Dawalibi Earth Resistivity PDF
Dawalibi Earth Resistivity PDF
Dawalibi Earth Resistivity PDF
2, February 1984
ABSTRACT In both cases, the overhead network and the earth path,
including buried metallic conductors such as counterpoises
Earth resistivity measurement interpretation techniques and ground electrodes, are part of the circuit in which the
developed as part of a major EPRI research project on surge or fault current circulates. Generally, an analysis of
transmission line grounding are described and discussed. The these abnormal conditions is based on a reasonably accurate
interpretation techniques include graphical curve matching representation of the overhead circuit. The earth path,
and an advanced computer program (RESIST). The curve however, is usually modelled as a perfect conductor or in a
matching technique requires a set of theoretical Master Curves very simplified form. This seldom leads to realistic results.
with which a field curve can be compared directly. Program The apparent inconsistency of these engineering approaches
RESIST is based on the analytical methods used in a more can be explained by the mathematical difficulties involved
elaborate computer program which has been in operation for in the solution of three dimensional current flow in earth.
several years. For an electrode spacing of 2.5 meters or Often, the wide variations observed in the characteristics of
greater, satisfactory agreement is obtained between measured earth, generally described as a semi-infinite nonhomogeneous
and computed results using both interpretation techniques. media, are used as justification for not pursuing detailed
modelling of the earth path for fault currents.
Thirty years ago, the lack of suitable high-speed digital
computers was a serious obstacle to accurate modelling of
the earth. Now, there are no computational limitations to
1.0 INTRODUCTION the development of an accurate model of the structure of
the earth. Recently published analytical works on power
This paper describes earth resistivity measurement system grounding describe accurate, computer based,
interpretation techniques developed as part of a major research computational techniques for the design of grounding systems.
project on transmission line grounding. The Final Report [1l
includes a comprehensive description of advanced theories
and techniques pertaining to the analysis, design and
measurement of transmission line grounding systems with a Large variations in earth resistivity need not be an obstacle
particular emphasis on safety and mitigation techniques to to the development of detailed earth structure models.
improve safety around exposed structures. Several analytical Relatively simple equivalent earth models can effectively be
methods described in the report are new or were not available used to accurately predict transmission line grounding
previously in the open literature. This is the case of the performance as evidenced by the field measurements described
resistivity interpretation method described in the appendix in reference [1]. Finally, the earth structure at any particular
of this paper. The research project was sponsored by the site can be accurately determined by a suitable selection of
Electric Power Research Institute (EPRI). the method and test equipment.
The design of a power system requires that normal and
abnormal conditions be considered in order to correctly 1.1 DISCUSSION OF MODELLING PROBLEM
determine the design requirements and characteristics of the
installed power equipment. Of the abnormal conditions which The development of a mathematical model to represent the
can occur on a power network the two most frequent are: electrical properties of earth can be a formidable task because
of the widely nonuniform characteristics of earth.
D Lightning strokes
Fortunately for transmission line grounding purposes, the earth
o Phase to ground faults can be reasonably approximated by a two-layered soil
structure. This soil structure is characterized by the layer
resistivities P1, P2 and the upper layer thickness h. The
* F. Dawalibi is the principal author of the EPRI report
lower layer is considered infinite. In some cases the thickness
of the upper layer is large enough so as the earth model
referenced in this paper C. Blattner served as an
.
may be considered fairly uniform.
industry advisor on the EPRI Task Force.
The variables P1, P2 and h are generally determined by
interpreting the apparent resistivity values measured using
the Wenner (or four probe) array.
Unlike most engineering problems, interpretation of earth
83 SM 456-1 A paper recommended and approved resistivity measurements is an "inverse" problem; i.e., from
by the IEEE Transmission and Distribution Committee the electrical response to impressed current at specific
of the IEEE Power Engineering Society for presenta- locations on the earth surface, the electrical properties of
tion at the IEEE/PES 1983 Summer Meeting, the conducting media (earth) are to be determined. In contrast,
Los Angeles, California, July 17-22, 1983. Manu- conventional electrostatic problems determine the electrical
script submitted January 10, 1983; made available response or the excitation current sources, based on the
lor printing May 13, 1983. known properties of the conducting material. These are known
0018-9510/84/0002-0374$01.00 ( 1984 IEEE
375
as the Laplace and Diriclet problems. Obviously, the "inverse" FOUR TERMINAL
problem, where the physical constants of the material are TEST SET
unknown, presents more difficulties than those problems where
the physical constants of the material are known functions
of position.
Moreover, the number of parameters required to represent a
model of the earth structure is usually so great that it is
difficult to choose initial values to these parameters and
have a computer algorithm converge to an acceptable solution
within a practical time frame. Consequently, the selection
of initial values becomes a fundamental task in the
CURRENT
interpretation process. POTENT AL PROBE
PROBES
I
close to the surface is also a typical cause of sudden changes
(1 -2) in apparent earth resistivity, as shown in Figure 1.5.
K(1+K )
[4(s
[4 (s inw-h/a 2cos2~]21
nub-h/a))2+cos2]2
where,
Pa = the apparent resistivity as measured by the Wenner
Method.
a = separation distance between current and potential L/)
probes.
P1 = resistivity of region on one side of vertical fault
line.
cL
a-
P2 = resistivity of region on opposite side of vertical
fault line.
P I PE SPAC NG a
h = distance from center of array direction and the
line of fault (See Figure 1.4).
ci = angle of array direction to line of fault (See
Figure 1.4). Figure 1.5 Presence of Buried Metallic Structures
377
The method used for interpreting the measurements can be measurements taken by an experienced crew under the best
grouped into two simplified categories: of conditions, will never give a perfect match with analytical
results computed from the optimum earth model derived from
o Empirical interpretation the measurement data.
o Analytical interpretation
2.0 LOGARITHMIC CURVE MATCHING
Analytical interpretation is, in theory, independent of the
person conducting the interpretation. In contrast, the results The apparent resistivity functions (equations 1-2 and 1-3)
of an empirical interpretation are significantly influenced by may be written in terms of the dimensionless ratios K, Pa'P1
the background and experience of the interpreter. and h/a:
It is preferable to use a combination of both approaches for Horizontal Two-Layer Earth
maximum accuracy and a minimum of uncertainty. For 00
)o
a
h
a
h -to -
PA
D
r
/10'
VERTICAL FAULT/
-.1
-.5
-.7
...
.... . . . . -. . . . .~~~~~~~~~~~~1.0
-.9 .
_2 _5 _1 .5 _1
-.99
M (x ,y)
MINIMUM Figure 4.3 Computation Results
Figure 3.1 The Method of Steepest-Descent A comparison between the actual measured resistivities and
the calculated apparent resistivities based on the two
layer earth structure determined by RESIST is shown in the
4.0 A TYPICAL EXAMPLE computer printout in Figure 4.4.
The apparent soil resistivity at the site of a power system SPACING CALCULATED APPARENT MEASURED APPARENT DISCREPANCY
grounding installation was measured using the Wenner method. (METERS) RESISTIVITY(OHMS-M) RESISTIVITY(DHMS-M) (PERCENT)
The results of the measurements are given in Table 4.1.
2.j00 3271.4372 320.0000 2.32
5.000 233.8807 245.0000 -4,54
PROBE APPARENT 7,500 187.4388 182 .0000 2.99
SPACING (i) RESISTIVITY (Q-m) 10.000 168.0307 162,0000 3. 72
2.5
5.0
320
245
12.500
15,000
159.5344
155 3505
168.0000
152.0000 iO
-5,04
i-220
7.5 182
10.0 162
12.5 168
15.0 152 Figure 4.4 Comparison of Resistivities
RESIST CURVES Mr. J. Dunlap, the EPRI Project Manager, and the Advisory
-------- ---------- Task Force members; Messrs. T. E. Bethke, A. C. Pfitzer,
G. B. Niles, and R. S. Baishiki, are also acknowleged for
Top Layer Resistivity 383 390 their assistance and guidance on this EPRI project.
Bottom Layer Resistivity 147.7 148-167
Top Layer Thickness 2.56 m 2.5 m
R EERENCES
Table 4.2 Comparison of Interpretation Results
1- F. Dawalibi, "Transmission Line Grounding", EPRI Research
Project 1494-1, Final Report EL 2699, October 1982.
2- F. Wenner, "A Method of measuring Resistivity", National
Bureau of Standards, Scientific Paper 12, NO. S-258, 1916,
P. p. 499.
P
3- G. F. Tagg, "Earth Resistances", George Newnes Ltd.,
London 1964 (book).
4- E. D. Sunde, "Earth Conduction Effects in
Transmission Systems", Dover Publications, New York, 1968
(book).
5- F. Dawalibi, D. Mukhedkar, "Influence of Ground Rods
on CGrounding Grids", IEEE Transactions on PAS, Vol. PAS-98,
No. 6, November/December 1979, pp. 2089-2098.
6- S. Stefanesco, C. & M. Schlumberger, "Sur la Distribution
Electrique Potentielle Autour d'une Prise de Terre Ponctuelle
dans un Terrain a Couches Horizontales Homogenes et
Isotropes", Journal de Physique et Radium, Vol. 1, Serie VII,
No. 4, 1930, pp. 132-140.
APPENDIX or
Let PO(aj), j = 1, n be the series of apparent resistivity values F-T p1 + [ a~
a) 2
12]
as measured at a given site by the Wenner method for n At =
IT +
(4)
different inter-electrode spacings aj. pil K~ rLh J
The sought for minimum is obtained when AW = 0 or practically
Let P (aj), j = 1, n be the calculated apparent resistivity when:
values, based on a two-layer earth model at the same spacings
aj used during the measurements.
IA < E (5)
The interpretation task consists of finding the most suitable where E is the desired accuracy.
earth model for which the difference between the set of
measured and calculated values, according to certain criteria, The main steps in the steepest-descent algorithm are
is a minimum. In theory any criterion can be used (e.g., sum therefore:
of the absolute value of the differences). In practice, the
classical least-square criterion is preferred. 1- Estimate initial values of P1, K and h (i.e., Pl
KO, h)
Let + ( P1, K, h) be the square error function defined as:
2- Calculate a suitable value of T
n~p(aj) _p (aj ) l2
')(Pj, K, h) = E[- )P(a ) J (1) 3- Determine AP1,AK and Ah
4- Estimate a new starting point:
The best fit is obtained when p is minimum. The values of
Pi, K, h which lead to this minimum are determined by the Pi 0) = (i-i) + AP
steepest-descent algorithm.
The gradient vector is defined as: K(i) K(1-i) + AK
V= X h( = h i-) + Ah
ap1 ah aK 5- Calculate Ail and compare it with a:
Each component of the potential vector is determined from
Equation 1. Thus: a- if Ai < a , the fit is completed.
n2n a
)P (2a)
b- if IAyI > E , continue the process at step 2
(or step 3 if T is maintained constant).
apJ
Ah = -T
(3c)
4 nKnl (A-: -
B) (8)
Where T is a positive value expressed in p.u. of V), suitably n=l
selected to generate a smooth search for the m-ninimum. The
above changes cause a small variation A in the error function where
11:
A = 1 + (2nh/a) 2
AWl= al APi + a* AK + a'p Ah
api 3K a~~h (9)
B = A + 3
382
Discussion In his closure will the author include equations for the Vertical Fault
case similar to Eqs. (6), (7) and (8) of the Appendix. Will his computer
Eldon J. Rogers, (Bonneville Power Adm., Vancouver, WA): It would technicque be adaptable to the case of the rod electrode penetrating
appear the author's computer technique for resolving Wenner test earth two-layer earth?
resistivity into two-component earth would start with parameters deter- The authors are to be congratulated for reviewing the logarithmic
mined from the logarithmic curve matching. I have used Roman's loga- curve matching technique and developing a computer program to fit the
rithmic curve fitting method for two-layer earth, described by the two-layer earth model to the earth resistivity survey.
authors, to analyze earth resistivity data measured for the substation
grid sit (Refer to [3], Ch. 3, pp. 72). Generally, Wenner resistivity sur- Manuscript received August 2, 1983.
vey data fall into several categories: The data are obviously due to two-
layer earth and logarithmic comparison is easily made; the data appear F. Dawalibi and C. J. Blattner: We thank Mr. Rogers for his discussion
to be two-layer but logarithmic fit is inaccurate; or, it is evident the data and pertinent comments.
are 3- or 4-layer earth. As most of the substation data fall in the last two The initial parameters required by the steepest-descent technique
categories, the author's computer technique could be useful to deter- could be determined from the logarithmic curve matching method. Mr.
mine their two-layer equivalent. Even for towers, earth resistivity varia- Rogers points out rightfully that our technique is particularly useful to
tions may require more than one Wenner test location to adequately determine an equivalent two-layer model for complex soil structures.
describe the earth volume. When soil is practically a two-layer configuration, then the logarithmic
One important aspect of resistivity survey is determining the earth's curve matching method provides accurate solutions.
resistivity near the surface. The earth's resistivity near the surface can Program RESIST is designed to give the best two-layer fit based on
be calculated from the measured resistance (Rn) of each Wenner test the Wenner test values.
probe (Pn = YY L Rn/(In8L/D- 1) ). For a typical test probe length
(L) of 0.3m, earth resistivity samples are obtained of an earth cylinder There is no selection of an initial value of the gradient vector V. The
0.5m in depth and 0.6m diameter. The composite earth surface layer components of this vector are defined by Eq. 2 of the paper. Guidance
resistivity is found by the parallel combination of all sample volumes for the selection of the accuracy is included in [1] (see p. B-3).
00 Eq. 4 has a correct numerator, (it was corrected after the review by
[Pi = n/I (1/Pn) ). the Technical Committee).
I
We are grateful to Mr. Rogers for reporting the typo errors in Eq. 7
and 8. It seems that these mistypes appeared a few years ago when the
When the composite Wenner test data for a grounding electrode site first author was involved in the revision of IEEE Guide 81. Unfortu-
differ significantly from the two-layer earth model (for example, data nately, the mistypes were reintroduced in this paper and also in Ref. 1.
from three-and four-layer earth), will the author's RESIST program Fortunately however, the code in program RESIST is correct.
determine the best two-layer fit? How are the p.u. value of V, "r", and The case of vertical layers requires that the direction of the traverse
the desired accuracy "e" Eq.(5) selected? It would appear their selec- and the location of each probe of the array be known relative to the ver-
tion depends on how well the data fit the theoretical model. Would the tical fault plane (interface betweeen layers). This introduces several
author please discuss? What are the theoretical considerations which possibilities with 3 equations similar to Eqs. 6, 7 and 8. Although we
justify the assumptions used to form Eqs. 3a, 3b, 3c shown in the Ap- have not yet derived all these new equations., we believe that it is a
pendix? There appear to be several typo errors in the Appendix: relatively easy task (see p. 4-26 of [1]).
Eq. (4): First term has incorrect numerator. The rod electrode penetrating two-layer earth requires major
Eq. (7): Should have a negative sign in front of 16. modifications to the computer algorithm.
a2, in the denominator
n2, between summation symbol and kn Manuscript received September 26, 1983.
Eq. (8): Should have P1 between 4 and summation symbol