Professor Yoshihiro Baba, Associate Professor, Department of Electrical Engineering, Doshisha University, Kyoto, JapanProfessor Baba received his PhD from the University of Tokyo. He was Visiting Scholar at the Lightning Laboratory at the University of Florida, USA, and is currently Editor of the IEEE Transactions on Power Delivery. His areas of interest include computational electromagnetics, electromagnetic compatibility and lightning protection.Professor Vladimir A. Rakov, Department of Electrical and Computer Engineering, University of Florida, USAProfessor Rakov studied for his PhD at Tomsk University in Russia and has written extensively on the subject of lightning in numerous international journals and conference proceedings. He is A Fellow of the IEEE and a Fellow of the American Meteorological Society, amongst others, and his areas of interest cover lightning, lightning protection and atmospheric electricity.

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• Preface xi1 Introduction 11.1 Historical Overview of Lightning Electromagnetic-Field and Surge Computations 11.2 Overview of Existing Electromagnetic Computation Methods 21.2.1 Method of Moments 21.2.2 Partial-Element Equivalent-Circuit Method 41.2.3 Finite-Element Method 41.2.4 Transmission Line Modeling Method 41.2.5 Constrained Interpolation Profile Method 51.2.6 Finite-Difference Time Domain Method 61.3 Summary 7References 72 Lightning 112.1 Introduction 112.2 Thundercloud 122.2.1 Formation of Thunderclouds 122.2.2 Mechanism of Cloud Electrification 142.3 Lightning Discharges 152.3.1 Categories of Lightning Discharges 152.3.2 Classification of Cloud-to-Ground Lightning Discharges 152.3.3 Downward Negative Lightning Discharges to Ground 162.3.4 Positive Lightning Discharges 232.3.5 Upward Lightning Discharges 232.3.6 Rocket-Triggered Lightning Discharges 252.4 Lightning Electromagnetic Fields 262.4.1 Measured Lightning Return-Stroke Electromagnetic Fields 262.4.2 Mathematical Expressions for Calculating Electric and Magnetic Fields 292.5 Lightning Surges 312.5.1 Surges Due to Direct Lightning Strike 312.5.2 Surges Induced by a Nearby Lightning Strike 322.5.3 Surges Coming from Grounding Due to Its Potential Rise 332.6 Lightning Surge Protection 342.6.1 Insulation Coordination 342.6.2 Protection against Direct Lightning Strikes 352.6.3 Back-Flashover Phenomena 372.6.4 Lightning Surge Protection Measures 382.7 Summary 40References 413 The Finite-Difference Time Domain Method for Solving Maxwell's Equations 433.1 Introduction 433.2 Finite-Difference Expressions of Maxwell's Equations 443.2.1 3D Cartesian Coordinate System 443.2.2 2D Cylindrical Coordinate System 493.3 Subgridding Technique 513.4 Absorbing Boundary Conditions 553.5 Representation of Lumped Sources and Lumped Circuit Elements 573.5.1 Lumped Voltage Source 573.5.2 Lumped Current Source 573.5.3 Lumped Resistance 593.5.4 Lumped Inductance 593.5.5 Lumped Capacitance 603.6 Representation of Thin Wire 613.7 Representation of Lightning Return-Stroke Channel 633.7.1 Lightning Return-Stroke Channel 633.7.2 Excitations 663.8 Representation of Surge Arresters 673.9 Summary 69References 704 Applications to Lightning Surge Protection Studies 734.1 Introduction 734.1.1 Overview 734.1.2 Lightning Electromagnetic Fields at Close and Far Distances 734.1.3 Lightning Surges on Overhead Power TL Conductors and Towers 754.1.4 Lightning Surges on Overhead Distribution and Telecommunication Lines 764.1.5 Lightning Electromagnetic Environment in Power Substations 774.1.6 Lightning Surges in Wind-Turbine-Generator Towers 774.1.7 Lightning Surges in Photovoltaic Arrays 784.1.8 Lightning Electromagnetic Environment in Electric Vehicles 784.1.9 Lightning Electromagnetic Environment in Airborne Vehicles 784.1.10 Lightning Surges and the Electromagnetic Environment in Buildings 794.1.11 Surges on Grounding Electrodes 794.2 Electromagnetic Fields at the Top of a Tall Building Associated with Nearby Lightning Return Strokes 804.2.1 Introduction 804.2.2 Methodology 814.2.3 Analysis and Results 854.2.4 Summary 964.2.5 Appendix: Comparison of Fields in the Absence of a Building Computed Using the FDTD Method and Thottappillil et al.'s (2001) Analytical Expressions 964.2.6 Appendix: Enhancement Factors Due to the Presence of Hemisphere or Rectangular Building in a Uniform Static Electric Field 974.3 Influence of Strike Object Grounding on Close Lightning Electric Fields 1004.3.1 Introduction 1004.3.2 Methodology 1034.3.3 Analysis and Results 1054.3.4 Discussion 1224.3.5 Summary 1284.3.6 Appendix: Comparison of Fields Due to a Lightning Strike to Flat Ground Calculated Using the FDTD Method in the 2D Cylindrical Coordinate System and Thottappillil et al.'s (2001) Analytical Expressions 1284.4 Simulation of Corona at Lightning-Triggering Wire: Current, Charge Transfer, and Field Reduction Effect 1294.4.1 Introduction 1294.4.2 General Approach 1354.4.3 Model 1364.4.4 Analysis and Results 1414.4.5 Discussion 1454.4.6 Summary 1494.4.7 Appendix: Geometry of a Wire Corona Sheath 1494.5 On the Interpretation of Ground Reflections Observed in Small-Scale Experiments Simulating Lightning Strikes to Towers 1514.5.1 Introduction 1514.5.2 Current Pulses Propagating along a Conical Conductor Excited at Its Apex or Base 1534.5.3 FDTD Simulation of Small-Scale Experiments 1574.5.4 Interpretation of Ground Reflections Arriving at the Tower Top 1624.5.5 TL Representation of a Tall Object on the Ground Plane 1644.5.6 Summary 1694.5.7 Appendix: FDTD Representation of Tower Models 1704.6 On the Mechanism of Attenuation of Current Waves Propagating along a Vertical Perfectly Conducting Wire above Ground: Application to Lightning 1714.6.1 Introduction 1714.6.2 Incident Current (Iinc), Incident E-field (Einc): Analytical Solution 1744.6.3 Total Current (Itot), Total E-field (Etot): Numerical Solution 1764.6.4 Scattered Current (Iscat), Scattered E-field (Escat): Iscat = Itot − Iinc, Escat = −Einc 1794.6.5 Dependences of Current Attenuation on the Source Length, Conductor Thickness, and Frequency 1814.6.6 Nonuniform TL Approximation 1844.6.7 Summary 1864.6.8 Appendix: Incident E-field for Two Parallel Vertical Phased Current Source Arrays—Analytical Solution 1874.6.9 Appendix: Total Current for Horizontal Configurations—Numerical Solution 1884.6.10 Appendix: Comparison of FDTD Simulation with an Analytical Solution 1904.6.11 Appendix: E-field Structure around a Vertical Nonzero-Thickness Perfect Conductor 1914.6.12 Appendix: Vertical E-field Produced by an Electrically-Short Vertical Dipole 1924.7 FDTD Simulation of Lightning Surges on Overhead Wires in the Presence of Corona Discharge 1934.7.1 Introduction 1934.7.2 Modeling 1954.7.3 Results and Discussion 1994.7.4 Summary 2094.8 FDTD Simulation of Insulator Voltages at a Lightning-Struck Tower Considering the Ground-Wire Corona 2124.8.1 Introduction 2124.8.2 Methodology 2124.8.3 Analysis and Results 2154.8.4 Summary 2244.9 Voltages Induced on an Overhead Wire by Lightning Strikes to a Nearby Tall Grounded Object 2244.9.1 Introduction 2244.9.2 Methodology 2284.9.3 Analysis and Results 2314.9.4 Discussion 2384.9.5 Summary 2404.9.6 Appendix: Testing the Validity of the FDTD Calculations against Experimental Data (Strikes to Flat Ground) 2424.9.7 Appendix: Comparison with Rusck's Formula (Strikes to Flat Ground) 2434.9.8 Appendix: Testing the Validity of the FDTD Calculations against Experimental Data (Strikes to a Tall Object) 2454.10 3D-FDTD Computation of Lightning-Induced Voltages on an Overhead Two-Wire Distribution Line 2474.10.1 Introduction 2474.10.2 Methodology 2494.10.3 Analysis and Results 2524.10.4 Summary 2604.11 FDTD Simulations of the Corona Effect on Lightning-Induced Voltages 2604.11.1 Introduction 2604.11.2 Methodology 2614.11.3 Analysis and Results 2634.11.4 Discussion 2694.11.5 Summary 2774.12 FDTD Simulation of Surges on Grounding Electrodes Considering Soil Ionization 2774.12.1 Introduction 2774.12.2 Representation of Soil Ionization and De-ionization 2784.12.3 Analysis and Results 2794.12.4 Conclusions 2884.13 Summary 288References 288Appendix: 3D-FDTD Program in C++ 299Index 311

Professor Yoshihiro Baba, Associate Professor, Department of Electrical Engineering, Doshisha University, Kyoto, JapanProfessor Baba received his PhD from the University of Tokyo. He was Visiting Scholar at the Lightning Laboratory at the University of Florida, USA, and is currently Editor of the IEEE Transactions on Power Delivery. His areas of interest include computational electromagnetics, electromagnetic compatibility and lightning protection.Professor Vladimir A. Rakov, Department of Electrical and Computer Engineering, University of Florida, USAProfessor Rakov studied for his PhD at Tomsk University in Russia and has written extensively on the subject of lightning in numerous international journals and conference proceedings. He is A Fellow of the IEEE and a Fellow of the American Meteorological Society, amongst others, and his areas of interest cover lightning, lightning protection and atmospheric electricity.

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• Preface xi1 Introduction 11.1 Historical Overview of Lightning Electromagnetic-Field and Surge Computations 11.2 Overview of Existing Electromagnetic Computation Methods 21.2.1 Method of Moments 21.2.2 Partial-Element Equivalent-Circuit Method 41.2.3 Finite-Element Method 41.2.4 Transmission Line Modeling Method 41.2.5 Constrained Interpolation Profile Method 51.2.6 Finite-Difference Time Domain Method 61.3 Summary 7References 72 Lightning 112.1 Introduction 112.2 Thundercloud 122.2.1 Formation of Thunderclouds 122.2.2 Mechanism of Cloud Electrification 142.3 Lightning Discharges 152.3.1 Categories of Lightning Discharges 152.3.2 Classification of Cloud-to-Ground Lightning Discharges 152.3.3 Downward Negative Lightning Discharges to Ground 162.3.4 Positive Lightning Discharges 232.3.5 Upward Lightning Discharges 232.3.6 Rocket-Triggered Lightning Discharges 252.4 Lightning Electromagnetic Fields 262.4.1 Measured Lightning Return-Stroke Electromagnetic Fields 262.4.2 Mathematical Expressions for Calculating Electric and Magnetic Fields 292.5 Lightning Surges 312.5.1 Surges Due to Direct Lightning Strike 312.5.2 Surges Induced by a Nearby Lightning Strike 322.5.3 Surges Coming from Grounding Due to Its Potential Rise 332.6 Lightning Surge Protection 342.6.1 Insulation Coordination 342.6.2 Protection against Direct Lightning Strikes 352.6.3 Back-Flashover Phenomena 372.6.4 Lightning Surge Protection Measures 382.7 Summary 40References 413 The Finite-Difference Time Domain Method for Solving Maxwell's Equations 433.1 Introduction 433.2 Finite-Difference Expressions of Maxwell's Equations 443.2.1 3D Cartesian Coordinate System 443.2.2 2D Cylindrical Coordinate System 493.3 Subgridding Technique 513.4 Absorbing Boundary Conditions 553.5 Representation of Lumped Sources and Lumped Circuit Elements 573.5.1 Lumped Voltage Source 573.5.2 Lumped Current Source 573.5.3 Lumped Resistance 593.5.4 Lumped Inductance 593.5.5 Lumped Capacitance 603.6 Representation of Thin Wire 613.7 Representation of Lightning Return-Stroke Channel 633.7.1 Lightning Return-Stroke Channel 633.7.2 Excitations 663.8 Representation of Surge Arresters 673.9 Summary 69References 704 Applications to Lightning Surge Protection Studies 734.1 Introduction 734.1.1 Overview 734.1.2 Lightning Electromagnetic Fields at Close and Far Distances 734.1.3 Lightning Surges on Overhead Power TL Conductors and Towers 754.1.4 Lightning Surges on Overhead Distribution and Telecommunication Lines 764.1.5 Lightning Electromagnetic Environment in Power Substations 774.1.6 Lightning Surges in Wind-Turbine-Generator Towers 774.1.7 Lightning Surges in Photovoltaic Arrays 784.1.8 Lightning Electromagnetic Environment in Electric Vehicles 784.1.9 Lightning Electromagnetic Environment in Airborne Vehicles 784.1.10 Lightning Surges and the Electromagnetic Environment in Buildings 794.1.11 Surges on Grounding Electrodes 794.2 Electromagnetic Fields at the Top of a Tall Building Associated with Nearby Lightning Return Strokes 804.2.1 Introduction 804.2.2 Methodology 814.2.3 Analysis and Results 854.2.4 Summary 964.2.5 Appendix: Comparison of Fields in the Absence of a Building Computed Using the FDTD Method and Thottappillil et al.'s (2001) Analytical Expressions 964.2.6 Appendix: Enhancement Factors Due to the Presence of Hemisphere or Rectangular Building in a Uniform Static Electric Field 974.3 Influence of Strike Object Grounding on Close Lightning Electric Fields 1004.3.1 Introduction 1004.3.2 Methodology 1034.3.3 Analysis and Results 1054.3.4 Discussion 1224.3.5 Summary 1284.3.6 Appendix: Comparison of Fields Due to a Lightning Strike to Flat Ground Calculated Using the FDTD Method in the 2D Cylindrical Coordinate System and Thottappillil et al.'s (2001) Analytical Expressions 1284.4 Simulation of Corona at Lightning-Triggering Wire: Current, Charge Transfer, and Field Reduction Effect 1294.4.1 Introduction 1294.4.2 General Approach 1354.4.3 Model 1364.4.4 Analysis and Results 1414.4.5 Discussion 1454.4.6 Summary 1494.4.7 Appendix: Geometry of a Wire Corona Sheath 1494.5 On the Interpretation of Ground Reflections Observed in Small-Scale Experiments Simulating Lightning Strikes to Towers 1514.5.1 Introduction 1514.5.2 Current Pulses Propagating along a Conical Conductor Excited at Its Apex or Base 1534.5.3 FDTD Simulation of Small-Scale Experiments 1574.5.4 Interpretation of Ground Reflections Arriving at the Tower Top 1624.5.5 TL Representation of a Tall Object on the Ground Plane 1644.5.6 Summary 1694.5.7 Appendix: FDTD Representation of Tower Models 1704.6 On the Mechanism of Attenuation of Current Waves Propagating along a Vertical Perfectly Conducting Wire above Ground: Application to Lightning 1714.6.1 Introduction 1714.6.2 Incident Current (Iinc), Incident E-field (Einc): Analytical Solution 1744.6.3 Total Current (Itot), Total E-field (Etot): Numerical Solution 1764.6.4 Scattered Current (Iscat), Scattered E-field (Escat): Iscat = Itot − Iinc, Escat = −Einc 1794.6.5 Dependences of Current Attenuation on the Source Length, Conductor Thickness, and Frequency 1814.6.6 Nonuniform TL Approximation 1844.6.7 Summary 1864.6.8 Appendix: Incident E-field for Two Parallel Vertical Phased Current Source Arrays—Analytical Solution 1874.6.9 Appendix: Total Current for Horizontal Configurations—Numerical Solution 1884.6.10 Appendix: Comparison of FDTD Simulation with an Analytical Solution 1904.6.11 Appendix: E-field Structure around a Vertical Nonzero-Thickness Perfect Conductor 1914.6.12 Appendix: Vertical E-field Produced by an Electrically-Short Vertical Dipole 1924.7 FDTD Simulation of Lightning Surges on Overhead Wires in the Presence of Corona Discharge 1934.7.1 Introduction 1934.7.2 Modeling 1954.7.3 Results and Discussion 1994.7.4 Summary 2094.8 FDTD Simulation of Insulator Voltages at a Lightning-Struck Tower Considering the Ground-Wire Corona 2124.8.1 Introduction 2124.8.2 Methodology 2124.8.3 Analysis and Results 2154.8.4 Summary 2244.9 Voltages Induced on an Overhead Wire by Lightning Strikes to a Nearby Tall Grounded Object 2244.9.1 Introduction 2244.9.2 Methodology 2284.9.3 Analysis and Results 2314.9.4 Discussion 2384.9.5 Summary 2404.9.6 Appendix: Testing the Validity of the FDTD Calculations against Experimental Data (Strikes to Flat Ground) 2424.9.7 Appendix: Comparison with Rusck's Formula (Strikes to Flat Ground) 2434.9.8 Appendix: Testing the Validity of the FDTD Calculations against Experimental Data (Strikes to a Tall Object) 2454.10 3D-FDTD Computation of Lightning-Induced Voltages on an Overhead Two-Wire Distribution Line 2474.10.1 Introduction 2474.10.2 Methodology 2494.10.3 Analysis and Results 2524.10.4 Summary 2604.11 FDTD Simulations of the Corona Effect on Lightning-Induced Voltages 2604.11.1 Introduction 2604.11.2 Methodology 2614.11.3 Analysis and Results 2634.11.4 Discussion 2694.11.5 Summary 2774.12 FDTD Simulation of Surges on Grounding Electrodes Considering Soil Ionization 2774.12.1 Introduction 2774.12.2 Representation of Soil Ionization and De-ionization 2784.12.3 Analysis and Results 2794.12.4 Conclusions 2884.13 Summary 288References 288Appendix: 3D-FDTD Program in C++ 299Index 311

Professor Yoshihiro Baba, Associate Professor, Department of Electrical Engineering, Doshisha University, Kyoto, JapanProfessor Baba received his PhD from the University of Tokyo. He was Visiting Scholar at the Lightning Laboratory at the University of Florida, USA, and is currently Editor of the IEEE Transactions on Power Delivery. His areas of interest include computational electromagnetics, electromagnetic compatibility and lightning protection.Professor Vladimir A. Rakov, Department of Electrical and Computer Engineering, University of Florida, USAProfessor Rakov studied for his PhD at Tomsk University in Russia and has written extensively on the subject of lightning in numerous international journals and conference proceedings. He is A Fellow of the IEEE and a Fellow of the American Meteorological Society, amongst others, and his areas of interest cover lightning, lightning protection and atmospheric electricity.

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• Preface xi1 Introduction 11.1 Historical Overview of Lightning Electromagnetic-Field and Surge Computations 11.2 Overview of Existing Electromagnetic Computation Methods 21.2.1 Method of Moments 21.2.2 Partial-Element Equivalent-Circuit Method 41.2.3 Finite-Element Method 41.2.4 Transmission Line Modeling Method 41.2.5 Constrained Interpolation Profile Method 51.2.6 Finite-Difference Time Domain Method 61.3 Summary 7References 72 Lightning 112.1 Introduction 112.2 Thundercloud 122.2.1 Formation of Thunderclouds 122.2.2 Mechanism of Cloud Electrification 142.3 Lightning Discharges 152.3.1 Categories of Lightning Discharges 152.3.2 Classification of Cloud-to-Ground Lightning Discharges 152.3.3 Downward Negative Lightning Discharges to Ground 162.3.4 Positive Lightning Discharges 232.3.5 Upward Lightning Discharges 232.3.6 Rocket-Triggered Lightning Discharges 252.4 Lightning Electromagnetic Fields 262.4.1 Measured Lightning Return-Stroke Electromagnetic Fields 262.4.2 Mathematical Expressions for Calculating Electric and Magnetic Fields 292.5 Lightning Surges 312.5.1 Surges Due to Direct Lightning Strike 312.5.2 Surges Induced by a Nearby Lightning Strike 322.5.3 Surges Coming from Grounding Due to Its Potential Rise 332.6 Lightning Surge Protection 342.6.1 Insulation Coordination 342.6.2 Protection against Direct Lightning Strikes 352.6.3 Back-Flashover Phenomena 372.6.4 Lightning Surge Protection Measures 382.7 Summary 40References 413 The Finite-Difference Time Domain Method for Solving Maxwell's Equations 433.1 Introduction 433.2 Finite-Difference Expressions of Maxwell's Equations 443.2.1 3D Cartesian Coordinate System 443.2.2 2D Cylindrical Coordinate System 493.3 Subgridding Technique 513.4 Absorbing Boundary Conditions 553.5 Representation of Lumped Sources and Lumped Circuit Elements 573.5.1 Lumped Voltage Source 573.5.2 Lumped Current Source 573.5.3 Lumped Resistance 593.5.4 Lumped Inductance 593.5.5 Lumped Capacitance 603.6 Representation of Thin Wire 613.7 Representation of Lightning Return-Stroke Channel 633.7.1 Lightning Return-Stroke Channel 633.7.2 Excitations 663.8 Representation of Surge Arresters 673.9 Summary 69References 704 Applications to Lightning Surge Protection Studies 734.1 Introduction 734.1.1 Overview 734.1.2 Lightning Electromagnetic Fields at Close and Far Distances 734.1.3 Lightning Surges on Overhead Power TL Conductors and Towers 754.1.4 Lightning Surges on Overhead Distribution and Telecommunication Lines 764.1.5 Lightning Electromagnetic Environment in Power Substations 774.1.6 Lightning Surges in Wind-Turbine-Generator Towers 774.1.7 Lightning Surges in Photovoltaic Arrays 784.1.8 Lightning Electromagnetic Environment in Electric Vehicles 784.1.9 Lightning Electromagnetic Environment in Airborne Vehicles 784.1.10 Lightning Surges and the Electromagnetic Environment in Buildings 794.1.11 Surges on Grounding Electrodes 794.2 Electromagnetic Fields at the Top of a Tall Building Associated with Nearby Lightning Return Strokes 804.2.1 Introduction 804.2.2 Methodology 814.2.3 Analysis and Results 854.2.4 Summary 964.2.5 Appendix: Comparison of Fields in the Absence of a Building Computed Using the FDTD Method and Thottappillil et al.'s (2001) Analytical Expressions 964.2.6 Appendix: Enhancement Factors Due to the Presence of Hemisphere or Rectangular Building in a Uniform Static Electric Field 974.3 Influence of Strike Object Grounding on Close Lightning Electric Fields 1004.3.1 Introduction 1004.3.2 Methodology 1034.3.3 Analysis and Results 1054.3.4 Discussion 1224.3.5 Summary 1284.3.6 Appendix: Comparison of Fields Due to a Lightning Strike to Flat Ground Calculated Using the FDTD Method in the 2D Cylindrical Coordinate System and Thottappillil et al.'s (2001) Analytical Expressions 1284.4 Simulation of Corona at Lightning-Triggering Wire: Current, Charge Transfer, and Field Reduction Effect 1294.4.1 Introduction 1294.4.2 General Approach 1354.4.3 Model 1364.4.4 Analysis and Results 1414.4.5 Discussion 1454.4.6 Summary 1494.4.7 Appendix: Geometry of a Wire Corona Sheath 1494.5 On the Interpretation of Ground Reflections Observed in Small-Scale Experiments Simulating Lightning Strikes to Towers 1514.5.1 Introduction 1514.5.2 Current Pulses Propagating along a Conical Conductor Excited at Its Apex or Base 1534.5.3 FDTD Simulation of Small-Scale Experiments 1574.5.4 Interpretation of Ground Reflections Arriving at the Tower Top 1624.5.5 TL Representation of a Tall Object on the Ground Plane 1644.5.6 Summary 1694.5.7 Appendix: FDTD Representation of Tower Models 1704.6 On the Mechanism of Attenuation of Current Waves Propagating along a Vertical Perfectly Conducting Wire above Ground: Application to Lightning 1714.6.1 Introduction 1714.6.2 Incident Current (Iinc), Incident E-field (Einc): Analytical Solution 1744.6.3 Total Current (Itot), Total E-field (Etot): Numerical Solution 1764.6.4 Scattered Current (Iscat), Scattered E-field (Escat): Iscat = Itot − Iinc, Escat = −Einc 1794.6.5 Dependences of Current Attenuation on the Source Length, Conductor Thickness, and Frequency 1814.6.6 Nonuniform TL Approximation 1844.6.7 Summary 1864.6.8 Appendix: Incident E-field for Two Parallel Vertical Phased Current Source Arrays—Analytical Solution 1874.6.9 Appendix: Total Current for Horizontal Configurations—Numerical Solution 1884.6.10 Appendix: Comparison of FDTD Simulation with an Analytical Solution 1904.6.11 Appendix: E-field Structure around a Vertical Nonzero-Thickness Perfect Conductor 1914.6.12 Appendix: Vertical E-field Produced by an Electrically-Short Vertical Dipole 1924.7 FDTD Simulation of Lightning Surges on Overhead Wires in the Presence of Corona Discharge 1934.7.1 Introduction 1934.7.2 Modeling 1954.7.3 Results and Discussion 1994.7.4 Summary 2094.8 FDTD Simulation of Insulator Voltages at a Lightning-Struck Tower Considering the Ground-Wire Corona 2124.8.1 Introduction 2124.8.2 Methodology 2124.8.3 Analysis and Results 2154.8.4 Summary 2244.9 Voltages Induced on an Overhead Wire by Lightning Strikes to a Nearby Tall Grounded Object 2244.9.1 Introduction 2244.9.2 Methodology 2284.9.3 Analysis and Results 2314.9.4 Discussion 2384.9.5 Summary 2404.9.6 Appendix: Testing the Validity of the FDTD Calculations against Experimental Data (Strikes to Flat Ground) 2424.9.7 Appendix: Comparison with Rusck's Formula (Strikes to Flat Ground) 2434.9.8 Appendix: Testing the Validity of the FDTD Calculations against Experimental Data (Strikes to a Tall Object) 2454.10 3D-FDTD Computation of Lightning-Induced Voltages on an Overhead Two-Wire Distribution Line 2474.10.1 Introduction 2474.10.2 Methodology 2494.10.3 Analysis and Results 2524.10.4 Summary 2604.11 FDTD Simulations of the Corona Effect on Lightning-Induced Voltages 2604.11.1 Introduction 2604.11.2 Methodology 2614.11.3 Analysis and Results 2634.11.4 Discussion 2694.11.5 Summary 2774.12 FDTD Simulation of Surges on Grounding Electrodes Considering Soil Ionization 2774.12.1 Introduction 2774.12.2 Representation of Soil Ionization and De-ionization 2784.12.3 Analysis and Results 2794.12.4 Conclusions 2884.13 Summary 288References 288Appendix: 3D-FDTD Program in C++ 299Index 311