Grounding Resistance 3

1130

IEEE Transactions on Power Apparatus and Systems, Vol. PAS-98, N;o. 3 May/June 1979 COMPUTER SIMULATION FOR DETERMINING STEP AND TOUCH POTENTIALS RESULTING FROM FAULTS OR OPEN NEUTRALS IN URD CABLE H. N. Nunnally, Member IEEE E. B. Joy, Member IEEE

R. P. Webb, Member IEEE A. P. Meliopoulos, Member IEEE

Georgia Institute of Technology School of Electrical Engineering Atlanta, Georgia 30332 Abstract - A computer simulation is described which enables the determination of voltages on the surface and within the earth caused by: (1) a phase-toneutral fault, (2) a fault with simultaneous open neutrals on either side, and (3) an open neutral. The buried cable and associated ground rods are modeled as a set of interconnected cylindrical segments situated in a three-dimensional, two-layered earth model. Simultaneous solution of the interconnected segment circuit and electromagnetostatic equations yields the desired solution. Output from the computer simulation is shown to match closely the data from field tests of faulted cables and other results from the literature. Work supported by EPRI contract RP797-1. INTRODUCTION

The maintenance of acceptable step and touch potentials in the presence of unusual operating conditions with underground distribution systems is a vital concern in the utility industry today. These cables, usually containing a concentr-ic neutral, are subject to faults from accidental dig-ins or to opens from corrosion of the neutral conductors. Such conditions produce touch and step potentials on the earth's surface defined in Figure 1. In this figure, VRG is the as voltage (referenced to remote ground) at the point of fault; VT is the "touch potential" difference between the fault point and the earth surface above the cable; and VSl, VS2, and VS3 are step potentials. A number of field testing programs designed to these potentials under fault conditions have been conducted [1-4], the most recent being that performed at Franksville, Wisconsin under EPRI contract RP-671 [5]. However, results from each of these

measure

L--3' Vs2

6'

Vs3

-

3'

are valid only for the particular cables and circuits used and the soil in which the tested cables were buried. Particular numerical results could be differentif the cable construction or soil conductivity and geometry were changed. It is impossible to field test all possible combinations of cable and soil conductivity, and even if thiswere r,ossible, it is not clear how one might extrapolate the test data to predict results in actual distribution systems under fault.

programs

This paper describes a computer program, entitled BCAB, which calculates touch and step voltages produced when aburied cable undergoes a fault or open neutral or a combination fault and open neutral. The program exists in two versions, one for execution on a large computer, and another which can be run with a suitable minicomputer. The cable and any associated ground rods are represented as a set of interconnected segments, each of which is described by certain electrical and geometric parameters. By suitably selecting the parameters, a given segment may simulate a length of ground rod or a length of cable with either a bare neutral, an insulated neutral, or a neutral covered with semiconducting material. Other parameter selections cause an open or shorted length of cable to be simulated. The surrounding soil is represented as two homogeneous layers, the top layer having variable thickness. Thus, the program can predict results which would be expected in any geographical region for which a soil model is known, for a large class of cable/soil combinations. The program, written primarily in support of the RP-671 test program, includes the capability of including, in detail, the complete circuit utilized in those experiments, but with suitable values inserted for circuit parameters it can simulate faults and opens in a general distribution system.

V5

THE COMPUTER PROGRAM General Description

V6

V12\

)VT

3/ VG/

>

Faulted Cable

Remote ground

VRG

Figure 1. Definition of Fault, touch

and step potentials.

F 78 694-2. A paper recamurnded and approved by the IEEE Insulated Conductors Cammittee of the IEEE Power Engineering Society for presentation at the IEEE PES Suilmr Meeting, Los Angeles, CA, July 1621, 1978. Manuscript submitted January 27, 1978; made available for printing April 25, 1978.

The analysis procedure used in the program is based modeling a short length (typically less than 50 meters) of the buried cable neutral and jacket and any ground rods as a set of 22 interconnected segments located in the earth, with the earth itself represented by two homogeneous layers of known conductivity. Because of the short lengths simulated, an electrostatic analysis is sufficient in solving for the segment voltThe segments are connected to ages and currents [6]. an external driving circuit described later. Each segment is of known length and outside diameter and has a known position in the problem coordinate system. on

Figure 2 depicts a typical segment cross-section as modeled. This shows the neutral conductor is treated as a uniform shell of conductor. The segment parameters needed for the program are the segment outer diameter, DIA, the jacket thickness TJ, the jacket conductivity, Phase conductor parameters are aj, and the length L. not needed, since they are incorporated into the impedance of the source driving the point of fault. Based on

0018-9510/79/0500-1130$00.75

1979 IEEE

Authorized licensed use limited to: NATIONAL INSTITUTE OF TECHNOLOGY JAMSHEDPUR. Downloaded on September 22, 2009 at 08:21 from IEEE Xplore. Restrictions apply.

1131 ZHI

Phase Conductor

Jacket, Conductivity aj

Shell representation of neutral

Figure 3. Circuit segment model

Figure 2. Cable segment cross-section these parameters, the electrical behavior of the segment is represented by a longitudinal impedance (assumed negligible for the short cable segments normally modeled), anda radial impedance, ZR' which defines the resistance to radial current flowing from the neutral into the earth. The expression for ZR is 1

R

2irLaJ

l

DIA

DIA-2

TJ

Note that by properly selecting aj and Tj, the segment fact represent a portion of bare or jacketed cable. Also, a section with open neutral is modeled by setting very large values for ZR and for longitudinal impedance.

may in

Ground rods and arcs are represented by segments If no rods are desired in with zero radial impedance. the simulation, the radial impedance of rod segments is simply set large enough to "insulate" the rods from the problem. The program provides simulations ting conditions. These are: Condition 1

-

A single

Condition 2

-

A

for three

opera-

phase-to-neutral fault

single phase-to-neutral fault accompanied by simultaneous open neutrals to either side of the fault

Condition 3

-

A single open neutral

For each of these, an appropriate arrangement of segments has been defined to simulate the condition. These include load impedances ZLOADl and ZLOAD2 attached at the cable ends to allow the program to incorporate an

external circuit. For the first two conditions, the circuit' segment model solved is shown in Figure 3. Here, a length, LC, of cable is buriedata depth dc. The surface soil layer is of depth D and conductivity a2, while the lower (semi-infinite) layer has conductivity al. Bus voltage, VS, is connected to the point of fault, with potential Fault current VRG, through a high-side impedance ZHI IFT flows to the fault and returns to the supply bus in two components: I2, the neutral return current (through low-side impedance ZLO) and IG, the current entering the earth directly from cable and ground segments (indicated

for conditions 1 and 2.

by the arrows in the figure) and returning through Neutral voltage is VN. station ground impedance ZSG. As indicated, two ground rods may also be included in simulation. For simulationsof the RP-671 field tests, the circuit shown in Figure 3 simulates all significant elements of the circuit. That is, the buried test cables were of finite length and attached to a specified supply bus with composed of the bus impedance, a a high-side impedance high-side current limiting impedance and the supply cable Also, the low-side consisted of the return impedance. and a low-side current-limiting impecable impedance dance. Some tests included two ground rods, while others included none. Also, a few tests incorporated an additional "system ground" consisting of a group of ground rods installed at a location removed from the testing area. This is not shown in Figure 3, but the program treats it as an additional impedance connected between the point at which VN is defined and remote ground. In addition, BCAB treats generalized distribution circuits with physical dimensions much greater than those associated with a field test. For such simulations, the approach is to simulate in detail only a finite length, Lc, of the cable near the fault. The region around this The portion of section is called the "Problem Space." the system outside the problem space is represented as This procedure the lumped elements ZHI, ZLO and ZSG' results in some errors near theproblem space boundaries, but if the space is large, the voltages predicted near the fault itself will be accurate.

It is noteworthy that accurate representation of the system external to the problem space is necessary only for the computation of the absolute fault voltage VRG. Step and touch potentials normalized to at-fault voltage are-almost independent of external system parameters. Thus, absolute voltages calculated from a given ZHI and ZLO can be adjusted to acount for expected tolerances in those values.

In a general utility circuit, the system impedances will normally be known in terms of positive- and zerosequence impedances. Therefore, BCAB sets

Z

HI

=Z

POS

ZERO LO where

Z

PoS

and Z

ZERO

POS

3 are the total

positive and

Authorized licensed use limited to: NATIONAL INSTITUTE OF TECHNOLOGY JAMSHEDPUR. Downloaded on September 22, 2009 at 08:21 from IEEE Xplore. Restrictions apply.

zero-

1132 sequence impedances from the reference bus to the point of fault. These may be expressed as the sum of the impedances of the various distribution links between reference bus and fault point. The general procedure for solving Condition 1 and Condition 2 problems is now outlined. Since the problem is assumed linear, it ispossible to consider the Figure 3 buried cable portion as a two-port network with input at the fault point and output at N, the point of junction of the neutral ends, as indicated, in the simplified circuit of Figure 4. The Za, Zb and Zc impedances of this figure are obtained in a conventional manner by solving just the buried cable portion of Figure 3 twice: once with point N open-circuited, and once with point N shorted to remote ground. These solutions represent a simultaneous solution of the segment network equations (composed of terms formed from the radial and longitudinal impedances of each segment) and the system electrostatic equations describing the segment interactions through a conducting earth. The latter, in turn, require the calculation of the mutual impedances through the earth between the segments, and the self-impedances of each segment. These impedances, functions of the soil electrical parameters and segment geometric parameters,are computed from a series of formulas embodying the analytic solution of the voltages at any point in a twolayered earth due to a uniform current leaving a single vertical or horizontal segment located also in the twolayered model [6]. With Za, Zb and Zc determined, VRG, VN and I2 are easily found. Finally, the buried cable portion of Figure 3 is again solved, this time with VRG specified and point N connected to remote ground through an impedance equal to the ratio of VN and I2 as previously determined.

operating current, or the available fault current if the effect of a fault occuring outside theproblem space is to be calculated. The current Iret is returned in the neutral to the problem space at point A. Part of it flows into the earth and through the open section, generating step and touch potentials. From Carson's formulas, Iret may be computed from Io by [9]: z

I

V (x,y,Z) =

I

k=l

ik

k(xIyIz)

Z

Z

For simulations of the third condition (the single open neutral), the applicable circuit segment impedances are the same as in the Figure 3 circuit. In this case, however, the cable excitation is described in terms of The phase conductor current the currents Io and Iret. Io leaves the problem space and enters the external system. This current can be specified as either the normal

ZHIFault

ZHI

Point

f~ ~~F v j

SC I 0

Z

(4)

s

s

= R

+ jO.0229

= r

s

+ r

g

D

en( )

+ jO.0229 Qn(

(5)

D

D

) ds

(6)

and D

e

=

2160i//a 1 f

the depth of the equivalent earth return (ft.)

d5

= sheath geometric meanradius

D

= distance from middle of sheath to conductor center

(ft.)

cs

(ft.)

(3)

where S1k(x,y,z), the mutual impedance between the kth segment and the point of evaluation, is found from the same formulas mentioned above.

ret

where

This last solution also yields theradial currents ik, k = 1,2,...,22 for each segment. From these, the voltage Vp(x,y,z) produced at any point (x,y,z) in the two-layer earth is computed from 22

=

r = 0. 301f x 10 g

= the earth return resistance

Rs

= sheath ac resistance (Q/1000

f

= frequency (Hz)

a1

= conductivityof lower soil

~~~~(Q/1000 ft.) ft.)

layer (U/m)

a Figure 5 is solved by assuming at point A and then solving the siequations for this system to find The sum of these currents and I2' must be the returned current for the assumed input voltage. Actual segment currents for the desired Iret of equation (4) are obtained by scaling by the ratio of the actual and computed Iret values. Equation (3) is

The system of particular voltage multaneous sets of the segment radial

ZHI

T-equivalent for cable

r RG l

c a

b

| N

) ~~~~~12 -Remote Ground .

Figure 4. Simplified circuit model for conditions 1 and 2, with cable replaced by its T-equivalent.

.

.

;. 7%. .

.

--u

I

-Li-iw -- .,

&

.

. p

,

a ...

.?

.

Ui

Figure 5. Circuit segment model for condition 3 simulations.

Authorized licensed use limited to: NATIONAL INSTITUTE OF TECHNOLOGY JAMSHEDPUR. Downloaded on September 22, 2009 at 08:21 from IEEE Xplore. Restrictions apply.

Iet;,

.., ;-.. -;.

*

,

1133 then employed to find the resulting voltage points in the two-layered earth.

at desired

Program Outputs

Results from the simulation program are available in both tabular and graphical form. The listed outputs VRG, are the following potentials defined in Figure 1: Graphical outVT, VG, V3, V6, V12, VS1, VS2 and VS3. put is in the form of two plots of equipotential contours--one showing contours on the earth surface centered over the fault point, and another showing contours on a plane normal to the cable and passing through the problem space midpoint. Computer Requirements

The large computer version of BCAB requires about 20K, 36-bit words memory, and execution time (exclusive of plots) is about twelve seconds using a CDC Cyber 74. The minicomputer version requires about 60K, 16-bit words of memory and executes on a NOVA 830 with disk in about five minutes. RESULTS Program Verification Two procedures have been employed to establish the validity of the equations used in the program: comparison of results using the programmed equations for mutual resistance between cable segments, with results in the literature; and comparison of simulation outputs to results of field experiments. The first procedure involved simulation of various configurations of conductors in earth and the calculation of the resistance to remote ground of those configurations based on program results. Data for comparison came from references [71 and [8], both of which give empirical results and analytical results obtained from equations differing from those programmed in BCAB. The following comparison results were obtained:

1.

Single Vertical Ground Rod. For a single rod inuniform soil, comparisons were performed for ten different rod lengths and three diameters. Computed resistances to remote earth were within 3 per cent of those given in [8].

2.

For three Three Vertical Ground Rods. rods in a trefoil configuration, six different triangle sizeswere employed. Computed remoteearth resistances were closer to measured data than the calculated values given in [7].

3.

Horizontal Wire. For a single wire in a uniform earth, agreement with [7] was within 1 per centfor ten wire lengths and two depths.

4.

Vertical Rod in Upper Layer. Fora single rod positioned in the upper layer of a two-

layer earth, comparisons were performed for ten ratios of soil conductivities. Agreement of program results with [71 was within five percent.

5.

Vertical Rod Penetrating Two Layers. For surface into a rod extending from ground the lower soil layer, comparisons were made for ten rod lengths. Agreement with [7] was within five per cent.

Program validation with field test data is presented in the next section.

Comparison of Simulated and Experimental Results The cable tests conducted for EPRI Project RP-671 provide the field data to which the program results In that test, several types of cable were compared. were used under various conditions of supply voltage, high and low side current limiting impedance, and grounding configurations. In all, 114 tests were conducted. The tests were performed in two main groups: a 15KV series conducted in Fall 1975 and a 35KV series done in Spring 1976. From all the field tests, 18 were selected for simulation with the BCAB. These span almost all the types of test configurations and cable types. The parameters used for the simulations were generally obtained from readily available field test data and ~manufacturer's cable data. However, the soil parameters required a more elaborate procedure, involving the measurement of the conductance from fault point to remote ground. This was necessary because we found that surface layers were so shallow that reliable measurements of surface conductivity, 02, were not possible using standard four-electrode techniques [7]. Furthermore, 02 varied throughout the total test period due to changes in surface layer moisture content. On the other hand, the deep layer conductivity, 01, was known from measurements. Therefore, the following procedure was adopted. The first step was to establish a set of base values. To do this, the 15KV bare neutral tests were simulated with 01 set equal to the value actually measured at the test site at the time of the tests. The upper layer conductivity, 02, and depth, D, step and were systematically varied until computed touch potentials matched as closely as possible to the The conductivity and depth values experimental data. obtained by this process, noted as 01, 02 and D, constituted a base set of values for other tests. To simulate other particular tests, was always taken as the measured value for the test, and 02 was obtained from

a2

=-

2

91

-

a2

(7)

where g1 is the measured conductance from the point of fault to remote ground through the parallel paths of buried cable and earth for the test under simulation; and gl is the measured parallel conductance for the base set. This process yielded 02 values which were from 1 to 6 times the al values. In all cases, D was initially set at X, but small (less than 20 per cent) adjustments were often necessary to yield agreement between the program and simulation results. This would simply reflect the fact that the effective depth of the surface soil layer depends on the actual location of the cable In all cases, D was between sample in the test plot. 1.0 and 1.2 meters. Results from the 18 simulations are shown in Table 1 and Figures 6, 7 and 8. Table 1 shows the fault voltage VRG (normalized by supply voltage) from both measured results and from BCAB simulation results. Cables are identified by neutralmaterial (AL = aluminum, CU = copper), neutral construction (FS = flat strap, CT = continuous tape, or "LC" type, CW = concentric wire), and insulation (I = insulated, B = bare, SC = semiconducting). Also shown is the neutral size and grounding arrangement. Figure 6 shows measured and simulated earth surface voltages normalized by fault voltage for Data for the 35KV cases the 15KV cases of Table 1. without "system ground" appear in Figure 7; while Figure 8 shows results from the 35KV cases with "system ground." Each of these figures was drawn by connecting the measured or simulated values for VG, V3, V6 and V12 (see Figure 1) with smooth lines. From the figures and

Authorized licensed use limited to: NATIONAL INSTITUTE OF TECHNOLOGY JAMSHEDPUR. Downloaded on September 22, 2009 at 08:21 from IEEE Xplore. Restrictions apply.

1134 table, it is apparent that the BCAB simulation results compare favorably with experimental results.

SURFACE

-t

to

Additional Examples

VOLTA6EVng £*

One of the advantages of a simultaneous program such as BCAB is that results from a specific field test may be easily extended to other circuit or soil For example, suppose the 35KV, CUconfigurations. CW-B, full neutral cable of Table 1 was faulted and also had 0.25-meter opens in the neutral, located 1 meter to either side of the fault. This would be a Condition 2 operating condition. Table 2 shows the results of such a simulation and compares the results with results from the fault without opens (Condition 1). Surface equipotential plots from both conditions are shown in Figures 9 and 10. Note the tabulated results show step and touch potentials several times larger for the fault with open neutral as compared to the

TABLE 1 SIMULATED AND MEASURED FAULT VOLTAGES--18 CASES

SUPPLY VOLTAGE (KV)

NEUTRAL SIZE

CABLE TYPE

GROUND RODS?

I

VRG

SURFACE

15 15 15 15 15 15 15 35 35 35 35 35 35 35 35

CU-CW-B CU-CW-I CU-CT-SC AL-FS-SC AL-FS-I AL-CT-I CU-CT-I CU-CW-B CU-CW-I CU-CT-SC CU-CT-I AL-FS-I AL-FS-I CU-CW-SC

FULL FULL FULL FULL FULL FULL FULL FULL FULL FULL FULL FULL FULL FULL

AL-CT-SC1FULL

AL-CT-SC FULL CU-CW-B ALF CU-CW-I ALF

35

35 35

NO NO NO NO NO NO NO NO NO NO NO NO NO NO YES YES NO NO

Is

1

VOLTASEIYRS M

ml -- -

limiting imgedances Low Side: 0.71 4 2Current limiting impedances Low Side: 0.057 1730

TET REULTS SIMULATED SULTn

0.23/0.22

O.04/o.0212 0.23/0.194 0.29/0.29

I 3

ICurrent

SURFACE

0.44/0.44 0.45/0.45 0.42/0.43 0.44/0.436 0.48/0.47 0.48/0.47 0.45/0.42 0.285/0.274 0.395/0.393 0.28/0.26 0.05/0.046 0.29/0.28 0.39/0.374 0.29/0.283

NO NO NO NO NO NO NO NO NO NO NO NO NO NO YES YES YES YES

a2 SFACEED

FISIRE 1. MEASUREO AND SIMULATED RESULl OF X KV CASES WTNOUT SYSTEM BROUND FROM TAKE I

(MEASURED/ SIMULATION)

SYSTEM GROUND?

g

3

DISTANCE FROM FAULTED BURIED CABLE

-

High Side:

1.48

-

High Side:

1.98

186

71°,

-=

._ 5

12

DISTANCE FROM FAULTEO BURIEO CAULE (UACE FEED

FIGURE L MEASURED ANO SIULATED RESUTS ff 25KV CASE WITH SYEM GROUN FROM TAK.E L

simple fault case. Figure 10 clearly shows the distorting effect on the surface equipotential contours of the disconnected cable sections.

VOLTAGEIVRgS ---

As a final example, Figure 11 shows the result of using BCAB for parametric studies. The figure plots fault, touch, and three-foot step potentials which would have occured if the 35KV, CU-CW-B test of Figure 7 had been conducted in soils with a wide range of ratios of surface layer conductivity to lower layer The strong dependence of these potenconductivity. tials on relative conductivities is clear from the figure. Through such studies as this, BCAB can be used to extrapolate field results obtained under one set of soil conditions to predict data which would come from the same tests conducted elsewhere.

TEST RESULT SIMATED _ESLTS

4.

0, AL-CT-I CU-CT-I CU-E-4 3

I

AL-FS-I CU-CT4I CU-CW-

CONCLUSIONS --I

-

It

I

DISTANCE FROM FAULTJES BURED CALI ISURFACE FEET FIGURE l. MEASURES A

SIMULATE RESULTS OF 1S KV CAS FM

TABKE 1.

With the development of the simulation program BCAB, the distribution engineer now has available a tool for the estimation of touch and step potentials resulting from several types of URD cable faults. The accuracy of the computed results does depend on the

Authorized licensed use limited to: NATIONAL INSTITUTE OF TECHNOLOGY JAMSHEDPUR. Downloaded on September 22, 2009 at 08:21 from IEEE Xplore. Restrictions apply.

1135

40.0

TABLE 2

METERS

FAULT,TOUCH,SURFACE AND STEP POTENTIALS FOR CABLE WITH FAULT ONLY AND FAULT COMBINED WITH OPENS IN NEUTRAL VOLTAGE NORMALIZED TO SUPPLY VOLTAGE FAULT WITH OPENS FAULT ONLY

I I

VRG

VT

VG

V3

V6

V12

VS1 VS2 VS3

0.273

0.967

0.161 0.135 0.104

0.235

0.585 0.382

0.083 0.190

0.140 0.0701 0.095

0.070 40.0

z

I.

0.1472

0.029 0.026 0.031

I I

METERS

.01 Figure 10. Surface equipotentials normalized to fault voltage for 35 KV CU-CW-B cable of Table 1 with single fault and simultaneous open neutrals on either side. Buried cable length 27.43 meters (90 feet). .5 .4

VRG

co*

> .2

VT

.1

en 0.

t .03

Figure 9. Surface equipotentials normalized to Fault voltage for 35 KV, CU-CW-B cable of Table 1 with single Fault at midpoint. Buried cable length 27.43 meters (90 feet). accuracy of the data used in the computer model. From a practical standpoint, this means that realistic values must be supplied for all required input parameters. This is straightforward for most of them, but the values needed for a2 and D are, in general, more However, with these specified, difficult to find. the program will accurately solve the problem since it in effect solves simultaneously the system circuit The only simpliand electromagnetostatic equations. fying assumption used is the representation of the cable and ground rods as a set of segments for which each has a uniformly distributed radial current.

Complete documentation and Fortran IV listings of the program may be obtained from the Electric Power Institute.

z

. .02 C 0

0.

An.

.1

Figure 11.

This work was supported by EPRI contract RP797-1. was provided by D. Rudolf. assistance

.2

.3.4.5

1

2

3

4 5

Fault voltage, VRG, touch voltage, VT, and 3-ft. Step potential, V.1 , versus soil layer conductivity ratio.

Industry participants were M. A. Martin, Georgia Power Company; and N. E. Piccione, Long Island Lighting ComWe also acknowledge the contributions of G. pany. Bahder and D. A. Silver, General Cable Corporation; and J. B. Prime, Florida Power and Light Company. REFERENCES 1.

Programming

Vsl

0 -.03

Cronin, L. D. and Sessler, L. H., "Random Separation--Development and Experience," IEEE Trans Power App. Syst., 89:673-680, 1970.

Authorized licensed use limited to: NATIONAL INSTITUTE OF TECHNOLOGY JAMSHEDPUR. Downloaded on September 22, 2009 at 08:21 from IEEE Xplore. Restrictions apply.

1136 2.

"Buried Power and Telephone Distribution Systems-Analysis of Primary Cable Fault Tests and Evaluation of Experience with Radome Separation," EEI Publication, 68-62, June 1968.

3.

Martin, M. A., Silver, D. A., Lukac, R. G. and Suarez, R., "Normal and Short-Circuit Operating Characteristics of Metallic Shielded Solid Dielectric Power Cable," IEEE Trans. Power App. Syst., 93:601-613, 1974.

4.

Piccione, N. E., Fault Testing of Various Concentric Neutral Cables With and Without Conductive Jackets, Preliminary Report to ICC Task Force 6-21. Long Island Lighting Company, March 1975.

5.

Bahder, G., Martin, M. A., Piccione, N., Prime, J. B., Jr., and Silver, D. A., Outdoor High Voltage and High Current Short Circuit Tests on Single Phase Extruded Dielectric Primary Distribution Final Report, EPRI Project RPCables, Phase II. 671, May 1977.

6.

Webb, R. P., Nunnally, H. N., and Joy, E. B., Computer Program for Determination of Earth Potentials Due to Faults or Loss of Concentric Neutral EPRI Project RP-797-1, on URD Cable, Final Report May 1977.

7.

Tagg, G. F., Earth Resistance, Corp., New York, 1964.

8.

9.

Pittman Publishing

Sunde, E. D., Earth ConductionEffects in Transmission Systems, Dover Publications, Inc., 1968. Anderson, P. M., Analysis of Faulted Power Systems, Iowa State University Press, 1973.

H. N. NUNNALLY (S'65-M'72) was born in Atlanta, GA, on December 28, 1944. He received the BEE, MSEE and Ph.D. degrees from Georgia Institute of Technology in 1966, 1968 and 1971, respectively. In 1971, he joined the faculty of the School of Electrical Engineering at Georgia Institute of TechnoloIn addition to gy, where he is an Assistant Professor. his work in the power systems area, he has been active in bioengineering projects. Dr. Nunnally is a member of the IEEE Power Engineering Society, Eta Kappa Nu, Tau Beta Pi, and Phi Kappa He is a registered professional engineer in the Phi. state of Georgia.

E. B. JOY (S'67-M'70) was born in Troy, New York on November 15, 1941. He received the BEE, MSEE and Ph.D. degrees from Georgia Institute of Technology in 1963, 1967, and 1970, respectively. In 1970, he joined the faculty of the School of Electrical Engineering at Georgia Instituteof Technology, where he is now an Associate Professor. Dr. Joy has interests in electromagnetics, power transmission and grounding, and computer graphics. Dr. Joy is a member of IEEE, URSI, Sigma Xi, and Eta Kappa Nu. R. P. WEBB (S'57-M'60) was born in Cedar City, Utah on He received the BSEE degree from December 28, 1936. the University of Utah in 1957, the MSEE degree from the University of Southern California in 1959, and the Ph.D. degree from Georgia Institute of Technology in 1964. Dr. Webb worked for the Douglas Aircraft Company and the Sperry Company before joining the Electrical Engineering Department at Georgia Institute of TechnoHis fields of logy in 1961, where he is a Professor. interest are electric power systems, instrumentation and control systems. Dr. Webb is a member of the IEEE Power Engineering Society, Eta Kappa Nu, Tau Beta Pi and is a registered professional engineer in the state of Georgia. A. P. MELIOPOULOS (S'69-M'76) was born in Katerini, Greece on March 19, 1949. He received the ME and EE

Diplomas from the National Technical University of Athens, Greece in 1972, and the MSEE and Ph.D. degrees from Georgia Institute of Technology in 1974 and 1976, respectively. In 1976, he joined the faculty of the Georgia Institute of Technologywherehe is an Assistant Professor in Electrical Engineering. His interests lie in the application of systems theory and operations research to large scale systems with emphasis on power systems. Dr. Meliopoulos is a member of the IEEE Power Engineering Society and the Hellenic Society of Professional Engineers.

Authorized licensed use limited to: NATIONAL INSTITUTE OF TECHNOLOGY JAMSHEDPUR. Downloaded on September 22, 2009 at 08:21 from IEEE Xplore. Restrictions apply.