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METHODOLOGY ANDTECHNOLOGY FORPOWER SYSTEMGROUNDING

METHODOLOGY ANDTECHNOLOGY FORPOWER SYSTEMGROUNDING

Jinliang He

Rong Zeng

Bo Zhang

Department of Electrical Engineering, Tsinghua University, China

This edition first published 2013

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Library of Congress Cataloging-in-Publication Data

He, Jinliang.

Methodology and technology for power system grounding / Jinliang He, Rong Zeng, Bo Zhang.

pages cm

Includes bibliographical references and index.

ISBN 978-1-118-25495-0 (cloth)

1. Electric currents–Grounding. 2. Electric power systems–Protection. I. Zeng, Rong, 1971- II. Zhang, Bo,

1976- III. Title.

TK3227.H425 2012

621.31902–dc232012024667

ISBN 9781118254950

Set in 9/11 pt Times by Thomson Digital, Noida, India

http://www.wiley.com

Contents

Preface xiii

Acknowledgements xv

1 Fundamental Concepts of Grounding 1

1.1 Conduction Mechanism of Soil 1

1.1.1 Soil Structure 1

1.1.2 Conduction Mechanism of Soil 1

1.2 Functions of Grounding Devices 2

1.2.1 Concept of Grounding 2

1.2.2 Classification of Grounding 3

1.2.3 Purpose of Grounding 5

1.3 Definition and Characteristics of Grounding Resistance 7

1.3.1 Definition of Grounding Resistance 7

1.3.2 Relationship between Grounding Resistance and Capacitance 8

1.3.3 Shielding Effect among Grounding Conductors 9

1.4 Grounding Resistance of Grounding Devices 11

1.4.1 Grounding Resistance of General Grounding Devices 11

1.4.2 Grounding Resistance of Grounding Device in Non-Homogeneous Soil 14

1.5 Body Safety and Permitted Potential Difference 19

1.5.1 Allowable Body Current Limit 19

1.5.2 Allowable Body Voltage 20

1.5.3 Allowable Potential Difference 21

1.5.4 Influence of Resistivity of Surface Soil Layer on Body Safety 23

1.6 Standards Related to Power System Grounding 25

References 26

2 Current Field in the Earth 27

2.1 Electrical Property of Soil 27

2.1.1 Soil Resistivity 27

2.1.2 Influence of Different Factors on Soil Resistivity 29

2.1.3 Permittivity of Soil 30

2.1.4 Frequency Characteristics of Soil Parameters 31

2.2 Basic Properties of a Constant Current Field in the Earth 36

2.2.1 Current Density in the Earth 36

2.2.2 Continuity of Earth Current Field 36

2.2.3 Potential of Stable Current Field 37

2.2.4 Current Field at the Interface of Layered Soil 37

2.3 Current Field Created by a Point Source in Uniform Soil 38

2.3.1 Laplace’s Equation 38

2.3.2 Current Field Created by a Point Source in Soil 39

2.3.3 Earth Current Field Produced by Two Opposite Point Current Sources

on the Ground Surface 41

2.3.4 Earth Current Field in Non-Uniform Soil 41

2.4 Potential Produced by a Point Source on the Ground Surface in Non-Uniform Soil 43

2.4.1 Horizontally Layered Soil 44

2.4.2 Horizontal Double-Layer Soil 45

2.4.3 Horizontal Triple-Layer Soil 46

2.4.4 Vertically Layered Soil 46

2.5 Potential Produced by a Point Source in Multi-Layered Soil 48

2.5.1 Analysis of Potential Produced by a Point Current Source 48

2.5.2 Numerical Integral Method to Calculate Green’s Function of a Point

Current Source 52

2.6 Computer Program Derivation Method of Green’s Function 55

2.6.1 Method of Obtaining Analytic Expression 55

2.6.2 Expression of Green’s Function Derived from Software Program 59

2.6.3 Calculation of Current Field in Multi-Layered Soil 62

2.7 Fast Calculation Method of Green’s Function in Multi-Layered Soil 62

2.7.1 Development of a Two-Stage Fitting Method 63

2.7.2 Application of the Fast Calculation of Green’s Function

in Multi-Layered Soils 66

2.8 Current and Potential Distributions Produced by a DC Ground Electrode 69

2.8.1 Current and Potential Distributions of DC in Uniform Soil 69

2.8.2 Current and Potential Distributions of DC Current in Non-Uniform Soil 72

References 78

3 Measurement and Modeling of Soil Resistivity 81

3.1 Introduction to Soil Resistivity Measurement 81

3.2 Measurement Methods of Soil Resistivity 83

3.2.1 Sampling Analysis Method of Soil Resistivity 83

3.2.2 Electrical Sounding Methods 83

3.2.3 Test Probe Configuration for Four-Probe Method 88

3.2.4 Field Test Technique of Soil Resistivity 90

3.2.5 Electromagnetic Sounding Method 93

3.3 Simple Analysis Method for Soil Resistivity Test Data 94

3.3.1 Electrical Sounding Curve Method for Two-Layered Horizontal

Soil Model 94

3.3.2 Analysis of a Three-Layered Horizontal Geological Structure 99

3.3.3 Resistivity of Vertically Layered Soil Structure 101

3.3.4 Estimation of Soil Model Parameter using the Three-Probe Method 102

3.4 Numerical Analysis for a Multi-Layered Soil Model 102

3.4.1 Typical Curves of Multi-Layered Soil Apparent Resistivity 102

3.4.2 Expression of Apparent Soil Resistivity 105

3.4.3 Inverting Soil Parameters 107

3.4.4 Numerical Analysis Method for Two-Layered Soil Model 108

3.5 Multi-Layered Soil Model by Solving Fredholm’s Equation 109

3.5.1 Solving the Forward Integral Equation 109

3.5.2 Inversing Parameters of Soil Models 113

3.5.3 Application in Estimation of Soil Parameters 116

vi Contents

3.6 Estimation of Multi-Layered Soil Model by Using the Complex Image Method 118

3.6.1 Estimation of Multi-Layered Soil Structure 119

3.6.2 Fast Calculation of the Soil Apparent Resistivity 119

3.6.3 Partial Derivatives of Calculated Apparent Resistivity 121

3.6.4 The Partial Derivative Expressions of f(l) 123

3.6.5 Determination of the Initial Soil Parameters 123

3.7 Engineering Applications 123

References 128

4 Numerical Analysis Method of Grounding 131

4.1 Calculation Method for Parameters of Substation Grounding Systems 131

4.1.1 Calculation of Grounding Parameters with Empirical Formulas 131

4.1.2 Numerical Analysis Method for Grounding System Parameters 132

4.2 Equal Potential Analysis of Grounding Grid 135

4.2.1 Approach of Green’s Function for Calculating Grounding Parameters 135

4.2.2 Superposition Method Under the Assumption of Nodal Leakage Current 139

4.2.3 Multi-Step Method Under the Assumption of Nodal Leakage Current 141

4.2.4 Integration Method Under the Assumption of Branch Leakage Current 143

4.3 Unequal Potential Analysis of a Large-Scale Grounding System 146

4.3.1 Analysis Model of a Grounding System with Unequal Potential 147

4.3.2 Problems in the Analytical Method for Solving a Mutual Resistance

Coefficient 148

4.3.3 Numerical Integration Method for Mutual Resistance Coefficient

Calculation 148

4.3.4 Multi-Step Method for Uniform Soil 149

4.4 Analyzing Grounding Grid with Grounded Cables 151

4.4.1 Principles of Setting up Equations 151

4.4.2 Calculating Self-Admittances of Conductors and Cables 153

4.5 MoM Approach for Grounding Grid Analysis in Frequency Domain 153

4.5.1 Basis Functions of MoM 153

4.5.2 Setting up the Equations 154

4.5.3 Green’s Functions and Generalized Sommerfeld Integral 155

4.6 Finite Element Method for a Complex Soil Structure 159

4.7 Time Domain Method for Electromagnetic Transient Simulation

of a Grounding System 161

4.7.1 Generalized MMC Method under EMQS Assumption 161

4.7.2 Numerical Approach Based on Time Domain Integral Equation

in a Lossy Medium 171

4.7.3 Finite Difference Time Domain Method 181

References 186

5 Ground Fault Current of a Substation 191

5.1 Power Station and Substation Ground Faults 191

5.1.1 Types of Power Station and Substation Ground Faults 191

5.1.2 Principle to Determine Maximum Ground Fault Current 191

5.1.3 Location of the Maximum Ground Fault Current 193

5.2 Maximum Fault Current through a Grounding Grid to the Earth 194

5.2.1 Maximum Grounding Grid Fault Current 194

5.2.2 Zero-Sequence Fault Current 194

5.2.3 Determining the Fault Current Division Factor 195

5.2.4 Determining the Decrement Factor 196

Contents vii

5.2.5 Determining the Correction Coefficient for Future Planning 198

5.2.6 Impact of Substation Grounding Resistance 199

5.2.7 Impact of Fault Resistance 200

5.2.8 Impact of Overhead Ground Wires and Neutral Lines 200

5.2.9 Impact of Buried Conduits and Cables 200

5.2.10 Steps to Determine a Proper Design Value of the Maximum Grounding

Grid Current 200

5.3 Simplified Calculation of a Fault Current Division Factor 201

5.3.1 Fault Current Division Factor Within a Local Substation 201

5.3.2 Fault Current Division Factor Outside a Local Substation 202

5.4 Numerical Calculation of the Fault Current Division Factor 203

5.4.1 Numerical Calculation Method of the Fault Current Division Factor 203

5.4.2 Matrix Method to Calculate the Fault Current Division Factor 207

5.4.3 Phase Coordinate Transformer Model for Calculating the Fault

Current Division Factor 207

5.5 Typical Values of the Fault Current Division Factor 213

5.5.1 Influence of Substation Grounding Resistance 213

5.5.2 Influence of Transmission Towers 214

5.5.3 Influence of Fault Location 216

5.5.4 Influence of Incoming Cables 216

5.5.5 Influence of Transmission Line Number 216

5.5.6 Influence of Transmission Line Length 217

5.5.7 Influence of Transformer 217

5.6 Influence of Seasonal Freezing on the Fault Current Division Factor 219

5.6.1 Influence of Seasonally Frozen Soil on the Fault Current Division Factor 219

5.6.2 Influence of Transmission Line Numbers Affected by Frozen Soil 221

References 221

6 Grounding System for Substations 223

6.1 Purpose of Substation Grounding 223

6.1.1 Function of Substation Grounding 223

6.1.2 Design Objective of a Substation Grounding System 224

6.1.3 Requirement on the Grounding System of a Substation 225

6.1.4 Specificity of Power Plant Grounding 225

6.1.5 Requirements for Grounding System Design 226

6.1.6 Design and Construction Procedures for a Grounding System 226

6.2 Safety of Grounding Systems for Substations and Power Plants 227

6.2.1 Design Criteria of Grounding Systems 227

6.2.2 Calculation of the Grounding Resistance of a Grounding System 228

6.2.3 Analysis of Grounding in Inhomogeneous Soil 230

6.2.4 Simplified Formula for Calculating Step, Touch and Mesh Voltages 234

6.2.5 Formulas in IEEE Standard 80-2000 for Calculating Mesh and Step

Voltages 235

6.2.6 Formulas to Calculate Touch and Step Voltages in Chinese Standards 237

6.2.7 Transfer Potential 238

6.2.8 Methods for Improving the Safety of a Grounding System 238

6.3 Methods for Decreasing the Grounding Resistance of a Substation 240

6.3.1 Basic Methods for Decreasing Grounding Resistance 240

6.3.2 Using Long Vertical Ground Rods to Decrease Grounding Resistance 241

6.3.3 Explosion Grounding Technique 248

viii Contents

6.3.4 Deep Ground Well 250

6.3.5 Slanting Grounding Electrode 253

6.4 Equipotential Optimal Arrangement of a Grounding Grid 254

6.4.1 Principle of the Unequal-Spacing Arrangement 254

6.4.2 Regularity of the Unequal-Spacing Arrangement 256

6.4.3 Unequal-Spacing Arrangement with Exponential Distribution 263

6.4.4 Influence of Vertical Grounding Electrodes on OCR 267

6.5 Numerical Design of a Grounding System 268

6.5.1 Grounding System Design of a 220-kV Substation 268

6.5.2 Grounding System Design of a 1000-kV UHV Substation 270

References 272

7 Grounding of Transmission and Distribution Lines 275

7.1 Requirement for a Tower Grounding Device 275

7.1.1 Requirement of Transmission Tower Grounding Resistance 276

7.1.2 Seasonal Factor for the Grounding Resistance of a Tower Grounding Device 276

7.2 Structures of Tower Grounding Devices 277

7.2.1 Basic Structures of Tower Grounding Devices 277

7.2.2 Using Natural Footings as Tower Grounding Devices 280

7.3 Properties of a Concrete-Encased Grounding 280

7.3.1 Function of a Concrete-Encased Grounding Device 280

7.3.2 Hygroscopic Properties of Concrete 281

7.3.3 Permissible Current through a Concrete-Encased Grounding Device 283

7.4 Computational Methods for Tower Grounding Resistance 284

7.4.1 Equivalent Cylindrical Conductor Method 284

7.4.2 Grounding Resistance of a Vertical Ground Rod Covered with Concrete 285

7.4.3 Grounding Resistance of a Fabricated Concrete-Encased Footing 286

7.4.4 Grounding Resistance of a Tower Grounding Device with Different

Structures 287

7.4.5 Utilization Coefficient 289

7.5 Step and Touch Voltages Near a Transmission Tower 290

7.5.1 Step Voltage and Touch Voltage 290

7.5.2 Shock Accident Possibilities Caused by Step and Touch Voltages 292

7.6 Short-Circuit Fault on Transmission Tower 294

7.6.1 Fault Current of Transmission Line 294

7.6.2 Distribution of Ground Potential around Transmission Towers 295

7.6.3 Methods to Improve Potential Distribution 296

7.7 Grounding Device of Distribution Lines 299

7.7.1 Vertically Driven Rods 300

7.7.2 Grounding of Wood Poles 301

7.7.3 Requirement for Grounding the Distribution Line 301

References 301

8 Impulse Characteristics of Grounding Devices 303

8.1 Fundamentals of Soil Impulse Breakdown 303

8.1.1 Electric Field Strength of Soil Breakdown 303

8.1.2 Phenomenon of Electrical Breakdown in Soil 312

8.1.3 Impulse Breakdown Delay Characteristics of Soil 319

8.1.4 Mechanism of Electrical Breakdown in Soil 321

8.1.5 Residual Resistivity of Ionized Soil 323

Contents ix

8.2 Numerical Analysis of the Impulse Characteristics of Grounding Devices 325

8.2.1 Equivalent Circuit Model 325

8.2.2 MoM Coupled with Circuit Theory 331

8.2.3 An Interpolation Model to Accelerate the Frequency Domain Response

Calculation 335

8.3 Impulse Characteristics of Tower Groundings 346

8.3.1 Field Test of Grounding Devices Impacted by a Large Impulse Current 346

8.3.2 Lightning Current Decay Along a Grounding Electrode 348

8.3.3 Definition of Impulse Grounding Resistance 350

8.3.4 Influence of Different Factors on the Impulse Grounding Resistance

of Grounding Devices 352

8.3.5 Influence of Different Factors on Impulse Coefficient 355

8.3.6 Regressive Formulas to Calculate Impulse Coefficients 357

8.3.7 Impulse Coefficient and Utilization Efficient Suggested in the Literature 359

8.3.8 Low Resistivity Material Effects to Decrease Impulse Grounding Resistance 360

8.4 Impulse Effective Length of Grounding Electrodes 362

8.4.1 Phenomenon of Impulse Effective Length 362

8.4.2 Regressive Formulas to Calculate the Effective Length of Counterpoise

Wires 364

8.4.3 Influence of LRM on the Impulse Effective Length of Counterpoise Wires 368

8.5 Impulse Characteristics of a Grounding Grid 370

8.5.1 Influence of the Structure of the Grounding Grid 370

8.5.2 Influence of Soil Parameters 374

8.5.3 Influence of Impulse Current Waveform on the Transient Performance

of Grounding Grids 375

8.5.4 Impulse Effective Regions of Grounding Grids 378

8.6 Lightning Electromagnetic Field Generated by a Grounding Electrode 381

8.6.1 Computation Methodologies 381

8.6.2 Disposal of a Lightning Current 383

8.6.3 Influence of Soil Ionization 383

References 385

9 DC Ground Electrode 391

9.1 Technical Requirements of a DC Ground Electrode 391

9.1.1 Technical Characteristics of a DC Ground Electrode 391

9.1.2 Basic Principles of DC Ground Electrode Design 392

9.2 Structure Types of DC Ground Electrodes 394

9.2.1 Land Electrode 394

9.2.2 Shore Ground Electrode 400

9.2.3 Sea Electrode 401

9.3 Main Design Aspects of a DC Ground Electrode 401

9.3.1 Main Design Items 401

9.3.2 Determination of DC Ground Electrode Size 403

9.3.3 Determination of Coke Section 405

9.3.4 Diameter of Feeding Rod 406

9.3.5 Burial Depth of Electrode 407

9.3.6 Selection of Ground Electrode Material 407

9.4 Numerical Analysis Methods for a Ground Electrode 413

9.4.1 Numerical Analysis of a Ground Electrode by MoM and BEM 414

9.4.2 Simplified Numerical Analysis Method 417

x Contents

9.5 Heat Generation Analysis of a DC Ground Electrode 418

9.5.1 Numerical Analysis of the Heat Dissipation of a Ground Electrode 419

9.5.2 Maximum Temperature Rise Limit 422

9.6 Common Ground Electrode of a Multiple Converter System 423

9.6.1 Demands on a Common Ground Electrode 424

9.6.2 Parameters of the Common Ground Electrode 427

9.6.3 Common Ground Electrode Design 429

9.7 Influence of DC Grounding on AC System 433

9.7.1 Influence of DC Electrode’s Current Field on AC System 433

9.7.2 Numerical Analysis of DC Current Entering a Neutral Grounded Transformer 436

9.7.3 Allowable DC Current of a Transformer 443

9.8 Methods to Decrease Winding DC Current of a Neutral Grounding Transformer 445

9.8.1 Injecting Reverse DC Current Method 445

9.8.2 Inserting Capacitor Method 446

9.8.3 Inserting Resistor Method 447

9.9 Corrosion of Underground Metal Pipes Caused by a DC Ground Electrode 455

9.9.1 Mechanism of Electrochemical Corrosion of Underground Metal Pipes 455

9.9.2 Leakage Current through a Metal Pipe Caused by Ground Electrodes 455

9.9.3 Protection Measures 456

References 458

10 Materials for Grounding 461

10.1 Choice of Material and Size for Conductors 461

10.1.1 Requirement on Material and Size of Grounding Conductors 461

10.1.2 Materials for a Grounding Conductor 463

10.1.3 Determination of Conductor Size 464

10.1.4 Grounding Conductor Size Determined by Ground Fault Protection 470

10.2 Soil Corrosion of Grounding Conductor 470

10.2.1 Features of Soil Corrosion 471

10.2.2 Natural Corrosion 471

10.2.3 Electrical Corrosion in Soil 474

10.3 Corrosion of Concrete-Encased Electrodes 476

10.4 Low-Resistivity Material 478

10.4.1 Principle of Reducing Grounding Resistance by LRM 478

10.4.2 Ingredients of LRM 482

10.4.3 Basic Requirements for LRM 485

10.4.4 Evaluation of LRM 487

10.5 Performance of LRM 488

10.5.1 Power Frequency Performance of LRM 488

10.5.2 Lightning Impulse Performance of LRM 493

10.6 Construction Method of LRM 495

10.6.1 Influence of LRM Bulk Shape on Reducing the Grounding Resistance Effect 495

10.6.2 Amount of LRM and Construction Method 495

10.6.3 Construction of a Complex Ground Device 497

References 497

11 Measurement of Grounding 499

11.1 Methods for Grounding Resistance Measurement 499

11.1.1 Simple Methods for Measuring the Grounding Resistance of Small

Grounding Devices 500

Contents xi

11.1.2 Principle of the Fall of Potential Method 501

11.1.3 Method of Far Placed Current Probe for Fall of Potential Method 502

11.1.4 Compensation Location of a Potential Probe for the Fall of Potential

Method 504

11.1.5 Compensation Method for the Fall of Potential Method 506

11.2 Instruments for Measuring Grounding Resistance 510

11.2.1 Ammeter–Voltmeter Method 510

11.2.2 Ammeter–Wattmeter Method 510

11.2.3 Ratio Meter Method 511

11.2.4 Bridge Method 513

11.2.5 Potentiometer Method 514

11.2.6 Single Equilibrium Transformer 514

11.2.7 ZC-8 Grounding Resistance Tester 515

11.2.8 Digital Measurement System of Grounding Resistance 516

11.3 Factors Influencing the Results from the Fall of Potential Method 519

11.3.1 Electromagnetic Interferences During Measurements 519

11.3.2 Impact and Elimination of Power Frequency Interference 520

11.3.3 Components of the Measured Voltage Signal for the Grounding

Resistance Test 521

11.3.4 Mutual Inductance Between Potential and Current Lead Wires 521

11.3.5 Short Measuring Leads Method 527

11.3.6 Accurate Location of Test Probe Positioning by GPS 529

11.3.7 Influence of a Metal Structure Buried Nearby 529

11.3.8 Method to Eliminate Measuring Interference 531

11.4 Grounding Resistance Test in Vertically Layered Soil 532

11.4.1 Grounding System Built in a Middle Low Resistivity Region 532

11.4.2 Grounding System Built in a Middle High Resistivity Region 534

11.4.3 Discussion of Analysis Results 535

11.5 Influence of Overhead Ground Wires on Substation Grounding Resistance

Measurement 535

11.5.1 General Analysis Model 536

11.5.2 General Discussion 536

11.5.3 Analysis of a 500 kV Substation 538

11.6 Measurement of Potential Distribution 539

11.6.1 Equipotential Line 539

11.6.2 Measurement of Equipotential Lines 540

11.6.3 Measurement of Step Voltage and Touch Voltage 541

11.7 Corrosion Diagnosis of Grounding Grids 542

11.7.1 Corrosion Diagnosis Model of a Grounding Grid 543

11.7.2 Implementation of the Diagnosis System 546

11.7.3 Field Test Results 547

References 550

Index 553

xii Contents

Preface

The development of modern power systems for the direction of extra-high voltage, large capacity, far

distance transmission and the application of advanced technologies, is placing higher demands on the

safety, stability and economic operation of power systems. A sound grounding system for substations is

a very important and fundamental countermeasure to guarantee the safe and reliable operation of power

systems and to ensure the safety of human being in the situation of a grounding fault in the power

system. It is also a key method to decrease electromagnetic interferences in substations. Considerable

operation results show that, if the grounding system has not been designed suitably, then control cables

will be destroyed and a high voltage will be led into the control room of the substation. This could make

control devices misfunction or reject operating instructions, which could then cause huge economical

loss and social effects. Further, the ground device directly decides the lightning protection character-

istics of transmission lines.

With the rapid expansion of the capacity of power systems, the short-circuit fault current rises enor-

mously. Under such situations, the grounding resistance should be low enough to guarantee the safety

of the power system. However, the locations of those substations constructed in urban areas are not

always in good sites with low soil resistivity. They are often on hills or in other regions with high soil

resistivity, which means we cannot always simply regard the soil as homogeneous.

Since the 1980s, with the development of computer technology and progress of the numerical analy-

sis technology of electromagnetic fields, the method of moments, boundary element method, complex

image method, finite element method and other direct numerical analysis methods have been widely

applied in the calculation of grounding system parameters. Now the design of grounding systems has

been moved from simple calculations based on the methods provided in standards to full numerical

analysis. Currently, grounding technology has become an interdiscipline related to electrical engineer-

ing, electric safety, electromagnetic theory, numerical analysis method, techniques of measurement and

geological prospecting.

Up to the present, the grounding technology of power systems has achieved much, in both methodol-

ogy and technology:

� Grounding system analysis has moved from a simple estimation based on homogeneous soils and

empirical formulas to a numerical analysis based on complicated soil models.� How to decrease the grounding resistance has become a shoo-in by adding vertical ground rods,

based on realizing the multi-layer structure of soil, rather than simply expanding the area occupied

by the ground grid.� We had gotten to the heart of the lightning impulse characteristics of tower ground devices based on

deeper experimental results of soil ionization performances.

This book contains 11 chapters. First, all fundamental and theoretical knowledge is introduced and

highlighted, including fundamental concepts of grounding, current field in the Earth, modeling of soil

resistivity, numerical analysis method of grounding, ground fault current of a substation and impulse

characteristics of grounding devices. Second, design guidelines for substations, transmission towers

and converter stations are presented, including grounding systems for substations, grounding of a trans-

mission line tower, DC ground electrodes and materials for grounding. Third, measurement methods

and techniques for grounding are introduced, including the measurement and modeling of soil resistiv-

ity, grounding resistance, potential distribution and corrosion diagnosis of grounding grids for power

substations.

This book covers all main aspects of the grounding technologies for power systems, including sub-

stations, converter stations and transmission towers. It introduces fundamental and advanced theories

and technologies related to power system groundings and the research achievements of the past

20 years. This reflects the recent research work of the authors and their students and colleagues at

Tsinghua University, especially the Ph.D. dissertations of Dr. Zeng Rong, Dr. Sun Weimin, Dr. Gao

Yanqing, Dr. Gong Xuehai, Dr. Kang Peng, Dr. Zhang Baoping and Dr. Wang Shunchao and the M.Sc.

theses of Ms. Li Siyun, Mr. Zhang Bo, Mr. Pan Xiyuan, Mr. Ding Qiangfeng, Mr. Yuan Jingping and

Mr. Du Xin. The authors have tried to cover all aspects of power system grounding, but it is hard to

avoid those that may have been left out. Numerous references have been cited in our book, each listed

in the appropriate chapter, but it is hard to avoid accidental omission, in which case we beg your

pardon. We are so sorry, but some formulas could not be traced back to their original references.

xiv Preface

Acknowledgements

Numerous references have been cited in our book, each listed in the appropriate chapter, but it is hard to

avoid accidental omission, in which case we beg your pardon. We are so sorry, but some formulas could

not be traced back to their original references.

During the drafting of this book, Prof. Chen Xianlu of Chongqing Univeristy, who was the director of

my M.Sc. thesis has led me into the door of grounding, provided many valuable comments and allowed

me to refer to his lecture notes and his book manuscript of Grounding. Mr. Du Shuchun, the famous

grounding and lightning protection expert in China, who works in China EPRI, read the manuscript

and gave many modification suggestions. Many colleagues have provided us with materials and sugges-

tions. I would like to extend my sincere thanks to them.

Special thanks also go to my students for their assistance in preparing the draft of this book, and to

my colleagues for their generous help in many ways so as to allow me to allocate time for working on

the book. Great gratitude is given to Mr. Wu Jinpeng for preparing the part manuscript of Chapter 5, to

Dr. Wang Shunchao for preparing the part manuscript of Chapter 4 and to Miss Wang Xi for her assist-

ance in the formatting and editing of the book.

A particular acknowledgment is given to Profs. Zeng Rong and Zhang Bo, the coauthors of this book.

They are the perfect choice for the task. Prof. Zeng has done excellent work in grounding measurement,

and Prof. Zhang has made many contributions in the numerical analysis of grounding systems.

Gratitude is extended to Ms. Shelley Chow, Project Editor at John Wiley & Sons, for her editorial

and technical review of this book. Her professionalism and experience have greatly enhanced the

quality and value of this book.

Last, but not least, my most special gratitude goes to my supporting and understanding family, to my

mother, Yang Ruiru, who taught me to enjoy this wonderful life, to my wife, Prof. Tu Youping, who has

done and is still doing a great job of supporting the family. Most of all, I am indebted to my son, Ziyu, I

have not given much time to enjoy his growing-up process.

Jinliang He

1

Fundamental Conceptsof Grounding

1.1 Conduction Mechanism of Soil

1.1.1 Soil Structure

Soil is a complex system, consisting of solid, liquid and gas components. The solid phase of normal soil

usually includes minerals and organic matter; the liquid phase means the water solution and the gas

phase is the air between the solid particles. The solid phase makes up of the basic structure of the soil,

the liquid and gas phases fill the voids within the structure, as shown in Figure 1.1. Different from

normal soil, a new kind of solid material, ice, is present in frozen soil.

Soil conductivity is strongly determined by water content and water state. According to the distance

from solid particles and the electrostatic force received from solid particles, the water in soil can be

classified into the following types [1]:

Strongly Associated Water. Near the surface of soil particles, the water molecules cram together

closely and cannot move freely due to the great intensity of the electrostatic field. This type of water

is called strongly associated water.

Weakly Associated Water. Being farther from the soil particles, the intensity of the electrostatic field

has comparatively decreased, so the water molecules are more active and weakly oriented. This type

of water is still mainly affected by the electrostatic field and is called weakly associated water.

Capillary Water. As the distance between soil particles and water molecules increases, the water mol-

ecules become mainly affected by gravity. Although the electrostatic field still plays a role, it does

not have a primary function. This type is called capillary water.

Gravity Water. As the distance between soil particles and water molecules continues to increase, the

effect of the electrostatic field becomes negligible to the water molecules, and the water molecules

are only controlled by gravity. This type is called gravity water or ordinary liquid water.

1.1.2 Conduction Mechanism of Soil

Research has shown that soil conductivity falls with dropping temperature. This can be explained by

the theory of electrochemistry [2,3], because the electrical conduction in soil is predominantly electro-

lytic conduction in the solutions of water-bearing rocks and soils. Accordingly, the resistivity of soil or

rock normally depends on the degree of porosity or fracturing of the material, the type of electrolyte

Methodology and Technology for Power System Grounding, First Edition. Jinliang He, Rong Zeng and Bo Zhang.� 2013 John Wiley & Sons Singapore Pte. Ltd. Published 2013 by John Wiley & Sons Singapore Pte. Ltd.

and the temperature. Metallic conduction, electronic semiconduction and solid electrolytic conduction

can occur but only when specific native metals and minerals are present [28]. Similar to the solid

medium, frozen soil is obviously distinguished from normal soil.

Because of the charges and ions attracted onto the surface of soil particles, soil can be considered as

a polyvalent electrolyte. Soil conductance is the contribution of both charged soil particles (known as

colloidal particle conductance, mainly decided by the amount of charge on the surface of soil particles)

and ions in solution (known as ion conductance, mainly decided by the diffusion velocity of ions).

When ions diffuse into the soil solution, the diffusion velocity is affected by the resistance of the water

molecules. As the temperature drops, the water becomes more viscous and its diffusion becomes slower

because the resistance of water molecules increases. In contrast, the ions are affected by the soil elec-

trostatic resistance. As the temperature lowers, the average kinetic energy of ions decreases and the

capacity to overcome the soil electrostatic resistance also decreases and the diffusion velocity slows

up. So, ion conductance decreases and soil resistivity increases as the temperature drops.

When the soil temperature decreases to 0 8C or even lower, most of the water in the soil is frozen

gradually and the ice (with high resistivity) fills the voids between the soil particles in the form of grains

or laminas, so the conductive cross-section of soil reduces. The thickness of the water film coating the

soil particles is reduced and the activity of the water molecules becomes weak. So, the resistivity of

frozen soil is significantly higher than that of normal soil. When the soil is chilled to a much lower

temperature, most of the soil water is frozen and the ion conductance created by ion movements gradu-

ally disappears. Finally, there would be only colloidal particle conductance created by the charges on the

surface of soil particles, which is not related to temperature, so a saturation phenomenon appears.

1.2 Functions of Grounding Devices

1.2.1 Concept of Grounding

Grounding is provided to connect some parts of electrical equipment and installations or the neutral

point of a power system to the earth. This provides dispersing paths for fault currents and lightning

currents in order to stabilize the potential and to act as a zero potential reference point to ensure the

safe operation of the power system and electrical equipment and the safety of power system operators

and other persons. Grounding is achieved by grounding devices (or ground devices) buried in soil. The

grounding devices of a power system can be divided into a relatively simple one for transmission line

towers, such as a horizontal grounding electrode (or ground electrode), vertical ground rod, or ring

grounding electrode, and the other is the grounding grid (or ground grid) for a substation or power plant.

Figure 1.1 Photo showing the microstructure of soil.

2 Methodology and Technology for Power System Grounding

The grounding device is a single metal conductor or a group of metal conductors buried in soil,

including horizontally or vertically buried metal conductors, metal components, metal pipes, reinforced

concrete foundations of structures, metal equipment, or a metal grid in soil. The grounding system

refers to the whole system, including the grounding device of a substation or power plant, and all metal

tanks for the power apparatus and electrical equipment, towers, overhead ground wires, neutral points

of transformers and the metal sheaths of cables connected with the grounding device.

The basic parameter to indicate the electrical property of a grounding device is grounding resist-

ance (or ground resistance), which is defined as the ratio of the voltage on the grounding device

with respect to the zero potential point at infinity and the current injected into earth through the

grounding device. If the current is a power-frequency alternating current (AC), the grounding

resistance is called a power-frequency grounding resistance. If the current is an impulse current,

such as a lightning current, then it is called an impulse grounding impedance, which is a time-

variant transient resistance. The impulse grounding resistance of a grounding device is usually

defined as the ratio of the peak value Vm of the voltage developed at the feeding point to the peak

value Im of the injected impulse current into the grounding device.

1.2.2 Classification of Grounding

The grounding devices of AC electrical equipment for a power system can be divided into three catego-

ries according to their functions: working grounding, lightning protection grounding and protective

grounding. Further, the instrumentation and control equipment of the substation should also be grounded.

1.2.2.1 Working Grounding

Based on whether the neutral point is grounded, an AC power system can be classified into a neutral-

point effective grounding system or a neutral-point ineffective grounding system (including neutral-point

ungrounded system, neutral-point resistance grounding system and neutral-point reactance grounding

system). In order to reduce the operating voltage on the insulation of the power apparatus, the neutral-

points of power systems of 110 kV and above are solidly grounded. This grounding mode is called a

working grounding. For the neutral-point effectively grounded operation mode, under normal situa-

tions, the voltage on the insulation of the power apparatus (such as a power transformer) is the phase

voltage. If the neutral-point is insulated, when the single-phase grounding fault occurs, the voltage on

the insulation of the power apparatus is the line voltage before the breaker cuts off the fault, which isffiffiffi3

ptimes as high as the phase voltage. The neutral-point effectively grounded operation mode can

effectively reduce the voltage on the insulation of the power apparatus and the insulation level of the

power apparatus is reduced, so the purpose of reducing the insulation size and lowering the cost of the

equipment is achieved. For the neutral-point solidly grounded system, the current through the ground-

ing device is the unbalanced current of the system under normal situations and, when a short circuit

fault occurs, a short-circuit current of tens of kilo-amperes (kA) will flow through the grounding device,

and usually the short-circuit current will last about 0.5 s.

Usually, the neutral point of the double-pole DC transmission system is grounded, which can operate

under single pole mode by using the earth as the return path. Operating in single pole mode, a current of

several kA will flow through the grounding electrode over a long period of time and we should pay

particular attention to the electrochemical corrosion of the grounding electrode.

For a power distribution system, a step-down transformer is used to connect the high-voltage system

with the low-voltage system and, according to whether the neutral point of the transformer is grounded,

the low-voltage distribution system can be classified into a grounded system (either solidly or through

impedance) or an ungrounded system. Figure 1.2 shows a low-voltage distribution system with neutral

point grounded. If someone touches the low-voltage conductor, a loop will be formed in which the

current through the body is related to the contact resistance between the body and earth. If the contact

resistance is small, a dangerous current will flow through the body and harm it.

Fundamental Concepts of Grounding 3

For water lighting and other power supply lines, it is necessary to add an insulated transformer

with a secondary side neutral point not grounded. This kind of system is called a neutral point

ungrounded system. As shown in Figure 1.3, when a person contacts the secondary circuit of the

neutral point ungrounded system, only a very small current flows through the loop circuit, which is

formed by the distributed capacitance, and it passes through the body, so it is much safer. One short-

coming of an ungrounded system is that there is no way to inhibit this abnormal voltage and it will

cause a hazard on the secondary side, when the system voltage is increased for some special reason,

such as the mixed contact of the high and low voltage circuits, a lightning impulse, a switching

voltage and so on. Another shortcoming is that an ageing insulation will possibly break down, thus

leading to a grounding accident.

1.2.2.2 Protective Grounding

When the insulation of electrical equipment fails, its enclosure becomes live and a person will suffer an

electric shock if he or she contacts its enclosure. In order to guarantee personal safety, the enclosures of

all electrical equipment should be grounded. This kind of grounding is called protective grounding.

When the enclosure of electrical equipment is live due to insulation damage, the fault current flowing

through the protective grounding device should trigger a relay protection device to cut off the faulty

equipment, and we can also reduce the grounding resistance to make sure that the voltage on the enclo-

sure is lower than the value of the body safety voltage, so that electric shock accidents caused by the

live enclosure can be avoided.

Figure 1.3 Ungrounded low-voltage distribution system.

Figure 1.2 Solid grounding of a low-voltage distribution system.


1.2.2.3 Lightning Protection Grounding

In order to prevent the hazard of lightning to power systems and human beings, lightning rods, shield-

ing wires, surge arresters and other lightning protection equipment are usually adopted. Such lightning

protection equipment should all be connected to suitable grounding devices to lead the lightning current

into the earth. This kind of grounding is called lightning protection grounding. The lightning current

through the lightning protection grounding device is huge and can reach hundreds of kilo-amperes, but

it has a very short duration, tens of microseconds in general.

1.2.2.4 Signal Reference Grounding

A large number of instrumentation and control devices based on solid electronic devices are widely used

in modern power systems, but these devices need a signal reference point when in operation. Signal

reference grounding plays a very important role in making sure that the electronic devices and the com-

puter control system work regularly. But in the modern power system, it is very difficult to provide a

pure signal reference ground without interference. So, how to improve the anti-interference ability of the

signal ground is one of the important issues that should be considered during signal ground design. From

the functional point of view, the signal reference grounding is a kind of special working grounding.

1.2.3 Purpose of Grounding

Reducing Insulation Level of Electrical Equipment. As mentioned earlier, the working grounding

formed by grounding the power system neutral point can decrease the operating voltage on the power

apparatus and thereby reduces the insulation level of the power apparatus.

Ensuring Safe Operation of Power System. The grounding resistance of transmission line towers

must be lower than a certain value to reduce the potential difference between the transmission tower

top and the phase conductor. A value of less than 50% of the impulse flashover voltage of the insula-

tor can guarantee the safe operation of transmission lines. If the grounding resistance is too large, it

could possibly cause a tower top potential which is high enough to trigger an insulators string flash-

over and a power outage might happen.

In addition, as mentioned before, lightning protection systems in substations, such as lightning

rods, shielding wires and surge arresters, must be grounded to the grounding devices to discharge

the lightning energy to the earth.

Ensuring Personal Safety. As mentioned above, the protective grounding is intended to make the

enclosures of all electrical equipment grounded. When damage or the aging of equipment insulations

make the enclosures live, it can ensure the safety of any person who contacts the shell of the equip-

ment. However, the grounding devices of substations can make sure that the personal touch voltage

and step voltage meet the desired safety requirements by reducing the grounding resistance and tak-

ing voltage equalization measures. The touch voltage is the potential difference between one hand

and one foot when a person contacts the equipment shell or metal components under power system

failure, while the step voltage is the potential difference between two feet.

Eliminating Electrostatic Accidents. Static electricity may cause an explosion and fire, and oil storage

tanks and natural gas pipelines are particularly susceptible to an explosion caused by electrostatic

discharge. Further, static electricity may interfere with the normal work of solid electronic devices.

Through grounding, the static charges generated and collected by friction and other factors can be

released to the earth as soon as possible to prevent accidents and damage caused by static interference.

Detecting Ground Faults. In order to ensure personal and property safety, leakage breakers and other

fault leakage protection devices are used in low-voltage circuits. If a ground fault happens at one

point in the circuit, there must be a very large ground fault current to bring the protection device into

action. In order to meet this condition, the neutral point on the secondary side of the step-down trans-

former should be grounded. In contrast, for a neutral point grounded circuit, if the enclosure of the


electrical equipment is not grounded, when the electrical equipment enclosure is charged due to

insulation damage or other reasons, the current generated in the circuit by the distributed capacitors

cannot trigger the protection device, so the equipment enclosure should be grounded, as shown in

Figure 1.4. The current I is:

I ¼ U

R0 þ RE

ð1:1Þ

where U is the phase voltage of the circuit, R0 is the grounding resistance of the neutral point (for a

380/220V low-voltage AC circuit, the value of the grounding resistance is generally selected as 4V)

and RE is the grounding resistance of the electrical equipment.

Equipotential Bonding. Equipotential bonding is a kind of connection mode to ensure that externally

exposed conductive bodies of a device have the same potential. The electrical equipment inside a

building can achieve equipotential bonding through grounding the equipment enclosure with the

main ground bus, as shown in Figure 1.5. The purpose of equipotential bonding is to prevent danger-

ous potential differences between different devices or to avoid forming a loop, because the loop

formed by grounding connection is vulnerable to external electromagnetic fields, and the loop cur-

rent will interfere with the normal operation of equipment.

Reducing Electromagnetic Interference. External electromagnetic interference may cause electronic

devices to malfunction, or may interfere with a signal transmitted by cable. This can be reduced or

eliminated by grounding the shielding shell of the electrical equipment and the cable shielding

sheath. Further, in order to prevent the high-frequency energy generated by electronic devices from

interfering with other devices, the electronic devices should also be grounded. Grounding to prevent

electromagnetic interference has different types, such as grounding of shielding rooms or shielding

layers, grounding of cable-shielding sheaths, grounding of transformer electrostatic shields, ground-

ing of the protection devices for precision instrumentations and so on. The power line filters at the

entrances of electric or electronic devices should also be grounded. In short, grounding against elec-

tromagnetic interference provides a channel for energy to be released into the earth.

Function Grounding. Some equipment needs to be grounded functionally, for example cathodic pro-

tection makes use of electrochemistry to prevent metal corrosion. In order to make the corrosion

current flow into the earth, the cathodic protection system should be grounded.

Additionally, a reference point with a stable potential must be adopted to ensure the regular oper-

ation of computers and other electrical equipment, which can be achieved by grounding.

Figure 1.4 Grounding of the enclosure of electrical equipment to ensure the protection device is triggered.


Work Grounding. When operating personnel work on transmission lines under power outages, the

energy stored in the transmission line and other equipment should be discharged by grounding, to

prevent any hazards to the operating personnel from the induced current through the transmission line.

Further, any fatal harm to operating personnel caused by anothers’ false operation can be prevented.

1.3 Definition and Characteristics of Grounding Resistance

1.3.1 Definition of Grounding Resistance

Grounding resistance is the ratio between the potential of the grounding device and the current flowing

into the earth through the grounding device, which is related to the soil characteristics and the size and

shape of the grounding device.

The soil resistance encountered when a current flows into the soil is called the current-dispersing

resistance. The grounding resistance consists of the ground lead resistance, the contact resistance

between the ground lead and the grounding device, the resistance of grounding conductors themselves,

the contact resistance between the grounding conductors and soil and the current-dispersing resistance

of the soil. Because the current-dispersing resistance is much greater than the other four kinds of resist-

ance, the grounding resistance of a grounding device approximates to the current-dispersing resistance.

Usually, the grounding resistance of a grounding device calculated by numerical methods or empirical

formulas is the current-dispersing resistance of the soil, but the actually measured value is generally

greater than the calculated result. This is because the actual contact between grounding conductors and

the soil is not a complete surface-like contact, but a point-like contact. This leads to a contact resistance

between the grounding conductors and the soil, especially in rocky areas, where the contact resistance

is sometimes quite high. This contact resistance has an uncertain value, which is related to the soil

compression degree during construction, the soil particle status, the soil moisture and so on, but the

contact resistance cannot be reflected in the calculation formula.

For example, as shown in Figure 1.6, the radius of a hemispherical grounding device is r0, the current

flowing into the earth through the grounding device is I, assuming the terra firma is an homogenous soil

Figure 1.5 Equipotential bonding of electrical equipment.


with resistivity of r. The potential of the point with a distance r to the center of the hemispherical

grounding device can be calculated by the potential formula of a point current source, which is:

v ¼ Ir

2prð1:2Þ

The potential v0 of the grounding device can be calculated by Equation 1.2 when r¼ r0:

v0 ¼ Ir

2pr0ð1:3Þ

The potential distribution of the hemispherical grounding device is shown in Figure 1.6. According

to the definition of grounding resistance, the grounding resistance of a hemispherical grounding

device is:

R ¼ v0

I¼ r

2pr0ð1:4Þ

1.3.2 Relationship between Grounding Resistance and Capacitance

According to the similarity between the electrostatic field and the constant current field, it is very easy

to obtain the relationship between the grounding resistance and the capacitance of a grounding device:

R ¼ reC

ð1:5Þ

where e is the dielectric coefficient of the soil (with units of F/m) and C is the capacitance of the

grounding device with respect to infinity (with units of F).

When the resistivity r and the dielectric coefficient e of soil are constants, the capacitance is in

inverse proportion to its size. From Equation 1.5, we can ascertain that the grounding resistance of the

grounding device is inversely proportional to its capacitance. Thus, the larger the size of the grounding

device, the greater is its capacitance and the lower is its grounding resistance. For an actual grounding

Figure 1.6 Hemispherical grounding device in homogeneous soil and the respective potential distribution.


project, the grounding resistance of a grounding grid is basically determined once the area of the

grounding grid is defined.

A grounding grid consisting of many horizontal conductors can be approximated to an isolated

plane, whose capacitance is mainly determined by its area. As shown in Figure 1.7, if short vertical

ground rods are connected to this plane, they have little influence on the capacitance and so the

grounding resistance decreases just slightly. According to analysis, the grounding resistance is

highly reduced only when the length of the vertical ground rods can match the equivalent radius of

the grounding grid.

1.3.3 Shielding Effect among Grounding Conductors

A grounding device usually consists of a group of grounding conductors and, when the current dif-

fuses into soil through one conductor, it is affected by the other conductors. Adding more horizontal

conductors to a grounding grid, or adding short vertical rods to a grounding grid, can only reduce the

grounding resistance by a little and this is because the internal conductors of the grounding grid are

shielded by the peripheral conductors. Strictly speaking, it is only when the distance between two

conductors is infinite that the electric field generated by one grounding conductor is not affected by

the other one. Considering this shielding effect, the grounding resistance of the grounding device is

not equal to the parallel value of the grounding resistances of all the grounding conductors.

Different grounding conductors of a grounding device diffuse currents with the same polarity into

soil, so we can use two adjacent point sources (as shown in Figure 1.8) to analyze the interaction

between them. Both point sources inject the same current I into the earth at the same time, but the

Figure 1.7 Grounding grid with short vertical ground rods.

Figure 1.8 Shielding effect between two neighboring point sources with the same polarity.


current lines do not radiate around as a single point source does, because the current diffusing from

source A cannot disperse to the right side of the vertical plane ON perpendicular to the midpoint of

AB connecting line, and the current diffusing from point source B cannot disperse to the left side of

the plane ON. The plane ON is like a shielding layer preventing the current from getting through.

This phenomenon is called the shielding effect between grounding conductors or the repulsive inter-

action of current lines. Because of the shielding effect among grounding conductors, the current

diffusing area is much smaller than that of one grounding conductor, and the corresponding ground-

ing resistance of one grounding conductor is larger than that of one grounding conductor. From

Figure 1.8 we can ascertain that, when the current from a point current source passes through the

cross-section, there is an increase in the resistance encountered during current diffusion, and this

resistance is called the current dispersing resistance.

Usually the mutual resistance between two grounding conductors is used to represent the interaction

between them, which means that a potential is generated on conductor B without a current applied

when grounding conductor A diffuses unit current into the soil, while the potential generated on

grounding conductor A itself is called self-resistance, the potentials of n grounding conductors can be

expressed as:

V1 ¼ R11I1 þ R12I2 þ � � � þ R1nIn

V2 ¼ R21I1 þ R22I2 þ � � � þ R2nIn

..

.

Vn ¼ Rn1I1 þ Rn2I2 þ � � � þ RnnIn

8>>>><>>>>:

; ð1:6Þ

where V1, V2, . . . , Vn are the potentials of all conductors, I1, I2, . . . , In are the corresponding currents

through them and Rii and Rki are the self-resistance of grounding conductor i and the mutual resistance

between conductors i and k.

When a current I diffuses into the soil through two adjacent conductors, the corresponding potential

equations are:

V1 ¼ R11I1 þ R12I2

V2 ¼ R21I1 þ R22I2

�ð1:7Þ

The two conductors are connected to each other, so they have the same potential V¼V1¼V2, and

I¼ I1þ I2, R12¼R21. Substituting these conditions in Equation 1.7, the grounding resistance of the

complex grounding device constituted by two adjacent conductors is:

R ¼ V

I¼ R11R22 � R2

12

R11 þ R22 � 2R12

ð1:8Þ

Obviously, the grounding resistance of the complex grounding device is not equal to the parallel

resistance RP of the two self-resistances:

RP ¼ R11R22

R11 þ R22

ð1:9Þ

The grounding resistance R of the complex grounding device is bigger than the parallel value RP of

self-resistances. As a result of the existence of the mutual resistance generated by the shielding effect,

the grounding resistance of a grounding device increases.

In engineering, the usage coefficient h is usually used to represent the shielding effect among con-

ductors of a grounding device, which is defined as:

h ¼ RP=R ð1:10Þand is always less than 1.0.


1.4 Grounding Resistance of Grounding Devices

1.4.1 Grounding Resistance of General Grounding Devices

1.4.1.1 Grounding Resistance of Simple Grounding Devices

For grounding devices with simple structures, according to the theoretical analysis of the electromag-

netic field we can obtain formulas to calculate their grounding resistances. But for grounding devices

with complicated structures, we can only derive approximate calculation formulas by regression analy-

sis of calculation results obtained from numerical methods for an electromagnetic field. Table 1.1 lists

commonly used formulas for calculating grounding resistances of different simple grounding devices

which were obtained from the literature [4–6].

The grounding resistance of a vertical ground rod can be calculated not only by the Sunde and

Dwight formulas listed in Table 1.1 but also by the following two formulas.

The analytical solution derived from rotating ellipsoid by Tagg and Ollendorf, Zingraff formula [4]:

R ¼ r

2pLln4L

dð1:11Þ

And the Rudenberg and Datta formula:

R ¼ r

2pLln2L

dð1:12Þ

Table 1.1 Formulas for calculating the grounding resistance of grounding devices with simple structures

Grounding type Shape and size of grounding Formula for calculating grounding

resistance

Hemisphere D R ¼ r

pD

Sphere deeply buried

in soil

D

hR ¼ r

pD0:5þ D

8h

� �ðD < hÞ

Circular flat-plate D R ¼ r

2D

Circular flat-plate deeply

buried in soilD h

R ¼ r

2D0:5þ D

4ph

� �ðD < 2hÞ

Vertical ground rodL

d

Sunde, Dwight formula

R ¼ r

2pLln8L

d� 1

� �ðd � LÞ

Ring-shaped grounding

electrodeD h

d

R ¼ r

2p2Dln16D2

hd

Horizontal grounding device L is the length of the grounding

conductor, d is the diameter

of the grounding conductor,

h is the burial depth

R ¼ r

2pLln

L2

dhþ A

� �A is the shape

factor, shown in Table 1.2 [5].


A vertical ground rod with burial depth h is shown in Figure 1.9 and its grounding resistance can be

calculated by the following two formulas [4]:

R ¼ r

2pLln2L

dþ 1

2ln3Lþ 4h

Lþ 4h

� �ð1:13Þ

R ¼ r

2pLln4L

d� 1þ 1

2ln3Lþ 4h

Lþ 4h

� �ð1:14Þ

the formula in Equation 1.13 corresponds to Equation 1.11 for calculating the grounding resistance of a

vertical ground rod with the rod top flush with the ground surface. The formula in Equation 1.14 corre-

sponds to the Sunde and Dwight formula for calculating grounding resistance of a vertical ground rod

listed in Table 1.1.

For a horizontal grounding electrode with length L, burial depth h and diameter d (as shown in

Figure 1.10) its grounding resistance can be calculated by formulas in Equations 1.15 to 1.18 [4–6].

1. Rudenberg and Zingraff formula:

R ¼ r

2pLln2L

d1þ

lnL

2h

ln2L

d

0B@

1CA ð1:15Þ

2. Tagg and Dwight formula:

R ¼ r

2pLln4L

dþ ln

L

h� 2þ 2h

L� h2

L2þ h4

8L2

� �ð1:16Þ

Table 1.2 The shape factor A of different horizontal grounding devices [5]. (Reproduced with permission from

G.R. Xie, Grounding technique of power system, China Hydraulic and Electrical Engineering Press, Beijing, 1991)

Shape of grounding

device

Shape factor A �0.60 �0.18 0 0.48 0.89 1.00 2.19 3.03 4.71 5.65

Figure 1.9 Vertical ground rod with burial depth h.


methodology and...5.2.5 determining the correction coefﬁcient for future planning 198 5.2.6 impact...

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