Guide for Transmission Line Grounding
A Roadmap for Design, Testing, and Remediation: Part I - Theory Book
Guide for Transmission Line
Grounding
A Roadmap for Design, Testing, and Remediation:
Part I—Theory Book
1013900
Final Report, December 2007
EPRI Project Manager
A. Phillips
ELECTRIC POWER RESEARCH INSTITUTE
3420 Hillview Avenue, Palo Alto, California 94304-1338 • PO Box 10412, Palo Alto, California 94303-0813 • USA
800.313.3774 • 650.855.2121 • askepri@epri.com • www.epri.com
DISCLAIMER OF WARRANTIES AND LIMITATION OF LIABILITIES
THIS DOCUMENT WAS PREPARED BY THE ORGANIZATION(S) NAMED BELOW AS AN
ACCOUNT OF WORK SPONSORED OR COSPONSORED BY THE ELECTRIC POWER RESEARCH
INSTITUTE, INC. (EPRI). NEITHER EPRI, ANY MEMBER OF EPRI, ANY COSPONSOR, THE
ORGANIZATION(S) BELOW, NOR ANY PERSON ACTING ON BEHALF OF ANY OF THEM:
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PROCESS, OR SIMILAR ITEM DISCLOSED IN THIS DOCUMENT.
ORGANIZATION(S) THAT PREPARED THIS DOCUMENT
KEMA Nederland B.V.
Kinetrics
J. Anderson
NOTE
For further information about EPRI, call the EPRI Customer Assistance Center at 800.313.3774 or
e-mail askepri@epri.com.
Electric Power Research Institute, EPRI, and TOGETHER…SHAPING THE FUTURE OF ELECTRICITY
are registered service marks of the Electric Power Research Institute, Inc.
Copyright © 2007 Electric Power Research Institute, Inc. All rights reserved.
CITATIONS
This report was prepared by
KEMA Nederland B.V.
P.O. Box 9035
Arnhem, 6800 ET
The Netherlands
Principal Author
C. Engelbrecht
Kinetrics
800 Kipling Avenue KL206
Toronto, Ontario M8Z 6C4
Canada
Principal Investigator
W. Chisholm
J. Anderson
525 Old Windsor Road
Dalton, MA 01226
Principal Investigator
J. Anderson
This report describes research sponsored by the Electric Power Research Institute (EPRI).
The report is a corporate document that should be cited in the literature in the following manner:
Guide for Transmission Line Grounding: A Roadmap for Design, Testing, and Remediation:
Part I—Theory Book. EPRI, Palo Alto, CA: 2007. 1013900.
iii
PRODUCT DESCRIPTION
Electrical utilities have a duty to provide effective grounding for managing steady-state and fault
currents, whether near a large generating station or at a remote distribution pole ground. For
transmission lines, this imperative is usually met with investment in overhead ground wires and
grounding electrodes. Effective grounding at each tower improves reliability—by providing low
path impedance to lightning strokes—and contributes to safety. However, the fundamental
physical parameters in ground electrode engineering vary with climate and location, so tower-bytower testing and validation are needed. Existing standards for successful testing are better suited
to substations or concentrated electrodes than to transmission towers, which can have several
large, effective foundation grounding electrodes in parallel. This leads to a wide discrepancy in
treatment and testing options from one utility to another.
Results and Findings
Tower-to-tower differences in soil resistivity are so large that each tower needs a different design
and execution method. This report facilitates good grounding engineering practice, showing the
users how to make effective choices, considering performance and life cycle costs. In particular,
the techniques in this report can help utilities decide whether to go deep or go wide and flat and
can also improve estimates of how deep or what ring size electrodes are required in order to
achieve design targets. Pre-engineering and pre-staging of materials have been shown to improve
the overall effectiveness of this approach, leading to the possibility of reduced overall project
cost despite the use of expensive resistivity surveys before or after tower spotting.
Challenges and Objectives
Most utility design guides and industry standards offer a bewildering set of equations, one for
every electrode shape and none suitable for a four-legged transmission tower with extra rods or
radial wire. This report treats complex electrode shapes and two-layer soil effects using methods
that are simple, accurate, easy to teach, and easy to use, even for a high school graduate with a
math credit and a scientific calculator. Stakeholders include the following:
•
Transmission line planners who need simple methods to evaluate the relative merits of
resistivity profiles in route and site selection
•
Transmission line designers and structural engineers with limited appreciation of how minor
design choices can improve the performance and longevity of electrical grounding
•
Protection and control designers who rely on effective grounding data to improve distance
relaying and fault location
v
•
Construction and inspection staff who must bridge the gaps between a 20-Ω specification and
a rock-anchored tower, a spool of wire, and a pile of ground rods
•
Asset managers who can use the test methods and equations to calculate the remaining life of
existing grounding
•
Risk managers who need to understand why the risk of electrocution near transmission
towers has proven to be so low compared with other public and worker exposures
Applications, Value, and Use
One near-term development described in this report is a method to measure the transient
impedance of grounding electrodes without isolating the overhead ground wires. Low-cost, fast,
and portable digital oscilloscopes with built-in memory have already made this approach
practical, leading to a factor-of-three improvement in test time. Development of the equipment,
refinement of the interpretation, and additional experience can reduce test time even more.
This report also highlights electromagnetic methods that can provide tower-by-tower
measurements of two-layer soil resistivity. The analysis and design methods in this report take
full advantage of the new data in the forward direction, computing resistance from two-layer
resistivity and electrode size. The methods also support an evaluation of footing condition in a
reverse direction, using simultaneously measured values of impedance and local resistivity to
establish performance benchmarks. This opens the possibility of using electromagnetic surveys
to assess ground electrode conditions.
EPRI Perspective
EPRI has been in the business of consolidating improvements in the analysis and design of
grounding systems for substations for more than 20 years. This project takes advantage of
continuous improvements in modeling and experimental data and maintains a focus on making
these technologies easier to use by providing simple applets and worked examples. In several
areas, especially remote sensing of resistivity and advanced measurements of local tower
impedance, EPRI will play an increasing role in improving the raw data needed for effective
grounding analysis and design, possibly taking this expert advice right to the base of every tower
at which there is work is to be done.
Approach
This report consolidates approaches to testing and modeling of grounding electrodes, identifies
appropriate simplifications, and adapts the methods specifically for transmission line grounding.
The report is supported by the EPRI Transmission Line Grounding Guide Software (EGGS),
Version 1.01 (1011654). There are nine modules in the EGGS that are intended either to
implement complex algorithms presented in this EPRI report or to explain complex concepts.
Keywords
Grounding
Surge impedance
Transmission lines
vi
Two-layer resistivity
Ionization
ACKNOWLEDGMENTS
EPRI would like to thank the following contributors for their reviews and suggestions to improve
the quality and usability of this report:
Eric Engdahl
American Electric Power
Ben Howat
National Grid UK
Rita Jo Livezey
Tennessee Valley Authority (TVA)
Gene Nelson
TVA
Allen Van Leuven
Bonneville Power Administration
Members of the EPRI Lightning and Grounding Task Force
In addition, the following individuals and organizations provided illustrations for the report:
J. L. Bermudez Arboleda
W. Chisholm and W. Janischewskyj
Fugro Airborne Surveys
Geophex
International Telecommunication Union (ITU)
Mineralogical Research Company
Hydro-One
NB Power
K. Nixon, University of the Witwatersrand, South Africa
J. P. Reilly
Tennessee Department of Environment and Conservation
Tennessee Valley Authority (TVA)
vii
CONTENTS
1 INTRODUCTION ....................................................................................................................1-1
1.1
General ........................................................................................................................1-1
1.2
Relationship to Line Design .........................................................................................1-2
1.3
History and Past Reports .............................................................................................1-3
1.4
Purpose and Structure of This Report .........................................................................1-4
2 ROLES OF TRANSMISSION LINE GROUNDING ................................................................2-1
2.1
Lightning ......................................................................................................................2-2
2.2
Correct Operation of the Transmission System ...........................................................2-3
2.3
Safety...........................................................................................................................2-3
2.3.1
Normal Operation................................................................................................2-4
2.3.2
Fault Conditions ..................................................................................................2-4
2.4
Electromagnetic Interference .......................................................................................2-5
3 DEFINITIONS .........................................................................................................................3-1
4 ELECTRICAL CHARACTERISTICS OF SOIL ......................................................................4-1
4.1
Introduction ..................................................................................................................4-1
4.2
Electrical Characteristics of Homogeneous Soil ..........................................................4-2
4.2.1
Basic Parameters That Influence Soil Resistivity................................................4-2
4.2.1.1 Type of Soil .....................................................................................................4-4
4.2.1.2 The Composition and Type of Salts Dissolved in the Ground Water..............4-4
4.2.1.3 Moisture Content ............................................................................................4-5
4.2.1.4 Temperature ...................................................................................................4-6
4.2.1.5 Variation with Electric Field.............................................................................4-7
4.2.1.6 Variation with Frequency ................................................................................4-7
4.2.2
4.3
Seasonal Variations ............................................................................................4-9
Electrical Characteristics of Nonhomogeneous Soil ..................................................4-10
ix
4.3.1
Soil Resistivity as a Function of Location..........................................................4-10
4.3.2
Horizontal and Vertical Layering .......................................................................4-12
4.3.2.1 Horizontal Layering .......................................................................................4-12
4.3.2.2 Vertical Layering ...........................................................................................4-13
4.4
Measurement of Soil Resistivity.................................................................................4-14
4.4.1
Wenner Four-Electrode Method........................................................................4-16
4.4.1.1 Required Equipment .....................................................................................4-17
4.4.1.2 Measurement Procedure ..............................................................................4-18
4.4.1.3 Analysis and Interpretation of the Results ....................................................4-23
4.4.1.4 Uniform Soil ..................................................................................................4-24
4.4.1.5 Layered Soil ..................................................................................................4-24
4.4.2
Other Multiple-Electrode Methods.....................................................................4-25
4.4.3
Driven Ground Rod Methods (Two- and Three-Electrode Methods) ................4-26
4.4.3.1 Required Equipment .....................................................................................4-27
4.4.3.2 Measurement Procedure ..............................................................................4-27
4.4.3.3 Analysis and Interpretation of the Results ....................................................4-28
4.4.3.4 Alternative Method ........................................................................................4-29
4.4.4
Passive Electromagnetic Methods ....................................................................4-31
4.4.4.1 Radio Wave Attenuation ...............................................................................4-31
4.4.4.2 Lightning Location System Observations......................................................4-33
4.4.5
Active Induction Methods ..................................................................................4-34
4.4.5.1 Theoretical Background of Inversion Problem ..............................................4-34
4.4.5.2 Electromagnetic Induction.............................................................................4-35
4.4.5.3 Ground-Based Two-Coil Multifrequency Electromagnetic Surveys ..............4-35
4.4.5.4 Aerial Multifrequency to 100 kHz or Transient ..............................................4-35
4.4.5.5 Active Transient Current Injection at Tower Base Using the EPRI
Zed-Meter ..................................................................................................................4-36
4.4.6
Choosing an Appropriate Method for Soil Resistivity Measurements ...............4-39
4.4.6.1 Resistivity Profile from Aerial Surveys ..........................................................4-41
4.4.6.2 Resistivity Information from Tower Footing Resistance Measurements .......4-41
4.4.6.3 Detailed Soil Resistivity Measurements........................................................4-41
4.4.6.4 Variations in Resistivity After Construction ...................................................4-42
x
5 CHARACTERISTICS OF A GROUND ELECTRODE ............................................................5-1
5.1
Introduction ..................................................................................................................5-1
5.2
Low-Frequency Ground Electrode Impedance ............................................................5-2
5.2.1
Derivation of the Ground Electrode Resistance of a Hemispheric Electrode......5-4
5.2.2
Analytical Expressions for the Calculation of Ground Electrode Resistance ......5-6
5.2.2.1 Dwight and Sunde Equations..........................................................................5-6
5.2.2.2 Equations for Calculating the Resistance of Typical Transmission Line
Tower Electrodes .........................................................................................................5-8
5.2.3
The Geometric and Contact Resistance Method ..............................................5-11
5.2.3.1 The Derivation of Geometric Resistance of Solid Spheroid Electrodes........5-11
5.2.3.2 Derivation of the Contact Resistance Term ..................................................5-15
5.2.3.3 Geometric and Contact Resistance Equations for Basic Electrode
Types .........................................................................................................................5-16
5.2.4
Calculation of Electrode Resistance in Two-Layer Soil.....................................5-17
5.2.5
Calculation of Resistance of Multiple Electrode Systems .................................5-18
5.2.6
Choosing an Equation to Calculate the Ground Electrode Resistance.............5-19
5.2.6.1 Single-Rod Electrode ....................................................................................5-19
5.2.6.2 Hemispheric Electrode:.................................................................................5-20
5.2.6.3 Round Plate Electrode ..................................................................................5-21
5.2.6.4 An Ellipsoid of Revolution Electrode .............................................................5-21
5.2.6.5 Summary ......................................................................................................5-23
5.2.7
5.3
Numerical Methods for Calculating Ground Electrode Resistance ...................5-24
Surface Potential Gradients .......................................................................................5-24
5.3.1
Calculation of Potential Gradients Around Grounding Electrodes ....................5-25
5.3.1.1 Theoretical Background ................................................................................5-25
5.3.1.2 Numerical Methods to Evaluate the Surface Potential Gradients .................5-27
5.3.2
Step and Touch Potential Around Transmission Line Towers ..........................5-28
5.3.2.1 Basic Principles.............................................................................................5-28
5.3.2.2 Evaluation of Step and Touch Potentials ......................................................5-29
5.3.2.3 Mitigation of Step and Touch Potentials .......................................................5-31
5.4
The Behavior of Grounding Electrodes When Discharging Lightning Current...........5-31
5.4.1
The Surge Impedance of a Ground Electrode System .....................................5-34
5.4.1.1 Surge Impedance of the Buried Ground Wires .............................................5-34
5.4.1.2 Surge Impedance of the Ground Plane ........................................................5-37
xi
5.4.2
Soil Ionization Effects at High-Voltage Gradients .............................................5-41
5.4.2.1 Liew-Darveniza Dynamic Model for Rod Electrodes.....................................5-44
5.4.2.2 Korsuncev Dimensionless Parameter Model ................................................5-47
5.4.3
Step and Touch Potentials Under Lightning Conditions....................................5-50
5.5
Electrical Properties of Concrete Foundations...........................................................5-51
5.6
Procedures for Testing Tower Grounding Electrodes................................................5-54
5.6.1
Introduction .......................................................................................................5-54
5.6.1.1 Motivation for Testing Grounding Electrodes................................................5-54
5.6.1.2 The Basic Principle of Measuring the Electrode Resistance ........................5-55
5.6.1.3 Effect of the Connected Ground Wires .........................................................5-56
5.6.1.4 Common Methods for Electrode Resistance Measurement .........................5-57
5.6.2
Fall-of-Potential Method ....................................................................................5-58
5.6.2.1 The Test Setup .............................................................................................5-59
5.6.2.2 Premeasurement Checks .............................................................................5-61
5.6.2.3 Performing the Measurement .......................................................................5-62
5.6.2.4 Analysis of the Results..................................................................................5-62
5.6.3
Oblique-Probe Method ......................................................................................5-63
5.6.3.1 The Test Setup .............................................................................................5-63
5.6.3.2 Performing the Measurement .......................................................................5-65
5.6.3.3 Analysis of the Results..................................................................................5-66
5.6.3.4 Accuracy of the Results ................................................................................5-67
5.6.4
Use of Stray Tower Current and Voltage for Footing Resistance .....................5-69
5.6.4.1 The Test Setup .............................................................................................5-70
5.6.4.2 Performing the Measurement .......................................................................5-71
5.6.4.3 Analysis of the Results..................................................................................5-71
5.6.4.4 Use of Stray Tower Current and Voltage for Resistivity................................5-71
5.6.5
Directional Impedance Measurements..............................................................5-72
5.6.6
Simulated Fault Method ....................................................................................5-74
5.6.6.1 The Test Setup .............................................................................................5-76
5.6.6.2 Performing the Measurements......................................................................5-76
5.6.7
High-Frequency (26-kHz) Impedance ...............................................................5-77
5.6.8
Active Transient Current Injection at Tower Base (Zed-Meter).........................5-78
5.6.8.1 The Test Setup .............................................................................................5-79
5.6.8.2 Performing the Measurements......................................................................5-79
xii
5.6.8.3 Analysis of the Results..................................................................................5-83
5.6.8.4 Accuracy of the Results ................................................................................5-84
5.6.9
Direct Method for Measuring Structure Resistance ..........................................5-86
5.6.10
Ground Electrode Integrity Assessment ........................................................5-87
5.6.10.1 Continuity Measurements ...........................................................................5-87
5.6.10.2 Use of Footing Resistance and Resistivity to Assess Intact Rod
Length........................................................................................................................5-88
5.6.11
Step and Touch Potential Measurements......................................................5-90
5.6.12
Assessment of the Interference to Other Infrastructure .................................5-91
5.6.13
Precautions Under Power Lines When Doing Measurements.......................5-92
5.6.13.1 Electrostatic, Induction, and Stray Ground Current PickUp ........................5-92
5.6.13.2 Signal-to-Noise Ratio in Selection of Equipment ........................................5-92
5.6.13.3 Additional Considerations Near Substations...............................................5-93
5.6.14
Choosing an Appropriate Method for Soil Resistivity Measurements ............5-94
6 USEFUL GUIDELINE DOCUMENTS AND RESOURCES ....................................................6-1
7 REFERENCES .......................................................................................................................7-1
7.1
Cited References .........................................................................................................7-1
7.2
Other References ........................................................................................................7-4
7.2.1
EPRI Reports ......................................................................................................7-4
7.2.2
International Standards .......................................................................................7-5
7.2.3
Books ..................................................................................................................7-5
7.2.4
Technical Papers ................................................................................................7-6
7.2.5
U.S. Military Publications ....................................................................................7-8
xiii
LIST OF FIGURES
Figure 1-1 Components of the Grounding System of a Transmission Line ...............................1-2
Figure 3-1 Definition of Ground Resistivity ................................................................................3-2
Figure 4-1 Definition of Resistivity and Resistance....................................................................4-2
Figure 4-2 The Effect of Grain Packing on the Volume of Voids in the Soil...............................4-4
Figure 4-3 Resistivity of Materials as a Function of Moisture Content .......................................4-5
Figure 4-4 Soil Resistivity as a Function of Temperature ..........................................................4-6
Figure 4-5 Typical Sand Fulgurite from East Texas...................................................................4-7
Figure 4-6 Ratio of Material Resistivity at 100 kHz and 100 Hz Versus Moisture Content ........4-8
Figure 4-7 Resistivity Distribution Between Electrodes at Tournemire, France .......................4-10
Figure 4-8 Generalized Geologic Map of Tennessee ..............................................................4-11
Figure 4-9 Areas in Tennessee Where Mean Resistivity Is Less than 150 Ωm.......................4-11
Figure 4-10 Areas in Tennessee Where Mean Resistivity Exceeds 1000 Ωm ........................4-12
Figure 4-11 Complex Soil Model with Various Types of Soil Layering.....................................4-12
Figure 4-12 Vertical and Horizontal Distribution of Resistivity Values from an Aerial
Electromagnetic Survey Near a 345-kV Power Line ........................................................4-14
Figure 4-13 Wenner Probe Technique for Measurement of Apparent Resistivity, ρa ...............4-16
Figure 4-14 Wenner Probe Arrangement Effect of Probe Spacing on the Depth of
Current Penetration..........................................................................................................4-17
Figure 4-15 Wenner Probe Positioning Strategy to Reduce the Amount of Work ...................4-21
Figure 4-16 Nonuniform Surface Probe Spacing for Multilayer Resistivity Survey ..................4-25
Figure 4-17 General Setup of the Driven Ground Rod Method to Determine Soil
Resistivity 4.4.3.1 Required Equipment ...........................................................................4-26
Figure 4-18 Vertical Rod Penetration Giving R (Ω) = Upper Layer Resistivity ρ1 (Ωm)............4-29
Figure 4-19 Electrode Setup for the Three-Terminal Setup for Measuring the Ground
Resistivity .........................................................................................................................4-30
Figure 4-20 Map of Extra-Low Frequency (<30 kHz) Conductivity in Millisiemens per
Meter ................................................................................................................................4-32
Figure 4-21 Map of Medium-Frequency (1 MHz) Conductivity in Millisiemens per Meter........4-33
Figure 4-22 Multifrequency Electromagnetic Sensor for Soil Resistivity..................................4-35
Figure 4-23 Example of an Aerial Multifrequency Electromagnetic Sensor for Soil
Resistivity .........................................................................................................................4-36
xv
Figure 4-24 Surge Impedance (Ω) of Insulated Wire on Ground Surface Versus Soil
Resistivity for Various Frequencies ..................................................................................4-37
Figure 5-1 The Potential Profile of a Hemispherical Electrode in Uniform Soil, Showing
the Parameters for Calculating Ground Resistance and Step and Touch Potentials.........5-4
Figure 5-2 Round Plate Electrode..............................................................................................5-9
Figure 5-3 Rod Electrode...........................................................................................................5-9
Figure 5-4 An Ellipsoid of Revolution.......................................................................................5-10
Figure 5-5 Three Types of Solid Spheroid Electrodes .............................................................5-12
Figure 5-6 General Two-Layer Soil Model with Horizontal Layering........................................5-17
Figure 5-7 Comparison of Equation 5-11 with Analytical Expressions for Rod,
Hemisphere, and Plate Electrodes...................................................................................5-22
Figure 5-8 Ratio of Expressions for Geometric Resistance to Equation 5-9............................5-23
Figure 5-9 The Potential Profile of a Hemispherical Electrode in Uniform Soil, Showing
the Parameters for Calculating the Step and Touch Potentials in Uniform Soil ...............5-26
Figure 5-10 Surface Potential Distribution for Rod and Mesh Electrodes................................5-28
Figure 5-11 Standard Values for AC Ventricular Fibrillation Current .......................................5-30
Figure 5-12 A Lightning Strike to a Transmission Line ............................................................5-32
Figure 5-13 Lightning Flashover Rate of Single-Circuit Lines Versus Footing Resistance......5-33
Figure 5-14 Example of the Time Variation of the Surge Impedance, the Leakage
Resistance, and the Resultant Effective Impedance of a Buried Counterpoise ...............5-35
Figure 5-15 Bewley Equivalent Circuit of a Counterpoise........................................................5-36
Figure 5-16 Experimentally Measured Currents on Peissenberg Tower at the Top and
Bottom of the Tower.........................................................................................................5-38
Figure 5-17 Tower-to-Base Reflection Coefficient ρg(ω) as a Function of Frequency for
Three Experimental Records in Figure 5-16 ....................................................................5-39
Figure 5-18 Modified Bewley Equivalent Circuit of a Counterpoise (Figure 5-15) with the
Addition of an Inductor to Represent the Surge Impedance of the Ground Plane ...........5-42
Figure 5-19 Resistance of a 48-Ω Driven Rod for Various Impulse Currents for 2.5/15 µs
Impulse Current (Typical of a Subsequent Stroke) ..........................................................5-43
Figure 5-20 Liew-Darveniza Ground Rod Surrounded by Concentric Shells of Earth .............5-44
Figure 5-21 Variation of the Soil Resistivity of Each Current Shell as a Function of the
Current Density ................................................................................................................5-45
Figure 5-22 Observed Relationships Between Dimensionless Parameters for Ionized
Resistance of Grounding Electrodes from Popolanský and Korsuncev ...........................5-48
Figure 5-23 Ventricular Fibrillation Current Versus Duration of a 60-Hz Stimulus for a
Wide Range of Exposure Durations .................................................................................5-51
Figure 5-24 Typical Transmission Line Concrete Foundations................................................5-52
Figure 5-25 Effect of Humidity on Concrete Weight Loss and Shrinkage ................................5-53
Figure 5-26 Effect of Water Saturation on Concrete Resistivity...............................................5-54
xvi
Figure 5-27 Principle of the Resistance Measurement of a Transmission Line Tower
Ground .............................................................................................................................5-55
Figure 5-28 Current Sharing Between Transmission Line Towers If the Overhead
Ground Wires Are Disconnected......................................................................................5-56
Figure 5-29 Current Sharing Between Transmission Line Towers If the Overhead
Ground Wires Are Connected ..........................................................................................5-57
Figure 5-30 Fall-of-Potential Method for Measuring Structure Resistance ..............................5-58
Figure 5-31 Top View of the Preferred Probe Layout for the Fall-of-Potential Method for
Measuring Structure Resistance ......................................................................................5-60
Figure 5-32 Measurement Error as a Function of the Voltage Probe Position in TwoLayer Soil .........................................................................................................................5-61
Figure 5-33 General Probe Layout for the Oblique-Probe Method ..........................................5-63
Figure 5-34 Top View of the Ideal Potential Probe Layout for the Oblique-Probe Method ......5-64
Figure 5-35 Top View of a Practical Potential Probe Layout for the Oblique-Probe
Method .............................................................................................................................5-65
Figure 5-36 Typical Data Analysis for Oblique-Probe Measurement of Resistance and
Resistivity with Probes at 90°...........................................................................................5-67
Figure 5-37 Measured Resistance for Fall-of-Potential and 90° Oblique-Probe Methods .......5-68
Figure 5-38 Typical Data Analysis for Three Angles (22.5°, 45°, and 90°) in ObliqueProbe Method...................................................................................................................5-68
Figure 5-39 Stray Tower Current Method for Testing of Ground Rods ....................................5-69
Figure 5-40 Setup of Tower Footing Resistance Measurement with Split-Core Current
Transformers Around the Tower Legs ............................................................................5-73
Figure 5-41 Excavation of Tower Leg to Allow Correct Installation of Big Norma Current
Transformer......................................................................................................................5-74
Figure 5-42 Setup for the Simulated Fault Method ..................................................................5-75
Figure 5-43 The Setup for the Active Transient Current Injection Method (Zed-Meter)...........5-78
Figure 5-44 Time Sequence of the Current Wave Injected into the Transmission Tower
Base .................................................................................................................................5-81
Figure 5-45 Waveforms of the Current Injected into the Tower (I1) and Current Lead (I2)
and the Voltage Measured at the Tower Base .................................................................5-82
Figure 5-46 Calculated Impedance from the Voltage and Current Waveforms Shown in
Figure 5-45.......................................................................................................................5-82
Figure 5-47 Typical Equivalent Circuit Seen by the Zed-Meter During the Optimal Time
of Measurement ...............................................................................................................5-83
Figure 5-48 Comparison of Low-Frequency Resistance with Zed-Meter Impedance for
Compact Electrodes.........................................................................................................5-85
Figure 5-49 Comparison of Low-Frequency Resistance with Zed-Meter Impedance for
Distributed Electrodes ......................................................................................................5-86
Figure 5-50 Setup for the Direct Method for Measuring the Structure Resistance ..................5-87
Figure 5-51 Setup for Continuity Measurement on a Looped, Continuous Counterpoise........5-88
xvii
Figure 5-52 Resistance Test Method for Towers with Continuous Counterpoise ....................5-90
Figure 5-53 Typical Variation in Tower-to-Tower Resistance for TVA 500-kV Line.................5-94
xviii
LIST OF TABLES
Table 3-1 Symbols Used in This Report ....................................................................................3-3
Table 4-1 Low-Frequency Resistivity, ρ, for Soil, Earth, and Concrete Material........................4-3
Table 4-2 Comparison of the Methods for Determining Soil Resistivity ...................................4-39
Table 5-1 Low-Frequency Ground Resistance of Electrodes ....................................................5-7
Table 5-2 Footing Resistance Expressions ..............................................................................5-8
Table 5-3 Equations for Calculating the Resistance of a Rod Electrode .................................5-10
Table 5-4 Equations Describing the Resistance of a Rod Electrode with Length L and
Radius a ...........................................................................................................................5-20
Table 5-5 Equations Describing the Resistance of a Hemispheric Electrode with Radius
a .......................................................................................................................................5-20
Table 5-6 Equations Describing the Resistance of a Round Plate Electrode with Radius
d .......................................................................................................................................5-21
Table 5-7 Comparison of Methods for Determining Soil Resistivity .........................................5-96
xix
1
INTRODUCTION
1.1
General
All electrical installations need a grounding system for safe and reliable operation. A grounding
system is defined as the total set of steps taken to provide a low-impedance connection between
the transmission line structures and the general mass of earth and to limit the buildup of potential
gradients around it. Typically, a transmission line grounding system comprises the following
components (see Figure 1-1):
•
A set of buried metallic conductors, called the ground electrode.
•
An overhead ground wire, which can also be called a static wire or shield wire. Overhead
ground wires are not necessarily installed on all transmission lines or line sections.
•
Connections between the components of the grounding system and the electrical installation
are made with ground conductors.
1-1
Introduction
Figure 1-1
Components of the Grounding System of a Transmission Line
1.2
Relationship to Line Design
The provision of an effective grounding system on overhead lines can be challenging and costly.
The design is usually determined by the lightning performance requirements of the line. Other
aspects that can influence the grounding system design are the requirement to manage the steadystate fault current along the line and the necessity to avoid the buildup of high potential gradients
around the tower base during line fault conditions.
Individual tower grounding must be considered both with respect to its impact on the
performance of the line and on the specific conditions near each tower. This can result in
different grounding designs from tower to tower because of the variation in grounding
parameters and conditions along the line route. Utilities manage this by generally following a
pragmatic approach based on a mixture of experience and empirical methods to design and
remediate transmission line grounding.
1-2
Introduction
1.3
History and Past Reports
EPRI has strived to support its members for more than 20 years in sponsoring research and
development of methods and tools that can help utilities in their pursuit of a well-performing and
cost-effective grounding system. A long-standing aim is to provide members with practical and
easy-to-use methodologies and tools that are based on the latest developments, theories, and
experimental data. This report serves as a consolidation of this knowledge base with the aim of
providing readers with guidelines and tools necessary for good grounding engineering practice.
This report and its companion volume “Part II – Practical guidelines”, replaces the EPRI report
Guide for Transmission Line Grounding: A Roadmap for Design, Testing, and Remediation
(1002021).
An important resource for the development of this report was the EPRI report Transmission Line
Grounding (EL-2699) [1]. In 768 pages, the two-volume report presents substantial theoretical
background and more than 340 design curves based on the EPRI Grounding Analysis of
Transmission Lines (GATL) software package. The approach was found to be accurate when
compared with measured results from staged-fault tests at three utilities on 765-kV and
500-kV lines.
Since the publication of that report in 1982, advances have been made in both analysis and
computation technology, including the following:
•
Successful adaptation of moment methods described in Harrington’s Field Computation by
Moment Methods and variational calculus described in Chow and Yovanovic’s “The Shape
Factor of the Capacitance of a Conductor” to reduce the need for tiny segmentation of
electrodes [2, 3]. This leads to simple, accurate expressions for ground resistance that can be
inverted more easily to determine how large the electrode must be for the local soil
conditions.
•
Development of vastly improved computer-based instrumentation that averages multiple
measurements to give an increased accuracy and noise rejection in grounding measurements.
•
Use of computer-based electromagnetic measurements to characterize the variation of soil
resistivity over large areas, along with validation programs by federal organizations such as
the United States Geological Service and the Geological Service of Canada.
•
Widespread availability of Microsoft Excel and other easy-to-use spreadsheets that contain
all the relevant and difficult mathematical functions used in grounding and allow users to
generate their own design curves and values efficiently.
•
An Internet-savvy generation of people who are comfortable using a web browser to navigate
through a logical series of web pages, entering data and evaluating visual output as they go.
1-3
Introduction
1.4
Purpose and Structure of This Report
A rich and bewildering set of technical resources is already available to the transmission line
designer who must specify a ground electrode. This report focuses mainly on electrode
treatments that reduce the ac and lightning impulse impedance of transmission towers to remote
earth. Other guides and standards listed in Section 6, References, provide details on managing
large fault currents in substations and coordinating power system fault current with nearby
railroads, pipelines, or telephone services.
This report is the first of two parts. Part I—Theory Book, provides the theory and basic principles
necessary for a solid understanding of good grounding engineering practice. Part II—Practical
Guidelines, provides easy-to-use guidelines, tools, and worked examples for several tower
configurations.
These reports are complemented by a set of software applications, EPRI Transmission Line
Grounding Guide Software (EGGS), Version 1.01 (1011654). The applets provide a set of simple
and easy-to-use tools that are intended as tutorials to illustrate and amplify the text of the reports
to help readers gain a better understanding of the underlying principles.
1-4
2
ROLES OF TRANSMISSION LINE GROUNDING
The grounding system is an essential part of both high- and low-voltage electric power networks
and serves at least four crucial electrical roles:
•
•
•
•
To protect against lightning and improve the lightning outage performance of the line by
performing the following functions:
–
Provide a low-impedance path to earth using mechanically and electrically robust
grounding connections
–
Limit potential differences across electrical insulation on towers that are struck by
lightning
–
Reduce the number of flashovers that occur
To ensure correct operation of the transmission system control and protection equipment by
performing the following functions:
–
Provide increased fault current levels to allow a rapid and unambiguous identification of
fault conditions for efficient relay and fuse coordination
–
Provide low zero-sequence impedance for the return of the unbalanced fraction of
three-phase ac to eliminate hazards associated with ungrounded systems
To ensure electrical safety for exposed humans by performing the following functions:
–
Allow the quick identification of faults, which leads to reduced fault duration
–
Limit touch or step potentials to levels that restrict body currents to safe values
To lower the electromagnetic interference of the line by having a grounding configuration
that is designed to suppress induced voltage and current on nearby conducting objects
All these functions are provided by an integrated grounding system made up of conductors,
hardware, foundations, and the local soil or rock. Each element of the system has its specific
purpose, but all the elements must function together in an electrically interconnected system that
must be designed and analyzed as a whole.
2-1
Roles of Transmission Line Grounding
2.1
Lightning
Transmission line grounding forms an integral part of the lightning protection system that
typically includes the following components:
•
Overhead ground wires (also called static wires or shield wires)
•
Grounding conductors or down conductors
•
Grounding electrodes
•
Surge arresters
•
Other connectors or fittings required for a complete system
On overhead lines, lightning can cause line outages in two ways: 1) as a result of induction when
it strikes in the vicinity of the line, and 2) by direct contact when it terminates either on a
grounded structure or shield wire or onto phase conductors.
Induction is not considered important for transmission lines because the level of induced voltage,
which is generally lower than 300 kV on unshielded lines, is lower than the line insulation level
and is unlikely to cause a flashover. On lines with overhead ground wires, lightning-induced
overvoltages are even lower; therefore, induction is not considered further in this report.
Direct strokes, or flashes, to the line can cause flashover in two ways.
1. By terminating on the phase conductor, which is called a shielding failure. Flashovers as a
result of shielding failure are prevented by the correct placement of the overhead ground
wires or shieldwires to intercept the lightning stroke and direct it to ground.
2. By terminating on the tower or shielding arrangement, which causes a so-called backflashover as a result of the voltage buildup over the grounding system. The most common
remedy for back-flashover is to lower the tower footing impedance.
The overhead ground wires intercept the lightning strokes and prevent them from terminating on
the phase conductors or other equipment that needs to be protected. The rest of the grounding
system provides a low-impedance path for the lightning current to discharge into the general
mass of the earth. It must do so without developing high voltages on the tower that could lead to
flashover of the line insulation.
From a transmission line grounding perspective, back-flashover is the most important lightning
condition that must be considered. Other aspects regarding the improvement of the lightning
performance of lines are treated in the EPRI report Handbook for Improving Overhead
Transmission Line Lightning Performance (1002019) [4].
2-2
Roles of Transmission Line Grounding
2.2
Correct Operation of the Transmission System
An important aspect of electric power system reliability is how well its protection can identify
and isolate fault locations. Relay systems are grouped into primary and backup protection, with
instantaneous or timed response as follows:
•
Instantaneous primary-protection relays detect system faults that could destroy system
integrity or equipment. These relays are set to respond quickly to basic parameters such as
overcurrent, changes in impedance, or differential currents. The clearing times vary with the
fault current magnitude, the type of breakers, and the fault location in the monitored zone.
Primary protection relays usually operate within approximately 200 ms for 69-kV, 115-kV,
and 138-kV systems and within approximately 100 ms for higher system voltages.
•
Timed primary-protection relays respond after a fixed or inverse time delay to system
conditions (such as overvoltage, undervoltage, loss of excitation, negative-sequence current,
voltage parameters, or frequency parameters) that will lead to deterioration or failure of
equipment.
•
Backup-protection relays trip breakers when the primary protection relays fail to clear a fault.
These situations re associated with breaker failure and transformer and bus backup
protections. The operating times are intentionally longer than those of the instantaneous
primary protection. Typical values range from 150 ms to 200 ms, independent of the system
voltage, but values as large as 800 ms are also used.
The transmission line grounding plays the following roles in helping the protection to locate and
isolate faults in the electrical system effectively:
•
The grounding system (overhead ground wires and grounding electrodes) provides a welldefined and stable zero-sequence impedance against which protection settings can be made.
•
It provides a low impedance to ground that will present a greater contrast between normal
and fault conditions, improving speed and accuracy of identification for the instantaneous
primary protection.
•
It provides a return path for fault current to the source.
•
It helps to prevent single-phase faults from escalating into multi-phase faults.
2.3
Safety
Permanent and temporary grounds can be used to ensure that transmission line structures and the
immediate surroundings pose a low risk, in terms of step and touch potentials, to humans and
livestock in the vicinity of the line both during normal operation of the line and during fault
conditions. Procedures, designs, and requirements are governed by regulations and company
policy. These aspects are outside the scope of this report.
2-3
Roles of Transmission Line Grounding
2.3.1 Normal Operation
During normal operation, transmission line structures carry a voltage that is the result of the
following factors:
•
Electrostatic coupling between the energized phase conductors and the overhead ground
wires, and between the phase conductors and the tower.
•
Magnetically induced current caused by the flux linkage between the load current in the
phase conductors and the loop formed by the overhead shield wire, tower, and ground. The
magnitude of this current is a function of the phase configuration, the magnitudes of the
phase current, the level current imbalance between the three phases, and the length of the
span. Differences between the current induced in adjacent spans are conducted to ground
through the earth electrode and its impedance, causing the tower base to rise in voltage.
These differential currents are most pronounced at sections with unequal span lengths or
where there is a change in the conductor configuration, such as at phase transposition points.
•
Unbalanced circuits that can result a steady-state neutral potential with its associated zerosequence current, which varies with line loads. This neutral potential is transferred to the line
towers in the vicinity of the substation through the overhead shield wires if they are
connected to the substation ground mat (as is the usual case).
•
Leakage currents as the result of insulator contamination that must also be shunted to ground
through the earth electrode, which will cause a momentary rise in potential.
For normal operation in which an effective grounding system is present, the sum of these ground
potentials is usually limited to less than 10 V.
2.3.2 Fault Conditions
Fault conditions, especially phase-to-ground faults, can result in large current magnitudes in the
grounding system. Most of the line-to-ground fault current is transported back to the substations,
sourcing the fault, through the overhead ground wires. However, a significant portion of the
current is still shunted to ground through the ground electrode, which can result in large potential
gradients in the soil surrounding the towers. The potential gradients are expressed in terms of
step and touch potentials, which can be evaluated in terms of the safety limits imposed by
regulations and company policy. The requirement to limit step and touch potentials around
transmission line towers could govern the ground electrode design and layout in some cases.
2-4
Roles of Transmission Line Grounding
2.4
Electromagnetic Interference
Transmission lines transport a large amount of energy over long distances. The resulting high
voltage, high current levels, and the electromagnetic field around the lines can cause interference
on nearby conducting objects such as other infrastructure (pipelines, fences, railways, and other
lines) that parallel the transmission lines. Of concern are the levels of induced voltages and
currents that might cause the following:
•
Exposure of people to unexpected discharges when they make contact with the supposedly
non-energized structures
•
Damage to the infrastructure itself
•
Damage to electronic equipment that is in contact with the infrastructure
•
Induced voltage and current into parallel running lines, pipelines, and railroads
The transmission lines themselves are immune to electromagnetic interference from other lines
in the vicinity because the induced voltages and currents are much lower than the normal
operating voltage or current. However, coupled voltages and currents are a concern when work is
performed on deenergized lines. In these cases, temporary grounds must be applied to ensure the
safety of personnel. The application of temporary grounds falls outside the scope of this report. It
is covered in the EPRI report Survey of Utility Practices for Establishing Equipotential Zones
During De-Energized Work (1001752) [5].
The mitigation of electromagnetic interference is a specialized study area. It requires a
combination of shielding, configuration changes, and grounding. This report does not cover
electromagnetic interference as a whole, but rather mentions it when necessary as a factor that
should be taken into account when deciding how to treat the grounding around transmission line
structures. Guidance on the electromagnetic interference to pipelines can be found in the Cigré
“Guide on the influence of high voltage ac power systems on metallic pipelines” (Technical
brochure 95) [58] and for railroad systems in the EPRI “Power System and Railroad
Electromagnetic Compatibility Handbook” (1005572) [55].
2-5
3
DEFINITIONS
Counterpoise. Horizontal buried wires installed for grounding of transmission lines. They can
be continuous from tower to tower or radial outward from the tower.
Earth surface potential Vx. The voltage between a point x on the earth’s surface and remote
earth.
Electrical resistivity ρ. A physical property with units of ohm-meters (Ωm) of all materials that
relate the electric field E (V/m) to the current density J (A/m2) using E = ρ J.
Electrode voltage (electrode potential) VE. The voltage occurring between the grounding
system and reference earth at a given value of the impressed earth current.
Equipotential zone. A concept that was introduced to protect people and animals from
hazardous or annoying potentials because of inadvertent energization or induction. Ensuring that
all equipment, conductors, anchors, and structures within a defined area are electrically
connected creates an equipotential zone.
Grounding conductor. A conductor that connects a part of an electrical installation, exposed
conductive parts, or extraneous conductive parts to a ground electrode or that interconnects
grounding electrodes. The grounding conductor is laid above the soil, or if it is buried in the soil,
it is insulated from it, meaning it does not function as a ground electrode.
Grounding electrode. A metal conductor or a system of interconnected metal conductors or
other metal parts acting in the same manner, embedded in the earth and electrically connected to
it or embedded in concrete that is in contact with the earth over a large area.
Grounding (grounding system). The total of all means and measures by which part of an
electrical circuit, accessible conductive parts of electrical equipment (exposed conductive parts),
or conductive parts in the vicinity of an electrical installation (extraneous conductive parts) are
connected to earth.
Grounding impedance. The overall impedance between the grounding system and reference
earth.
Ground potential rise (GPR). The potential with respect to far earth to which a ground
electrode will rise when discharging current into the soil.
3-1
Definitions
Ground resistance. The resistive part of the grounding impedance between the grounding
system and reference earth. In most cases, the ground resistance is a good approximation of the
grounding impedance.
Ground resistivity (specific earth resistance) ρ. The resistance measured between two
opposite faces of a 3.3-ft (1-m) cube of earth (see Figure 3-1), expressed in Ωm.
Figure 3-1
Definition of Ground Resistivity
Reference earth. That part of the ground, particularly on the earth surface, located outside the
sphere of influence of the considered ground electrode. One test (real or conceptual) for sphere
of influence is to impress a current through the electrode and establish the locations where there
is no perceptible voltage between two random points resulting from this grounding current flow.
The potential of reference earth is always assumed to be zero.
Step potential. The potential difference between two points on the ground that are 3.3 ft (1 m)
apart.
Touch potential. The potential difference between a person’s outstretched hand, which is
touching an earthed structure, and the person’s foot. A person’s maximum reach is assumed to be
3.3 ft (1 m). The touch potential can be equal to the full ground potential rise if the object is
grounded at a point remote from the place where the person is in contact with it.
3-2
Definitions
Table 3-1 defines the symbols used in this report.
Table 3-1
Symbols Used in This Report
Symbol
Definition
π
pi, 3.14159
δ
A complex number expressing the skin depth, which is defined as the depth at which the eddy
current density has decreased to 1/e, or approximately 36% of that at the ground surface
σ
The soil conductivity in siemens per meter (S/m), equal to 1/ρ, where ρ is the soil resistivity in
Ωm
ρ
The soil resistivity
ω
The frequency in radians/s
τ
A time constant defined as the time at which a signal has fallen to 1/e (36%) of its initial value.
µο
4π 10-7 H/m
εο
The permittivity of free space, 8.854x10-12 farads per meter
εr
The relative earth permittivity (dielectric constant)
A
Surface area
a
Radius
ax
Horizontal dimension from the center of an electrode along a line
ay
Horizontal dimension from the center of an electrode across a line
az
Vertical dimension from the center of an electrode to the surface of the ground
c
The velocity of light, 3 x 108 m/s
C1, C2
The current terminals
D
Distance
dT
The depth of the upper soil layer
E0
The critical dielectric ionizing gradient of the soil, typically 300–400 kV/m
f
The test frequency (Hz)
g
h
a x2 + a y2 + a z2 , geometric radius
The height above ground level
3-3
Definitions
Table 3-1 (continued)
Symbols Used in This Report
Symbol
Definition
I
The current through an object
J
The current density
kcmil
1000 circular mils, where a circular mil is the area of a circle with a diameter of 0.004 in.
(0.0025 cm)
L
The length of an object
ln
Natural logarithm (to base e), or loge
P1, P2
The potential terminals
r
The radius of an overhead conductor
R
The resistance of an object
s
The characteristic distance from the center of an electrode to its outermost point
t
Time
T
Temperature
V
Voltage
X
Reactance
3-4
4
ELECTRICAL CHARACTERISTICS OF SOIL
4.1
Introduction
The ability of soil to conduct current is of fundamental importance to the grounding of electrical
systems. Conduction of current through soil can take place by electronic or electrolytic current
flow. Electronic conduction is characterized by the movement of free electrons in the material
itself as a result of the electric field impressed on it. Electrolytic conduction is characterized by
the movement of ions through a solution. In soil, electronic conduction typically takes place
through conductive metal ores, metallic objects such as pipelines, or carbon deposits. Electrolytic
conduction takes place through water that is carrying dissolved minerals and salts.
Of these two, electrolytic conduction is predominant because soil always contains some amount
of moisture that—in combination with salts present in the soil—can serve as an electrolyte for
current flow. Electronic conduction becomes important deep in the earth where the deep rocks
are subjected to a high overburden pressure. Electronic conduction can also be important in
surface deposits that contain conducting minerals such as magnetite, graphite, or pyrite.
The electrical conduction in soil is expressed in terms of the soil resistivity, ρ, in ohm-meters
(Ωm). Resistivity is defined as the relationship between the resistance (R) of an object, its length
(L), and its cross-sectional area (A). Resistance is defined as the relationship between the voltage
(V) across the object and the current (I) through the object. See Equation 4-1 and Figure 4-1.
ρ=
R⋅ A V A
= ⋅
L
L I
Equation 4-1
Definition of Resistivity
4-1
Electrical Characteristics of Soil
Figure 4-1
Definition of Resistivity and Resistance
When calculating the grounding resistance of electrode systems, the soil resistivity features as a
linear term, usually in the following form:
Ground electrode resistance is directly proportional to the soil resistivity ×
electrode shape factor
electrode size
The following sections describe soil resistivity and its measurement.
4.2
Electrical Characteristics of Homogeneous Soil
4.2.1 Basic Parameters That Influence Soil Resistivity
Because electrolytic conduction is the predominant process by which current flows through soil,
the resistivity of soil is highly dependent on the presence and factors that influence the
electrolyte in the soil. Some of the primary factors that influence the electrolyte in the soil are the
following:
•
The type of soil
– The grain size and grain size distribution of the material
– The closeness of the packing of the grains and the pressure on the soil
– The size and shape of voids and interconnecting passages in the soil
– The extent to which the passages are linked by water paths
4-2
Electrical Characteristics of Soil
•
The chemical composition of the salts dissolved in the ground water
•
The concentration of the salts dissolved in the ground water
•
The moisture content of the soil
•
The temperature of the soil
Secondary factors that influence the conduction through soil, and by implication the soil
resistivity, are the level of the electric field in the soil (which is a function of the current density
in the soil) and the frequency of the applied voltage.
Variations in these parameters result in differences in soil resistivity of nearly four orders of
magnitude. This is shown in Table 4-1, which lists typical ranges of resistivity for different soils
and concrete at room temperature. Although some of these parameters remain constant over
time, others such as moisture content and temperature can vary over time as a result of seasonal
changes. This can introduce large seasonal variations in the soil resistivity, depending on the type
of climate.
Table 4-1
Low-Frequency Resistivity, ρ, for Soil, Earth, and Concrete Material
Resistivity in Ωm
Material
Range of Values
Average Value
Boggy ground
2–50
30
Adobe clay
2–200
40
Silt and sand-clay ground, humus
20–260
100
Sand and sandy ground
50–3000
200 (moist)
Peat
1–200
200
Gravel
50–3000
1,000 (moist)
Stony and rocky ground
100–8000
2,000
Electrically conductive concrete (see note)
5–10
8
Concrete with 1:3 cement–sand mix
50–300
150
Concrete with 1:5 cement–gravel mix
100–8000
400
Type of Soil or Earth
Type of Concrete
Note: Measured after a 30-day cure on rectangular slabs.
In the past, it was common practice to assume that the soil resistivity is equal to 100 Ωm when
no better information was available. However, actual soil resistivity can differ from this
assumption, and it is often significantly higher. As a result, ground electrode designs based on
the 100-Ωm assumption are often undersized.
4-3
Electrical Characteristics of Soil
4.2.1.1 Type of Soil
In terms of soil resistivity, the most important characteristic of the soil is the grain size
distribution because it influences how the soil carries moisture. For example, clay retains
moisture and dissolved chemicals in a tight matrix. Compared with sandy ground, clay has low,
relatively constant resistivity that changes only by a factor of 10 over a 0–20% range of moisture
content. As explained by Tagg in Earth Resistances, coarse gravel of uniform size has a very
high resistivity [6].
Another important soil characteristic is the amount of free space between sand grains. This
determines at what moisture level the soil becomes saturated, which is the point at which all the
voids in the soil are filled with water. The size of the voids in the soil depends on the
effectiveness of the packing in the soil, which in turn depends on the shape and size distribution
of the grains in the soil. This is illustrated in Figure 4-2, which shows the different packing
arrangements of spherical grains. In tightly packed soil (Figure 4-2a), the volume of the voids
amount to approximately 26% of the total volume, and in the least compact soil (Figure 4-2b),
the volume of the voids amount to 48% of the total. In typical soils (Figure 4-2c), the grains are
not exactly spherical or of uniform size, which results in generally lower volumes of voids. As an
indication, the volume of free space in the soil can vary from 25% for porous conglomerates, to
8–15% for ordinary clays and sand, to 0.2–2 % for rocks.
Figure 4-2
The Effect of Grain Packing on the Volume of Voids in the Soil. Please note that the circles
in the diagram represent spheres.
4.2.1.2 The Composition and Type of Salts Dissolved in the Ground Water
Because the conduction of electric current through soil is largely electrolytic, the amount and
types of salts dissolved in the soil’s water are an important factor in determining soil resistivity.
Especially at low salt concentrations, the amount of salt dissolved has a large influence on the
resistivity of the solution [6]. Furthermore, the type of salt present in the solution has a marked
influence on the conductivity of an electrolyte. For example, common sea salt (sodium chloride)
4-4
Electrical Characteristics of Soil
results in a more conductive solution than sodium sulphate and copper sulphate do. Sulphuric
acid, on the other hand, results in a higher conductivity solution than sodium chloride does at the
same concentration [6].
4.2.1.3 Moisture Content
The amount of electrolyte in the soil, which is related to the moisture content, is one of the most
important factors that influence the soil resistivity. Generally, soil resistivity decreases with an
increase in the moisture content.
Typical moisture levels can range from 5% for desert regions up to approximately 80% for
temperate, swampy regions. The moisture content rarely exceeds 40% in the typical conditions in
which transmission lines are located [6]. The influence of moisture on resistivity tends to
decrease at moisture levels greater than 20%, which corresponds to the moisture saturation level
of the soil. Figure 4-3 shows that resistivity increases rapidly at less than 20% moisture content.
Figure 4-3
Resistivity of Materials as a Function of Moisture Content
4-5
Electrical Characteristics of Soil
4.2.1.4 Temperature
Temperature variations influence the resistivity of the soil. For practical transmission lines, the
effect is most prominent when the temperature is less than 32°F (0°C). When the water contained
in the soil freezes, ion mobility is greatly reduced, leading to a dramatic increase in soil
resistivity, as Hoekstra and McNeill described in “Electromagnetic Probing of Permafrost” (see
Figure 4-4a) and Keller and Frischknecht explained in Electrical Methods in Geophysical
Prospecting (see Figure 4-4b) [7, 8].
Figure 4-4
Soil Resistivity as a Function of Temperature
Sources: Hoekstra and McNeill, Keller and Frischknecht
In most areas, only the topmost layer of the soil freezes when the ambient temperature drops to
less than 32°F (0°C). Deeper down, where the soil is insulated from the ambient, the soil
temperature assumes the average yearly temperature of the region. The increase in resistivity
typically does not coincide precisely with 32°F (0°C) because the salts dissolved in the ground
water lower its freezing point [1].
4-6
Electrical Characteristics of Soil
4.2.1.5 Variation with Electric Field
Ionization, or electrical breakdown, of the soil occurs when the electrical field exceeds
approximately 400 kV/m. This typically happens around concentrated electrodes when they
conduct high currents (for example, during a lightning strike). This important aspect of soil
behavior is described further in Section 5.4, The Behavior of Grounding Electrodes When
Discharging Lightning Current.
The breakdown of soil under high-current conditions can lead to the formation of fulgurites, also
known as fossilized lightning, which are hollow glass tubes that are fused as a result of the
passage of lightning current through sand. Figure 4-5 shows the hollow tube formed in sandy soil
when the lightning current heats and fuses the silicon dioxide (SiO2) into glass at a temperature
in excess of 1600°C. After triggered lightning experiments in Florida, Martin Uman excavated a
pair of fulgurites that were 16 and 17 ft (about 5 m) long and donated another specimen to EPRI
in appreciation of EPRI’s support.
Figure 4-5
Typical Sand Fulgurite from East Texas
Source: Mineralogical Research Company, www.minresco.com/fulgurites/fulgurites.htm
High electric fields lead to a high current density, which generates heat as a result of the resistive
losses (I2R). This can lead to drying of the soil in areas with a high current density, when
relatively high currents are conducted for a prolonged period. As a result, the local resistivity of
the soil increases. The current densities in typical grounding electrodes are low enough that this
effect is not a major concern.
4.2.1.6 Variation with Frequency
Measurements have shown that the resistivity of most types of soil does not remain constant with
frequency. Rather, the resistivity decreases as the frequency increases. Because lightning is a
transient phenomenon, having a fundamental frequency of 80 to 120 kHz, this dependence can
result in a different ground electrode impulse response than one would predict using soil
resistivity measurements performed at a single low frequency.
4-7
Electrical Characteristics of Soil
Nevertheless, most engineers currently use low-frequency resistivity or ground electrode
resistance measurements (approximately 100 Hz) to predict the response of transmission line
grounding electrodes to lightning, although frequencies of around 100 kHz are of more interest.
This issue is addressed by instruments, such as the EPRI Zed-meter, that measure the response of
grounding electrodes using higher frequencies or impulses.
The data from Visacro and Portella’s “Soil Permittivity and Conductivity Behavior on Frequency
Range of Transient Phenomena in Electric Power Systems” (illustrated in Figure 4-6) suggest
that the change in impedance with frequency varies, depending on soil type[9]. This is because,
physically:
•
Sandy soil is made up of uniform, intermediate-sized particles, classed from very coarse
(< 0.08 in. [<2 mm]) to very fine (<0.005 in. [<0.125 mm]). Sand is suitable for the growth
of pine, fir, and spruce forests. Although the resistivity of sand varies considerably with
moisture content the values at 100 Hz and 100 kHz track fairly closely.
•
In geology, till is soil that is smeared into place by glaciers. It contains a wide range
of particle sizes, from boulders (>10.1 in. [>256 mm]) to pebbles to sand to silt
(0.002–0.0002 in. [0.0625–0.004 mm]). Till retains moisture much better than sand
does, and it supports hardwood forests or farming.
•
Clay contains the smallest particles (<0.00008–0.001 in. [<0.002–0.004 mm]), and its
resistivity has the strongest frequency dependence, dropping by 60–90% as frequency
increases from 100 Hz to 100 kHz.
Figure 4-6
Ratio of Material Resistivity at 100 kHz and 100 Hz Versus Moisture Content
4-8
Electrical Characteristics of Soil
4.2.2 Seasonal Variations
No two sets of ground measurements will ever agree precisely, especially if they are taken days,
weeks, or months apart. In Germany, Rudolph and Winter (in EMV nach VDE 0100) reported a
±30% sinusoidal variation around average values of grounding resistance [10]. They found that
the maximum resistivity is reached in February and the minimum occurs during August. The
values measured in May and November correspond to the yearly average value.
These seasonal variations are a result of changes in humidity and changes in temperature.
Seasonal variations in rainfall and humidity affect the moisture content of the soil. The soil
resistivity can vary by a factor of 10 with high resistivity values in the dry season and lower
values during the wet season. Studies documented in Scott and May’s Earth Resistivities of
Canadian Soils show that soil resistivity varies by a factor of 10 or more in areas where the soil
freezes [11]. This can result in significantly higher values during the cold months of the year.
Freezing, like drying, increases resistivity by one to two orders of magnitude, but the effect is
generally restricted to the top 3.9 in. to 3.3 ft (0.1 to 1 m) of soil.
Seasonal variations are more pronounced in the resistivity of the upper layer compared with that
of the bottom layer. In deeper layers, the moisture content stabilizes and the temperature
approaches the yearly average values. Measurements in France have shown that these changes
can reach as deep as 65.6 ft (20 m) below the surface [12]. Figure 4-7 (redrawn from [14]) shows
the results from measurements on two arrays of 21 electrodes each, spaced at 7.9-in. (0.2-m)
intervals, which were installed in boreholes approximately 4 ft (1.2 m) apart. The derived
resistivity values presented in Figure 4-7 show a feature at a depth of 59 ft (18 m) with a
resistivity of 89–113 Ωm in January 1999, 54–69 Ωm in April 1999, and 26–33 Ωm in
September 2000.
4-9
Electrical Characteristics of Soil
Figure 4-7
Resistivity Distribution Between Electrodes at Tournemire, France
4.3
Electrical Characteristics of Nonhomogeneous Soil
In the preceding sections, the basic parameters that influence soil resistivity have been presented
for homogeneous soil. In practice, however, soil can rarely be considered homogeneous because
geological features cause soil types to vary from location to location, and the presence of
bedrock or ground water can result in significant changes in resistivity as a function of depth. For
transmission lines with their concentrated grounding electrodes at each tower base, it is
important to be aware of the impact that the vertical and horizontal variations in soil resistivity
can have on the performance of a line.
4.3.1 Soil Resistivity as a Function of Location
Most maps of local geology, such as the example for Tennessee (see Figure 4-8), show areas
where geology is relatively constant over distances of 20 mi (40 km) and other areas where
geology changes over a distance of 1–5 mi (2–8 km) [13]. Moving between different geological
zones, such as from Precambrian to Paleozoic areas, the resistivity can drop by four orders of
4-10
Electrical Characteristics of Soil
magnitude. Overhead lines that traverse two or more geologic areas can require different
grounding treatments in each area. Generally, geologic maps give an indication of the underlying
layer resistivity.
In the Tennessee Valley Authority (TVA) network, the ground resistivity is managed as a
corporate resource through a TTHOR database of local values [14]. Two examples extracted
from this database show areas where the mean resistivity is less than 150 Ωm (see Figure 4-9)
and areas where the values exceed 1000 Ωm (see Figure 4-10) [14]. The areas with low
resistivity are associated with sand, silt, clay, and gravel. The areas of high resistivity include
regions identified in Figure 4-8 as Mississippian limestone and Cambrian and Precambrian rock.
Figure 4-8
Generalized Geologic Map of Tennessee
Source: Tennessee Department of Environment and Conservation
Figure 4-9
Areas in Tennessee Where Mean Resistivity Is Less than 150 Ωm
Source: Tennessee Valley Authority
4-11
Electrical Characteristics of Soil
Figure 4-10
Areas in Tennessee Where Mean Resistivity Exceeds 1000 Ωm
Source: Tennessee Valley Authority
4.3.2 Horizontal and Vertical Layering
From the perspective of transmission line grounding, variations in soil resistivity take the form of
horizontal and vertical layering (see Figure 4-11). These formations are closely related to the
local soil type and geological structures, as described in Section 4.3.1, Soil Resistivity as a
Function of Location.
Figure 4-11
Complex Soil Model with Various Types of Soil Layering. (A) Horizontal layering (B)
Vertical layering.
4.3.2.1 Horizontal Layering
Horizontal layering in the soil (indicated by A in Figure 4-11) can be present as a result of
differences in levels of moisture and temperature and as a result of the geological soil structure.
Surface evaporation increases resistivity near the surface, even in areas where the soil is
relatively uniform. A distinct drop in resistivity can occur at the depth of the water table. In
climates with cold winters, a drop in resistivity occurs during the cold months in the frozen top
4-12
Electrical Characteristics of Soil
layer, and the deeper soil layer converges to the local mean annual average temperature (if it is
greater than 32°F (0°C). The local geology is composed of horizontal strata of different soil
types with different resistivity values, such as bedrock that has a high resistivity covered by an
overbunden of material that has a lower soil resistivity.
Horizontal layering plays an important part in the behavior of grounding electrodes. In areas
where a low-resistivity overburden covers high-resistivity rock, the top layer might be the only
material that provides a low-resistance path for current. Deep grounding electrodes might not be
effective in such areas; therefore, consideration should be given to wide, shallow electrodes such
as ring electrodes or a counterpoise. In areas where a top layer of high-resistivity soil covers a
low-resistivity layer, the grounding electrode should consist of several vertical rods to make
contact with the low resistivity layer.
For transmission line grounding, it is important to take horizontal layering into account, but it is
usually sufficient to use a simplified soil model consisting of one or more layers in grounding
calculations, even if more layers might be present.
4.3.2.2 Vertical Layering
Changes in resistivity can also be present as vertically orientated soil layers (indicated by B in
Figure 4-11). The most obvious of these layers is where there is a rapid change of the depth of
the overburden over a rock layer or at the borders of geological zones.
Generally speaking, these vertical layers do not affect the design of individual tower footing
electrodes unless the electrode is located on a vertical border. More important, however, are the
changes in soil conditions that can occur from tower to tower. As a result, modeling all towers on
a line or line segment with the same model is an oversimplification that can lead to inaccurate
results on individual towers.
In actual conditions, the soil structure is a combination of vertical and horizontal or slanted
layers. Figure 4-12 shows a resistivity profile along the route of a 345-kV line based on the
results from an aerial electromagnetic survey. The technique is described in Section 4.4.5, Active
Induction Methods.
4-13
Electrical Characteristics of Soil
Figure 4-12
Vertical and Horizontal Distribution of Resistivity Values from an Aerial Electromagnetic
Survey Near a 345-kV Power Line
Source: Fugro Airborne Surveys, NB Power
Each color in the figure represents a different soil resistivity; warmer colors have lower
resistivity. Figure 4-12 illustrates the following conditions, all of which occur within 3 mi (5 km)
or approximately 15 transmission spans:
•
In the areas marked O, there is a conductive overburden of 300 Ωm (typically 3–16 ft
[1–5 m] thick) on top of poorly conducting 3000 Ωm rock. These are areas in which wide,
flat electrodes provide an advantage.
•
In the area marked D, the overburden is approximately 230 ft (70 m) thick and has a
resistivity of 500 Ωm.
•
In the area marked G, the relatively thin overburden covers low-resistivity soil
(approximately 100 Ωm). In this area, it would be practical to apply driven rods to reach the
lower resistivity soil.
•
The blue areas marked H are areas of extremely high resistivity (7000 Ωm). These areas
present difficult grounding conditions because there is no low-resistivity earth in the vicinity
that can be used to establish a good contact with the earth.
4.4
Measurement of Soil Resistivity
As the fundamental parameter, it is important to obtain some information about the soil
resistivity when designing grounding electrodes and transmission lines. More specifically, the
reasons for obtaining information about soil resistivity are the following:
•
Soil resistivity has a direct influence on tower potential rise from lightning flashes.
Uncertainties in estimates of resistivity dominate our ability to compute transmission line
back-flashover rates. For typical lines, it can be shown that a 10% change in resistivity will
lead to a 10% change in the lightning tripout rate because there is a direct relationship
between soil resistivity and the value of footing resistance.
4-14
Electrical Characteristics of Soil
•
Soil resistivity has a marked influence on the earth return impedance (or zero-sequence
impedance) of a transmission line at 60 Hz, as reported by Carson in “Wave Propagation in
Overhead Wires with Ground Return” and by Deri in “The Complex Ground Return Plane—
A Simplified Model for Homogenous and Multi-Layer Earth Return” [15, 16]. Therefore, it
directly affects the efficiency of power transfer and the magnitude of imbalance current in the
line, and it must be accounted for in overvoltage simulations and protection settings.
•
The value of soil resistivity, as well as the nature of its layering near the surface, has
important safety implications. The resistance under the foot, which depends on upper-layer
soil resistivity (ρ1), acts as an important electrical barrier around transmission lines. The
touch potentials near electrical systems and the zone of electrical influence to nearby
communication, pipeline, and rail systems are strongly affected by the ratio of upper- to
lower-layer resistivity.
When considering the measurement of soil resistivity, several points must be considered. The
electrical resistivity of the different materials contained in soil can vary by over 20 orders of
magnitude. In addition, the soil resistivity depends on temperature, moisture content, and
frequency for many materials, including most soils and rock types. No single technique or
instrument can measure soil resistivity over such a wide range. Therefore, it is necessary to select
techniques and instruments that enable a practical measurement of soil resistivity and an
assessment of the related experimental errors.
Soil resistivity is typically measured at low voltage gradients, low current densities, and
relatively low frequencies. These are generally considered as secondary effects and are normally
not taken into account. However, the effects become important when grounding electrodes
discharge lightning currents. They are described in detail in Section 5.4, The Behavior of
Grounding Electrodes When Discharging Lightning Current.
Over the years, several methods have been developed for the measurement of soil resistivity,
including the following:
•
Resistivity measurements directly on soil core samples at the same time they are being
evaluated for civil engineering work. Often, a time-domain reflectometer instrument is used
to carry out this measurement.
•
Direct galvanic measurement of the soil resistivity with an electrode array such as the
Wenner, Schlumberger, or Lee array.
•
Passive electromagnetic methods.
•
Active induction methods.
4-15
Electrical Characteristics of Soil
Of these methods, the most well known within the electrical utility industry is the Wenner fourelectrode method. For this reason, it is described from a theoretical point of view in the following
subsection. The other methods are treated in less detail, and the indirect methods are introduced
as candidates for future development with a view of making large-scale soil resistivity surveys
possible. Several methods are described in EPRI report EL-2699 [1]. This section focuses on the
theory behind these methods; the practical aspects are covered more thoroughly in Part II of this
report.
4.4.1 Wenner Four-Electrode Method
Four-electrode methods are used to determine the soil resistivity based on the measurement of
the potential profile that is established around a pair of electrodes when they are used to circulate
current through the soil. The most well known four-electrode method is the Wenner array, which
consists of four equally spaced surface probes at spacing s (see Figure 4-13). Current is
circulated between the two outer, or current, electrodes (C1 and C2), and the potential difference
is measured between the two inner, or voltage, probes (P1 and P2). The ratio between the current
and the voltage can then be used to calculate the apparent soil resistivity at a depth that is related
to the probe spacing.
Figure 4-13
Wenner Probe Technique for Measurement of Apparent Resistivity, ρa
This four-terminal geometry is selected for two reasons. First, it is possible to theoretically
calculate the current density in the soil, which establishes the potential difference between the
voltages of the two inner probes. The relationship between the voltage and the current density is
the soil resistivity, as shown in Equation 4-1. Second, the voltage measurement on the inner
probes is not affected by the voltage drop over the contact resistance of the outer electrodes when
the inject current into the soil.
Information about horizontal and vertical soil layering can be obtained by doing repeated
measurements. Horizontal soil layers are investigated by progressively increasing the
spacing between the current electrodes, forcing the current to penetrate deeper into the soil
4-16
Electrical Characteristics of Soil
(see Figure 4-14). Vertical soil layers are detected by performing the resistivity measurement at
various locations in the area of interest. The lines in the figure indicate the current flow path in
the soil.
Figure 4-14
Wenner Probe Arrangement Effect of Probe Spacing on the Depth of Current Penetration
The simplicity of this equal-spacing probe arrangement and its accuracy over a wide range of
probe spacings (that is, 3 ft [1 m] < s < 700 ft [200 m]), makes it the preferred method for many
transmission applications. However, it is relatively time-consuming, which limits its application
for use in relation to transmission line grounding design.
4.4.1.1 Required Equipment
The required equipment for a four-electrode soil survey includes test probes, leads, and a
measuring instrument or earth tester that includes the current source and the voltage meter.
The test probes can be steel rods of 0.2- to 0.4-in. (5- to 10-mm) diameter that are pushed by
hand or hammered at least 6 in. (150 mm) into the soil. In dry conditions, it might be necessary
to use water to improve the contact resistance between the probe and soil. Copper rods do not
wet as well as steel, and they tend to be too soft for repeated use.
4-17
Electrical Characteristics of Soil
Four insulated leads—two for the potential measurement and two for the current measurement—
are required to connect the measuring instrument to the probes. The leads must be long enough
(approximately 490 feet [150 m]) to reach the two outer current leads for the longest interprobe
spacing. The leads and insulation should be mechanically strong enough to be drawn across
rough terrain and to withstand the voltages applied by the instrument.
The current source and voltage meter are often combined into an earth tester, which can range
from a hand-cranked, oak-cased megger to a plastic, rechargeable digital instrument. It is also
possible to use a separate, variable-frequency current source and frequency-selective voltmeters
to do the same measurement. The frequency of the injected ac should not be related to the power
frequency or any harmonic of that frequency. The current source should be strong enough to
overcome the contact resistance of the outer probes and to establish a measurable voltage profile
between the two outer probes. When selecting the current source, it is also important to consider
the safety aspects of applying high voltages to the current electrodes.
It is important to select an earth tester based on its ability to provide sufficient test current,
adequate voltage sensitivity, and sufficient resolution for accurate Wenner measurements.
Low-resistivity soil and long probe spacing distances place special demands on the accuracy of
the instruments used. For example, the measured value of resistance (Rmeas) for a probe spacing of
s = 330 ft (100 m) and soil with a resistivity of ρa = 10 Ωm is 0.016 Ω. Accurate measurement of
this resistance requires a specialized instrument with the following desirable characteristics:
•
Sufficient resolution, typically 1 mΩ (giving 6% error in the previous case)
•
The ability to detect the presence of excessive power frequency interference and to indicate
an error if the interference affects the measurement
•
The ability to measure current probe resistance directly or as a trouble indicator
•
The ability to change current and potential circuits quickly (internally or using an external
four-pole double-throw switch)
•
Qualities that make it desirable for use in field conditions (that is, it should be portable,
lightweight, rugged, and self-contained)
4.4.1.2 Measurement Procedure
In broad terms, a set of measurements can be taken by following these steps:
1. Select the location of the resistivity profile.
2. Prepare the equipment and consider safety precautions.
3. Select the probe spacing, and drive the current and voltage probes into the soil at the selected
probe spacing.
4. Connect the current and voltage leads.
4-18
Electrical Characteristics of Soil
5. Perform the measurement.
6. Repeat steps 3–5 until measurements are performed at a sufficiently wide probe
spacing range.
A set of resistance measurements performed in this way is called a survey. The survey provides
details about the horizontal soil layers at the survey location. Performing several surveys at the
same place but in different directions reduces measurement errors. More information is obtained
about vertical soil layers by performing surveys at different locations in the area of interest. It is
usually not necessary to obtain a resistivity profile at each tower, but only at representative
towers, to obtain a global trend of soil resistivity. More detail is provided in the following
paragraphs.
Location of the resistivity profile. It is sufficient to perform resistivity profiles along the
right-of-way, offset approximately 65 ft (20 m) from the tower or the proposed tower location,
where it is usually easier to gain access to enough terrain to obtain data for the longer probe
spacings. If sufficient space is available, profiles should be run in both directions across the
right-of-way, again offset 65 ft (20 m) to each side of the tower, to provide additional data. The
aim should be to cover an area somewhat larger than the area of the ground electrode or grid
arrangement. Existing grounding electrodes, uninsulated pipelines, rails, line structures, and
metallic fences should be avoided because these can make the soil appear artificially conductive.
The current probes in resistivity surveys close to substations should be routed, when possible, to
a distance of 10 times the station diagonal dimension away from the center of the station to
minimize influence of the substation grounding grid on the results. The diagonal dimension of
the substation includes the station fences, which are usually bonded electrically to the station
grid.
Equipment preparation. The following preparations should be completed before performing
the measurements:
•
The measurement instrument should be checked for calibration by measuring a known fixed
resistance (typically 50 or 100 Ω) prior to performing a resistivity survey. Reduced battery
output in cold weather and condensation in humid conditions can affect this calibration.
•
A voltmeter should be used to measure the ac voltage on the potential leads to check for the
level of interference of nearby electrical installations. The results should be checked against
the manufacturer’s specification of tolerable limits. Many modern instruments give direct
indications of high interference, but a measurement will save time and protect the instrument.
The conversion factor between measured root-mean-square interference and the peak-to-peak
noise specifications used by equipment manufacturers is 2√2 or 2.82, so that 20 Vp-p
capability is adequate if the voltage is less than 7 Vrms.
4-19
Electrical Characteristics of Soil
•
A two-point resistance measurement should be performed between the current probes (C1
and C2), by disconnecting the leads to the potential probes and tying together the potential
and current terminals (that is, P1 to C1 and P2 to C2) on the tester. This is done to verify that
the instrument can supply adequate test current to overcome the contact resistances of the
probes and to ensure continuity of the leads used. This is not always necessary because some
instruments have a built-in alarm to indicate excessive resistance in the current circuit.
•
Likewise, it is recommended to check the continuity of the potential circuit by performing a
similar two-point resistance measurement between the potential probes (P1 and P2). On
instruments that have internal verification of the spike resistance, a four-pole, two-position
reversing switch can be used to temporarily swap the current and resistance leads for this
continuity measurement.
Safety precautions. The following safety precautions should be considered when performing
soil resistivity surveys:
•
The usual advice to helpers, “Keep one hand in your pocket,” should be reinforced at an
informal meeting before initiating the tests.
•
The use of personal protective equipment, including dielectric rated shoes or overshoes and
leather or insulating gloves, might be appropriate.
•
Taking measurements during lightning storms should be avoided. Suspend work if lightning
is seen or heard within the area.
•
Connections should be made after laying out the test leads. Most instruments deliver limited
test current, but the open-circuit potentials can give a painful or distracting shock.
Inexpensive VHF walkie-talkies that work well under power lines are recommended to
maintain communication among probe spotters.
•
The standing potentials on leads should be measured before each measurement to verify that
they fall within the capability of the tester. Large potentials can sometimes be found near
stations.
•
Because the fault current at structures near substations will be higher, it might be advisable to
wear insulated shoes and gloves or to block reclosing. The latter should be relatively easy to
obtain on test days in fine weather, and the tests might need to be rescheduled to avoid
adverse weather.
•
Near substations, grounding conductors on the tower under test should not be cut and remade
unless appropriate safety measures are taken. Relatively high potentials can appear on the
grounding connection if a fault occurs during the time the work is being performed.
Specialized tools and techniques are needed to restore the connection with good long-term
integrity.
Selection of probe spacings. The number of measurements and the respective probe spacings
are selected based on the amount of detail required of the soil. For a detailed soil model, a large
number of probe spacings is required. For transmission line grounding systems, an ideal survey
should start with a probe spacing of s = 3 ft (1 m) to explore near-surface conditions. It should
4-20
Electrical Characteristics of Soil
also include a measurement at a spacing equal to the largest diagonal dimension of the proposed
grounding system to ensure that sufficiently deep layers are included in the measurement. The
technique varies for a detailed versus a simple profile.
For a detailed profile, a time-saving procedure uses a leapfrog technique in which the probe
spacing is doubled or tripled each time by moving only two probes (see Figure 4-15). Additional
measurements can be obtained by taking measurements with both increasing and decreasing
probe spacings. This takes a bit of practice, but a laser rangefinder or nonconductive
measurement rope can be used to avoid mistakes. For the example presented in Figure 4-15, the
ground resistivity measurements are taken for both increasing and decreasing probe spacings.
Probe spacings going out are s = 1, 3, 9, 27, and 81 m (3, 10, 30, 90, and 270 ft) and on the
return path are s = 54, 18, 6, and 2 m (180, 60, 20, and 6 ft).
Figure 4-15
Wenner Probe Positioning Strategy to Reduce the Amount of Work
For a simple profile, linear increases in probe spacing (for example s = 10, 20, 30, and 40 m [30,
60, 90, and 120 ft]), are adequate to get a general indication of the general structure of the soil in
order to decide which type of ground electrode to implement.
4-21
Electrical Characteristics of Soil
Connection of the leads. The voltage and current leads are rolled out with a separation distance
of more than 3 ft (1 m) to minimize mutual coupling. Modern instruments reject the inductive
component of the mutual impedance, but the resistive component will contribute an offset of
approximately 0.01 Ω, which could become significant for large probe spacings. This can be
illustrated with Equation 4-2, which describes the mutual impedance resulting from inductive
coupling.
⎛ 510000 ρ ⎞
⎟⎟
Z m = 0.99f + j0.63f ln⎜⎜
2
⎝ f ⋅ DCur − Potl ⎠
Equation 4-2
Inductive Coupling Mutual Impedance
Where:
Zm
is the mutual impedance per meter of parallel exposure (µΩ)
f
is the test frequency (Hz)
ln
is the natural logarithm (to base e)
ρ
is the soil resistivity (Ωm)
DCur-Potl
is the separation between current and potential leads (m)
For typical test frequencies of 130 Hz, soil resistivity of 100 Ωm, and test leads of 328.1-ft
(100-m) length separated by 3.3 ft (1 m), Zm is 0.012 + j 0.1 Ω.
Measurements. On most instruments, the measurement is performed with the touch of a button,
and the measurement is most often displayed as a resistance value. This reading is noted along
with the probe spacing at which it was obtained. If a separate current source and voltage meter
are used, then both the current and voltage should be noted for further analysis. In this case, the
measured resistance is obtained by dividing the measured voltage by the injected current.
4-22
Electrical Characteristics of Soil
4.4.1.3 Analysis and Interpretation of the Results
The result from a Wenner soil resistivity survey is a series of resistance values at different probe
spacings as shown for example in Figure 4-15. These values are then converted to express the
apparent resistivity for each probe spacing. The list of apparent resistivities can then be used to
fit an appropriate soil model (that is, a uniform soil model or a model with horizontal layering).
The fitted parameters of the soil model serve as input for the electrode resistance and potential
gradient calculations. The apparent resistivity, ρa, at a probe spacing, s, can be calculated by
either Equation 4-3 or Equation 4-4 [1]:
ρa =
4π s Rmeas
or
2s
s
−
1+
s 2 + 4 L2
s 2 + L2
Equation 4-3
Where:
s
is the spacing between the probes (m)
Rmeas
is the ratio of the voltage between the two inner probes and the current that is fed
into the two outer probes
L
is the length of insertion of the probe (m)
ρa =
2πLRmeas
⎛2+ E ⎞
s
⎟⎟ + 2 F − E −
2ln⎜⎜
L
⎝ 1+ F ⎠
Equation 4-4
Where:
s
is the spacing between the probes (m)
Rmeas
is the ratio of the voltage between the two inner probes and the current that is fed
into the two outer probes
L
is the length of insertion of the probe (m)
E
is 4 + s2/L2
F
is 1 + s2/L2
4-23
Electrical Characteristics of Soil
In most cases, this equation can be simplified by neglecting the length of the probe insertion if it
is small compared to the electrode spacing, as shown in Equation 4-5:
ρ a = 2πsRmeas
Equation 4-5
4.4.1.4 Uniform Soil
If the calculated values of apparent resistivity are the same for all probe spacing ranging from
one-third to ten times the electrode size, the soil is uniform and the effective resistivity (ρe) is
equal to the apparent resistivity (ρa).
4.4.1.5 Layered Soil
In most measurements, the value of apparent resistivity (ρa) will change with probe spacing. If
apparent resistivity increases with larger spacing (s), this is an indication that the bottom surface
layer is more resistive than the top layer. Conversely, a decrease in ρa with probe separation s
suggests that the lower layer is more conductive than the top layer.
The interpretation of the measurement results is not straightforward. In the past, various
graphical and quasi-analytical methods for interpretation have been developed [1]. However,
with greater access to computers, it is now possible to use dedicated software to interpret of soil
resistivity surveys. One such program (GG-1) is included as an applet with this report. It
provides a fit of a two-layer soil model based on an infinite series of terms, as shown in
Equation 4-6 [8]:
⎧
⎡
⎤⎫
⎪
⎢
⎥⎪
∞
4K n
2K n
⎪
⎢
⎥⎪
−
ρ a = ρ a ⎨1 + ∑ ⎢
⎬
2
2 ⎥
⎪ n=1 ⎢
⎛ 2ndT ⎞
⎛ ndT ⎞ ⎥ ⎪
1+ ⎜
1+ ⎜
⎟
⎟ ⎪
⎪
⎢⎣
⎝ s ⎠ ⎥⎦ ⎭
⎝ s ⎠
⎩
Equation 4-6
4-24
Electrical Characteristics of Soil
Where:
s
is the spacing between the probes in meters
dT
is the top layer thickness
K
is the reflection coefficient between the layers:
K=
n
ρ 2 − ρ1
ρ 2 + ρ1
is a series term that typically runs from 1 to 50
4.4.2 Other Multiple-Electrode Methods
Variations on the equally spaced probe arrangement have been introduced to eliminate or reduce
the problems experienced with the Wenner array at large electrode spacings. These arbitrary
probe arrangements can also be analyzed with applet GG-1, which accompanies this report.
Some well-known four-probe arrangements are described in this section.
The Schlumberger array uses a close spacing between P1 and P2 compared with the distance s
between potential and current electrodes. This probe configuration improves the accuracy of the
method at large probe spacings.
In “Grounding Resistance of Buried Electrodes in Multi-Layer Earth Predicted by Simple
Voltage Measurements Along Earth Surface—A Theoretical Discussion,” Chow proposed a
nonuniform surface probe spacing to obtain improved accuracy in multilayered soil [17]. The
arrangement of four unevenly spaced electrodes is shown in Figure 4-16.
Figure 4-16
Nonuniform Surface Probe Spacing for Multilayer Resistivity Survey
Other measurement techniques add more potential probes to obtain more information about the
fall of potential (or potential profile) between the current probes. Two examples of such probe
implementations are the Lee array and the EPRI Smart Ground Meter.
4-25
Electrical Characteristics of Soil
The Lee array modifies the Wenner array by using a third potential measurement electrode, P3,
halfway between P1 and P2 as a way to quickly determine whether or not the soil resistivity is
uniform. For each probe spacing, two potential readings are taken (that is, between P1 and the
central electrode, P3, and between P2 and P3). The soil is considered nonuniform if the apparent
resistivity results calculated from the two measurements are not the same. This method can
identify only whether vertical layers are present within the range of the probe array.
The EPRI Smart Ground Meter supports up to six potential probe locations, which can be used to
estimate a parameter, ke, that relates soil structure to the grounding system geometry.
Meliopoulos described this method in “A PC Based Ground Impedance Measurement
Instrument” [18]. The Smart Ground Meter comes with software to fit a suitable soil model.
Utility experience with the Smart Ground Meter has been mixed—some utilities have obtained
good and consistent results, but others report a wide range in readings depending on trivial
changes in probe locations.
4.4.3 Driven Ground Rod Methods (Two- and Three-Electrode Methods)
One common and quick method for measuring the upper layer soil resistivity is to measure
the resistance of a ground rod relative to that of a well-grounded pipe or electrical system (see
Figure 4-17). The advantage of this method is that the top layer soil resistivity can be determined
with reasonable accuracy with minimal effort.
Figure 4-17
General Setup of the Driven Ground Rod Method to Determine Soil Resistivity 4.4.3.1
Required Equipment
4-26
Electrical Characteristics of Soil
4.4.3.1 Required Equipment
The required equipment for the driven ground rod method includes a test probe, leads, and a
measuring instrument or earth tester that includes the current source and the voltage meter.
The test probe can be a steel rod with a diameter of 3/8–1 in. (10–25 mm) and a length greater
than 3 ft (1 m). The steel rod should be smooth, clean, and wet for best results. Two leads are
required to connect the measuring instrument to the probe and the tower leg. One lead should be
long enough (approximately 330 ft [100 m]) to reach the test probe. The other lead should be
long enough to reach from the measuring instrument to the tower leg (approximately 15–30 ft
[5–10 m]). The leads and insulation should be mechanically strong enough to be drawn across
rough terrain.
The current source and voltage meter are often combined into an earth tester, which can range
from a hand-cranked, oak-cased megger to a plastic, rechargeable digital instrument. It is also
possible to use a separate, variable-frequency current source and frequency-selective voltmeters
to do the same measurement. The frequency of the injected ac should not be related to the power
frequency or any harmonic of that frequency. The current source should be strong enough to
overcome the contact resistance of the outer probes and to establish a measurable voltage profile
between the two outer probes. When selecting the current source, it is also important to consider
the safety aspects of applying high voltages on the current electrodes.
4.4.3.2 Measurement Procedure
The resistance of a driven rod close to a transmission line can be determined as follows:
•
The test probe is driven into the ground at least five tower-base lengths away from the
grounded network. As a general guideline, the rod should be driven into the ground to a
depth of approximately 2.7 ft (0.82 m). If a thin 3/8-in. (0.95-cm) rod is used, a depth of 3 ft
(0.91 m) is more appropriate.
•
If the soil near the surface is dry, it might be necessary to wet the probe to improve the
contact resistance. The probes tend to vibrate and enlarge the hole around the rod so that the
rod does not make complete contact with the soil. Although water helps, smooth, square
driving techniques (or an axial dumbbell weight) give more representative values.
•
A two-point ac resistance measurement is then performed between the reference electrode
and the driven rod. One should avoid the use of a dc resistance meter because the cathodic
potentials on dissimilar metals will invalidate the results. Close to transmission lines, the
resistance of a driven rod can alternatively be determined with an earth tester or by
measuring the stray voltage and the short-circuit ac between the test probe and the
transmission line tower with volt-meter and a sensitive, clamp-on ammeter.
4-27
Electrical Characteristics of Soil
4.4.3.3 Analysis and Interpretation of the Results
The measured resistance of the probe (in ohms) is equal to the soil resistivity, if the probe
dimensions and insertion depth are as specified in the preceding section. This relationship can be
explained by inspection of the equations that describe the resistance of a single vertically
installed ground rod (Rprobe), in terms of its diameter (dprobe), the insertion depth (Lprobe), and the soil
resistivity (ρ). Three commonly used equations are presented in Equation 4-7. For more details
on these equations, refer to Section 5.2.6, Choosing an Equation to Calculate the Ground
Electrode Resistance.
For Long, Thin Rods
2π L probe
ρ=
ln
2.95L probe
d probe
Dwight [19]
R probe
For Short, Thick Rods
ρ=
2π L probe
ln
4 L probe
R probe
d probe
Rudenberg, Sunde [20, 21]
2π L probe
ρ=
ln
3.76 L probe
R probe
d probe
Geometric Resistance
Equation 4-7
Inversion of Upper Layer Resistivity from Probe Resistance
To facilitate comparison, the three equations have been rearranged to the following form (see
Equation 4-8), where KC is the ratio between the probe resistance and the upper soil resistivity
layer:
ρ = K c ⋅ R probe
Equation 4-8
For the driven rod method, the dimensions of the electrode have been selected to result in a
KC = 1. The effect of the driven rod dimensions on the factor KC is illustrated in Figure 4-18,
which shows for a wide range of rod diameter—from 3/8 to 1 in. (0.95 to 2.54 cm)—that driving
a rod vertically to a depth of approximately 2.7 ft (0.82 m) will give a good estimate of local
upper-layer resistivity. This is a little less than the rule of thumb (3-ft [0.91-m] rod resistance =
resistivity), which is biased toward good accuracy with thinner 3/8-in. (0.95-cm) rods.
4-28
Electrical Characteristics of Soil
Figure 4-18
Vertical Rod Penetration Giving R (Ω) = Upper Layer Resistivity ρ1 (Ωm)
4.4.3.4 Alternative Method
Another variation on this method is the so-called “three-point method,” or three-terminal setup.
In this configuration, three electrodes are driven into the ground at an equal distance from one
another. Two of the rods are used as current electrodes, and the potential is measured between
the third electrode and one of the current electrodes (see Figure 4-19).
4-29
Electrical Characteristics of Soil
Figure 4-19
Electrode Setup for the Three-Terminal Setup for Measuring the Ground Resistivity
The apparent resistivity is calculated, as for the driven rod method, from any of the three
equations given in Equation 4-7. If a symmetrical setup is used, it is possible to obtain more
information about local soil uniformity by performing three measurements for each electrode
setup, so that each electrode is in turn used as the P2 terminal.
As with the Wenner method, it is possible to obtain information about the soil resistivity by
performing a series of measurements at different probe spacings with the three terminal setup. In
this case measurements are taken for various P2 positions with a fixed C2 probe. This does not
give detailed resistivity information, but the analysis gives an effective resistivity relevant to the
P1-C1 electrode, which can be either a probe or a tower foundation. If the P2 survey line is taken
at several points along the C1-C2 path, this variation of the three-terminal survey is known as a
“Fall-of-Potential” method (See section 5.6.2); when the P2 survey is taken along a line at an
angle to the C1-C2 path, this is an “Oblique-Probe” method (See Section 5.6.3). Both can be used
to establish local resistivity using the GG-1 Applet or other analysis.
4-30
Electrical Characteristics of Soil
4.4.4 Passive Electromagnetic Methods
Passive electromagnetic methods obtain information about the soil resistivity as a by-product
from the analysis of the attenuation of electromagnetic signals in the atmosphere. Two
methods—radio wave attenuation and lightning system observations—are described in this
section. Both methods rely on high-frequency measurement of the soil resistivity, which makes
the results presented in the following sections more relevant to the lightning performance of
transmission lines. The soil resistivity at power frequency (that is, 50-60 Hz) can be higher by a
up to a factor of 10 (see Figure 4-6 in Section 4.2.1.6, Variation with Frequency). Nevertheless,
the conductivity maps provided in the following sections can be useful as a source of information
when it is not possible to measure the soil resistivity directly.
4.4.4.1 Radio Wave Attenuation
The radiation-field signal strength from a vertical antenna in the range of 10 kHz–10 MHz can be
described accurately and efficiently using the Sommerfeld-Norton expressions for attenuation. In
the case of a perfect or highly conducting ground plane, the signal strength falls off inversely
with distance. For high soil resistivity and at higher frequencies, there is a transition to an
attenuation characteristic that is proportional to the square of the distance. The input parameters
to the Sommerfeld-Norton model are the soil resistivity and permittivity.
As each AM broadcast station is installed, most regulators require proofs of performance to
ensure that the broadcast power is not excessive, possibly causing interference with existing
signals. These proofs of performance involve measurements of signal strength as a function of
radial distance from the antenna in several directions. It is a normal part of the analysis to fit the
observed decay in signal strength (typically between 1/d and 1/d2) with an estimate of the ground
resistivity or conductivity.
In the Unites States, Canada, and Mexico, proofs of performance have been analyzed and
grouped by the U.S. Federal Communications Commission (FCC) into a medium-frequency
conductivity map. Applet GG-12, which is provided with this report, allows the user to click on
any map location and read an interpolated value of resistivity based on the FCC data.
The World Atlas of Ground Conductivity tabulates data for many countries and provides
continental maps of the conductivity at extra-low frequency (ELF), which is up to 30 kHz, and at
medium frequency (MF), which is 1 MHz. The maps for ELF and MF are presented in
Figure 4-20 and Figure 4-21, respectively [23]. (Numbers on the legends indicate ground
conductivity in millisiemens per meter. To obtain resistivity in Ωm, divide 1000 by the value.)
These maps are useful in two respects: 1) The fundamental frequency of lightning is a 120-kHz
sine wave that matches the median dI/dt (24 kA/µs) for the median peak current (31 kA), so the
extra-low frequency map is somewhat closer to the lightning surge application. 2) For cases in
4-31
Electrical Characteristics of Soil
which a discrepancy between ELF and MF conductivity is found, this gives a strong indication
that the soil is layered. The depth of penetration of the 30-kHz ELF signal is six times greater
than at 1 MHz.
Figure 4-20
Map of Extra-Low Frequency (<30 kHz) Conductivity in Millisiemens per Meter
Source: International Telecommunication Union
4-32
Electrical Characteristics of Soil
Figure 4-21
Map of Medium-Frequency (1 MHz) Conductivity in Millisiemens per Meter
Source: International Telecommunication Union
4.4.4.2 Lightning Location System Observations
Bardo, in a study titled “Lightning Current Parameters Derived from Lightning Location
Systems: What Can We Measure?” reported measurements of the observed median rise time of
lightning signals in the North American Lightning Detection Network (NALDN) as a function of
location [24]. A significant variation was found, from less than 1 µs over the ocean
4-33
Electrical Characteristics of Soil
(corresponding to the equipment measurement limit) to more than 12 µs in areas of high
resistivity, such as the Canadian Shield in the north of Canada. They also overlaid the FCC MF
conductivity data and applet GG-12, and they found excellent matches to large features. As
expected, slow rise times corresponded to areas of high resistivity [24].
This is an interesting new method for evaluating the average resistivity along the propagation
paths from lightning to the receivers. However, some development work is still needed before it
becomes a practical alternative to obtain soil resistivity information. Specifically, the spatial
resolution of the method should be improved by focusing on the measured rise times of
subsequent strokes closest to the calibrated receivers.
4.4.5 Active Induction Methods
Electromagnetic survey methods use relatively low sine-wave frequencies to achieve the depth of
penetration needed to characterize lower-layer resistivity. Resistivity of surface and lower soil
layers can be measured using instruments developed by geophysicists for electromagnetic
sounding [8]. These instruments generally detect small variations in inductive coupling between
source and receiver coils, which are spaced 6.6–65.6 ft (2–20 m) apart. There is no electrical
(galvanic) connection to the soil, so surveys can be carried out more rapidly and even under
conditions in which the ground is frozen or the surface is hard. By changing the coil spacing and
orientation (horizontal or vertical), it is possible to adjust the depth of penetration and sensitivity
of the readings. High-frequency soil resistivity measurements using helicopter-towed coils are
useful for modeling the transient response of grounding systems, as Chisholm reported in
“Recent Progress in Design and Test Methods for Transmission Line Grounding Electrodes”
[25]. However, the electromagnetic survey method has some limitations:
•
It is sensitive to noise, giving incorrect readings under power lines.
•
It becomes inaccurate for soil resistivity values greater than 1000 Ω-m.
•
It is unable to probe much deeper than the coil spacing or ac skin depth.
•
Surveys with low frequency of excitation are affected by conducting metallic objects, such as
fences, buried pipes, cables, and overhead ground wire systems.
4.4.5.1 Theoretical Background of Inversion Problem
J. R. Wait’s analysis showed that the impedance ratio of the two horizontal coplanar coils is
changed from free space values in the presence of a resistive medium [22]. For the case of a
two-layer soil, there is a Bessel function solution of the primary vector potentials for the three
media leading to a slowly converging Sommerfeld integral solution. Wait adapted these solutions
for digital computation [22]. Measurements of the magnitude and phase of mutual impedance
between the coils provide the input data needed for this model to predict resistivity. Coils on the
surface of the earth in a variety of orientations are described in Electrical Methods in
Geophysical Prospecting [8].
4-34
Electrical Characteristics of Soil
4.4.5.2 Electromagnetic Induction
Measurements using induced electric or magnetic field, rather than direct injection of electrical
current into ground probes, are fast and inexpensive because direct contact with the earth is not
required. Induction methods can be used to detect the changes in soil resistivity that might
indicate the presence of voids or areas of fill. Therefore, induction can be used to make
qualitative assessments of soil and rock distribution at a specific location. In addition, induction
is used in many areas to locate buried metallic services, well casings, archaeological artifacts,
and valuables.
4.4.5.3 Ground-Based Two-Coil Multifrequency Electromagnetic Surveys
Figure 4-22 shows a commercial device for performing electromagnetic resistivity surveys,
which Huang described in “Real-Time Resistivity Sounding Using a Hand-Held Broadband
Electromagnetic Sensor” [26]. This device uses two coils, one to transmit signals and a second,
located a fixed distance away, tuned to receive the electromagnetic energy. When the antennas
are held near a conductive disturbance, such as lossy earth, there are small changes (usually
measured in parts per thousand or parts per million) in the in-phase and quadrature responses.
These changes can be interpreted using the mutual coupling ratio to obtain an indication of the
soil resistivity.
Figure 4-22
Multifrequency Electromagnetic Sensor for Soil Resistivity
Source: Geophex Limited
4.4.5.4 Aerial Multifrequency to 100 kHz or Transient
Horizontal loop coils placed in an array and towed beneath a helicopter (see Figure 4-23) give
low noise and high resolution in electromagnetic surveys. Accuracy is limited by the ability to
fly the terrain with a consistent and low coil height. The high speed of transit reduces the overall
survey cost for large projects. In a recent pilot study, good Wenner profiles were obtained on the
4-35
Electrical Characteristics of Soil
ground near 20 towers at the same cost as a helicopter-based survey that included 70 pairs of
towers and all the right-of-way between the towers [25]. Staging (getting equipment and
permission) exceeds the cost of flying with this technology.
Figure 4-23
Example of an Aerial Multifrequency Electromagnetic Sensor for Soil Resistivity
Source: Fugro Airborne Surveys
The inversion process of the collected aerial data using an array towed under a helicopter is
similar to that described in the previous section for ground-based surveys. Generally, excellent
insight can be obtained by simply using the apparent resistivity or with a little more processing to
carry out a two-layer inversion, giving the resistivity and depth of the upper soil layer and the
resistivity of the lower layer. An example of the results from an aerial survey was presented in
Figure 4-12.
4.4.5.5 Active Transient Current Injection at Tower Base Using the EPRI Zed-Meter
The surge impedance of an insulated cable laid directly on the ground is affected by the
resistivity of the soil beneath. With the Carson correction described by Deri, the surge impedance
of a cable lying on the ground becomes the following [16]:
⎛ 2h + p ⎞
Z wire = 60 ⋅ ln⎜
⎟
⎝ r ⎠
δ=
1
jωµ0σ
Equation 4-9
Surge Impedance of Insulated Wire over Conductive Earth
4-36
Electrical Characteristics of Soil
Where:
h
is the height above ground level
r
is the radius of the conductor
δ
is a complex number expressing the skin depth in meters, which is defined as the
depth at which the eddy current density has decreased to 1/e, or approximately 36% of
that at the ground surface
ω
is the frequency in radians/s
µo
is equal to 4π 10-7 H/m
σ
is the soil conductivity in S/m, equal to 1/ρ, where ρ is the soil resistivity in Ωm
ln
is the natural logarithm (to base e)
Equation 4-9 is an accurate and simple substitute for Carson’s integral expressions for
inductance. Figure 4-24 illustrates the computed impedance of an infinitely long insulated wire
of 0.4-in (10-mm) diameter laid directly on the earth’s surface. The impedance with this
approach is a slowly varying function of both soil resistivity (ρ) and frequency.
Figure 4-24
Surge Impedance (Ω) of Insulated Wire on Ground Surface Versus Soil Resistivity for
Various Frequencies
4-37
Electrical Characteristics of Soil
This change in the observed surge impedance with resistivity and frequency can be exploited to
obtain an estimation of the resistivity of the underlying soil by inverting the equations of the
fitted trend lines in Figure 4-24, as shown in Equation 4-10.
ρ =e
Z wire −330
30
Equation 4-10
Resistivity of the Soil as a Function of the Surge Impedance of a 0.4-in. (10-mm) Wire on
the Ground
The choice of the 330-Ω offset is appropriate for a 100-kHz frequency. Lower frequencies have
greater depth of penetration and are more useful for studying deep layers; higher frequencies
indicate the properties of surface layers.
This method can be realized with a slight modification to the EPRI Zed-meter, which is currently
under development to measure the transient tower footing impedance. The Zed-meter
instrumentation is used to apply a 200-V surge pulse with a rectangular wave shape to two
coaxial cables that are laid out on the ground in different directions. The input voltage and
current to each of the cables are measured with a high-speed digitizer. From this, the measured
surge impedance can be calculated and compared with the theoretical equations to obtain the soil
resistivity. The resistivity is observed to vary with time. A slight increase would be associated
with uniform soil, and any decrease would suggest that the lower layers have less resistivity than
the top layer.
The advantages of this approach are numerous. The most significant is that this test uses the
same leads that are used when the transient tower footing resistance is measured. Second,
because it is not necessary to make a galvanic connection to the earth, most problems associated
with the use of driven rods in methods such as the Wenner method are eliminated.
Preliminary tests and comparisons with other soil resistivity measurements have demonstrated
that this is a feasible method to determine soil resistivity, as described in the EPRI reports Field
Testing of the EPRI Zed-Meter: Transient Impedance of Transmission Line Grounds (1010235),
and Summary of Zed-Meter Field Tests: Transient Impedance of Transmission Line Grounds
(1012314) [5, 27, 28]. This method still required substantial development, which is the focus of
an EPRI-sponsored project.
4-38
Electrical Characteristics of Soil
4.4.6 Choosing an Appropriate Method for Soil Resistivity Measurements
In the preceding sections, several methods have been introduced to obtain information about the
soil resistivity at the location of transmission lines. A summary of the methods is provided in
Table 4-2 to help users decide which method is most appropriate for their particular situations.
Each measurement technique has its own merits and can be appropriate under certain
circumstances. It is not possible to be prescriptive, but several typical applications are mentioned
in the following subsections.
Table 4-2
Comparison of the Methods for Determining Soil Resistivity
Method
Wenner
Schlumberger
Level of
Detail
High
Relative
Effort
Required
Medium
Access
to
Tower?
Comments
Yes
This method is the industry standard for
measuring resistivity. It is a simple method
with sufficient accuracy for transmission line
applications.
Yes
This method is a bit more complicated than
the Wenner, but it provides better information
at large probe spacings. Therefore, this
method is more appropriate for substations.
High
Medium
Nonuniform
surface probe
spacing
High
Labor
intensive
Yes
This method can provide greater detail about
the soil structure, but at the cost of simplicity.
The additional soil layering information is
generally not required.
Lee
High
Medium
Yes
This probe array can be useful to identify the
presence of vertical soil layering with a
minimal increase in effort.
EPRI Smart
Ground Meter
Medium
Medium
Yes
This method can be combined with the
measurement of the tower footing resistance.
Two-point driven
ground rod
method
Medium
Low
Yes
This is a quick method to obtain information
about the upper soil layer resistivity.
Yes
This is a quick method to obtain information
about the upper soil layer resistivity. This
method can be extended to obtain
information about the layering in the soil, but
it becomes more labor-intensive than the
Wenner because the probe array is extended
in three directions.
Three-point
driven ground rod
method
Medium
Medium
4-39
Electrical Characteristics of Soil
Table 4-2 (continued)
Comparison of the Methods for Determining Soil Resistivity
Method
Three-point
driven ground
rod method (Fall
of potential
Three-point
driven ground
rod method
(Oblique probe)
Level of
Detail
Medium/High
Relative
Effort
Required
Medium
Access
to
Tower?
Comments
Yes
Normally performed as part of a tower
footing measurement. The slope of the
change of potential with distance is
processed to give uniform soil resistivity
estimate. Analysis may be difficult if
detailed knowledge of the foundation
dimensions and depths are not available.
Yes
Normally performed as part of a tower
footing measurement. The slope of the fall
of potential to the inverse of distance is
processed to give a uniform soil resistivity
estimate;
Low
Medium
Radio wave
attenuation
Low
Low (read
from
available
maps)
No
This is an excellent method to estimate
ground resistivity at minimal cost. However,
the level of detail is not sufficient to identify
local (tower-to-tower) variations in soil
resistivity.
Lightning
location system
observations
Low
N/A
No
This method is not ready for general use.
Electromagnetic
induction
Medium
Low
Yes
This is a quick method to obtain information
about variations in upper soil layer
resistivity.
Yes
This is a quick method to obtain information
about the upper soil layer resistivity.
However, a certain level of expertise is
required to extract resistivity information.
No
This is a quick method to obtain information
about the upper soil layer resistivity.
However, a certain level of expertise is
required to extract resistivity information.
Yes
It is possible to extract detail information
about the soil resistivity profile. However, the
practicality of performing such
measurements at tower bases is not proven.
Yes
This method holds promise because it can
be used in combination with tower footing
resistance measurements. However, some
development is still needed.
Ground-based
two-coil multifrequency
electromagnetic
surveys
Aerial
multifrequency to
100 kHz or
transient
Groundpenetrating radar
Transient current
injection
(Zed-meter)
4-40
Medium
High
High
Medium
Low
Low
Medium
Low
Electrical Characteristics of Soil
4.4.6.1 Resistivity Profile from Aerial Surveys
Aerial surveys of resistivity before construction can be used to for initial planning of what types
of grounding electrodes will be needed for satisfactory reliability. In some cases, aerial surveys
make it clear that the grounding situation is difficult, which can lead to the use of unshielded
lines with either single-pole reclosing or transmission line surge arresters.
4.4.6.2 Resistivity Information from Tower Footing Resistance Measurements
Some major utilities use an indirect measure of resistivity—the as-constructed footing
resistance—to decide on treatments. The process is usually as follows:
1. A standard foundation and ground electrode is installed.
2. Ground resistance readings are taken after installation is complete.
3. The initial values are used to design additional grounding to address deficiencies before the
tower is erected.
At other utilities, the footing resistance is measured using a fall-of-potential method after the
tower is erected but before the overhead ground wires have been installed. If the resistance
exceeds a standard value, treatment rules indicate what is to be done.
Footing resistance measurements using the oblique-probe method or fall-of-potential readings
(see Section 5.6, Procedures for Testing Tower Grounding Electrodes) taken with more than one
potential probe location close to the tower can give designers the resistivity of the soil near the
new tower. Two or three readings will not take much longer than one, and interpretation is
relatively fast.
4.4.6.3 Detailed Soil Resistivity Measurements
Detailed soil resistivity surveys used in combination with the applets (GG-1 and GG-3) provided
with this report can be used to obtain information about the layering of the soil. With such a
detailed soil model, it is possible to decide whether to extend radial counterpoise outward from
the tower or to drive rods (or drill a well) vertically to reach an underlying area of low resistivity.
4-41
Electrical Characteristics of Soil
4.4.6.4 Variations in Resistivity After Construction
One concern with on-the-spot treatment of footings to achieve a desired fixed value is that the
tower footing resistance varies over time as a result of either seasonal variations in the soil
resistivity (see Section 4.2.2, Seasonal Variations) or variations in settling, especially of poured
concrete foundations, which can change considerably in the days and weeks after construction as
the concrete dries out and adjusts to the average relative humidity of the environment. Variations
in settling could be interesting to monitor but are likely to have only a small effect compared
with the changes in resistivity with seasons. For this reason, specifications using the summer
(that is, lightning season) values of resistivity might be most appropriate to design grounding
electrodes for lightning performance.
4-42
5
CHARACTERISTICS OF A GROUND ELECTRODE
5.1
Introduction
A ground electrode is generally a metal conductor or a system of interconnected metal
conductors buried in the earth or concrete to provide an electrical connection to the general mass
of earth. It typically consists of a combination of driven rods, buried conductors, and encased
conductors. When current is discharged into the soil through a ground electrode, potential
gradients are set up in the soil as a result of the conduction of current through the resistive
medium (the soil).
The extent to which the potential of the electrode rises with respect to far earth is called the
ground potential rise (GPR). The relationship between the GPR and the current conducted to
ground is called the electrode impedance. The derivation of the electrode impedance is described
in Section 5.2, Low-Frequency Ground Electrode Impedance. The electrode impedance is an
important factor that determines the lightning performance of the line. This aspect is described in
Section 5.4, The Behavior of Grounding Electrodes When Discharging Lightning Current.
Potential gradients around the grounding electrode can affect humans and livestock in the
vicinity of the line if large currents are conducted to ground. The potential gradients are normally
quantified and evaluated in terms of step and touch potentials. The definitions of step and touch
potentials and their evaluation are described in Section 5.3, Surface Potential Gradients.
The foundation of the tower, if it contains embedded conductive parts such as reinforcing, also
forms part of the ground electrode. Therefore, the tower foundation has to fulfill both a civil
engineering function and an electrical function. The impact of the foundation and its concrete
encasing on the electrical characteristics of the ground electrode are explained in Section 5.5.
Other aspects civil engineering aspects are presented in Part II, Section 6.5 Civil and Mechanical
Engineering Aspects, where it is explained that the life of the buried conductors must be
compatible with that of the structure. This is especially in light of the possibility of electrolytic
corrosion of the buried metal structures.
Another aspect of the ground electrode design is the sizing of the conductors to handle the ac and
lightning current to which it will be subjected and to withstand the mechanical forces that might
be applied to it. This aspect is described in Part II Section 6.7, Sizing of Grounding System
Conductors.
5-1
Characteristics of a Ground Electrode
Section 5.6, Procedures for Testing Tower Grounding Electrodes, provides theoretical
background details on the measurement techniques and procedures that are available to evaluate
the quality and condition of ground electrode systems.
5.2
Low-Frequency Ground Electrode Impedance
The overall impedance of the ground electrode, ZG, is given by the relationship between the
potential rise of the electrode, VE, and the current discharged into the ground, IE (that is,
ZG = VE/IE. It consists of four components:
•
Resistance RL and reactance XL of the ground electrode leads.
•
The contact resistance RC between the surface of the electrode and the surrounding soil.
When an electrode is driven into or buried in the soil, there is not always perfect contact
between the soil and the surface of the electrode. This is represented by the contact
resistance, which reduces as the soil settles around the electrode.
•
The dissipation resistance RE of the soil surrounding the electrode is calculated as the
resistance of the earth between the surface of the earth electrode and a fictitious metal
hemisphere electrode (remote earth) on the same axis at an infinite radius.
•
The reactance of the current paths in the soil XE.
In ac circuits, the impedance between the grounding system and the reference earth, ZG, at a
given frequency can be described by Equation 5-1:
Z G = ( R + jX ) E + RC + ( R + jX ) L
Equation 5-1
The series resistance of the metallic conductors making up the ground electrode and leads is
typically much lower than the contact resistance and the resistance of the surrounding soil. On
the other hand, the reactance of the metallic conductors and the leads is much higher than the
reactance of the current dissipated in the soil. Equation 5-1 can therefore be simplified to
Equation 5-2:
Z G ≈ RE + RC + X L
Equation 5-2
5-2
Characteristics of a Ground Electrode
For seasoned grounding electrodes, the contact resistance can typically be neglected when the
soil has settled around the conductors making up the electrode. At power frequencies, the
reactance of the grounding conductors and leads, XL (given by XL=2πfL)—assuming that the lead
inductance is approximately L=1 µH/m—becomes negligible compared to the dissipation
resistance, RE. Therefore, at low frequencies, the grounding impedance is sufficiently described
by the dissipation resistance (Equation 5-3):
Z G ≈ RE
Equation 5-3
For high-frequency phenomena such as lightning, the inductive reactance of the grounding
system must be considered (see Section 5.4, The Behavior of Grounding Electrodes When
Discharging Lightning Current).
In this section, the intent is to derive equations to calculate the ground resistance of electrode
shapes that are relevant to transmission systems. These include the following:
•
Simple surface radial electrodes in the form of horizontal strips or wires, extending radially
outward from the tower
•
Simple surface ring electrodes in the form of horizontal strips or wires, buried in a circle at a
constant distance from the tower.
•
Meshed surface electrodes that are constructed as rectangular grids, rings, or radial
arrangements buried at shallow depth
•
Cable with exposed metal sheath or armor that behaves like a long radial electrode
•
Single-rod electrodes made from a solid rod, hollow pipe, or other long, thin metal electrode,
usually driven vertically or buried to a depth of 10–100 ft (3–30 m)
•
Multiple-rod electrodes made from several single-rod electrodes that are spaced 15–70 ft (5–
20 m) from one another
•
Foundation electrodes formed from conductive structural parts of the tower and reinforcing,
embedded in concrete foundations to provide a large area of contact with the earth
In this list, three general types of electrodes can be identified:
•
The first four arrangements are surface earth electrodes, which usually consist of strip wires
or bands arranged as radial, ring, or meshed electrodes (or a combination of these) buried at
depths of up to approximately 3.3 ft (1 m). An advantage of surface electrodes is their
favorable surface potential distribution, which results in generally lower step and touch
potentials.
•
Single- and multiple-rod electrodes belong to the class of deep-earth electrodes. These have
the ability to pass through various soil layers, which can be useful in places where the
5-3
Characteristics of a Ground Electrode
shallow upper layers have high resistivity. This is often an easy way to obtain and retain a
target electrode resistance. Deep-earth vertical-rod electrodes can be installed in places where
a limited surface area is available.
•
Foundation electrodes (or concrete-encased electrodes) represent a concentrated electrode at
the tower base. These electrodes are an inherent part of the civil construction, and in good
soil conditions, they can be sufficient to reach the target resistance value. However, the
design of the concrete foundation and its reinforcing must take into account its function as
ground electrode. One way is to ensure that there are electrical connections between all
conductive parts embedded in the concrete.
In practice it is usually necessary to apply a combination of deep-earth and surface electrodes to
fulfill the dual criteria of a good resistance and safe surface potential gradients. Foundation
electrodes are often ignored, but they can offer additional areas of contact with the soil that can
improve both ground resistance and surface potential gradients.
5.2.1 Derivation of the Ground Electrode Resistance of a Hemispheric Electrode
As shown in Section 5.2, Low-Frequency Ground Electrode Impedance, the low-frequency
impedance of a ground electrode is described with sufficient accuracy by the dissipation
resistance of the soil surrounding it. The fundamentals of calculating the dissipation resistance
can be described by considering a hemispheric electrode with a radius (a) that is buried in
uniform soil (see Figure 5-1).
Figure 5-1
The Potential Profile of a Hemispherical Electrode in Uniform Soil, Showing the
Parameters for Calculating Ground Resistance and Step and Touch Potentials
5-4
Characteristics of a Ground Electrode
When the electrode discharges current into the soil, the current (IE) will flow uniformly and
radially away in every direction because of the spherical symmetry of the setup. Equipotential
surfaces are formed by the electrode surface and on any hemispherical cross sections (dx) of the
ground centered on the electrode. The lines of current flow are perpendicular to these surfaces.
The current density is greatest at the surface of the electrode, and it becomes less as the distance
from the electrode increases. Because the total current in the soil remains constant, the current
density on a hemisphere at a distance (x) is given by Equation 5-4:
Current Density =
Total current
2πx 2
Equation 5-4
The resistance (dR) of a thin hemispherical element with thickness dx is obtained from
fundamental principles (see Equation 5-5):
dR =
ρ
2π ⋅ x 2
dx
Equation 5-5
The electrode resistance is the integral of dR from the hemisphere surface to infinity (see
Equation 5-6):
R=
∞
ρ dx
ρ
=
2
∫
2π a x
2π a
Equation 5-6
The potential of any point located at distance (x) from the center of the hemisphere electrode in
which an earth current (IE) flows, is given by Equation 5-7:
Vx =
ρI E
2π x
Equation 5-7
The hemispheric electrode is a base case that provides a handy benchmark for comparing the
resistances and voltage profiles of other electrode shapes. Equation 5-7 illustrates the parameters
that determine electrode resistance. The electrode resistance is directly proportional to the
ground resistivity and inversely proportional to the size of the electrode.
5-5
Characteristics of a Ground Electrode
Another factor that is not apparent from Equation 5-7 is the shape of the ground electrode. This
influences to a large extent how quickly the potential drops as one moves away from the
electrode. Ring or mesh electrodes have potential profiles that fall off less rapidly than 1/x;
vertical driven rods have a greater change in surface potential with distance.
The derivation in Equation 5-6 might give the impression that the resistance of ground electrode
configurations can easily be derived from first principles; however, that is not the case. For
real-life electrode shapes or in layered soil conditions, the mathematics is complex and several
simplifying assumptions are generally necessary to obtain closed form equations. Several
methods have been devised for the calculation of electrode resistance, of which three types are
described in this report:
•
Analytical expressions (see Section 5.2.2, Analytical Expressions for the Calculation of
Ground Electrode Resistance)
•
The geometric and contact resistance method (see Section 5.2.3, The Geometric and Contact
Resistance Method)
•
Numerical methods (see Section 5.2.7, Numerical Methods for Calculating Ground Electrode
Resistance)
5.2.2 Analytical Expressions for the Calculation of Ground Electrode Resistance
This section presents equations that are in common use in order to provide a reference library of
equations.
5.2.2.1 Dwight and Sunde Equations
Dwight and Sunde published expressions to calculate the resistance to remote earth for several
practical electrode shapes; they are presented in Tables 5-1 and 5-2 [19, 21]. A software
implementation of these equations is provided in applet GG-3.
5-6
Characteristics of a Ground Electrode
Table 5-1
Low-Frequency Ground Resistance of Electrodes
Electrode
Dimensions
Equation
Single vertical
rod
Length L , radius a
R=
ρ ⎛
4L ⎞
− 1⎟
⎜ log e
2πL ⎝
a
⎠
Two vertical rods
Separation s with s>L
R=
⎞
ρ ⎛
4L ⎞ ρ ⎛
L2 2 L4
⎜⎜ 1 − 2 +
− 1⎟ +
+ K⎟⎟
⎜ log e
4πL ⎝
a
3s
5 s4
⎠ 4π s ⎝
⎠
Two vertical rods
Separation s with s<L
R=
⎞
ρ ⎛
4L
4L
s
s2
s4
⎜⎜ log e
+ log e
−2+
−
+
− K⎟⎟
2
4πL ⎝
a
s
2 L 16 L 512 L4
⎠
Buried horizontal
wire
Length 2L, depth s/2
R=
⎞
ρ ⎛
4L
4L
s
s2
s4
⎜⎜ log e
+ log e
−2+
−
+
− K⎟⎟
2
4πL ⎝
a
s
2 L 16 L 512 L4
⎠
Right-angle turn
of wire
Arm length L, depth s/2
R=
ρ ⎛
2L
2L
s
s2
s4 ⎞
⎜ log e
+ log e
− 0.2373 + 0.2146 + 0.1035 2 − 0.0424 4 K⎟⎟
4πL ⎜⎝
a
s
L
L
L ⎠
Three-point star
Arm length L, depth s/2
R=
ρ ⎛
2L
2L
s
s2
s4 ⎞
⎜⎜ log e
+ log e
+ 1.071 − 0.209 + 0.238 2 − 0.054 4 K⎟⎟
6πL ⎝
a
s
L
L
L ⎠
Four-point star
Arm length L, depth s/2
R=
ρ ⎛
2L
2L
s
s2
s4 ⎞
⎜⎜ log e
+ log e
+ 2.912 − 1.071 + 0.645 2 − 0.145 4 K⎟⎟
8πL ⎝
a
s
L
L
L ⎠
Six-point star
Arm length L, depth s/2
R=
2L
2L
s
s2
s4 ⎞
ρ ⎛
⎜⎜ log e
+ log e
+ 6.851 − 3.128 + 1.758 2 − 0.490 4 K⎟⎟
12πL ⎝
a
s
L
L
L ⎠
Eight-point star
Arm length L, depth s/2
R=
ρ ⎛
2L
2L
s
s2
s4 ⎞
⎜⎜ log e
+ log e
+ 10.98 − 5.51 + 3.26 2 − 1.17 4 K⎟⎟
16πL ⎝
a
s
L
L
L ⎠
Ring of wire
Diameters ring D, wire d
and depth s/2
R=
8D
4D ⎞
ρ ⎛
+ log e
⎜ log e
⎟
d
s ⎠
2π 2 D ⎝
Buried horizontal
strip
Length 2L, section a by
b, (a>8b), depth s/2
R=
⎞
4 L a 2 − πab
4L
s
s2
s4
ρ ⎛
⎜⎜ log e
+
+ log e
−1+
−
+
− K⎟⎟
2
2
4πL ⎝
a 2( a + b )
s
2 L 16 L 512 L4
⎠
Buried horizontal
round plate
Radius a, depth s/2
(for s>2a)
R=
Buried vertical
round plate
Radius a, depth s/2
R=
ρ
8a
ρ
8a
+
⎞
ρ ⎛
7 a 2 33 a 4
⎜⎜ 1 −
+
+ K⎟⎟
2
4
4πs ⎝ 12 s
40 s
⎠
+
⎞
ρ ⎛
7 a 2 99 a 4
⎜⎜ 1 −
+
+ K⎟⎟
4πs ⎝
24 s 2 320 s 4
⎠
5-7
Characteristics of a Ground Electrode
Table 5-2
Footing Resistance Expressions
Electrode
Dimensions
Equation
Single vertical
rod
Length L, radius a
R=
ρ ⎛
4L ⎞
− 1⎟
⎜ log e
2π L ⎝
a
⎠
Two vertical rods
on circle of
diameter D
Length L, radius a
R=
1 ρ ⎛
4L
L⎞
−1+ ⎟
⎜ log e
2 2π L ⎝
a
D⎠
Three vertical
rods on circle of
diameter D
Length L, radius a
R=
⎛
⎞
1 ρ ⎜
4L
2L ⎟
−1+
log e
⎜
a
3 2π L ⎜
D sin π ⎟⎟
3⎠
⎝
Four vertical
rods on circle of
diameter D
Length L, radius a
R=
1 ρ ⎛⎜
4L
2L
L ⎞⎟
log
1
−
+
+
e
4 2π L ⎜
a
D⎟
D sin π
4
⎠
⎝
Six vertical rods
on circle of
diameter D
Length L, radius a
R=
L ⎞⎟
2L
1 ρ ⎛⎜
4L
2L
−
+
+
+
log
1
e
a
D ⎟⎟
6 2π L ⎜⎜
D sin π
D sin π
3
6
⎝
⎠
n vertical rods on
circle of
diameter D
Length L, radius a
R=
4L
2nL
2n ⎞
1 ρ ⎛
−1 +
log e
⎜ log e
⎟
n 2π L ⎝
a
πD
π ⎠
n rods in line,
separation s
Length L, radius a
R=
1⎡ ρ ⎛
4L ⎞ ρ ⎛ 1 1 1
1 ⎞⎤
− 1⎟ + ⎜ + + + K + ⎟⎥
⎜ log e
⎢
n ⎣ 2π L ⎝
a
n ⎠⎦
⎠ πs ⎝ 2 3 4
Buried horizontal
wire
Length L, radius a,
depth d
R=
ρ ⎛
2L
⎞
− 1⎟
⎜ log e
πL ⎝
2ad
⎠
n buried
horizontal radial
wires
Length L, radius a,
depth d
R=
n −1
⎛
ρ ⎡
2L
1 + sin (π m n ) ⎞⎤
⎟⎥
⎜⎜ log e
log
1
−
+
⎢ e
∑
nπ L ⎣
sin (π m n ) ⎟⎠⎦
2ad
m =1 ⎝
5.2.2.2 Equations for Calculating the Resistance of Typical Transmission Line Tower
Electrodes
In addition to the equations listed in Tables 5-1 and 5-2, other expressions are commonly used to
calculate the resistance of transmission line grounding electrodes. This section presents some of
the equations for plate, rod, and solid ellipsoid electrodes.
5-8
Characteristics of a Ground Electrode
Resistance of a round plate electrode. The resistance of a round plate electrode (see
Figure 5-2) with radius a on the soil surface is given by Equation 5-8 [6]:
Figure 5-2
Round Plate Electrode
R=
ρ
4a
Equation 5-8
Resistance of a Round Plate Electrode
Resistance of a rod electrode. A selection of the analytical expressions describing the resistance
of a rod electrode (see Figure 5-3) is presented in Table 5-3.
Figure 5-3
Rod Electrode
5-9
Characteristics of a Ground Electrode
Table 5-3
Equations for Calculating the Resistance of a Rod Electrode
Source
Equation
ρ ⎡ ⎛ 4L ⎞ ⎤
ln⎜ ⎟ − 1
2π L ⎢⎣ ⎝ a ⎠ ⎥⎦
Sunde, Dwight [21, 19]
R=
Rudenberg, Sunde [20, 21]
R=
Liew and Darveniza [29]
R=
ρ ⎛a+L⎞
ln ⎜
⎟
2πL ⎝ a ⎠
Chisholm and Janischewskyj [30]
R=
ρ ⎡
⎛ L ⎞⎤
1 + ln⎜ ⎟⎥
⎢
2π L ⎣
⎝ a ⎠⎦
ρ
2π L
⎛ 2L ⎞
ln⎜ ⎟
⎝ a ⎠
Resistance of an electrode in the shape of an ellipsoid of revolution. The resistance of an
ellipsoid of revolution (see Figure 5-4) with a major semi-axis (L) and a minor semi-axis (a) is
given by Equation 5-9 [21]:
Figure 5-4
An Ellipsoid of Revolution
R=
α=
ρ α +1
ln(α )
4π L α − 1
α0 ⎡
4 ⎤
⎢1 + 1 − 2 ⎥
2 ⎣
α0 ⎦
2
⎛ 2L ⎞
α0 = ⎜ ⎟ − 2
⎝ a ⎠
Equation 5-9
Resistance of an Ellipsoid of Revolution
For ellipsoids that are wider than they are long, α in Equation 5-9 becomes complex, and the
evaluation requires complex arithmetic.
5-10
Characteristics of a Ground Electrode
5.2.3 The Geometric and Contact Resistance Method
A reasonably accurate estimate of the resistance of a ground electrode can be obtained by
approximating it as a solid spheroid electrode. This estimate is called the geometric resistance,
and it can be determined relatively easily. The accuracy of this estimate can be improved by
introducing a factor, called the contact resistance, to correct for the fact that the actual ground
electrode is a wire frame and not solid. This calculation method can be described mathematically
as shown in Equation 5-10:
RE = Rgeometric + Rcontact
Equation 5-10
Where:
RE
is the resistance of the ground electrode
Rgeometric
is the resistance of an equivalent solid spheroid electrode
Rcontact
is a correction term from solid to wire-frame electrodes
In most cases, the contact resistance is small, but operating conditions can influence it.
Variations in the resistivity of the top layer soil affect the contact resistance term, but usually not
the geometric resistance. For example, freezing of the top layer of soil leads to an increase of the
contact resistance term. For lightning surge conditions, soil ionization (see Section 5.4.2, Soil
Ionization Effects at High-Voltage Gradients) reduces the contact resistance term, and the effects
of the ground-plane surge impedance increases it.
In the following sections, details are provided on the derivation of the geometric and contact
resistances. The equations are expressed in terms of the effective resistivity of the soil, ρe.
Section 5.2.4, Calculation of Electrode Resistance in Two-Layer Soil, explains how the effective
resistivity is determined.
5.2.3.1 The Derivation of Geometric Resistance of Solid Spheroid Electrodes
Three types of solid spheroid electrodes are shown in Figure 5-5. These shapes can be used as
approximations of typical transmission line grounding electrodes:
•
The prolate spheroid (a long, thin electrode) is used to approximate deep-earth electrodes.
•
The spherical is a special case in which the x, y, and z electrode dimensions are the same.
•
The oblate spheroid (a plate-like electrode) is used to approximate surface-earth electrodes.
5-11
Characteristics of a Ground Electrode
Figure 5-5
Three Types of Solid Spheroid Electrodes
Using the techniques developed for the calculation of electrode capacitance in free space, it is
possible to derive an equation describing the resistance of solid spheroid electrodes in uniform
soil, as Chisholm described in “Transmission System Transients—Grounding” and Oettle
explained in “A New General Estimation Curve for Predicting the Impulse Impedance of
Concentrated Earth Electrodes” [31, 32]. Equation 5-11 is the generalized equation.
R=
ρe
(Q)
2πg
⎛ 11.838 ⋅ g 2 ⎞
⎟⎟
Q = ln⎜⎜
A
⎝
⎠
Equation 5-11
Resistance of Solid Spheroid Electrodes
Where:
R
is the electrode resistance to remote earth
ρe
is the effective soil resistivity
ln
is the natural logarithm, to base e
g
is the geometric sum of electrode radii in each direction from the center, given by
ax2 + a y2 + az2
Q
is the shape factor
A
is the surface area of the electrode
The value 11.838 is theoretically (2πe√3)/3. The quotient ρe/2πg is common to most expressions
for electrode resistance and results in a decrease of the electrode resistance, with an increase in
size in any dimension.
5-12
Characteristics of a Ground Electrode
The shape factor, Q, is a dimensionless number that is constant for each electrode shape,
independent of its size. For example, it ranges from a minimum value of approximately 1.09 for
a half cube, to 1.33 for a fat cylinder (length = radius), to √3 for a hemisphere, to 2 for a plate, to
3 for a trench, to a maximum value of 6 for rod electrodes. Because of this property, Equation
5-11 can be readily inverted to give the required dimensions of the electrode to meet a target
resistance value.
Estimations of the resistance of the three important electrode shapes—rod, hemisphere,
and plate—have been obtained by substituting the dimensions of these electrode types into
Equation 5-11.
Resistance of a rod electrode. Assume a rod with length L and radius a. The geometric distance
is g = L2 + a 2 , and the surface area is A = πa 2 + 2πaL . Equation 5-11 becomes the following:
(
)
⎛ 2πe 3 L2 + 2a 2 2 ⎞
ρe
⎟
R=
ln⎜
2
2
2
⎜
⎟
a
+
aL
3
(
π
2
π
)
2π L + a
⎝
⎠
Equation 5-12
Geometric Resistance of a Rod Electrode
For the general case, it can be assumed that L>>a. The equation simplifies then to Equation 5-13:
R=
ρ e ⎛ 1.878 L ⎞
ln⎜
⎟
2π L ⎝ a ⎠
Equation 5-13
Simplified Geometric Resistance of a Rod Electrode
Resistance of a hemispheric electrode. Assume a hemispheric electrode with radius a. The
geometric distance is g = a 2 + a 2 + a 2 , and the surface area is A = 2πa 2 . Equation 5-11
becomes the following:
5-13
Characteristics of a Ground Electrode
(
2πe 3 3 a 2
R=
ln
3 × 2π a 2
2π 3a 2
ρe
R=
R=
ρe
2 3π a
ρe
ln
)
2
2πe 3 × 3
3 × 2π
3
2 3π a
ρe
R=
2π a
Equation 5-14
Geometric Resistance of a Hemispheric Electrode
Resistance of a round plate electrode. Assume a circular, round plate with a radius d. The
geometric distance is g = d 2 + d 2 , and the surface area is A = πd 2 . Equation 5-11 becomes the
following:
ρe
⎛ 11.8 × 2d 2 ⎞
⎟⎟
ln⎜⎜
2
2π 2d 2 ⎝ πd
⎠
ρe
⎛ 2 × 11.8 ⎞
R=
ln⎜
⎟
2 2πd ⎝ π ⎠
0.226 ρ e
R=
d
R=
Equation 5-15
Geometric Resistance of a Round Plate Electrode
5-14
Characteristics of a Ground Electrode
5.2.3.2 Derivation of the Contact Resistance Term
The contact resistance is essentially a correction term to improve the estimation of the ground
electrode resistance for the cases in which the electrode consists of a collection of thin wires (that
is, a wire frame) instead of a solid electrode for which the geometrical equation is valid. An
example is the case in which a solid plate electrode is used to approximate a grid electrode. For
buried grids, it is common to estimate the contact resistance with the simple expression shown in
Equation 5-16 [33]:
Rcontact ≤
ρ1
L
Equation 5-16
Where:
Rcontact
is the electrode contact resistance
ρ1
is the upper-layer resistivity
L
is the total length of wire
Generally, Equation 5-16 is a conservative estimate that is accurate for practical radial
electrodes, but it results in too high an estimate of the contact resistance for ring electrodes. A
more accurate estimate for the contact resistance have been obtained by analyzing a range of
practical electrode shapes. Equation 5-16 is then modified to:
Rcontact = MAX
ρ1
A
ln
,0
2πL
2 Awire
Equation 5-17
Where:
Rcontact
is the electrode contact resistance
ρ1
is the upper-layer resistivity
L
is the total length of wire
A
is the outer surface area of the equivalent solid electrode
Awire
is the surface area of the actual electrode in contact with the soil.
Note, Rcontact in Equation 5-17 may result in values that is marginally greater than ρ/L for very,
impractical, thin wires. Rcontact is set always greater than, or equal to, zero – the log term is
negative for electrodes with considerable inward-facing surface area that does not carry much
current density, but for these cases the log term is set to zero.
5-15
Characteristics of a Ground Electrode
5.2.3.3 Geometric and Contact Resistance Equations for Basic Electrode Types
The geometric and contact resistance terms have been derived for some basic electrode types.
Buried horizontal wire. For a buried horizontal wire with length L, wire radius a, and burial
depth s, the following equation is used:
Rgeometric =
⎛ 11.8 g 2 ⎞
ρe
⎟
ln ⎜⎜
2πg ⎝ A ⎟⎠
Where:
(L 2)2 + s 2 + a 2
A = 2 Ls + πaL
g=
Equation 5-18
Rcontact = MAX
ρ1
s
1
ln
+ ,0
2πL
2πa 4
Equation 5-19
Circular ring electrode. For a circular ring electrode with diameter D, wire radius a, and burial
depth s, the following equation is used:
ρe
11.8 g 2
ln
R geometric =
2πg
A
Where:
2
g = D 2 + s2
D
A = πD s +
4
Equation 5-20
s + D4
ρ1
Rcontact = 2 ln
2πa
2π D
Equation 5-21
5-16
Characteristics of a Ground Electrode
5.2.4 Calculation of Electrode Resistance in Two-Layer Soil
Horizontal layering in the soil must be taken into account when designing grounding electrodes.
In most cases, it is sufficient to approximate local ground conditions with a soil model that is
composed of two horizontal layers (see Figure 5-6).
Figure 5-6
General Two-Layer Soil Model with Horizontal Layering
The upper soil layer resistivity (ρ1) its estimated depth (dT), and the lower soil layer resistivity
(ρ2) can be estimated from a series of apparent resistivity values at different probe spacings (see
Section 4.4, Measurement of Soil Resistivity, and applet GG-1). In order to use the simple
resistance calculations introduced in the previous section, it is necessary to convert the two-layer
soil model to an equivalent, uniform soil described by its effective resistivity (ρe). Three cases
can be identified:
•
The ground electrode size is small, relative to the depth of the upper soil layer.
In this case, most of the voltage drop will occur in the upper soil layer, and the effective
resistivity ρe will be equal to ρ1.
•
The depth of the upper soil layer is small, relative to the ground electrode size.
In this case, the resistance of the electrode will be dominated by the bottom-layer resistivity
ρ2.
•
The size of the ground electrode is comparable to that of the upper soil layer.
A top soil layer thickness in the range of 1–10 meters is comparable to the equivalent size of
the ground electrode on typical transmission line towers. For these cases the transmission line
grounding is often in a transition region, where the effective resistivity is between ρ1 and ρ2.
5-17
Characteristics of a Ground Electrode
A good (within 5%) estimate of the effective resistivity for all three cases is given by:
1+ C
ρ e = ρ1
⎧
⎪ ρ1 > ρ 2
⎪
⎪⎪
⎨
⎪ρ > ρ
2
⎪ 1
⎪
⎪⎩
ρ2r
ρ 1 dT
1+ C
r
dT
C=
C=
1
⎛ρ ⎞
1.4 + ⎜⎜ 2 ⎟⎟
⎝ ρ1 ⎠
0.8
⎛ρ ⎞
1.4 + ⎜⎜ 2 ⎟⎟
⎝ ρ1 ⎠
0.8
1
⎛ρ r ⎞
⎟⎟
+ ⎜⎜ 2
⎝ ρ 1 dT ⎠
0.5
Equation 5-22
Effective Resistivity for a Plate Electrode in Two-Layer Soil
Where:
ρe
is the effective resistivity of the soil
ρ1
is the resistivity of the upper soil layer (Ωm)
ρ2
is the resistivity of the lower soil layer (Ωm)
dT
is the depth of the upper soil layer (m)
r
is the equivalent radius of the ground electrode (m)
This can be estimated from the size of the transmission tower foundations by
r = L/√π with L equal to the side leg spacing of the mast.
The effective resistivity (ρe) can be substituted for the ground resistivity in calculations of
geometric resistance using Equations 5-11 through Equation 5-21.
5.2.5 Calculation of Resistance of Multiple Electrode Systems
Most of the equations presented in the preceding sections are valid for single electrodes in earth.
Practical transmission line electrodes usually require that one or more of the electrode
configurations be combined to obtain a suitably low footing resistance. In such cases, it is not
sufficient to calculate the resistance of each element in isolation because there is conductive
coupling between nearby conductive objects in the ground. Conductive coupling occurs when a
nearby object—such as a parallel ground rod, another footing, a nearby fence, a pipeline, or a
5-18
Characteristics of a Ground Electrode
buried object—rises in potential because of the current flowing in the ground. Therefore, these
mutual resistance effects must be included when evaluating grounding electrodes. In such cases,
it is recommended to rely on dedicated computer software such as applet GG-9, which is
included with this report, to calculate the electrode resistance.
5.2.6 Choosing an Equation to Calculate the Ground Electrode Resistance
One of the frustrating aspects of ground electrode resistance calculations is that several different
equations can be used to calculate the resistance of a ground electrode and each equation results
in a slightly different answer. Therefore, a question arises about which equation is the most
appropriate to use when designing a ground electrode. In this section, the equations presented are
compared to show that they are in effect equivalent and that the differences in the results fall
within the accuracy limits imposed by not fully knowing the soil structure and resistivity.
The comparison focuses on comparing the geometric resistance with the analytical equations for
the following electrode types, all of which are ellipsoids of revolution:
•
Rod electrode
•
Hemisphere
•
Round plate electrode
5.2.6.1 Single-Rod Electrode
To facilitate comparison, all analytical expressions describing the resistance of a rod are
rearranged to the following common form:
R=
ρ ⎡
⎛ L ⎞⎤
K rod + ln⎜ ⎟⎥
⎢
2π L ⎣
⎝ a ⎠⎦
Equation 5-23
Where:
ρ
is the resistivity of the soil
L
is the length of the rod
Krod
is a constant based on the assumptions made
ln
is the natural logarithm (to base e)
a
is the radius
5-19
Characteristics of a Ground Electrode
The analytical expressions that describe the resistance of a rod presented in this report are
summarized in Table 5-4. It shows that the Krod factor can vary between 0 and 1. For practical rod
lengths, the value of ln(L/a) of Equation 5-23 will be approximately 6, leading to a ±9% variance
in the calculated electrode resistances based on the different assumptions about the currents and
fields around the vertical rod.
Table 5-4
Equations Describing the Resistance of a Rod Electrode with Length L and Radius a
Name
Reference
Common Form
Chisholm from Oettle [31]
Equation 5-13
R=
ρe ⎡
⎛ L ⎞⎤
0.63 + ln⎜ ⎟⎥
⎢
2π L ⎣
⎝ a ⎠⎦
Sunde, Dwight [21, 19]
Table 5-3
R=
ρe ⎡
⎛ L ⎞⎤
0.38 + ln⎜ ⎟⎥
2π L ⎢⎣
⎝ a ⎠⎦
Rudenberg, Sunde [20, 21]
Table 5-3
R=
ρe ⎡
⎛ L ⎞⎤
0.69 + ln⎜ ⎟⎥
⎢
2π L ⎣
⎝ a ⎠⎦
Liew and Darveniza [29]
(see note)
Table 5-3
R=
ρe ⎡
⎛ L ⎞⎤
0.003 + ln⎜ ⎟⎥
⎢
2π L ⎣
⎝ a ⎠⎦
Chisholm and Janischewskyj
[30]
Table 5-3
R=
ρe ⎡
⎛ L ⎞⎤
1 + ln⎜ ⎟⎥
⎢
2π L ⎣
⎝ a ⎠⎦
Note: Calculated with a rod length of 9.8 ft (3 m) and a radius of 0.39 in. (0.01 m).
5.2.6.2 Hemispheric Electrode:
The equations describing the resistance of a hemispheric electrode with radius a are given in
Table 5-5. The table shows that the three equations agree closely for this electrode type.
Table 5-5
Equations Describing the Resistance of a Hemispheric Electrode with Radius a
Name
Reference
Common Form
Chisholm from Oettle [31]
Equation 5-14
R=
Theoretical derivation
Equation 5-6
R=
Sunde [21]
Equation 5-9
ρe
2π a
ρe
2πa
ρ
R = e (see note)
2πa
Note: Equation 5-9 is singular for the hemispheric case, but it approaches the equation given as “a”
approaches “L”.
5-20
Characteristics of a Ground Electrode
5.2.6.3 Round Plate Electrode
The equations describing the resistance of a round plate electrode with radius d and zero burial
depth are presented in Table 5-6. The table shows that the first two equations agree closely for
this electrode type.
Table 5-6
Equations Describing the Resistance of a Round Plate Electrode with Radius d
Name
Reference
Common Form
Chisholm from Oettle [31]
Equation 5-15
R=
Tagg [6]
Equation 5-8
R=
Dwight [19]
Table 5-1
R=
0.226 ⋅ ρ e
d
ρe
4d
ρe
4d
(see note)
Note: Obtained by the multiplying the Dwight resistance for a plate buried at infinite depth, (homogeneous
soil in all directions), by two to obtain the resistance of the half space.
5.2.6.4 An Ellipsoid of Revolution Electrode
A quantitative comparison of equations has been done based on the calculated resistance of
spheroid electrodes. The length of the electrode was fixed at 9.8 ft (3 m) and diameter ranged
from 0.39 in–328.1 ft (0.001–100 m). The calculated resistances are presented in Figure 5-7.
Equation numbers are shown in square brackets in the figure.
5-21
Characteristics of a Ground Electrode
Figure 5-7
Comparison of Equation 5-11 with Analytical Expressions for Rod, Hemisphere, and Plate
Electrodes
In Figure 5-8, the resistance is compared relative to that given by Equation 5-9, which is the
Sunde equation for an ellipsoid of revolution [21]. (Equation numbers are shown in brackets in
the figure.) Figure 5-8 shows that the simple expression for the geometric resistance (Equation 511) remains within a ±5% deviation from the considerably more involved expression of Sunde
(Equation 5-9) over an extremely wide range of electrode shapes [21]. This means that resistance
for electrodes of any intermediate shapes (thick buried discs, fat cylinders, combinations of
vertical rods, and surface grids) can be estimated with similar accuracy using the simple
expression. Also, these expressions are easily inverted to obtain the required electrode size for a
given electrode shape and target resistance value.
5-22
Characteristics of a Ground Electrode
Figure 5-8
Ratio of Expressions for Geometric Resistance to Equation 5-9
5.2.6.5 Summary
The results presented in this section show that the results obtained from the different equations
agree quite well over a wide range of electrode shapes. The reported differences in results of up
to 10% should be considered against the background of the uncertainties in the information that
is available about the soil resistivity, structure, and seasonal variations. These uncertainties will
result in much larger variations of the resistance of the electrode.
Although the analytical equations cover a wide range of situations, they do not provide
particularly accurate estimates for simple cases in which vertical and horizontal electrodes are
combined. Furthermore, it can be difficult to invert the analytical expressions for the cases in
which it is necessary to estimate the electrode size when a target resistance value must be
reached. As shown in this section, the geometric and contact resistance approach overcomes
these difficulties without a marked loss of accuracy. Applet GG-10 provides an easy-to-use
implementation for the calculation of electrode size in two-layer soil, based on the latter
approach.
5-23
Characteristics of a Ground Electrode
5.2.7 Numerical Methods for Calculating Ground Electrode Resistance
Analytical equations such as those presented in the previous sections do not cover all possible
electrode shapes and combinations. To derive equations for these exceptions, which are typically
complex and meshed earth electrodes, is difficult because the mathematical relations become
complicated. In such cases, the use of numerical methods such as those implemented in applet
GG-9 is required. Using a sophisticated three-point moment method, the applet calculates the
ground resistance of electrodes of any shape in a two-layer soil.
5.3
Surface Potential Gradients
Under fault conditions, some fraction of the stored electrical energy of the power system appears
as temporary power-frequency voltages and currents in transmission tower grounding systems.
The voltage to which the grounding system rises—that is, the ground potential rise (GPR)—
depends on the supply voltage of the line, the equivalent network impedance, and the impedance
of the total grounding system (that is, all parallel towers if an overhead ground wire is present).
The resulting surface potential gradients around transmission line structures are evaluated in
terms of step and touch potentials.
Step potential is defined as the potential difference between two points on the earth’s surface,
which are spaced some distance apart, to represent a person or animal standing near the structure.
For a person’s outstretched feet, a separation distance of 3.3 ft (1 m) is assumed. It is also
assumed that the person is not in contact with any other electrical path.
Touch potential is defined as the potential difference between a person’s outstretched hand,
which is touching an earthed structure, and the person’s foot. A person’s maximum reach is
assumed to be 3.3 ft (1 m). The touch potential can be equal to the full GPR if the object is
grounded at a point remote from the place where the person is in contact with it.
Step and touch potentials and the design limits are determined from applicable regulations and
company policy. Section 5.3.2, Step and Touch Potential Around Transmission Line Towers,
describes the underlying principles for determining the safe body current withstand levels. It is
generally easier to obtain a safe design in terms of step potential than of touch potential, for
several reasons:
•
There is higher body path impedance for the case of evaluating step potentials. The two feet
appear in series rather than in parallel.
•
There is a much lower fraction of heart current (4%) for leg-to-leg electrocution compared
with arm-to-legs contact (IEC TS 60479-1, Effects of current on human beings and livestock
– Part 1: General aspects, Fourth edition, 2005-07) [50].
•
The high resistivity of many common surface layers, including grass, asphalt, and gravel
provides an additional resistance that limits body current.
5-24
Characteristics of a Ground Electrode
Step and touch potentials around transmission line structures are typically considered only in
special cases for the following reasons:
•
Fault currents along the lines are lower than those in substations.
•
An interconnected system of many grounded towers shares the current.
•
Sensitive protection and high-speed switching out of the line when a fault occurs limit the
exposure to high step and touch potentials
•
The probability of exposure is low.
In some situations, it is necessary to provide gradient control rings to reduce step and touch
potentials. This section provides an overview of the surface potential profiles around towers and
describes common gradient control measures. It does not provide guidance on the cases in which
such mitigation measures are required; the requirements are typically covered adequately by the
applicable standards and company directives.
5.3.1 Calculation of Potential Gradients Around Grounding Electrodes
5.3.1.1 Theoretical Background
The surface potential around a hemispheric electrode when a current, IE, is injected into the soil
is given by Equation 5-7 illustrated in Figure 5-9.
The ground potential rise of the ground electrode, VE, is given by Equation 5-24:
VE = I E × RE
Equation 5-24
Where:
IE
is the current discharged into the ground
RE
is the resistance of the ground electrode
5-25
Characteristics of a Ground Electrode
Figure 5-9
The Potential Profile of a Hemispherical Electrode in Uniform Soil, Showing the
Parameters for Calculating the Step and Touch Potentials in Uniform Soil
From Equations 5-6 and 5-7, the fall of potential (Vx) at a distance x from the electrode can be
divided by the electrode potential (VE), to obtain a normalized potential Vx* profile, as shown in
Equation 5-25:
ρI E
V
Vx* = x = 2πx
VE ρI E
2πa
Vx* =
a
x
Equation 5-25
The shape of the potential profile for hemisphere electrodes gives a benchmark for comparing
profiles of other electrode shapes. Ring or mesh electrodes have potential profiles that fall off
less rapidly than a/x, and vertical driven rods have a steeper fall-off in surface potential.
5-26
Characteristics of a Ground Electrode
The touch potential (VT) for this electrode is the difference in potential between a point at the
edge of the electrode (that is, x=a) and a point on the earth’s surface at a radial distance x=a+∆x,
as shown in Equation 5-26:
VT +
1 ⎞
ρI E ⎛ 1
⎜ −
⎟
2π ⎝ a a + ∆x ⎠
Equation 5-26
The step potential (VS) is calculated in a similar fashion as the potential difference between two
points on the earth’s surface located at a distance x and at a radial distance x + ∆x, where x >a:
VS +
1 ⎞
ρI E ⎛ 1
⎜ −
⎟
2π ⎝ x x + ∆x ⎠
Equation 5-27
IEEE Standard 80 [33] recommends using ∆x = 3.3 ft (1 m) for both step and touch potential.
This represents a hand-to-hand reach of 6.6 ft (2 m) [33].
5.3.1.2 Numerical Methods to Evaluate the Surface Potential Gradients
The calculation of surface potential gradients around grounding electrodes is not easy, and it is
advisable to use dedicated computer programs for this purpose. A rule of thumb is based on a
hemispheric electrode. The assumption is that the potential profile falls away as 1/distance.
However, this approximation can result in poor estimates near the structure, especially if the
electrode is a driven rod that has a faster decay with less transferred potential or a set of two or
more electrodes separated by a few meters. The accuracy of this rule of thumb is also poor in the
case of two-layer soil (see Section 5.3.2, Step and Touch Potential Around Transmission Line
Towers).
A computer program for this purpose, applet GG-9, is provided with this report. Applet GG-9
takes advantage of adaptation of moment methods for calculating the capacitance of arbitrary
sets of objects in free space or under power lines. There is a dual relationship between
capacitance and resistance that is exploited by doing the calculation in free space, inverting and
dividing the answer by two to get the resistance in a half-space of uniform soil. In “Grounding
Resistance of Buried Electrodes in Multi-Layer Earth Predicted by Simple Voltage
Measurements Along Earth Surface—A Theoretical Discussion,” Chow provides extensions of
this simplified method to multilayer soil [17].
5-27
Characteristics of a Ground Electrode
Applet GG-9 can be used as a tutorial to visualize the potential gradients on the surface of the
earth for transmission line grounding electrodes. Ring and rod electrodes can be placed in
arbitrary locations and orientations, and a sophisticated segmentation method will calculate the
self and mutual resistances. Plots of surface potentials can be viewed as an output. Concrete
footings should conservatively be treated as large cylinders with this applet because the voltage
drop from metal to concrete should be much lower than the voltage drop from concrete to soil.
5.3.2 Step and Touch Potential Around Transmission Line Towers
5.3.2.1 Basic Principles
Figure 5-10 shows the situation around a typical transmission line tower without (on the left) and
with (on the right) potential grading measures.
Figure 5-10
Surface Potential Distribution for Rod and Mesh Electrodes
In Figure 5-10, the ground electrode conducts current to the ground, resulting in a ground
potential rise (VT) and a surface potential distribution around the pole. People in the vicinity of
the tower at this time can be exposed to the following voltages:
•
Person A is subject to a step potential (VS) that is given by the difference in potential between
the person’s two feet.
5-28
Characteristics of a Ground Electrode
•
Persons B and C are exposed to a touch potential (VT), which is the difference between the
ground potential rise of the tower and the voltage on the surface of the ground where the
person is standing. Since the person is touching the energized pole, the full touch potential
appears from hand to feet.
•
Persons D and E, standing some distance away from the pole, can also be exposed to a touch
potential if they touch any conductive object that is in contact with the grounding system of
the line or with a remotely grounded point. This is the so-called “transferred potential”
condition. The transferred touch potential increases as the person moves away from the pole.
With respect to the potential distribution around the pole shown in Figure 5-10, the following
generalizations can be made:
•
The value of potential rise (VE) is the product of the electrode resistance and the portion of
the fault current shunted by the local ground electrode. The configuration of the electrode
establishes how the potential rise is distributed along the earth surface. It also influences the
electrode resistance, as described by the geometric resistance and effective resistivity in
Section 5.2.3, The Geometric and Contact Resistance Approach. Adequate design must
therefore consider both resistance and configuration in an iterative process.
•
The rod electrode (left side of Figure 5-10) might have a low resistance, but it also has the
steepest (most unfavorable) potential distribution. The meshed electrode (right) has a much
flatter earth potential profile.
•
The touch potential for person B, near the rod electrode, is considerably larger than that for
person C, near the meshed electrode. This means that step potentials for person A are higher
near the edge of the meshed electrode but not as high as the step potential at an equal
distance away from the rod.
•
Meshed electrode systems cover large areas, giving a lower resistance, but it is not practical
to bury them deeply, so they are more susceptible to changes in soil moisture content.
Improved stability of resistance can be achieved by including several long, vertical rods in
the mesh.
•
Within the mesh, an area of approximate equipotential exists that limits the touch potential
close to the tower because practical meshes will extend several meters beyond any metal
structure as well as the 3.3-ft (1-m) reach limit of a person.
5.3.2.2 Evaluation of Step and Touch Potentials
The design of grounding systems with regard to human safety focuses on the ac safety criteria.
This section briefly introduces the topic. For more information, refer to IEEE Standard 80,
IEC 60479, and EPRI report EL-2699 [33, 50, 1].
5-29
Characteristics of a Ground Electrode
Starting in the 1950s, Dalziel and his co-workers carried out a wide range of tests on animals and
humans to establish a quantitative model of the relationship between electrocution current and
duration of application [51]. They determined that the risk of ventricular fibrillation, a serious
disorder of the heart’s electrical activity, varied with a square root of time-dependence (see
Figure 5-11).
Biegelmeier extended the range of knowledge about the body impedance variation as a function
of voltage, including self-experimentation with hand-to-hand electrical contacts between heart
beats using commercial ground-fault interruption devices for protection [52]. As shown in Figure
5-11, his findings are in general agreement with Dalziel, but he found both a lower threshold of
50 mA, below which fibrillation was unlikely for any duration, and an upper threshold of 500
mA, which posed some risk of fibrillation for any duration if applied during a vulnerable interval
just after each heartbeat.
Figure 5-11
Standard Values for AC Ventricular Fibrillation Current
These body current limits are translated into a touch or step potential limit by making some
assumption about the body impedance. In IEEE Standard 80 [33], a body impedance of 1000 Ω
at 60 Hz is used along with models of under-foot resistance; the IEC published a set of curves to
determine body impedance for a range of conditions [50]. A wide range of bioelectric impedance
measurements show that the IEEE assumption for body impedance is reasonable for a wide
frequency range (that is, up to 50 kHz) and that it is relatively constant for a wide range of body
shapes, including children and the elderly.
5-30
Characteristics of a Ground Electrode
5.3.2.3 Mitigation of Step and Touch Potentials
The most important safety barrier in the safety precedence sequence is to limit the energy by
using fast-acting protection to identify and switch out faults. In addition, the choice of ground
electrode size and shape can also be used to reduce the energy level to which people might be
exposed. With high-speed fault identification and breaker operations, electrical utilities are
generally able to limit exposure durations on transmission lines to less than 100 ms. Figure 5-11
shows the current needed to cause ventricular fibrillation is 400–500 mA with both the Dalziel
and the Biegelmeier approach [33, 50].
Overhead ground wires can be connected electrically to the grounding system of all the
individual towers by using connections with suitable current ratings. When this is done, a low
fault impedance is obtained by the parallel connection of the towers and their grounding
electrodes, resulting in a faster fault identification, better management of fault currents, and a
lower of ground potential rise of the faulted tower. However, the entire line acts as one unit, and
although the overall potential rise is much lower, it appears at a larger number of locations.
If the overhead ground wire is deliberately insulated (for example, to limit induced currents or to
reduce electromagnetic coupling to AM radio sources), each tower must be engineered to
dissipate the local fault current into the local ground electrode because the ground potential rise
during a fault might not be high enough to cause a flashover on the ground wire insulator.
Step and touch potentials can also be mitigated by using a combination of vertical driven rods,
radial crowfoot electrodes, and rings to grade the fall of potential around the tower base. Larger
electrodes have lower levels of local potential rise. Flat electrodes limit gradients and touch
potentials within their perimeter to safe levels even if they have high potential rise. For towers
situated in areas of high public exposure, such as parking lots, the use of ring electrodes is
preferred because they grade the electric field near towers at the same time that they improve
reliability.
5.4 The Behavior of Grounding Electrodes When Discharging Lightning
Current
One of the primary functions of transmission line grounding electrodes is to discharge lightning
current. To explain this function, it is necessary to briefly describe the lightning flashover
mechanism. Conceptually, it can be explained using Figure 5-12.
5-31
Characteristics of a Ground Electrode
2000 kV
Figure 5-12
A Lightning Strike to a Transmission Line
In Figure 5-12, a 50-kA lightning flash terminates at a transmission tower with a 40-Ω footing
resistance. The potential rise of the tower can be calculated as 50 kA x 40 Ω = 2000 kV, which is
also the voltage that appears on the cross-arm end of the insulator. The difference in potential
between the cross-arm and the phase conductor (that is, 2000 kV) appears across the insulators.
This can flash over an insulator length of nearly 13 ft (4 m). The voltage across the insulators
(Vins) is directly proportional to the grounding resistance (Rg) and the lightning discharge current
(I), as shown by Equation 5-28.
Vins ∝ Rg ⋅ I
Equation 5-28
From Equation 5-28, it follows that reducing the footing resistance will result in a reduction of
the insulator voltage. This means that the lower the footing resistance is, the higher the stroke
current that is required to flash the insulator.
5-32
Characteristics of a Ground Electrode
This is an oversimplification of the back-flashover process. Aspects such as the presence of
overhead ground wires and ionization of the soil are important contributors to lowering the
voltage across the insulator. However, the basic principle remains the same: a lower tower
footing resistance leads to a lower back-flashover rate. This can be illustrated by using a
simplified algorithm to calculate the back-flashover rate of single-circuit 69-kV, 138-kV, and
345-kV transmission lines. The calculated flashover rates as a function of the footing resistance
are presented in Figure 5-13.
Figure 5-13
Lightning Flashover Rate of Single-Circuit Lines Versus Footing Resistance
Figure 5-13 shows that the relationship between the back-flashover rate and the footing
resistance is almost linear, which indicates the importance of a good tower footing to obtain a
good lightning performance. The scope of this section is to provide an overview of the important
parameters that must be considered when designing or improving grounding electrodes. It is not
the intent to provide exhaustive treatment of the lightning performance of transmission lines. The
EPRI reports Handbook for Improving Overhead Transmission Line Lightning Performance
(1002019) and Transmission Line Reference Book 345 kV and Above—Second Edition, Revised
(EL-2500) specifically cover that subject [4, 35].
5-33
Characteristics of a Ground Electrode
When considering the behavior of grounding electrodes during lightning discharges, several
aspects play a role in determining the magnitude and shape of the transient voltage that appear at
the tower base, including the following:
•
Surge impedance of buried wires (see Section 5.4.1.1)
•
Surge impedance of the ground plane (see Section 5.4.1.2)
•
Soil ionization (see Section 5.4.2)
These effects are generally not considered in simplified lightning performance calculations such
as the one described in this section, but they could have important implications in critical
situations such as poor grounding conditions. For critical situations, computer programs such as
the EPRI TFlash software (TFlash 5.0, 12/2007, 1013739) can take these effects into account.
5.4.1 The Surge Impedance of a Ground Electrode System
For surge impedance of the ground electrode system, two aspects must be considered. One is the
surge impedance of the buried ground electrode conductors, and the other is the surge impedance
of the ground plane. The surge impedance of the buried ground conductors describes the initial
response of the ground electrode. The surge impedance of the ground plane describes the initial
response from the base of the tower.
5.4.1.1 Surge Impedance of the Buried Ground Wires
The surge impedance of buried horizontal conductors was investigated in the 1920s by a series of
field tests using a portable 1000-kV impulse generator and a cold-cathode oscillograph, as
Bewley described in Traveling Waves on Transmission Systems, Second Edition [36]. The
counterpoise under test was a buried 925-ft (281.9-m) steel wire. In this important study, if was
found that the effective impedance of a buried horizontal wire (or counterpoise) was not
constant; instead, it varied over time. An example of this behavior is shown in Figure 5-14 [37].
The experimental findings could be explained by considering surge propagation along the buried
conductor. It was found that the transient impedance of the counterpoise was the combination of
the surge impedance of the buried wire (ZC) and a leakage resistance (RC).
5-34
Characteristics of a Ground Electrode
Figure 5-14
Example of the Time Variation of the Surge Impedance, the Leakage Resistance, and the
Resultant Effective Impedance of a Buried Counterpoise
Some conclusions from this experimental study are the following [36]:
•
The effective impedance is initially equal to the surge impedance (ZC) of the buried wire and
it reduces in 1–10 µs, depending on the counterpoise length, to a level that corresponds to the
leakage resistance (RC).
•
The time of transition from the initial surge impedance to the final leakage resistance is
accomplished in approximately three round-trip travel times along the counterpoise.
•
Multivelocity current waves exist on a counterpoise, but the only one of importance is very
slow, traveling at approximately 30% of the velocity of light.
•
The surge impedance (ZC) of the counterpoise rose abruptly in less than 1µs to approximately
200 Ω and increased at a slow rate thereafter (see Figure 5-14).
•
The leakage resistance (RC) is initially a very high value, but it decreases as the reflection of
the traveling waves builds up the voltage along the conductor. Its final value is equal to the
low-frequency resistance; it can be calculated from the equations in Tables 5-1 and 5-2.
5-35
Characteristics of a Ground Electrode
Bewley suggested that the time-varying behavior of counterpoise electrodes could be represented
by the simple equivalent circuit presented in Figure 5-15 [36]. In this figure, the symbols
represent the following:
•
RC represents the counterpoise leakage resistance.
•
Rs is a resistor that is selected so that the high-frequency impedance of the circuit corresponds
to the surge impedance of the counterpoise (ZC).
•
l is the length of the counterpoise.
•
LC is the inductor, which is responsible for the transition from the surge impedance to the
low-frequency impedance; its value is dependent on the length (l) of the counterpoise.
Figure 5-15
Bewley Equivalent Circuit of a Counterpoise
Based on the field measurements, it was concluded that counterpoises of more than 200–300 ft
(60–90 m) in length were not justifiable. Several short counterpoises were shown to be more
effective in reducing the tower voltage because the parallel connection of electrodes is an
efficient way to reduce the ground electrode surge impedance.
Bewley further observed that the transient counterpoise capacitance was on the order of
-11
8x10 farads per meter [36]. For a 164-ft (50-m) counterpoise with soil conditions such that the
total leakage resistance is 20 Ω, which corresponds to a leakage resistance per meter of 1 kΩ, the
resistance–capacitance (R–C) time constant is 8x10-11 x 1x103 = 8x10-8 s or 0.08 µs. This
extremely small time constant indicates that resistance effects quickly cover up the capacitance
effects during counterpoise current propagation. A general measure of this is the relaxation time
(τE) of the soil, which is given by Equation 5-29.
τ = εoεr ρ
Equation 5-29
Relaxation Time of Soil
5-36
Characteristics of a Ground Electrode
Where:
τE
is the soil relaxation time (s)
εr
is the relative earth permittivity (dielectric constant)
εo
is the permittivity of free space, 8.854x10-12 farads per meter
ρ
is the soil resistivity (Ωm)
A typical relative earth permittivity of 10 and a resistivity of 300 Ωm yield a relaxation time of
0.024 µs. Therefore, resistance quickly dominates as a current wave propagates along the
counterpoise. An additional complicating factor is soil ionization that leads to an additional
decay in the electrode resistance when high currents are discharged into the soil. The nature and
extent of this decay is an important aspect of ongoing research into the response of counterpoise
electrodes when conducting lightning current. Soil ionization is further decribed in Section 5.4.2,
Soil Ionization Effects at High-Voltage Gradients.
The surge impedance of relatively concentrated electrodes (that is, lengths shorter than 16.4–
32.8 ft (5–10 m) can typically be neglected. For example, using a 2-µs equivalent front time for
the lightning current, a 9.8-ft (3-m) ground rod presents a series impedance of
3 µH/2 µs = 1.5 Ω. This impedance adds to the resistance of the electrode itself, which is
typically much bigger—on the order of 10 Ω or higher.
5.4.1.2 Surge Impedance of the Ground Plane
Chisholm and Janischewskyj noted in studies of surge response and reported in “Lightning Surge
Response of Grounding Electrodes” that the initial reflection coefficient defined between the
impedance of the tower (Zt) and the impedance of the ground (Zg) was approximately 0.6, even
for a test geometry using a conical antenna in a closed metal cage designed to result in a
reflection coefficient of 1.0 [30]. This imperfect reflection was observed during the high-current
impulse tests performed for the EPRI report High Current Impulse Testing of Full-Scale
Grounding Electrodes (1006866) [38]. The results of the tests are presented in Section 5.4.2, Soil
Ionization Effects at High-Voltage Gradients. For all levels of current, the initial transient
impedance of the electrode at less than 2 µS was found to be on the order of 50–60 Ω.
The imperfect reflection was also observed during measurements of upward lightning from tall
towers whenever there is sufficient rate of current rise to excite a reflection, as Bermudez
described in “Lightning currents and electromagnetic fields associated with return strokes to
elevated strike objects” [39]. The Bermudez study is particularly illustrative, based on the
analysis that was performed. The measurements showing the effects of this imperfect reflection
are presented in Figure 5-16, which shows three pairs of current waveforms taken at the top and
bottom of an instrumented tower in Germany.
5-37
Characteristics of a Ground Electrode
Based on a conventional quasi-static analysis, it is expected that the initial current waves in
Figure 5-16 (that is, [a] 10 kA, [b] 10 kA, and [c] 6 kA) will double after reflecting back from
the ground plane. Experimentally, however, it was found that reflections were only
approximately 40% of the initial step.
Bermudez used advanced fast Fourier transformation processing to obtain the tower-to-base
reflection coefficient ρg(ω) as a function of frequency, as is presented in Figure 5-17 [39]. It
shows that the reflection coefficient at low frequency is unity, which is in agreement with quasistatic analysis using the method of images. At greater than 30 kHz, however, the reflection
coefficient is approximately 0.8, and it falls to approximately 0.7 at 800 kHz. This finding is
qualitatively in agreement with the minimum reflection coefficient of 0.62 for hemisphere
electrodes.
Figure 5-16
Experimentally Measured Currents on Peissenberg Tower at the Top and Bottom
of the Tower
Source: J. L. Bermudez Arboleda
5-38
Characteristics of a Ground Electrode
Figure 5-17
Tower-to-Base Reflection Coefficient ρg(ω) as a Function of Frequency for
Three Experimental Records in Figure 5-16
Source: J. L. Bermudez Arboleda
The effective impedance of ground was approximately 60 Ω at the base of the tower, decreasing
to 30 Ω when the electromagnetic wave had traveled sideways by one tower height and
eventually reaching the low impedance of the closed geometry. This behavior can be explained
by considering the time that is needed to charge the capacitance of a thin disc with radius a on
the surface of the earth. This capacitance (Cself), can be calculated from the low-frequency
resistance (R), of the electrode. This is possible because the calculations of both resistance and
capacitance are based on the same assumptions and equations, with the only difference being the
substitution of permittivity for resistivity. For an object of surface area A, the capacitance can be
approximated with Equation 5-30 [3].
Cself = ε oCF 4πA
CF =
4πg
⎛ 4πe 3 g 2 ⎞
⎟
4πA ln⎜⎜
⎟
⎝ 3A ⎠
Equation 5-30
5-39
Characteristics of a Ground Electrode
Where:
is the surface area of the object (in m2)
A
g = rx2 + ry2 + rz2
is the geometric radius of the object (in m)
CF
is a shape factor, usually near unity
εo
is the permittivity of free space, 8.854x10-12 farads per meter
The time required to charge this capacitance (Cself) is given by the travel time (te) required to
reach the maximum extent of the electrode at the speed of light. The surge impedance of this
object is given by Z= te /Cself.
For a thin circular disc of radius a, the two-sided surface area is A=2πa2, the travel time is t=a/c
and the geometric radius is g = 2a 2 . This gives a transient impedance of Z=47 Ω for a disc of
any radius. For the case of a hemisphere, and again counting the top of this object in the surface
area calculation, the surface area is A=3πa2, the travel time is t=a/c and the geometric radius is
g = 3a 2 . This gives a transient impedance of Z=35 Ω for any hemisphere radius. This presents
a reflection coefficient to a 150-Ω tower of -0.62 for voltage and +0.62 for current, which agrees
closely with the observed behavior.
Chisholm and Janischewskyj suggested from their results that the apparent impedance of the
ground plane as a function of time can be described by the following [30]:
Z=
h
60h
, t > tt =
ct
c
Equation 5-31
Where:
h
is the height of the tower (in m)
c
is the velocity of light, 3 x 108 m/s
t
is time
tt
is the surge travel time of the tower
Baba and Rakov performed a numerical analysis that confirms Equation 5-31, with its initial
relatively high 60-Ω impedance that decreases with time, as they described in “On the
Interpretation of Ground Reflections Observed in Small-Scale Experiments Simulating Lightning
Strikes to Towers” [40]. In their interpretation, however, the imperfect reflection should rather be
viewed as an engineering approximation to account for the neglected attenuation of upward
propagating waves on a conical tower. This means that the tower, rather than the ground plane,
5-40
Characteristics of a Ground Electrode
should be considered as the element with a variable surge impedance. However, in both cases,
the resulting level of the reflected wave at the tower top is the same.
It is possible to approximate the initial surge response of a perfectly grounded tower as an
inductance that is a function of tower height. The value of this inductance can be calculated from
the average value for the footing impedance. The average impedance (Zaverage) is obtained by
integrating Equation 5-31 with respect to time from t= tt to the equivalent front time, tf, of the
lightning surge, as follows:
Zaverage =
[
]
60tt ln(t f ) − ln(tt )
(t − t )
f
t
Equation 5-32
The equivalent footing inductance is then given by Equation 5-33, which is valid for the normal
case, in which the front time tf is much greater than the tower travel time tt, which is calculated by
height (h) divided by the velocity of light (c).
Laverage = Z average ⋅ t f = 60
⎛t ⎞
⎛t ⎞
ln⎜⎜ f ⎟⎟ ≈ 60tt ln⎜⎜ f ⎟⎟
t f − tt ⎝ tt ⎠
⎝ tt ⎠
tt t f
Equation 5-33
A typical 98.4-ft (30-m) tower and an equivalent front time of 2 µs correspond with a Zaverage of
9.5 Ω, which can be modeled as an additional series 19 µH inductance in the Bewley equivalent
circuit, as shown in Figure 5-18. Longer front times give higher values of average inductance,
but the voltage rise from the footing inductance (V=LI/tf) at the crest current (I) is actually lower.
The effect of the ground surge response can be calculated with applet GG-5.
5.4.2 Soil Ionization Effects at High-Voltage Gradients
Under lightning surge conditions and some ac fault conditions, the high current density in the
soil increases the electric field strength up to values that cause electrical discharges in small air
pockets in the soil. This can happen repeatedly, usually without changing the characteristics of
the soil. Sometimes fulgurites are created if the current is high enough to fuse the sand grains
together. The plasma of the discharges has a lower resistance than that of the surrounding soil, so
there is an apparent decrease in the ground resistivity in the areas where the ionization occurs.
Since ionization occurs mainly near the electrode where the current density is highest, it
increases the effective size of the electrode, thereby resulting in a significant reduction in the
electrode resistance and lower insulator voltages, reducing the risk for a back-flashover.
5-41
Characteristics of a Ground Electrode
Figure 5-18
Modified Bewley Equivalent Circuit of a Counterpoise (Figure 5-15) with the Addition of an
Inductor to Represent the Surge Impedance of the Ground Plane
Electrical breakdown occurs in the soil at an average surface ionization gradient of
approximately 300–400 kV/m. In some soil types, the ionization gradient can reach as high as
1000 kV/m [32]. The threshold level and intensity of the ionization are especially high when the
soil is dry or when it has a high resistivity. Depending on the electrode configuration, ionization
can take place under impulse currents as low as 1 kA.
Surface arcing can occur when the electric stress along the interface of air and wet soil exceeds
the 50–100 kV/m flashover strength. The ionization process takes place along several discrete
paths, leading radially away from the struck electrode.
As a product of soil ionization, sand fulgurites are an important source of information about the
extent and power of subsurface ionization from concentrated electrodes, as described in the EPRI
report Tower Grounding and Soil Ionization Report (1001908) [41]:
•
The thickness of the fulgurites, typically approximately 1 in. (2.54 cm) diameter, indicates
roughly how thick the lightning channel is, which in turn makes it possible to determine the
plasma characteristics, channel surge impedance, and other properties.
•
The extent of the fulgurites provides information on how close critical infrastructure (such as
pipelines or buried cables) can be routed near transmission line structures in sandy soil.
•
Because the fulgurites form by melting sand, it shows that the temperature of the plasma
channels in the soil is much greater than 3000°F (1600°C), which is high enough to melt
metals on contact.
The soil ionization around typical grounding electrodes approaches a hemispheric shape for very
high levels of current. The maximum extent of this hemispheric zone of ionization rarely exceeds
10 m for typical lightning surge currents of up to 200 kA. This means that the ionization will
5-42
Characteristics of a Ground Electrode
usually occur in the top layer of the soil. In terms of the electrode resistance, it can be concluded
that ionization will reduce the contact resistance term without modifying the geometric resistance
of the electrode. The effect of soil ionization is more pronounced on small, concentrated
electrodes, and it can be negligible for large four-footing foundations. Therefore, the nature and
the extent of this reduction in electrode resistance are important research topics to better
understand the lightning response of small grounding electrodes [38, 41].
Figure 5-19
Resistance of a 48-Ω Driven Rod for Various Impulse Currents for 2.5/15 µs Impulse
Current (Typical of a Subsequent Stroke)
Figure 5-19 shows results of a test series in which increasing levels of surge current are injected
into a vertical 8.9-ft (2.7-m) rod [38]. The test levels of 7–34 kA were selected to be
representative of typical installations, which have two to four ground rods at each tower to
dissipate the lightning current. The tests were performed on a rod that was driven through a 6.2-ft
(1.9-m) layer of sandy loam (435 Ωm) into a layer of clay (97 Ωm) to give a resistance without
ionization of 48 Ω. This is also the resistance measured during the 1-kA surge, which indicates
that no ionization occurred at this surge magnitude. For the surge amplitudes of 7 kA and higher,
the effect of soil ionization is clear. At 7 kA, the resistance of the rod is halved with respect to
the value without ionization.
5-43
Characteristics of a Ground Electrode
In Figure 5-19, the initial impedance of the electrode was measured to be approximately 50–
60 Ω, which corresponds to the reflection coefficient of the ground plane (see Section 5.4.1, The
Surge Impedance of a Ground Electrode System).
5.4.2.1 Liew-Darveniza Dynamic Model for Rod Electrodes
In 1974, Liew and Darveniza published a paper describing their development of theoretical
models of the dynamic response of ground rods to high currents and comparisons with field tests
[29]. Basically, they assumed each ground rod to be surrounded by a series of concentric shells,
as shown in Figure 5-20.
Figure 5-20
Liew-Darveniza Ground Rod Surrounded by Concentric Shells of Earth
Impulse current applied to the rod flows radially outward through each shell. Depending on the
initial resistance and the current density of each shell, the soil in the shell starts to ionize, and
consequently, the shell resistance drops. Assuming uniform current flow out of the rod, the
current density in each shell is easily calculated. If this current density is sufficient to create a
shell gradient greater than E0 (where E0 is the critical dielectric ionizing gradient of the soil) the
shell resistance will decay exponentially with time. When the surge current eventually decays,
the gradient across one or more of the shells will fall to less than E0, and those shells will start
deionizing, their resistances increasing exponentially with time to their original low-current
values.
As a result of ionization, the resistivity of the soil in each concentric shell changes as a function
of the current density, as is shown in Figure 5-21. Above the ionization gradient, the resistivity
5-44
Characteristics of a Ground Electrode
of the soil decreases with an increasing current density. After the peak current, when current
density falls to less than the ionization gradient, the soil resistivity recovers as the soil deionizes.
This leads to the hysteresis behavior shown in Figure 5-21. An important contribution of the
Liew-Darvienza model was that ionization and deionization were not assumed to occur
instantaneously. Rather, it was found that soil ionization had a time constant (τ1) of
approximately 2 µs, and deionization had a time constant (τ2) of approximately 10 µs [29].
Figure 5-21
Variation of the Soil Resistivity of Each Current Shell as a Function of the Current Density
Source: K. Nixon
Liew and Darveniza derived an equation for the sum of the nonionizing resistance of an infinite
number of shells surrounding a single rod and compared the result with the classical formula for
the resistance of a single rod. The result was close to the theoretical value, demonstrating that the
shell algorithm met the theoretical requirements. The resulting Liew-Darveniza equation for
low-frequency resistance of a single rod is shown in Equation 5-34 [29]. Table 5-4 in Section
5.2.6.1 compares this equation to other estimates of the resistance of a vertical rod.
R=
ρ 0 ⎛ a0 + L ⎞
⎟
ln⎜
2πL ⎜⎝ a0 ⎟⎠
Equation 5-34
Low-Frequency Resistance of Single Rod Using Shells
5-45
Characteristics of a Ground Electrode
Where:
R
is the rod low-frequency resistance (Ω)
ρ0
is the low-current soil resistivity (Ωm)
L
is the rod length (m)
a0
is the rod radius (m)
ln
is the natural logarithm (to base e)
Ionization of any shell occurs when it reaches the critical current density, as shown in
Equation 5-35:
Jc =
E0
ρ0
Equation 5-35
Critical Current Density for Ionization
Where:
JC
is the critical current density in any given shell (A/m2)
E0
is the earth critical ionizing gradient (V/m)
ρ0
is the low-current soil resistivity (Ωm)
This ionization process leads to a rapid, exponential decay in resistivity of each shell when E0 is
exceeded.
ρ s = ρ 0 exp
-t
τ1
Equation 5-36
Resistivity of Ionized Shell
Where:
ρs
is the shell resistivity during ionization (Ωm)
ρ0
is the low-current soil resistivity (Ωm)
t
is the time after start of ionization (µs)
τ1
is a soil ionization time constant (µs; assumed 2.0µs for many tests)
5-46
Characteristics of a Ground Electrode
During the later deionization process of the shells, the deionization resistivity (ρ) of any shell
increases exponentially. Liew and Darveniza suggest the following equation [29]:
⎛
- t ⎞⎛
J ⎞
ρ s = ρi + (ρ0 − ρi )⎜⎜1 − exp ⎟⎟⎜⎜1 − ⎟⎟
τ 2 ⎠⎝ J c ⎠
⎝
2
Equation 5-37
Resistivity of Shell After Deionization
Where:
ρ0
is the low-current soil resistivity (Ωm)
ρi
is the value of resistivity when J = JC on current decay (Ωm)
t
is the time measured from onset of deionization (µs)
J
is the current density (A/m )
JC
is the critical current density in any given shell (A/m )
τ2
is the deionization time constant (µs)
2
2
This ionization model can be extended to also predict the dynamic and ionization response of
multiple rod and horizontal conductor electrodes. These models are implemented in two applets:
applet GG-2 displays the dynamic resistance time and current for single and multiple rod
electrodes, and applet GG-4 displays the dynamic resistance time and current for horizontal
electrodes.
5.4.2.2 Korsuncev Dimensionless Parameter Model
Korsuncev carried out a dimensional analysis of the nonlinear behavior of grounding electrodes,
using what is known in North America as the Buckingham Pi method [42]. Dimensionless ratios
of relevant parameters are often used in complex problems to allow manipulation of the data and
to provide insight in interdependencies between parameters. Familiar dimensionless ratios used
in thermodynamics are the Reynolds and Nusselt numbers. Korsuncev recommended the
following two dimensionless parameters (Π1 and Π2) for describing the ionization of grounding
electrodes [42]:
(a )Π1 =
sR
ρ
( b )Π 2 =
ρI
E0 s 2
Equation 5-38
Dimensionless Parameters for Ground Electrode Ionization
5-47
Characteristics of a Ground Electrode
Where:
Π1 and Π2 are dimensionless parameters for describing the ionization of grounding
electrodes
s
is the characteristic distance from the center of the electrode to its outermost point
R
is the footing resistance under ionized conditions (Ω)
ρ
is the soil resistivity in the ionization zone near the electrode (Ωm)
I
is the instantaneous value of current (kA)
E0
is the critical breakdown gradient, typically 300–400 kV/m
Chisholm and Janiscewskyj consolidated the observed relationships between Π1 and Π2 for a
variety of electrode shapes, as shown in Figure 5-22 [30].
Figure 5-22
Observed Relationships Between Dimensionless Parameters for Ionized Resistance of
Grounding Electrodes from Popolanský and Korsuncev
Source: W. A. Chisholm and W. Janiscewskyj
In Figure 5-22, two separate regions of response can be identified. On the left side of
Figure 5-22, for low values of Π2, there is insufficient current to cause ionization, and the
electrode resistance is independent of current and equal to the low frequency resistance (see
Section 5.2, Low-Frequency Ground Electrode Impedance). The horizontal lines in Figure 5-22
is located at Π01, which is unique for each electrode shape. Π01 ranges from 0.159 for a
5-48
Characteristics of a Ground Electrode
hemisphere to approximately 1.26 for a 32.8-ft (10-m) long, 0.4-in. (10-mm) radius rod. It can be
calculated from the geometric resistance equation given in Section 5.2.3, The Geometric and
Contact Resistance Approach:
Π1o =
1 ⎛ 2π e s 2 ⎞
⎟
ln⎜
2π ⎜⎝ A ⎟⎠
Π1o ≈
1 ⎛ 11.8 g 2 ⎞
⎟ from Equation 5 − 11
ln⎜
2π ⎜⎝ A ⎟⎠
Equation 5-39
Dimensionless Parameter for Un-Ionized Footing Resistance
Where:
A
is the surface area of the electrode
e
is 2.71828
s
is the characteristic distance from the center of the electrode to its outermost point
g
is the geometric sum of the electrode radii in each direction from the center,
given by
a x2 + a y2 + a z2
The second region of response is on the right side of Figure 5-22. For high values of Π2, the
current injected into the electrode is high enough to result in ionization. In the main area of
interest, the relationship between Π2 and Π2 is given by Equation 5-40.
Π1 = 0.263 ⋅ Π −20.308
Equation 5-40
Dimensionless Parameter for Footing Resistance During Ionization
A step-by-step procedure using the Korsuncev relations to calculate the dynamic resistance at
high currents is the following [42]. (A software implementation of this algorithm is provided in
applet GG-2.)
1. Calculate Π2 for the required I using Equation 5-38(b).
2. Calculate Π1 from Equation 5-39, using either of the equations presented depending on
whether the maximum extent of the electrode (s) or its geometric size (g) is available.
o
3. Calculate Π1 from the minimum of Π1o and Π2 as is given in Equation 5-40.
4. Calculate the dynamic resistance using Equation 5-38a.
The EPRI report High Current Impulse Testing of Full-Scale Grounding Electrodes (1006866)
showed that the simple Korsuncev model provides a reasonable dynamic tracking of the voltage–
5-49
Characteristics of a Ground Electrode
current relationship for simple grounding electrodes under lightning impulse conditions up to
40 kA [38]. The shape of the ionized zone can be estimated from the resulting value of Π1,
knowing that the area A increases but dimension s does not change if Π1 is greater than 0.159.
When Π1 is less than 0.159, the footing is fully ionized, the zone is hemispherical, and the zone
radius can be calculated from the expression for the resistance of a hemisphere.
The disadvantage of the Korsuncev model is that the model does not incorporate any time
constants for ionization or deionization. Therefore, this model is not as accurate as the LiewDarveniza model described in Section 5.4.2.1 to replicate the dynamic response of grounding
electrodes under high surge current conditions. However, it does predict the minimum electrode
resistance under ionization.
Applet GG-2 provides an implementation of the Korsuncev model. It also provides the capability
to directly compare the resulting dynamic resistance with that of the Liew-Darveniza model [29].
5.4.3 Step and Touch Potentials Under Lightning Conditions
A transmission line can effectively protect people who are near the line by intercepting and
diverting lightning strikes to its grounding system. It can also be shown that the human body can
tolerate much higher voltages from lightning than at power frequency. (The lower part of the
graph in Figure 5-23 labeled 2, 3 and 4 is similar to the Biegelmeier curve in Figure 5-11.)
Figure 5-23 shows that the human body can withstand a 100-µs monophasic (one-sided pulse)
lightning surge current, which is a factor of 30 higher than the 500-mA power frequency
ventricular fibrillation current indicated by 2 in Figure 5-23 [53]. A hand-to-foot impulse current
of 15 A would require an impulse potential of approximately 15 kV through a body impedance
of approximately 1 kΩ.
5-50
Characteristics of a Ground Electrode
Figure 5-23
Ventricular Fibrillation Current Versus Duration of a 60-Hz Stimulus for a Wide Range of
Exposure Durations
Source: J. P. Reilly
5.5
Electrical Properties of Concrete Foundations
Ancient concrete structures, such as the Roman Pantheon and Coliseum, survive because
concrete can be a remarkably durable material. In his work, Ufer described the excellent
performance of 1/2-in. (1.2-cm) steel reinforcing rods set into concrete foundations as grounding
electrodes in Arizona [43]. The rods were installed in 1942 and monitored until 1960. Despite
low levels of rain and humidity, and without interconnection to plumbing systems, these
foundation electrodes measured to have low resistance levels of 2–4 Ω without requiring any
maintenance.
Generally, all transmission tower concrete foundations will carry significant lightning surge
currents, whether by design or by chance. It is the role of the transmission line engineer to take
full advantage of the positive electrical benefits of concrete foundations in direct contact with the
soil (large cross section and surface areas, giving low impedance) without introducing problems
that will shorten the service life. Figure 5-24 (adapted from “Transmission Tower Foundation in
Japan,” by Y. Morinaga et al.) shows some typical side views of concrete foundations [44]. The
leg-to-leg separation varies from 19.7 ft (6 m) to more than 49.2 ft (15 m), depending on tower
strength requirements.
5-51
Characteristics of a Ground Electrode
Figure 5-24
Typical Transmission Line Concrete Foundations
The mat foundation in Figure 5-24 can function as a low-impedance Ufer grounding system, as
used in buildings. The pad-and-chimney and anchor foundations form four large disc electrodes
whose resistance is nearly the same as that of the mat after correcting for mutual resistance. The
lowest resistance is expected from the caisson and pile foundations because of their greater
depth.
Like most materials, concrete’s electrical resistivity varies drastically as its moisture content
changes. Fully reacted Portland cement contains approximately 0.24 g of non-evaporable water
per gram of cement [45]. It takes approximately a year to reach this state, although most water is
stabilized after a 30-day cure. This means that tower footing resistance for a new concrete
footing is likely to be somewhat high immediately after construction, to reach a minimum value
at 30 days, and tend to increase to its nominal value as the internal water saturation level reaches
equilibrium with the average moisture content of the soil. Estimating the resistivity of an aged
concrete foundation is a three-step process:
1. From Figure 5-25, determine the concrete weight loss from the average humidity of the soil.
For example, for dry soil with a relative humidity of 10%, Figure 5-25 shows the weight loss
to be equal to 20%.
5-52
Characteristics of a Ground Electrode
2. Determine the water saturation level of the concrete by subtracting the weight loss
determined in step 1 from 100%. In the example. the water saturation level is calculated as
100 - 20 = 80%.
3. Use Figure 5-26 to determine the range of resistivity for the water saturation level determined
in step 2. (The gray area in the figure indicates the range of resistivity values.) For the
example, the concrete resistivity is found to be 70–150 Ωm.
Using this approach, it can be shown that for a practical relative humidity range of 45–75%, the
typical range for concrete resistivity is 70–150 Ωm.
Figure 5-25
Effect of Humidity on Concrete Weight Loss and Shrinkage
5-53
Characteristics of a Ground Electrode
Figure 5-26
Effect of Water Saturation on Concrete Resistivity
5.6
Procedures for Testing Tower Grounding Electrodes
5.6.1 Introduction
5.6.1.1 Motivation for Testing Grounding Electrodes
Ground electrode measurements form an important part of the life-cycle management of the
grounding system. Some of the important reasons for performing resistance measurements are
the following:
•
To verify during construction of the line that the installed grounding electrode resistance falls
within the prescribed limits, and to identify those structures for which additional measures
are required.
•
To provide input data for detailed lightning performance calculations on poorly performing
lines (for example, by using the EPRI TFlash software [TFlash 5.0, 12/2007, 1013739]), or to
identify rogue structures for which specific improvement measures are required.
5-54
Characteristics of a Ground Electrode
•
To provide input data that enable the accurate calculation of the current in overhead ground
wires under normal and fault conditions.
•
To verify that touch, step, and transferred potentials around the transmission line towers fall
within the required limits and to identify the need for additional gradient control conductors.
•
To assess the ground resistance of the ground electrode after several years in service.
This section presents most of the commonly used field measurement techniques so that readers
can select the most appropriate method for their specific situations.
5.6.1.2 The Basic Principle of Measuring the Electrode Resistance
The basic principle involved in determining the resistance of a ground electrode is, in theory,
very simple. Generally, a three-point measurement is used, as is illustrated in Figure 5-27. The
overhead shield wires must be disconnected from the tower.
Figure 5-27
Principle of the Resistance Measurement of a Transmission Line Tower Ground
With this method, a current (I) is injected into the ground through the electrode under test.
During this time, the rise in potential of the electrode relative to far earth (GPRT) is measured,
and the resistance (RE) can be calculated from the ratio between resulting potential rise of the
earth electrode and the injected current: RE = GPRT/I.
5-55
Characteristics of a Ground Electrode
5.6.1.3 Effect of the Connected Ground Wires
The basic method gives meaningful results only when the tower under test is isolated from the
rest of the grounding system (that is, the overhead ground wires). The reason for this can be
explained with reference to Figure 5-28. Ground testers that are used for three-point
measurements measure only the total current produced by the instrument (I). It is assumed that
the measured voltage rise is the result of the total instrument current flowing into the electrode
under test. This assumption is true when the overhead ground wires are disconnected from the
tower. Figure 5-28 shows that the current in the ground electrode current under test (IE0) is equal
to the total current produced by the tester because no other current paths are available.
Figure 5-28
Current Sharing Between Transmission Line Towers If the Overhead Ground Wires Are
Disconnected
If the overhead ground wires are bonded to the towers, an electrical ladder network is formed
(see Figure 5-29). The equivalent impedance of this network on typical lines is usually less than
2 Ω. The current injected by the tester (I) is divided between the ladder network (IL = IE1+IE2 and
so on) and the local tower footing (IE0). Because the local tower footing resistance is usually
greater than the 2-Ω equivalent impedance, it follows that most of the current injected will flow
through the ground wires to neighboring towers (IL > IE0). This renders the measurement useless
unless the tower is temporarily insulated from any connected ground wires.
5-56
Characteristics of a Ground Electrode
Figure 5-29
Current Sharing Between Transmission Line Towers If the Overhead Ground Wires Are
Connected
It is generally preferred to perform classic three-point resistance measurements after foundations
are prepared and while the towers are being erected and phase conductors are being installed but
before stringing the overhead ground wires, because there is then no electrical connection from
tower to tower. This provides a good opportunity to measure the resistance of each tower to
remote earth and to install any supplementary grounding electrodes, such as rods or buried radial
wires, to meet a design specification.
5.6.1.4 Common Methods for Electrode Resistance Measurement
Two methods follow the basic three-point measurement principle. One is the fall-of-potential
method (see Section 5.6.2, Fall-of-Potential Method), and the other is the oblique-probe method
(see Section 5.6.3, Oblique-Probe Method).
Several methods have been devised to perform the ground electrode measurement with the
overhead ground wires in place, including the following:
•
Use of stray tower current and voltage for footing resistance. This method exploits the
current and local rise in potential associated with unbalanced power system induction into
overhead ground wires. This method is described in Section 5.6.4, Use of Stray Tower
Current and Voltage for Footing Resistance.
•
Directional impedance measurement. The current injected into the grounding electrode is
measured with split-core, clamp-on current transformers to exclude the current flowing
through the overhead ground wires from the measurement. Examples of this method are
described in Section 5.6.5, Directional Impedance Measurements.
•
Simulated fault. This is a variant of the directional impedance measurement current in
which the phase conductors, which are short-circuited in the substations, are used as the
current return path. This method is described in Section 5.6.6, Simulated Fault Method.
5-57
Characteristics of a Ground Electrode
•
High-frequency impedance. The frequency of the current injected for the measurement is
increased so that the impedance of the overhead ground wires is higher than the ground
electrode impedance. A commercial implementation of this method is described in Section
5.6.7, High-Frequency (26-kHz) Impedance.
•
Transient current injection (Zed-meter). In a recently developed method, the grounding
system is excited with an impulse current source to obtain a measurement of the surge
response of the grounding system. With this method, it is relatively easy to correct the results
for the presence of the overhead ground wires. This method is described in Section 5.6.8,
Active Transient Current Injection at Tower Base (Zed-Meter).
•
Direct measurement of the structure’s resistance. Another method to negate the effect of
the overhead ground wires is to place the current source for the measurement between the
overhead ground wire and the tower. This method is described in Section 5.6.9, Direct
Method for Measuring Structure Resistance.
5.6.2 Fall-of-Potential Method
The fall-of-potential method is the classic method for determining the resistance of a ground
electrode. Figure 5-30 shows the test arrangement. (The connections to the tester terminals are
indicated in square brackets.) This method gives meaningful results only when the tower under
test is isolated from overhead ground wires.
Figure 5-30
Fall-of-Potential Method for Measuring Structure Resistance
5-58
Characteristics of a Ground Electrode
5.6.2.1 The Test Setup
Typical four-terminal earth testers used for fall-of-potential measurements have two current
terminals (C1 and C2) as well as two potential terminals (P1 and P2). These instruments normally
display the measured resistance, which is the value of P2 -P1 divided by the current circulating
between terminals C1 and C2.
Terminals C1 and P1 on the earth tester are normally tied together and connected with one lead to
the earth lead of the tower under test. If there is surface corrosion or high contact resistance at
the tower, a separate lead should be used between the structure and P1.
The C2 terminal is connected to the remote current return probe located at distance D1 from the
center of the tower. The distance (D1) is selected depending on the required accuracy, the size of
the ground electrode under test, and the structure and layering of the soil. The following rules
apply:
•
Normally, it is sufficient to select a distance D1 that is equal to or greater than 5 times the
maximum diagonal dimension of the ground electrode. For this distance, errors in the
measured resistance will be less than 10% for uniform soil or for a two-layer soil in which
the thickness of the top layer is greater than the maximum extent of the electrode.
•
If no information is available about the extent of the ground electrode, distance D1 can be
selected so that it is at least 10 times the tower diameter.
•
The soil between the remote current probe and the tower should be free of external
conductive connections (such as lines, cables, and pipes). The distance from the current
return electrode to any such buried conductive structure should be greater than distance D1.
For a four-legged tower, the size of the tower electrode can be taken as the tower footprint. For a
guyed structure, the size should include the footprint of the guy wires.
Figure 5-31 shows the preferred probe layout for the fall-of-potential method. It shows that the
placement of the probes should be perpendicular to the line direction to minimize inductive
coupling from the line to the leads. (The connections to the tester terminals are indicated in
brackets.)
5-59
Characteristics of a Ground Electrode
Figure 5-31
Top View of the Preferred Probe Layout for the Fall-of-Potential Method for Measuring
Structure Resistance
The remote potential probe, P2, is placed at distance D2 on the line between the center of the
tower and the current injection point, C2 (see Figure 5-31). In principle, it is possible to obtain
the electrode resistance from just one measurement point; however, in practical situations, more
than one measurement is required. Distance D2 is selected according to the following rules:
•
If the soil is uniform or with horizontal layering, the measured value exactly equals the
tower footing resistance when D2 is 0.618 x D1 [46]. The expected error in the measurement
as a function of the location of the potential probe (P2) in two-layer soil is presented in Figure
5-32. It shows that the error in the measurement decreases as the location of the potential
probe reaches 62% of D1.
•
If the soil has a known nonuniformity, refer to the graphs in EPRI report EL-2699 to
determine where D2 should be placed to obtain the correct reading [1].
•
If the soil structure is unknown, but there is evidence that the lower layer resistivity is less
than three times the surface resistivity, the design curves in Volume 2 of EPRI report
EL-2699 show that the true impedance will fall within the range measured with D2 at 0.5 D1
and 0.7 D1 [1].
5-60
Characteristics of a Ground Electrode
Figure 5-32
Measurement Error as a Function of the Voltage Probe Position in Two-Layer Soil
It is recommended practice to perform several voltage measurements at different distances D2 to
obtain an impedance profile between the tower and the current return electrode. The reasons for
this are the following:
•
After the test equipment is set up, it does not take much longer to obtain resistance readings
at two or more probe locations, fixing D1 and varying D2. The measured impedance should
increase as D2 moves toward D1.
•
Several additional values improve the robustness of the measurement and give greater
confidence in the estimate of the electrode perimeter (that is, the distance around the outside
of the electrode) which can be computed from the ratio of resistivity to resistance: ρ/Rmeas.
•
Additional measured values provide the possibility to determine the soil resistivity.
5.6.2.2 Premeasurement Checks
Before the actual measurement starts, it is recommended to perform the following
premeasurement checks:
•
Measure the 60-Hz interference voltages across potential and current leads and compare it
with the rejection capability of the instrument.
•
Perform an on-site calibration of the tester against a noninductive reference, such as a 50 Ω
coaxial termination resistor, to detect high-frequency interference, which can cause an offset
in instrument readings.
•
Record the resistances of the remote potential and current probes to confirm continuity of all
the leads and connections.
5-61
Characteristics of a Ground Electrode
5.6.2.3 Performing the Measurement
Record the resistance readings from potential probe locations D2 = 50%, 60%, and 70% of D1.
The median (middle) of these readings is the best estimate of resistance, and the spread provides
an indication of the error. Errors beyond a 10% tolerance might result if there is a thin layer of
conductive soil over a high-resistivity rock layer. In this case, readings should be repeated with a
larger value D1, most conveniently by leaving the current probe in place as the new D2 and
leapfrogging to D1 = 2D1. Consistent results at 50%, 60%, and 70% indicate that the new distance
D1 is large enough.
5.6.2.4 Analysis of the Results
For analysis, the impedance ratio of measured voltage P2 to test current C2 is plotted as a function
of distance from the tower, D1. The impedance should increase as the position of P2 approaches
C1. There is typically a plateau at 50–80%, which indicates that these measurement points fall
outside the area of influence of both the tower under test and the remote current return electrode.
The resistance value of this plateau is the tower footing resistance.
In cases where there is not such a plateau, the results indicate that the probes are too closely
spaced. This can be remedied by increasing distance D1 (see Section 5.6.2.3) or by performing a
more detailed data analysis by correcting for probe proximity with Equation 5-41. A handy
software implementation for such an analysis is provided in applet GG-1 (choose “three-terminal
setup”). Distances D1, D2, and D12 can be measured with a pair of conventional 100-m measuring
tapes or with three reflective targets (such as inexpensive reflector markers for driveways) and a
laser rangefinder, even in relatively high vegetation.
RElectrode = R −
ρ
ρ
ρ
+
+
2π D12 2π D1 2π D2
Equation 5-41
Where:
RElectrode
is the electrode resistance to remote earth
R
is the measured resistance in three-terminal measurements
D12
is the distance from the potential probe to the current probe
ρ
is the resistivity of the soil
5-62
Characteristics of a Ground Electrode
5.6.3 Oblique-Probe Method
The oblique-probe method is a variation of the fall-of-potential method that should be used when
nothing is known about the local soil resistivity or when the site is congested with other metal
services below grade. The general test setup is shown in Figure 5-33. Like the fall-of-potential
method, this method gives meaningful results only when the tower under test is isolated from
overhead ground wires.
Figure 5-33
General Probe Layout for the Oblique-Probe Method
5.6.3.1 The Test Setup
The apparatus used for the oblique probe method is identical to that of the fall-of-potential
method. This method also requires the use of a four-terminal earth tester with the C1 and P1
terminals bonded together and connected to the tower earth lead.
The C2 terminal is connected to the remote current return probe located at distance D1 from the
center of the tower in the direction of the line right-of-way. This distance should be large enough
to minimize its influence on the potential rise of the tested electrode. The following rules apply
for the selection of distance D1:
•
Normally, it is sufficient to select a distance D1 that is equal to or greater than five times the
maximum diagonal dimension of the ground electrode. For this distance, errors in the
measured resistance will be less than 10% for uniform soil or for a two-layer soil in which
the thickness of the top layer is greater than the maximum extent of the electrode.
•
If no information is available about the extent of the ground electrode, distance D1 can be
selected so that it is at least 10 times the tower diameter.
5-63
Characteristics of a Ground Electrode
•
The soil between the remote current probe and the tower should be free of external
conductive connections (such as lines, cables, and pipes). The distance from the current
return electrode to any such buried conductive structures should be greater than distance D1.
The oblique probe method differs from the fall of potential method in the placement of the
potential probe, P2. In this case, it is placed at an angle to the right-of-way as shown in
Figure 5-33 and not on the line between the current return probe C1 and the tower. Ideally, the
potential probe should be positioned successively with increasing distances from the tower, D1,
so that distance D12 remains the same, as shown in Figure 5-34.
Figure 5-34
Top View of the Ideal Potential Probe Layout for the Oblique-Probe Method
5-64
Characteristics of a Ground Electrode
Figure 5-35
Top View of a Practical Potential Probe Layout for the Oblique-Probe Method
In practice, it can be difficult to realize the ideal potential probe trajectory. A simpler approach
(see Figure 5-35) is to take the potential readings with increasing distances D2 from the tower, in
a straight line that is angled between 60° and 90° with respect to the current probe. If possible,
the potential profile should extend so that the longest distance from the tower, Dz2, is at least
equal to the distance between the current return electrode and the tower (that is, Dz2 = D1).
5.6.3.2 Performing the Measurement
Resistances are measured using the same equipment as for the fall-of-potential measurement.
The ratio of voltage to current is recorded to obtain a resistance profile extending from the tower.
5-65
Characteristics of a Ground Electrode
5.6.3.3 Analysis of the Results
For the case in which D1 and D2 are larger than the footing radius, the electrode resistance can be
expressed in terms of the resistance measured at potential probe position D2, as follows:
Rmeas = R −
ρ
ρ
ρ
+
+
2π D12 2π D1 2π D2
Equation 5-42
For profile angles of between θ = 45° and θ = 90°, which are used in the oblique probe method,
the distance of the current probe to the tower is approximately equal to the distance between the
current and potential probes (that is, D1≅D12). Equation 5-42 simplifies to the following:
Rmeas ≈ R +
ρ
2π D2
Equation 5-43
Where:
R
is the electrode resistance to remote earth
Rmeas
is the measured resistance in the oblique-probe method with θ = 45–90°
D12
is the distance from the potential probe to the current probe
ρ
is the resistivity of the soil
The measured resistances, Rmeas, are then plotted against the inverse distance of the potential
probe to the tower (that is, 1/D2) Both the tower footing resistance and the soil resistivity can be
extracted relatively easily by doing a linear curve fit to the plotted measurement points.
Extrapolating these points to zero provides an estimate of the tower footing resistance, as Pillai
described in “A Review on Testing and Evaluating Substation Grounding Systems” [47]. The
slope of this linear curve fit, when multiplied by 2π, is a good estimate of the local soil
resistivity.
Figure 5-36 shows an example of how the analysis can be performed by using the linear
regression (add trendline) option in Microsoft Excel or a similar spreadsheet program. In Figure
5-36, the tower footing resistance has been calculated as 39.1 Ω and the resistivity as 586 Ωm.
(The letters in Figure 5-36 refer to the probe positions indicated in Figure 5-35.)
5-66
Characteristics of a Ground Electrode
Figure 5-36
Typical Data Analysis for Oblique-Probe Measurement of Resistance and Resistivity with
Probes at 90°
5.6.3.4 Accuracy of the Results
Figure 5-37 shows a comparison of the resistance values that would be measured for the fall-ofpotential method (θ = 0°) with those for the oblique-probe method (θ = 90°). The vertical dashed
line in the figure shows the distance at which the P2 probe distance D2 is 61.8% of the current
probe distance D1. The resistance measured with the fall-of-potential method at the 61.8%
potential probe location corresponds exactly with the extrapolated resistance with a 1/D2 spacing
of zero. This shows that the two methods result in the same estimate of the tower footing
resistance.
The accuracy of the oblique-probe method depends on how closely the ideal potential trajectory
is followed (that is, how well the relationship D12 = D1 was maintained). If the probe layout is
exactly as shown in Figure 5-34, the D12 and D1 terms in Equation 5-43 cancel out precisely. If a
more practical potential probe layout is followed (see Figure 5-35), the difference in the D12 and
D1 terms introduces an error in the estimate of the tower footing resistance.
This error has been investigated for various angles (ranging from 22.5° to 90°) between the
current and the potential leads. The results (see Figure 5-38) show that the error in the estimate
of the tower footing resistance and soil resistivity will be less than 1% and 3%, respectively, for
angles from 45° to 90°.
5-67
Characteristics of a Ground Electrode
Figure 5-37
Measured Resistance for Fall-of-Potential and 90° Oblique-Probe Methods
Figure 5-38
Typical Data Analysis for Three Angles (22.5°, 45°, and 90°) in Oblique-Probe Method
5-68
Characteristics of a Ground Electrode
5.6.4 Use of Stray Tower Current and Voltage for Footing Resistance
Any ac transmission structure that supports an energized set of phase conductors conducts a
small stray current to earth. This current originates as a result of inductive and capacitive
coupling between the phase conductors and overhead ground wire. On typical transmission lines
in operation, the induced current in the overhead ground wire can be as high as 10% of the load
current in the phase conductors.
The stray currents depend on the conductor configuration on the line and the degree of phase
imbalance. On a line with identical spans, the induced currents in the ground wires are identical,
resulting in no current in the towers. If the spans are not identical, a small stray current will flow
down the tower to equalize the difference in the induced currents between the different spans.
The net tower currents flowing into the tower footing resistances result in a small ac voltage,
which is usually less than 10 V, at each tower base. There is a significant harmonic content
present in the tower stray current because both the capacitive and inductive coupling circuits acts
as differentiators.
It is relatively easy to measure the tower potential rise, and if the current can also be measured
accurately, the ratio of voltage to current yields the tower low-frequency footing resistance. This
situation is illustrated in Figure 5-39.
Figure 5-39
Stray Tower Current Method for Testing of Ground Rods
The quality of results in stray-current test methods can be improved by deliberately increasing
the stray current. Calculations suggest that lines with unequal span lengths from tower to tower
will tend to have higher stray currents than lines with uniform spans. This extra stray current
5-69
Characteristics of a Ground Electrode
will also be higher at times of peak load. The effect of unequal span lengths can be exploited
further by isolating one or more towers from the overhead ground wires to deliberately create
unequal span lengths. At isolated towers, the conventional fall-of-potential method (described
in Section 5.6.2) should be used to give reference results for comparison with the stray-current
values.
Alternatively, it is also possible to shunt away a fraction of the tower current into a known
ground resistance (driven rod) at a remote location and to measure the change in tower base
potential when this lead is connected and disconnected. However, in many transmission line
situations, the circuits are well balanced, giving lower values of stray tower current that vary too
rapidly for easy measurement using either of these approaches.
5.6.4.1 The Test Setup
On single-pole structures, the current can be monitored by using a clip-on ammeter with a
low-current range of approximately 100 mA full-scale with a 1-mA sensitivity. For H-frame
towers with two ground bonds and rods, a pair of clip-on ammeters should be used to monitor
both currents at the same time. For transmission lines with multiple large-diameter foundations
or tower steel, it is not possible to capture the current down the legs of the tower with simple
clamp-on current transformers (CTs). In this case, the use of flexible, large-diameter coils
(Rogowski coils) should be considered. These coils might not have sufficient sensitivity to
measure the tower currents of than 100 mA.
The voltage measurement is made with a high-impedance voltmeter, which is connected to the
tower on one side and to the potential probe on the other. This potential probe should be placed
far enough from the tower to be outside the zone of influence of the electrode under test. In
practice, this means that the distance to the potential probe, D1, should be at least five to ten
times the tower diameter, depending on the extent of the installed ground electrode. Even greater
distances of D1 might be needed if the tower is situated on two-layer soil with the low-resistivity
layer on top of the high-resistivity one. The preferred layout is to place the potential probe in a
direction perpendicular to that of the line to reduce the possibility of placing the potential probe
within the zone of influence of adjacent grounding electrodes.
It is also good practice to check that the potential probe is far enough away by taking several
resistance measurements at increasing potential probe distances until the readings are all the
same. Because the tower voltage can fluctuate over time, it is recommended that the voltage be
based on voltage readings that are taken in quick succession on two probes at different distances.
5-70
Characteristics of a Ground Electrode
5.6.4.2 Performing the Measurement
Several simultaneous readings of the ground electrode current and remote potential should be
recorded. A practical alternative is to use a modern, two-channel recording digital oscilloscope
or voltmeter. A good check of the validity of the readings is to look at the stability of the
calculated resistance over time. Unstable readings indicate that this test method is unsuitable for
that particular tower.
5.6.4.3 Analysis of the Results
The ground electrode resistance is determined by dividing the voltage by the measured current.
For example, if the average current (Ix) is measured to be 70 A and the average voltage probe
readings are Vprobe = 2.5 V, 2.8 V, and 3.0 V for probe spacings of 15, 20, and 25 m (5, 7, and
8 ft), respectively, the last voltage reading can be considered as the full ground potential rise of
the tower. Equation 5-44 gives the measured resistance (Rmeas) as follows:
Rmeas =
V probe
3.0V
=
= 40 Ω
Ix
0.07 A
Equation 5-44
Estimate of Rod Resistance from Stray Current and Voltage
There are many possible problems with implementing this approach, but if it is done carefully
and under favorable system conditions, this approach has good safety aspects and low equipment
cost.
5.6.4.4 Use of Stray Tower Current and Voltage for Resistivity
It is possible to use the stray current, if it is stable enough, as a source to determine the
upper-layer resistivity according to the method described in Section 4.4.3, Driven Ground Rod
Methods (Two- and Three-Electrode Methods).
5-71
Characteristics of a Ground Electrode
An approach for obtaining an estimate of resistivity is to measure the potentials according to the
layout shown in Figure 5-39 using probe locations close to and far away from the electrode under
test (for example, Dx = 10 ft (3 m) and D10x = 100 ft (30 m). For the known electrode current Ix,
the potential difference between these two probes, ∆V = (V10x - Vx ), can give a resistivity estimate
as follows:
∆V = (V10x − Vx )
ρ1 ≈
2π∆V
Ix
Equation 5-45
Estimate of Resistivity from the Potential Difference Between Two Probes
5.6.5 Directional Impedance Measurements
For testing transmission and distribution pole bonds consisting of single conductors with a
maximum diameter of less than 0.47 in. (12 mm) (AWG 4/0), clamp-on ground resistance testers
are offered in the market. Clamp-on ground resistance testers find their main use in
multigrounded systems in which it is time-consuming to disconnect the ground under test. The
units allow a convenient measurement of structure footings connected through bonding wires, wood
pole grounds, or guy wire anchors. These instruments generally run at an excitation frequency of
approximately 2 kHz. The currents in each direction are monitored to give the driving point
impedance, and the fraction of current that flows down into the ground electrode is used to
calculate the local electrode resistance. The measurements can then be used to ensure intact
ground systems and to prove the initial quality of the grounding connections and bonds.
Resistance and continuity of grounding loops around pads and buildings can also be measured
with these instruments.
The main limitation of these instruments is that the jaws do not fit around transmission tower
legs. They can measure a minimum resistance of 2 Ω, but loop inductance exceeding 300 µH
(for a typical transmission line span) can introduce errors when reading resistances under 10 Ω,
which is often the case. One desirable feature is that, from proximity effects, the parallel
resistance of several nearby electrodes can be larger than the parallel combination of their
individual measured resistances, giving a more realistic estimate of the true resistance to remote
earth.
Recently, a 12-inch split-core current transformer named “Big Norma” and a corresponding
meter to perform clamp-on style measurements have been commercially introduced to perform
resistance testing on lattice transmission tower legs and pole bonds. It is used in combination
with a standard fall-of-potential lead arrangement with the difference that the current injected
into the tower leg, instead of the output current of the meter, is monitored, as shown in
Figure 5-40.
5-72
Characteristics of a Ground Electrode
Figure 5-40
Setup of Tower Footing Resistance Measurement with Split-Core Current Transformers
Around the Tower Legs
In the usual setup, the current return electrode is located approximately 90 m away and the
potential probe is driven at 61.8% of this distance (56 m). The instrument uses relatively low
measurement frequencies of 94, 105, 111, and 128 Hz for two-, three-, and four-terminal
resistance readings. During this procedure, the resistance is measured individually for each leg in
turn, and then the parallel combination of the values is computed. Any fraction of the current lost
to the overhead ground wires and adjacent towers increases only the power consumption of the
signal generator.
The major problem with using the Big Norma is that it is often necessary to excavate the lattice
tower leg in order to fit the CT around the narrow part of the tower leg (see Figure 5-41).
5-73
Characteristics of a Ground Electrode
Figure 5-41
Excavation of Tower Leg to Allow Correct Installation of Big Norma Current Transformer
5.6.6 Simulated Fault Method
With the simulated fault method, a floating current source is used to inject a current at low
frequency between the phase conductor and tower arm, as shown in Figure 5-42. The remote
ends of the phase under test are grounded at substations to provide the return path for the current.
Potential measurements are performed at several locations away from the tower to determine the
potential gradients around the ground electrode in the same way as described in Section 5.6.4,
Use of Stray Tower Current and Voltage for Footing Resistance.
5-74
Characteristics of a Ground Electrode
Figure 5-42
Setup for the Simulated Fault Method
This method has several advantages that need to be balanced with the additional planning and
work needed to remove a transmission line from service and to access the phase conductors for
the testing. The main advantages are the following:
•
It excites the same shielding and coupling effects of the conductors, grounding electrodes,
and nearby infrastructure (such as cable sheaths, parallel fences, rails, and communication
circuits) as would be the case during actual fault conditions.
•
The substation grounding grids provide an excellent and remote grounding electrode, which
eliminates all proximity effects.
•
A higher level of excitation current can be used to obtain reliable results without endangering
(by electric shock or tripping) the public or animals during testing.
•
The simulated fault tests have particular merit at sites with limited access or at road and river
crossings.
It is also possible to use a lightning impulse instead of a low frequency as injected current;
however, the results are not as definitive because the lightning waveform is not well defined in
the frequency domain.
5-75
Characteristics of a Ground Electrode
5.6.6.1 The Test Setup
For power-frequency measurements, several aspects should be considered when selecting and
setting up the current source:
•
The test source frequency should be near but not exactly 60 Hz. This is to avoid 60-Hz
interference from other nearby electric circuits and because inductive reactance, shielding
factors, and current splits vary with frequency. A frequency of 65–70 Hz might be needed to
resolve small test signals from power-line interference.
•
The test source must be robust enough to sink currents induced from parallel operating
circuits, which can reach 10 A.
•
Diesel-powered 120/240 V generators are preferred to gasoline generators because they have
no ignition systems that can couple noise into the current measurement.
•
The speed governor of the generator can be adjusted to generate the desired frequency.
•
A variable autotransformer should be used to control the test current.
The potential profile of the grounding system is determined by measuring the voltage between a
potential probe and the tower (see Figure 5-42). The orientation of the potential profile should
preferably be perpendicular to the line right of way.
5.6.6.2 Performing the Measurements
During simulated fault tests, it is necessary to determine the current split between the local
ground electrode and the overhead ground wires (see Figure 5-42). Measurements should also
include all other conductors near the tower, such as cable shields, interconnected distribution
neutrals, pipelines and railway tracks. If there are pipe-type cables nearby that use polarizing
cells, these should be bypassed during the test because they have uncertain impedance at low
currents.
Currents are measured either with split-core CTs in combination with a local shunt or with
clamp-on current transducers. Because measured currents might be small, it is necessary to select
the shunts so that they apply the maximum possible burden according to the CT accuracy
specification (considering both magnitude and phase) to obtain reasonable signal levels. The CT
signals should be routed to test instruments through twisted-pair cables to minimize interference.
The system can be calibrated by measuring the injected current.
5-76
Characteristics of a Ground Electrode
A two-channel, low-frequency spectrum analyzer should be used to record the measurements.
A CT on the test injection lead drives the reference channel. The second channel measures either
the potential difference or the current split relative to the reference. Current splits in different
conductors tend to vary in phase angle, so either the spectrum analyzer must be able to resolve
vector quantities or a digital oscilloscope capable of calculating triggered and averaged Lissajous
figures (X versus Y plots) should be used. The ratio of the two channels gives a vector reading
(transfer impedance or current split) referenced to the injected current.
If there is a single current path into each tower, a single simulated-fault location can be used to
energize several adjacent structures and measure the ground impedances, using multiple potential
probe readings plotted against the inverse of distance measured from the center of each structure as
described in Section 5.6.5, Directional Impedance Measurements. The potential profile readings
and analysis are done in the same way as described in Section 5.6.4, Use of Stray Tower Current
and Voltage for Footing Resistance.
5.6.7 High-Frequency (26-kHz) Impedance
In 1976, Brown Boveri Ltd (BBC)—which is now ASEA Brown Boveri (ABB)—introduced a
three-terminal impedance meter to allow the measurement of a local tower footing resistance
without disconnecting the overhead ground wires. It uses a 26-kHz sine wave source in
combination with a power amplifier with a 50-V output to inject current into the local ground
electrode. The built-in instrumentation can measure 50 mA accurately. Cables are provided to
place the return current electrode 75 m (250 ft) from the tower and the voltage probe at a
distance of 40 m (133 ft), which is 53% of the current electrode distance. In practice, it is easy to
use this instrument, which has a one-touch measuring operation.
At the 26-kHz test frequency, the impedance of the overhead ground wires is high enough that
footing resistances of less than 20 Ω can be established accurately. The manufacturer further
claims that the high test-frequency has the additional advantage of measuring only the extent of
the electrode that is active during lightning strikes.
Comparative field trials have confirmed the instrument’s accuracy for tower footing resistances
of less than 20 Ω. At great than this value, however, the instrument loses resolution as the low
parallel impedance of the adjacent towers starts to exert a stronger influence on the readings.
5-77
Characteristics of a Ground Electrode
5.6.8 Active Transient Current Injection at Tower Base (Zed-Meter)
In recent years, EPRI has been active in the development of an instrument that can overcome the
difficulties experienced with the traditional methods. The instrument under development, called
the Zed-meter, is based on the active transient current injection at the tower base, and it is in
broad terms very similar to the other methods described previously. The general layout of the test
equipment is shown in Figure 5-43. The measurement is performed using the following steps:
1. Inject a transient current surge into the tower base.
2. Measure the potential rise of the tower to remote ground.
3. Calculate the ratio of potential rise to current as a function of time.
4. Calculate the tower footing resistance by accounting for the effect of the connected overhead
ground wires.
The interpretation of the measured data takes place in the time domain. This allows users to
reject noise and early oscillations related to surge response of the wiring and tower structure,
retaining only the features associated with the ground electrode response.
Figure 5-43
The Setup for the Active Transient Current Injection Method (Zed-Meter)
5-78
Characteristics of a Ground Electrode
The use of this methodology has the following specific advantages:
•
There is no need to insulate overhead ground wires.
•
The input and injected current signals are chosen to be safe for use. The applied pulse energy
is less than 10 mJ.
•
The equipment is lightweight and robust to enable measurements at typical tower locations.
•
The use of impulse currents results in relatively short test leads.
•
The measurement is immune to power frequency coupling effects, so there is flexibility in
routing the test leads to suit the right of way.
•
The test procedure is quick and simple to perform, resulting in a fast test time.
•
The use of a transient current impulse enables the measurement of the transient surge
response of the tower footing that is relevant for lightning performance of the line.
5.6.8.1 The Test Setup
A 295.3-ft (90-m) coaxial lead, which will be used for the current injection, is laid out on the
surface of the ground away from the tower, but in the direction of the line right of way. This lead
is terminated on the far side with a ground spike. The transient current source is connected
between the lead and the tower. A second 295.3-ft (90-m) coaxial cable is laid out in the opposite
way from the current lead, or at 90° to minimize the electromagnetic coupling between the leads.
This lead serves as the zero potential reference. This lead is also terminated on the far side onto a
ground spike.
5.6.8.2 Performing the Measurements
The voltage between the tower and the reference potential lead, as well as the currents injected
into the current base, are recorded in the time domain with a digital oscilloscope for later
analysis. The current and voltage transducers should have a sufficiently high frequency response
to capture the signals accurately. This voltage divided by the measured current (in the time
domain) gives the measured impedance as a function of time.
To fully understand the measured signals, it is necessary to look at the time sequence of the surge
propagation along the tower and current lead, as illustrated in Figure 5-44. The numbering of the
description corresponds to that of the figure. The sequence is as follows:
a) The surge is injected between the tower leg and the horizontal current lead.
b) The surge current flows into the current lead, whose surge impedance is constant. The surge
also starts to propagate along the tower leg. The measured impedance corresponds to the
parallel combination of the current lead and the one tower foot.
5-79
Characteristics of a Ground Electrode
c) The surge continues to propagate along the current lead, still with a constant surge
impedance. The surge traveling up the tower has now reached the other tower footings, but it
is also still traveling up the tower. During this time, the impedance measurement is not stable
because the surge impedance of the tower increases and the surge travels up the tower.
d) The surge traveling up the tower reaches the top of the tower, and the measured impedance
changes as the current splits into the overhead ground wires.
e) The situation stabilizes as the surge travels along the ground wires and the current lead. This
is the optimal time to start measuring and recording the total impedance. The total impedance
is the parallel combination of the current lead, the overhead ground wires, and the local
ground electrode resistance (see Section 5.6.8.3, Analysis of the Results).
f) The optimal time for impedance measurement continues as the surge travels along the fairly
constant surge impedance of the overhead ground wires. At this stage, the surge reaches the
end of the current lead, and a negative reflection from earth spike will start propagating back
to the tower.
5-80
Characteristics of a Ground Electrode
Figure 5-44
Time Sequence of the Current Wave Injected into the Transmission Tower Base
As time continues, the reflections from adjacent towers start to interfere with the measured
signal, and the tower footing impedance can no longer be extracted reliably from the
measurement results.
This sequence of events can also be indicated on the measurements performed on an “ideal”
tower with a low footing resistance. The injected current wave is shown on the left side of
Figure 5-45, and the measured voltage is shown on the right.
5-81
Characteristics of a Ground Electrode
Figure 5-45
Waveforms of the Current Injected into the Tower (I1) and Current Lead (I2) and the
Voltage Measured at the Tower Base
Figure 5-46 shows the impedance calculated from the voltage and current waves. It also shows
the sequence of the events, using the same numbering that is used in the description of the
sequency. Figure 5-46 shows that the uncorrected measured tower footing resistance is 19 Ω.
Figure 5-46
Calculated Impedance from the Voltage and Current Waveforms Shown in Figure 5-45
5-82
Characteristics of a Ground Electrode
5.6.8.3 Analysis of the Results
The measured impedance is a parallel combination of the tower footing resistance and the
impedance of the overhead ground wires. The surge impedance of each overhead ground wire
(ZGW) is calculated by Equation 5-46:
⎛ 2h ⎞
Z GW = 60ln⎜ ⎟
⎝ r ⎠
Equation 5-46
Where:
ln
is a natural logarithm (to base e)
h
is the height above ground level
r
is the radius of the ground wire
For example, the tower footing resistance can be calculated as follows (see Figure 5-47).
Figure 5-47
Typical Equivalent Circuit Seen by the Zed-Meter During the Optimal Time of Measurement
The overhead ground wire height was measured with a laser rangefinder to be 16.3 m. The two
ground wires on this line were identified as 7#8 (see Table 7-4), which has a radius of 0.19 in.
(4.9 mm). Using Equation 5-46, the surge impedance of one ground wire is calculated as ZGW =
528 Ω. The parallel combination of the four wires (that is, two in each direction) is
ZGW = 528/4=132 Ω.
5-83
Characteristics of a Ground Electrode
The Zed-meter indicated a median impedance of Rmeas = 19 Ω, which is the parallel combination
of the overhead ground wires and the tower footing resistance. With the impedance of the ground
wires (ZGW) known, the footing impedance (RT) can be calculated as follows:
RT =
Rmeas Z GW
= 22 Ω
Z GW − Rmeas
Equation 5-47
5.6.8.4 Accuracy of the Results
During 2004–2005, an extensive test program was conducted to compare the performance of the
Zed-meter with other traditional methods of determining the tower footing resistance. The
results, which were published in the EPRI report Summary of Zed-Meter Field Tests: Transient
Impedance of Transmission Line Grounds (1012314), were positive [28]. For concentrated
grounding electrodes, such as rods or tower foundations, it was found that there is a strong
correlation between Zed-meter measurements and those of the oblique-probe method. A
summary of the results is shown in Figure 5-48. It can be seen that the Zed-meter results are
consistently lower than the power frequency measurement, but this can be ascribed to the
reduction of soil resistivity as a function of frequency as was shown in Figure 4-6. The larger
spread of results at less than 1 Ω is a result of the accuracy limits of the instruments used for the
Zed-meter.
5-84
Characteristics of a Ground Electrode
Figure 5-48
Comparison of Low-Frequency Resistance with Zed-Meter Impedance for Compact
Electrodes
For extended electrodes, such as buried radial or continuous counterpoise, the comparative
results (see Figure 5-49) showed much less correlation than was found for the concentrated
electrode. The Zed-meter results have a tendency to show higher resistance values than the
low-frequency oblique-probe measurements do. This behavior can be explained in terms of the
high-frequency behavior of distributed electrodes (see Section 5.4.1, The Surge Impedance of a
Ground Electrode System).
5-85
Characteristics of a Ground Electrode
Figure 5-49
Comparison of Low-Frequency Resistance with Zed-Meter Impedance for Distributed
Electrodes
5.6.9 Direct Method for Measuring Structure Resistance
Footing resistance can be measured by directly connecting a ground resistance tester between the
structure and one overhead ground wire, as is shown schematically in Figure 5-50. The P1 and C1
terminals are connected to the structure, and the P2 and C2 terminals are connected to the
overhead ground wire. All other overhead ground wires must be locally disconnected or isolated.
The overhead ground wire is used as a zero-potential reference on that structure, and it should be
bonded to several adjacent structures in at least one direction, so that its resistance to remote
ground is small compared with the structure under test. Occasionally, the 60-Hz interference
voltage level should be recorded across the instrument terminals and compared with the rejection
capability of the instrument.
5-86
Characteristics of a Ground Electrode
Figure 5-50
Setup for the Direct Method for Measuring the Structure Resistance
This method might have advantages over the fall-of-potential method for the following reasons:
•
It provides a direct reading of the structure resistance.
•
It is independent of anomalies in the local soil.
•
It does not require running probe leads through congested areas.
However, the method is less practical when the overhead ground wires are continuously isolated
or when bonding of these wires is incomplete on both sides of the tower under test.
5.6.10 Ground Electrode Integrity Assessment
Tower footing resistance measurements are often made to assess the condition of already
installed grounding electrodes. Two aspects are assessed: the intact length of the electrodes and
the continuity of the ground conductors and connections in the case of a continuous
counterpoise.
It is important to check the condition of grounding electrodes frequently during the life of the
grounding electrodes, especially continuous counterpoises, which can degrade quickly as a result
of the continuous low-level stray current. This is true even for areas with a relatively high soil
resistivity (that is, on the order of 4000 Ωm) where leakage current would be low. Some
experiences indicate that an installed life can be as short as eight years.
5.6.10.1 Continuity Measurements
Measurements of the conductor resistance between accessible contact points can be used to
check the integrity of a continuous counterpoise. Typically, these are performed with a
four-terminal micro-ohm meter that uses a dc test current in the 100-A range. This approach is
most practical at a tower where there are two continuous counterpoise wires that form a loop at
the far structure (see Figure 5-51). The continuity test becomes easier to interpret if both the
5-87
Characteristics of a Ground Electrode
counterpoise conductors can be disconnected at the tower where the measurement is performed.
If this is not possible, the measurement should be compared with the combined resistance of all
counterpoise and overhead ground wires.
For a looped counterpoise (see Figure 5-51), the measured resistance is compared with the
calculated estimate based on the conductor length and per-unit length resistance. For example, a
2
21 mm (#4 AWG) copper conductor has a resistance of approximately 815 µΩ/m. If the
measured resistance value corresponds to 0.65 Ω, it can be calculated to correspond to an
equivalent counterpoise length of 780 m. If this agrees approximately with double the span
length, it indicates that the counterpoise is intact. A similar approach can be used for other types
of conductors. (Data for the physical characteristics of common ground wires are provided in
Part II, Section 6.7.4, Typical Conductors in Use.)
Figure 5-51
Setup for Continuity Measurement on a Looped, Continuous Counterpoise
Another technique common in station testing uses injection of power-frequency test current
between accessible grid loops. A transformer can be used to increase current levels to more than
400 A when a source that is rated at several kilowatts is available. This is especially useful for
end-of-life tests in conjunction with an infrared camera because a high test current tends to heat
any poor connections, which makes corrosion more apparent.
5.6.10.2 Use of Footing Resistance and Resistivity to Assess Intact Rod Length
For concentrated tower electrodes, the ratio of the measured resistivity (Ωm) to resistance (Ω)
gives a characteristic footing dimension, in meters. This is related to the expected physical size
of the ground electrode, and it offers a method for assessing the condition of the tower footing.
The characteristic footing dimension can be determined as follows:
•
A four-legged tower with a foundation can be approximated by a hemispheric electrode. In
this case, the characteristic footing dimension will be the perimeter of this hemisphere at the
ground level.
5-88
Characteristics of a Ground Electrode
•
If the electrode is a surface disc, the characteristic footing dimension will be four times the
ring radius.
•
If the electrode is a thin vertical rod, the characteristic footing dimension will be the length of
the rod.
A more accurate estimate of the characteristic dimension can be obtained by inverting the
equation for geometric and contact resistance. This is especially helpful when all the towers have
the same base dimensions. The applets are useful in this regard because it computes the
equivalent size of the electrode based on input about the shape (box, ring, four radial wires,
hemisphere, two poles, two radial wires, or rod). The estimated size of the electrode can be
compared with the dimensions as designed to determine whether it is corroded or whether it was
not installed.
The assessment of the ground electrode becomes trivial if the ground electrode comprises a
single driven rod, as follows:
Lrod ≈
ρ1
Rx
Equation 5-48
Estimate of Intact Rod Length from Resistivity and Resistance
Where:
Lrod
is the length of the rod
ρ1
is the upper-layer resistivity
Rmeas
is the measured resistance of the rod
For a single ground rod in good condition, this dimension should be approximately the same as
the driven length of the rod in the ground. Equation 5-48 is accurate enough for a practical rod
length of Lrod = 7–25 ft (2–8 meters). Correction factors can be read from Figure 4-18 for shorter
rod lengths.
5-89
Characteristics of a Ground Electrode
Figure 5-52
Resistance Test Method for Towers with Continuous Counterpoise
Buried counterpoise is often used in soils that have a high resistivity value (for example, sand,
gravel, or rock) to reduce structure footing impedance. Such grounding systems are usually quite
extensive, which makes it difficult to measure the electrode resistance. In the case of the fall-ofpotential method, it is difficult to define the center of the electrode to use as basis for the
measurement. High-frequency measurements using clamp-on resistance testers might give results
that depend on brand and operating characteristics because the impedance of a counterpoise is
significant at high frequencies. The most practical option is to use the methods described in
Section 5.6.9, Direct Method for Measuring Structure Resistance. In this case, it is necessary to
disconnect and roll back the continuous counterpoise for approximately 6.6-ft (2-m) from the
tower base at which the measurement is performed and to do the same at the next tower, as
shown in Figure 5-52.
The most important use of the measured electrode resistance is to establish whether the
continuous counterpoise is still intact. This can be done by comparing resistance readings before
and after pulling back the connections in each direction. The resistance of the tower and a single
span of counterpoise should be less than the contact resistance of the conductor, given by
Equation 5-17.
5.6.11 Step and Touch Potential Measurements
The test setup for step and touch potential measurements around transmission line structures is in
principle the same as that used for fall-of-potential measurements shown in Figure 5-27. A test
current is injected into the tower base, using a remote current return electrode as the reference.
The overhead ground wires must be disconnected from the tower when the measurements are
performed. The current return electrode should be located at a distance (D1) that is effectively
outside the zone of influence of the tower footing. For low resistivity soil extending to a depth
greater than the maximum diagonal dimension of the complete ground electrode, D1 should be at
least five times this diagonal dimension. If rock is present near the surface, several larger values
of D1 should be used and compared for consistent results.
5-90
Characteristics of a Ground Electrode
Touch potentials are measured between the structure and a probe located 3.3 ft (1 m) away. Step
potentials are measured between two probes that are 3.3 ft (1 m) apart. Multiple measurements
should be made, and there should be a smooth downward trend for concentrated electrodes. The
largest touch values are likely to occur near the outward-facing corners of footings or around guy
anchors, although gradient control rings will modify this pattern. The largest step potential
values are likely to be measured at the ends of radial crowfoot wires and at the edge of rings.
For isolated structures, the test voltage readings divided by the injected currents give values of
transfer resistance in ohms. The fault step and touch potentials are the product of this test
resistance and the fault current calculated for each structure footing. Alternatively, the test
voltage readings can be normalized by the total potential rise of the structure during the test,
found using a remote potential electrode. The fault step and touch potentials are then determined
by scaling this total potential rise to actual faulted levels. The latter method also works for tests
on structures that still have their overhead ground wires connected.
During testing, the resistance of the current and potential electrodes should be monitored to
prove continuity. Occasionally, the 60-Hz common-mode interference voltage on the voltage
terminals should be monitored and compared with the instrument capabilities. Twisted-pair wires
should be used between the instrument and remote step-potential probe pairs to reduce
interference and coupling to the current lead. The instrumentation should have an overall
resolution of milliohms because step and touch potentials at distant locations tend to be small
fractions of the ground potential rise at the tower.
5.6.12 Assessment of the Interference to Other Infrastructure
During faults, metallic structures near towers, such as communication cables, railways and
pipelines, tend to be exposed to the ground potential rise as well as induced voltages from
conductor and ground grid currents. The voltages on remotely grounded cable pairs or coaxial
cable are difficult to calculate, but they are easy to measure with the simulated fault method (see
Section 5.6.6). Interference caused by lightning transients or system faults can also be measured
using appropriate surge generators, 20-MHz current transformers, and oscilloscopes in the time
domain or network analyzers in the frequency domain.
Potentials are best measured locally at the stressing location (for example, between a remotely
grounded control cable conductor and a nearby, grounded object). The ability to measure the
conversion of common-mode signals to the differential mode is another important advantage of the
simulated fault method because this parameter is also used when establishing electromagnetic
compatibility. Generally, averaging using a shielded external trigger or synchronization signal
contributes to successful measurements.
5-91
Characteristics of a Ground Electrode
5.6.13 Precautions Under Power Lines When Doing Measurements
The following items must be considered when developing work practices and procedures for
performing grounding measurements:
•
Electrodes rise in potential as a result of injected test current.
•
Potential appears on remote leads when test lead breaks away from ground probe.
•
Capacitive coupling between lines at potential and test conductors leads to stray pickup.
•
Magnetic induction between faulted lines and test conductors introduces extra ac, leading to
longitudinal potential differences.
•
Light rain reduces the isolation achieved by shoes, clothes, and gloves.
•
Potential appears on clamp-on CTs as a result of loss of shunt.
•
An internal fault in the test instrument results in 120 V appearing on the case.
•
System faults result in local ground potential rise relative to grounded test leads.
•
Distant lightning or adverse weather increases the probability of system faults.
•
Nearby lightning induces transient overvoltages and ground potential rise.
•
An energized conductor can fall across a test lead during conductor replacement.
5.6.13.1 Electrostatic, Induction, and Stray Ground Current PickUp
For heavily loaded circuits, significant induced voltages can appear between a structure and the
isolated overhead ground wire when using the direct method of electrode resistance
measurement. It is good practice to provide a temporary connection between a structure and an
overhead ground wire that should be lifted using proper procedures. Relatively long test leads
used in the fall-of-potential method can increase the exposure of personnel to the fault-related
voltages appearing on the tested structure.
5.6.13.2 Signal-to-Noise Ratio in Selection of Equipment
Many combinations of instruments and procedures can be used to measure grounding system
impedances or soil resistivity. A selection might be based on the required accuracy, test current
level, 60-Hz noise rejection capability, availability, and convenience.
5-92
Characteristics of a Ground Electrode
Passive sensors such as clip-on current transducers can measure current splits in various
conductors (for example, pole bonds, overhead ground wires, and connections to buried wire or
rods). A pair of 0.24 in. (6-mm) steel rods and a differential input to the potential detector can
measure step potentials, and an alligator clip on a steel structure and single steel rod can measure
touch potentials. Remotely grounded pairs in a communication cable can measure longitudinal
induction. Electromagnetic interference caused by lightning can be measured with a surge source
and an oscilloscope in the time domain or a network analyzer in the frequency domain.
Active instruments with nonlethal energy output include induction-type instruments to measure
soil resistivity and many portable instruments that contain a current source and potential detector,
displaying the ratio in ohms. These include the following:
•
Normal two-terminal ohmmeters
•
Four-terminal ohmmeters with enhanced 60-Hz noise rejection (ground testers)
•
Balancing ohmmeter bridges
•
Hand-cranked ohmmeters
•
The EPRI Smart Meter (pseudo-random noise source)
•
The EPRI Zed-meter (impulse source)
Active instruments with lethal energy output usually consist of separate current sources and
potential detectors configured into a test system. Examples include the following:
•
A 60-Hz transformer, ammeter, and voltmeter
•
A high-power oscillator, frequency-selective ammeter, and voltmeter
•
A staged fault system and oscillograph
•
A network analyzer with an amplifier
•
A portable generator operated at 55 Hz or 65 Hz with a spectrum analyzer
These systems require a power-frequency electrical supply from generators or inverters, which
present an additional set of hazards in field work.
5.6.13.3 Additional Considerations Near Substations
Near substations, ac system fault currents are higher than those at the center of the line because
the fault impedance to the source is lower. Overhead ground wires or continuous buried
counterpoise wires are often installed for a few spans outside stations to help manage this fault
current. These treatments lower the power-frequency ground impedance and reduce the
incidence of lightning outages close to the station. However, the interconnections will also tie the
treated towers closer to the station ground potential rise under fault conditions. This must be
factored in to test plans in order to provide workers with adequate barriers.
5-93
Characteristics of a Ground Electrode
5.6.14 Choosing an Appropriate Method for Soil Resistivity Measurements
The decision to measure tower footing resistances rests on a financial evaluation of the cost to
take the measurements versus the cost savings of installing extensive grounding electrodes only
where they are needed. Examples are the following:
•
For large transformer and generating stations, the cost of a soil resistivity test and customized
grid design can be much less than that of a conservative installation that is safe for all
conditions.
•
The cost of a footing resistance test on a transmission structure is low compared with the
installation of a counterpoise where it is not needed or driven rods where they will not be
effective.
•
Spot tests to establish the integrity of grounding electrodes are probably less costly than
replacing the entire grounding system as corrosion of the buried wires takes its toll.
The effectiveness of grounding measurements can best be shown by a real-life example.
Figure 5-53 shows the results of grounding measurements from a Tennessee Valley Authority
(TVA) 500-kV line. The graph shows that there is a large tower-to-tower variation in the
measured footing resistances, which is typical for many lines. In this example, the resistance
varies from 0.2 Ω at one end to more than 100 Ω at the other. However, only 34 of the 254
towers have values greater than 20 Ω, which is a common upper limit specified by utilities. For
this line, only a limited number of towers must be considered for improvements. (Note the
logarithmic scale on the y axis of Figure 5-53.)
Figure 5-53
Typical Variation in Tower-to-Tower Resistance for TVA 500-kV Line
5-94
Characteristics of a Ground Electrode
Several methods have been introduced to measure the ground electrode resistance of
transmission lines. For easy reference, Table 5-7 provides a summary of the methods described
in this section and their applicability for use on transmission lines.
5-95
Characteristics of a Ground Electrode
Table 5-7
Comparison of Methods for Determining Soil Resistivity
With
Overhead
Ground
Wires
Present?
Multifoot
Towers
Needs
Current
Return
Electrode
Provides
Resistivity
Time
Requirement
Method
Range
Fall of potential
0.01 Ω–20 kΩ
No
Yes
Yes
Yes, needs
special
analysis
Medium
Several measurements are required.
It is difficult to measure continuous
counterpoise.
Oblique probe
0.01 Ω–20 kΩ
No
Yes
Yes
Yes
Medium
Several measurements are required.
It is difficult to measure continuous
counterpoise.
Use of stray
current
Dependent on
level of current
available
Yes
Yes
No
Yes
Medium
Stray current might vary too much to get
a stable measurement.
Stray current might be too low to
measure accurately.
Directional
measurement
1 Ω–1.2 kΩ
Yes
Some
methods
can
No
No
Medium
It might be difficult to find a CT that can
go around the tower footing.
Yes
Yes
No
Yes
High
Line outage is required.
It is difficult to inject current at the
conductor height.
Simulated fault
Comments
High frequency
2 Ω–25 Ω
Yes
Yes
Yes
No
Low
This has limited applicability.
Active transient
injection
3 Ω–3 kΩ
Yes
Yes
Yes
Yes
Low
This is being developed now.
Direct
measurement
Dependent on
level of current
available
No
Yes
No
No
Medium
Measurement is not performed at
ground level.
5-96
6
USEFUL GUIDELINE DOCUMENTS AND RESOURCES
Several standards, guides, and books can be used in combination with this report. This section
provides a short synopsis of some of the most popular guides and standards. See Section 7,
References, for details on the documents listed in this section.
IEEE Standard 80-2000, Safety in AC Substation Grounding
IEEE Standard 80-2000, Guide for Safety in AC Substation Grounding, provides a design
process in 95 equations and 200 pages for ensuring safe grounding practice in ac substation.
Grounding serves a dual purpose: to carry electric currents to ground under normal and fault
conditions without damage or service interruption, and to ensure that a person near the grounded
facility is not exposed to the danger of critical electric shock. IEEE Standard 80-2000 continues
the use of the Dalziel expression (see Section 5.3.2, Step and Touch Potential Around
Transmission Line Towers, in this report) for electrocution current and converts this current to
voltage limits for step, touch, and mesh potentials using hand-to-foot or foot-to-foot body
impedance models. The body impedance is taken as 1000 Ω and the foot resistance is calculated
from the resistivity of the upper soil layer and an equivalent disc of 0.08-m radius.
IEEE Standard 81-1983, Measuring Earth Resistivity
IEEE Standard 81-1983, Guide for Measuring Earth Resistivity, Ground Impedance and Earth
Surface Potentials of a Ground System, and its companion 81.2-1991, Guide for Measurement of
Impedance and Safety Characteristics of Large, Extended or Interconnected Grounding Systems
support the calculations in IEEE 80-2000. IEEE Standard 81-1983 describes the Wenner test for
resistivity and mentions both the fall-of-potential and oblique-probe methods.
IEEE Standard 1048-2003, Protective Grounding of Power Lines
Revised from its 1990 version, IEEE Standard 1048-2003, Guide for Protective Grounding of
Power Lines, provides guidelines for safe protective grounding methods for de-energized
transmission line maintenance. Protective grounding practices from power utilities in North
America are consolidated.
6-1
Useful Guideline Documents and Resources
EPRI Transmission Line Grounding, Volumes 1 and 2 (EL-2699)
The EPRI report Transmission Line Grounding (EL-2699) was an important reference for this
report. In 768 pages, the two-volume report presents substantial theoretical background and more
than 340 design curves based on the Grounding Analysis of Transmission Lines (GATL)
software package. This approach was found to be accurate when compared with measured results
from staged-fault tests at three utilities on 765-kV and 500-kV lines.
Ontario Hydro Transmission and Distribution Grounding Guide (1994)
This 134-page guide in paper format covers general principles; tolerable body withstand levels;
design practices for stations, transmission, and distribution lines; wiring practices for control,
metering, relaying and instrumentation; measurement and test procedures; and references. The
tolerable body withstand equation is that of Dalziel for a 50-kg body weight. A body resistance
of 1000 Ω and a foot resistance under crushed stone of 3000 Ωm are added in station design. The
guide has 84 references.
The transmission design section notes the nonuniform distribution of fault current on a
multigrounded line, and calls for use of overhead ground wires, paralleled by counterpoise, to
provide adequate fault current capability. The footing resistance calculations use the effective
resistivity of two-layer soil. A radius rf from a point at the soil surface above the center of the
electrode to the furthest extremity of the electrode, and an area Af of a hypothetical excavation
that is convex in shape and needed to expose the entire electrode, are used in the basic
calculation of resistance. A four crowfoot counterpoise, shown terminated in ground rods, is
shown as a preferred treatment. Methods and motivations are given for continuous counterpoise
installation, including ac fault current management and near stations with high dc asymmetry.
Bonding to adjacent structures is also mentioned, with aluminum or clad steel being suitable
above ground and copper or copper-clad steel suitable for underground bonds.
A section is devoted to the use of flat or variable-depth gradient control mats for step and touch
potential mitigation. Ancillary issues include switch structures (<50 Ω), isolated overhead
ground wires (provide wire catches should these insulators fail), tap-off structures (use
counterpoise), station-entrance structures (bring overhead ground wire to grade using 600-V
insulated cable, bonded to station ground grid above grade to allow measurement of current
splits), and parallel fences on the transmission right-of-way (select span to keep short-circuit
current less than 5 mA). Underground and submarine transmission lines are designed with
single-point grounding. Polarization cells, connected in parallel with the dc cathodic protection
source, are described. Sheath protectors such as ring gaps or arresters firing at 10–15 kV are
prescribed for cross-bonding and at cable interfaces.
6-2
Useful Guideline Documents and Resources
The transmission line design goal is stated as follows:
To prevent excessive ground potential rise and back-flashovers across line insulators, the
footing resistance should be coordinated with the structure geometry, insulator electrical
strength, and line potential using software, such as the IEEE FLASH program. Otherwise,
a resistance limited to 20 Ω is generally considered necessary to obtain good lightningoutage performance. A lower value might be required for lines with reduced insulation.
The design process uses Wenner measurements, graphical interpretation of apparent resistivity,
and graphical interpretation of effective resistivity. The process is set up for station ground grids
with the advice to use the effective resistivity at a disc radius equal to rf .
Recent Books
Soares Book on Grounding is a typical general-use text containing 288 pages of detail for
grounding of electrical systems. Topics covered include to ground or not to ground, rules for
grounding electrical systems and services, service and main bonding jumpers, grounding
electrodes and conductors, bonding enclosures and equipment, clearing ground faults, isolated
systems, multipoint grounding, ground fault current interrupters, special locations (swimming
pools, barns, and health care facilities), and a small section on systems over 600 V.
The Electric Power Engineering Handbook, Second Edition, 2007 contains in Volume 2 “Power
Systems” some advanced material on the calculation of transmission tower ground electrode
surge response in the section titled “Transmission Line Transients—Grounding.”
Insulation Coordination for Power Systems, 1999 places lightning outages into the overall
context of selecting an appropriate insulation level for transmission system voltages.
Military Handbook 419A
Grounding, Bonding and Shielding for Electronic Equipments and Facilities, Volume 1 of 2:
Basic Theory is a comprehensive 419-page handbook giving some particular advice for
grounding of combustibles and explosives. The handbook is available on the Internet in
electronic format at http://www.jsc.mil/jsce3/emcslsa/stdlib/lib.asp (accessed November 2006).
Software and Training Materials
Several developers of numerical software for evaluation of grounding systems also provide
training material and resources. Typical sources include the following:
•
W. Carman, Safearth Engineered Solutions, a division of Energy Australia
(www.safearth.com)
•
F. Dawalibi, Safe Engineering Services and Technologies Ltd. (www.sestech.com), CDEGS
programs
6-3
Useful Guideline Documents and Resources
Utility Guides
Many EPRI members have indicated that they have formal or informal internal documents that
spell out appropriate grounding practices. These documents are useful sources of information for
benchmarking a utility’s grounding practices. The available guides have been used in developing
this report.
6-4
7
REFERENCES
7.1
Cited References
1. Transmission Line Grounding, Volumes 1 and 2. EPRI, Palo Alto, CA: 1982. EL-2699.
2. R. F. Harrington. Field Computation by Moment Methods. Wiley/IEEE Press, New York
1968 (reprinted 1993).
3. Y. L. Chow and M. M. Yovanovic, “The Shape Factor of the Capacitance of a Conductor.”
Journal of Applied Physics, Vol. 52, December 1982.
4. Handbook for Improving Overhead Transmission Line Lightning Performance. EPRI, Palo
Alto, CA: 2004. 1002019.
5. Survey of Utility Practices for Establishing Equipotential Zones During De-Energized Work.
EPRI, Palo Alto, CA: 2003. 1001752.
6. G. F. Tagg. Earth Resistances. George Newnes, London, England 1964.
7. P. Hoekstra and D. McNeill. “Electromagnetic Probing of Permafrost,” Geophysics, 1973:
pp. 517–526.
8. G. V. Keller and F. C. Frischknecht. Electrical Methods in Geophysical Prospecting.
Pergamon Press, New York 1977.
9. S. Visacro F. and C. M. Portella, “Soil Permittivity and Conductivity Behavior on Frequency
Range of Transient Phenomena in Electric Power Systems.” Proceedings of 5th ISH,
Paper 93.06, August 1987.
10. W. Rudolph and O. Winter, EMV nach VDE 0100. VDE-Schriftenreihe 66. VDE-Verlag
GmbH. Offenbach, Berlin, Germany: 1995.
11. W. J. Scott and A. E. May, Earth Resistivities of Canadian Soils. Canadian Electrical
Association Report 143 T 250, July 1988.
12. R. Miehe, N. Jockwer, T. Rothfuchs, “Qualification of Clay Barriers in Underground
Repository Systems,” EUROSAFE 2000, Cologne, Köln, November 6–7, 2000.
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Tennessee (Large). http://www.state.tn.us/environment/tdg/images/geolog_l.jpg. Accessed
November 2006.
14. TTHOR: A Geographic Screening Tool for Estimating Soil Resistivity in the Tennessee
Valley. Version 1.0B, Public Power Institute, 2004.
7-1
References
15. J. R. Carson, “Wave Propagation in Overhead Wires with Ground Return.” Bell System
Technical Journal, Vol. 5, 1926: pp. 539–554.
16. A. Deri, G. Tevan, A. Semlyen, and A. Castanheira, “The Complex Ground Return Plane—A
Simplified Model for Homogenous and Multi-Layer Earth Return.” IEEE Transactions PAS,
Vol. 100, No. 8, August 1981: p. 3686.
17. Y. L. Chow, J. J. Yang, and K .D. Srivastava, “Grounding Resistance of Buried Electrodes
in Multi-Layer Earth Predicted by Simple Voltage Measurements Along Earth Surface—
A Theoretical Discussion.” IEEE Transactions PWRD, Vol. 10, No. 2, April 1995:
pp. 707–715.
18. A. P. S. Meliopoulos, G. Cokkinides, H. Abdallah, S. Duong, and S. Patel, “A PC Based
Ground Impedance Measurement Instrument.” IEEE Transactions PWRD, Vol. 8, No. 3,
July 1993: pp. 1095–1106.
19. H. B. Dwight, “Calculation of Resistances to Ground.” Electrical Engineering, Vol. 55,
1936: pp.1319–1328.
20. R. Rudenberg, “Grounding Principles and Practice. I—Fundamental Considerations on
Ground Currents.” Electrical Engineering, Vol. 64, January 1945: pp. 1–13.
21. E. D. Sunde, Earth Conduction Effects in Transmission Systems. D. Van Nostrand Company,
New York, NY 1949.
22. J. R. Wait, “Mutual Electromagnetic Coupling of Loops over a Homogeneous Ground.”
Geophysics. 20, 1955: pp. 630–637.
23. Recommendation 832. World Atlas of Ground Conductivities. CCIR Rec. 832.1. International
Telecommunication Union (ITU). Geneva, Switzerland. 1999.
24. E. A. Bardo, K. L. Cummins, and W. A. Brooks, “Lightning Current Parameters Derived
from Lightning Location Systems: What Can We Measure?” Proceedings of 2004 IDLC,
Ref. No. 39, Helsinki, Finland, June 2004.
25. W. A. Chisholm, J. Williamson, S. Burnett, and G. Hodges, “Recent Progress in Design and
Test Methods for Transmission Line Grounding electrodes.” Invited Lecture at VII
International Symposium on Lightning Protection, Curitiba, Brazil (November 17–21, 2003).
26. H. Huang and I. J. Won, “Real-Time Resistivity Sounding Using a Hand-Held Broadband
Electromagnetic Sensor.” Geophysics, Vol. 68, No. 4, July 2003: pp. 1224–1231.
27. Field Testing of the EPRI Zed-Meter: Transient Impedance of Transmission Line Grounds.
EPRI, Palo Alto, CA: 2005. 1010235.
28. Summary of Zed-Meter Field Tests: Transient Impedance of Transmission Line Grounds.
EPRI, Palo Alto, CA: 2006. 1012314.
29. A. C. Liew and M. Darveniza, “Dynamic Model of Impulse Characteristics of Concentrated
Earths.” IEE Proceedings, Vol. 121, No. 2, Institution of Electrical Engineers (IEE),
February 1974: pp. 123–135.
7-2
References
30. W. A. Chisholm and W. Janischewskyj, “Lightning Surge Response of Grounding
Electrodes.” IEEE Transactions PWRD, Vol. 4, No. 2, 1989: pp. 1329–1337.
31. W. A. Chisholm, “Transmission System Transients—Grounding,” The Electric Power
Engineering Handbook. L. L. Grigsby, ed., Section 10.7, CRC Press, Boca Raton, FL 2001.
32. E. E. Oettle, “A New General Estimation Curve for Predicting the Impulse Impedance
of Concentrated Earth Electrodes.” IEEE Transactions PWRD, Vol. 3, October 1988:
pp. 2020–2029.
33. IEEE 80-2000. IEEE Guide for Safety in AC Substation Grounding. 2000.
34. Ontario Hydro Transmission and Distribution Grounding Guide. Ontario Hydro. 1994.
35. Transmission Line Reference Book 345 kV and Above—Second Edition, Revised. EPRI,
Palo Alto, CA: 1982. EL-2500.
36. L. V. Bewley. Traveling Waves on Transmission Systems, Second Edition. Dover, New York,
NY 1933, reprinted in 1951 and 1963.
37. L. V. Bewley, J. H. Hagenguth, “Fixing Counterpoise Length: Best results when length in
thousands of feet is one-sixth of wave-front time in microseconds,” AIEE Lightning
Reference Book 1918-1935, American Institute of Electrical Engineers, New York 1937,
pp. 1447–1450.
38. High Current Impulse Testing of Full-Scale Grounding Electrodes. EPRI, Palo Alto, CA:
2002. 1006866.
39. J. L. Bermudez. “Lightning currents and electromagnetic fields associated with return strokes
to elevated strike objects.” École Polytechnique Fédérale de Lausanne, PhD Thesis No. 2741.
2003. http://library.epfl.ch/theses/?nr=2741. Accessed November 2006.
40. Y. Baba and V.A. Rakov, “On the Interpretation of Ground Reflections Observed in SmallScale Experiments Simulating Lightning Strikes to Towers,” IEEE Transactions EMC,
Vol. 47 No.3, August 2005, pp 533–542.
41. Tower Grounding and Soil Ionization Report. EPRI, Palo Alto, CA: 2002. 1001908.
42. A. V. Korsunev, “Application on the Theory of Similarity to Calculation of Impulse
Characteristics of Concentrated Electrodes.” Elektrichestvo, No. 5. 1958: pp. 31–35.
43. H.G. Ufer, IEEE Conference Paper CP-61-978, 1961.
44. Y. Morinaga, M. Kamiji, S. Imoto, S. Ogawa, K. Iwamori, “Transmission Tower Foundation
in Japan,” IEEE Publication 0-7803-7525-4, 2002, pp 2162–2165.
45. H. M. Jennings, J. J. Thomas, D. Rothstein, and J. J. Chen. “Cements as Porous Materials,”
and “Cement Paste as a Porous Material,” Chapter 6.11 in Handbook of Porous Solids, edited
by F. Schuth, K. Sing, J. Weitkamp. H. M. Jennings, J. J. Thomas, J. J. Chen, and D.
Rothstein. Wiley-VCH, 5 2971-3028, New York, NY 2002.
46. IEEE 81-1991. IEEE Guide for Measurement of Impedance and Safety Characteristics of
Large, Extended or Interconnected Grounding Systems. Volume 2, 1991.
7-3
References
47. P. R. Pillai and E. P. Dick, “A Review on Testing and Evaluating Substation Grounding
Systems.” IEEE Transactions PWRD, Vol. 7, No. 1, January 1992: p. 53.
48. IEEE 1243-1997. IEEE Guide for Improving the Lightning Performance of Transmission
Lines. 1997.
49. W. A. Chisholm, “Technique for Transient Stray Voltage Measurements in Livestock
Barns.” Final Report for CEA, Contract 178 D 885, May 1996.
50. IEC 60479. Effects of Current on Human Beings and Livestock—Part 1: General Aspects,
1994; Part 2 – Special Aspects, 1987. International Electrotechnical Commission, Geneva,
Switzerland.
51. C. F. Dalziel and R. W. Lee, “Re-Evaluation of Lethal Electric Currents,” IEEE
Transactions. IGA Vol. 4, No. 5, October 1968: p. 467.
52. G. Beigelmeier, “New Knowledge on the Impedance of the Human Body,” pp. 115–132,
Electric Shock Safety Criteria. Pergamon, New York 1985.
53. J. P. Reilly. Applied Bioelectricity: From Electrical Stimulation to Electropathology.
Springer-Verlag, New York 1998.
54. National Electric Safety Code, American National Standard C2, 1997.
55. Power System and Railroad Electromagnetic Compatibility Handbook: First Edition. EPRI,
Palo Alto, CA; Oncor Energy Delivery Systems, Dallas, TX; The National Grid Transco
Company, Warwick, UK; Association of American Railroads (AAR), Washington, DC; and
American Railway Engineering and Maintenance-of-Way (AREMA), Landover, MD: 2004.
1005572.
56. Corrosion of Metals in Concrete, Report 222R-96. American Concrete Institute, ACI
Committee 222 222R-1, May 1996.
57. National Electrical Code. NFPA 70, National Fire Protection Association, Inc., Quincy, MA:
1999.
58. Cigré Working Group 36.02. “Guide on the influence of high voltage ac power systems on
metallic pipelines”, Cigré brochure 95, 1995.
7.2
Other References
7.2.1 EPRI Reports
The EPRI Zed-Meter: A New Technique to Evaluate Transmission Line Grounds. EPRI,
Palo Alto, CA: 2004. 1008734.
7-4
References
7.2.2 International Standards
IEC 60621-2. Electrical Installations for Outdoor Sites under Heavy Conditions - General
Protection Requirements. International Electrotechnical Commission, Geneva, Switzerland.
1987.
IEEE 10-1972. IEEE Standard Dictionary of Electrical & Electronic Terms. 1972.
IEEE 367-1996. IEEE Recommended Practice for Determining the Electric Power Station
Ground Potential Rise and Induced Voltage From a Power Fault. 1996 (Revised 2002).
IEEE 487-1992. IEEE Recommended Practice for the Protection of Wire Line Communication
Facilities Serving Electric Power Stations. 1992.
IEEE 665-1987. IEEE Guide for Generating Station Grounding. 1987.
IEEE 837-1989. IEEE Standard for Qualifying Permanent Connections Used in Substation
Grounding. 1989.
IEEE 1048-2003. IEEE Guide to the Protective Grounding of Transmission Lines. 2003.
IEEE 1410-2004. IEEE Guide for Improving the Lightning Performance of Electric Power
Distribution Lines. 2004.
National Electrical Code. NFPA 70, National Fire Protection Association, Inc., Quincy, MA:
1999.
7.2.3 Books
American Water Works Association. External Corrosion: Introduction to Chemistry and
Control. Denver, CO 1987.
M. Darveniza. Electrical Properties of Wood and Line Design. University of Queensland Press,
Brisbane, Australia 1978.
R. H. Golde, ed. Lightning. Academic Press, London, England 1977.
L. L. Grigsby, ed. The Electric Power Engineering Handbook. Second Edition, Vol. 2 (Power
Systems) CRC Press, Boca Raton, FL 2007.
A. R. Hileman. Insulation Coordination for Power Systems. Marcel Dekker, New York 1999.
S. Meliopoulous. Power System Grounding & Transients–An Introduction. M. Dekker, New
York 1988.
H. W. Ott. Noise Reduction Techniques in Electronic Systems, 2nd Edition. John Wiley & Son.
Hoboken, NJ 1988.
7-5
References
J. P. Simmons. Soares Book on Grounding, 7th Edition. International Association of Electrical
Inspectors, Richardson, TX 1999.
U.S. Environmental Protection Agency. Use of Airborne, Surface and Borehole Geophysical
Techniques at Contaminated Site: A Reference Guide. Office of Research & Development,
EPA/625/R-92/007, 1993.
J. R. Wait. Electromagnetic Waves in Stratified Media. Pergamon Press, Oxford, England 1970.
Westinghouse. Electrical Transmission and Distribution Reference Book. Trafford, PA 1964.
7.2.4 Technical Papers
K. O. Abledo and D. N. Laird, “Measurement of Substation Resistivity,” IEEE Transactions
PWRD. Vol. 7, No. 1, January 1992: p. 295.
Y. L. Chow and K. D. Srivastava, “Non-Uniform Electric Field Induced Voltage Calculations.”
Final Report for Canadian Electrical Association, Contract 117 T 317, August 1984.
F. Dawalibi and D. Mukhedkar, “Ground Electrode Resistance Measurements in Non-Uniform
Soils.” IEEE Transactions PAS, Vol. 93, No. 1, January 1974: p. 109.
E. P. Dick, C. C. Erven, and S. M. Harvey, “Grounding System Tests for Analysis of FaultInduced Voltages on Communication Cables.” IEEE Transactions PAS, Vol. 98, No. 6,
November 1979: p. 2115.
A. Elek, “Variations of Foot-Resistance on Crushed Stone.” Ontario Hydro Research Report,
December 1960: p. 6.
J. Endrenyi, “Analysis of Transmission Tower Potentials During Ground Faults.” IEEE
Transactions PAS, Vol. 86, No. 10, October 1967: p. 1274.
A. Geri, “Behavior of Grounding Systems Excited by High Impulse Currents, The Model and Its
Validation.” IEEE Transactions PWR, Vol. 14, No. 3, July 1999: pp. 1008–1017.
IEEE Working Group on Lightning Performance of Transmission Lines, “A Simplified Method
for Estimating the Lightning Performance of Transmission Lines.” IEEE Transactions PAS,
Vol. 104, No.4, April 1985: p. 919.
H. Jinliang et al., “Laboratory Investigations of Impulse Characteristics of Transmission Tower
Grounding Devices.” IEEE Transactions PWRD, Vol. 18, No. 3, July 2003: pp. 994–1001.
D. N. Laird, “Tolerable Touch and Step Voltages.” Practical Applications of ANSI/IEEE
Standard 80-1986, IEEE Power Engineering Society Tutorial 86 EH0253-50PWR, 1986.
7-6
References
W. W. Loucks and W. A. Lemire, “Transmission and Distribution Grounding in the HydroElectric Power Commission of Ontario.” AIEE Transactions, Vol. 70, 1951: p. 1493.
T. McComb, E. A. Cherney, H. Linck, and W. Janischewskyj, “Preliminary Measurements of
Lightning Flashes to the CN Tower in Toronto, Canada.” Canadian Electrical Engineering
Journal, Vol. 5. 1980: pp. 3–9.
A. P. S. Meliopoulos, S. Patel, and G. J. Cokkinides, “A New Method and Instrument for Touch
and Step Voltage Measurements.” IEEE Transactions PWRD, Vol. 9, No. 4, October 1994:
pp. 1850–1860.
A. P. S. Meliopoulos, F. Xia, E. B. Joy, and G. J. Cokkinides, “An Advanced Computer Model
for Grounding System Analysis.” IEEE Transactions PWRD, Vol. 8, No. 1, January 1993:
pp. 13–23.
Y. Morinaga, M. Kamiji, S. Imoto, S. Ogawa, and K. Iwamori, “Transmission Tower Foundation
in Japan.” IEEE-PES APM Conference Proceedings, 2003.
A. M. Mousa, “The Soil Ionization Gradient Associated with Discharge of High Currents into
Concentrated Electrodes.” IEEE Transactions PWRD, Vol. 9, July 1994: pp. 1669–1677.
P. R. Pillai, “Field Measurements of Soil Resistivity.” Ontario Hydro Research Division Report
90-148-K, June 1990.
E. D. Sunde, “Surge Characteristics of a Buried Wire.” AIEE Transactions, Vol. 59, 1940:
pp. 987–991.
B. Thapar, V. Gerez, and P. Emmanuel, “Ground Resistance of the Foot in Substation Yard.”
IEEE Transactions PWRD, Vol. 8, No.1, January 1993: p. 1.
R. Velaquez, “Analytical Modeling of Grounding Electrode Transient Behavior.” IEEE
Transactions PAS, Vol. 103, November 1984: pp. 1314–1322.
R. Verma, “Impulse Impedance of Buried Ground Wire.” IEEE Transactions PAS, Vol. 99,
September 1980: pp. 2000–2007.
S. Visacro F., Performance of Transmission Line Grounding Electrodes for Lightning Currents.
CIGRE Working Group 33.01 Task Force 33.01.04 Report.
G. Weitzenfeld, “Power System Ground Fault Current Distribution Using the Double-Sided
Elimination Method.” IEEE Transactions PS, Vol. 1, No. 1, February 1986: p. 17.
7-7
References
7.2.5 U.S. Military Publications
Grounding, Bonding and Shielding for Electronic Equipments and Facilities, Volume 1 of 2:
Basic Theory. MIL-HDBK-419A, December 1987.
Available from http://www.jsc.mil/jsce3/emcslsa/stdlib/lib.asp. Accessed November 2006.
Grounding Systems. Air Force Instruction 32-1065 1, October 1998.
Available from http://www.e-publishing.af.mil/afpubs.asp. Accessed November 2006.
7-8
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