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IET ENERGY ENGINEERING 114 Lightning-Induced Effects in Electrical and Telecommunication Systems Othervolumesinthisseries: Volume1 PowerCircuitBreakerTheoryandDesignC.H.Flurscheim(Editor) Volume4 IndustrialMicrowaveHeatingA.C.MetaxasandR.J.Meredith Volume7 InsulatorsforHighVoltagesJ.S.T.Looms Volume8 VariableFrequencyACMotorDriveSystemsD.Finney Volume10 SF SwitchgearH.M.RyanandG.R.Jones 6 Volume11 ConductionandInductionHeatingE.J.Davies Volume13 StatisticalTechniquesforHighVoltageEngineeringW.Hauschildand W.Mosch Volume14 UninterruptiblePowerSuppliesJ.PlattsandJ.D.StAubyn(Editors) Volume15 DigitalProtectionforPowerSystemsA.T.JohnsandS.K.Salman Volume16 ElectricityEconomicsandPlanningT.W.Berrie Volume18 VacuumSwitchgearA.Greenwood Volume19 ElectricalSafety:Aguidetocausesandpreventionofhazards J.MaxwellAdams Volume21 ElectricityDistributionNetworkDesign,2ndEditionE.Lakerviand E.J.Holmes Volume22 ArtificialIntelligenceTechniquesinPowerSystemsK.Warwick,A.O.Ekwue andR.Aggarwal(Editors) Volume24 PowerSystemCommissioningandMaintenancePracticeK.Harker Volume25 Engineers’HandbookofIndustrialMicrowaveHeatingR.J.Meredith Volume26 SmallElectricMotorsH.Moczalaetal. 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Volume51 ShortCircuitCurrentsJ.Schlabbach Volume52 NuclearPowerJ.Wood Volume53 ConditionAssessmentofHighVoltageInsulationinPowerSystem EquipmentR.E.JamesandQ.Su Volume55 LocalEnergy:DistributedgenerationofheatandpowerJ.Wood Volume56 ConditionMonitoringofRotatingElectricalMachinesP.Tavner,L.Ran, J.PenmanandH.Sedding Volume57 TheControlTechniquesDrivesandControlsHandbook,2ndEdition B.Drury Volume58 LightningProtectionV.Cooray(Editor) Volume59 UltracapacitorApplicationsJ.M.Miller Volume62 LightningElectromagneticsV.Cooray Volume63 EnergyStorageforPowerSystems,2ndEditionA.Ter-Gazarian Volume65 ProtectionofElectricityDistributionNetworks,3rdEditionJ.Gers Volume66 HighVoltageEngineeringTesting,3rdEditionH.Ryan(Editor) Volume67 MulticoreSimulationofPowerSystemTransientsF.M.Uriate Volume68 DistributionSystemAnalysisandAutomationJ.Gers Volume69 TheLighteningFlash,2ndEditionV.Cooray(Editor) Volume70 EconomicEvaluationofProjectsintheElectricitySupplyIndustry, 3rdEditionH.Khatib Volume72 ControlCircuitsinPowerElectronics:Practicalissuesindesignand implementationM.Castilla(Editor) Volume73 WideAreaMonitoring,ProtectionandControlSystems:Theenablerfor SmarterGridsA.VaccaroandA.Zobaa(Editors) Volume74 PowerElectronicConvertersandSystems:Frontiersandapplications A.M.Trzynadlowski(Editor) Volume75 PowerDistributionAutomationB.Das(Editor) Volume76 PowerSystemStability:Modelling,analysisandcontrolA.A.Sallamand OmP.Malik Volume78 NumericalAnalysisofPowerSystemTransientsandDynamicsA.Ametani (Editor) Volume79 Vehicle-to-Grid:LinkingelectricvehiclestothesmartgridJ.Luand J.Hossain(Editors) Volume81 Cyber-Physical-SocialSystemsandConstructsinElectricPower EngineeringS.Suryanarayanan,R.RocheandT.M.Hansen(Editors) Volume82 PeriodicControlofPowerElectronicConvertersF.Blaabjerg,K.Zhou, D.WangandY.Yang Volume86 AdvancesinPowerSystemModelling,ControlandStabilityAnalysis F.Milano(Editor) Volume87 Cogeneration:Technologies,optimisationandimplementationC. 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Al-Jassim(Editors) Volume167 PowerGridswithRenewableEnergyStorage,Integrationand DigitalizationA.A.SallamandOmP.Malik Volume172 LightingInteractionwithPowerSystems,2VolumesA.Piantini(Editor) Volume905 PowerSystemProtection,4Volumes Lightning-Induced Effects in Electrical and Telecommunication Systems Yoshihiro Baba and Vladimir A. Rakov The Institution of Engineering andTechnology PublishedbyTheInstitutionofEngineeringandTechnology,London,UnitedKingdom TheInstitutionofEngineeringandTechnologyisregisteredasaCharityinEngland& Wales(no.211014)andScotland(no.SC038698). †TheInstitutionofEngineeringandTechnology2021 Firstpublished2020 ThispublicationiscopyrightundertheBerneConventionandtheUniversalCopyright Convention.Allrightsreserved.Apartfromanyfairdealingforthepurposesofresearch orprivatestudy,orcriticismorreview,aspermittedundertheCopyright,Designsand PatentsAct1988,thispublicationmaybereproduced,storedortransmitted,inany formorbyanymeans,onlywiththepriorpermissioninwritingofthepublishers,orin thecaseofreprographicreproductioninaccordancewiththetermsoflicencesissued bytheCopyrightLicensingAgency.Enquiriesconcerningreproductionoutsidethose termsshouldbesenttothepublisherattheundermentionedaddress: TheInstitutionofEngineeringandTechnology MichaelFaradayHouse SixHillsWay,Stevenage Herts,SG12AY,UnitedKingdom www.theiet.org Whiletheauthorsandpublisherbelievethattheinformationandguidancegiveninthis workarecorrect,allpartiesmustrelyupontheirownskillandjudgementwhenmaking useofthem.Neithertheauthorsnorpublisherassumesanyliabilitytoanyoneforany lossordamagecausedbyanyerrororomissioninthework,whethersuchanerroror omissionistheresultofnegligenceoranyothercause.Anyandallsuchliabilityis disclaimed. 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BritishLibraryCataloguinginPublicationData AcataloguerecordforthisproductisavailablefromtheBritishLibrary ISBN978-1-78561-353-1(Hardback) ISBN978-1-78561-354-8(PDF) TypesetinIndiabyMPSLimited PrintedintheUKbyCPIGroup(UK)Ltd,Croydon Contents Abouttheauthors xi Preface xiii 1 Lightningreturn stroke andits modeling 1 1.1 Introduction 1 1.2 Lightning 2 1.2.1 Categories of lightning discharges 2 1.2.2 Classification of cloud-to-groundlightning discharges 3 1.2.3 Downwardnegative lightning discharges to ground 3 1.2.4 Positive lightning discharges 11 1.2.5 Upward lightning discharges 12 1.2.6 Rocket-triggered lightning discharges 14 1.3 Lightning models 16 1.3.1 Overview of modeling of the lightning return stroke 16 1.3.2 Engineering models 17 1.3.3 Equivalency between the lumped-source and distributed-source representations 22 1.3.4 Extension of models to include a tall strike object 23 1.4 Testing model validity 24 1.4.1 “Typical-event” approach 25 1.4.2 “Individual-event” approach 30 1.5 Summary 33 References 34 2 Calculation of lightningelectromagnetic fields 37 2.1 Introduction 37 2.2 Derivation of equations for computing lightning electric and magnetic fields 38 2.2.1 Differential current element at z0 ¼ 0in free space; field pointat z>0 38 2.2.2 Elevated differential current element (z0>0) and its image 45 2.2.3 Elevated differential current element above ground and its image; field point on the ground surface (z¼ 0) 46 2.2.4 Vertical lightning channel above ground; field point on the ground surface (z¼ 0) 47 viii Lightning-Induced Effects in Electrical andTelecommunication Systems 2.3 The reversal distance for electrostatic and induction electric field componentsof a short current element 50 2.4 Non-uniqueness of electric field components 51 2.5 Shortchannel segmentvs. total radiating channel length 53 2.6 Channel-base current equation 55 2.7 Propagationeffects 57 2.8 Summary 59 References 59 3 Distributed-circuit models of electromagnetic coupling to overhead conductor 63 3.1 Introduction 63 3.2 Model of Taylor, Satterwhite, and Harrison(1965) 65 3.3 Model of Agrawal, Price, and Gurbaxani (1980) 70 3.4 Model of Rachidi (1993) 75 3.5 Equivalence of the three coupling models 77 3.6 Summary 78 References 80 4 Finite-difference time-domainmethod 83 4.1 Introduction 83 4.2 Finite-difference expressions of Maxwell’s equations 85 4.2.1 3DCartesian coordinate system 85 4.2.2 2Dcylindrical coordinate system 90 4.2.3 2Dspherical coordinate system 93 4.3 Subgridding technique 96 4.4 Representationof lumped sources and lumped circuit elements 100 4.4.1 Lumped voltage source 100 4.4.2 Lumped current source 100 4.4.3 Lumped resistance 102 4.4.4 Lumped inductance 103 4.4.5 Lumped capacitance 104 4.4.6 Lumped series resistance and inductance 105 4.5 Representationof thin wire 108 4.6 Representationof lightning channel and excitation 110 4.6.1 Lightning return-stroke channel 110 4.6.2 Excitation methods 114 4.7 Representationof surge arrester 115 4.8 Representationof corona ona horizontal conductor 118 4.9 Absorbingboundary conditions 120 4.10 Summary 122 References 122 Contents ix 5 Applicationsof the FDTDmethod 129 5.1 Introduction 130 5.1.1 Classification of applications of the FDTDmethod 130 5.1.2 General overview of applications 133 5.2 Voltages induced onan overhead single conductor by lightning strikes to a nearby tall grounded object 140 5.2.1 Introduction 140 5.2.2 Methodology 144 5.2.3 Analysis and results 149 5.2.4 Discussion 153 5.2.5 Summary 157 Appendix 5.2.A Testing the validity of the FDTDcalculations against experimental data (strikes to flat ground) 158 Appendix 5.2.B Comparison with Rusck’sformula (strikes to flat ground) 162 Appendix 5.2.C Testing the validity of the FDTDcalculations against experimental data(strikes to a tall object) 163 5.3 Lightning-induced voltages onan overhead two-conductor distribution line 164 5.3.1 Introduction 164 5.3.2 Methodology 166 5.3.3 Analysis and results 169 5.3.4 Summary 174 5.4 Lightning-induced voltages onan overhead single conductor in the presence of corona discharge from the conductor 175 5.4.1 Introduction 175 5.4.2 Methodology 175 5.4.3 Analysis and results 178 5.4.4 Discussion 183 5.4.5 Summary 191 5.5 Lightning-induced voltages onoverhead multiconductor lines with surge arresters and pole transformers 192 5.5.1 Introduction 192 5.5.2 Methodology and configurations studied 194 5.5.3 Analysis and results 198 5.5.4 Summary 202 5.6 Lightning-induced voltages onoverhead multiconductor lines in the presence of nearby buildings 203 5.6.1 Introduction 203 5.6.2 Methodology and configurations studied 203 5.6.3 Analysis and results 206 5.6.4 Summary 211 5.7 Lightning-induced currents in buried cables 211 5.7.1 Introduction 211 5.7.2 Description of the experiment 212