such a situation is shown in Figure 4.13, and the corresponding induced voltages at the points x ¼ 0 m, x ¼ 500 m and x ¼ 1,000 m are depicted in Figure 4.14. In the case of perfectly conducting ground (Figure 4.14(a)), the behaviour of the induced voltages is similar to that illustrated in Figure 4.10(a), although their magnitudes are much lower because the contributions of the voltages induced at other points of the line are smaller due to the position of the lightning channel relative to the line. For the case of finite ground conductivity (Figure 4.14(b)), not only the voltage amplitude but also its waveform varies significantly along the line. At the point

600

600 ρ = 1,000 Ωm

ρ = 1,000 Ωm 480

360 240 ρ = 500 Ωm 120 0

(a)

Voltage (kV)

Voltage (kV)

480

4

6 8 Time (μs)

10

12

240 ρ = 500 Ωm 120

ρ = 0 Ωm 2

360

ρ = 0 Ωm 0

14

(b)

2

4

6 8 Time (μs)

10

12

14

Figure 4.11 Lightning-induced voltages considering different values for the soil resistivity (r) [10]. I ¼ 50 kA; b ¼ 0.3; h ¼ 10 m; d ¼ 50 m; x ¼ 0 m. (a) tf ¼ 3 ms. (b) tf ¼ 1 ms

124

Lightning interaction with power systems, volume 2 200

300 ρ = 0 Ωm

Voltage (kV)

100 ρ = 1,000 Ωm 0

Voltage (kV)

ρ = 0 Ωm ρ = 500 Ωm

200 ρ = 500 Ωm 100 0

–100

2

4

6 8 Time (μs)

(a)

10

12

14

ρ = 1,000 Ωm

–100

2

4

(b)

6 8 Time (μs)

10

12

14

Figure 4.12 Lightning-induced voltages considering different values for the soil resistivity (r) [10]. I ¼ 50 kA; b ¼ 0.3; h ¼ 10 m; d ¼ 50 m; x ¼ 1,000 m. (a) tf ¼ 3 ms. (b) tf ¼ 1 ms x = 1,800 m

x=0

Lightning strike point

x = 3,600 m

50 m

Figure 4.13 Lightning strike point close to one of the line ends (not to scale) 120

Voltage (kV)

x=0 80 x = 500 m x = 1,000 m 40

0

4

2

(a)

6 8 Time (μs)

10

12

14

240 Voltage (kV)

1) x = 0

1

180

2) x = 150 m

120

3) x = 250 m

2

60

3

0

4) x = 500 m 5) x = 1,000 m

4

–60

5 –120 (b)

2

4

6 8 Time (μs)

10

12

14

Figure 4.14 Lightning-induced voltages at different positions (x) along the line for the situation indicated in Figure 4.12 [10]. I ¼ 50 kA; tf ¼ 3 ms; b ¼ 0.3; h ¼ 10 m; d ¼ 50 m. (a) r ¼ 0 Wm. (b) r ¼ 500 Wm

Lightning interaction with MV overhead power distribution systems

125

closest to the lightning channel (x ¼ 0 m), the voltage is positive and reaches about 185 kV. At x ¼ 150 m, the maximum value is approximately 70% lower (57 kV), but it is possible to identify an initial negative excursion with peak value of about –3 kV. At x ¼ 250 m, the voltage is also bipolar, but the absolute value of the negative peak (around 17 kV) is larger than that of the positive peak (around 11 kV). At x ¼ 500 m and x ¼ 1,000 m, the voltages are negative and reach peak values of –56 and –86 kV, respectively. The absolute value of the negative peak tends to increase as the observation point moves away from the line end closest to the stroke location. At the other line termination, supposedly matched, the induced voltage (not shown in the figure) peak value is about –127 kV. This remarkable influence of the soil resistivity is due to the contribution, to the total voltage, of the voltage component associated with the lightning horizontal electric field, whose effect tends to be more significant at the farthest points from the stroke location.

4.2.2.7 Soil permittivity The influence of the soil permittivity on the lightning horizontal electric field was investigated in [51] for two soil types: good conductive (r ¼ 50 Wm) and very poorly conductive (r ¼ 5,000 Wm). Simulations were performed considering the limits of the ground relative permittivity given in [52] (4–30, for good conductive, and 1–3, for very poorly conductive ground). For good conductive ground, the variations of the horizontal electric field were found to be negligible within the range indicated. For the very poorly conductive ground and current propagation velocity of 0.8c, the difference between the first field peak (negative) corresponding to the cases of eR ¼ 1 and eR ¼ 3 was about 11% at a distance of 500 m from the stroke channel. The induced voltages corresponding to soils with the same resistivity (500 Wm) but different relative permittivities (1 and 30) are compared in Figure 4.15. It can 450

1

1) εR = 1 2) εR = 30

Voltage (kV)

2 300

150

0

2

4

6 8 Time (μs)

10

12

14

Figure 4.15 Lightning-induced voltages for soils with different relative permittivities (eR). Adapted from [11]. I ¼ 50 kA; tf ¼ 3 ms; b ¼ 0.3; h ¼ 10 m; d ¼ 50 m; x ¼ 0 m; r ¼ 500 Wm

126

Lightning interaction with power systems, volume 2

readily be seen that the influence of this parameter is very small (the difference between the voltage amplitudes is approximately 2%). For r ¼ 5,000 Wm, the difference between the peak values of the voltages relevant to the cases of eR ¼ 1 and eR ¼ 3 is even smaller (less than 1%) [11].

4.2.2.8

Occurrence of an upward leader

A model for the calculation of lightning-induced voltages taking into account the effect of an upward leader was presented in [28]. As the stepped leader approaches the ground, the electric field at the earth’s surface increases. When it exceeds the air breakdown field strength (about 30 kV/cm at standard temperature and pressure), corona discharges take place, leading eventually to the formation of an upward leader. The polarity of the charges in the upward leader channel is opposite to that of the charges of the downward stepped leader. When the two leaders meet, the return stroke phase begins. The attachment usually occurs at a height between some tens and some hundreds of meters from the earth, and from this point two current waves begin to propagate. The currents have the same polarity, but propagate in opposite directions. If their propagation velocities are equal and the linear charge density is the same in the two channels, they will have the same magnitude. The influence of the upward leader on the induced voltages is illustrated in Figure 4.16, which presents the voltages calculated at the point closest to the stroke location under the following conditions: ●



stroke current: magnitude I ¼ 50 kA, triangular waveform (front time tf ¼ 3 ms and time to zero of 200 ms); line: single phase, 10-km long, matched at both ends;

240 ht = 0 200

Voltage (kV)

160 120 ht = 100 m 80 40 0 –40

0

3

6 9 Time (μs)

12

15

Figure 4.16 Lightning-induced voltages considering (ht ¼ 100 m) or not (ht ¼ 0) the occurrence of an upward leader. Adapted from [22]

Lightning interaction with MV overhead power distribution systems ●



127

lightning strike point at a distance d ¼ 60 m from the line and equidistant from its terminations; ground: assumed as perfectly conducting.

The upward leader causes a reduction of the induced voltage magnitude, since the effect of the charges in its channel opposes that of the charges in the downward leader channel. For the situation considered, the induced voltage waveshape is unipolar in the absence of the upward leader. However, when it is present, the voltage may present a bipolar waveshape, with an initial negative incursion for the most common case of a negative downward flash. The amplitude and duration of this negative part increases with the height of attachment (ht) [22].

4.2.2.9 Presence of nearby buildings Buildings nearby urban overhead power lines are expected to reduce the number of direct strikes to the line conductors and to attenuate the lightning electromagnetic pulse (LEMP) radiated by indirect lightning strokes. Indeed, the presence of buildings near to the power line decreases the lightning threats for two main reasons: (a)

the buildings, as well as trees and other objects, may intercept several lightning flashes that would strike the line conductors without their presence; (b) the buildings may attenuate the LEMP of indirect strokes and hence cause a reduction of the lightning-induced voltage on the line. In lightning performance calculations, effect (a) is usually taken into account by the use of the shielding factor SF [1], discussed in Section 4.1. This item focuses on effect (b). Experimental observations show that the LEMP can experience significant attenuation when sensors are located close to a building, particularly due to the induced currents in metallic beams and other conducting parts in the building [53]. The effect of such an attenuation for the calculation of lightning-induced overvoltages on overhead lines has been addressed by making use of a reduced scale model [45,54,55] and of three-dimensional (3D) FDTD [56] and finite element method (FEM) in time domain [57] numerical approaches. For illustration and considering the test configuration shown in Figure 4.17, relevant to a scale model experiment [58,59], Figure 4.18 presents a comparison between phase-to-ground induced voltages measured at the transformer of the main feeder located at a distance of 20 m from the lightning strike point, for buildings’ heights of 5 and 15 m. The use of numerical electromagnetic analysis methods, either FDTD or FEM, for the calculation of the LEMP in a domain so large to contain a realistic power distribution line requires a huge amount of computer memory. Moreover, the long processing time required by these numerical methods for the evaluation of the effects of a single strike makes them not suitable for lightning performance assessment studies that require the evaluation of a large number of events. For accomplishing a fast calculation of the LEMP attenuation due to nearby buildings, Tossani et al. [60] proposes to apply weighting functions to the

128

Lightning interaction with power systems, volume 2 90

210

210

150

150

210

210

170 22 150

M 75

150

148

174 80

Stroke location

80

40

80

30

80

Figure 4.17 Top view of the test configuration relative to the presence of buildings in the vicinity of the line. Distance of 20 m between main feeder and stroke location. Triangles and circles represent transformers and surge arresters, respectively, while squares and rectangles denote blocks with buildings 5-m high. ‘M’ corresponds to the measuring point. All dimensions in meters. Adapted from [58]

300 5m

Voltage (kV)

200

100

15 m

0 0

1

2

3

4

5

6

7

8

9

10

–100

–200

Time (μs)

Figure 4.18 Measured induced voltages on an urban line configuration for buildings’ heights of 5 and 15 m. Stroke current of 50 kA with front time of 2 ms. Distance of 20 m between line and stroke location. All parameters referred to the full-scale system. Adapted from [58] electrostatic, induction and radiation field terms calculated by using the Master and Uman equations [61] and the Cooray–Rubinstein formula for the case of lossy ground [62,63]. The parameters of the weighting functions are identified through the least square minimization of the differences with the results provided by the

Lightning interaction with MV overhead power distribution systems Config. A

129

Config. B

Lightning channel

Lightning channel

10 m

10 m Line

Building 15 m

Line Building 15 m 10 m

10 m

10 m

10 m d

d

Config. C

Lightning channel 10 m

Config. D 10 m

10 m

10 m

Line

Line

Building 15 m 10 m 8m d

Lightning channel

18 m

Building 15 m

Building 15 m 10 m 8m

Building 15 m

18 m d

Figure 4.19 Considered line-building configurations: A and B with one building; C and D with the line in the space between two buildings. Adapted from [60]

FEM model presented in [57]. The LEMP attenuated by the surrounding buildings is used for the calculation of the induced voltages due to indirect lightning events by using the LIOV code (described in Chapter 12 of this volume and in [14]) based on the LEMP-to-line coupling model proposed by Agrawal et al. [64]. Figure 4.19 shows the line-buildings cross-section geometries considered in [60]. A 1-km long single horizontal conductor is placed at height h ¼ 10 m above soil and parallel to one building (configurations A and B) or inside the space between two buildings (configurations C and D). The length of the buildings exceeds the line ends for 50 m in order to study the relevant shielding effect for all the length of the line. The cross-section width of each building is 10 m and the height is 15 m. The cross-section dimension is assumed constant for all the considered configurations as it has a minor influence on the LEMP attenuation. Configuration B is motivated by the observation that the amplitude of the exciting electric field components that are responsible for the generation of lightning-induced overvoltages is reduced also by buildings situated at the opposite side of the line with respect to the lightning channel [55,57]. Configurations C and D are considered as the representatives of urban overhead lines located at one of the sides of the roadway. For illustrative purposes, Figures 4.20 (configuration A) and 4.21 (configuration C) show the stream lines of the electric field around the line conductor and the buildings. The field is produced by the lightning current with stroke location at y ¼ 0 m and it is

30

20

20

15

10

10

0 –10

0

20

40

60

30

20

20

15

10

10

5

0

5

0

–10

y (m)

(a)

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20

40

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Electric field intensity (kV/m)

Lightning interaction with power systems, volume 2

z (m)

z (m)

130

0

y (m)

(b)

40

20

30

15

10 0 –10

(a)

20 15

z (m)

z (m)

20

40 30 20 10 10 5 0 –10 0 0 (b)

0

20

40 y (m)

60

80

10 5 20

40 y (m)

60

80

Electric field intensity (kV/m)

Figure 4.20 Cross-sectional view of the electric field lines for configuration A. Adapted from [60]. (a) Ideal ground. (b) Ground resistivity r ¼ 100 Wm (colour scale saturated at 20 kV/m)

0

Figure 4.21 Cross-sectional view of the electric field lines for configuration C. Adapted from [60]. (a) Ideal ground. (b) Ground conductivity r ¼ 100 Wm (colour scale saturated at 20 kV/m) evaluated 6 ms after the beginning of the return stroke. The figures show that the penetration of the electric field lines into the lossy ground below the overhead line is reduced by the presence of the buildings, especially for the case of buildings located at both sides of the line (Figure 4.21(b)). These results were obtained with the following assumptions: ●





the channel is placed at distance d from the overhead line and equidistant to the line terminations; the spatio-temporal distribution of the lightning current is defined by the TL return stroke engineering model [38], with a return stroke wave-front velocity equal to 1.5  108 m/s and a current waveform ‘F’, which is represented by using the Heidler function [65] and the following parameters I0 ¼ 29.3 kA, t1 ¼ 1.44 ms, t2 ¼ 91.8 ms and n ¼ 2; the building is represented by a perfectly conducting cuboid. As shown in [57], almost the same results are obtained by representing the steel-reinforced concrete by a mesh of 5-m long metallic thin wires.

The calculation of the induced voltages is performed by applying the Agrawal et al. coupling model [64] that, at each time step, requires the evaluation of the two

Lightning interaction with MV overhead power distribution systems 120

Voltage (kV)

100

131

No building LSQ FEM

80 60 40

Ideal ground

ρ = 100 Ωm

20 0 –500

–250

0 Position (m)

250

500

Figure 4.22 Voltage peak amplitudes along the line for configuration A; d ¼ 100 m and waveform ‘F’. Adapted from [60] components of the lightning-originated electric field at each spatial step along the line, namely, the horizontal electric field Ex (i.e., the component along the line direction) and the vertical electric field Ez. Figures 4.21 and 4.22 compare the induced voltages on the overhead line using LEMP components Ex and Ez evaluated by the following two different methods: (a) FEM (directly obtained by the FEM model); (b) LSQ (obtained by using the specific weighting functions applied to the electrostatic, induction, and radiation terms of the LEMP analytical expressions valid for open terrain equations, as proposed in [60]). For both the cases of ideal soil and lossy ground, the parameters of the weighting functions are identified through the least square minimization of the differences with the results provided by an FEM model that is assumed as a reference for the configurations analysed. The weighting functions can be used for lightning return stroke current waveform and distances between the line and the stroke location different from those used for their identification with reasonable accuracy. Figures 4.22 and 4.23 show the peak values of the induced voltages along the line for configurations A and C, respectively, obtained assuming d ¼ 100 m for both the cases of ideal ground and ground conductivity sg ¼ 10 mS/m. The figures show also the peak values obtained without the buildings. In configuration A, the presence of the buildings results in peak voltage reduction at the mid-point of the line of 47% and 55%, for infinite and finite ground conductivities, respectively. In configuration C, the voltage reduction ratios become 67% and 75%, respectively. The figures show that the presence of the buildings reduces the difference between the results obtained for the case of ideal and lossy ground, that is, the buildings reduce the effect of the finite conductivity of the soil, in particular for configuration C (Figure 4.23).

132

Lightning interaction with power systems, volume 2 120 100

No building LSQ FEM

Voltage (kV)

80 60

ρ = 100 Ωm

Ideal ground 40 20 0 –500

–250

0 Position (m)

250

500

Figure 4.23 Voltage peak amplitudes along the line for configuration C; d ¼ 100 m and waveform ‘F’. Adapted from [60] The advantage of using the weighting functions with respect to the use of the FEM model lies in the reduced computational effort. While the induced voltage calculation by using the weighting functions is performed in a few seconds for the case of a single line, the same calculation with the LEMP provided by the FEM model requires from 5 to 6 hours [60].

4.3 Lightning protection of MV systems The basic measures to improve the lightning performance of MV distribution lines involve the increase of the line insulation withstand capability [1,3,4,66–68], the use of periodically grounded shield wires [1,3,4,10,40,68–80] and the installation of line arresters [1,3,4,10,17,66,75,76,81,82]. A 10-m high distribution line located in open ground in an area with ground flash density of 1/(km2year) collects on average approximately 11 flashes/ (100 kmyear). The use of a shield wire in conjunction with arresters on every pole and every phase is effective against direct strokes and theoretically eliminates flashovers. The shield wire protects the arresters from excess energy dissipation, and the arresters prevent backflashovers [1,4]. This is certainly the best protection configuration under the technical point of view, but a cost-benefit analysis should be performed to verify whether this is indeed the optimum solution for a specific case. A discussion on the effectiveness of the main techniques to mitigate lightning overvoltages is presented in this section.

4.3.1

Increase of the line withstand capability

An increase of the critical flashover overvoltage (CFO) of the line structures will practically not affect the number of faults caused by direct strokes, unless a shield

Lightning interaction with MV overhead power distribution systems

133

wire earthed at every pole with low ground resistance is used or surge arresters are installed on all phases at very short intervals. On the other hand, an increase of the line CFO can lead to a substantial decrease of the frequency of flashovers associated with indirect strokes, but, in this case, surges with high magnitudes will travel over long distances and increase the stresses on line equipment [1,4].

4.3.2 Use of shield wires Although a multi-grounded shield wire may collect most of the flashes that otherwise would hit the phase conductors, its effectiveness against direct strokes is very limited. The reason is that the potential rise due to the current flow through the pole ground impedance causes a large voltage difference between the ground lead and the phase conductors, which in turn causes a backflashover in the great majority of the cases. Therefore, in order to mitigate the effects of direct strikes, the shield wire should not only be grounded at every pole but also the line should have sufficient CFO between the ground lead and the phase conductors, and the ground resistances should be low. Ground resistances must be less than 10 W if the CFO is less than 200 kV, whereas for CFO in the range of 300 to 350 kV, a ground resistance of 40 W will provide similar performance [1]. On the other hand, due to its coupling with the phase conductors, a shield wire or a neutral reduces the magnitudes of the overvoltages associated with nearby strokes irrespective of its position. Its effectiveness varies from case to case, as it depends on the combination of the values of several parameters as, for example, the relative position of the shield wire with respect to the phase conductors, the grounding spacing, the ground resistance, the soil resistivity, the stroke current waveshape, etc. The greater the coupling, the more significant the voltage reduction. In addition, the presence of a shield wire or a neutral conductor has different effects on the phase-to-ground and phase-to-shield wire (or phase-to-neutral) voltages. If we consider an infinite line with one phase conductor and a shield wire grounded at a single point x1, the following relationship exists between the current Ig(x1, t) which will flow to ground in the event of a nearby lightning stroke and the voltage Ug(x1, t) which would be induced at point x1 in the absence of the connection to ground [69]:   Zg dIg ðx1 ; tÞ Ug ðx1 ; tÞ ¼ þ Rg Ig ðx1 ; tÞ þ L (4.7) 2 dt where Zg is the surge impedance of the shield wire, Rg represents the ground resistance and L is the ground lead inductance. Although, strictly speaking, the term ‘ground impedance’ is more appropriate than ‘ground resistance’, in this chapter the ground impedance is represented by the DC resistance at the grounding point, that is, by the ground resistance. This is a reasonable approximation in the case of grounding systems of small dimensions – which is typically the case of power distribution networks – for which the inductive and capacitive components of the ground impedance can be neglected in comparison with the resistive component.

134

Lightning interaction with power systems, volume 2 The induced voltage Up(x2, t) at point x2 on the phase conductor is given by [69]:   1 jx2  x1 j 0 (4.8) Up ðx2 ; tÞ ¼ Up ðx2 ; tÞ  Zm Ig x1 ; t  2 c

where Up0 (x2, t) is the voltage that would be induced at point x2 of the phase conductor in the absence of the shield wire, Zm is the mutual impedance between the conductors and c is the velocity of light in free space. Equation (4.8) shows that, due to the electromagnetic coupling between the shield wire and the phase conductor, the induced voltage on the latter will be reduced regardless of the relative position of the wires. Figure 4.24(a) presents the voltage components of (4.8) for the case of a singlephase, 1.4 km long line with a shield wire grounded at just one point, in front of the stroke channel, with ground resistance equal to 56 W. The situation refers to a test carried out on the 1:50 scale model – detailed described in [36,45,78] – according to the configuration depicted in Figure 4.25. There were two lines, one with and the other without a shield wire, so that the induced voltages Up and Up0 could be measured simultaneously. The lines were matched at both terminations and the heights of the phases and shield wire were, respectively, 20 and 22 cm (corresponding to 10 and 11 m in the full-scale system). The conductors had the same diameter, 0.4 mm, and the observation point was in the middle of the line, in front of the grounding point (i.e., dg ¼ 0). The stroke channel model was 1.4 m from the line (equivalent to a distance of 70 m) and equidistant from its terminations. The current, whose waveform is shown in Figure 4.26, had a mean propagation velocity along the channel model of 11% of that of light in free space. Ground could be assumed as perfectly conducting. 5

6 Up′ Voltage (V)

Voltage (V)

0

Up

3 2

Up (calc.)

1 100

200

–2 Time (ns) (a)

Up′ (meas.)

4

4

2

Up′ (calc.)

Up (meas.)

300 0

– 1 ZmIg 2

0

100

200

300

Time (ns) (b)

Figure 4.24 Phase-to-ground induced voltages on the two lines of Figure 4.25, at the point closest to the stroke location. dg ¼ 0, Rg ¼ 56 W. (a) Induced voltage components calculated according to (4.8). (b) Measured and calculated induced voltages on the lines with and without shield wire (Up and Up0 , respectively)

Lightning interaction with MV overhead power distribution systems 14 m

135

14 m dg

Stroke channel model

Shield wire 0.75 m

OP 1.4 m Phase conductor

1.4 m

Grounding point OP: observation point

OP

Figure 4.25 Top view of the test configuration corresponding to Figure 4.24, showing the lines with and without shield wire

Current (A)

1.5

1.0

0.5

0 0

100

200

300

Time (ns)

Figure 4.26 Measured ‘stroke’ current corresponding to the induced voltages presented in Figure 4.24 As the induced voltages are obtained in front of the grounding point (dg ¼ 0, hence x2 ¼ x1), there is no delay and the effect of the shield wire is felt instantaneously. For illustration, in Figure 4.24(b) the measured induced voltages on the lines with and without shield wire are compared with those calculated using the ERM [22,35–37]. A good agreement is found between theoretical and experimental results. The influence of the distance of the shield wire grounding to the observation point (dg) is illustrated in Figure 4.27, which presents the voltage components corresponding to a situation which is similar to that considered in Figure 4.25, but with a distance of 9 m (corresponding to 450 m in the full-scale system) between the observation and grounding points. The ‘stroke’ current is that shown in Figure 4.26 and the value of the ground resistance is 0 W. As in this case dg ¼ |x2  x1| ¼ 9 m, there is a delay of approximately 60.4 ns until the effect of the shield wire is ‘felt’ at the observation point. Such delay can be decomposed into two parts: the first is due to the different times of arrival of the electromagnetic field (produced by the propagation of the current along the channel model) at the observation and grounding points, while the second corresponds to the propagation of the voltage (–0.5ZmIg) from the grounding to the observation point. Due to this delay, the reduction of the induced voltage amplitude is quite small and the shield wire affects mainly the voltage wavetail.

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Lightning interaction with power systems, volume 2 6

5 Up′ Voltage (V)

Voltage (V)

4 Up

2

Up′ (calc.)

4 Up′ (meas.)

3 Up (calc.)

2 1

0

Up (meas.)

300

200

100

0 –2 Time (ns)

(a)

– 1 ZmIg 2

0

100 200 Time (ns)

300

(b)

Figure 4.27 Phase-to-ground induced voltages, at the point closest to the stroke location, on the two lines of Figure 4.25. dg ¼ 9 m, Rg ¼ 0 W. (a) Induced voltage components calculated according to (4.8). (b) Measured and calculated induced voltages on the lines with and without shield wire (Up and Up0 , respectively) The effectiveness of the shield wire in reducing lightning-induced voltages depends on the line configuration, soil characteristics and parameters of the stroke current. It can be evaluated through the shielding factor, which is defined as the ratio of the induced voltages with and without the presence of the shield wire [40]. However, as shown in [70,71], the shielding factor has different behaviours depending on whether it is the phase-to-ground (Up) or the phase-to-shield wire (Up-sw) voltage that is being considered. Therefore, two shielding factors are required to evaluate the effect of the shield wire, namely SFg and SFsw. The former is defined as the ratio of the peak values of Up and the voltage that would be induced on the phase conductor in the absence of the shield wire (Up0 ) at the point of the line closest to the stroke location. The latter is defined in a similar way, but with the voltage Up replaced with Up-sw. Thus, SF g ¼

Up Up 0

SF sw ¼

(4.9)

Up-sw  Up 0

(4.10)

According to the definitions shown in (4.9) and (4.10), the lower the factor, the more significant the voltage reduction in relation to Up0 and, consequently, the higher the effectiveness of the shield wire. For the case of a shield wire at height hg connected to ground at only one point, the shielding factor SFg is given by Rusck [40] as: SF g ¼ 1 

hg 1  Zm  h 2Rg þ Zg

(4.11)

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137

Return stroke channel h xg

Usw

xg/2 xg/2

hg

d

Up-sw

Up

xg

Figure 4.28 Basic configuration adopted in the simulations and definition of the voltages Up, Usw and Up-sw. Base case: line length ¼ 3 km (both terminations matched); d ¼ 50 m; h ¼ 10 m; hg ¼ 11 m; xg ¼ 300 m; Rg ¼ 50 W; r ¼ 1,000 Wm, induced voltages calculated at the point closest to the stroke location (equidistant from the closest grounding points and from the line terminations). Only the poles corresponding to the shield wire grounding points are shown in the figure. Adapted from [69] In [83], Andreotti et al. show that, in practice, (4.11) is valid independently of the position of the grounding point. However, besides the assumption of a single connection to ground, the expression was developed for the case of a perfectly conducting soil. In order to investigate the influences of the most important parameters on the effect of a shield wire, a base case is considered. The basic configuration adopted in the simulations is that considered in [69,70] and illustrated in Figure 4.28. The three-phase line is 3-km long and the height of the phase conductors is 10 m, with distance of 0.75 m between adjacent phases. The shield wire is equidistant from the outer phases, at the height of 11 m. The diameter of all the conductors is 1 cm, the grounding interval (xg) is 300 m and the inductance of the ground lead is 11 mH. The stroke channel is vertical, 3-km long, without branches and the TL model [38] is assumed for the calculation of the current distribution along the lightning channel. The stroke current is represented by a triangular waveshape with peak value of 30 kA, front time of 2 ms, time to half-value of 80 ms and propagation velocity of 40% of that of light in free space. The induced voltages are calculated at the point of the line closest to the stroke location, which is equidistant from the line terminations and from the closest shield wire grounding points. The soil resistivity is 1,000 Wm, the relative permittivity is equal to 10 and the distance between the line and the lightning strike point is 50 m. Figure 4.29 presents, for the base case and ground resistance of 50 W, the induced voltage waveforms Up, Up-sw and Up0 , as well as the shield wire-to-ground voltage (Usw). The corresponding values for the shielding factors SFg and SFsw are 0.817 and 0.368, respectively, meaning that in the presence of the shield wire and

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under the conditions considered, the phase-to-ground and phase-to-shield wire voltages reach, respectively, about 82% and 37% of the peak value of the phase-toground voltage that would be induced in the absence of the shield wire. If surge arresters are not present and corona is disregarded, the system is linear and the induced voltages are directly proportional to the lightning current. Therefore, the shielding factors depend on the stroke current waveshape and propagation velocity, but not on its magnitude. On the other hand, both SFg and SFsw may vary along the line and, for the same stroke location, large differences may be observed on the shielding factors corresponding to different observation points. In the evaluation of the dependence of the effectiveness of the shield wire presented in the next items, the calculations refer to the closest point to the stroke location, on which the largest overvoltages are usually induced. The simulations were run using the ERM [22,35–37] and, unless otherwise indicated, the values of all parameters are the same as those adopted for the base case.

4.3.2.1

Ground resistance and soil resistivity

The value of the ground resistance depends not only on the soil resistivity – which may vary widely – but also on the dimensions, depth and arrangement of the grounding electrodes. Therefore, for the same soil resistivity, different values of the ground resistance are obtained in the case of different grounding systems. Figure 4.30 presents the shielding factors SFg and SFsw as function of the ground resistance Rg for hg ¼ 11 m, xg ¼ 300 m, tf ¼ 2 ms, d ¼ 50 m, and soil resistivities of

320 Up′

Voltage (kV)

240

Up

160

Usw

80 Up-sw 0 –80

2

4

6

8 10 Time (μs)

12

14

16

Figure 4.29 Lightning-induced voltages at the point closest to the stroke location. Base case: I ¼ 30 kA; tf ¼ 2 ms; vf ¼ 0.4c; d ¼ 50 m; h ¼ 10 m; hg ¼ 11 m; xg ¼ 300 m; Rg ¼ 50 W; r ¼ 1,000 Wm; stroke location equidistant from the closest grounding points. (a) Phase-to-ground voltage which would be induced in the absence of the shield wire (Up0 ); (b) phase-to-ground voltage (Up); (c) shield wire-to-ground voltage (Usw); (d) phase-to-shield wire voltage (Up-sw). Adapted from [69]

Lightning interaction with MV overhead power distribution systems

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1.0 SFg Shielding factor

0.8 Eq. (4.11) 0.6

1,000 Ωm 100 Ωm

10 Ωm

0.4 SFsw

0.2 0.0 0.0

300 100 200 Ground resistance (Ω)

400

Figure 4.30 Shielding factors as functions of the ground resistance for different values of the soil resistivity. hg ¼ 11 m; xg ¼ 300 m; tf ¼ 2 ms; vf ¼ 0.4c; d ¼ 50 m. Adapted from [69]

10 Wm, 100 Wm and 1,000 Wm. For comparison purposes, the curve obtained using Rusck’s formula – (4.11) – is also presented. The shielding factors SFg and SFsw have opposite behaviours with respect to the ground resistance; the former increases and the latter decreases as Rg increases. This means that the effectiveness of the shield wire in reducing the phase-to-ground voltages is lower for high values of Rg. On the other hand, the higher the value of Rg, the higher the effectiveness of the shield wire in reducing the phase-to-shield wire induced voltage. This can be explained as follows: an increase in the ground resistance leads to an increase in the phase-to-ground voltages Up, since higher values of Rg correspond to lower currents to ground and, consequently, to lower amplitudes of the voltage component responsible for the reduction of the induced voltages [70,73]. On the other hand, as the shield wire-to-ground voltage (Usw) is more sensitive to the variation of Rg, the increase of this voltage is more significant than the decrease of Up, and therefore the net result is a decrease of the voltage between phase and shield wire (Up-sw) as Rg increases [69]. The effect of the ground resistance tends to be more pronounced in the case of low-resistivity soils. For r ¼ 1,000 Wm, a variation of Rg in the range of 10–400 W leads to a variation of about 15% (from to 0.792 to 0.911) in SFg; for r ¼ 10 Wm, the corresponding variation is approximately 32% (from 0.648 to 0.854). An increase in the soil resistivity leads to an increase in SFg and a decrease in SFsw, but the variations of SFsw with both r and Rg tend to be more significant. For instance, in the case of Rg ¼ 10 W, SFg increases about 22% (from 0.648 to 0.792) when the soil resistivity increases in the range 10–1,000 Wm, whereas, under the same conditions, the variation (decrease) of SFsw is 36% (from 0.619 to 0.399). The effect of the soil resistivity on SFsw tends to be more pronounced in the case of shorter distances between the line and the stroke location [70].

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In [84], a simplified expression is derived by Rachidi et al. for the estimation of the ratio between the peak values of the induced voltages on multi-conductor and single-conductor lines of the same height. In addition, results relevant to the use of the simplified formula proposed by Rusck for the evaluation of the shielding effect of ground wires are presented for a line with vertical configuration. The values predicted by (4.11) for that specific case are about 6% lower in comparison with the calculations performed by the authors. Taking into account the uncertainties with which different parameters of the lightning discharge are known, the authors conclude that the accuracy of the Rusck formula is quite reasonable. Although, according to [76], the Rusck formula allows for an accurate prediction of the mitigation effect of the shield wire only when the number of groundings is large, Figure 4.30 shows that, for the situations considered, the shielding factor SFg calculated using (4.11) almost coincides with the results corresponding to r ¼ 10 Wm. However, the differences increase with the soil resistivity, so that the use of the simplified equation is not recommended for the case of moderate or poor-conducting soils. As the influence of r increases with the reduction of the ground resistance, the largest errors are associated with the case of high-resistivity soils and low ground resistance values.

4.3.2.2

Distance between the line and the lightning strike point

The induced voltages, especially the phase-to-ground ones (Up and Up0 ), are highly dependent on the distance d between the line and the stroke location, and thus the shielding factors are also affected. Such influence tends to increase in importance in the case of stroke currents with short front times [73]. The effect of the distance on the shielding factors is illustrated in Figure 4.31, where SFg and SFsw are presented as functions of the ground resistance for distances of 50, 100 and 400 m. SFg tends to be higher for shorter distances, whereas SFsw has the opposite behaviour. This means that, the shorter the distance, the 1.0 SFg

Shielding factor

0.8 50 m

0.6

100 m

400 m

0.4 SFsw 0.2 0.0

0

100

300 200 Ground resistance (Ω)

400

Figure 4.31 Shielding factors as functions of the ground resistance for different distances between the line and the stroke location. r ¼ 1,000 Wm; hg ¼ 11 m; xg ¼ 300 m; tf ¼ 2 ms; vf ¼ 0.4c. Adapted from [69]

Lightning interaction with MV overhead power distribution systems

141

lower the reduction of the phase-to-ground voltages and the greater the reduction of the phase-to-shield wire voltages. Figure 4.31 shows also that the variation of SFg is much smaller in comparison with that of SFsw. For instance, in the case of Rg ¼ 10 W, SFg decreases from 0.792 to 0.681 (about 14%) when d varies from 50 to 400 m, whereas SFsw increases from 0.399 to 0.615 (about 54%) for the same variation. Larger variations of SFsw are observed also with respect to the ground resistance. For d ¼ 100 m and Rg in the range 10–400 W, the variation of SFg was from 0.736 to 0.873 (about 19%), whereas the corresponding variation of SFsw was from 0.492 to 0.260 (about 47%).

4.3.2.3 Shield wire height A shield wire must be installed above the phase conductors in order to reduce the incidence of direct lightning strokes to them. However, a consequence of an increase in the height of the line is that more flashes are attracted to it, thus increasing the risk of backflashovers. Therefore, in practice hg is usually not much higher than about 11 or 12 m. On the other hand, a neutral conductor, which functions as a shield wire, is usually placed at a height around 7 m. In this typical range of hg, for the conditions of the base case, the variation of the shielding factor SFg is not so significant. This is illustrated in Figure 4.32, which presents the shielding factors as function of the ground resistance for shield wire heights of 7, 9 and 11 m. The decrease of SFg when hg increases from 7 to 11 m is, for the case of Rg ¼ 10 W, about 13% (from 0.910 to 0.792). The influence of the shield wire height on SFg tends to diminish with Rg. A larger influence is observed on SFsw, which, for Rg ¼ 10 W and the same variation of hg, decreases approximately 19% (from 0.494 to 0.399). Unlike what happens with SFg, the influence of hg on SFsw tends to increase with the ground resistance; for instance, in the case of Rg ¼ 400 W, SFsw decreases from 0.298 to 0.216 (about 28%) when hg varies from 7 to 11 m. 1.0

SFg

Shielding factor

0.8 7m

0.6

9m

11 m

0.4 SFsw

0.2 0.0

0

100

200 300 Ground resistance (Ω)

400

Figure 4.32 Shielding factors as functions of the ground resistance for different heights of the shield wire. r ¼ 1,000 Wm; xg ¼ 300 m; tf ¼ 2 ms; vf ¼ 0.4c; d ¼ 50 m. Adapted from [69]

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Lightning interaction with power systems, volume 2

Figure 4.32 also shows that, unlike the soil resistivity, the ground resistance, and the distance between the line and the stroke location, the shield wire height affected the shielding factors similarly in the cases considered, that is, a decrease in hg resulted in an increase in both SFg and SFsw.

4.3.2.4

Grounding spacing

The spacing between adjacent groundings is an important parameter in the analysis of the effectiveness of a shield wire. The variations of the shielding factors with the ground resistance are presented in Figure 4.33 for grounding intervals of 100, 300, 450 and 600 m. Under the conditions considered, SFg is approximately 1.0 for spacings longer than about 600 m within the whole range of Rg, since the voltage components originated in the shield wire groundings are either relatively low or arrive at the observation point after the voltage has reached its peak. This is in fact a predictable result, which is in accordance with previous theoretical (e.g., [36,72]) and experimental (e.g., [78]) works where different line configurations were considered. For shorter spacings, SFg tends to increase with xg, and such a variation is more significant in the case of low ground resistance values. The behaviour of SFg can be explained by the fact that each grounding point gives rise to a voltage component that, due to the coupling between the shield wire and the phase conductor, overlaps the voltage induced on the latter. As the polarity of such components is opposite to that of the induced voltage, the latter is reduced. Therefore, the greater the grounding density is, the greater will the number of these components be. Thus, the reductions on the amplitudes of the phase-to-ground induced voltages tend to be more significant as the grounding spacing becomes shorter. It should be noted, however, that the arrival of the reflections from the grounding points must take place before the induced voltage reaches its peak, otherwise no amplitude reduction will occur. 1.0 SFg Shielding factor

0.8 600 m

0.6

450 m

300 m

100 m

0.4 SFsw

0.2 0.0

0

100 200 300 Ground resistance (Ω)

400

Figure 4.33 Shielding factors as functions of the ground resistance for different grounding spacings. r ¼ 1,000 Wm; hg ¼ 11 m; tf ¼ 2 ms; vf ¼ 0.4c; d ¼ 50 m. Adapted from [69]

Lightning interaction with MV overhead power distribution systems

143

On the other hand, the variation of SFsw with the grounding interval is more complex. Depending on the combination of the values of the various parameters, SFsw may decrease as xg decreases up to a certain interval and, then, have an opposite behaviour, that is, for intervals shorter than this one, it may increase as xg decreases. This behaviour can be readily observed in Figure 4.33; for instance, in the case of Rg ¼ 10 W, SFsw diminishes from 0.556, for xg ¼ 600 m, to 0.399, for xg ¼ 300 m. The value corresponding to xg ¼ 450 m is 0.501. On the other hand, for the combination considered for the parameters, SFsw tends to increase with xg in the case of spacings shorter than about 300 m. For xg ¼ 100 m and the same ground resistance, the corresponding value of SFsw is 0.559 (approximately, 40% larger than the value obtained for xg ¼ 300 m). The reason for this somewhat unexpected behaviour can be more readily understood with the aid of Figure 4.34, which presents the phase-to-ground (Up), shield wire-to-ground (Usw) and phase-to-shield wire (Up-sw) voltages for Rg ¼ 10 W and spacings of 100, 300 and 600 m. In the case of large grounding spacings, the shield wire-to-ground voltage presents a relative low frequency of oscillation (in comparison with the case of short intervals) and may exhibit a large variation with time, as heavy oscillations are observed in the case of low ground resistance values, as shown in Figure 4.34(b). For xg ¼ 600 m, Usw varies from 336 to –20 kV from 400

400 600 m 300 m

240 160 80

100 m

240

80 0

–80

–80

2

4

8 6 Time (μs)

10

12

300 m

160

0

(a)

600 m

320 Voltage (kV)

Voltage (kV)

320

100 m 2

(b)

4

6 8 Time (μs)

10

12

400

Voltage (kV)

320 100 m

240

600 m

300 m

160 80 0 –80

(c)

2

4

6 8 Time (μs)

10

12

Figure 4.34 Lightning-induced voltages Up, Usw and Up-sw at the point closest to the stroke location for Rg ¼ 10 W and grounding spacings of 100, 300 and 600 m. Adapted from [69]. (a) Up. (b) Usw. (c) Up-sw

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Lightning interaction with power systems, volume 2

2.2 to 4.3 ms. The peak value of Up-sw occurs when Usw reaches its minimum in the first cycle – at about 4.3 ms for xg ¼ 600 m, long after the peak value of Up, which occurs at about 2.2 ms. As the grounding interval decreases, Up diminishes, but Usw oscillates with a higher frequency and presents lighter oscillations, so that its ‘first minimum’ value – caused by the contributions arriving from the grounding points – may be higher in comparison with the case of longer spacing. Therefore, the peak value of Up-sw not only decreases but is also reached at a shorter time (at about 2.6 ms in the case of xg ¼ 300 m). For spacings shorter than a certain ‘critical’ value, the reduction in the value of Usw becomes more significant than the reduction of Up and, in addition, due to the multiple reflections its variation in time tends to be lower in comparison with cases corresponding to larger spacings. The consequence is that, for intervals shorter than the ‘critical’ one – which for the conditions of the base case is about 300 m – Up-sw tends to increase as xg decreases. It can also be observed in Figure 4.33 that, although up to the critical grounding interval SFsw decreases as xg decreases, the differences between the values of SFsw tend to diminish with the ground resistance. For high values of Rg, SFsw presents just the opposite behaviour, that is, it increases as xg decreases. The reason is that the amplitudes of the oscillations in Usw are much lower in comparison with the cases corresponding to low values of Rg and, therefore, Usw does not reach values as low as in those cases. For example, in the situation illustrated in Figure 4.34(b) (Rg ¼ 10 W), Usw reaches about –20 kV at 4.3 ms for xg ¼ 600 m, whereas for Rg ¼ 500 W the corresponding value is about 161 kV [69]. Therefore, in the case of high values of the ground resistance, the reduction in Usw associated with shorter grounding intervals dominates and Up-sw (and, consequently, SFsw) increases as xg decreases.

4.3.2.5

Relative position of the lightning channel and grounding points

The shield wire factors vary according to the relative position of the stroke location and the closest grounding point. In Figure 4.35, the variations of SFg and SFsw with the ground resistance are compared for the base case and stroke location in front of a shield wire grounding. As in the previous cases, the observation point is in front of the lightning channel. If, keeping the same distance from the line, the stroke channel is moved from a point equidistant from the closest grounding points to another one located in front of a shield wire grounding, both Up and Usw decrease, as the delay of the effect of the groundings becomes shorter. The reduction of Up causes a reduction in SFg. However, as Usw undergoes a larger variation in comparison with Up, the phase-toshield wire voltage increases and so does SFsw. As expected, much larger variations with the ground resistance are observed on both shielding factors when the stroke location is in front of a shield wire grounding, as in this case the effect of the grounding is felt almost instantaneously at the observation point. The influence of the relative position of the lightning channel and grounding points on the shielding factors also depends on the distance between the line and the

Lightning interaction with MV overhead power distribution systems

Shielding factor

1.0 SFg

0.8 In front of a Equidistant from the grounding point closest grounding points

0.6

SFsw

0.2 0.0

0

100 200 300 Ground resistance (Ω)

Equidistant from the closest grounding points

Stroke location

0.4

145

Shield wire grounding

In front of a grounding point

400

Figure 4.35 Shielding factors as functions of the ground resistance for different positions of the stroke location with respect to the grounding points. r ¼ 1,000 Wm; hg ¼ 11 m; xg ¼ 300 m; tf ¼ 2 ms; vf ¼ 0.4c; d ¼ 50 m; observation point in front of the stroke channel. Adapted from [69]

stroke location. As shown in [70], the influence on SFg tends to decrease as lightning moves away from the line (i.e., as d increases); whereas in the case of SFsw, such influence may increase or decrease with the distance, depending on the value of the ground resistance. In general, SFsw tends to increase when lightning strikes in front of a grounding point in the case of low values of ground resistance. However, as its variation with Rg is larger in comparison with the case of lightning channel equidistant from the closest grounding points, the difference between the values corresponding to the different stroke locations decreases with Rg and, for a certain value of Rg – which depends on parameters such as the distance d – this behaviour inverts. Therefore, in the case of high values of ground resistance, the minimum value of SFsw may take place when the lightning channel is in front of a shield wire grounding.

4.3.2.6 Lightning current parameters The influence of the stroke current wavetail on the shielding factors can be disregarded, and thus the parameters of interest are the front time and propagation velocity. In general the amplitudes of the induced voltages tend to increase with vf for high-resistivity soils, whereas the opposite behaviour is observed in the case of low-resistivity values [71]. The effect of the propagation velocity is related also to the stroke current front time. For stroke currents with steep fronts, which is usually the case of subsequent strokes, the induced voltage magnitude tends to increase with vf, whereas for currents with slower fronts, typical of first strokes, it may present the opposite behaviour [71]. For the situations considered in the base case, SFg increases with vf; for Rg ¼ 10 W the variation is about 7% (from 0.764 to 0.819) when vf changes from

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0.2 to 0.8c. The variation is smaller if higher values of Rg are considered (about 3% for Rg ¼ 450 W). By its turn, SFsw decreases as vf increases and it presents a larger variation than SFg. For the same range of vf, SFsw decreases from 0.434 to 0.376 (about 13%) for Rg ¼ 10 W and from 0.221 to 0.193 (about 13%) for Rg ¼ 450 W [69]. The stroke current front time may have an important effect on the shielding factors. Although for the conditions considered in the base case and front times longer than 2 ms such influence is relatively small on both shielding factors; for shorter times, the influence may be significant. For example, in the case of Rg ¼ 10 W, SFg increases from 0.792 to 0.958 (about 21%) when tf decreases from 2 to 1 ms; whereas under the same conditions, SFsw increases from 0.399 to 0.692 (about 74%) [69].

4.3.3

Application of surge arresters

In order to protect effectively an unshielded MV line against direct strokes, surge arresters should be installed on all the phases of every pole. According to the analysis performed in [1], in the case of two spans between arresters, even a line with CFO of 350 kV and ground resistance of 10 W would experience flashovers in about 70% of the direct strikes. Such estimate refers to a span length of 75 m and assumes that the neutral is grounded at every pole. For three spans between arresters, the corresponding number is 80%. However, as pointed out by McDermot et al. [82], arresters applied to protect an unshielded line against direct strokes may have a significant failure rate due to excess energy dissipation. On the other hand, most of the studies agree that the application of surge arresters in MV lines can be effective in reducing the number of flashovers caused by indirect strokes, provided that the arrester spacing is not too large. According to the results obtained by Silva et al. [66], relevant to a 83-km long 13.8 kV distribution line, the installation of surge arresters every 300 m, on all phases, associated with the increase of the insulation level of the rural sections of the feeder, would reduce the number of lightning outages in approximately 50%, with a reduction around 75% of the number of faults caused by indirect strokes. The analysis presented by Paolone et al. [76] considered a single conductor, 2-km long line with arrester spacings of 2 km, 1 km, 500 m and 200 m. Information is given about the maximum amplitude of the induced voltage along the line as function of the spacing between two adjacent arresters for the cases of lossy (resistivity of 1,000 Wm) and perfectly conducting ground. The simulations revealed a shortcoming of the effectiveness of surge arresters when they are separated by large distances (e.g., one surge arrester every 1 km). The results showed also that an important reduction of the induced overvoltages can be achieved only with a large number of arresters, namely one surge arrester every 200 m. According to McDermot et al. [82], MV lines can be effectively protected against nearby strokes by installing arresters on each phase every 360 m; Yokoyama [75] suggests an installation interval of 200 m. In [17], Piantini and Janiszewski carried out an investigation about the effectiveness of surge arresters through the use of both an 1:50 scale model and a fullscale system implemented specifically for this purpose. The scale model was used

Lightning interaction with MV overhead power distribution systems

147

to simulate a typical 15 kV distribution line. The results showed that surge arresters can be effectively used for improving the lightning performance of distribution lines even if they are not applied at every pole, but the influence of the distance between adjacent surge arresters on the induced voltages is significant. The shorter the arresters’ spacing, the lower the voltage magnitudes. In the next subsections, the dependence of the effect of the arresters on the stroke current magnitude and waveshape, ground resistance, arrester spacing and relative position of the stroke location and arresters are discussed.

4.3.3.1 Stroke current magnitude and waveshape Due to the surge arrester non-linear characteristics, the voltages induced on a protected line will depend not only on the lightning current waveform but also on its magnitude. In order to illustrate such dependence, let us consider the results presented in Figure 4.36, relevant to the ratios of the peak values of voltages induced on lines with and without surge arresters for currents varying in the range of 20–65 kA. The experiment was carried out on a 1:50 scale model and the voltages were measured simultaneously at the closest points to the stroke location. One of the lines was straight, three-phase (without neutral) and 1.4-km long. The diameter of the conductors was 2 cm and they were in a horizontal configuration (height of 10 m) with the distance of 0.75 m between middle and outer phases. It had neither transformers nor laterals and was at a distance of 70 m from the channel model. Surge arresters were added on all phases; the spacing and grounding conditions were varied. The other line, single-phase, with the same length and matched at both ends, was placed symmetrically with regard to the stroke location, so that the voltages induced simultaneously on both lines, by the same stroke current, could be compared directly. The stroke current front time and time to half-value were about 3.2 and 58 ms, respectively. Previous measurements of induced voltages with both lines 60

(a)

Rg = 200 Ω Rg = 100 Ω Rg = 50 Ω Rg = 0 Ω

40

20

0 20

35

50 Current (kA)

Uwith /Uwithout (%)

Uwith /Uwithout (%)

60

(b)

40

20

0 20

35

50 Current (kA)

Figure 4.36 Ratio of the peak values of the voltages induced on lines with and without surge arresters (Uwith/Uwithout) as function of the stroke current magnitude for tf ¼ 3.2 ms; d ¼ 70 m, arrester spacing ¼ 300 m and perfectly conducting ground. All parameters referred to the full-scale system. Adapted from [17]. (a) Stroke location in front of a set of arresters. (b) Stroke location equidistant from two sets of arresters

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without arresters showed that under the same conditions the results were the same. Further details of the experiment can be found in [17]. In general, when the lightning strike point is in front of a set of surge arresters (Figure 4.36(a)), the reduction of the induced voltage tends to be more significant, especially for larger stroke current magnitudes. This behaviour is more evident for low ground resistance values, as in these cases the voltage on the protected line varies very little with the return stroke current magnitude (it is very close to the voltage at the surge arrester terminals), while the voltage on the line without arresters is proportional to the current. In case of strokes equidistant from two sets of arresters and currents with the same front time (Figure 4.36(b)), the reduction of the induced voltage in general does not depend significantly upon the stroke current magnitude. However, for currents with the same time-variation rate (di/dt), the front time increases with the current, which results in a more significant reduction on the induced voltage amplitude (with respect to that of the line without arresters) as the current increases. Regarding the stroke current front time, when it is long in comparison with the time required for the reflections at the surge arresters to arrive at the observation point, the voltage magnitudes are significantly reduced. On the other hand, if the voltage peak value is reached before the arrival of the reflections, only the voltage wavetail is affected. Therefore, the greater the stroke current steepness, the smaller the effect of the surge arresters. By its turn, the influence of the current wavetail can be disregarded.

4.3.3.2

Ground resistance

As shown in Figure 4.36, the ground resistance may have a great influence on the reduction of the induced voltage magnitude, especially when the lightning strike point is in front of a set of arresters. This is due to the fact that, as the resistance diminishes, the current that flows to ground (through the surge arresters) increases, thus increasing the value of the voltage component that, by coupling, reduces the voltages induced on the phase conductors. Figure 4.37, obtained from scale model experiments, presents measured induced voltages corresponding to ground resistances of 0 and 200 W.

4.3.3.3

Surge arrester spacing and relative position of the lightning strike point and arresters

The influence of the relative position of the stroke location and surge arresters is, in general, not significant for small arrester spacing, that is, when the time for propagation of the reflected waves between two surge arresters is much smaller than the rise time of the induced voltage. This is usually the case for arrester spacing less than 300 m. If the spacing is large, the variations of the distances from the stroke location to the surge arresters become important, and the same occurs with the suppressive components that by coupling cause reduction of the voltages induced on the phase conductors. The closer the surge arrester is from the lightning strike point, the greatest will its contribution be concerning the voltage reduction – assuming that the observation point is in front of the stroke location. Besides, in this case, the contribution of the arrester is felt almost instantaneously. In Figure 4.38, the

Lightning interaction with MV overhead power distribution systems

149

200 Line without arresters

Voltage (kV)

150 Rg = 200 Ω

100

Rg = 0 Ω

50

0 5

–50

10

15

20

Time (μs)

Figure 4.37 Phase-to-ground lightning-induced voltages on lines with different ground resistance values, at the point closest to the stroke location. Lightning strike point in front of a set of arresters, I ¼ 38 kA; tf ¼ 3.2 ms; d ¼ 70 m, arrester spacing ¼ 600 m; perfectly conducting ground. Adapted from [81]

180 Line without arresters

Voltage (kV)

144 Arrester spacing = 600 m

108

Arrester spacing = 300 m

72 36 0 5 –36

10

15

20

Time (μs)

Figure 4.38 Phase-to-ground induced voltages, on lines with different arrester spacings, at the point closest to the stroke location. Lightning strike point equidistant from two sets of arresters, I ¼ 38 kA; tf ¼ 3.2 ms; d ¼ 70 m; Rg ¼ 50 W, perfectly conducting ground. Adapted from [81]

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Lightning interaction with power systems, volume 2

voltages induced on an 1.4-km long straight line without surge arresters are compared with those corresponding to arrester spacings of 300 and 600 m. The closer the arresters are from the observation point, the shorter the delay for their contributions to arrive there and, thus, the greater the reduction in the induced voltages. Unlike lines located in rural areas, an urban line is characterised by a higher density of transformers and surge arresters, by many laterals and, besides, by the presence of structures and buildings in its vicinity. As the presence of buildings changes the lightning electromagnetic field, the induced voltages are consequently affected and the effectiveness of surge arresters may differ from that relevant to the case of rural lines. The effect of surge arresters on the induced voltages, considering the presence of buildings of different heights in the vicinity of the line, is illustrated in Figure 4.39. The results, obtained from scale model experiments [17,24], refer to a distance of 20 m between the stroke location and the main feeder and to a stroke current with magnitude of 34 kA, front time of 2 ms and time to half-value of 85 ms. Buildings were represented by grounded aluminium boxes with heights (hb) corresponding to 5 or 15 m, depending on the test configuration. Figure 4.40 presents one of the configurations corresponding to hb ¼ 5 m, whereas Figure 4.41 shows the distances between the buildings and the main feeder. It can be clearly noticed that the presence of buildings causes reduction on the induced voltage amplitude. The reduction is more significant in the case of higher buildings, which provide a more effective shielding of the line.

300 120

hb = 0 m

hb = 0 m

Voltage (kV)

Voltage (kV)

hb = 5 m

hb = 5 m

90

hb = 15 m

60

0

30

0 (a)

150

2

4 6 Time (μs)

8

hb = 15 m

2

4

6

8

10

10 (b)

–150

Time (μs)

Figure 4.39 Phase-to-ground induced voltages measured at the main feeder of the configuration shown in Figure 4.40, for buildings of different heights hb. Adapted from [24]. I ¼ 34 kA; tf ¼ 2 ms; d ¼ 20 m; perfectly conducting ground. (a) Case 1: se ¼ 75 m; sd ¼ 75 m. (b) Case 2: se ¼ 148 m; sd ¼ 174 m

Lightning interaction with MV overhead power distribution systems 90

210

210

150

150

210

210

151

170

22 150

M se

sd

75

150

Stroke location 80

Surge arresters

80 40

80

Transformers Grounding point (neutral)

30

80

Buildings

Figure 4.40 Top view of one of the test configurations with hb ¼ 5 m. ‘M’ corresponds to the measuring point (transformer of the main feeder). Distance between main feeder and channel model ¼ 20 m. The neutral conductor is grounded at the points indicated and also at all transformer installation points. Surge arresters placed at the ends of the laterals and at distance se and sd from the measuring point. All dimensions in meters. Adapted from [17]

10 m 8m hb (5 m or 15 m)

Building

Building

6m

10 m

6m

Figure 4.41 Distances between buildings and the main feeder. Adapted from [24]

In Figure 4.39, two situations are considered regarding the distances se and sd between the measuring point and the closest set of surge arresters. The dependence of the voltage amplitudes with respect to se and sd tends to decrease as the building height increases. In the absence of buildings, the ratio between the crest values of the induced voltages on cases 1 (se ¼ sd ¼ 75 m) and 2 (se ¼ 148 m, sd ¼ 174 m) is

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Lightning interaction with power systems, volume 2

approximately 0.54. For hb ¼ 5 m the ratio is 0.57, while for hb ¼ 15 m the ratio is 0.96. This can be explained by the fact that, in the absence of buildings, the difference between the induced voltages is due only to the different distances between the measuring point and the nearest sets of arresters. This influence is very significant, especially when the stroke location is close to the line. On the other hand, the amplitude of the total electromagnetic field near the line diminishes as the height of the buildings increase, as a consequence of the shielding, that becomes more effective. Therefore, in the test conditions, for hb ¼ 15 m the induced voltages are influenced more significantly by the presence of buildings than by the surge arresters. Figure 4.42 presents the voltages at the transformer placed at the end of the lateral which is closest to the lightning strike point for a stroke current magnitude corresponding to 50 kA and distances of 150 (Case 3) and 75 m (Case 4) between the measuring point and the closest set of arresters. The distances from the stroke location to the main feeder (d) and to the closest lateral (dr) were 70 and 20 m, respectively. Surge arresters were placed at the ends of all laterals, with the exception of that in which the voltage was measured (in this one, they were placed at a distance sr from the measuring point). Figure 4.43 shows the test configuration corresponding to the absence of buildings; the other configurations were exactly the same, except for the presence of buildings with heights of 5 and 15 m in the vicinity of the line. As in the previous case, the results show that the effectiveness of the surge arresters on the reduction of the induced voltages magnitudes tends to decrease as the buildings height increases, as a result of the diminution of these voltages due to the decrease of the total electromagnetic field associated with the line shielding.

hb = 0 m hb = 5 m

Voltage (kV)

400

hb = 15 m

200 0 2

4

6

hb = 0 m

160

8

–200

10

12

Voltage (kV)

600

hb = 15 m hb = 5 m

80

0

2

4

6

8

10

12

–400 –600 (a)

–80

Time (μs)

Time (μs)

(b)

Figure 4.42 Phase-to-ground induced voltages measured at the end of a lateral (configuration shown in Figure 4.43) for buildings of different heights hb. Adapted from [85]. I ¼ 50 kA; tf ¼ 2 ms; d ¼ 70 m; dr ¼ 70 m; perfectly conducting ground. (a) Case 3: sr ¼ 150 m. (b) Case 4: sr ¼ 75 m

Lightning interaction with MV overhead power distribution systems 90 m

210 m

150 m 148 m

210 m

148 m

42 m 132 m

346 m

210 m

284 m

210 m

153

170 m

152 m 150 m

150 m 70 m

75 m

150 m

sr Stroke location

M 20 m

Surge arresters Transformers

Grounding point (neutral)

M Measuring point

Figure 4.43 Top view of one of the test configurations without buildings. ‘M’ corresponds to the measuring point (transformer at the end of the lateral). The neutral conductor is grounded at the points indicated and also at all transformer installation points. Surge arresters placed at the ends of the laterals and at distance sr from the measuring point. Adapted from [17]

4.4 Lightning performance of overhead distribution lines In sections 4.1, 4.2 and 4.3, a procedure to estimate the number of direct strokes to a given line was presented, the influences of several parameters on the lightning overvoltages were discussed, and the effectivenesses of the measures to mitigate the surges associated to both direct and indirect strokes were analysed. In this section, the method described in Chapter 1 of this volume is applied to distribution lines with different configurations and their estimated lightning performances are compared. Especially in urban or suburban areas, indirect lightning is usually the main problem of interest for distribution lines due to the presence of tall objects around them capable of attracting lightning strokes in lieu of the line conductors. However, in some cases, such as hybrid configurations in which a MV and a HV line are mounted together on the same poles, direct lightning flashes to the structure hosting the lines becomes more likely to occur and the estimation of the lightning performance should consider also the occurrence of direct strikes.

4.4.1 Influence of the environment around the line For the problem of interest, it is convenient to refer to three types of situations: (a) the distribution overhead line/system is located above an open ground; (b) the distribution overhead line/system is surrounded by elevated objects, such as trees or buildings; (c) the distribution overhead line/system is mounted on the same pole where a HV line is mounted too (hybrid configuration).

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Lightning interaction with power systems, volume 2

For cases (b) and (c), the presence of objects or an additional line on the same poles has a 2-fold effect: (i) (ii)

the first one, the buildings (as well as trees and other objects) may intercept several lightning flashes that would strike the line conductors in their absence; the second is that whatever elevated object be stricken by lightning (buildings, trees or poles), the calculation of the relevant LEMP exciting the MV line conductors must consider its presence.

Concerning point (i), quite a few models have been proposed in the literature to describe the ‘attachment process’. In [86], a review aimed at assessing some of the most popular lightning striking distance expressions is proposed; in Chapter 5 of Volume 1, a review of the expressions for the lightning attachment to a single horizontal conductor is given. Concerning point (ii), such an effect has been taken into account either concerning elevated objects (e.g., [87,88]) or the presence of buildings around the line [57,60]). In what follows, results are presented relevant to the three situations (a), (b) and (c) mentioned above.

4.4.2

Lines located above open ground

In this subsection, the procedure depicted in Chapter 1 of this volume is applied to a 10-m high, 2-km long line consisting of a single conductor, with diameter equal to 1 cm, above an ideal ground. The line is matched at both terminations and the stroke locations are equidistant from the line ends. This configuration is assumed to be equivalent to an infinite long line, as illustrated in [14]. If the ground flash density is assumed to be equal to 1 flash/km2/year, the estimated number of direct strikes to the line, according to (4.4), is 11.1 flashes/ 100 km/year. Protecting an overhead distribution line against direct strokes is very difficult and it can, in general, be assumed that all direct strokes will lead to a line flashover as far as typical configurations are considered. Therefore, a 10-m high line will experience about 11 flashovers/100 km/year. On the other hand, the presence of a multi-grounded shield wire or neutral conductor and/or surge arresters can mitigate overvoltages induced by nearby strokes. In this subsection, the LIOV– MC procedure described in Chapter 12 of this volume is applied to evaluate the performance of the line against indirect strokes.

4.4.2.1

Unprotected lines

Figure 4.44 shows the comparison between the flashover rates of the single conductor line above an ideal ground and above lossy ground with resistivities of 100 and 1,000 Wm, as function of the CFO. The results can be explained observing that, as known [47], when evaluating lightning-induced voltages, the finite value of the ground conductivity, on the one hand, increases the transient propagation losses in the line, but, on the other hand, also has an influence on the LEMP propagation. While the former effect tends to decrease the surges propagating along the line, the

Lightning interaction with MV overhead power distribution systems

155

100.000

Flashovers/100 km/yr

10.000 1.000 0.100

0.010 0.001 50

(A) LIOV–MC (ideal ground) (B) LIOV–MC (ρ = 100 Ωm) (B) LIOV–MC (ρ = 1,000 Ωm)

100

150 200 CFO (kV)

250

300

Figure 4.44 Flashover rates of a single conductor 10-m high line above an ideal ground and above a lossy ground with resistivities of 100 and 1,000 Wm. Adapted from [89] latter tends to enhance the amplitude of the induced voltages. It is this second effect that, overall, causes maximum values of induced voltages higher than those calculated for the case of an ideal ground [14,47].

4.4.2.2 Lines with a shield wire or neutral conductor Let us now consider the case in which a shield wire having the same diameter of the phase conductor, namely 1 cm, is added to the line considered in Section 4.4.2.1. The height of the shield wire is 8.37 m and the ground is assumed as perfectly conducting. The ground resistance Rg ¼ 0, in accordance to the ideal ground assumption. In order to illustrate the influence of the spacing between adjacent groundings on the lightning performance of the line, Figure 4.45 shows a comparison between the flashover rate curves obtained with the shield wire grounded each 30 m and grounded each 500 m for the case of a fixed stroke current front time of 1 ms. The results of Figure 4.45 have been obtained by assuming the flashover occurring only from the phase conductor to ground. In principle, the line could experience flashovers between the phase conductor and the grounded conductor too. Figure 4.46 shows the flashover rates calculated by considering the two different flashover paths, namely the phase-to-ground path and the phase-to-grounded wire one. The results of Figure 4.46 must be interpreted while keeping in mind that the two different flashover paths are characterized by different CFOs, especially for wooden poles and crossarms. Let us consider, for example, the curves of Figure 4.46 relevant to the soil resistivity of 1,000 Wm and Rg ¼ 100 W. If we assume a CFO of 200 kV for a phase-to-ground path and a CFO of 130 kV for a phaseto-grounded wire path, we obtain 2.2 flashovers/100 km/year and 4.8 flashovers/ 100 km/year (and not 0.52 flashovers/100 km/year, as would be the case by improperly assuming the same CFO for the two cases), respectively.

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Lightning interaction with power systems, volume 2 100.000

Flashovers/100 km/yr

10.000

1.000

0.100

0.010

0.001

50

Grounding each 30 m Grounding each 500 m

100

150

200

CFO (kV)

Figure 4.45 Flashover rates of the single conductor 10-m high line with the shield wire at the height of 8.37 m for grounding spacings of 30 and 500 m and fixed stroke current front time of 1 ms. Perfectly conducting ground. Adapted from [89]

100.0000

Flashovers/100 km/yr

10.0000 1.0000 0.1000 Phase to ground (ρ = 1,000 Ω m, Rg = 100 Ω) Phase to grounded wire (ρ = 1,000 Ω m, Rg = 100 Ω) Phase to ground (ρ = 100 Ωm, Rg = 10 Ω) Phase to grounded wire (ρ = 100 Ω m, Rg = 10 Ω) Phase to ground (ideal ground) Phase to grounded wire (ideal ground)

0.0100 0.0010 0.0001

50

100

150

200

CFO (kV)

Figure 4.46 Phase-to-ground and phase-to-grounded-wire flashover rates of the single conductor 10-m high line with the shield wire at the height of 8.37 m for grounding spacing of 200 m and different soil resistivities and ground resistances. Adapted from [89]

Lightning interaction with MV overhead power distribution systems

157

4.4.2.3 Lines with surge arresters The influence of the presence of surge arresters on the line lightning performance, considering different arrester spacings, is illustrated in Figure 4.47 both for the case of ideal and lossy ground. The surge arresters were simulated using their V–I nonlinear characteristics [90]. 100.000 Without surge arresters

Flashovers/100 km/yr

Surge arresters located every 500 m 10.000

Surge arresters located every 200 m

1.000

0.100

0.010 50

100

(a)

150 CFO (kV)

200

1,000.000 Without surge arresters Surge arresters located every 500 m Flashovers/100 km/yr

100.000

Surge arresters located every 200 m

10.000

1.000

0.100

0.010 50 (b)

100

150

200

CFO (kV)

Figure 4.47 Flashover rates of the single conductor 10-m high line considering the absence of surge arresters and surge arresters located every 200 and 500 m for Rg ¼ 0 W and different soil resistivities. Adapted from [89]. (a) Perfectly conducting ground. (b) Lossy ground (r ¼ 1,000 Wm)

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Lightning interaction with power systems, volume 2

The results show that a significant improvement of the line lightning performance can be obtained by reducing the spacing between the surge arresters below 300 m, which is in accordance with the results published in [90]. Interestingly, for low CFO values, the lightning performance of the line may be even worsened by the presence of surge arresters. This is due to the surge reflections occurring in correspondence of surge arrester operations, particularly important for stroke locations distant from the line and for large intervals between consecutive arrester stations [91,92].

4.4.3

Lines surrounded by buildings

In order to evaluate the lightning performance of a line located in an urban area, the effects due to the presence of nearby buildings should be taken into account. In the calculations presented in this subsection, the reduction of the number of flashes collected by the line is taken into account by applying the electrogeometric model to distinguish direct strikes to the line, strikes to the buildings or to ground. The attenuation of the LEMP is taken into account by using the weighting functions mentioned in Section 4.2.2.9. The lightning performance of the line discussed in Section 4.2.2.9 is evaluated by applying the Monte Carlo procedure presented in Chapter 1 of this volume and in [89] by assuming the annual ground flash density Ng ¼ 1 flash/km2/year. Figures 4.48 and 4.49 show the lightning performances Fp(V) of the line with buildings at one or both sides, respectively. The distances between the line and the buildings are those illustrated in Figure 4.19. Both figures show the results calculated:

Number of events having amplitude larger than the abscissa/yr

100

Ideal ground ρ = 100 Ωm Without buildings

Shielding only Shielding and LEMP attenuation

10–1

100

150

200

250

300

350

Voltage (kV)

Figure 4.48 Lightning performance of the line with buildings at one side and without buildings. Adapted from [60]

Lightning interaction with MV overhead power distribution systems

Number of events having amplitude larger than the abscissa/yr

100 Without buildings

159

Ideal ground ρ = 100 Ωm

Shielding only

10–1

Shielding and LEMP attenuation

10–2 100

150

200

250

300

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Voltage (kV)

Figure 4.49 Lightning performance of the line with buildings at both sides and without buildings. Adapted from [60] (a) without the presence of the buildings; (b) by taking into account the presence of the buildings concerning only the distinction between direct strikes to the line and indirect events, that is, only the shielding effect of the buildings is considered*; (c) by taking into account both the shielding effect and the attenuation of the LEMP provided by the buildings. As shown in the figures, all the calculations are carried out for the cases of both ideal and lossy ground with resistivity r ¼ 100 Wm. Without buildings, the expected annual number of overvoltages with peak amplitude larger than 150 kV (a typical insulation level of MV lines [94]) is 0.26 for ideal ground and 0.34 for lossy ground, with an increment of 31%. For the case of a line with buildings at one side only (Figure 4.48), if only the shielding effect is taken into account the numbers of overvoltages larger than 150 kV are 0.22 (ideal ground) and 0.30 (lossy ground), with an increment of 36%, while when LEMP attenuation is also taken into account the number is 0.21 for both ideal ground and lossy ground. For the case of a line with buildings at both sides (Figure 4.49), if only the shielding effect is taken into account the numbers of overvoltages are 0.21 (ideal ground) and 0.27 (lossy ground), with an increment of 29%. On the other hand, when the LEMP attenuation is also taken into account the number is 0.08 for both ideal ground and lossy ground. * When only the shielding effect of the buildings is considered, the induced voltages due to all the indirect events are calculated by using the LIOV code with the LEMP components provided by the Master and Uman equations [61] without weighting functions, as done in [93].

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Figures 4.48 and 4.49 show that when the LEMP attenuation due to the presence of the buildings is considered, the influence of the finite soil conductivity becomes almost negligible, especially for the case of a line with buildings at both sides. According to these results, the LEMP attenuation provided by the buildings significantly improves the lightning performance: for a line with a 150 kV withstand voltage and buildings on both sides, the annual number of overvoltages is reduced by around 70% and 76% for the cases of ideal and lossy ground, respectively. It is important, therefore, to consider the LEMP reduction effect in addition to the shielding effect already included in the procedures recommended by the Standards.

4.4.4

Hybrid configuration (MV and HV lines mounted on the same poles)

As known, in some areas characterized by low availability either of land or ways of right for building overhead lines, it is convenient to install a medium voltage distribution line on the same pylons or poles holding a HV TL. The resulting multivoltage overhead line configuration poses peculiar issues with respect to both the electromagnetic coupling between the conductors of the MV and HV lines, as analysed in [95], and the voltages across the insulators due to direct strikes [96]. The presence of the HV conductors reduces the induced overvoltages in the MV line due to indirect lightning events. However, due to the presence of the HV conductors, the number of direct events hitting the overhead ground wire (OHGW) of the hybrid line is significantly higher than the one expected to strike a MV line in open terrain. This justifies a specific section for this double circuit configuration. The two configurations considered in this subsection are depicted in Figure 4.50(a) (69 kV line) and Figure 4.50(b) (138 kV line). In both cases, the MV line (15 kV insulation class) has a compact structure, that is, insulated phase wires (without shield) with reduced distances secured by periodical spacers suspended by an upper unenergised wire called messenger. The MV line is located below the HV conductors, 7 m above ground in the case of the 69 kV line and 9 m in the 138 kV line. On the top of both structures, there is an OGHW grounded at every pole. Moreover, the 138-kV line has an underbuilt ground wire (UGW) located 2 m below the lowest phase conductor, grounded at each pole, that reduces the back flashover rate, as described in [97]. Between two consecutive poles of the HV line, in the middle of each span, there is a shorter MV pole, having the function of sustaining the compact MV line. The span distances between the 69 kV line poles and the 138 kV line poles are 70 and 80 m, respectively. The value adopted for the ground resistivity is equal to 1,000 Wm in all the simulations presented in this subsection. The value of the pole surge impedance has been assumed equal to Zp ¼ 200 W according to the experimental data presented in [98]. As shown in Figure 4.50(a), the pole of the 69 kV configuration has been split in two equal parts, one between the OHGW connection and the messenger connection (point M) and the other between point M and ground. The 138 kV pole has been split in three portions: 5 m

Lightning interaction with MV overhead power distribution systems 0.15 m

2 m 2.275 m

Ph1

Zp

Ph2

Ph2

Ph3

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Zp

OHGW

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Ph3

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Rp2

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1859

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M

24 m

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M R

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M

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Street

Ø 0.707 m

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(a)

Lp2

7m

Communication

5.87 m

Low voltage

Lp

4.97 m

Rp

0.5 m

15.225 m

L

Zp

(b)

Figure 4.50 Geometry and EMTP model of the considered concrete poles of the double-circuit line. Adapted from [97]. (a) 69-kV TL. (b) 138-kV TL between OHGW and UGW, 5 m between UGW and point M, and 10 m between point M and ground (Figure 4.50(b)). The values of the dumping resistance and inductance of the model shown in Figure 4.50 have been estimated according to [99]. Their values are Rp ¼ 33 W and Lp ¼ 5.33 mH for the 69 kV line and Rp2 ¼ 16.6 W and Lp2 ¼ 2.66 mH for the 138 kV line. The effect of soil ionization is represented by using Weck’s formula [100], according to [97]. Figures 4.51–4.54 show the lightning performance of the MV line in case the HV conductors are present or not, for the four different configurations: 69 kV and Rg ¼ 20 W (Figure 4.51), 138 kV and Rg ¼ 20 W (Figure 4.52), 69 kV and Rg ¼ 40 W (Figure 4.53), and 138 kV and Rg ¼ 40 W (Figure 4.54). Both direct and indirect events are considered. As anticipated, the overall lightning performance of the MV line of the multicircuit configuration is improved with respect to the case of a MV line alone. The main reasons for the better performance are: ●



although the number of direct strikes increases in the double-circuit configurations with respect to the MV line alone, the groundings of the OHGW and the UGW, when present, are effective in limiting the voltage stress of the MV line; the voltage induced in the OHGW is larger than in the messenger, causing a significant ground potential rise that reduces the voltage across spacers and insulators.

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Number of events having amplitude larger than the abscissa/yr/100 km

102

MV line alone

101

100 Double circuit 10–1

10–2 50

100

150

200

250

300

350

400

450

500

550

600

Voltage (kV)

Figure 4.51 Lightning performance of the 69 kV configuration considering both direct and indirect events. Rg ¼ 20 W. Adapted from [101]

Number of events having amplitude larger than the abscissa/yr/100 km

102

MV line alone

101

100 Double circuit 10–1

10–2 50

100

150

200

250

300 350 400 Voltage (kV)

450 500

550 600

Figure 4.52 Lightning performance of the 138 kV configuration considering both direct and indirect events. Rg ¼ 20 W. Adapted from [101]

Lightning interaction with MV overhead power distribution systems

163

Number of events having amplitude larger than the abscissa/yr/100 km

102

MV line alone

101

100

Double circuit

10–1

10–2 50

100

150

200

250

300

350

400

450 500

550

600

Voltage (kV)

Figure 4.53 Lightning performance of the 69 kV configuration considering both direct and indirect events. Rg ¼ 40 W. Adapted from [101]

Number of events having amplitude larger than the abscissa/yr/100 km

102

MV line alone

101

100 Double circuit

10–1

10–2 50

100

150

200

250

300

350

400

450

500

550 600

Voltage (kV)

Figure 4.54 Lightning performance of the 138 kV configuration considering both direct and indirect events. Rg ¼ 40 W. Adapted from [101]

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4.5 Concluding remarks In this chapter, the effects of lightning strokes on overhead power distribution systems were examined. Starting from the estimation of the number of lightning flashes collected by a line, the chapter presented a discussion of the effects of several parameters on lightning overvoltages, as well as an evaluation of the main protection methods considering different line configurations. The last part of the chapter focused on the lightning performance of power distribution lines with and without the presence of shield wires and surge arresters, taking into account the soil resistivity, the grounding spacing and the value of the ground resistance. The effect of the presence of buildings around the right of way on the line lightning performance was also evaluated. All the statistical results are supported by the analysis carried out in the first parts of the chapter. The statistical analysis showed that the factor that contributes most to the worsening of the lightning performance is the soil resistivity: the larger the resistivity, the poorer the lightning performance. On the other hand, the presence of buildings around the line causes an improvement in its lightning performance by providing a shielding that leads to a decrease of the number of direct strokes that hit the line conductors and by modifying the electromagnetic environment around the line. Such a modification of the electromagnetic field may contribute significantly to reduce the magnitudes of lightning-induced overvoltages. Concerning shield wires, the shorter the grounding spacing, the larger the effectiveness in attenuating lightning-induced voltages. Similarly, the shorter the arrester spacing, the better the line lightning performance. For distribution systems located in urban or suburban areas, indirect lightning is usually the main problem of interest due to the presence of tall objects around the lines, which are capable of attracting lightning strokes in lieu of their conductors. However, for hybrid configurations, in which both a MV and a HV line are mounted together on the same poles, direct lightning flashes becomes more likely to occur, and should always be considered. The performances of lines with hybrid configurations were analysed considering different conditions and the results showed that the performance of a MV line that shares the structures with a HV line tends to be better than that of a MV line alone.

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[84] Rachidi F., Nucci C.A., Ianoz M. and Mazzetti C. ‘Response of multiconductor power lines to nearby lightning return stroke electromagnetic fields’. IEEE Transactions on Power Delivery, 1997;12(3):1404–11. [85] Piantini A. and Janiszewski J.M. ‘Lightning induced voltages on distribution lines close to buildings’. Proceedings of the 25th International Conference on Lightning Protection (ICLP), Rhodes, Greece, Sep. 2000, pp. 558–63. [86] Cooray V., Kumar U., Rachidi F. and Nucci C.A. ‘On the possible variation of the lightning striking distance as assumed in the IEC lightning protection standard as a function of structure height’. Electric Power Systems Research, 2014;113:79–87. [87] Guerrieri S., Nucci C.A., Rachidi F. and Rubinstein M. ‘On the influence of elevated strike objects on directly measured and indirectly estimated lightning currents’. IEEE Transactions on Power Delivery, 1998;13(4):1543–55. [88] Krider E.P., Guerrieri S., Napolitano F., et al. ‘Effect of traveling-waves of current on the electromagnetic response of a tall Franklin rod considering various lightning return stroke models’. Proceedings of the 28th International Conference on Lightning Protection (ICLP), Kanazawa, Japan, Sep. 2006, vol. 1, pp. 273–8. [89] Borghetti A., Nucci C.A. and Paolone M. ‘An improved procedure for the assessment of overhead line indirect lightning performance and its comparison with the IEEE Std. 1410 method’. IEEE Transactions on Power Delivery, 2007;22(1):684–92. [90] Borghetti A., Nucci C.A., Paolone M., Bernardi M., Malgarotti S. and Mastandrea I. ‘Influence of surge arresters on the statistical evaluation of lightning performance of distribution lines’. Proceedings of the International Conference on Probabilistic Methods Applied to Power Systems, Sep. 2004. [91] IEEE Fast Front Transients Task Force, ‘Modeling guidelines for fast front transients’. IEEE Transactions on Power Delivery, 1996;11(1):493–506. [92] Paolone M., Schoene J., Uman M., et al. ‘Testing of the LIOV-EMTP96 code for computing lightning-induced currents on real distribution lines: triggeredlightning experiments’. Proceedings of the 27th International Conference on Lightning Protection (ICLP), Avignon, France, Sep. 2004. [93] Napolitano F., Fossani F., Borghetti A., et al. ‘Lightning performance of a real distribution network with focus on transformer protection’. Electric Power Systems Research, 2016;139:60–7. [94] IEEE Std. C62.82.1–2010: ‘IEEE standard for insulation coordination’. New York, 2011. (Revision IEEE Std 1313.1–1996). [95] Moraes L.B., Lopes G., Violin A., et al. ‘Assessment of the electromagnetic coupling between lines of different voltages sharing the same structures’. CIRED - Open Access Proc. J.,vol. 2017, no. 1, pp. 531–534, Sep. 2017. [96] Rugthaicharoencheep N., Thansiphraserth W. and Phayomhom A. ‘Comparison voltage across insulator strings of 69 kV and 24 kV lines due to lightning strokes to top pole and mid span’. Proceedings of the 47th International Universities Power Engineering Conference (UPEC), vol. 7, pp. 1382–1387, 2012.

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Lightning interaction with power systems, volume 2 Borghetti A., Ferraz G.M., Napolitano F., Nucci C.A., Piantini A. and Tossani F. ‘Lightning protection of a compact MV power line sharing the same poles of a HV line’. Proceedings of the 34th International Conference on Lightning Protection (ICLP), Rzeszow, Poland, Sep. 2018. Nakada K., Sugimoto H. and Yokoyama S. ‘Experimental facility for investigation of lightning performance of distribution lines’. IEEE Transactions on Power Delivery, 2003;18(1):253–7. Ametani A. and Kawamura T. ‘A method of a lightning surge analysis recommended in Japan using EMTP’. IEEE Transactions on Power Delivery, 2005;20(2):867–75. Cigre´ Working Group 33.01, ‘Guide to procedures for estimating the lightning performance of transmission lines (TB 63)’. CIGRE, Paris, France, 1991. Borghetti A., Ferraz G.M., Napolitano F., Nucci C.A., Piantini A. and Tossani F. ‘Lightning protection of a multi-circuit HV-MV overhead line’. Electric Power Systems Research, 2020;180:1–9 (https://doi.org/10.1016/ jepsn.2019.106119)

Chapter 5

Lightning interaction with low-voltage overhead power distribution networks Alexandre Piantini1

The growing use of sensitive electronic devices and components, as well as the increasing demand of utility customers for stability of the power supply, has highlighted the importance of improving the reliability and power quality levels of electric systems. As lightning is a major source of faults on overhead lines and damages to or malfunction of sensitive electronic equipment, it is essential to evaluate the lightning electromagnetic environment in order to mitigate its effects and improve the power system quality. The surge-withstand capabilities of low-voltage (LV) networks are much lower than those of medium-voltage (MV) lines, and therefore they are more susceptible to lightning-caused disturbances. There are various ways by which lightning can disturb LV lines. Transients may be originated from direct strokes (to the MV or LV networks or to LV power installations) or indirect ones (intracloud or cloud-toground (CG) flashes). The magnitudes and waveforms of these transients depend on many lightning parameters and are substantially affected by the LV network configuration, which is usually complex and vary widely. The evaluation of the overvoltages associated with indirect strokes entails the calculation of lightning fields, which are defined by the spatial and temporal distribution of the stroke current along the channel, as well as by the soil characteristics. Once the electromagnetic fields are evaluated, a suitable coupling model is required for the analysis of their interaction with the line conductors. Additionally, the frequency responses of distribution transformers and consumers’ installations have also great influence on the surges. This scenario demonstrates that the evaluation of lightning transients on LV networks is a complex matter. Although an in-depth and comprehensive discussion of the problem has been made in [1,2], the analysis of the surges caused by nearby strokes considered mainly the case of low-resistivity soils, a condition that is not satisfied in many practical situations. In this chapter, the simulations are performed using the

1

Institute of Energy and Environment, Lightning and High Voltage Research Center, University of Sa˜o Paulo, Sa˜o Paulo, Brazil

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Extended Rusck Model (ERM) [3], which enables the calculation of lightninginduced voltages taking into account the soil electrical parameters. This chapter describes, initially, some typical LV network configurations and grounding practices. Then, using the models described in Chapter 10 of Volume 1 to represent the most important system components, the major mechanisms by which lightning overvoltages can be produced are explained. As underground networks are much less prone to lightning disturbances than overhead ones, focus is given to the latter. The general characteristics of the overvoltages are evaluated and their dependence upon the network configuration and some of the most important ground and stroke parameters is assessed, with emphasis given to the voltages induced by indirect strokes and to those transferred from the MV system, which are the most important ones on account of their magnitudes and frequencies of occurrence. The effectiveness of the installation of secondary arresters along the network is examined in the last part of the chapter, which is devoted to the lightning protection of secondary networks, including the LV side of transformers and the entrance of LV power installations.

5.1 Typical configurations of LV networks The low-voltage (LV) network comprehends that part of the electric distribution system in which the voltage levels are up to 1,000 V. That includes the LV side of distribution transformers, the secondary circuit and the consumers’ installations. There are various possible configurations for the LV grids [1]. The most common layouts are the radial, mesh, open-ring and link. The former has just one infeed point, whereas in a meshed network there are at least two possible electrical paths through which consumers can be supplied. The open-ring arrangement provides at least two alternative paths to each consumer. In normal operation, each section of the ring can be treated as a radial feeder. In the event of a fault, after its isolation a normally open switch is closed and supply can be restored to the other parts of the ring. In the link arrangement, two secondary substations are interconnected. However, due to a normally open switch the system operates as two radial feeders. The optimum design is strongly associated with the load density, since each arrangement has its own advantages and disadvantages in terms of cost, simplicity, reliability, flexibility, voltage drop, short-circuit power and degree of protection sophistication. Link, open ring and meshed networks are employed in densely populated urban areas, where the consumers are normally fed through underground cables. By their turn, radial overhead networks are used in both rural and urban regions. There is a large diversity of combinations concerning the grid structure, operating criteria and load types. Distribution transformer rating and connections, voltage level, number and type of conductors, total line length, as well as grounding practices may vary from country to country and are much dependent on the characteristics of the particular district concerned [4,5].

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Three-phase systems may have either three or four conductors, depending on whether the neutral is present or not, whereas single-phase systems are in general composed of three conductors, two phases plus neutral. Both bare and separately covered conductors are commonly used at LV. Also usual is the bunched cable, in which the phase conductors are isolated and twisted around the bare neutral, that also has the mechanical function of supporting the line. In urban areas, the LV network is commonly installed below the MV line. A typical vertical clearance between the lines is 3 m. The minimum height of the conductors above ground level is usually between about 4 and 6 m, depending on the locality. Aluminium conductors with cross sections in the range of 35 to 70 mm2 are normally used. The total length of a LV network may vary from 100 to about 2,000 m. In rural areas, a typical length is 1,000 m, while 300 m is more representative of urban networks [5]. Average distances between loads are typically 300 and 50 m on rural and urban networks, respectively. Distances between neutral grounding points are usually in the range of 150 to 300 m; a common spacing is 200 m [6]. The maximum length of the service drop from the pole to the customer’s premises depends on the load, but it usually does not exceed 30 m [1]. Different types of system grounding arrangements are used in LV distribution networks. The IEC Publication 60364 series classifies these practices according to the relationships of the power system conductors and of the exposed conductive parts of components and equipment in the electrical installation with respect to the grounding system [7]. The IEC nomenclature adopts basically two letters to designate the systems. The first, which may be either ‘I’ or ‘T’, is related to the system grounding; ‘I’ means that all live parts of the system are isolated from ground or that points of the network are connected to ground through impedances. On the other hand, ‘T’ signifies a direct connection of at least one point in the network to ground. The second letter refers to the equipment grounding, and may be ‘T’ or ‘N’. ‘T’ signifies that accessible conductive parts of the equipment in the installation are directly connected to ground, independent of the grounding of any point of the power system, whereas ‘N’ means a direct connection of accessible conductive parts of the equipment to the grounding points of the power system. These connections may be made by means of a protected earth neutral (PEN) or protected earth (PE) conductor. There are basically three types of system grounding, namely IT, TT and TN, although the latter can be further subdivided into TN-C, TN-S and TN-C-S depending on the way the neutral and protective functions are provided. In the TN-C system, a single conductor (PEN) performs both functions, whereas in the TN-S system separate conductors (neutral and PE) are used. The TN-C-S system is a combination of the TN-C and TN-S systems, as the neutral and protective functions are combined in one conductor from the distribution transformer to the service entrance equipment and provided by separate conductors beyond this point. The TN-C-S system is the most commonly used in public LV networks [4,8].

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5.2 Lightning surges on LV power systems Lightning transients on LV networks can be produced by several mechanisms, which can be classified into the following categories [1]: ● ●

● ●

intracloud (IC) or cloud-to-cloud (CC) lightning; direct strikes to the LV system (either to the line conductors or end-user installations); indirect strikes (CG lightning); and transference from the MV system.

In this section, the characteristics of the surges associated with each of these types are evaluated. Emphasis is given on the overvoltages caused by indirect strikes and on those transferred from the MV system, which are the most important ones on account of their magnitudes and frequencies of occurrence.

5.2.1

Cloud discharges

Cloud discharges, which include IC, CC and cloud-to-air flashes, last typically between 200 and 500 ms [9] and are the most frequent type of discharges, representing about 75% of the global lightning activity [10,11]. Nevertheless, the number of studies conducted about this phenomenon is relatively scarce in comparison with that bearing on CG flashes, which have a much greater impact in terms of deleterious effects. The main practical interest in cloud flashes lies in the protection of aircraft and space craft, although the short interval between the associated induced voltage pulses may cause degradation, damage and failure of electronic components of sensitive apparatus connected to the LV power supply [1]. Some studies related to measurements of voltages induced on LV power installations by IC and/or CG discharges are reported in [12–18]. The investigation carried out by Galva´n et al. [12] refers to two small networks isolated from the power supply. Simultaneous measurements of the incident vertical lightning electromagnetic fields and the corresponding induced voltages across a 50-W resistor connected between one of the phase conductors and ground were performed. The technique proposed by the authors uses these measurements to extract the transient response of the power installation, irrespective of its complexity. The peak-to-peak values of the four voltages induced by cloud flashes shown in the paper are below 2 V, and in all cases a relatively good agreement was found between measured and calculated results. The experimental study conducted by Silfverskio¨ld et al. [13] compares the amplitudes of the common-mode voltages induced on a residential installation in the complete duration of typical CG (negative and positive) and IC flashes. The installation was disconnected from the power distribution line. The measurements of the vertical component of the electric field and the corresponding induced voltages on the power installation showed that the discharge events that take place inside the cloud, preceding CG and IC flashes, give rise to bipolar pulses with very fast rise time. According to the authors, the pulse trains associated with such processes may induce voltages with

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magnitudes of the same order of (and even higher than) those induced by the return stroke itself. These events are therefore important and should be taken into account in the evaluation of the interference problems caused by lightning electromagnetic pulses. From the analysis of the obtained results, the authors estimate a few tens of induced voltage pulses exceeding 400 V peak-to-peak from a typical lightning within a distance of a few kilometres from the LV power installation network. A further investigation of the transient response of LV power installations to lightning electric fields was performed by Galva´n and Cooray in [14], where comparisons between measured and calculated induced voltages using the measured lightning electric field (both inside and outside the installation) as the driving source are also presented. The amplitudes and waveforms of the induced voltages were found to be highly dependent on the soil resistivity and on the loads connected to the LV power installation. In [15], Galva´n et al. apply the technique proposed in [12] to a simple circuit and to a complex wiring system. Comparisons between measured and simulated induced voltages, presented for both systems, are in good agreement. Discussions are provided on the advantages and limitations of the method, which represents a useful tool for evaluating induced voltages in electrical installations with linear behaviour. Voltages induced by cloud discharges at both open-circuited terminations of an unenergised 460-m long distribution line, as well as the corresponding electric fields, are reported by Rubinstein and Uman [16]. The line consisted of two conductors arranged in a vertical configuration, and the peak-to-peak voltages induced at the top conductor by a flash at an altitude greater than about 5 km were around 140 V. Time, frequency and energy correlations of voltages induced by CC discharges on an isolated dwelling unit in Sri Lanka were studied by Sapumanage et al. [17]. The internal wiring was configured to the TT topology and energized by the 230 V, 50 Hz and single-phase utility supply. Surge protective devices (SPDs) were not connected to the LV power installation and all electrically driven equipment and appliances were isolated throughout the data acquisition period. A total of 191 induced voltages due to CC flashes with peak-to-peak voltage of 150 V or more were identified and grouped into three basic types: unipolar (20), bipolar (11) and pulse burst (160). These three types had already been identified by Nanayakkara et al. [18] in a previous study in the same installation. The peak-to-peak voltage of one of the pulse burst voltages shown in [17] is about 950 V, while the highest recorded induced surge reported by Nanayakkara et al. [18] was 1,294 V, corresponding to a bipolar-type voltage. Even though further investigations are necessary to better characterise the voltages induced by cloud discharges as well as the significance of their effects on sensitive loads, protection measures against the more severe types of lightning surges are likely to be effective against such transients.

5.2.2 Direct strikes If a flash hits a LV line, multiple flashovers occur and a rough estimation of the overvoltage can be obtained – if the propagation effects are disregarded – by

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multiplying the stroke current by the equivalent ground impedance. However, even in the case of a low value for the effective impedance, voltages much larger than the line lightning impulse withstand level would result, which would lead to further flashovers. In general, LV networks are not that prone to direct strikes due to their relatively short lengths and the shielding provided by the MV line, trees and nearby structures. However, in some rural and semi-urban areas, exposed LV lines longer than 1,000 m do exist, and in case of direct lightning hits, the resulting overvoltages can damage unprotected connected equipment. A direct strike to the lightning protection system or other parts of an end-user building causes a ground potential rise that may lead to the operation of SPDs or flashovers between the structure and the line conductors. In both situations, a portion of the stroke current is injected into the power line, producing overvoltages that propagate along the network. This portion depends mainly on the relative impedance of the line with respect to the impedances of all the other possible current paths (local ground, metallic pipes and other services such as telecommunications lines). The division of the lightning current between the grounding system of a test house and the neutral of the power supply was investigated at the International Center for Lightning Research and Testing at Camp Blanding, Florida, by means of the rocket-triggered lightning technique [19,20]. Small rockets trailing thin wires were used to trigger lightning and inject its current into the lightning protection system of the test house, whose electrical circuit was connected to the secondary of a pad-mounted distribution transformer [21,22]. The distance between the house and the transformer was about 50 m, and the primary was connected to a 650-m long unenergised underground power cable. Test configurations varied with respect to the lightning current injection point, number of down conductors, grounding system of the test house and use of SPDs. The current waveforms observed in the ground rods differed substantially from those recorded in other parts of the system. The ratio between the peak values of the currents entering the power supply neutral to the injected lightning current varied from about 22% to over 80%, depending on the test configuration. In the event of a direct strike to the MV line, part of the stroke current is injected into the neutral conductor, causing overvoltages on the LV network. This mechanism will be discussed in Section 5.2.4.1.

5.2.3

Indirect strikes

When lightning strikes the ground or an object in the vicinity of a distribution network, the voltages that arise on the LV conductors may be subdivided as follows [1]: ●





voltages induced ‘directly’, due to the electromagnetic coupling between the line and the stroke channel; voltages associated with the part of the stroke current that is intercepted by the grounding points of the neutral conductor; voltages transferred from the MV line, which will be dealt with in Section 5.2.4.2.

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From experiments performed at Camp Blanding using the rocket-and-wire technique to trigger lightning, Rakov and Uman [19] and Fernandez et al. [23] showed that when the strike point is at tens of meters from the line, an appreciable fraction of the total current enters the system from the neutral groundings. In three cases reported in [19], in which the distances between the line and the strike point were 60, 40 and 19 m, the observed peak values of the currents entering the system from its ground connections were, respectively, 10%, 5% and 18% of the stroke current peak. The voltages ‘directly’ induced are in general the most important on account of their severity and frequency of occurrence. Rocket-triggered lightning experiments with simultaneous measurements of induced voltages on a 210-m long overhead LV line with twisted conductors are reported by Clement and Michaud [6]. The line was connected to a transformer at one of the ends, and to a 60-m long underground cable, terminated by LV arresters, at the other. The stroke location was either on a tower close to the underground cable termination or on the firing area, 50-m away from this point. The induced voltages were measured at the LV transformer terminals for a total of 12 launchings. The stroke currents varied in amplitude from 4 to 50 kA, and the corresponding phase-to-ground and neutral-to-ground voltages reached maximum values in the range of 2 to 12 kV. The analysis carried out by Hoidalen in [24] made use of the Agrawal et al. coupling model [25] for the calculation of lightning induced voltages on LV systems. From frequency-response measurements, simple models were proposed for the input impedances of typical distribution transformers and LV power installations, and their influences upon the lightning-induced voltages on simple TN and IT systems were investigated. The line considered in the simulations was 500-m long and the phase conductors were simulated by a single wire with characteristic impedance of 300 W. In one end, there was a transformer, modelled as an inductance of 10 mH, whereas an impedance representing the power installation was connected at the other termination. The voltage magnitudes were found to have a high dependence on the load, the lowest values being associated with larger installations. A comprehensive investigation was conducted by Hoidalen in [26], where the effect of the finite ground conductivity on the induced voltages on TN and IT systems is thoroughly discussed. In [27] and [28], the authors concluded that the induced voltages are characterised by a high-frequency damped oscillation with a period equal to twice the travel time of a span (portion of the line between two adjacent neutral groundings). The simulations were performed with the LIOV-EMTP code [29–31], which is based upon the Agrawal et al. coupling model, and considered overhead cables with two or four twisted conductors, with neutral grounding spacing in the range of 250 to 400 m. Due to the high transient electromagnetic coupling between the conductors, for the configuration examined the wire-to-wire voltages were disregarded and line-to-ground voltages, assumed to be the same on the different conductors, were presented.

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The influences of various parameters on the lightning-induced voltages were evaluated by Piantini and Janiszewski [32] for the case of a 300-m long, singlephase line. In [33], a line with twisted conductors was considered. In both cases, the distribution transformer and the LV power installations were represented according to models described in Chapter 10 of Volume 1. The main difference between the bunched cable and the open wire configuration is that the former is characterised by a stronger coupling between the wires, which are much closer. The greater the mutual surge impedance between the neutral and phase conductors, the smaller the induced voltage magnitudes. If the conductors are twisted, this impedance varies along the line. However, as the distance between the wires is much smaller than their heights above ground, the variation is small and for practical cases it can be neglected. The simulations, performed using the ‘Extended Rusck Model’ (ERM) [3,34–36] for the case of a perfectly conducting ground, showed that induced voltages have a great impact on the lightning performance of LV distribution lines. Measurements performed by Hoidalen [37] in Norway, where the ground flash density is mostly below 1/(km2year), show that more than 1,000 voltages above 500 V should be expected per year in a typical rural LV overhead line with isolated neutral. Voltages up to 5 kV were recorded, and according to the study, overvoltages can be induced by strokes more than 20-km away from the line. The voltages induced on and transferred to the LV network in the case of nearby lightning strokes were calculated by Piantini [38] using the ERM. In order to evaluate their relative contributions, these two kinds of voltages were calculated separately. The simulations considered a typical distribution transformer and a common LV power installation. It was shown that parameters such as the stroke current front time, the ground resistance, and the distance between the line and the lightning strike point have a pronounced influence on the lightning-induced voltages. In comparison with the induced voltages, those transferred through the distribution transformer tend to reach lower magnitudes. Due to their high frequency of occurrence and to their magnitudes – the phase-to-ground voltages commonly reach peak values of the order of some tens of kV – the overvoltages associated with indirect strokes should be taken into account when analysing possible measures that could be taken to mitigate lightning-caused problems either on distribution transformers or LV networks. In view of the fact that an important part of problems related to distribution transformer failures and damages to customers’ sensitive electronic equipment may be associated with the so-called low-side surge phenomena, Piantini and Janiszewski analysed the characteristics of lightning-induced overvoltages on secondary networks [39]. The calculations were performed using the ERM [3,34–36] and different topologies were considered for the LV network. The high-frequency behaviours of transformer and loads were taken into account and the influences of parameters such as the stroke current front time and the ground resistance were investigated, as well as the effect of the presence of SPDs at different points of the LV line. The simulations were performed for the case of perfectly conducting ground. An attempt to evaluate lightning overvoltages on loads installed in urban distribution networks considering the simultaneous effect of lightning-induced

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voltages and surges transferred from MV to LV lines through distribution transformers was made by De Conti et al. in [40]. It was shown that, for stroke locations relatively close to a given LV line, the presence of nearby LV lines can be neglected without affecting the peak values of estimated load overvoltages significantly. On the other hand, for stroke locations relatively far from the LV line under consideration, the inclusion of nearby LV lines may be of some importance for the characterization of load overvoltages, especially if those lines are illuminated by the incident electromagnetic field before the line under analysis. An experimental study involving measurements of voltages induced by CG flashes at the electrical power entrance of an isolated rural residential LV power installation was performed by Nanayakkara et al. [41]. The house did not have any electrical loads or surge protection devices connected. The voltages were measured simultaneously with the vertical component of the electric field at the site. During the observation period of April–May 2014, 144 CG flashes that resulted in 319 induced pulses which peak-to-peak voltage higher than 150 V were observed. The majority of the induced voltages were unipolar and with peak values varying in the range of 164.6–2,763 V. A study about the behaviour of SPDs against transient voltages generated by CG flashes was conducted by Sapumanage et al. [42,43]. The analysis revealed that lightning-generated transient voltages may impart detrimental effects on SPDs. It was also observed that the inter-pulse durations of the current impulses are much smaller than the inter-pulse durations of the impulses generated in laboratory to test SPDs according to IEC standards. The analysis of the characteristics of such surges is of great importance, since they have a high frequency of occurrence and can often reach large magnitudes. The severity of the induced voltages depends on many lightning parameters, on the soil characteristics and is substantially affected by the network configuration. The understanding of the way the various parameters involved in the induction mechanism affect their amplitudes and waveforms is, therefore, of great importance. A comprehensive analysis of the lightning-induced voltages on overhead LV power distribution lines can be found in [1], which includes the influences of the most important parameters on the induced surges for the case of perfectly conducting ground. As the results apply mainly to lines over low-resistivity soils, in this subsection the evaluation of the induced voltages considers the case of lossy ground. The calculations are performed using the ERM [3]. As mentioned in [1], Cooray [44] and Michishita and Ishii [45] demonstrated that, for the case of an electromagnetic field irradiated by a lightning channel perpendicular to the ground plane, the Rusck’s model [46] leads to results identical to those obtained from the more general coupling model proposed by Agrawal et al. [25]. However, in its original formulation, the line and the stroke channel are assumed to be infinitely long and realistic line configurations cannot be considered. Due to these restrictions, the model was modified and extended [3,34–36,47,48] so as to allow the analysis of practical situations. The so-called ERM enables also to consider the incidence of lightning flashes to nearby elevated objects and the occurrence of upward leaders, as well as the case of a line with various sections of

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different directions. The presences of transformers, a multi-grounded neutral or shield wire and non-linear equipment such as surge arresters and SPDs can also be taken into account. The validity of the ERM has been demonstrated through hundreds of comparisons between measured and calculated lightning-induced voltages in several situations and involving full-scale and scale-model experiments in Japan [49,50] and in Brazil [47,48,51]. It represents an extension to the Rusck model in the sense that, unlike the original model, its features allow for taking into account situations of practical interest, including the case of finite ground conductivity [3]. For illustration, Figure 5.1 shows a comparison involving measured and calculated lightning-induced voltages. The experiment was performed under controlled conditions, on a 1:50 scale model. The line had two copper conductors – phase and shield wire – placed at heights corresponding to 10 and 11 m, respectively, and supported by PVC (polyvinyl chloride) poles spaced every 60 cm (corresponding to 30 m in the full-scale system). It was 28-m long (corresponding to a length of 1.4 km), matched at both ends, and 1.4 m (equivalent to 70 m) from the model of the stroke channel, which was equidistant from the line terminations. The voltages were obtained at the closest point to the lightning channel model and the values of the other parameters, referred to the real system, were: stroke current magnitude, front time and propagation velocity of 36 kA, 3.1 ms and 11% that of light in free space, respectively, distance of 300 m between adjacent

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Figure 5.1 Measured and calculated (using the ERM) phase-to-ground induced voltages at the point of the line closest to the model of the stroke channel (adapted from [3]). Perfectly conducting ground. (a) Induced voltages. (b) Current

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grounding points, ground resistance of 50 W. The channel model was placed in front of a grounding point. Further details of the scaled system can be found in [1,47,48,51,52]. Figure 5.2 presents comparisons of measured and calculated induced voltages relevant to the same scale model, but obtained on a three-phase line with surge arresters on all phases, which were placed at the same height, corresponding to 10 m. The distance between adjacent conductors was equivalent to 0.75 m. The observation point was in front of the channel model and the values of the other parameters, referred to the full-scale system, were: stroke current magnitude equal to 52 kA, stroke current front time of 3.2 ms, distance between adjacent surge arresters of 600 m, distance between the line and the stroke channel model equal to 70 m, and ground resistance of 50 W. The channel model was in front of a set of arresters and equidistant from the line ends, which were matched. A comparison between measured and calculated currents induced at one end of a 2,600-m long telecommunications line with height of 5 m and surge impedance of 440 W is presented in Figure 5.3. The line, made of standard 50 pairs/0.40 mm plastic insulated cable, was located in an area with average soil resistivity of 400 Wm. The investigation, carried out by Paulino et al. [53], involved rockettriggered lightning experiments and the test configuration is presented in Figure 5.4. The outer diameter of the cable, which had an aluminium sheath 0.2-mm thick, was 14.6 mm. The shield was grounded at both ends and the ground resistances were 40

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Figure 5.2 Measured and calculated induced voltages at the point of the line closest to the model of the stroke channel. Perfectly conducting ground. All parameters referred to the full-scale system. (a) Induced voltages. (b) Measured current

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350 m (b) 100 m

Figure 5.3 Measured and calculated induced currents at the farthest termination from the lightning strike point. Average value of the soil resistivity: 400 Wm. (a) Induced currents (adapted from [3]). (b) Line configuration considered in the simulation (adapted from [53])

and 228 W, the lower value corresponding to the nearest terminal to the rocket launch pad. The cable pairs were bonded together and grounded only at the termination with ground resistance of 40 W. The measured stroke current waveform (downward negative flash) was approximated by the sum of two Heidler functions [54] with the following parameters: I01 ¼ 15.0 kA; t11 ¼ 1.15 ms; t12 ¼ 2.0 ms; I02 ¼ 8.5 kA; t21 ¼ 3.2 ms; t22 ¼ 45 ms. In the simulations, the line was considered to be straight, as shown in Figure 5.3b, and the stroke current propagation velocity was assumed constant and equal to 130 m/ms [53]. In order to evaluate how the lightning-induced voltages on LV lines are affected by some parameters, let us consider, initially, the situation illustrated in Figure 5.4, in which lightning strikes a point 50 m from a LV line, midway between its terminations. The line is three-phase, 1-km long, matched at both ends and lossless. As demonstrated by Rachidi et al. [55], when the line length does not exceed a certain critical value (typically 2 km), the surge propagation along it is not appreciably affected by the finite ground conductivity as long as this conductivity is not lower than about 0.001 S/m.

Lightning interaction with LV overhead power distribution networks

185

500 m

500 m

50 m

(a)

Lightning strike point 500 m

500 m Phases Neutral 6.5 μH

6.5 m 6.485 m

20 Ω (b)

Figure 5.4 LV line matched at both ends, without any loads connected. The triangle denotes the input impedance of the LV side of the distribution transformer. (a) Top view. (b) Side view

The heights of the phase and neutral conductors are, respectively, 6.5 and 6.485 m, and both wires have the same diameter, namely 1 cm. The distance between the central and outer phases is 1.5 cm. This configuration is intended to simulate, in a simplified way, a multiplexed line. Some simulations carried out considering the injection of currents directly into the conductors confirm the conclusions of Dugan and Smith [56] that the cable capacitance does not affect significantly the lightning surges in the LV side, and therefore the insulating cable cover is not taken into account. The helical arrangement of the conductors is also neglected due to the very small variation of the conductors’ heights. The neutral is grounded at a single point, very close to the transformer. The value of the ground resistance (Rg) is 20 W and the ground lead inductance is 6.5 mH. The transformer is located in the middle of the line. For the estimation of the lightning-induced voltages on the secondary network, the most important information regarding the transformer is the high frequency behaviour of its impedance seen from the LV side. A typical 30 kVA, 13.8 kV – 220/127 V transformer [1] is considered, whose input impedance can be approximated by a simple parallel RLC circuit with the following parameters, per phase: R ¼ 3.3 kW, L ¼ 144 mH and C ¼ 0.25 nF. All the LV power installations are disconnected from

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Lightning interaction with power systems, volume 2

the network; the soil resistivity and relative permittivity are equal to 500 Wm and 10, respectively. Two stroke current waveforms are considered in order to simulate typical negative downward flashes. The first stroke current has a peak value of 30 kA and its waveform is mathematically described by the Heidler function [54]:    1=n t1 t  : n:t2 I0 ðt=t1 Þn t 1 eðt=t2 Þ ; h ¼ e 2 ; (5.1) iðtÞ ¼ n h ½ðt=t1 Þ þ 1 with I0 ¼ 28.3 kA, t1 ¼ 1.75 ms, t2 ¼ 130 ms and n ¼ 2. The subsequent stroke current has a peak value of 12 kA and its waveform is simulated by the sum of two Heidler functions with the following parameters: I01 ¼ 10.7 kA, t11 ¼ 0.25 ms, t12 ¼ 2.5 ms; I02 ¼ 6.5 kA, t12 ¼ 2.1 ms, t22 ¼ 230 ms and n1 ¼ n2 ¼ 2. These current peak values have a probability of about 50% of being exceeded [57,58]. The propagation velocity is assumed to be 50% of that of light in free space for both currents. The lightning channel is vertical, 4-km long, has no branches and is modelled according to the transmission line (TL) model by Uman and McLain [59]. As already mentioned, all the induced voltage calculations presented hereafter have been performed using the ERM [3]. The waveforms of the two stroke currents are presented in Figure 5.5, together with the corresponding voltages induced at the middle of the line in the absence of the transformer and of the neutral conductor. The first stroke induces a voltage with larger magnitude, but as the subsequent stroke has a higher time-variation rate, the ratio between the voltage peak values is smaller than that between the current peaks (approximately 1.7 against 2.5). Such a difference, however, can vary greatly depending on the values of other parameters such as, for example, the soil resistivity. Figure 5.6 presents the phase-to-ground and phase-to-neutral voltages induced by the first and subsequent strokes in the middle of the line shown in Figure 5.4, 30

180

FS FS Voltage (kV)

Current (kA)

24 18 12

SS

120

60

SS

6 0

0 0

(a)

10

20 Time (μs)

30

40

(b)

4

8

12

16

Time (μs)

Figure 5.5 Stroke currents and corresponding induced voltages in the middle of the line shown in Figure 5.4 in the absence of the transformer and of the neutral conductor. (a) First (FS) and subsequent stroke (SS) currents waveforms. (b) Induced voltages

Lightning interaction with LV overhead power distribution networks 25

25

Up-g

20

15

Voltage (kV)

Voltage (kV)

20

Up-n 10 5 0 –5

(a)

187

10 5 0

2

4

6 Time (μs)

8

–5

10

(b)

Up-g

15

Up-n 2

4

6 Time (μs)

8

10

Figure 5.6 Phase-to-ground (Up-g) and phase-to-neutral (Up-n) induced voltages in the middle of the line for the situation indicated in Figure 5.4 and stroke currents shown in Figure 5.5(a). (a) First stroke. (b) Subsequent stroke that is, at the LV transformer terminals. The differences between the voltages induced on the phase conductors are not significant, although slightly higher values are induced on the outer phases due to the slightly smaller coupling with the neutral. Unless otherwise indicated, the induced voltages presented in this section always refer to the outer phase which is closest to the stroke location. All the voltage magnitudes are much lower than those presented in Figure 5.5(b), as the connection of the neutral to ground gives rise to currents, on the neutral, that, by coupling, reduce the voltages on the phase conductors. These voltages are further reduced because of the connection that exists between the wires through the transformer. Although in this case the highest amplitude of the phase-to-ground voltage occurs for the first stroke, the phase-to-neutral voltage is slightly higher in the case of the subsequent stroke. This can be explained by considering that the transformer input impedance seen from the LV side is predominantly inductive in the frequency range of interest, which makes the peak value of the phase-to-neutral voltage very closely associated with the maximum time derivative of the current flowing through the inductance, which is higher in the case of the subsequent stroke current. In fact, if the transformer impedance (parallel RLC circuit) is represented simply by an inductance of 144 mH per phase, the corresponding induced voltages are almost identical to those shown in Figure 5.6. Phase-to-neutral voltages affect directly the majority of the equipment connected to the LV network and stress the insulation between the phase and the grounded conductive parts of apparatus in TN systems. On the other hand, phaseto-ground and neutral-to-ground voltages are important in the TT arrangement, as well as in the case of equipment connected to an independent grounding system. These simulations of simple situations indicate that the analysis of lightninginduced voltages on LV networks is not so straightforward. Many factors must be taken into account and it is convenient to define a base case in order to evaluate how the voltages are affected by the various parameters involved in the induction mechanism. Therefore, unless otherwise indicated, all the induced voltage calculations presented henceforth are made under the following assumptions:

188 ●







● ●



Lightning interaction with power systems, volume 2 the lightning strike point is 50 m from the line and in front of the distribution transformer, as shown in Figure 5.7; the lightning channel is vertical, 4-km long, has no branches and is modelled according to the TL model [59]; the currents, representative of the first and subsequent stroke currents, have the waveforms shown in Figure 5.5(a) with amplitudes of 30 and 12 kA, respectively, and propagation velocity along the channel equal to 50% of that of light in free space (c); the LV line is three-phase, lossless and 1-km long. All the wires have the same diameter, namely 1 cm, and the heights of the phase and neutral conductors are, respectively, 6 m and 6.485 m; the distance between adjacent neutral groundings is 200 m; the transformer input impedance seen from the LV side is represented by an equivalent parallel RLC circuit with the following parameters (per phase): R ¼ 3.3 kW, L ¼ 144 mH and C ¼ 0.25 nF; the LV power installations are simulated according to the circuit indicated in Figure 5.8 (TN system), obtained by Hoidalen [24], which is equivalent to the parallel connection of the loads on the three phases. The loads are distributed along the line as shown in Figure 5.7;

200 m

200 m

200 m

200 m

200 m

50 m

Lightning strike point

(a) 200 m

200 m

200 m

200 m

200 m

Phases (6.5 m) Neutral (6.485 m) 6.5 μH

6.5 μH

6.5 μH

6.5 μH

6.5 μH

6.5 μH

20 Ω

100 Ω

20 Ω

100 Ω

100 Ω

20 Ω

(b)

Figure 5.7 LV line configuration (base case). The triangles and the rectangles denote, respectively, the distribution transformer (equivalent impedance seen from the LV side) and the LV power installations. (a) Top view. (b) Side view

Lightning interaction with LV overhead power distribution networks ●







189

the LV power installations are close to the line and, thus, in Figure 5.7(b) each impedance formed by an inductance of 6.5 mH in series with a resistance of 20 W corresponds to the equivalent impedance of the ground connections of the neutral and of the closest consumer’s installation. In this way, each equivalent impedance takes into account the inductances of the ground lead and of the service drop, as well as the ground resistances at that neutral grounding point and at the closest service entrance; the resistivity and the relative permittivity of the soil are equal to 500 Wm and 10, respectively; the induced voltages are calculated at the outer phase, at the point closest to the stroke location, that is, at the transformer LV terminals; neither the line nor the LV power installations have secondary arresters.

The values adopted for the lightning current parameters are typical of downward negative flashes. Although the load model has been derived from measurements performed on a residential apartment [24], the configuration depicted in Figure 5.7 is more representative of a rural network. The presence of the MV conductors causes a slight reduction on the induced voltages on the LV line. However, unlike the case of urban regions, where the LV network is usually below the MV conductors, in rural areas the lines frequently form angles with each other, as illustrated in Figure 5.9, which shows, as an example, the topology of an actual system. This results in a smaller coupling, which can usually be disregarded. In order to illustrate the effects of the system components, the phase-to-neutral, phase-to-ground and neutral-to-ground voltages induced by the first stroke are presented in Figure 5.10(a) for the situation shown in Figure 5.7, but without the

16 Ω 1Ω 8 μF

3.5 μH

Figure 5.8 Equivalent circuit of the input impedance of typical residential installation (TN system) (adapted from [24])

LV line MV line

Figure 5.9 Example of an actual system showing the relative position between MV and LV lines (adapted from [1])

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Lightning interaction with power systems, volume 2

presence of the transformer and the loads. The line is therefore composed only of the phase and neutral conductors, the neutral being connected to ground at the six points indicated in Figure 5.7. The results corresponding to the same situation, but considering the presence of the transformer, are shown in Figure 5.10(b). If the neutral is not considered and only the phase conductors are present, the phase-to-ground induced voltage reaches approximately 164 kV and is very close to the voltage shown in Figure 5.5(b) (‘FS’ wave), since in this case the two situations are about the same, except for a slight difference between the relative position between the line and the stroke location. Figure 5.10(a) shows that the neutral, connected to ground every 200 m, causes a significant reduction in the amplitude of the phase-to-ground voltage, which decreases from 164 to 53 kV. Due to the inductance of the down conductor and, mainly, to the ground resistance, the neutral potential rises and reaches 41 kV. However, the peak values of the phase-to-ground and neutral-to-ground voltages do not occur simultaneously and the phase-to-neutral voltage reaches 26 kV. When the transformer is inserted in the circuit, its input impedance, seen by the secondary, causes an additional reduction on the phase-to-ground voltage, whose maximum value reaches approximately 40 kV. As the voltage induced on the neutral conductor practically does not change – in fact, a small increase occurs, but negligible in the case considered – the phase-to-neutral voltage decreases from 26 to 11 kV. The presence of the loads between the phases and the neutral produces oscillations in the phase-to-ground and phase-to-neutral voltages, as shown in Figure 5.11(a), which corresponds exactly to the base case shown in Figure 5.7. The induced voltages corresponding to the current representative of a subsequent stroke are presented in Figure 5.11(b). In this case, the voltage oscillations are much more

60

60

Up-g

40

50

Un-g

30 20

Voltage (kV)

Voltage (kV)

50

Up-n

10 0 –10

(a)

40

Un-g Up-g

30 20 10

Up-n

0

5

10

15 Time (μs)

20

25

–10

30

(b)

5

10

15

20

25

30

Time (μs)

Figure 5.10 Phase-to-ground (Up-g), phase-to-neutral (Up-n) and neutral-toground (Un-g) induced voltages at the point closest to the stroke location, considering or not the presence of the transformer, for the first stroke current. Line configuration shown in Figure 5.7, without the loads. (a) Without the transformer. (b) With the transformer

Lightning interaction with LV overhead power distribution networks 48

191

24 Up-g

18

Up-g

Voltage (kV)

Voltage (kV)

36 24 12

Up-n

0 –12

(a)

12 6

Up-n

0 5

10

15 20 Time (μs)

25

–6

30

5

(b)

10

20 15 Time (μs)

25

30

Figure 5.11 Phase-to-ground (Up-g) and phase-to-neutral (Up-n) induced voltages at the LV transformer terminals for the first and subsequent stroke currents shown in Figure 5.5(a). Line configuration shown in Figure 5.7 (base case). (a) First stroke. (b) Subsequent stroke

pronounced due to the much shorter current front time in relation to that of the first stroke. The influences of some parameters that affect the induced voltages are discussed in Section 5.2.3.1.

5.2.3.1 Stroke current magnitude and waveform Since, in practice, the induced currents that flow through the neutral groundings are not high enough to cause soil ionisation [1] and the line is not equipped with secondary arresters, the system is linear and, therefore, the induced voltages are directly proportional to the stroke current magnitudes as long as the current waveform and the other parameters remain unaltered. Figure 5.12 presents the phase-to-ground and phase-to-neutral induced voltages at the transformer LV terminals for the typical current waveforms shown in Figure 5.5(a). The equivalent front times (tf30) are about 4.9 and 0.5 ms for the first and subsequent stroke currents, respectively. This parameter (tf30) is defined as the time to peak of a current with linearly rising front which has the same time interval between the points corresponding to 30% and 90% of the maximum value. The situation corresponding to Figure 5.12 differs from that considered in Figure 5.10(b) only because of the presence of the impedances representative of the consumers’ loads. The reflections associated with these loads cause oscillations in the induced voltages and currents, which are more intense for the subsequent stroke, whose current has a shorter front time in comparison with the first stroke. The neutral-to-ground voltages corresponding to these two situations have practically the same amplitude and waveform; in the case of the first stroke, the peak value corresponding to the situation illustrated in Figure 5.12 is approximately 1% larger in relation to the situation shown in Figure 5.10(b). In order to better illustrate the effect of the current front time, in the following simulations the currents have triangular shape and tail time (time to half-value)

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Lightning interaction with power systems, volume 2 12

48

FS

Voltage (kV)

Voltage (kV)

FS 6

0

32

SS 16

SS –6

4

8

(a)

12

0

16

4

(b)

Time (μs)

8

12

16

Time (μs)

Figure 5.12 Phase-to-neutral (Up-n) and phase-to-ground (Up-g) induced voltages at the LV transformer terminals for the first (FS) and subsequent (SS) stroke currents shown in Figure 5.5(a). Line configuration shown in Figure 5.7 (base case). (a) Phase-to-neutral. (b) Phase-to-ground

16

48 2 μs

2 μs 4 μs

Voltage (kV)

Voltage (kV)

12 8 8 μs 4

32 4 μs 8 μs 16

0 –4

(a)

4

8

Time (μs)

12

0

16

(b)

4

8

12

16

Time (μs)

Figure 5.13 Induced voltages at the LV transformer terminals for currents representative of first strokes with amplitude of 30 kA, triangular waveform and different front times. Line configuration shown in Figure 5.7. (a) Phase-to-neutral. (b) Phase-to-ground

equal to 50 ms. Concerning the induced voltages, the subsequent stroke currents described by the Heidler function [54] can be reasonably well approximated by both triangular and trapezoidal waveforms with the same equivalent front time (tf30). Such correspondence, however, is not so straightforward in the case of currents representative of the first stroke [1]. The phase-to-ground and phase-to-neutral induced voltages at the LV transformer terminals are compared in Figure 5.13 for currents with amplitude of 30 kA and front times (which, for triangular waveshapes, correspond to times to crest) of 2, 4 and 8 ms. Such currents are representative of first stroke currents. In Figure 5.14, the simulations are more representative of subsequent stroke currents: amplitude of 12 kA and front times of 0.25 and 1 ms. The stroke current front time has usually a significant influence on both the voltage amplitude and waveform. Voltages induced by currents with steeper fronts

Lightning interaction with LV overhead power distribution networks 16

24 0.25 μs

0.25 μs

Voltage (kV)

1 μs

Voltage (kV)

193

8

0

16

8 1 μs

–8 (a)

2

4

6 Time (μs)

8

10

0

12

2

(b)

4

6

8

10

12

Time (μs)

Figure 5.14 Induced voltages at the LV transformer terminals for currents representative of the subsequent strokes with amplitude of 12 kA, triangular waveform and different front times. Line configuration shown in Figure 5.7. (a) Phase-to-neutral. (b) Phase-to-ground

are generally characterized by higher amplitudes, shorter front times and more pronounced oscillations. However, in the case of lines with relatively short grounding intervals, as, for example, the configuration under analysis, the reflections cause a reduction of this effect in relation to the case of absence of points of discontinuity. In other words, the influence of the current front time tends to be more important in cases of larger grounding spacing. Such influence tends to increase also as the observation point moves away from the nearest grounding. By comparing Figures 5.13 and 5.14, it can be seen that the differences between the peak values of the phase-to-neutral voltages are less significant for the subsequent stroke. The variation is more pronounced for the first stroke because the attenuation of the induced voltage as result of the reflected waves is more intense in the case of currents with longer rise times, since a larger number of reflections occurs before the voltage peak is reached. The longer the voltage front time, the more significant the effect of the reflections in reducing the peak value. Although lightning-induced voltages tend to become slower (i.e., with longer front times) as soil resistivity increases, for short distances between the line and the stroke location the phase-to-ground and neutral-to-ground voltages tend to reach their maximum values at a time relatively close to that of the stroke current. However, the reflections that occur at the transformer and at the consumers’ entrances can also have an appreciable effect on the voltage time to peak, which, as can be seen in Figure 5.14(b), can be much longer than the stroke current front time due to the oscillations. The influence of the stroke current tail time is small and can usually be neglected as far as the voltage peak value is concerned.

5.2.3.2 Relative position between the line and the stroke location The situation considered in Figure 5.7(a) (base case), where the lightning strike point is in front of the transformer, corresponds to the most critical one in terms of

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Lightning interaction with power systems, volume 2

the amplitudes of the overvoltages induced at the transformer LV terminals, as the voltages at this point tend to decrease as the flash moves in direction to one of the line ends. In the situation indicated in Figure 5.15, the distance between the line and the lightning strike point is the same (50 m), but the stroke location is equidistant from the transformer and the nearest load and, therefore, is farther from the transformer in comparison with the base case. The phase-to-ground and phase-to-neutral voltages induced at the transformer LV terminals in the two situations are compared in Figure 5.16. As expected, the closer the distance between the transformer and the stroke location, the larger the voltage magnitude across its terminals. In Figure 5.17, the voltages relevant to the base case are compared to those observed at the point of the line closest to the stroke location in the situation depicted in Figure 5.15. It can be seen that the phase-to-neutral voltage decreases in the latter case, while the phase-to-ground voltage increases. This is due to the fact that the potential of the neutral reaches a much higher value in this case, as, because of the small difference between the heights of the phase and neutral conductors, the phase-to-ground and neutral-to-ground voltages are nearly the same until the waves 200 m

200 m

100 m 100 m

200 m

200 m

50 m Lightning strike point

Figure 5.15 Lightning strike point midway between the transformer and a consumer load LV power installation (top view) 12

48

1

1

4 0 –4

(a)

Voltage (kV)

Voltage (kV)

8

32 2

16

2

4

8 Time (μs)

12

0

16

(b)

4

8 Time (μs)

12

16

Figure 5.16 Induced voltages at the LV transformer terminals for two relative positions of the stroke location with respect to the line. First stroke current. Curve 1: stroke location in front of the transformer (Figure 5.7 – base case); Curve 2: stroke location equidistant from the transformer and the closest load (Figure 5.15). (a) Phase-to-neutral. (b) Phase-to-ground

Lightning interaction with LV overhead power distribution networks 2

8 4 0 –4

(a)

80

1 Voltage (kV)

Voltage (kV)

12

195

60 40

1

20

2

4

8 Time (μs)

12

0

16

(b)

4

8 Time (μs)

12

16

Figure 5.17 Induced voltages at the point closest to the stroke location for two relative positions of the lightning strike point with respect to the line. First stroke current. Curve 1: stroke location in front of the transformer (Figure 5.7 – base case); Curve 2: stroke location equidistant from the transformer and a LV power installation (Figure 5.15). (a) Phase-to-neutral. (b) Phase-to-ground

reflected at the closest groundings arrive at the observation point. When the reflected waves arrive, the neutral-to-ground voltage decreases and the phase-toneutral voltage increases, but the peak value of the latter is well below that corresponding to the base case. The phase-to-ground and neutral-to-ground voltages corresponding to the two situations analysed are compared in Figure 5.18. The arrival of the reflected waves causes the voltages to oscillate with frequency ( f) governed mainly by the distance (xg) between the transformer and the closest load to the observation point. In this case, xg ¼ 200 m, and thus the frequency is approximately f ¼ c/(2  xg) ¼ 750 kHz. However, the oscillations depend also on other parameters such as the ground impedance, the stroke current front time and the distance between the observation point and the closest groundings. In general, similar conclusions apply in the case of currents representative of subsequent strokes. However, as they reach their peak values in much shorter times, the relative position between the line and the stroke location tends to have a more significant influence on the induced voltages. This is illustrated in Figure 5.19, which presents a comparison between the voltages relevant to the base case (Figure 5.7) and those observed at the point of the line closest to the stroke location in the situation depicted in Figure 5.15. That is, the difference between Figures 5.17 and 5.19 is that the former refers to the first stroke and the latter, to the subsequent stroke. Figure 5.19 shows that, when the lightning strike point is equidistant from the transformer and the nearest load, both the phase-to-neutral and phase-to-ground voltages reach higher values than those induced by the first stroke. As the voltage front time is quite short, the effects of the input impedances of the transformer and the LV power installations are felt, at the observation point, only when the phaseto-ground voltage is close to the peak value of the voltage shown in Figure 5.5(b),

196

Lightning interaction with power systems, volume 2 80 1

Voltage (kV)

60 2 40 3 4 20

0 4

12

8

16

Time (μs)

Figure 5.18 Phase-to-ground and neutral-to-ground induced voltages at the point closest to the stroke location for two relative positions of the lightning strike point with respect to the line. First stroke current. Curve 1: phase-to-ground voltage, stroke location equidistant from the transformer and the closest load (Figure 5.15); Curve 2: neutralto-ground voltage, stroke location equidistant from the transformer and the closest load (Figure 5.15); Curve 3: phase-to-ground voltage, stroke location in front of the transformer (Figure 5.7 – base case); Curve 4: neutral-to-ground voltage, stroke location in front of the transformer (Figure 5.7 – base case) 12

100

2

3 Voltage (kV)

Voltage (kV)

6 0 –6

1

50

0

2

1

–12

(a)

2

4

6

8

Time (μs)

10

–50

12

(b)

2

4

6

8

10

12

Time (μs)

Figure 5.19 Induced voltages at the point closest to the stroke location for two relative positions of the lightning strike point with respect to the line. Subsequent stroke current. Curve 1: stroke location equidistant from the transformer and the closest load (Figure 5.15); Curve 2: stroke location in front of the transformer (Figure 5.7 – base case); Curve 3: line without the transformer, consumers’ loads and neutral conductor (Figure 5.5(b)). (a) Phase-to-neutral. (b) Phase-to-ground

Lightning interaction with LV overhead power distribution networks

197

in which the transformer, the loads and the neutral conductor are not present. Another consequence of the shorter front time is that the phase-to-neutral voltage corresponding to the situation shown in Figure 5.15 (i.e., Curve 1 in Figure 5.19(a)) oscillates, unlike that corresponding to the first stroke, with the same frequency of the phase-to-ground voltage, which is approximately 750 kHz. Due to the slower current rate of rise of the current of the first stroke, the oscillations (Curve 1, Figure 5.17(a)) have smaller amplitude and some of them cannot even be perceived, so that the frequency is approximately equal to half of that of the phase-toground voltage.

5.2.3.3 Distance between the line and the lightning strike point The distance between the line and the lightning strike point has a considerable influence on the induced voltages, particularly on their amplitudes. This is illustrated in Figures 5.20 and 5.21, which present the phase-to-ground and

18

80 25 m

12

Voltage (kV)

Voltage (kV)

25 m 50 m

6 0

100 m

–6

60 50 m

40 100 m

20

4

8 Time (μs)

(a)

12

0

16

4

8 Time (μs)

(b)

12

16

Figure 5.20 Induced voltages at the LV transformer terminals for different distances between the line and the lightning strike point. First stroke current depicted in Figure 5.5(a). (a) Phase-to-neutral. (b) Phase-to-ground 24

40 25 m

Voltage (kV)

Voltage (kV)

25 m 12 50 m

100 m

0

–12

50 m 20 10 100 m

0 2

(a)

30

4

6

Time (μs)

8

10

12

2

(b)

4

6

8

10

12

Time (μs)

Figure 5.21 Induced voltages at the LV transformer terminals for different distances between the line and the lightning strike point. Subsequent stroke current depicted in Figure 5.5(a). (a) Phase-to-neutral. (b) Phase-to-ground

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Lightning interaction with power systems, volume 2

phase-to-neutral voltages at the transformer LV terminals for distances (d) of 25, 50 (base case) and 100 m for the first and subsequent strokes, respectively. As expected, the shorter the distance, the larger the induced voltage magnitudes. For the situations considered, the ratios between the magnitudes of the phase-to-neutral voltages corresponding to the distances of 50 and 25 m with respect to that relative to d ¼ 100 m are about 1.7 and 2.5, respectively, for the first stroke current. The ratios corresponding to the phase-to-ground voltages are approximately 1.8 (for d ¼ 50 m) and 3.1 (for d ¼ 25 m). For the subsequent stroke, the ratios corresponding to the phase-to-neutral and phase-to-ground voltages are more similar: approximately 1.9 and 3.3 for phase-to-neutral voltages (distances of 50 and 25 m, respectively) and 1.9 and 3.2 for the phase-to-ground voltages.

5.2.3.4

Ground resistance and type of grounding system

It has been assumed so far that the LV power installations are close to the line and thus each impedance to ground corresponds to the equivalent impedance of the ground connections of the neutral and of the closest consumer’s installation. The value of 20 W, adopted for the ground resistance (Rg) in the base case, can be visualised as equivalent, for instance, to Rg ¼ 25 W at the neutral and Rg ¼ 100 W at the service entrances of the LV power installations. It should be noted that ground resistance depends on both the soil resistivity and grounding system, that is, it is possible to obtain different values of Rg for the same type of soil, as well as the same value of Rg in soils with different resistivities. The ground resistance may appreciably affect the phase-to-ground and neutralto-ground voltages. Both voltages increase with Rg, so that the difference between them (i.e., the phase-to-neutral voltage) is less affected by the variation of the resistance. Besides, as the neutral-to-ground voltage presents a larger variation, the phase-to-neutral voltage decreases as Rg increases. This is illustrated in Figures 5.22 and 5.23, which present the results corresponding to the equivalent resistances of 5 and 100 W for the first and subsequent stroke currents, respectively.

80

12

100 W

8

Voltage (kV)

Voltage (kV)

5W 20 W

4 0

60 20 W 40 5W 20

100 W –4

(a)

4

8

Time (μs)

12

0

16

(b)

4

8

12

Time (μs)

Figure 5.22 Induced voltages at the LV transformer terminals for different values of the ground resistance. First stroke current depicted in Figure 5.5(a). (a) Phase-to-neutral. (b) Phase-to-ground

16

Lightning interaction with LV overhead power distribution networks 40

15 5W

100 W 20 W

Voltage (kV)

Voltage (kV)

10 5 0 –5

30 20 W 20 10

100 W –10

(a)

199

2

4

6

8

10

0

12

Time (μs)

(b)

5W 2

4

6

8

10

12

Time (μs)

Figure 5.23 Induced voltages at the LV transformer terminals for different values of the ground resistance. Subsequent stroke current depicted in Figure 5.5(a). (a) Phase-to-neutral. (b) Phase-to-ground In the case of the first stroke current, the peak value of the phase-to-neutral voltage decreases approximately 31% (from 11.7 to 8.1 kV) when the ground resistance goes from 5 to 100 W. On the other hand, the phase-to-ground voltage has a much more significant variation; it increases 192% (from 25.3 to 74 kV) for the same variation of Rg. In contrast to what happens to the phase-to-neutral voltages, which reach their maximum values at about the same time, around 1.8 ms, the times to peak of the phase-to-ground voltages are quite different: 4.4 ms for Rg ¼ 100 W, 11.4 ms for Rg ¼ 20 W and 28.2 ms for Rg ¼ 5 W. For the subsequent stroke current, the peak values of the phase-to-neutral voltages occur at about the same instant (0.8 ms). There is a reduction of approximately 28% (from 12.3 to 8.8 kV) in the peak value when the ground resistance increases from 5 to 100 W. For the same variation of Rg, the phase-to-ground voltage increases about 133% (from 15.5 to 38.4 kV). The effect of the ground lead inductance may be important in the case of low ground resistance values, especially on the neutral-to-ground voltages. As far as phase-to-neutral voltages are concerned, however, even in this condition the influence is very small. The presence of the multi-grounded neutral, the low impedances of the consumers’ loads, and the transformer grounding reduce the induced voltages in TN systems. Voltages of much higher magnitudes are induced on IT systems, as pointed out by Hoidalen [24,26]. IT systems are also more sensitive to the soil resistivity, which can bring about voltages substantially larger.

5.2.3.5 Soil electrical parameters The main soil electrical parameters are the resistivity (r) and the relative permittivity (eR), and both have broad ranges of variation. The resistivity in particular, which is the most important parameter and of greater influence on the ground resistance, varies not only with the temperature and chemical composition of the soil, but mainly with its moisture content, as shown by Coelho et al. [60]. According to Saveskie [61], the relative permittivity of soils with good conductivity (resistivity less than approximately 50 Wm) is in the range of 4 to 30,

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whereas for soils with low conductivity (resistivity of the order of 5,000 Wm) the range of variation is from 1 to 3. However, the range of resistivity variation is much higher. As pointed out by Romero, Piantini and Cooray [62], soils with resistivities higher than 1,600 Wm are relatively common, particularly in mountainous regions, and this requires special attention in the design of grounding systems of structures such as wind turbines. The voltages induced on a given line depend on the lightning electromagnetic fields, which by their turn are affected by the soil electrical parameters. The results obtained by Rachidi et al. [55] show that the approximation of a perfectly conducting ground is in general reasonable for the calculation of both the azimuthal magnetic field and the vertical component of the electric field for distances not exceeding about 1 km. However, the time derivatives of both fields may be significantly affected by propagation effects, as pointed out by Cooray [63,64]. The ground resistivity has a remarkable effect on the horizontal component of the electric field [62,65–70], and, by extension, on the lightning-induced voltages. Figure 5.24 illustrates the effect of the soil resistivity on the phase-to-neutral and phase-to-ground voltages induced at the transformer secondary for the first stroke current. Four values are considered for the soil resistivity, namely 0 Wm, that is, perfectly conductive ground, 500, 1,000 and 2,000 Wm. The results corresponding to the subsequent stroke current are presented in Figure 5.25. The relative permittivity, eR, was kept constant and equal to 10 (a typical value) in all cases. Figure 5.24 clearly shows that soil resistivity has a significant effect on induced stresses, especially on the phase-to-ground voltages. Voltages tend, in general, to increase with increasing resistivity, but this behaviour depends on the relative position between the observation point and the stroke location. In certain situations, an increase in the soil resistivity may result in a reduction and even in a change in the polarity of the induced voltage. It can also be noticed that the induced voltage front time tends to increase with the soil resistivity, this behaviour being much more pronounced in the phase-to-ground voltages.

20 16

120

1,000 W

12

Voltage (kV)

Voltage (kV)

140

2,000 W

500 W

8

0W

4 0 –4

(a)

2,000 W

100

1,000 W

80 60

500 W

40 20

2

4

6

8

10

Time (μs)

12

14

0

16

(b)

0W 2

4

6

8

10

12

14

16

Time (μs)

Figure 5.24 Induced voltages at the LV transformer terminals for eR ¼ 10 and different values of the ground resistivity. First stroke current depicted in Figure 5.5(a). (a) Phase-to-neutral. (b) Phase-to-ground

Lightning interaction with LV overhead power distribution networks

8

–8

0W

500 W 2

4

6

Time (μs)

2,000 W

30

0

–16

(a)

40 2,000 W 1,000 W

Voltage (kV)

Voltage (kV)

16

201

8

10

1,000 W

20

500 W

10 0 –10

12

(b)

2

4

6

8

0W 10 12

Time (μs)

Figure 5.25 Induced voltages at the LV transformer terminals for eR ¼ 10 and different values of the ground resistivity. Subsequent stroke current depicted in Figure 5.5(a). (a) Phase-to-neutral. (b) Phase-to-ground It can be seen, by comparing Figures 5.24 and 5.25, that the voltages induced by the first stroke are more drastically affected by the soil resistivity than those induced by the subsequent stroke. This observation is valid for both phase-toneutral and phase-to-ground voltages, although for the latter the difference is even more significant. As shown in [71] for the case of a MV line, the influence of the soil resistivity can be is even more significant when the lightning strike point is close to one of the line terminations. In [26], Hoidalen shows that the influence of the soil resistivity is much more pronounced on IT systems than on TN systems. It is also shown that, depending on the situation, the magnitudes of the induced voltages on IT systems may increase more than ten times when the soil resistivity increases from zero (case of perfectly conducting ground) to 1,000 Wm. As observed by Romero, Piantini and Cooray [62], the effect of the relative permittivity on the horizontal component of the electric field is much smaller than that of the resistivity. In [71], Piantini compares the voltages induced on a MV line considering the soil resistivity of 500 Wm and different values for the relative permittivity (1 and 30). The difference between the voltages’ amplitudes is approximately 2%. For the resistivity of 5,000 Wm, the difference between the peak values of the voltages relevant to eR ¼ 1 and eR ¼ 3 (the range of variation of eR for very poorly conductivity ground, according to Saveskie [61]) is even smaller (less than 1%). For the base case discussed in this subsection (configuration shown in Figure 5.7, with r ¼ 500 Wm), a variation of eR in the range of 1 to 30 results in a variation of less than 7% in the peak value of the phase-to-neutral induced voltage, whereas the amplitudes of the phase-to-ground voltages remain unchanged.

5.2.4 Transference from the MV line Lightning overvoltages on the LV network can be originated from the primary circuit either in the case of a direct hit or a nearby stroke. In both situations, the transformer plays an important role in the transference mechanism.

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5.2.4.1

Direct strikes

Direct strikes to the primary circuit produce overvoltages on the LV network due to transference from the distribution transformer and to injection of current into the neutral conductor. The latter is a consequence of the ground potential rise caused by the flow of current through the ground resistance following the operation of MV surge arresters and/or the occurrence of flashovers across the MV insulators. The transferred voltages may vary widely depending on the strike and observation points, stroke current magnitude and waveform, network configuration and characteristics of the distribution transformer and protective devices. The overvoltages that result on a typical LV distribution network in the case of direct lightning hits on the primary line were studied, for example, in [1,27 and 72–77]. A typical distribution network was considered by Piantini, Kanashiro and Obase [72] and the voltages at different points of the LV line were calculated in order to study the basic characteristics of the surges transferred to a typical secondary network for the case of direct strokes to the MV line. The simulations were performed with the alternative transients program (ATP) [78]. Flashovers across the MV and LV insulators were taken into account according to the ‘Disruptive Effect Model’, with the parameters estimated according to the procedure proposed by Darveniza and Vlastos [79]. It was shown that a correct representation of the distribution transformer is essential and the well-known purely capacitive PI-circuit is generally not adequate for the evaluation of transferred surges. The simulations showed also that voltage magnitudes of some tens of kilovolts may occur at the transformer LV terminals and at the consumers’ entrances in the absence of SPDs. Even the installation of surge arresters very close to the primary transformer terminals may not prevent its failure from lightning transients, since severe stresses may be caused by surges coming from the LV side. The influences of the stroke current magnitude and front time, ground resistance and number of LV power installations on the voltages transferred to the LV network were discussed by Obase, Piantini and Kanashiro in [73]. The results showed that the flashovers that take place across MV and LV insulators affect significantly the magnitudes and waveforms of the transferred voltages and thus should always be taken into account. In most of the cases, the largest phase-toneutral voltages occur at the transformer terminals. The voltages are characterised by oscillations originated from the various reflections throughout the secondary network and therefore are strongly affected by the spacing between adjacent grounding points. For a given line, the general trend of the phase-to-neutral voltage magnitudes is to decrease with the number of consumers. In general, the shorter the distance between the transformer and the lightning strike point, the higher the magnitudes of the transferred voltages. However, the insulator flashovers tend to diminish this effect [1]. In a study by Obase, Piantini and Kanashiro [74], in which the equivalent impedances of the LV power installations were represented as pure inductances, resistances or capacitances, it was shown that the voltages along the line may increase or decrease with the load impedance depending on the magnitudes of the reflected waves at the various

Lightning interaction with LV overhead power distribution networks

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discontinuity points. Concerning the line configuration, the results obtained by Piantini et al. [80] and by De Conti and Visacro [81] showed that both the overvoltage and current levels through the loads and SPDs are usually much lower in the case of the bunched cable in comparison with the open wire line. Examples of overvoltages transferred to the secondary of a distribution transformer due to a direct lightning strike at the primary circuit, at a distance of 800 m from the observation point, are presented in [1]. The simulations, performed using the ATP [78], considered the typical first and subsequent stroke currents shown in Figure 5.5(a) and a 10-km long primary line with four conductors (three phases plus neutral), wood poles and horizontal configuration. The heights of the phase and neutral conductors were 10 and 6.48 m, respectively. A perfectly conducting ground plane was assumed, and the gapless ZnO surge arresters connected at the highvoltage transformer terminals were simulated by non-linear resistors. The possibility of the occurrence of flashovers across the MV and LV insulators was taken into account by means of switches placed at every pole between all the conductors and ground. The absolute values of the maximum voltage magnitudes were about 10 and 14 kV for the first and subsequent stroke currents, respectively. Comparisons of secondary surges caused by direct lightning strikes to the MV circuit, considering wooden and concrete poles as well as different distances between the MV arresters and the distribution transformer, were performed by Piantini et al. [76]. An example of the obtained results is presented in Figure 5.26, where a and b correspond to the distances between the transformer and the energized arrester terminal and between the transformer tank and the grounded arrester terminal, respectively. The simulations refer to a real single-phase distribution line section characterized by a high transformer lightning failure rate [76,77], whose configuration is shown in Figure 5.27. The strike point was 100 m from the transformer, at whose terminals the voltages were calculated. The first and subsequent

24 a = 1.5 m, b = 1.7 m a = 0.5 m, b = 0.3 m

Voltage (kV)

Voltage (kV)

14

7

0

12

0

a = 1.5 m, b = 1.7 m a = 0.5 m, b = 0.3 m –7

–12 0

(a)

2

4

6

Time (μs)

8

10

12

0

(b)

2

4

6

8

10

12

Time (μs)

Figure 5.26 Phase-to-neutral transferred voltages at the transformer closest to the lightning strike point (distance of 100 m) for different distances between the transformer and surge arrester (adapted from [76]). Single-phase line with concrete poles shown in Figure 5.27. (a) First stroke. (b) Subsequent stroke

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Matching resistor

d1 d1 d1 d1 d1 d1 d1 d1

d1 d1 d1 d1 d1 d1 d1 d1 d1

d2 d2

d1 d1 d1

MV line LV line Transformer (10 kVA) Pole d1 = 100 m (MV) d2 = 80 m (LV)

Figure 5.27 Distribution line configuration corresponding to the voltages shown in Figure 5.26 (adapted from [77]) stroke currents were represented by triangular waveshapes with time to zero of 100 ms and magnitudes and front times of 31.1 kA and 3.8 ms and 12.3 kA and 0.7 ms, respectively. The soil resistivity was 500 Wm and the ground resistance at the transformer was 20 W. The ground resistances of the neutral and consumers were 220 W; while 440 W was considered for the poles at which the neutral was not grounded. The effect of soil ionization was taken into account according to the procedure recommended by IEEE Std. 1410 [82]. The transformer fed six consumers whose input impedances were represented by inductances of 60 mH. The overvoltages at the MV bushing vary significantly with the distance between the transformer and the surge arrester. The shorter the distance, the lower the voltage. As shown in [76], in the case of concrete poles and the subsequent stroke current a reduction of about 40% in the peak value is obtained when the distances a and b are reduced from 1.5 and 1.7 to 0.5 and 0.3 m, respectively. On the other hand, the voltages on the secondary side are much less affected by the position of the MV surge arrester with respect to the transformer. As shown in [76] for the case of wooden poles, the differences between the voltages calculated for the two distances are negligible. In some conditions, the secondary voltages may even have the opposite behaviour, that is, reach higher values for smaller distances, as for example in the case of concrete poles illustrated in Figure 5.26. The influence of the distance on the behaviour of the secondary voltages depends on the transformer transfer characteristics, network configuration, ground resistance and possible occurrence of flashovers. The magnitudes of the voltages transferred to the secondary due to direct strikes to the primary circuit may reach values sufficiently high to cause insulation failure of the LV transformer windings. As shown by Piantini et al. [76,77], the overvoltages corresponding to a typical subsequent stroke current can reach amplitudes above 30 kV, which is a typical value for the lightning impulse withstand voltage of LV transformer windings, and, depending on the transformer insulation condition, can lead to its failure. Further discussion on this topic will take place in Section 5.3, which will consider also the application of SPDs in the LV network.

5.2.4.2

Indirect strikes

The assessment of the voltages transferred from the MV line due to lightning strikes in the vicinity of the distribution network requires the knowledge of the

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205

transformer high-frequency behaviour, as well as the voltages induced at the primary side. This subject is discussed by Borghetti et al. [83] and Piantini and Malagodi [84,85] for the case of unloaded transformers; the presence of the LV line is considered by Piantini [1,38] and Borghetti et al. [86]. A suitable transformer model is essential for the evaluation of transferred surges. In the well-known purely capacitive PI-circuit, the transformer is represented by the capacitances C1 (between primary and ground), C2 (between secondary and ground) and C12 (between primary and secondary). This circuit, however, is not adequate for evaluating transferred surges, as it greatly overestimates the overvoltages. This is illustrated in Figure 5.28, which presents the measured and calculated voltages transferred to the secondary (in open circuit) when a standard 1.2/50 ms impulse voltage of 1.7 kV is applied to the primary terminals, short-circuited, of a typical 30 kVA distribution transformer. For comparison purposes, the voltage calculated using the model presented in Chapter 10 of Volume 1 is shown as well. The absolute value of the ratio between the peak values of the calculated – using the PI-circuit – and measured voltages is 17.5 (700 against 40 V). It can be readily seen that not only the magnitudes but also the voltage waveforms differ considerably. Let us now consider the situation indicated in Figure 5.29. The stroke location is in front of the transformer, at a distance of 50 m from the MV network. The primary circuit has a horizontal configuration and the height of the conductors is 10 m. The LV line configuration is that depicted in Figure 5.7, and no coupling is considered with the MV conductors. The other conditions are the same as those indicated in Section 5.2.3. Although the voltages induced ‘directly’ on the LV line may reach 0.8

Voltage (kV)

0.6 Capacitive PI-circuit 0.4 0.2 Measured

Model presented in Chapter 10

0 2

4 6 Time (μs)

8

10

Figure 5.28 Measured and calculated phase-to-neutral voltages transferred to the secondary of a typical 30 kVA distribution transformer, in the no-load condition, for a standard 1.2/50 ms impulse voltage of 1.7 kV applied to its primary terminals short-circuited. Equivalent capacitive PI-circuit: C1 ¼ 0.138 nF, C2 ¼ 0.423 nF and C12 ¼ 0.305 nF (adapted from [1])

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Lightning interaction with power systems, volume 2 Lightning strike point MV line 400 m

50 m

600 m

LV line

Figure 5.29 Relative position between the MV and LV lines

160

Without surge arresters –0.5 Voltage (kV)

Voltage (kV)

120 80

With surge arresters

40 0

(a)

0

Without surge arresters

2

4

6

8

10

Time (μs)

12

14

–1 –1.5 –2

16

(b)

With surge arresters 2

4

6

8

10

12

14

16

Time (μs)

Figure 5.30 Phase-to-neutral voltages at the transformer terminals considering or not the presence of surge arresters at the MV side. First stroke current depicted in Figure 5.5(a). (a) Induced voltages at the MV side. (b) Transferred voltages at the LV side high magnitudes, in this subsection they are disregarded and we will focus on the voltages transferred from the primary side through the transformer. Figure 5.30(a) presents the phase-to-neutral voltages at the transformer terminals, both with and without surge arresters at the MV side, considering the typical first stroke current depicted in Figure 5.5(a). The surge arrester V  I characteristic is that shown in [1] (Figure 12.39a). The corresponding voltages transferred to the LV side of the 30 kVA transformer are presented in Figure 5.30(b). The calculations corresponding to the subsequent stroke current are presented in Figure 5.31. The transferred voltages oscillate with a frequency governed by the configuration of the LV network, especially by the distance between adjacent loads, and the transformer transient response. Both Figures 5.30 and 5.31 show that the difference between the voltage amplitudes at the LV transformer terminals is much lower than that observed in the primary, and the same outcome was verified by Borghetti et al. [86] and Piantini [1] for soil resistivities of 1,000 and 0 Wm (perfectly conductive soil), respectively. The presence of arresters close to the transformer causes a larger current to flow through the ground lead, which results in a larger neutral-to-ground voltage and may cause a decrease in the phase-to-neutral voltage. The influence of the MV arresters on the transferred surges depends on the configuration of the secondary

Lightning interaction with LV overhead power distribution networks 100

2

80

1

207

Voltage (kV)

Voltage (kV)

Without surge arresters Without surge arresters 60 40 20

0 –1 –2

With surge arresters

With surge arresters 0

(a)

2

4

6

Time (μs)

8

10

–3

12

2

(b)

4

6

8

10

12

Time (μs)

Figure 5.31 Phase-to-neutral voltages at the transformer terminals considering or not the presence of surge arresters at the MV side. Subsequent stroke current depicted in Figure 5.5(a). (a) Induced voltages at the MV side. (b) Transferred voltages at the LV side network and may be more significant in comparison with the cases illustrated in Figures 5.30 and 5.31, as shown by Piantini [38]. A comparison between the two figures also shows that, even though on the MV side the voltages of higher magnitudes are induced by the first stroke – especially when arresters are not present – the higher transferred voltages are associated with the subsequent stroke. The reason is that the voltages induced by the subsequent stroke have steeper fronts and, thus, broader frequency spectra. This, combined with the transformer frequency response, result in transferred voltages with higher magnitudes.

5.3 Lightning protection of LV networks Lightning overvoltages have often high magnitudes and are usually the major cause of failures or damage to transformers and consumers’ electric appliances, especially in the case of lines characterised by poor pole grounding conditions and located in regions with high lightning incidence. A fault on a transformer is always sustained, that is, it requires the intervention of the maintenance team, and the corresponding costs are related to the repair or replacement of the equipment and the service interruption. Protection measures such as the application of secondary arresters and the reduction of the ground resistance at the transformer pole can improve the lightning performance of LV networks. However, although there has been an increasing awareness of the effectiveness of the application of LV arresters, this practice has not been widespread among electric utilities. With few exceptions, for example [87], this measure is usually taken only to meet cases where the action – mainly for improving the ground connections – did not give satisfactory results [6] or solve recurrent problems. This is in fact an economic issue, a trade-off between the lightning costs and the investment in the protection scheme. The failure rate of the SPDs has also to be considered in the cost-benefit analysis.

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Dugan et al. [88] and Darveniza [89] point out that, even without taking into account the costs of damages to consumers’ equipment, the application of LV arresters to the transformer terminals can be justified in areas with high lightning damage rates. However, it is important to note that this procedure must be preceded by an analysis in which the characteristics of both the transformers and the distribution network are taken into account. As shown by Piantini et al. [76,77], in certain situations the simple installation of surge arresters in the secondary may not be effective for the protection of transformers, as will be discussed later in this section. Gapless secondary arresters of the metal oxide varistor (MOV) type are the most appropriate to protect the LV network. The impact, on the lightning overvoltages, of the application of such devices to the transformer and service entrances will be discussed in Sections 5.3.1 and 5.3.2, respectively.

5.3.1

Distribution transformers

Although several factors can cause distribution transformers to fail, in lightningprone regions failure rates can be more than twice the norm, which according to Marz and Mendis [90] is typically between 0.8% and 1.5%, for non-interlaced, and 0.4% and 0.7%, for interlaced transformers. Most of the additional failures may be due to current surges in the LV windings [91]. These surges can be created whenever a significant portion of the stroke current is injected into the neutral between the transformer and the power installations and, with the exception of cloud discharges, this situation can occur for all the mechanisms discussed in Section 5.2. The problems related to the so called ‘LV side surges’ or ‘secondary side surges’ have been discussed in [1,88,90–94]. In order to illustrate the phenomenon, let us consider the case of a direct strike to the primary line, as illustrated in Figure 5.32. The MV arrester discharge current splits so that one portion flows through the pole ground lead and another is injected into the neutral conductor. The division of the bulk of the stroke current is determined by the ground resistances, but in the beginning of the transient it is highly

Meter gaps

Consumer loads

MV arrester

Transformer pole

Service entrance

Figure 5.32 Injection of current into the neutral due to a direct strike to the MV line (adapted from [1])

Lightning interaction with LV overhead power distribution networks

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dependent on the ratio between the inductances of the two paths. Therefore, as the path to the pole ground is shorter and the corresponding inductance is lower, initially a greater portion of the current flows through the transformer ground lead. After a few microseconds, when the current time derivative becomes smaller, the influence of the inductances decreases and the division is controlled by the resistances. The lower the ground resistance of the service entrance in comparison with that of the transformer pole, the larger the magnitude of the surge current that enters the neutral and the worse the problem. If the configuration is symmetric, the voltage drop across the neutral, produced by the surge current, gives rise to equal currents in the two phase conductors, which can damage loads and cause meter gaps to flashover. These currents flow through the transformer secondary, as indicated in Figure 5.32, and induce a surge voltage in the primary which can cause part of the winding to short out. This would change the transformer ratio and subject the load to sustained overvoltages, resulting in damage to consumers’ equipment. The surge voltage can also cause a layer-to-layer insulation breakdown and a subsequent transformer failure and power outage. As pointed out by Dugan et al. [88], the surge voltage distribution inside the transformer is such that the primary arrester has little effect on the prevention of this failure. Although for the symmetric configuration the surge current divides equally into the secondary windings, there is a significant, equal and opposite voltage induced in each half of the MV winding so that the net voltage across the primary terminals is nearly zero. Therefore, the presence of the arrester does not prevent the occurrence of transformer failure. The magnitude of the induced voltage is approximately proportional to the voltage across the secondary windings and it can be estimated reasonably well by considering only the inductances [88]. Hence, transformers with lower secondary impedances have a better performance against this type of surge. This is the case when the secondary windings are interlaced, as in such condition the impedance at surge frequencies is about a tenth that of non-interlaced transformers [90]. On the other hand, interlacing the secondary windings is not effective to solve the problem in the case of unbalanced surges, that is, when the currents through the secondary windings are not equal. This situation happens, for instance, if flashover or arrester operation occurs on only one side of a service. According to Marz and Mendis [90], up to half of all interlaced transformer failures may be due to secondary side surges. A better solution involves the application of LV arresters to the transformers, as in this case protection is provided against both balanced and unbalanced surges, regardless of winding connection. The situation illustrated in Figure 5.32 refers to just one power installation connected to the LV line. In the case of multiple services from the transformer, a lower voltage drop will develop across the neutral and therefore less current will be forced into the secondary transformer terminals. The stresses on both the transformer and the consumers’ loads will then be reduced in comparison with the single service case. On the other hand, multiple services mean higher line lightning exposure and a possible increase in the number of surges may counteract this effect.

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Longer lengths of the LV circuit lead to larger voltage drops and consequently to current surges of higher magnitudes impressed on the transformer secondary. This voltage increase is however not linear, as the ratio of resistance to inductance of the entire circuit generally increases, changing the dynamic response of the circuit and reducing the rate of rise of the surge currents [91]. In [56], Dugan and Smith compared surge currents in secondary windings for three types of cable, namely the open wire, triplex and shielded, and showed that the best results, that is, the lower currents, were obtained with the shielded cable. Due to the greater spacing between conductors and lower mutual coupling between wires, an open wire line has higher inductance than a triplex cable of the same length, and therefore a larger net voltage develops across the neutral, causing a surge current of higher magnitude to flow in the transformer and consumers’ loads. Long-term studies performed by Darveniza and Mercer [87] led to an improved lightning protection scheme for exposed pole mounted transformers in Australia. The protection measures consisted in the relocation of primary surge arresters close to the terminals and in the fitting of secondary arresters. The lightning damage rates decreased from about 2 to 0.3 per 100 transformers per year after the implementation of the protection system [89], and the authors attribute this reduction mainly to the installation of secondary arresters. It is important to note that protecting the transformer by means of interlaced secondaries or LV arresters results in larger surge currents, as both measures provide a low impedance for the surge. As a consequence, customers’ devices may be subjected to higher voltage stresses [1]. Concerning the transformer LV arrester, discharge levels of 2 to 5 kV are considered adequate. Although the lightning impulse withstand level of a transformer secondary is typically in the range of 20 to 30 kV, insulation degradation may be caused by overloading, so that lower protective levels may be beneficial. Secondary arrester classes between 175 and 650 V are in principle suitable, but 440 or 480 V arresters have some advantages over both the limits. They have better coordination with the primary arrester than 175 V arresters, which are susceptible to thermal failures caused by switching events [90,91,93], and have a lower discharge voltage than a 650 V arrester, thus reducing the risk of damage to sensitive consumers’ devices. As pointed up by Dugan et al. [88], the LV transformer arresters must not substitute one type of failure for another and should be designed so that the possibility of failure is remote. Although the magnitude of a typical secondary current surge may be less than 1 kA, the arresters should have a current discharge capability of at least half of that for a standard distribution class arrester, that is, in the range of 20 to 40 kA. As mentioned in the introduction of this section, in certain situations the simple installation of arresters in the secondary may not be effective for the protection of transformers. The effectiveness of this solution is strongly related to the transformer types and the characteristics of the distribution network. In [76] and [77], Piantini et al. present results of an investigation which aimed at analysing field data apparently inconsistent with the literature and establishing an effective and

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economically feasible method to reduce the distribution transformers failure rate of a power company to an acceptable level. A brief discussion about the findings of the study is presented below. A power company with an unacceptably high distribution transformer failure rate – about 6% per year – in a region in Southern Brazil characterized by a ground flash density in the range of 10–15 flashes/(km2year) initiated a pilot project, which consisted in the installation of LV arresters in two sub-regions of its concession area. Although all the transformers were protected with MV arresters, an investigation conducted over a period of 8 years indicated that approximately 47% of the failures were caused by lightning [77]. After 3 years from the start of the project, failures associated with lightning transients were observed also in the case of transformers protected with arresters both at the MV and LV sides, and this fact arouse the power company’s suspicion about the actual effectiveness of secondary arresters. Such result was highly unexpected in view of the findings of several studies according to which the installation of LV arresters should lead to a great reduction in the failure rate of pole-mounted transformers [56,87–94]. A study was then carried out involving laboratory tests, development and application of models for the main power distribution system equipment, computer simulations considering various situations representative of 15 and 25 kV networks, and analysis of field data. According to the power company, the surge arresters were of good quality and presented low failure rate. Several simulations were performed considering different pole configurations (wooden pole and pin insulator; concrete pole and pillar type insulator) and distances between the MV arrester and the transformer. The analysis of the transformer failure data and results of computer simulations, taking into account the fact that the vast majority (75%) of lightning-caused failures occur in rural lines [77], allowed to establish recommendations for transformer protection. The simulations indicated that the main reason for the high failure rate was related to surges coming from the primary side. This result was in agreement with a survey conducted by the power company which showed that, in the entire region under their responsibility, 93% of the lightning-caused failures occur in the primary side, that is, only 7% of the failures occur in the secondary. Therefore, the installation of secondary arresters should not be expected to significantly change the transformers failure rate and, thus, the main recommendation was to install MV arresters at a distance shorter than 0.4 m from the transformer bushings and connect their grounding terminals to the transformer tank through a cable shorter than 0.4 m [77]. Such measure should result in a substantial reduction of the probability of occurrence, at the transformer terminals, of lightning overvoltages with magnitudes higher than its insulation capability. Regarding the secondary side and taking into account also economic aspects, the installation of LV arresters was recommended only when the line is exposed to direct strikes, that is, when it is not below the MV line, and its length exceeds 500 m [77]. Also in this case the arresters should be installed at a distance shorter than 0.4 m from the transformer terminals. It is important to understand the reasons for the difference between the recommendation resulting from the project and other studies. The main conclusion

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drawn from investigations conducted in Australia [87,89] and the USA [56,88,90– 94] is that the installation of arresters at the secondary terminals leads to a significant reduction in the distribution transformer failure rate. The initiative of the power company to develop the pilot project was thus widely supported by the results of these studies. However, in neither area where the pilot project was applied the transformers protected with LV arresters presented lower failure rates in comparison with the other transformers. The results of the various computational simulations, in which not only the characteristics of the rural and urban networks but also the behaviour of the main distribution equipment was reproduced as faithfully as possible, were consistent with those obtained in the pilot project. That is, also according to the simulations the main problem was related to surges coming from the primary side, so that the installation of LV arresters should not drastically change the transformer failure rate. In spite of the opposite conclusions, however, actually there is no contradiction between these findings and those of [56,87–94]. The investigations conducted in the USA dealt primarily with single-phase transformers with three-wire centretapped ‘split-phase’ secondary. This transformer type is very susceptible to failures due to surges injected into the secondary winding, according to the mechanism illustrated in Figure 5.32, and the application of arresters at the LV terminals is a good protection measure against low-side surges. However, the power company had only a few transformers of this type. In the studies conducted in Australia, the high transformer failure rate was attributed to two main causes: (i) the relatively long distance between the MV surge arresters and transformers, which in some cases exceeded 3 m, and (ii) the existence of many secondary lines longer than 500 m and exposed to direct strikes. However, despite the existence of secondary circuits with lengths exceeding 500 m in the concession area of the Brazilian power company, that was not the prevailing situation and the incidence of direct strokes to the LV circuits could not explain the high transformer failure rate. It is worth mentioning that the application of LV arresters on the secondary is certainly beneficial and contribute to reducing the transformer failure rate. However, in cases such as the one previously described such a measure may not be justified under the economic point of view, except when the LV line is longer than about 500 m and exposed to direct strokes. Therefore, the decision about the best solution, considering technical and economic aspects, requires that both the transformer type and the characteristics of the distribution network be taken into account.

5.3.2

LV power installations

The characteristics of the lightning overvoltages on the secondary network depend on a number of parameters, but in general those induced by nearby strokes or transferred from the MV line due to direct strikes to the primary conductors play a more significant role in the network performance [1]. These overvoltages may have a damaging effect on the customers’ loads, and the use of properly coordinated SPDs at the service entrance and at susceptible equipment is recommended especially in regions with high lightning incidence.

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The arresters applied at the service entrance should be similar in rating to the transformer arrester and have a discharge voltage of less than 2 kV [1]. This level, which is already too high for sensitive electronic equipment [2], may be much higher within the installation due to voltage oscillations caused by reflections at various points. Therefore, local protection is required for such loads. Regarding energy handling, the arresters at the service entrance should have higher capability than those placed at internal parts of the premises – sometimes referred to as ‘suppressors’ – and divert the bulk of the surge current. None of the protective devices should be overloaded, and this is the concept of arrester coordination. Besides the energy-absorption capability, the clamping voltages and the distances between the secondary arresters and the suppressors should also be considered for achieving a successful coordination. This topic is specifically addressed in [95–99]; guidelines for installing SPDs are given in [100]. In order to illustrate how the overvoltages induced at the service entrances are affected by the application of secondary arresters, the following configurations will be considered, taking Figure 5.33 as a reference: 1. 2. 3.

arresters not installed (configuration 1); arresters only at the transformer terminals (configuration 2); arresters at the transformer terminals and at all service entrances, excepting at Point 4 (configuration 3).

The SPDs at the transformer and service entrances are assumed to have the same characteristics and are represented by a capacitor of 780 pF in parallel with a non-linear resistor with the voltage–current (V–I) characteristic shown in Figure 5.34, which is representative of a typical 440 V varistor [1]. The inductance of the connections is neglected. The transformer input impedance seen from the secondary side is simulated by means of a lumped inductance of 144 mH per phase, which corresponds to the inductance of the 30 kVA transformer model presented in

200 m 1

200 m

200 m 3

2

200 m 4

200 m 5

6

50 m A

B

Lightning strike point

Figure 5.33 LV line configurations. The triangle and the rectangles denote, respectively, the distribution transformer and the LV power installations. Configuration 1: line without arresters; configuration 2: arresters only at Point 3; configuration 3: arresters at Points 1, 2, 3, 5 and 6

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Voltage (kV)

2.0 1.5 1.0 0.5 0 10–5 10–4 10–3 10–2 10–1 100 101 102 103 104 Current (A)

Figure 5.34 V–I characteristic of the non-linear resistor which, in parallel with a 780 pF capacitor, constitutes the equivalent circuit of the secondary MOV arresters Chapter 10 of Volume 1. It should be noted that the representation of the transformer impedance through a pure inductor leads to results very similar to those obtained when considering the RLC circuit adopted in Section 5.2.3, especially in the case of configurations 2 and 3, in which the SPDs are in parallel with the LV windings. The circuit shown in Figure 5.8 and adopted in the analysis presented in Section 5.2.3 to represent the impedance seen by the power line at the service entrances is typical of a relatively large power installation. The equivalent load impedance significantly affects the induced voltages, larger impedances leading to higher voltages. A more conservative condition is considered henceforth, and the loads, in the TN system, are simulated by means of an inductance of 30 mH per phase, which is representative of smaller installations [26]. The other parameters remain the same as in the base case of Section 5.2.3. Figure 5.35 presents the phase-to-neutral voltages induced at Point 4 for the line configurations 1 and 2 considering the lightning currents depicted in Figure 5.5(a). The comparisons refer to the most critical situation from the point of view of a power installation, that is, that in which the stroke location is in front of it (Point B in Figure 5.33). For the situation considered the subsequent stroke induces higher voltages in comparison with the first stroke, but a much more expressive difference was observed by Piantini [1] for the case of perfectly conducting ground. In Figure 5.35, the peak value of the voltage induced by the subsequent stroke is approximately 54% larger than the recommended protection level of 2 kV. In the case of subsequent stroke (Figure 5.35(b)) the effect of the SPDs is felt only after the voltage has reached its maximum. It is clear, however, that even in the case of the first stroke (Figure 5.35(a)) the presence of SPDs near the transformer does not change significantly the voltage induced on Point 4. Therefore, for the line configurations considered, if the stroke location is in front of an unprotected service entrance the presence of arresters at other points of the line will not be effective in reducing the induced voltage magnitude at that point.

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Figure 5.36 shows the phase-to-ground and neutral-to-ground voltages corresponding to the first and subsequent stroke currents for the line configuration 2. The curves relevant to configuration 1 (not shown) are very similar, especially those corresponding to the first stroke. The peak values of the voltages induced by the first stroke (Figure 5.36(a)) are high, ranging from 42 to 45 kV, whereas the range corresponding to the subsequent stroke is from 14 to 16 kV (Figure 5.36(b)). A more favourable condition, from the consumers’ point of view, occurs when the lightning strike point is in front of the transformer (Point A in Figure 5.33). In this case, for the line configuration 2, which corresponds to SPDs installed only at the transformer terminals, the magnitudes of the phase-to-neutral voltages are lower than 2 kV at all consumers’ entrances for both the first and subsequent stroke currents depicted in Figure 5.5(a).

4

3

Voltage (kV)

Voltage (kV)

3 2

Config. 2 Config. 1 1

Config. 2 2

Config. 1

1 0

0

2

4

6

(a)

8

10

12

14

–1

16

Time (μs)

2

4

(b)

6

8

10

Time (μs)

Figure 5.35 Phase-to-neutral induced voltages at Point 4 of Figure 5.33 when the stroke location is in front of it, at a distance of 50 m (Point B of Figure 5.33). Stroke currents depicted in Figure 5.5(a). (a) First stroke. (b) Subsequent stroke

20

50 Up-g

Up-g 16

Voltage (kV)

Voltage (kV)

40 30 Un-g 20 10 0

(a)

12 Un-g

8 4

2

4

6

8

10 12 14

Time (μs)

16

0

18

(b)

2

4

6

8

10

Time (μs)

Figure 5.36 Phase-to-ground (Up-g) and neutral-to-ground (Un-g) induced voltages at Point 4 of Figure 5.33 for configuration 2 (SPDs only at the transformer terminals) and the stroke currents depicted in Figure 5.5(a). Stroke location: Point B of Figure 5.33. (a) First stroke. (b) Subsequent stroke

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Let us consider now a more severe condition, in which the first and subsequent stroke currents have the same waveforms depicted in Figure 5.5(a), but their magnitudes are, respectively, 88.5 and 29.2 kA. These values have a probability of only 5% of being exceeded [57,58]; the maximum time derivatives are about 36 and 120 kA/ms for the first and subsequent strokes, respectively. Figure 5.37 shows that the presence of SPDs at the transformer terminals does not prevent the voltages induced at the entrances of the consumers’ installations to reach amplitudes higher than the recommended limit. For this condition, the amplitudes of the voltages induced by the subsequent stroke exceed the level of 2 kV at all the service entrances even in the case of very low soil resistivity. Under favourable conditions, that is, good conductive soils, the voltages induced by the first stroke remain below 2 kV [1]. The application of secondary arresters to an end-use installation can be effective in reducing the overvoltage levels at that point to acceptable limits. However, in certain circumstances such a measure may result in higher voltage stresses at unprotected premises, as shown by Piantini in [1] for a perfectly conducting soil. For comparison purposes, the phase-to-neutral induced voltages corresponding to the line configuration 3 are shown in Figure 5.38 for the first and subsequent strokes, considering both ‘severe’ currents, that is, with amplitudes exceeded in only 5% of cases. In all service entrances, except for the unprotected one (Point 4), the voltages remain below approximately 1.4 kV. A comparison of the induced voltages corresponding to the subsequent stroke and line configurations 3 and 2 (i.e., Figures 5.38(b) and 5.37(b)) shows that the presence of SPDs at the entrances of the other installations resulted, at Point 4, in higher voltages in comparison with the previous case, in which there were SPDs only at the transformer terminals. Although the induced voltage tends to increase with the soil resistivity, depending on the circumstances it may present the opposite behaviour. In the specific case shown in Figure 5.38(b), the phase-to-neutral voltage at Point 4 reaches 3.2 kV for the considered resistivity (500 Wm) and 3.3 kV for perfectly conducting ground. This behaviour, however, is not monotonic and, for the considered conditions, from a certain value of resistivity the absolute value of the negative voltage 2

4

Point 2

0

Point 3

Voltage (kV)

Voltage (kV)

Point 3 Point 4

–2 Point 2

2 0 –2 Point 4

–4

(a)

5

10

15

20

Time (μs)

25

–4

30

(c)

2

4

6

8

10

Time (μs)

Figure 5.37 Phase-to-neutral induced voltages at Points 2, 3 and 4 of Figure 5.33 for configuration 2 (SPDs only at the transformer terminals) and the stroke currents with the waveforms depicted in Figure 5.5(a), but with different amplitudes. Stroke location: Point A of Figure 5.33. (a) First stroke (I ¼ 88.5 kA). (b) Subsequent stroke (I ¼ 29.2 kA)

Lightning interaction with LV overhead power distribution networks 4

3 Point 3

Point 3

Voltage (kV)

Voltage (kV)

2 1 0 –1

Point 2

–2

2 0 –2

Point 2 Point 4

Point 4 –3

–4 5

(a)

217

10

15

20

Time (μs)

25

30

2

(b)

4

6

8

10

Time (μs)

Figure 5.38 Phase-to-neutral induced voltages at Points 2, 3 and 4 of Figure 5.33 for configuration 3 (SPDs at the transformer terminals and at all service entrances, excepting at Point 4) and the stroke currents with the waveforms depicted in Figure 5.5(a), but with different amplitudes. Stroke location: Point A of Figure 5.33. (a) First stroke (I ¼ 88.5 kA). (b) Subsequent stroke (I ¼ 29.2 kA)

peak exceeds that of the positive peak and the amplitude of the voltage begins to increase with the increase of the soil resistivity. For the network configuration 3, the ‘severe’ subsequent stroke current considered, and soil resistivity of 2,000 Wm, it is only when the distance between the line and the stroke location is larger than 130 m that the peak voltage at Point 4 becomes lower than 2 kV. Thus, in order to protect LV power installations against lightning overvoltages, properly rated and coordinated SPDs should be installed at all service entrances. In comparison with TN systems, IT systems are in general subject to much larger induced voltages and are also far more affected by the finite ground conductivity, as shown by Hoidalen [26]. When lightning strikes the MV network, short duration pulses of several tens of kilovolts may be transferred to the secondary circuit either by the first and subsequent strokes. Multiple insulator flashovers on the primary side bring about heavy voltage oscillations at the transformer terminals, which can be transferred to the secondary side. The presence of arresters at various places of the LV line does not prevent high voltages from arising at unprotected points, where the peak values may often exceed 10 kV.

5.4 Concluding remarks Lightning causes various power quality problems and has usually a considerable impact on the number of equipment damages and failures, voltage sags and unscheduled power supply interruptions experienced by LV customers. Due to the widespread use and the growing dependence on the continuous operation of sensitive electronic equipment, there has been an increasing awareness of the importance of mitigating such effects. In this chapter, the major mechanisms by which overvoltages are stemmed from lightning were discussed. Particular emphasis was given to the voltages

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induced on overhead LV networks by nearby strokes and to those transferred from the MV system, which are the most important ones on account of their magnitudes and frequencies of occurrence. Simple and effective models were used to represent the high frequency behaviour of typical distribution transformers and LV power installations. The surge magnitudes and waveforms depend considerably on the soil characteristics and on many line and lightning parameters, which may combine in an infinite variety of ways. Therefore, a sensitivity analysis was carried out and a typical LV distribution network, representative of rural lines, was taken as reference. The basic characteristics of the overvoltages, as well as their dependence upon the network configuration and the most important stroke parameters, were assessed. Phase-to-ground voltages induced by nearby strokes can reach some tens of kilovolts in various points along the network, especially if the stroke location is not in front of a neutral grounding point. Lower magnitudes are observed at the transformer and customers’ entrances, but the value of 10 kV may often be exceeded in the case of strikes closer than about 50 m. Phase-to-neutral voltages of some kilovolts are common if SPDs are not applied. In the case of direct strikes to the MV line, short duration pulses of several tens of kilovolts may be transferred to the secondary circuit. In regions of high lightning activity, surges originated in the LV side can be responsible for a great number of transformer failures or damages, even if arresters are placed close to the primary terminals. The application of arresters on transformer secondaries may significantly reduce the lightning damage rates of exposed transformers. However, the decision about the best solution, considering technical and economic aspects, requires that both the transformer type and the characteristics of the distribution network be taken into account. Such measure, however, does not prevent overvoltages from arising at the service entrances. Similarly, the application of secondary arresters to a power installation can effectively reduce the local overvoltages to acceptable limits, but in some circumstances this may result in higher voltage stresses at unprotected premises. Therefore, unless they are applied at every service entrance, exposed sensitive electronic equipment can be damaged. In fact, voltage oscillations caused by reflections at various points within the installation can give rise to internal overvoltages with higher magnitudes than that limited by the arresters placed at the service entrance. Therefore, local protection is required for such susceptible loads.

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[53] Paulino J.O.S., Barbosa C.F., Lopes I.J.S. and Miranda G.C. ‘Time-domain analysis of rocket-triggered lightning-induced surges on an overhead line’. IEEE Transactions on Electromagnetic Compatibility, 2009:51(3):725–32. [54] Heidler F. ‘Analytische Blitzstromfunktion zur LEMP - Berechnung’. Proceedings of the 18th International Conference on Lightning Protection (ICLP), Munich, 1985, pp. 63–6. [55] Rachidi F., Nucci C.A., Ianoz M. and Mazzetti C. ‘Influence of a lossy ground on lightning-induced voltages on overhead lines’. IEEE Transactions on Electromagnetic Compatibility, 1996;38(3):250–64. [56] Dugan R.C. and Smith S.D. ‘Low-voltage-side current-surge phenomena in single-phase distribution transformer systems’. IEEE Transactions on Power Delivery, 1988;3(2):637–47. [57] Anderson R.B. and Eriksson A.J. ‘Lightning parameters for engineering application’. Elektra, 1979;69:65–102. [58] Rakov V.A., Borghetti A., Bouquegneau C., et al. ‘Lightning parameters for engineering applications’. CIGRE Working Group C4.407. 117 p. (CIGRE, Paris, Technical Brochure 549, 2013). [59] Uman M.A. and Mclain D.K. ‘Magnetic field of the lightning return stroke’. Journal of Geophysical Research, 1969;74:6899–910. [60] Coelho V.L., Piantini A., Almaguer H.A.D., Coelho R.A., Boaventura W.C. and Paulino J.O.S. ‘The influence of seasonal soil moisture on the behavior of soil resistivity and power distribution grounding systems’. Electric Power Systems Research, 2015;118:76–82. [61] Saveskie P.N. ‘Earth constants’. TAI Incorporated Consuletter International, Worldwide Telecommunications Series, 1977;6(5). [62] Romero F., Piantini A. and Cooray V. ‘On the influence of stroke current propagation velocity on lightning horizontal electric fields’. IEEE Transactions on Electromagnetic Compatibility, 2014;56(4):940–8. [63] Cooray V. ‘On the validity of several approximate theories used in quantifying the propagation effects on lightning generated electromagnetic fields’. Proceedings of the 8th International Symposium on Lightning Protection (SIPDA), Sa˜o Paulo, November 2005, pp. 112–9. [64] Cooray V. ‘Propagation effects due to finitely conducting ground on lightning generated magnetic fields evaluated using Sommerfeld’s integrals’. Proceedings of the 9th International Symposium on Lightning Protection (SIPDA), Foz do Iguac¸u, November 2007, pp. 151–6. [65] Zeddam A. and Degauque P. ‘Current and voltage induced on a telecommunication cable by a lightning stroke’. Electromagnetics, 1987;7(3 and 4):541–64. [66] Nucci C.A., Rachidi F., Ianoz M. and Mazzetti C. ‘Lightning-induced overvoltages on overhead lines’. IEEE Transactions on Electromagnetic Compatibility, 1993;35(1):75–86. [67] Nucci C.A. ‘Lightning-induced voltages on distribution systems: influence of ground resistivity and system topology’. Proceedings of the 8th International

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Lightning interaction with power systems, volume 2 Symposium on Lightning Protection (SIPDA), Sa˜o Paulo, November 2005, pp. 761–73. Shoory A., Moini R., Sadeghi S.H.H. and Rakov V.A. ‘Analysis of lightning radiated electromagnetic fields in the vicinity of lossy ground’. IEEE Transactions on Electromagnetic Compatibility, 2005;47(1):131–45. Romero F. and Piantini A. ‘Evaluation of lightning horizontal electric fields over a finitely conducting ground’. Proceedings of the 9th International Symposium on Lightning Protection (SIPDA), Foz do Iguac¸u, November 2007, pp. 145–50. Barbosa C.F. and Paulino J.O.S. ‘An approximate time-domain formula for the calculation of the horizontal electric field from lightning’. IEEE Transactions on Electromagnetic Compatibility, 2007;49(3):593–601. Piantini A. ‘Lightning-induced overvoltages on overhead medium-voltage lines’. Proceedings of the 2016 IEEE International Conference on High Voltage Engineering and Application (ICHVE), Chengdu, September 2016, DOI: 10.1109/ICHVE.2015.7800825. Piantini A., Kanashiro A.G. and Obase P.F. ‘Lightning surges transferred to the low-voltage network’. Proceedings of the 7th International Symposium on Lightning Protection (SIPDA), Curitiba, November 2003, pp. 216–21. Obase P.F., Piantini A. and Kanashiro A.G. ‘Overvoltages transferred to low-voltage networks due to direct strokes on the primary’. Proceedings of the 8th International Symposium on Lightning Protection (SIPDA), Sa˜o Paulo, November 2005, pp. 489–94. Obase P.F., Piantini A. and Kanashiro A.G. ‘Overvoltages on LV networks associated with direct strokes on the primary line’. Proceedings of the 28th International Conference on Lightning Protection (ICLP), Kanazawa, 1, September 2006, pp. 479–84. De Conti A. and Visacro S. ‘Calculation of lightning-induced voltages on low-voltage distribution networks’. Proceedings of the 7th International Symposium on Lightning Protection (SIPDA), Sa˜o Paulo, November 2005, pp. 483–8. Piantini A., Carvalho T.O., Obase P.F., Janiszewski J.M., Santos G.J.G. and Fagundes D.R. ‘The influence of surge arrester location on over-voltages caused by direct lightning strikes to MV lines’. Journal of Energy and Power Engineering, 2014;8:508–14. Piantini A., Janiszewski J.M., Carvalho T.O., Obase P.F. and Santos G.J.G. ‘Lightning-caused transformer failures in distribution systems’. Proceedings of the 2014 International Conference on Lightning Protection (32nd ICLP), Shanghai, September 2014, pp. 706–11. ATP. Alternative transients program rule book. Leuven EMTP Center, 1987. Darveniza M. and Vlastos A.E. ‘The generalized integration method for predicting impulses volt-time characteristics for non-standard wave shapes – a theoretical basis’. IEEE Transactions on Electrical Insulation, 1988; 23(3):373–81.

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[80] Piantini A., Bassi W., Matsuo N.M. and Nosaki S. ‘Lightning overvoltages and currents in low-voltage networks with bunched cables’. Proceedings of the Conference of Technological Innovation in Electric Energy (I CITENEL), Brası´lia, November 2001, t. 14, pp. 1–4. [81] De Conti A. and Visacro S. ‘Evaluation of lightning surges transferred from medium voltage to low-voltage networks’. IEE Proceedings Generation Transmission Distribution, 2005;152(3):351–6. [82] IEEE Std. 1410: ‘IEEE Guide for improving the lightning performance of electric power overhead distribution lines’. New York, 2010 (Revision of IEEE Std. 1410–2004). [83] Borghetti A., Iorio R., Nucci C.A. and Pelacchi P. ‘Calculation of voltages induced by nearby lightning on overhead lines terminated on distribution transformers’. Proceedings of the International Conference on Power Systems Transients (IPST), Lisbon, September 1995, pp. 311–5. [84] Piantini A. and Malagodi C.V.S. ‘Voltages transferred to the low-voltage side of distribution transformers due to lightning discharges close to overhead lines’. Proceedings of the 5th International Symposium on Lightning Protection (SIPDA), Sa˜o Paulo, May 1999, pp. 201–5. [85] Piantini A. and Malagodi C.V.S. ‘Voltage surges transferred to the secondary of distribution transformers’. Proceedings of the 11th International Symposium on High Voltage Engineering (ISH), London, 1, August 1999, pp. 1365–8. [86] Borghetti A., Morched A.S., Napolitano F., Nucci C.A. and Paolone M. ‘Lightning-induced overvoltages transferred from medium-voltage to lowvoltage networks’. Proceedings of the IEEE St. Petersburg Power Tech., St. Petersburg, June 2005. [87] Darveniza M. and Mercer D.R. ‘Lightning protection of pole mounted transformers’. IEEE Transactions on Power Delivery, 1989;4(2): 1087–95. [88] Dugan R.C., Kershaw Jr S.S. and Smith S.D. ‘Protecting distribution transformers from low-side current surges’. IEEE Transactions on Power Delivery, 1990;5(4):1892–901. [89] Darveniza M. ‘Lightning arrester protection of distribution transformers – revisited’. Proceedings of the 6th International Symposium on Lightning Protection (SIPDA), Sa˜o Paulo, November 2001, pp. 385–9. [90] Marz M.B. and Mendis S.R. ‘Protecting load devices from the effects of low-side surges’. IEEE Transactions on Industry Applications, 1993;29(6): 1196–203. [91] Task force on low-side surge requirements for distribution transformers. ‘Secondary (low-side) surges in distribution transformers’. IEEE Transactions on Power Delivery, 1992;7(2):746–55. [92] Puri J.L., Abi-Samra N.C., Dionise T.J. and Smith D.R. ‘Lightning induced failures in distribution transformers’. IEEE Transactions on Power Delivery, 1988;3(4):1784–801.

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Chapter 6

Lightning protection of structures and electrical systems inside of buildings Fridolin Heidler1

The scope of this chapter is dedicated to the lightning protection of common buildings (common structures), including their installations and content as well as persons. Rules for the protection of common buildings (common structures) against lightning are given in the international standard series IEC 62305 [1–4]. The standard series consists of the four parts: Part 1 [1] provides the general principles, Part 2 [2] deals with the risk due to lightning, Part 3 [3] provides the protection against physical damages and life hazard in a structure, and Part 4 [4] provides the principles of lightning protection of electrical and electronic systems within structures. The European Union (EU) accepted the IEC standard series and transferred it into the European EN 62305 standard series. The standard series is mandatory for all members of the EU. Many other nations also included the IEC standards series in their national standardization, often with adaptions and modifications due to the requirements in the country. Therefore, this standard series is the worldwide basis for the protection against lightning. Common buildings are immobile structures located on earth. They are typically connected to different kinds of lines as water lines, gas pipes, electrical power lines, telecommunication lines, data lines, etc. Mobile systems as vehicles, ships, or aircrafts and moveable systems as tents or containers are commonly not connected to such lines or only to a minor number of them, and they are not equipped with earth-termination systems comparable to buildings. For the mobile and moveable systems, different or additional rules apply. For instance, rules for the lightning protection of aircraft are given in [5] and by the standards of EUROCAE (e.g. see [6,7]). Additional or different regulations are also necessary for special structures as nuclear power plants, wind turbines, railway system, offshore installations, underground systems, pipelines, telecommunication lines, power lines (outside the building), etc. Moreover, the requirements for military equipment are also different. The lightning protection of military equipment is fixed in separate standards.

1 Department of Electrical Engineering and Information Technology, University of the Federal Armed Forces, Munich, Germany

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Lightning interaction with power systems, volume 2 The lightning threat involves the following scenarios:









Direct lightning strike to a building: A direct lightning strike to a building or to a line connected to the building can cause mechanical damages, fire and explosion, injury and even death to living beings, and failures or malfunction of internal systems. Direct lightning strike to a line connected to a building: A direct lightning strike to a line can transfer high currents and over-voltages to a building. This can also cause fire and explosion, injury and even death to living beings, and failures or malfunction of internal systems. Indirect lightning strike close to a building: An indirect lightning strike (nearby lightning strike) to a building can cause failure or malfunction of the internal systems due to the coupling of the radiated electric and magnetic field. Indirect lightning strike close to a line connected to a building: An indirect lightning strike (nearby lightning strike) to line connected to a building can cause failure or malfunction of the internal systems due to over-voltages induced on connected lines and transmitted to the building.

Considering the different scenarios, it is not sufficient to build up a lightning protection only inside of the building, because the outer systems connected a building (incoming lines, earthing, air termination, down conductor, etc.) may be the source of damages and malfunctions. Therefore, the efficient lightning protection of structures, including their content, requires the combination of external and internal counter measures.

6.1 Lightning currents Two different types of lightning to ground exist: ●



Cloud-to-ground lightning (downward flashes, downward lightning): Cloudto-ground lightning are the most common type of lightning to ground. They are initiated by a leader moving downward from the thundercloud to ground. Ground-to-cloud lightning (upward flashes, upward lightning): Ground-tocloud lightning are restricted to high-rise structures as tall towers or tall wind turbines. They are initiated by a leader moving upward from earthed structures to the thundercloud.

The lightning current is the primary source of damages and malfunctions. A lightning current may be composed by several components. It is generally assumed that the threat due to the current components of the ground-to-cloud lightning does not exceed the threat due to the current components of the cloud-to-ground lightning. Therefore, the lightning current parameters of the ground-to-cloud lightning are considered to be covered by the lightning current parameters of the cloud-toground lightning. A cloud-to-ground lightning transfers either positive or negative charge to ground. If it transfers positive charge to ground, it is called positive cloud-to-ground lightning, otherwise negative cloud-to-ground lightning. Negative cloud-to-ground lightning

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Current (kA)

have often a first negative return stroke and one or more subsequent negative return strokes. The positive cloud-to-ground lightning is commonly a single-stroke flash with a first positive return stroke, but without having a subsequent return stroke. Figure 6.1 shows the current records of a first negative return stroke and of a subsequent negative return stoke stroke. The impulsive current of the first return stroke is the first current component of cloud-to-ground lightning. Typically, the current of the first return stroke lasts less than 2 ms and has peak values of several tens of kiloamperes (Figure 6.1(a)). In standards (e.g. see [1]), the currents of the first positive return stroke and of the first negative return stroke are taken into account by the first positive impulse current and the first negative impulse current. The currents of the subsequent (negative) return strokes differ from the currents of the first return strokes. In standards (e.g. see [1]), the currents of the subsequent (negative) return strokes are taken into account by the subsequent impulse current. A continuing current may follow each of the return stroke currents (Figure 6.1(b)). The continuing current is a slowly varying current with typical duration of some tens to some hundreds of milliseconds and amplitude of some tens to more than thousands of amperes. In standards (e.g. see [1]), the continuing current is taken into account by the long-duration current. The continuing current may be superimposed by additional impulsive currents, the so-called M-components (not shown in Figure 6.1(b)). Because the M-components are

0

200 200

Time (µs) 800 1,000

400

–8 –16 –24 –32 –40

Current (kA)

(a) 20

Time (ms)

40

0 –5

Continuing current

–10 –15

Subsequent return stroke

–20 (b)

–25

Figure 6.1 Current record as a function of time (a) of a negative first return stroke, and (b) of a negative subsequent return stoke. The currents were measured at the Peissenberg Tower, Germany

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much weaker compared to the impulsive current of the return strokes, they are not taken into account in lightning standards. The threat of the M-component is considered to be covered by the return stroke current.

6.1.1

Current components

6.1.1.1

Impulsive currents

The return stroke current rises suddenly up to the maximum and declines slowly. In lightning standards [1], the return stroke current is taken into account as impulsive current with a continuously fast rising front and a slow approximately exponential decay. Figure 6.2 shows a schematic drawing of the impulsive current. The waveform of the current is characterized by the front time (T1), the peak current (imax), and the time to half value (T2).

6.1.1.2

Long-duration current

In standards, the continuing current of natural lightning is taken into account as long-duration current or long-stroke current [1]. In this chapter, we refer to as longduration current. Figure 6.3 shows the schematic drawing of the long-duration current. Opposite to the impulsive current, the long-duration current does not exhibit a fast rising front and an exponential decay like the impulsive current. The long-duration current has approximately constant amplitude from the onset to the cessation of the current. The long-duration current is characterized by the charge (Qlong) and the duration (Tlong). The duration (Tlong) is the time period in which the current level is higher than 10%.

6.1.2

Lightning protection level

The concept of lightning protection is based on lightning data from long-term measurements. The most important current data were acquired from lightning strikes to two telecommunication towers located on the Mount San Salvatore,

100% 90%

i(t) Current decay

Current front i max

50%

10%

t

T1 T2

Figure 6.2 Definitions for the impulsive current according to [1]

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231

i 100% 10%

Qlong

10%

Tlong

Figure 6.3 Definitions for the long-duration current according to [1]

Table 6.1 Probability according to IEC 62305-1 [1] that the current parameters of a lightning are lower or higher than the fixed value Probability that the current parameters of a lightning are Lower than the fixed value (%) Higher than the fixed value (%)

LPL I

II

III

IV

99 1

98 2

97 3

97 3

Switzerland. Based on these long-term-studies, from the International Council of Large Electrical Systems the probability is derived for each lightning parameter that it exceeds a certain level (e.g. [1,8–10]). It is obvious that, for instance, a hospital needs a better lightning protection than a simple barrack. Therefore, in IEC 62305-1 [1] four lightning protection levels (LPL) are defined accepting that the lightning currents may exceed the defined levels with certain probability. For each protection level (I–IV), a set of current parameters is fixed. Protection level LPL I represents the highest protection level and LPL IV the lowest protection level. For the different LPL, Table 6.1 gives the probability that the current parameters of a lightning are lower or higher than the fixed value. The fixed values relevant for LPL I are not exceeded, with a probability of 99%, i.e. it is tolerated that 1% of the lightning have current parameters higher than the fixed values. For LPL II and LPL III/IV, the tolerable fraction is increased to 2% and 3%, respectively. The threat of the lightning current is quantified by the following current parameters: ● ● ● ●

Peak current: imax Maximum current steepness:Ð di/dtmax Charge of the current: Q ¼ idt Ð Specific energy of the current: W/R ¼ i2dt

Table 6.2 contains the fixed values for the different LPL. The values of the first positive impulse current are deduced from the currents of the first positive return strokes. The first positive impulse current covers the threat of all other return

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Table 6.2 Fixed values for the different lightning protection levels according to IEC 62305-1 [1] Symbol

First positive impulse current Peak current imax Impulse charge Qshort Specific energy W/R Waveform T1/T2 First negative impulse current Peak current imax Average steepness di/dt Waveform T1/T2 Subsequent impulse current Peak current imax Average steepness di/dt Waveform T1/T2 Long duration current Charge Qlong Duration Tlong Total flash Flash charge

Qflash

Unit

LPL I

II

III

IV

kA C MJ/W ms/ms

200 100 10

150 75 5.6 10/350

100 50 2.5

kA kA/ms ms/ms

100 100

75 75

50 50

kA kA/ms ms/ms

50 200

37.5 150 0.25/100

25 100

C s

200

150

100

C

300

1/200

0.5 225

150

strokes regarding the impulse charge (Qshort), the peak current (imax), and the specific energy (W/R). The values of the subsequent impulse current are deduced from the currents of the negative subsequent return strokes. The subsequent impulse current covers the threat of all other return strokes regarding the maximum current derivative (di/dtmax). Because the maximum current derivative (di/dtmax) is commonly not available from measurements, the average current front steepness (imax/T1) is used alternatively [1] (see Table 6.2). The values of the first negative impulse current are deduced from the currents of first negative return strokes. Apart from some inductive coupling effects, the treat of the first negative return stroke current is covered by the first positive impulse current and the subsequent impulse current (see Section 6.8.3). The long-duration current covers the threat due to the charge of the continuing currents. The damage patterns due to the charge of the long-duration current (Qlong) are quite different from the damage patterns due to the charge of the impulse currents (Qshort). Therefore, both types of charges have to be taken into account. The treat of the total lightning is given by the flash charge (Qflash). The flash charge is the sum of the charge of the long-duration current and the charge of the first positive impulse current.

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Table 6.3 Parameters for the lightning current function of (6.1)

imax (kA) k t1 (ms) t2 (ms)

First positive impulse current (10/350 ms)

First negative impulse current (1/200 ms)

Subsequent impulse current (0.25/100 ms)

LPL

LPL

LPL

I

II

III–IV

I

II

III–IV

I

II

III–IV

200 0.93 19.0 485

150 0.93 19.0 485

100 0.93 19.0 485

100 0.986 1.82 285

75 0.986 1.82 285

50 0.986 1.82 285

50 0.993 0.454 143

37.5 0.993 0.454 143

25 0.993 0.454 143

6.1.3 Simulation of the lightning currents for analytical purpose In IEC 62305-1 [1], the following function is recommended for the simulation of the lightning currents for analytical purpose: i¼

imax ðt=t1 Þ10   et=t2 k 1 þ ðt=t1 Þ10

(6.1)

where imax denotes the peak current, and k is the correction factor of the peak current. The wave shape is determined by the front time constant t1 and the tail time constant t2. Table 6.3 summarizes the parameters of the current function for the first positive impulse current, the first negative impulse current, and the subsequent impulse current. The impulse currents have the waveform 10/350, 1/200, and 0.25/100 ms, respectively. The front of the impulse currents is characterized by a first section with no significant current change. Figure 6.4 shows the waveform of the first positive impulse current during the rise (Figure 6.4(a)) and during the exponential decay (Figure 6.4(b)). The maximum current steepness is approximately at the half value of the peak current. It is approximately given by   pffiffiffi imax di  2 (6.2) dt max T1

6.2 Lightning protection of buildings All measures for protection against lightning form the overall lightning protection. For the lightning protection of buildings, two groups of protection measures are realized: ●

The first group gives the rules and protection measures to reduce the physical damage and life hazard in a structure. This task is achieved with the lightning

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Current

100%

0%

10

0

20

30 Time (µs) 40

T 1 = 10 µs

(a)

Current

100%

0% (b)

Time (ms) 0

0.2

0.4

0.6

0.8

1

T 2 = 350 µs

Figure 6.4 Waveform of the first positive impulse current (a) during the rise, (b) during the decay



protection system (LPS). The LPS, however, does not cover the necessary protection of the electric and electronic devices installed in the building. The second group gives the rules and protection measures to reduce failures and malfunctions of electrical and electronic systems and devices inside of building. This task is achieved with the surge protection measure (SPM) system.

Table 6.4 summarizes the topics, aims, and tasks for the protection systems. The LPS protects the building against lightning strike, whereas the SPM system reduces the surges which passed the LPS. The SPM requires that the LPS be already installed. In simple houses without or with only few electric and electronic devices, the installation of the LPS may be sufficient. The complete lightning protection requires the installation of both systems.

6.2.1

Lightning protection zone

According to IEC 62305-4 [4], the lightning electromagnetic impulse (LEMP) includes all types of surges and electromagnetic fields, which are produced by the lightning current via resistive, inductive, and capacitive coupling. (Note: in lightning research, a different definition is used: the name LEMP stands only for the electromagnetic field radiated by lightning.)

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Table 6.4 Topics, aims, and tasks of the protection systems Protection system

Lightning protection system (LPS)

Surge protection measure (SPM) system

Standard Topic Aim, task

IEC 62305-3 [3] Lightning protection Protection of persons against lightning strike, protection of buildings against fire, and mechanical damage

IEC 62305-4 [4] EMC protection Protection of electrical and electronic systems and devices against malfunction, disturbance, and damage

Antenna LPZ 0 Electrical power line Mast or railing LPZ 1

LPZ 2 Device

Device

Boundary of LPZ 2

Boundary of LPZ 1

Water pipe Telecommunication line Bonding of incoming services directly or by suitable SPD

Figure 6.5 General principle for the division into different lightning protection zones (LPZ)

Protection against LEMP is based on the lightning protection zone (LPZ) concept. The principle of LPZ requires the forming of nested zones of successively reduced values of the electromagnetic environment. For this purpose, the electromagnetic field is reduced by shields installed at the boundaries of the LPZ, and the surges on lines are reduced by equipotential bonding also at the boundaries of the LPZ. Figure 6.5 depicts the principles of the LPZ concept. The LPZs are assigned volumes where the LEMP severity is compatible with the immunity level of the internal systems enclosed. Successive LPZ are characterized by significant reduction of the LEMP.

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Lightning interaction with power systems, volume 2 The LPZ can be subdivided into outer (external) and inner (internal):

Outer LPZ LPZ 0

Zone is endangered by the un-attenuated lightning field and by surges up to the full or partial level of the lightning current. LPZ 0 is subdivided into LPZ 0A and LPZ 0B Zone is endangered by direct lightning strikes, by the un-attenuated lightning field and by the full level of the lightning current Zone is protected against direct lightning strike, but the zone is endangered by the un-attenuated lightning field and by surges up to the full or partial level of the lightning current

LPZ 0A LPZ 0B

Inner LPZ LPZ 1 LPZ 2, . . . , n

6.2.2

The surges are limited by current sharing and SPD at the boundary. The lightning fields can be attenuated by spatial shielding In LPZ 2, the surges are further limited by current sharing and by SPD at the boundary. The lightning fields are usually attenuated by spatial shield. LPZ 3 or higher may be necessary for further reduction of the surges and fields

Lightning protection system

The LPS protects the structures and buildings against fire and damage and the persons inside against injuries caused by step and touch voltage. The LPS usually represents the boundary between the LPZ 0 and LPZ 1. It consists of an external and internal LPS according to Figure 6.6.

6.2.2.1

External and internal LPS

The functions of the external LPS are (1) to intercept a lightning flash to the building, (2) to conduct the lightning current safely to earth, and (3) to disperse it into the earth. Components of the external LPS are (see Figure 6.6) ● ● ●

air-termination system, down-conductor system, and earth-termination system.

The external LPS may be isolated totally from the structure to be protected, e.g. a separate mast may be installed close to the building. More often a partly isolated external LPS is used, e.g. the air-termination system or the downward conductor system are isolated from the structure by keeping a certain distance. For instance, a certain distance is necessary, if the roof or the walls are covered by combustible material. In most cases, a non-isolated external LPS is used. The air-termination system and the down-conductor system are attached on the roof and the walls of the building directly.

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LPZ 0 Air-termination system Lightning equipotential bonding by means of SPD

SPD 0A/1

s

LPZ 1

Separation distance against dangerous sparking

Downconductor system

Ground SPD 0A/1

Earth-termination system

Figure 6.6 Lightning protection system (LPS) as boundary between LPZ 0 and LPZ 1 The internal LPS consist of the following components (see Figure 6.6): ● ●

Equipotential bonding Separation distance

In the case of direct lightning strike, dangerous sparking may occur between the external LPS and metal installations inside the building. The function of the internal LPS is to prevent such dangerous sparking. This can be achieved either by lightning equipotential bonding or by electrical insulation of the external LPS by keeping a separation distance (s) between the external LPS and the conductive installations inside the building.

6.2.2.2 Classes of LPS It is obvious that, for instance, the tower of an airport needs a better lightning protection than a simple building. Therefore, in IEC 62305-3 [3] four classes of LPS are defined corresponding to the four LPL. Table 6.5 contains the relation between the different LPL and the classes of LPS. LPS-class I represents the highest protection level and LPS-class IV represents the lowest protection level. Very simple buildings as sheds or barracks may be protected according to LPSclass IV. Normal buildings as residential buildings, office buildings, hotels, restaurants, and the similar others are usually protected according to LPS-class III. Buildings with increased protection requirements may be protected according to higher LPS-class II. Typical examples are police buildings, fire stations, hospitals, and buildings with increased risk of fire. Computer centres, towers of the airport,

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Lightning interaction with power systems, volume 2 Table 6.5 Lightning protection level (LPL) and class of lightning protection system (LPS) Lightning protection level (LPL)

Class of the lightning protection system (LPS)

I II III IV

I II III IV

and buildings with explosive contents are typically protected according to the highest LPS-class I. Each class of LPS is characterized by two sets of parameters and protection measures. The first set depends on the requirements of the individual class and varies therefore from class to class. The second set does not vary from class to class, i.e. this set is independent from the class of LPS. The class of LPS on which the following set of parameters and protection measures depends on are ● ● ● ● ●

lightning parameters (see Table 6.2); rolling sphere radius, mesh size, and protection angle (see Section 6.3); distances between down-conductors (see Section 6.4.2); minimum length of the earth electrodes (see Section 6.5.1); and separation distance against dangerous sparking (see Section 6.7).

The following parameters and protection measures are the same for all classes of LPS: ● ●



lightning equipotential bonding (see Section 6.6). material, form, minimum dimensions, and use of the LPS components, especially used for air-termination system and down-conductor system (see Section 6.4.3). minimum dimensions of connecting conductors (see Section 6.6.1).

It is recommended that electrically conductive parts of a building are used as socalled natural components of the LPS. Natural components are conductive parts installed not specially for lightning protection. For instance, natural components of the air-termination and down-conductor system are metal roofs, metal facades, or metal attics. The use of natural components requires that they always remain in/ on the structure, that they are not modified incorrectly, that they are interconnected correctly to other parts of the LPS, and that they fulfil the specifications of the LPS, e.g. regarding the minimum required cross-section of the material.

6.2.3

Surge protection measure (SPM) system

The function of the SPM system is to reduce the risk of damages, permanent failure and mal-function due to the LEMP within a structure. The systems to be protected are located inside of LPZ 1 or higher (Figure 6.7). (Note: The SPM system is

Lightning protection of structures and electrical systems inside

LPZ 0A

Lightning protection system (LPS)

Air-termination system

Structure (shield of LPZ 1)

LPZ 0 B Safety SPD 0 B/1 distance d s

Apparatus

Line connected to structure

239

LPZ 1 Room (shield of LPZ 2)

SPD 0A/1

ds

Down-conductor system

SPD 1/2 LPZ 2 Ground

SPD 1/2

Erdniveau SPD 0A/1 Line connected to structure Earth-termination system

Figure 6.7 Subdivision of a structure into different LPZs in order to build up the SPM

named LEMP protection measures system (LPMS) in older versions of the standard IEC 62305-4 [11].) The SPM is based on the following methods and principles: ● ●

● ● ●

LPZ concept: The structure is subdivided into LPZ 1 and higher. Improved grounding and equipotential bonding: The potential differences are minimized and the magnetic field may be reduced. Shielding: Spatial shields reduce the magnetic field inside the LPZ. Line routing: Improved wiring minimizes induction loops. Surge protection device (SPD): The use of coordinated SPD reduces the surges on lines at the boundary of the LPZ.

The LPS may act as spatial shield at the boundary between LPZ 0 and LPZ 1. Often an additional spatial shield is installed in order to increase the shielding efficiency. If such an additional shield is installed at the boundary between LPZ 0 and LPZ 1, no dangerous sparking inside the structure has to be considered. In this case, no separation distance (s) has to be taken into account, but a safety distance (ds) from the wall must be respected (see Figure 6.7). A safety distance from the wall (ds) is also necessary for LPZ 2 or higher (see Section 6.9). Figure 6.8 shows a typical situation in the case of a direct lightning strike to a building. The region outside of the building (in LPZ 0) is endangered by the unattenuated lightning field (H0) and by the lightning current (I0) up to the full level.

240

Lightning interaction with power systems, volume 2 Shield LPZ 1 Shield LPZ 2

Shield LPZ 3

LPZ 0

I0 , H 0

LPZ 1

LPZ 2

H2

H1

SPD 2/3

SPD 1/2

U2 , I2

U1 , I1

H0 SPD 0/1

LPZ 3 Apparatus, equipment

U0 , I0 Partial lightning current

Figure 6.8 Example for a structure equipped with a surge protection measure (SPM) system The un-attenuated magnetic field in LPZ 0 (H0) is reduced in LPZ 1 (H1) by the spatial shield located between LPZ 0 and LPZ 1. The magnetic field inside of LPZ 1 (H1) is further reduced in LPZ 2 (H2) by the spatial shield located between LPZ 1 and LPZ 2. The apparatus located in LPZ 2 has to withstand the (reduced) magnetic field (H2). If the apparatus has a metal housing, the magnetic field is further reduced and the apparatus itself may build up an LPZ 3. The lightning current (I0) is the primary source to harm the electric and electronic systems. The threat of the lightning current is given by the first positive impulse current with the waveshape 10/350 ms, the first negative return stroke current with the waveshape 1/200 ms, the subsequent impulse current with the waveshape 0.25/100 ms, and the long-duration current. The magnitude of the currents depends on the individual level, i.e. LPL I to LPL IV. The partial currents, which enter the LPZ 1, are reduced and the waveforms are changed due to the switching and limiting characteristics of the used surge protective devices (SPD; type SPD 0/1). Therefore, the surges (U1, I1) entering LPZ 1 depend essentially on the type of SPD, but not on the class of the LPS (or LPL). For the same reason, the surges entering LPZ 2 (U2, I2) may have very different wave shapes and magnitudes. Because the voltages and currents may be unipolar or oscillating, different test procedures are in use. SPD used in low power installation network between LPZ 1 and LPZ 2 (SPD 1/2) and higher (SPD 2/3) are commonly tested with impulse currents with the wave shape 8/20 ms and impulse voltages with the wave shape 1.2/50 ms. The effects due to the electric field couplings are generally very small when compared to the magnetic field coupling. The shields at the boundaries of the LPZs reduce the electric field to a greater extent compared to the magnetic field. Therefore, the threat of the electric field is taken into account by the protection measures against the magnetic field.

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241

6.3 Volume protected against direct lightning strike 6.3.1 Striking distance When a downward leader approaches an object on ground, an upward connecting leader is initiated from the object whenever the electric field exceeds a critical value. The connecting leader bridges the striking distance between the downward leader and the struck object. Weak lightning have smaller striking distances compared to strong lightning, because the charge of the downward leader of weak lightning is smaller and thus the electric field at the struck object is also smaller. According to IEC 62305-1 [1], the striking distance (r) of first return strokes can be calculated by the following formula: r ¼ 10ðimax Þ0:65 with r in m; imax in kA

(6.3)

With decreasing peak current (imax), the striking distance also decreases and thus the risk increases that the lightning penetrates the air-termination system and terminates at the volume to be protected. The accepted risk depends on the LPL. For each protection level (I–IV), a value for the peak current is fixed accepting that a lightning with smaller peak current may penetrate the air-termination system. In the highest LPL I, the peak current (imax) is fixed to 3 kA. It is accepted that currents with peak values lower than 3 kA may pass the air-termination system and terminate at the building to be protected. About 1% of the lightning have a peak value smaller than the fixed peak current of 3 kA. For LPL II, LPL III, and LPL IV the tolerable fraction of the lightning, which may pass the air-termination system, is increased to 3%, 9%, and 16%, respectively. Table 6.6 summarizes the fixed values for the peak current (imax), the probability that a lightning has smaller peak current, and the striking distance (r) for the four LPL I to LPL IV.

6.3.2 Rolling sphere method In IEC 62305-1 [1], the electro-geometric model is used to define the volume protected against direct lightning strike. The electro-geometric model is based on the assumption that a lightning strike occurs as soon as the tip of the downward Table 6.6 Fixed values for the peak current (imax), probability that a lightning has smaller peak current, and striking distance/rolling sphere radius according to IEC 62305-1 [1] Parameters for the interception of lightning

Lightning protection level (LPL) I

Fixed peak current (imax) (kA) 3 Probability for a current peak smaller than imax (%) 1 Striking distance/rolling sphere radius r (m) 20

II

III

IV

5 3 30

10 9 45

16 16 60

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leader arrives at the striking distance. The possible striking points can be detected by a sphere, which is rolled around and over the structure to be protected. Lightning strikes are only possible to such locations, which can be touched by the sphere. The radius of the rolling sphere is given by the striking distance (r). It is assumed that the subsequent return strokes follow the path of the first return stroke and have the same striking point as the first stroke. Therefore, only the first stroke has to be taken into account regarding possible striking points. Figure 6.9 shows an example on how to use the rolling sphere method. The points, which can be touched by the sphere, are endangered by direct lightning strike. The shaded areas mark possible striking points (LPZ 0A). The un-shaded areas cannot be touched by the sphere. They are not exposed to direct lightning strikes (LPZ 0B).

6.3.3

Simplifications of the rolling sphere method

The rolling sphere method requires either a computer model or a scale model of the structure to be protected. Because the development of such models is very timeconsuming and expensive, the rolling sphere model is simplified. Simplifications are the protection angle method and the mesh method.

6.3.3.1

Protection angle method

Figure 6.10 shows an example for the application of the protection angle method. According to the rolling sphere method, the volume is protected against direct stroke (LPZ 0B), if it remains below the curved surface of the sphere. Using the protection angle method, the piece of the curved surface from the top of the structure (h) to the ground reference plane is substituted by a straight line. The volume is protected against direct stroke (LPZ 0B), if it remains below the straight line. The protection angle (a) is the angle between the straight line and the vertical direction. The protection angle is chosen in such a way that the area A1 and the area A2 are equal. The protection angle a is given by the following formula: "pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  # h 2rh  h2 r 2rh  h2 r2 a ¼ arctan (6.4) þ  2 arccos 1  r h h2 h

Rolling sphere

Figure 6.9 Application of the rolling sphere method by dividing a structure into un-shaded areas protected against direct lightning strike (LPZ 0B) and shaded areas endangered by direct lightning strike (LPZ 0A)

Lightning protection of structures and electrical systems inside

Area A1 α h

243

r Boundary of the protected volume acc. to the protection angle method Boundary of the protected volume acc. to the rolling sphere method

Area A2 Ground reference plane

Figure 6.10 Comparison of the protected volume using the rolling sphere method and the protection angle method

Rolling sphere radius r Boundary of the rolling sphere

Air-termination conductor

Sag

Air-termination conductor

Figure 6.11 Comparison of the protected volume using the rolling sphere method and the mesh method The protection angle depends on the height of the structure (h) above a reference plane. The earth surface is commonly the reference plane, but for larger buildings, it may be necessary to define additional reference planes. If the structure is too complex, it is often not possible to find adequate reference planes. In this case, the protection angle method cannot be used. The protection angle method can also not be used, if the height of the structure exceeds the striking distance (h > r).

6.3.3.2 Mesh method The mesh method can be used for plane surfaces as for the flat roof of a building protected by a mesh of conductors. Figure 6.11 shows an example for the application of the mesh method. According to the mesh method, the volume below the air-termination conductors is protected against direct lightning strike (LPZ 0B). The mesh method requires that the distance between the air-termination conductors (mesh size) is relatively small. In this case, the sag built up by the curved surface of

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Lightning interaction with power systems, volume 2

Table 6.7 Rolling sphere radius and mesh size corresponding to the class of LPS Class of LPS

Rolling sphere radius r (m)

Mesh size (m)

I II II IV

20 30 45 60

55 10  10 15  15 20  20

the rolling sphere (between the air-termination conductors) can be neglected. Table 6.7 summarizes the maximum tolerable values of the mesh size for the four classes of LPS.

6.4 Air-termination and down-conductor system 6.4.1

Air-termination system

The function of the air-termination system is to intercept a lightning flash. The airtermination system can be composed by any combination of vertical and horizontal rods and wires and meshed conductors, including natural components. The components (rods, wires, etc.) should be connected together at roof level.

6.4.1.1

Positioning of the air-termination system

The air-termination system should be installed in such a way that the rest of the building is protected against direct lightning strikes. Components of the airtermination systems should be located especially at corners, edges, and exposed points of the building. For the detection of possible striking points and the positioning of the air-termination system, the rolling sphere method or the protection angle method or the mesh method can be used (see Section 6.3). The flammability of the roof structure is an important criterion for the design of the air-termination system. If the roof of the buildings consists of non-flammable or fire-resistant materials, a non-isolated air-termination system may be realized. In this case, the air-termination system (wires, rods, etc.) may be directly placed on the roof of the building. If the roof of the buildings contains combustible material, the air-termination system has to be isolated from the building by keeping a safety distance. The spacing between the air-termination system and the combustible material should be 10 cm at least. Electrical and electronic equipment and electrical conductors inside the building should not be installed with distances to the air-termination system shorter than the separation distance defined in Section 6.7. An isolated air-termination may be necessary in order to keep the required separation distance.

6.4.1.2

Natural components for the air-termination system

Metal components of the roof constructions can and should be used as natural components of the air-termination system. Examples for natural components are

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245

Table 6.8 Minimum thickness of metal sheets or metal pipes in air-termination systems Material

Minimum thickness to prevent Minimum thickness, if puncture is puncture t (mm) tolerable t0 (mm)

Lead Steel (stainless, galvanized) Titanium Copper Aluminium Zinc

– 4

2.0 0.5

4 5 7 –

0.5 0.5 0.65 0.7

metal sheets, metal ornamentations, railings, and rain gutters. Metal components of the roof construction as trusses may also be used. If metal sheets are used as natural components, it is important whether a puncture is tolerable. Puncture is not tolerable for readily combustible or explosive mixtures or materials in touch with the metal sheets, e.g. tanks with fuel. Puncture is also not tolerable for metallic pipes containing readily combustible or explosive materials. In this case, a minimum thickness of the metallic material is required to prevent puncture. Table 6.8 summarizes the minimum required thickness for typical materials depending on whether puncture is tolerable (thickness t0 ) or puncture should be prevented (thickness t).

6.4.2 Down-conductor system It is recommended that the down-conductors are installed in such a way that they form a direct continuation of the air-termination system. Several (parallel) current paths should exist from the striking point to ground. The length of the current paths should be as short as possible. A building is commonly equipped with several down conductors. At least, two down conductors are necessary. Table 6.9 contains typical values for the distance between down conductors according to the class of LPS. The values are recommendations and may change depending on the size of the building. If possible, a down conductor should be installed at each corner of the building. The use of natural components is recommended such as metal facades, the steel reinforcement, steel frame constructions, and other metallic constructions.

6.4.3 Materials and dimensions For typical materials, the dimensions and minimum cross-sectional areas of airtermination conductors, air-termination rods (Franklin rods), earth lead-in rods, and down-conductors are given in Table 6.10. For all materials, a minimum crosssectional area of 50 mm2 or more is required. For solid round materials, the crosssectional area of 50 mm2 meets the diameter of 8 mm.

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Lightning interaction with power systems, volume 2 Table 6.9 Typical values for the distance between down conductors according to the class of LPS Class of LPS

Typical distance (m)

I II III IV

10 10 15 20

Table 6.10 Materials, configuration, and minimum cross-sectional area of air-termination conductors, air-termination rods (Franklin rods), earth lead-in rods, and down-conductors (see [3]) Materials

Copper Tin-plated copper

Configuration

Minimum cross-sectional area (mm2)

Air-termination conductor, down conductors

Air-termination rods (Franklin rods), earth lead-in rods

Solid tape, solid round, stranded

Solid round

50 176

Solid tape, solid round, stranded

Solid round

50 176

Aluminium

Solid tape solid round, stranded

70 50

Aluminium alloy

Solid tape, solid round, stranded

Solid round

50 176

Hot-dipped galvanized steel

Solid tape, solid round, stranded

Solid round

50 176

Stainless steel

Solid tape, solid round Stranded Solid round

50 70 176

With respect to lightning protection, the cross-sectional area of 50 mm2 is only necessary for steel, whereas for copper a cross-sectional area of 16 mm2 and for aluminium a cross-sectional area of 25 mm2 would be sufficient to withstand the specific energy (10 MJ/W) of the highest lightning protection LPL I. The higher cross-sectional area covers the threat by mechanical stresses such as wind and snow load. The cross-sectional area may be reduced for conductors where mechanical strength is not an essential requirement. A higher cross-sectional area of 176 mm2 is required for air-termination rods (Franklin rods) in order to withstand the mechanical stress. For air-termination rods, where mechanical stress (wind load) is not critical, the use of a 9.5-mm diameter (3/8 in.) and 1-m long rod is recommended in IEC 62305-3 [3]. A higher cross-sectional area of 176 mm2 is also required for earth lead-in rods.

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247

6.5 Earth-termination system 6.5.1 Earth-termination system for the lightning protection system (LPS) Buildings are often equipped with more than one earth-termination system, e.g. one for the grounding of the power system and the other one for the grounding of the telecommunication system. If possible, the different earth-termination systems should be interconnected in order to build up a single integrated earth termination system for the total structure. The interconnection of the different earth termination systems lowers the earth resistance of the total earth-termination system. A low earth resistance is recommended of less than 10 W measured at low frequency (50 or 60 Hz). A reference length (l1) is introduced in order to qualify the earth-termination systems. In most cases, the reference length is not equal to the real length of the earth electrode. Figure 6.12 shows the reference length (l1) as a function of the soil resistivity (r). The reference length depends on the class of the LPS. For the LPSclasses III and IV, the reference length is fixed to 5 m, independently from the soil resistivity (r). For LPS-class I and LPS-class II, the reference length increases if the soil resistivity exceeds 500 and 800 W m, respectively. The following two basic types of earth electrode arrangements are considered: 1.

Arrangement A The type A arrangement is based on horizontal or vertical earth electrodes. An earth electrode should be connected to each of the down conductors. The total number of earth electrodes should not be less than 2. For each earth electrode, the following minimum length is required: lmin ¼ l1 ; for the horizontal electrode;

(6.5a)

lmin ¼ 0:5  l1 ; for each vertical electrode

(6.5b)

100 (m) 90 Class I

80 70 l1

60 50

Class II

40 30 20 10

Class III and IV

0 0

500

1,000

1,500

2,000 ρ

3,000 2,500 (Ωm)

Figure 6.12 Reference length (l1) of earth electrodes depending on the class of LPS and the soil resistivity r

248

2.

Lightning interaction with power systems, volume 2 The earth electrodes should be installed outside the structure at a depth of at least 0.5 m. Arrangement B The type B arrangement is based either on a ring conductor or on a foundation earth electrode. The mean radius (re) of the area enclosed by the ring conductor or the foundation earth electrode should be equal of higher than the reference length (l1): re  l1

(6.6)

If the reference length (l1) is greater than the mean radius (re), additional horizontal or vertical electrodes are necessary. The following values are recommended for the minimum length of each additional earth electrode: lr ¼ l1  re ; for each vertical electrode;

(6.7a)

lv ¼ 0:5ðl1  re Þ; for the vertical electrode;

(6.7b)

The number of such additional electrodes should not be less than the number of the down conductors. If an external ring electrode is installed, the ring electrode should be buried at a depth of at least 0.5 m. The material of the earth electrodes should be selected with respect to the resistance to corrosion in the soil. For typical materials, the form and the minimum dimensions of the earth electrodes are summarized in Table 6.11.

Table 6.11 Materials, form, and minimum dimensions of earth electrodes Materials

Form

Dimensions Earth rod diameter (mm)

Copper, tin-plated copper Hot-dipped galvanized steel Bare steel Copper-coated steel Stainless steel

Solid tape, solid round, stranded Solid round Pipe Solid round Pipe Solid tape Stranded Solid round Solid tape Solid round Solid tape Solid round Solid tape

Earth conductor (mm2) 50

15 20 14 25

14 15

78 90 70 78 75 50 90 78 100

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249

6.5.2 Improved earth-termination system for the surge protection measure (SPM) system The SPM requires that the earth-termination system for the LPS is already installed. Structures equipped with a type B earthing arrangement have normally a much better performance compared to structures equipped with a type A earthing arrangement. Therefore, the type B earthing arrangement is recommended for buildings, which require a higher protection level such as structures containing electronic systems. For structures, which contain only electrical systems, a type A earthing arrangement may be sufficient. The earth-termination system for the SPM has an additional function, because it is also part of the bonding network. It is recommended that the earth-termination system forms a meshed system of grounding electrodes. Figure 6.13 shows an example. The industrial plant comprises three buildings. Ring earth electrodes are installed around each of them. The ring earth electrode is integrated in the meshed earth-termination system as well as the buried cable ducts between the buildings. The mesh size should not be larger than 5 m in the close vicinity of the structures. It is recommended that the mesh is extended under the building by a meshed network with small mesh size. This can be achieved by using the reinforcement in the basement of the building.

C

Building 1

Building 3 R

R C

C

R Building 2

Figure 6.13 Meshed earth-termination system of an industrial plant (C, cable duct; R, ring earth electrode)

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Lightning interaction with power systems, volume 2

6.6 Lightning equipotential bonding 6.6.1

Lightning equipotential bonding required for LPS

Figure 6.14 shows the measures of the lightning equipotential bonding for the most common case of a non-isolated external LPS. The lightning equipotential bonding should be realized at the basement or at ground level. For this purpose, an equipotential bonding bar should be installed. The metallic service lines entering the structure should be connected to the equipotential bonding bar via bonding conductors. The bonding conductors should be as short as possible in order to minimize the voltage drop along the bonding conductors in the case of a lightning strike. The equipotential bonding bar must be connected to the earth-termination system via bonding conductors. Small buildings as dwelling-houses are commonly equipped by a single equipotential bonding bar. Large buildings as industrial buildings have often more than one equipotential SPD for information technology lines

Equipotential bonding bar

SPD for low voltage power supply

Supply voltage

Telecommunication system

Sewer pipe

Telephone Water metre

Water pipe Gas metre Gas Isolator

Isolating spark gap

Tank pipe, cathodic protected

Radio and television Foundation earth electrode

Figure 6.14 Lightning equipotential bonding at the entrance into the building (typically at the basement)

Lightning protection of structures and electrical systems inside

251

Table 6.12 Minimum cross-section of bonding conductors [3] Material

Copper Aluminium Steel

Bonding conductors connecting different equipotential bonding bars or connecting the bonding bar and the earth-termination system Cross-section (mm2)

Bonding conductors connecting internal installations and the equipotential bonding bar

16 25 50

6 10 16

Cross-section (mm2)

bonding bar. If several equipotential bonding bars are installed in a building, the equipotential bonding bars should be connected together by bonding conductors. The bonding conductors have to withstand the part of the lightning current, which may flow through them during the lightning strike. For the bonding conductors connecting different equipotential bonding bars or connecting the bonding bar and the earth-termination system, the current share is higher compared to the bonding conductors connecting internal installations and the equipotential bonding bar. Therefore, the required cross-sections are higher for bonding conductors connecting different equipotential bonding bars or connecting the bonding bar and the earth-termination system. Table 6.12 summarizes the minimum required cross-sections for the most common materials. The cross-sections are the same for all classes of LPS (LPS I–IV). The lightning equipotential bonding is realized via bonding conductors, which are either directly connected to the equipotential bonding bar or indirectly connected to the equipotential bonding bar by the use of SPD. The use of SPD is required, if no direct contact is possible as shown in Figure 6.14. The SPD makes contact only during the short period of the lightning discharge. The following rule applies for the direct and indirect connection: ●



Conductors and metal parts, which do not conduct currents during normal operation, should be directly connected to the bonding bar. For instance, metallic cable shields and the protective earth are directly connected. Live conductors, which conduct currents during normal operation, are indirectly connected to the bonding bar by the use of SPD. For instance, the phase conductors (L1, L2, and L3) and the neutral conductor (N) of the low-voltage power supply should be indirectly connected to the bonding bar by the use of SPD.

6.6.2 Lightning equipotential bonding according to the surge protection measure (SPM) system 6.6.2.1 Bonding network The lightning equipotential bonding system of the SPM is an improvement of the existing lightning equipotential bonding system of the LPS. The aim is to build up a meshed bonding network interconnected with the earth-termination system.

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Lightning interaction with power systems, volume 2

Figure 6.15 shows an example. The lightning equipotential bonding consists of a three-dimensional arrangement of meshed bonding wires, which are interconnected with each other and with the earth-termination system. A small mesh size minimizes the potential differences inside the building and reduces the overvoltages between the conductors of the individual lines. It also reduces the magnetic field inside of the LPZ. The three-dimensional bonding network should be realized with a mesh size not larger than about 5 m. The three-dimensional (equipotential) bonding network can be improved by integrating all conductive parts of the structure as natural components. Natural components are the concrete reinforcement, elevator rails, cranes, metal roofs, metal facades, metal frames of windows and doors, metal floor frames, service pipes, cable trays, etc. Bonding bars, magnetic shields, and the metal housing of the equipment should be integrated in the same way. An equipotential bonding bar should be installed in every internal LPZ (LPZ 1 and higher). All metallic components of the internal systems (metallic housings, racks, cabinets, etc.) should be connected to the equipotential bonding bar. The connecting lines, which enter the LPZ, should also be connected to the equipotential bonding bar either directly or indirectly by the use of SPD. If possible, the connecting lines should enter the structure at the same entry point. In this case, the connection lines can be connected to the same equipotential bonding bar, which should be located close to the entry point. If a common entry point cannot be realized, additional equipotential bonding bars should be installed at each entry point of the lines. The different equipotential bonding bars should be

Bonding network

Earth-termination system

Figure 6.15 Example for a three-dimensional bonding network with multiple interconnections to the earth-termination system

Lightning protection of structures and electrical systems inside

253

interconnected to each other. For this purpose, a ring bonding bar (ring conductor) is recommended.

6.6.2.2 Configuration of the bonding conductors The bonding conductors are commonly installed together with the electrical cables and lines. The bonding conductors may be arranged in the following ways: ● ●

Star point configuration S Meshed configuration M

Figure 6.16 shows the star point configuration S and the integration into the mesh of the bonding network. All cables and lines interconnecting the different apparatuses should run in parallel to the bonding conductors to the star point S in order to avoid induction loops. Grounding and bonding is only allowed at the star point S via direct and indirect (via SPD) connection to a bonding bar at the earthing reference point (ERP). In consequence, all metal parts of the electric and electronic system should be isolated from the earth potential. The isolation effects that no significant current flows through the connected lines and bonding conductors in the case of a lightning strike. The star point configuration S requires that all lines enter the LPZ at the star point S. In practice, this requirement can be fulfilled only for relatively small zones. Therefore, the star point configuration S is more or less restricted to small areas. Figure 6.17 shows the meshed configuration M and the integration into the mesh of the bonding network. If the meshed configuration M is used, it is not necessary that the metal parts of the electric and electronic system are isolated from the earth potential. On the contrary, they should be integrated into the bonding network by multiple connections. The meshed configuration M should be preferred ●





for internal systems extended over relatively wide zones or over the whole structure, if many lines and cables are used to interconnect the electric and electronical apparatuses, if lines and cables enter the structure at several locations.

Apparatus

Bonding network

Apparatus

Apparatus

Apparatus

Bonding conductor Apparatus

Apparatus

S, ERP (earthing reference point)

Figure 6.16 Star point configuration S and integration into the mesh of the bonding network

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Lightning interaction with power systems, volume 2

Bonding network

Apparatus

Apparatus

Apparatus

Apparatus

Apparatus

Apparatus

Figure 6.17 Meshed configuration M and integration into the mesh of the bonding network

Combination 1 App.

App.

Combination 2 App. Bonding network

App. App.

App.

App.

App.

App.

App.

App.

App.

ERP

ERP

App.

App.

App.

App.

App.

App.

App.

App.

App.

App.

App.

App.

Figure 6.18 Combination of the star point configuration S and the meshed configuration M and the integration into the mesh of the bonding network (App., apparatus) In the case of a lightning strike, it cannot be avoided that partial currents flow in the bonding conductors and through the connections between the apparatuses. On the other hand, the current share for an individual bonding conductor is minimized by multiple interconnections to the bonding network. The advantages of the star point configuration S and the meshed configuration M can be used if both configurations are combined. Figure 6.18 shows two basic arrangements for the combination of both configurations and the integration into the bonding network.

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255

Arrangement 1 shows a star point configuration where the lines interconnecting the different apparatuses run in parallel to the bonding conductors to the star point S. In configuration 2, the apparatuses are directly interconnected with each other and only one bonding wires is used for the connection to the bonding network at the ERP.

6.7 Separation distance In the case of direct lightning strike to a building, the lightning current flows through the external LPS to ground. The current generates high magnetic fields, which in turn induce high-voltage peaks up to several megavolts between the external LPS and internal installations. The high voltage may cause dangerous sparking between the external LPS and metal installations inside the building. Dangerous sparking can be avoided by keeping a separation distance between the external LPS and the conductive installations inside the building. The separation distance is the minimum clearance required at the proximity of conductive parts inside the building and the external LPS to avoid side flashes. For the calculation of the separation distance, the general equation is given by [3]: s ¼ ki 

kc l km

(6.8)

where l is the length; km is the material coefficient; ki is the current steepness coefficient; kc is the configuration coefficient. The length (l) is the distance along the air termination and the down conductor from the point, where the separation distance is to be considered, to the nearest equipotential bonding point or the earth termination. Figure 6.19 shows an example.

100% Air termination

Length l

s Separation distance 50%

50% Down conductor

Electrical installation

k c = 0.5

Figure 6.19 Separation distance (s) according to IEC 62305 [1,3]

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Lightning interaction with power systems, volume 2

Table 6.13 Values of the material coefficient km Materials

km

Air Concrete, bricks, and wood

1 0.5

Table 6.14 Value of the current steepness coefficient ki LPL/LPS

ki

I II III and IV

0.08 0.06 0.04

6.7.1

Material coefficient km

The material coefficient (km) takes into account the influence of different materials at the location of the proximity. For air km ¼ 1 applies. For real construction materials other than air (e.g. brick, concrete, etc.), this coefficient is reduced to the half and fixed to km ¼ 0.5. Table 6.13 contains the values for the material coefficient (km).

6.7.2

Current steepness coefficient ki

The current steepness coefficient (ki) takes into account the highest voltage expected at the proximity of a loop in air to a rod (see Figure 6.19). Because the voltage is determined by the steepness of the lightning current (u ~ di/dt) due to the magnetic coupling into open loops, the value of ki depends on the LPL and on the associated class of the LPS. Table 6.14 contains the values of the current steepness coefficient (ki).

6.7.3

Configuration coefficient kc

The configuration coefficient (kc) takes into account the percentual current share through the individual air-termination conductors/down conductors at the location where the separation distance is considered. Because the percentual current share does not depend on the magnitude of the lightning current, the configuration coefficient (kc) is the same for all classes of LPS. Figure 6.19 visualizes the configuration coefficient kc for the case of a simple building. Because half of the lightning current (50%) flows through each of the two down conductors, the configuration coefficient results in kc ¼ 0.5. The configuration coefficient kc can be determined only for very simple arrangements via simple equations. For more complex structures, the determination of the configuration coefficient kc requires the use of powerful computer codes. Therefore, in the standard IEC 62305-3 [3] two different approaches are given with respect to practical application.

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257

6.7.3.1 Simplified approach for the configuration coefficient kc The simplified approach is based on three basic arrangements for the airtermination conductors and the down conductors. The three arrangements give predefined values for the configuration coefficient kc considering typical one-, two-, or three-dimensional configuration of the air-termination and down-conductor system. They take into account the voltage, which is induced in an open loop with the length l by the magnetic field (see Figure 6.20). Figure 6.20(a) shows the one-dimensional arrangement. It is based on a direct lightning strike to a Franklin rod. Because the total current (100%) flows through the rod, the configuration coefficient results in kc ¼ 1. Figure 6.20(b) shows the second arrangement based on a corner strike to a two-dimensional structure of a meshed air-termination conductor/down conductor system. Because approximately 66% of the lightning current flows through the outer down conductor, that current share gives the value kc ¼ 0.66. Figure 6.20(c) shows the third arrangement based on a corner strike to a three-dimensional structure of a meshed air-termination conductor/down conductor system. Because the fraction of current flowing through the corner down conductor becomes about 44%, it results kc ¼ 0.44. For the three-dimensional structure (Figure 6.20(c)), the spacing between the down conductors and the length of the down conductors are given by the mesh size (w). In IEC 62305-3 annex C [3], an additional approach is given taking into account that the spacing between the down conductors (c) and the length of the down conductors (h) are different. The configuration coefficient (kc) is given by (n: total number of down conductors): 1 kc ¼ þ 0:1 þ 0:2  2n

rffiffiffi 3 c h

(6.9)

6.7.3.2 Detailed approach for the configuration coefficient kc For a three-dimensional structure with an air-termination mesh, the simplified approach may overestimate the configuration coefficient kc, if the lightning strike is to other locations than to the corner. For this purpose, a detailed approach is developed. The detailed approach is based on the assumption that the airtermination conductors and the down conductors have different values of currents flowing down their length (l1, l2, . . . ) due to current division. The detailed approach uses the following relationship: s¼

ki  ðkc1 l1 þ kc2 l2 þ    þ kcn ln Þ km

(6.10)

Assuming three different injection points for the lightning current (points A, B, C), Figure 6.21 shows an example for the calculation of the coefficients kc1, kc2, etc. At the injection point, the current and therefore the coefficient kc is divided by the number of possible current paths into the meshed air-termination system.

258

Lightning interaction with power systems, volume 2 i0 (t)

Franklin rod

Metallic/electric installation

s

Down conductor l

Loop

i0 (t)

kc = 1

(a)

i0 (t)

Air-termination wire s

Outer down conductor

w Loop

w l

Down conductor

0.66 • i0 (t)

kc = 0.66

(b)

Air-termination mesh Corner down conductor

i0 (t) w

0.44 • i0 (t)

s Loop

l (c)

w Down conductor

Down conductor

k c = 0.44

Figure 6.20 Separation distance (s) according to IEC-standard IEC 62305-3 [3]. Configuration coefficient for a typical (a) one-dimensional, (b) two-dimensional, and (c) three-dimensional air-termination and down-conductor system

Lightning protection of structures and electrical systems inside

Joint

kc3

1 16

1 8

kc2

kc1

1 4

kc1

kc2

1 4

kc3

1 8 kcn

1 2

259

1 16

B A

kcn

kc3

kcn

1 24 1 4

kc1

1

kc2

1 2

C

1 8

Down conductors Number of down conductors: n = 24 Injection points of the lightning current: A, B, C

Figure 6.21 Top view of a meshed air-termination system with 24 down conductors. The points A, B, C are the considered striking points Because the injection point A is connected to four wires, it results kc1 ¼ 0.25. Because the injection point B is connected to two wires, it results kc1 ¼ 0.5. For injection point C, it results kc1 ¼ 1, because the full lightning current flows through the air-termination conductor. At the next junction (joint) of the air-termination mesh the current is reduced to 50% and it results kc2 ¼ kc1/2. The current is reduced by 50% at any further joint of the air-termination mesh. The same rule applies for the junctions of the down-conductor system, but the value of kcn must not be less than 1/n (n: number of down conductors). Therefore, it results kcn ¼ 1/24 for the current injection in point A. The values of kc have to be considered from the point of strike to the edge of the roof using the shortest path. In Figure 6.21, the arrows indicate the paths from the different injection points of the current to the edge of the roof. The lengths of the arrows correspond to the length l1, l2, . . . , ln in (6.10).

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Lightning interaction with power systems, volume 2 Building 1 LPZ 1

LPZ 0 Building 2

Connection line it SPD 0/1

LPZ 1

SPD 0/1

Earth

it Earthing system

Earthing system

Figure 6.22 Unshielded connection line protected by SPD at the entrance of buildings Building 1 LPZ 1

Connection line Shield

LPZ 1

Building 2 it

LPZ 1 Earth it

Earthing system

Earthing system

Figure 6.23 Shielded connection line between two buildings

6.8 Currents and voltages on lines 6.8.1 Protection of connection lines at the entrance into LPZ Figure 6.22 shows two buildings, which are interconnected by an unshielded line. The line is located in LPZ 1 inside of the buildings and in LPZ 0 outside of the buildings. An essential current share (it) will flow along the connection line, if one of the buildings is struck by lightning. For unshielded connection lines, an SPD of type SPD 0/1 should be installed at the entrance of the line into the building. The same rule applies for unshielded connection lines between two LPZ 2 (or higher). If two LPZ 2 are interconnected via an unshielded connection line through LPZ 1, an SPD of type SPD 1/2 should be installed at the entrance of the line into LPZ 2. If two buildings are interconnected by a shielded line through LPZ 0, the volume inside of the shield belongs to LPZ 1. Therefore, the installation of SPD 0/1 is not necessary at the entrance of the building (Figure 6.23). The same rule applies for shielded connection lines between two LPZ 2 (or higher). If two LPZ 2 are interconnected via shielded connection line through LPZ 1, it is not necessary to install SPD 1/2 at the entrance of the line into LPZ 2. Figure 6.24 shows two basic arrangements for the connection between LPZ 0 and LPZ 2. If an unshielded connection line enters the building, it is necessary that a first SPD of type SPD 0/1 is installed at the entrance of the line into the building

Lightning protection of structures and electrical systems inside Example 1: Connection via unshielded line

261

Example 2: Connection via shielded line

LPZ 1

LPZ 1 LPZ 0

LPZ 2

LPZ 2

SPD 0/1/2

SPD 0/1

SPD 1/2 Unshielded line

Shielded line

Figure 6.24 Connection of LPZ 1 and LPZ 2 via unshielded and shielded line Metal shield s r

it

Conductor 2r + s ul

l

Figure 6.25 Voltage drop (ul) due to the current (it) flowing along the metal shield and that a second SPD of type SPD 1/2 is installed at the entrance of the line into LPZ 2 (example 1). If the line is shielded between LPZ 0 and LPZ 2, the volume inside of the shield belongs to LPZ 2. In this case, a combined SPD of type SPD 0/1/2 can be used at the entrance of the line into the building (example 2).

6.8.2 Shielded connection lines Shielded connection lines are either equipped with an outer metal shield or they run in metal pipes. In the case of a lightning strike, a fraction of the lightning current (it) will flow along the shield. The current flow causes a voltage drop (ul) between the shield and the conductors inside (Figure 6.25). The voltage drop is due to the coupling impedance (Z). For low frequency, the coupling impedance is given by the DC-resistance of the shield (Figure 6.26). For shields consisting of solid materials as metal pipes, the coupling impedance decreases with increasing frequency due to the skin effect. If the shield has openings, the coupling impedance increases at high frequency. The high-frequency field coupling through the openings can be ignored, if the openings are small enough as for common cables with braided shield. Thus, for the voltage drop (ul/max) the worst

Lightning interaction with power systems, volume 2

Coupling impedance |Z|

262

Shielded cable

RDC

Metal pipe Frequency f

Figure 6.26 Absolute value of the coupling impedance as a function of the frequency case is covered by taking into account the highest current share (it/max) and the coupling impedance by the DC-resistance (RDC): ul=max ¼ it=max  RDC

(6.11)

The DC-resistance RDC depends on the resistivity of the metallic material (r) and on the length (l), the thickness (s), and the radius (r) of the shield (see Figure 6.25). It is given by RDC ¼

rl p  s  ðs þ 2rÞ

(6.12)

The maximum voltage drop follows to ul=max ¼

rl  it=max p  s  ðs þ 2rÞ

(6.13)

Equation (6.11) applies for cable shield consisting of non-ferromagnetic materials such as aluminium and copper. Because ferromagnetic materials have a much higher permeability (mr), the ferromagnetic materials have a much better shielding effectiveness compared to non-ferromagnetic material. If (6.11) is used for ferromagnetic materials such as steel pipes, the voltage drop is commonly overestimated.

6.8.3

Lines in reinforced concrete cable duct

In industrial plants and power plants, large reinforced concrete tunnels are used as cable ducts for the routing of power, data, and control cables between individual buildings. Such cable ducts typically have inside dimensions of 2 m  2 m and are walkable for inspection purposes. The length of these cable ducts can vary from 10 m up to a 100 m, or so. At both ends, the reinforcement of the cable duct is connected to the reinforcement of the buildings. In the case of a direct lightning strike to one of the buildings, a fraction of the lightning current flows along the cable duct reinforcement coupling voltages and currents to the cables running inside.

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Table 6.15 Coupling impedance Z0 as a function of the type of lightning Arrangement

Type of lightning

Cable duct (2 m  2 m)

Negative subsequent stroke Negative first stroke Positive stroke

Front time T1 (ms) 0.25 1.0 10

Coupling impedance per length Z0 (mV/m) 0.50 0.30 0.08

Similar to shielded connection lines, the current through the reinforcement causes a voltage drop along the lines running inside of the cable duct. The induced voltage depends on the coupling impedance per length of the cable duct (Z0 ), on the length of the cable duct (l), and on the current share (it) flowing through the reinforcement of the cable duct. The maximum of the induced voltage is given by ul=max ¼ it=max  Z 0  l

(6.14)

Table 6.15 contains values for the coupling impedance per length (Z 0 ) according to the German standard for nuclear power plants [12]. The coupling impedance as a function of the frequency depends on the wave shape of the lightning current. Therefore, the values for the coupling impedance per length (Z 0 ) are different for the negative subsequent stroke, the negative first stroke, and the positive stroke. Common cable ducts consist of several segments with expansion joints in between. Each expansion joint increases the induced voltage because the shield (reinforcement) is interrupted at that location. To remedy this situation, the expansion joints are bridged by conducting connections. The shielding effectiveness increases with increasing number of bridging connections, i.e. the voltage drop caused by the expansion joints is lowered with increasing number of the bridging connections. The voltage drop caused by the expansion joints behaves as if the cable channel is prolonged. The prolongation is taken into account by an equivalent length, which has to be added to the real length of the cable duct for each expansion joint in (6.14). Table 6.16 summarizes the values for the equivalent length (lDF). The equivalent length decreases with increasing number of bridging connections. For instance, if a cable duct consists of four segments with three expansion joints, the equivalent length has to be taken into account three times. If eight bridging connections are installed at each expansion point, the cable duct is prolonged by 3  30 m ¼ 90 m considering the current of the negative subsequent stroke (see Table 6.16). Considering the first negative stroke, the cable duct is prolonged by 3  20 ¼ 60 m.

6.8.4 Current share on lines in case of direct lightning In the case of a direct lightning to a building, a part of the lightning current flows to ground via the earthing system. The other part of the lightning current is diverted to the electrical and metallic service lines connected to the building. In order to cover the worst case, it is assumed that one half of the lightning current flows into the

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Lightning interaction with power systems, volume 2

Table 6.16 Equivalent length lDF as a function of the number of expansion joint bridging connections Type of lightning

Front time T 1 (ms)

Negative 0.25 subsequent stroke Negative first 1.0 stroke Positive 10 stroke

Equivalent length lDF (m) Sixteen bridging connections

Eight bridging connections

Four bridging connections

Two bridging connections

15

30

50

70

10

20

35

55

5

10

20

30

earth-termination system of the struck building and the other half of the current is distributed to the service lines connected to the building. In a simple approach, it is further assumed that each connection line carries the same amount of current [1]. The fraction of the lightning current flowing on each line is given by (n: number of connection lines): 0:5 (6.15) n For an unshielded connection line, it is assumed that each of the conductors of the line carries an equal part of the lightning current. The fraction of the lightning current flowing on each conductor of the connection line is given by (n0 : number of conductors): ke ¼

ke0 ¼

ke n0

(6.16)

For shielded lines or lines in a metal conduit (metal pipe, cable duct), the fraction of the lightning current flowing on each of the inner conductors depends on the resistance of the shield (Rs) and on the resistance of the inner conductors (Rc). It is given by ke0 ¼

6.8.5

n0

ke  R s  R s þ Rc

(6.17)

Reduction of the induced over-voltage on internal lines by line routing

Over-voltage on internal lines can be reduced by suitable line routing. It should be avoided that the different connection lines (power supply line, data line) form large induction loops (Figure 6.27, left picture). The connection lines should be installed close to each other (Figure 6.27, right picture), and they should be routed close to the metal components of the bonding network. It is recommended to run the connection lines in metal enclosures as U-shaped conduits or the like.

Lightning protection of structures and electrical systems inside

Apparatus 2

Induction loop

265

Apparatus Induction loop

1

1

2

Apparatus

Apparatus

1: Power supply line

2: Data line

Figure 6.27 Reducing the induction loop area by line routing

6.9 Grid-like spatial shield The concept of LPZ requires that (the electric and) the magnetic field is attenuated by shields at the boundary of the LPZ. Large volume shields are usually composed of natural components such as the metal framework, the metal roof, the metal facade, and the metal reinforcement in the ceilings, walls, and floor. The metal reinforcement of buildings should be used as grid-like spatial shield, shown in Figure 6.28. The individual metallic rods should be interconnected with each other at the intersection points by welding or clamping. A practical approach might be a defined connection at about every 1 m. Because in practice the different layers of reinforcement touch each other at more points, the parts of the reinforcement have much more ‘natural’ contact points. Therefore, the mesh size (w) is commonly much smaller. The threat of the magnetic field involves the following scenarios: ●



In the case of a direct lightning strike, the volume inside the structure is exposed to the magnetic field generated by the lightning current flowing through the reinforcement. In the case of a nearby lightning, the volume inside the structure is exposed to the magnetic field attenuated by the reinforcement.

6.9.1 Magnetic field inside LPZ 1 in the case of a direct lightning strike Figure 6.29 shows the situation inside of LPZ 1 in the case of a direct lightning strike to the roof of a building. A grid-like spatial shield is installed at the boundary between LPZ 0 and LPZ 1. The magnetic field strength H1 at a location inside LPZ 1 is given by the following formula [4]: H1 ¼ 0:01 

i0  w pffiffiffiffi ðA=mÞ dw  dr

(6.18)

where dr is the shortest distance to the roof (m); dw is the shortest distance to the wall (m); w is the mesh width (m); i0 is the lightning current (A).

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Lightning interaction with power systems, volume 2 Mesh width w Direct lightning strike

Nearby lightning strike

Figure 6.28 Grid-like spatial shield Direct lightning strike

Lightning current i0

Roof

LPZ 0 LPZ 1

dr

Wall dw

H1

Figure 6.29 Situation for LPZ 1 in the case of a direct lightning strike to the roof of a building A minimum safety distance (ds/1) should be kept form the shield at the wall and at the roof. The minimum safety distance is given by (w: mesh size): ds=1 ¼ w

6.9.2

(6.19)

Magnetic field inside LPZ 1 in the case of a nearby lightning strike

Figure 6.30 shows the situation inside LPZ 1 in the case of a nearby lightning. A grid-like spatial shield is installed at the boundary between LPZ 0 and LPZ 1. In a

Lightning protection of structures and electrical systems inside Nearby lightning

Magnetic field H0

LPZ 0

Magnetic field H1

LPZ 1

Lightning current i0 sa

267

Centre

Figure 6.30 Situation for LPZ 1 in the case of a nearby lightning strike first step, the un-attenuated magnetic field outside of the building (H0) is calculated for the distance from the striking point to the centre of the shielded volume (sa). With the total lightning current (i0), the un-attenuated magnetic field (outside of the building) is given by [4]: H0 ¼

1 1   io ðtÞ 2p sa

(6.20)

In a second step, the attenuated magnetic field inside of the building (H1) is evaluated from the un-attenuated magnetic field (H0) considering the shielding factor (SF) of the grid-like shield. The attenuated magnetic field inside of the building (H1) is given by [4]: H1 ¼

H0

(6.21)

SF

1020

where H1 applies for all locations inside the building. A minimum safety distance (ds/2) should be kept from the shield at the wall and at the roof. The minimum safety distance is given by [4]: ds=2 ¼ w  ds=2 ¼ w

SF for SF  10 10

(6.22a)

for SF < 10

(6.22b)

Table 6.17 contains the SF in (dB) for the materials copper, aluminium, and steel. In the case of steel, the SF is different for the first positive return stroke. For the minimum safety distance (6.22a) and (6.22b), the higher value should be considered.

6.9.3 Magnetic field inside LPZ 2 and higher Figure 6.31 shows the situation inside LPZ 2 in the case of a direct and nearby lightning strike. Grid-like spatial shields are installed at the boundaries between LPZ 0 and LPZ 1 and between LPZ 1 and LPZ 2. In a first step, the magnetic field (H1) is evaluated inside of LPZ 1. In the case of a direct strike to the building, the magnetic field (H1) is calculated using (6.18). The parameters dr and dw represent the shortest distances from the shield at the roof and at the wall. In the case of a nearby strike, the magnetic field (H1) is calculated using (6.20) and (6.21).

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Lightning interaction with power systems, volume 2

Table 6.17 Shielding factor of a grid-like shield Materials

First positive return stroke

First negative return stroke, subsequent negative return stroke

Copper, aluminium Steel

SF ¼ 20  logð8:5=wÞ

SF ¼ 20  logð8:5=wÞ

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi SF ¼ 20  logðð8:5=wÞ= 1 þ ð18  106 =r2 ÞÞ

SF ¼ 20  logð8:5=wÞ

SF, shielding factor (dB); w, mesh with of the grid-like shield (m); r, radius of a rod of the grid-like shield (m).

Roof

Direct lightning

LPZ 0 LPZ 1 dr

H1

Wall dw

LPZ 2 H2 Nearby lightning

Figure 6.31 Situation for LPZ 2 in the case of a direct and nearby lightning strike In a second step, the attenuated magnetic field inside of LPZ 2 (H2) is evaluated from the magnetic field inside of LPZ 1 (H1). It is considered that no or no significant lightning current flows through the grid-like shield between LPZ 1 and LPZ 2. With the SF according to Table 6.17, the magnetic field inside of LPZ 2 (H2) is given by [4]: H2 ¼

H1 SF

1020

(6.23)

References [1]

IEC 62305-1. Protection against lightning – Part 1: General principles. 2nd edn. Geneva: International Electrotechnical Commission; 2010. [2] IEC 62305-2. Protection against lightning – Part 2: Risk management. 2nd edn. Geneva: International Electrotechnical Commission; 2010. [3] IEC 62305-3. Protection against lightning – Part 3: Physical damage to structures and life hazard. 2nd edn. Geneva: International Electrotechnical Commission; 2010.

Lightning protection of structures and electrical systems inside [4]

[5] [6] [7]

[8] [9] [10] [11]

[12]

269

IEC 62305-4. Protection against lightning – Part 4: Electrical and electronic systems within structures. 2nd edn. Geneva: International Electrotechnical Commission; 2010. Fisher F. A., Plumer J. A., and Perala R. A. Lightning protection of aircraft. 2nd edn. Pittsfield: Lightning Technologies Inc.; 2004. EUROCAE ED-91. Aircraft lightning zoning standard. Paris: European Organization for Civil Aviation Equipment; 1998. EUROCAE ED-84. Aircraft lightning environment and related test waveforms standard. Paris: European Organization for Civil Aviation Equipment; 2013. IEC 62305-1. Protection against lightning – Part 1: General principles. 1st edn. Geneva: International Electrotechnical Commission; 2006. Berger K., Anderson R. B., and Kroeninger H. ‘Parameters of lightning flashes’. Electra. 1975, vol. 41, pp. 23–37. Anderson R. B., and Eriksson A. J. ‘Lightning parameters for engineering application’. Electra. 1980, vol. 69, pp. 65–102. IEC 62305-4. Protection against lightning – Part 4: Electrical and electronic systems within structures. 1st edn. Geneva: International Electrotechnical Commission; 2006. KTA 2206. Design of nuclear power plants against damaging effects from lightning. Salzgitter: Kerntechnischer Ausschuss; 2009.

Chapter 7

Lightning protection of Smart Grids William A. Chisholm1 and Kenneth L. Cummins2

The popular term Smart Grid describes the benefits that can accrue from the overlay of pervasive communications infrastructure onto the existing electric power system technologies. What distinguishes a Smart Grid from a conventional grid, using proportional/integral/derivative control strategies, is the modern possibility of reliable and low-cost two-way communication. As one example, a multi-tariff metre is intended to shift customer consumption to off-peak periods overnight compared to daytime and early evening. There is a considerable financial incentive, on the order of $2/W in avoided generation cost, to a utility that manages consumption in this way. However, a multi-tariff metre is not ‘smart’ until its interface can inform the utility in real time and change its setpoints, for example allowing different off-peak periods in summer and winter. Smart Meters provide two-way automatic metering infrastructure that allows frequent transmission of meter measurements over dedicated, secure communication networks. This extends the Smart Meter capability from simple readout of consumption to include advanced reporting of the location and extent of distributionlevel outages, which leads to faster restoration of service and supports more precise historical analyses. It is predicted that the number of Smart Meters will exceed the number of automobiles, both slightly above 1 billion, in 2022. Electrical utility engineers who were already employed in 2005, when the term Smart Grid became popular, will insist that the grid has always been ‘smart’ [1]. Some of the first cathode ray oscilloscopes were applied, just after invention, to measure lightning surge voltages on power lines in the 1920s and 1930s. One of the first applications of lightning location systems (LLSs), based on wideband radiated fields, was to provide situational awareness to power system operators, who used the intelligence to turn on and turn off storm limits on a timely basis. This has been a successful Smart Grid initiative since the 1980s, as it effectively combines local intelligence in the sensors with two-way communication, sophisticated remote data processing and presentation of results using a graphical user interface.

1 2

Consultant, Toronto, Ontario, Canada Department of Hydrology and Atmospheric Sciences, University of Arizona, Tucson, USA

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Lightning interaction with power systems, volume 2

In this chapter, a broad view of ‘lightning protection’ includes the use of lightning in all proactive protection strategies. A summary of measurement technologies used on electric power systems and achievements of research campaigns will show the origins of some traditional surge waveforms, such as the 1.2/50 standard lightning impulse voltage wave, from nearly 100 years ago. Some of these methods and many results still apply to present-day Smart Grid component protection. We also cover the sequential evolution of the following: ●

● ●

Traditional travelling wave systems (TWS) for finding faults along individual cables and lines, from 1940s. The modern LLS based on travelling waves in two dimensions, from 1980s. The recent wide-area power system monitoring and measurement systems, using time-synchronized measurements of voltage and current phasors (synchrophasors) from 2005, classed as a ‘Smart Grid’ initiative.

7.1 Introduction: history of power system technologies The perception that the world’s most complex and important machine, its electric power system, was somehow ‘not smart’ prior to 2005 can be dispelled by reviewing the continuous application of math and science over its 125-year history.

7.1.1

Electric power systems and mathematics

Many branches of engineering and science, including lightning protection, rely on empirical models, where mathematical formulas are fitted to observations. Empirical models also have some important roles in electrical engineering, but the basic behaviour of power systems is well described by closed-form equations with analytic solutions. Gibbs [2] set out the mathematics behind the ‘Watt’ centrifugal mechanical governor system for proportional control of water turbines in its earliest form, a set of revolving steel balls linked to a vertical spindle. Gibbs also described the overshoot that occurs when summing the Fourier series at a discontinuity, in a process more familiar to electrical engineers. Three-phase AC power, eliminating the need for return wires and allowing transformation to high voltage at lower current to minimize losses, and its phasor analysis by Steinmetz were also rather ‘smart’ ideas exploiting the mathematics of their times. Electric power has retained closer links to mathematics than many other branches of engineering, partly because the problems are tractable but also because feedback is available in the form of precise, low-cost System Control and Data Acquisition (SCADA) observations. Stability and load flow analysis for large networks of overhead lines are poorly conditioned, large mathematical problems that can now be solved on a minute-by-minute basis to support operational decisions at many utilities. This dependence on mathematics and precise control will only increase as Smart Grid technology evolves to deliver datasets of reliable, continuous observations of the system state at every node.

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7.1.2 Electric power systems and communication 7.1.2.1 Power system frequency AC grids have always provided a common channel of communication, in the form of the frequency of operation. Individual generators can maintain constant frequency. Flow of power affects the phase angles of voltages and currents within power system. Individual control systems for generators react to local measurements of the deviation of frequency from a 50- or 60-Hz setpoint. Small generators such as photovoltaic systems may use ‘bang-on bang-off’ control, interrupting power when the frequency is measured to be outside a desired range. Medium-sized generators originally used centrifugal governors, the revolving-ball technology borrowed from steam engines, to achieve automatic proportional control and constant rotation speed [2]. Since the 1970s, electronic controls for large generators also react to the rate of change of frequency (ROCOF), giving the advantages of derivative control such as superior damping of oscillations. Constant power system frequency allows synchronization of multiple generators to provide a diverse and robust energy supply. As loads are added to such a network, the power system frequency slows down. On a time scale of hours, power system operators provide integral control actions by monitoring the cumulative deviation of power frequency cycles against a reference clock. Operators may run the system frequency a bit faster than setpoint to bring synchronous clocks back to the correct time.

7.1.2.2 Dedicated pilot wire systems for relay protection Communication between relay systems via pilot wire was explored for power system protection in the 1920s. Advantages included immunity to faults outside of the zone between the sensors, response that was independent of load current, fast detection of both phase and ground faults and simple construction with no need for measuring the line voltage. The ‘Translay’ [3] in Figure 7.1 used a pair of wires to Current transformer

Current transformer

10

10a

20

20a

11

11a

15

12

15a

12a 18

18a

24

13

13a

16

16a

24a

Pilot wires

Figure 7.1 Twin pilot-wire protection scheme for single-phase feeder [3]

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Lightning interaction with power systems, volume 2

trip the circuit breakers when there was a difference between currents between source and load. Limitations of the pilot-wire system, using end to end communication, were the cost of the wire pair, including neutralizing transformers to mitigate ground potential rise (GPR) at substations, the need for closely matched current transformer characteristics and the need to ensure that there was continuity in the pilot wire loop.

7.1.2.3

Plain old telephone service

Remote control of the UK power network in 1936 made use of 150 automatic systems linking transformer and generating stations to a National Control Centre in London [4]. Instruments showing the ROCOF were added in 1947. By 1958 [5], the original UK system was standardized to use ordinary-grade post office (telephone) lines with (a) earth-return phantom DC signals for low-traffic purpose and (b) above-speech voice frequency signal with time-division multiplex 50-baud transmission, giving ten continuous readings for a single channel with 120-Hz bandwidth. The quick response of telephone service providers after reporting outages was cited as an advantage over dedicated circuits, owned and maintained by the utility. Standardization of control systems was more difficult on the European continent, with different standards for plain old telephone service (POTS) in different countries. France, Belgium, Holland, Federal Germany, Switzerland and Italy resolved these problems and joined to form a 35-GW network control system on 18 December 1957. Reliability of POTS has often been excellent, but scalability to serve the needs of Smart Grid initiatives is limited compared to modern wireless alternatives.

7.1.2.4

Power line carrier

Power line carrier (PLC) technology that ‘rode for free’ on phase conductors was also explored starting in 1923 to provide end-to-end communication along power lines [6]. A transmission line phase has about 400 W surge impedance, and an attenuation of about 0.04 dB/km at 20 kHz, or 0.1 dB/km at 150 kHz. In contrast, an underground cable has lower surge impedance of 20–30 W and higher, constant attenuation of 1.6 dB/km from 40 to 200 kHz. PLC systems offered a limited number of channels and, in service, proved to be sensitive to disturbances including induced lightning overvoltages. Interest in PLC has waxed and waned and was most recently covered in IEEE P1901-2010TM standards for narrowband and broadband over power lines.

7.1.2.5

Microwave networks

Even in 1950 [7], it proved less expensive and more reliable to commission microwave stations, operating in 1.7–1.85 GHz, to serve utility communication requirements involving four or more carrier channels, than to use PLC. However, microwave towers installed in substations are tall enough to attract significant lightning activity. One preferred configuration for lightning protection in Figure 7.2

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(b)

(a)

(c)

Figure 7.2 Typical electrical substation microwave tower, with lightning protection details (a) electrical utility microwave tower, (b) equipotential bonding bar for incoming services and (c) location of microwave shed inside tower legs

places the microwave transceivers in a shielded metallic enclosure, located inside the legs of the structure. The outer and inner steel lattice elements of the tower provide a pair of Faraday cages for electromagnetic (EM) shielding as well as protection from direct strokes. By the 1980s, the microwave bands assigned to utilities were saturated, with increasing demand for protection and control data streams. At the same time, analogue telecommunication equipment was being replaced by digital systems, and penetration of computers into society called for increased system reliability and fewer momentary voltage dips. These led to widespread adoption of optical fibre communication technology within electric utilities.

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7.1.2.6

Fibre optic networks

The most recent advances in power system communication involved the deployment of optical fibres, usually placed in buffer tubes inside optical fibre groundwires (OPGW). The OPGW are located above the phase conductors and are normally at earth potential, as their main function is to shield the phases from direct lightning strokes. In some cases, where reliability is not important, all-dielectric self-supporting cables are strung on towers. Optical fibres offer immunity to EM fields, no fading from heavy rain – a problem with microwave systems – and high bandwidth of Gb/s. Single-mode dispersion-shifted fibres gave low dispersion and low attenuation at 1,550 nm. The original version of the IEEE Standard on OPGW (1138-1994TM) mentioned lightning in one place. The same year [8], OPGW service experience in Japan, dating back to 1983, suggested a damage rate of 0.08 (100 km)1 year1. Several forms of lightning-resistant construction were proposed. The present version of Standard 1138-2009TM states, ‘An OPGW cable shall be designed so that lightning arcs striking the cable do not impair the long term functionality . . . ’. To this end, the IEEE adopted the IEC 60794-1-2 Method H2 test, applying a pulse current of 0.5 s duration to deliver charge of 50, 100, 150 or 200 Coulomb to the tensioned cable. After the damaging arc ablation, the remaining strength of the OPGW must remain above 75% of its rated tensile strength, and any increase in fibre attenuation is limited to 0.05 dB per fibre. In the 1990s, many utilities installed OPGW containing many individual fibres, with 48 or 96 being common. Improvements in optical technology made some of these investments obsolete in the new millennium, as it became practical to multiplex many optical channels on the same fibre.

7.1.2.7

Standards for lightning protection of Smart Grid communication systems

Smart Grid implementations imply widespread, broadband and reliable communications. Standards exist to balance these requirements against costs. As an example, lightning protection of communication systems applied to Smart Grids is covered by the IEEE 487TM series of standards, which are organized by technology as follows: ● ● ● ●

● ●

IEEE Std 487TM for general considerations; IEEE Std 487.1TM for applications using on-grid isolation equipment; IEEE Std 487.2TM for applications consisting entirely of optical fibre cables; IEEE Std 487.3TM for applications of hybrid facilities where part of the circuit is on metallic wireline and the remainder of the circuit is on optical fibre cable; IEEE Std 487.4TM for applications using neutralizing transformers; and IEEE Std 487.5TM for applications using isolation transformers.

7.1.3

Electric power systems and lightning measurements

Over the centuries, application of each new measurement technology to overhead power line lightning research, design and operation has a productive history. These

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applications reflected a fundamental understanding that to mitigate lightning effects, we needed to understand and quantify them. In this section, we review the technologies and results that led to modern lightning protection standards. The first sensitive detector of EM waves, a Branly ‘coherer’ of 1890 [9], was used by Popov in 1894 to detect EM waves from lightning. One of the first uses of the Norinder cathode ray oscilloscope was to measure overvoltages on overhead lines caused by direct strokes from natural lightning [10]. Radio direction-finding of remote thunderstorms used crossed-loop antennas and receivers tuned to 30 kHz in 1947 [11]. Through the 1940s and 1950s, there were at least 12 different designs of lightning flash counters (LFC) that register individual signals for every flash within 3–30 km [12]. These were the focus of CIGRE standardization in the late 1960s. First, a 500-Hz design with horizontal antenna responded to signals exceeding 5 V/m [13]. Later, a vertical-antenna design with filtering at 10 kHz and sensitivity of 27 V/m provided a calibrated range of 20 km [14] and improved rejection of signals from cloud-to-cloud activity. Real-time data from LFC helped some utilities to arm specific countermeasures for mitigating anticipated lightning outages on their transmission lines. These countermeasures included dispatch of additional spinning reserve, as well as reduction in power flow from remote sources, to ensure post-fault stability of the entire network. Without real-time lightning data from LFC at substations, these protective measures were ●



initiated as reactive measures after the first-line lightning faults from passing storms were observed within a network or initiated in anticipation of a lightning storm in a grid square, based on weather observations that had reporting delays of 1–4 h [15].

Single-station detection of lightning strokes [16] evolved to LLS networks of gated wideband receivers and digitizers in the 1980s [17]. Tracking of lightning location and the presentation of storm movement using wide-area monitoring and visualization were adopted in the operations of many utilities. The real-time data from LLS helped utilities minimize the use of some pre-existing adaptive protection measures such as flow restrictions and simultaneous generation/load rejection schemes as lightning storms were observed to move past critical transmission systems. Analysis of line faults after-the-fact based on synchronized records of peak EM fields [18] provided greater discrimination of fault location as well as better precision in the assessment of vulnerability to shielding and backflashover failures [19]. These asset management tools can support decisions about repair and maintenance priority for all components in electrical networks [20]. In the evolution of sensing and measurement technologies, digital systems to record power-line transients in the presence of triggered or natural lightning [18] were deployed across networks starting in the early 1990s [21]. These had lower cost of operation than travelling wave fault recording systems of the 1940s [22] based on oscilloscopes and robot film cameras. Programmes deploying hundreds of digitizer channels have delivered important results in lightning research programmes lasting a decade or more [23].

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7.2 Smart Grid functions and technologies The Smart Grid is a basket of technology applications, bringing digital processing and communications to the electric power grid. These applications have many objectives, including provision of superior power quality (PQ), improved selfhealing and efficiency, and higher component load factors. The term became popular in 2005 [24] to describe systems that fit between the traditional protection systems, operating rapidly and having limited interaction with other nearby devices, and the centralized SCADA and ‘Energy Management Systems’ monitoring many variables over an extended grid area. The Smart Grid is viewed as a new integration of digital technologies, communications and controls into electric power networks to improve safety, security, reliability and efficiency. The concept of an electrical system where both sources and loads can be monitored and controlled in real time differentiates the new initiatives from present practice. Smart Grid functions and technologies, defined in [25], illustrate some of the specific roles that lightning research plays in successful integration of digital technologies into electric power systems. The subsections that follow describe these roles in more detail.

7.2.1

Wide-area monitoring and visualization

Wide-area monitoring and visualization consolidate data from time-synchronized sensors using communications and information processing to observe and understand the condition with enough lead time to take effective corrective actions. Interestingly, this statement is equally applicable to the power system as a whole and to LLS that contributes to system protection and operation. LLS, with networks of 10–200 receivers, represents one of the earliest widearea monitoring technologies, adopted by electrical utilities starting in the 1980s. Early utility applications included dispatch of repair crews, but the data also proved its value in setting and de-activating storm limits [26]. Movement of lightning ground flash locations in relation to line corridors is a common and useful display of real-time data in all modern electrical utility control rooms. New methods for consolidating electrical power system voltage, current and phase data, such as the PowerWorld software [27], can display deviation from nominal voltage, load and phase angle as coloured contour plots. These improve situational awareness of power system operators in real time, helping them to identify transmission congestion and stability issues in the time scale of hours. Networks of phasor measurement units (PMUs) that support wide-area monitoring of phase angle seem to be following a development and integration path rather like that of LLSs. The PMU sensors were first developed in 1988 [28], compared to gated wideband lightning technology in 1976 [16]. The first synchrophasor standard, IEEE 1344, was published in 1995 and updated after the August 2003 East Coast NA blackout as IEEE C37.117-2005. A west-coast PMU network described in 2007 [29] expanded in late 2009 into a cooperative, sparse

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2015

Legend Networked PMU locations Installed PMU locations Transmission owner data concentrator Regional data concentrator

Figure 7.3 Networked PMUs in North America Increased from 166 in 2009 to over 1,700 in 2015 [30] continent-wide USA network shown in Figure 7.3. A factor-of-ten increase in sensor count was reported for the PMU network in 2015 [30]. Deployments around the world followed similar patterns. In China, 300 PMU were installed in 2007 [31], with state financial support of $US 12 million, and more than 2,400 installed by 2013. A recent survey of PMU deployments around the world [32] recognizes the following enabling technologies: ●





Reliance on one pulse per second signals from Global Positioning System (GPS) receivers for 1 ms coincidence. Synchronization through Ethernet computer networks using the Precision Time Protocol in IEEE Standards 1588-2008 and C37.238-2011. Reporting at frame rates Fs (frames/s) from 10 Hz to the power system frequency (50 or 60 Hz) with latency of 2/Fs for protection purposes and 5/Fs for precision measurements.

The 2015 deployment of PMU in Figure 7.3 represents an investment exceeding $US 357 million and was cited as the first time that many independent system operators (ISO) and regional transmission operators (RTO) in North America cooperated to enable data sharing and visibility across the continent [30]. However, the PMU deployment is not the first time that these electrical utilities have cooperated in a continent-wide situational awareness initiative. The evolution of the National Lightning Detection Network (NLDN) in the USA migrated from an east coast network, active in 1984 [17], to full coverage in 1989 as shown in Figure 7.4. The PMU network in Figure 7.3 from 2009 is like the 1988 configuration of lightning sensors in Figure 7.4, reflecting a 20-year delay in mature implementation of the later technology. Both systems take advantage of GPS satellite time synchronization, which achieved an order-of-magnitude improvement in precision in May 2000 to the 10-ns level when ‘selective availability’ degradation was abandoned [34].

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1985

1987

1986 1988 Lightning Detection Network coverage

Figure 7.4 Evolution of National Lightning Detection Network coverage [1,33]

CLDN NLDN IMPACT TOA

Figure 7.5 Lightning location stations in North America, 1998 [35] One of the lessons learned in the integration of lightning location networks [33,35] was that participation of sensors outside the region of interest was fundamental to achieving good accuracy, resolution and fault tolerance when a few receivers are out of service. The present configuration of the North American Lightning Detection Network in Figure 7.5 demonstrates this preferred approach with uniform baseline coverage and central management of all sensors from Arizona [35].

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Another possible lesson applicable to Smart Grid protection that can be learned from the evolution of the NLDN [33] was that utilities and universities eventually grew tired of the day-to-day operation, maintenance and calibration duties for cooperative LLSs as the technology matured. Utility consortiums such as EPRI [17,33,36] recognized the ongoing benefits of lightning location and supported a smooth transition to the present situation, where manufacturers of receiver hardware, and independent third parties, offer full-time supervision and operation of many networks. This simplifies the responsibility and authority for delivery of accurate, high-quality data. In North America, utilities tend to own the PMUs but the data are used by ISOs and RTOs. Applying these insights directly to the Smart Grid evolution, it may well be beneficial for electric power utilities to consider third-party ‘borderless’ management and dissemination of monitoring-related information that could then be used by individual utilities for control/action activities.

7.2.2 Flow control Flow control techniques are applied at transmission and distribution levels to influence the paths travelled by real and reactive power. Smart Grid flow control anticipates the use of tools such as thyristor switched series capacitors, flexible AC transmission systems (FACTS) and phase angle regulating transformers for a continuous range of adjustment. At present, the ability to compute flows for large power networks is mature. Suites of load flow calculations are often carried out several times an hour to identify limitations should any one element fail. Flow control actions based on the calculation results then make use of rather discrete operational manoeuvers, such as reconfiguration of generation. There are usually a limited number of options, some presenting considerable cost penalties such as generation and load cuts. Lightning identification and tracking technologies fulfil two duties in the present-day flow control. The presence of lightning is often used to arm discrete flow-control measures at generation and load points in anticipation of one or more contingencies. Customers often pay a reduced rate for interruptible supply that is the first to be cut-off in these conditions. Control actions may be initiated after the first-line tripout on summer afternoons, but most utilities now take more proactive flow control measures using their sophisticated wide-area monitoring and visualization capabilities. LLSs proved to have greater operational value to electrical utility operations in the reduction of clearing times – the 4–24-h intervals following adjustments of flow – than in the early identification of possible problems. The absence of lightning (storm clearing) provides a reliable basis to disable load rejection schemes, redispatch any out-of-merit ‘safe posture’ generation configurations and send home maintenance crews on standby. Advanced flow-control systems in a future Smart Grid may take advantage of LLS data in several phases. First, during commissioning and as operational experience develops, flow limits may be programmed in a restricted range during

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periods of lightning when disturbances are likely. Then, once sufficient reliability has been demonstrated, lightning location data may be used to preconfigure settings to the most favourable post-contingency values to minimize PQ issues.

7.2.3

Enhanced fault identification

Enhanced fault detection may improve the power system operation through better discrimination of fault types and locations, leading to more specific and targeted control actions than can be achieved with present methods [31]. Travelling wave methods were applied for finding faults in de-energized underground cables in the 1940s. There are two classifiers for Travelling Wave Fault Locators (TWFL) – single (A/C) or double ended (B/D), and active (B/C) pulse injection or passive (A/ D), relying on the fault itself to produce the travelling waves. The principles of passive Types A and D are shown in Figure 7.6. Smart Grid digital technologies support the processing of real-time voltage and current signatures for impedance-based fault calculations on operating lines [38]. Digital technologies can also improve the precision of time synchronization into the sub-microsecond level for improved TWFL results. Coordination of lightning ground stroke timing data with travelling wave fault records [18] can rapidly identify lightning-caused disturbances with high efficiency. This finding from USA work is confirmed by data from CEMIG in Brazil [39]. Records from 64 digital fault recorders (DFR) indicate in Figure 7.7 that lightning caused half of the voltage dips resulting in load loss. Observed at A S/S A

T1A

T2A

T3A

S/S A

T1A

T2A

Fault location

Observed at B

S/S B T1B

(a)

T2B

T3B

S/S B

T4B

T1B

T2B

(b)

Figure 7.6 Principle and typical signals in passive travelling wave fault location methods: (a) type A TWFL: single ended, passive, and (b) type D TWFL: double ended, passive.  1993. Adapted, with permission, from [37]

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17 11

10 7 73 2

23 62

378 84

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Lightning Unknown Meadows fire Animals Windstorm Broken line Trees Isolation failure Foreign body Line surge arresters Protection failure Towers breakdown Human accident

155

Figure 7.7 Causes of faults leading to load loss at CEMIG, 2004–2007 [1,39] The enabling technologies for near-real-time TWS analysis include the following: ● ●





High-speed and secure communication from substations to data concentrators. Advanced GPS systems providing coincidence of better than 100 ns for 30 m resolution. Sensor bandwidth, digitizer sampling rates and dynamic range that satisfy requirements for high-voltage impulse testing, such as 100 MHz, 100 MS/s and 8 bit resolution in IEEE Std. 4 [40]. Local intelligence to classify complicated TWS records, for example extrapolating rising edges of waves back to the local zero crossings for assessment of signal arrival times.

Improved communications can also allow aggregation of measurement data from multiple devices with time delay that is short enough to support automatic operations. For distribution applications, wider application of local DFR systems may be able to detect and isolate disturbances prior to or early in the evolution of fault current. This would require latent times of 10 ms or less, including communication and processing delays as well as propagation time from the disturbance source to receivers. These latencies cannot be achieved with present LLS, which have long sensor baselines as well as significant communication delay leading to latency on the order of 1 s. Some recent studies of the waveforms collected by PQ monitors [41] in Figure 7.6 show strong seasonal and time-of-day changes with fault type that can be exploited. The experiments [41] also suggested that high-resolution monitoring of voltage resolved 50-V changes in arc voltage that helped to identify the type of fault.

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Enhanced ‘Smart Grid’ fault protection systems for transmission lines are planned to use high-speed communications among stations to protect entire regions, rather than the protection of single elements achieved now with DFR. They may also use the latest TWFR techniques to advance beyond the limitations of conventional impedance relaying. Prompt, accurate lightning information will be critical to these ‘smarter’ operations. As historical context, operation of TWFR across the province of British Columbia was described in 1996 [21]. Direct lightning flashes to unshielded 500-kV phase conductors were detected at distances up to 1,500 km, with sufficient signal-to-noise ratio for detection even after travelling through seven different substations. Induced overvoltages, which are not expected to exceed 400 kV even in areas of high-soil resistivity and lightning nearby, were also recorded at a high rate. Overall, of 76 TWFR registrations in one summer, only 23 were actual faults. Similar findings were obtained in a Georgia Power study in 1996 [18]. These studies suggest new opportunities for coordinated lightning transient event analyses, discussed in various contexts later. Advanced operation of accurate, sensitive and robust TWFR systems may thus call for an advanced form of lightning protection – using software as well as traditional hardware. Spatial and temporal correlation, using real-time stroke location data, can classify and blank out the multiple, spurious TWFR registrations from induced overvoltages for each flash near instrumented lines. The inter-stroke intervals between strokes of a flash are random and on the order of 50 ms apart, providing additional data to improve confidence that a set of TWFR triggers is indeed caused by lightning near the line, rather than a tree contact or insulator problem of greater interest. Fault location ambiguity with TWFR techniques is a difficult problem in tapped or meshed networks. Resolution of ambiguities using TWFR instrumentation at every node can be expensive, although it is a Smart Grid goal to decrease the cost through mass production. There is a practical possibility of measuring radiated fields from some power system faults using receivers like LLSs. The combined operation of TWFR in conjunction with radiated field measurements for fault location has been considered [42] to resolve the problem of multiple solutions to faults that are not necessarily related to lightning.

7.2.4

Adaptive protection and automated feeder switching

Adaptive protection is envisioned as the real-time adjustment of relay settings based on signals from local sensors or a central control system. For examples, using the knowledge from Figure 7.8, the tripout current sensitivity could be increased in the fall, when more tree contacts are expected; in real time, the reclosing time interval and feeder transfer strategy could be adjusted when lightning is present. Adaptive protection can also help to resolve two-way power flow issues associated with local distributed generation, for example by changing relay settings when a local wind turbine or micro-hydro resource is online during a lightning storm.

Lightning protection of Smart Grids Animal contact

Tree contact

285

Lightning

100

% of events

80 60 40 20 0 Summer

Spring

Winter

Fall

Figure 7.8 Seasonal distribution of faults from animals, trees and lightning (data from [41]) 140 Sure lightning

Number of disturbances

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Possible lightning

100

No lightning

80 60 40 20 0 Jan

Feb

Mar Apr

May

Jun

Jul

Aug

Sep

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Figure 7.9 Time-of-year trend in momentary disturbances for two distribution stations in Ontario, Canada (1989–1991) [44] Automated feeder switching uses sensors and controls to isolate faulted distribution feeders and to reconfigure the remaining lines. These devices can operate with local intelligence, responding to local events or signals, or they can also respond to commands from a central control system. Adaptive protection and feeder switching schemes making use of lightning data may not require precise location of individual flashes [43,44]. A 4-year study of faults used 16 channels of voltage and current with adaptive thresholds at a pair of distribution substations [44]. While lightning location data were available to this study, the simultaneous recording of the digital output from a CIGRE 10 kHz LFC proved to be the most effective real-time discriminator, labelled as ‘sure lightning’ in Figure 7.9.

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The ‘possible lightning’ designation was associated with nuisance fuse operations within 24 h of lightning storms, typically when reaching normal loads on the day after overnight storms. Distribution system fuses, typically rated at 10 A, are easily damaged by lightning surge currents in ways that cause them to operate only when load current suddenly picks up. A fuse that is damaged by lightning overnight will thus not fail (open) until the next day. The adaptive protection response, adopted over several years, was to select fuse characteristics with increased immunity to the impulse currents flowing through to surge arresters across transformer terminals. Existing lightning location network data have time latency associated with long-distance propagation of signals as well as transmission via satellite to a central processor for redistribution. The present latency of real-time LLS data is on the order of 1 min, where advanced Smart Grid protection systems would require inputs that allow local-area decisions within half a cycle (8.3 or 10 ms). Some of the adequately developed but older methods for lightning location, such as flash counters with limited range, can be applied or developed further to deliver the desired low latency in many applications.

7.2.5

Automated islanding and reconnection

The traditional electric power network had a few large sources of energy that fed transmission systems. Many networks are evolving into configurations with distributed sources, interconnected by distribution systems that were designed only to carry power only in one direction, from the distribution station to customer loads. Presently, ‘islanding’ of power system components within a traditional network is an undesirable consequence of faults and operation of protective systems. There is usually an unbalance between load and generation within each large island, leading to changes in power frequency that complicate re-synchronization. If there is too much generation for the remaining load, the system may become unstable. An increasing penetration of distributed generation offers the possibility of mitigating some of the worst risks of islanding by giving sufficient operator scope for remotely controlled or even automated resynchronization after severe faults and contingencies. In Smart Grid systems where islanding detection, management and restoration are deployed [30], it could prove to be useful to deliberately create islands in adverse weather such as lightning. This control action can minimize the effects of widespread voltage dips caused by anticipated faults to the backbone transmission grid, without resorting to present-day measures such as temporary load shedding. Islanding could give a wider range and reach of flow control options with minimal cost penalty to operators, and transparent to users, compared to investment in a few, centralized FACTS flow-control devices. Clearly, accurate wide-area lightning information will be critical for such strategies to be effective.

7.2.6

Diagnosis and notification of equipment condition

Online monitoring and analysis of condition, with operator notification of trouble and readout of a trouble code, were cited as one benefit of ECU applications in

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automobile engines. However, the benefits of the monitoring accrue when the sensor systems themselves operate. The Smart Grid initiative can deploy many, inexpensive sensors to detect breaker condition (voltage across contacts), wind speed, temperature, vibration, leakage current and many other parameters. Out-oflimit readings would automatically notify asset managers and operators of conditions that could soon lead to equipment failure. However, the ability to deploy sensors that are likely to outlive the monitored assets may presently be out of reach. As a likely leading cause of Smart Grid sensor failures, lightning data may find an important new use to censor out-of-limit results prior to any automatic notification. As an example, in weather or leakage current monitoring, if the standard deviation of a monitored variable suddenly falls to zero, then the time that this occurred can be checked against locations and times of lightning near the instrument. This validation process could eliminate spurious results in an asset monitoring database and pick out the onset time of deviations originally caused by lightning damage. In this way, lightning data can help to limit database overload from spurious alarm reports as well as reduce the decision uncertainty in Smart Grid equipment assessment. Considering the issues of assessing the condition of power equipment, lightning location data have proved to be of value in backflashover and shielding failure fault analysis as well as in normalization of year-to-year variation in reliability. However, aspects of this analysis remain to be exploited. Travelling wave recorders in Smart Grid configurations may respond to unique bipolar currents induced on phase conductors resulting from current flow in the tower. These records can be combined with time-synchronized radiated field measurements to yield parameters of flashes that did not cause backflashovers. Averaged over the long term, this monitoring would give a health index for individual tower grounding systems. Monitoring of total lightning exposure on lines can also be used to establish suitable inspection and end-of-life criteria for other power system components. Charge ablation damage along overhead groundwires and conductors leads to multiple spots of corrosion damage, loss of strength and eventual moisture ingress into any optical fibre cables inside. Porcelain disc insulators tend to be prone to longer term wear-out failures, starting initially as a partial puncture from cap to pin that withstands considerable voltage and eventually failing as the number of steep voltage impulses accumulates over decades. Zinc oxide line surge arresters also show some changes in their V–I characteristics with repeated exposures to lightning stress, leading to the use of surge counters in some applications that have limited Smart Grid functionality.

7.2.7 Dynamic thermal rating capabilities Dynamic capability rating determines the ability of a line, cable or transformer to carry load in real time based on local electrical and environmental conditions. Overhead line ampacity is strongly affected by the wind speed averaged between attachment points (dead-end towers). Cable thermal ratings depend on soil temperature and moisture content, with longitudinal variations that can lead to local hot

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spots. Transformer thermal ratings, like cable ratings, have long thermal time constants and online monitoring of oil temperature and chemistry can be used to manage external cooling systems. Dynamic line rating (DLR) systems are needed the most in adverse weather conditions, specifically low wind speed. One successful monitoring technology uses sonar, looking up from the ground in Figure 7.10 to measure conductor clearance. The average temperature in Figure 7.10 was computed for a 30-km stringing section between strain towers. The average conductor temperature approaches its maximum rating in hot, humid summer afternoons and matches the time of peak system loads from air conditioning. These are the same hot, humid weather conditions that promote lightning activity. The equipment shown in Figure 7.10 operates from the ground at midspan. This volume is shielded from lightning strokes by Overhead Groundwires (OHGW), in the same way that the microwave tower legs in Figure 7.2 protect the instrumentation shed. In contrast, patented double-shielding measures [45] are needed to protect load cells mounted in-line with tension insulators because they connect directly to conductors or towers that carry lightning to earth. DLR sensors mounted on phase conductors are exposed to lightning energy from shielding failures and backflashovers but are relatively immune to flashes that terminate on towers or overhead groundwires. Overvoltage protection of low-voltage sensors and equipment is discussed further in [46] and Section 7.4.

7.3 Lightning and digital recording technology Early collection of lightning data involved considerable engineering labour, to monitor analogue oscilloscope operation as well as to maintain data storage using photographic film. Improvements in triggering and robot cameras, still based on photographic film, allowed unattended operation [47]. Continuing improvements in technology have eased the labour burden on the collection of lightning data of high value. This trend extends to today’s Smart Grid initiatives that monitor many variables and locations at low cost. Fundamental studies on research lines in the USA [10], South Africa [48], France and Japan and on instrumented towers mainly made use of analogue oscilloscopes with automatic photography or frequency modulated (FM) magnetic recorders. The NEERI station in Figure 7.11 represented the state of the art in 1980, with its use of a TV camera and video-tape recorder. There were traditional wideband compensated potential dividers on each phase. A local diesel generator provided power and remote control was achieved via very high frequency (VHF) radio.

7.3.1

Digital recording systems for lightning overvoltages

The transition from analogue-to-digital measurements of lightning-induced overvoltages occurred in the early 1980s. Digital transient recording systems built by the USA Jet Propulsion Laboratories were used to record line voltages, arrester

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(b) (a)

Average conductor temperature (°C) measured from sonar clearance

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Figure 7.10 Sonar ‘Smart Grid’ real-time ground-clearance measurement technology, applied to dynamic thermal rating of an overhead line stringing section from Niagara Falls, Canada, during summer 2006: (a) sonar measurement head, looking up to twin bundle phase and offset OHGW (author photo), (b) sonar echo level (dB) versus height of phase and OHGW above ground (m), (c) results of field observations of conductor clearance, converted to average temperature in stringing section and times of all-time system peak loads

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(a) 11 kV lines TV camera Compensated potential dividers

Video-tape recorder

Electromagnetic shielding Matching amplifier

Radio-control systems

Trigger camera control delay lines

Low-impedance ear thing Oscilloscope

Camera

Flash counters Trigger

Sky camera

Station event recorder

Diesel control

(b)

Figure 7.11 Station for oscilloscope recording of transients on distribution line [48]; (a) NEERI 11-kV station and (b) block diagram of observations currents and electric fields on distribution lines starting in 1978 [49]. The initial problems included damage to integrated circuits by high EM fields, coupling of external fields and common-mode signals into the measurements, data loss from communication and power supply problems and failures related to heat and

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moisture. Initial problems and limitations in the digital circuits were resolved in a second design iteration [50] using a dedicated recorder with complementary metal oxide semiconductor (CMOS) circuits for 30 mW standby power dissipation, along with semiconductor memory having 5 MS/s maximum sample rate. The dedicated and relatively inexpensive Macrodyne digital circuit [50] provided performance equivalent to the commercially available Biomation 805 digitizer of 1978. The interface to Macrodyne recorder used an optical fibre link and EM compatibility was achieved by using an internal and isolated battery pack. The tradeoff between operating life and noise coupling was met using disposable packs of four lithium thionyl chloride batteries, providing 7 V for 9 months from 27 Ah capacity. Conformal coating on the circuit boards was used to ensure that the leakage current was acceptably low even when the board was immersed in water. In service, programmes to deploy 68 recorders encountered problems with manufacturing (cold solder joints), component failures and limited battery life in hot climates. In one phase of the research project, rough handling knocked semiconductors from their sockets in half of the installations. These problems are mentioned because they tend to plague every new instrumentation system, including many associated with Smart Grid initiatives such as DLR, and they can sometimes be avoided by ensuring that new systems meet existing standards for durability and reliability. Once the Macrodyne recorder problems were resolved, they remained in productive service from 1988 to 2001 [51], at which time they were replaced with commercial digital oscilloscopes of improved specification and lower cost. A similar 11-year service life was reported for 10 MS/s digital recorders with 10-bit resolution, applied on 60 transmission towers in Japan [23]. This project, from 1994 to 2004, also made use of GPS time synchronization to establish parameters of lightning currents in towers of 60–140 m height.

7.3.2 Voltage sensors for lightning overvoltages High-voltage potential dividers with sufficient bandwidth for lightning impulse measurements using cathode ray oscilloscopes (CRO) [52] have evolved since the use of capacitive dividers, using cap and pin insulator strings or transformer bushing as shown in Figure 7.12. Generally, a resistive-capacitive divider provides the most satisfactory broadband impulse performance, but those manufactured for lightning impulse measurements above 1 MV tend to be expensive and unsuitable for long-term outdoor exposure. Improved performance of an insulator string potential divider can be obtained when discs or posts with semiconducting glaze are substituted. For example, a string of 14 cap-and-pin disc insulators, each coated with semiconducting glaze for conduction of 1 mA under line voltage, was placed in series with a glass disc that was bypassed by a step-down autotransformer. The resulting voltage divider, constructed from standard power-system components and an automobile ignition coil autotransformer, gave 900 kV impulse withstand, 100-ns rise time and 200,000:1 division ratio.

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Transmission line

C1

R-Z

Earthed oil tank

Cable of surge impedance Z

Oscillograph

C2

(b)

(a)

Figure 7.12 Surge potential dividers used for lightning overvoltage measurements on transmission lines 1932 [52]: (a) capacitive potential dividers based on cap and pin disc capacitance and (b) capacitive divider based on transformer bushing tap. Cable delays signal to oscillograph, allowing sweep to initiate The output of a potential divider normally feeds into an automatic digital recorder rather than an oscilloscope. For satisfactory lightning impulse measurements in either case, IEEE Standard 4TM-2013 now requires the system to have a bandwidth of at least 100 MHz, with digitizer sample rate of at least 100 MS/s and resolution of 8 bits or higher [40].

7.3.3

Combined current and voltage sensor for lightning measurements

Initial lightning research trials in Florida [49] used a parallel plate capacitive potential divider rated at 300 kV to measure lightning overvoltages. Another approach was adopted in 1993 [53], illustrated in Figure 7.13, which shows a thin circular slice of metal oxide placed in series with a standard set of cylindrical metal oxide varistor (MOV) blocks. The resulting potential divider measured median subsequent stroke rise times of 500 ns [53] when used with the Macrodyne recorders described earlier. A coaxial shunt measured the current flow through individual arresters, which were summed to estimate the total lightning current for direct strokes. The built-in surge protection of the MOV voltage sensor in Figure 7.13 simplifies design of a low-voltage monitoring circuit. However, current flow through the arrester will vary considerably for a small change in voltage, calling for a wide dynamic range if a fixed value of coaxial shunt resistance is used. Field experience [53,54] suggested that full-scale peak arrester current of 6 kA was sufficient for

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Upper cap

Metal oxide blocks

Spacer (copper) Thin metal oxide disk Spacer (copper) Coaxial shunt

Lower cap Signal lead

Figure 7.13 Metal oxide sensor for arrester discharge voltage and current [53] most monitoring projects. To some extent, the arresters reporting the largest currents were closest to the flash terminations. The development of commercial surge-protective devices for households now packages thin MOV elements with 20–40 mm diameter in housings that provide good environmental performance. One of these low-voltage high-energy arresters can be bolted to a distribution class surge arrester, normally used by an electrical utility across every transformer, as in Figure 7.14. The resulting voltage division in this case was about 100:1, from the 12-kV arrester rating and the 120-V rating of the low-voltage device. The faithful wave-front and wave-tail reproduction is partly a function of the close match in the diameter of the MOV elements in each surge arrester. Similar positive results have also been reported with other stacked arrester configurations when used as wideband potential dividers. The ‘MOA Dividing Mode’ in IEEE Standard 1894TM-2015 achieves bandwidth from power frequency to more than 1 MHz [55].

7.3.4 Non-contact sensors for impulse voltage and current Isolation from the current lead in arrester configurations can be achieved with the use of ferrite-core current monitors. These can be purchased with several core cross

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(b)

Figure 7.14 Implementation of low-cost, wideband MOV potential divider for Smart Grid applications, based on distribution system arrester: (a) pulse generator, wideband high-voltage probe and distribution-class surge arrester in series with low-voltage SPD having same MOV element diameter, and (b) comparison of output from reference divider (upper trace, 5 kV/division) and low-cost divider (lower trace, 50 V/division). Horizontal sweep 50 ms per division sections and through-hole sizes. The hole size and insulation should be chosen to achieve an impulse breakdown strength that coordinates with the digitizer surge protection. Most current monitors provide output impedance of 50 W, and the matching impedance at the digitizer helps to mitigate the EMI limitations of coaxial cable systems compared to twisted pair wiring with reduced bandwidth. Non-contact methods for measuring voltage and current on energized lines can also make use of multiple sets of magnetic and electric field sensors. One example is the use of three, 2-axis B-field sensors to establish the power frequency currents in each of the three phases [56]. This approach can also make effective use of ultrawideband, sensitive electric and magnetic field sensors [57]. For example, electric field sensors with sensitivity of 1.4 V/(kV/m) with bandwidth from 47 Hz to 100 MHz, and wideband magnetic field sensors with 0.17 V/(A/m) sensitivity [58], have been utilized in long-term lightning studies [59]. These wideband sensors are also suitable for monitoring power system transients at or near ground level. Non-contact field sensors can provide information for enhanced fault location on lines with multiple taps, as well as data for temporary studies of line disturbances to be coordinated with lightning data.

7.3.5

Commercial current sensors for equipment monitoring

Arrester manufacturers provide a wide range of surge counters and leakage current monitors for their products. At present, none of these are integrated into the arrester housing directly. However, with sufficient utility interest, the porcelain-housed design in Figure 7.13 could be updated to make a useful and inexpensive wideband

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transient sensor for accurate fault location on multiple-tap distribution systems. Reliability considerations would argue for the elimination of internal air spaces in an improved, modern polymer-housed MOV design. Present-day signal sources such as magnetic current and voltage transformers generate signal levels of 5 A and 70 or 120 V that are high compared to those associated with electronic signal transducers. High-impedance electronic sources, with reduced voltage and current, are more vulnerable to external EM disturbances from lightning. This can be mitigated using optical or wireless isolation, which requires power, or through passive EM shielding.

7.4 Lightning protection of Smart Grid sensors Traditional surge waveforms, such as the 1.2/50 standard lightning impulse voltage wave, were measured and standardized nearly 100 years ago. These stresses also affect present-day Smart Grid components and infrastructure. Standardized design criteria for Smart Meters include transient immunity and surge immunity tests simulate the harsh service environment of an electrical system based on wire connections when exposed to the lightning EM field pulse at close range. The specific prescriptions in ITU-T Recommendation K, described here, are coordinated with IEC 62305 requirements discussed elsewhere in this book.

7.4.1 Reliability requirements for Smart Grid sensors and systems Risk assessment is a standard consideration in the design of the present-day power systems. For example, insulation level is set by the anticipated power system overvoltage levels, applied to insulators that have conductive condensation resulting from outdoor exposure. Effects of direct and nearby lightning flashes are calculated, based on the impedance of grounding systems at the flash location, the prospective surge current and the EM coupling to and within the wire structures. Safety-related concerns are met with ‘fail-safe’ designs, where detection of an unsafe condition overrides any control system to isolate the electrical supply. Risk calculations for more complex Smart Grid systems can become large and costly undertakings. Overcurrent breakers are examples of equipment that now provide an on-demand safety function, as they limit the exposure time to GPR at a fault location. Some Smart Grid systems may also provide a continuous safety function, such as maintaining a minimum overhead wire clearance above ground at a road or river crossing. For the same Safety Integrity Level in the two cases, IEC Standard 61508 [60] calls for factor of 104 improvements in ‘equivalent mean time to dangerous failure’ for the continuous safety functions compared to on-demand systems. Reliable systems have a low probability of failure but are not necessarily failsafe. Reliability requirements can sometimes be met with the use of redundant control networks with an electronic ‘arbitrator’ that acts on the majority opinion and may also identify and isolate a failing control system. The redundancy can mix

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technologies, rather than duplicate the same system, for improved capability. An example would be a dynamic rating system that uses the loss of signal from a clearance monitor, combined with a sudden increase in tension from a load cell and a measured ambient temperature near the freezing point, to identify the onset and accumulation rate of ice on the monitored conductor. Another example is a mixed set of optical and EM sensors, which can offer unambiguous detection of nearby lightning. Smart Grid component reliability is a function of the reasonably foreseeable environment, common to other existing monitoring equipment, including the following: ● ●





Mechanical effects including shock and 106–107 cycles of vibration. Chemical attack from humidity, temperature, salt spray, pollution and acid by-products from partial discharge activity. An EM environment with elevated power frequency electric and magnetic fields as well as strong EM fields from the flow of lightning and fault currents. Overvoltage and overcurrent stresses applied to every wire connection.

Lightning effects may limit the effective long-term deployment of power system equipment sensors in two ways: upset from anomalous impulse signals from the sensor wiring and permanent damage. In some cases, the vulnerability of alarm systems to lightning becomes unacceptable. Incorrect operation of fire suppression systems at Frankfurt airport from lightning activity was described in 1992 [46]. At one utility, an advanced provincewide meteorological monitoring system for ice accretion was found to generate series of false trips, each corresponding to 0.05 mm ice accumulation, in the summer. The false trips were infrequent at first, then rose to a steady rate and fell away. The false trips from lightning activity near the sensor were managed with masking. For example, readings that occurred above 10  C were rejected. False alarms can also be blanked out using real-time lightning data, whether global (in the form of a data feed from LLS) or local, using the output of a local lightning detector as sometimes used in security monitoring systems. This same approach is relevant to reduce the error rate in collection and processing of automatic meter reading (AMR) data. For example, metering data collection can be suspended temporarily during local lightning activity, and monitoring adapted instead to survey the presence of power at all metres on a more frequent monitoring cycle. As real-time control of customer loads through advanced metering infrastructure (AMI) installation becomes prevalent, and the need for this control is greatest during storms, IT strategies could adopt policies to reset any AMR or AMI systems whose internal programmes may have been garbled by a nearby lightning stroke. Lightning also plays a role in the management of data from an extensive Smart Grid network. Lightning will probably cause the end of life of many Smart Grid sensors – with only the questions of when and how close to be balanced between nature and engineering. For long-term reliable service, the systems may also be placed inside some form of structure, as defined in IEC 62305-2010 [61,62]. This

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means that the sensor or meter damage rate is an economic trade-off between the decreasing cost of the sensor and the constant or increasing cost of its standardbased lightning protection. When a sensor fails to report or starts to report data that are out of specification, one of the first lines of investigation should be to interrogate an LLS for lightning activity near that location. The security industry, involving coaxial television cables as well as fire and burglar alarms, tolerates a high degree of equipment damage from nearby lightning, relying on low sensor cost and ease of physical access for replacement. Miniaturization of equipment, using surface mount technology and digital components, reduced the power consumption and increased the battery life of security system components in the late 1990s. The close lead spacing and the decreased surge damage threshold from these changes have also promoted a shift to wireless or optical fibre links in hazard monitoring systems, especially when connecting among buildings. Alarm monitoring systems normally draw electrical power from the protected buildings and rely on internal batteries only for short-duration outages. This is also a practical option when applying sensors to distribution systems. However, whether using a solar panel, the electric or the magnetic field from the power line, or wind power, lightning surge protection of the Smart Grid transmission sensors presents some interesting challenges. Each non-contact approach requires additional wiring and power conversion electronics and introduces local energy storage that may become an unintended capacitive sink for surge energy.

7.4.2 Candidate wiring configurations for Smart Grid sensors Smart Grid systems consist of electrical and electronic circuits with internal energy storage as well as a communications interface. DLR systems for overhead transmission lines are representative Smart Grid initiatives that make use of these elements. DLR systems may use a variety of configurations of advanced instrumentation and communications technologies, including 1. 2.

3.

4.

direct mounting of a load cell [45] or video camera on the transmission tower at conductor height, powered by solar panel, communicating by wireless; direct mounting of sensors (conductor temperature, tilt, acceleration, magnetic field) on the phase conductor, with power harvested from the line voltage or current, communicating by wireless; protected mounting of a sensor (optical or sonar rangefinder, wind speed, ambient temperature, magnetic field) beneath the phase at midspan, as in Figure 7.10, powered by a low-voltage circuit and communicating by POTS or wireless; and protected mounting of voltage and current sensors (synchrophasors, travelling wave fault recorders) at substations, used to monitor end-to-end resistance or surge impedance and then infer average line temperature or height above ground, powered from station batteries and communicating directly to existing SCADA systems.

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In the terms of IEC 61508 [60], the possibility rank (1–4) of a direct lightning flash corresponding to each of these categories of dynamic rating systems on a transmission system is as follows: 1.

2. 3. 4.

Probable; in a moderate climate, each transmission tower would typically receive a flash every few years, having a median peak current, IˆF ¼ 31 kA in the first stroke and median rate of rise of 40 kA/ms rate of rise in median subsequent stroke, ˆIS. The tower flash rate is a function of both line height and ground flash density. Occasional; a shielding failure could occur about 5% of the time, resulting in a flash with low ˆIF (