F. P. Dawalibi Senior Member, IEEE Safe Engineering Services & Technologies Ltd.

12201 Letellier Montreal, Canada H3M 229

ABSTRACT In North America, ANSI/IEEE Standard 80 universally applied to determine electrica flowing through the human body as the resul

IEEE Transactions on Power Delivery, Vol. 5, No. 2, April 1990

VALIDITY OF CONVENTIONAL APPROACHES

FOR CALCULATING BODY CURRENTS RESULTING

FROM ELECTRIC SHOCKS R. D. Southey Member, IEEE R. S. Baishiki Safe Engineering Services

12201 Letellier 77 Beale Street Montreal, Canada H3M 229

Senior Member, IEEE Pacific Gas & Electric Co.

San Francisco, CA 94106

& Technologies Ltd.

s almost currents of touch

and step voltages near transmission and di tribution facilities. This paper shows, however, that significant inaccuracies can occur when the ANSI/IEEE Standard 80 based method is applied without understanding the assumptions which underlie it. In particular, errors can occur when the method i s applied to grounding situations where the remote foot resistance of a human is much different from the resistance through ground between a human's feet and the buried grounding system under study. This paper discusses the problem of determining body currents from measilred touch voltages and presents an improved model for doing so . 1. INTRODUCTION The conventional ANSI/IEEE method of determining body currents occurring during electric shocks is performed in two steps. First, the pre-existing stress voltage in the absence of the victim of the electric shock is calculated using a variety o f methods, including very simple formulas [l] and sophisticated computer programs [21, [3], [4], [51. Next, the body current is calculated by assuming that the pre-existlng stress voltage is applied across the body points which are in contact with the energized path. This paper is not concerned with the methods used to calcuibte the pre-existing stress voltage (Step 1). It assumes, therefore, that this value is available with the necessary accuracy, either by computations or direct measurements. The main focus of this paper is on the validity of the two-step methodology described above, especially the adequacy of the assumptions and techniques used to determine body currents from the pre-existing stress voltage (Step 2). Hence, this paper poses and addresses the following questions:

a - Is the two-step methodology valid in all cases? If not, under which circumstances is it inaccurate?

b - If the conventional two-step methodology is not always valid (as will be demonstrated in this paper), it then becomes important to develop new approaches (one step or multi-step) to determine accurately the prospective body current resulting from electric shocks. In this

88 WM 108-3 A paper recommended and approved by the IEEE Substations Committee of the IEEE Power Engineering Society for presentation at the IEEE/PES 1988 Winter Meeting, New York, New York, .January 3 1 - February 5, 1988. Yanuscript submitted August 26, 1987; made available for printing December 7, 1987.

613

case, which approach among the various ones described in this paper ,,(some of which are based on commonly used intuitive" circuit models) is the most appropriate?

c - Assuming that a valid two-step methodology can be developed, then which electric circuit models are sui table for carrying out accurately the calculations required in Step 2 for high voltage (HV), medium voltage (MV), and low voltage (LV) electric networks?

Although this study initially appeared to be quite straightforward, a significant number of fundamental questions arose, which needed to be reviewed, studied, and developed. It became clear that it was essential to proceed with a comprehensive parametric analysis to estimate adequately the effects of all variables, which significantly affect the physical process being investigated. For these reasons, it was decided to subdivide the scope of work in two phases. This paper describes the result of Phase 1 of the study.

The objectives of Phase 1 of the study were:

1. Develop an accurate method for calculating body currents resulting from electric shocks, assuming a constant current electric power source.

2. Compare the results obtained based on this accurate approach to a conventional one, in this case, the methodology described in ANSI/IEEE Standard 80 [6].

3. Identify and discuss the cases where differences between the accurate and conventional methodologies are to be expected.

4 . Illustrate the preceding points using realistic practical exampl es .

Phase 2 of the study, which will be completed at a later date, will address in detail subjects not covered in the first phase. Among these let us mention the following:

a - Effects of an insulating surface layer (such as gravel ) .

b - Influence of the electric power source impedance on the various methodologies (non constant current power sources such as in LV electric systems).

c - Detailed parametric analyses on the effects of soil structure models, grid configurations and sizes, types of stress voltage considered (step and touch voltages), and relative Positions of the feet with respect to the power system ground.

d - Electric shocks in distribution networks

0885-8977/90/0100-0613$01.00 0 1990 IEEE

614

R 1 .

including effects on livestock facilities in rural areas.

2. BACKGROUND This section describes how a touch voltage electric shock scenario is modelled based on the ANSI/IEEE Standard 80 approach. The reader should refer to other national and international documents and compare the discussions of touch voltage shock scenarios as discussed here. 2.1 Touch Voltage Shock Scenario Figure 2.la illustrates a typical electric shock scenario in which a human stands on the soil surface above a grounding system and contacts a metallic structure electrically connected to the grounding system with his/her hands. The total earth current It available from the electric network is assumed to be independent of the presence of the human. Figure 2.lb shows the various voltages which exist in the absence of the human.

- - I RO

I I

Grounding System

(a) Actual Situation

i"" Remo,eSoil 10 Volt Reference)

-

(b) Pre - existing Voltages Figure 2.1 Illustration of touch voltageelectricshockscenario

Coupling Effects

-

Figure 2.2 Identification of the dominant physical parameters

Figure 2.2 shows the various physical parameters which may have a significant effect on the magnitude of the body current. Several simplifying assumptions, both explicit and implicit, have been made by the AIEE committee [7], which developed the first release of Guide No. 80. Most of these assumptions were adopted (in some cases with further explanations and clarifications) by the working group which prepared the most recent release of ANSI/IEEE Standard 80. These assumptions are essenti a1 ly the foll owing:

1. Hand contact resistances may be very low and therefore are neglected. Hands are not protected

with gloves.

2. Resistance of shoes is highly variable and indeed may be very low for damp leather shoes, according to test measurements [8]. It is also neglected, along with the shoe contact resistance.

3. The resistances of the hands, trunk and legs are all lumped together and a value of 1000 ohms is presently used regardless of the stress voltage level. The validity of this approximation is not discussed here as this subject alone deserves a special study of its own [9], [IO].

4. Conductive coupl ing effects between feet are neglected. Since this assumption leads to a safe conservative approach for touch voltages, it is acceptable in all cases. It results in a slight overestimation of body currents.

5. Conductive coupling effects between the grounding system and feet is either neglected or grossly estimated, at least as far as we can tell from most standards, guides, and publications available in the open literature. This conductive coupl ing effect constitutes the main substance of the discussions which follow.

stress voltage which exists between hand and foot Prior to the presence of the victim of the electric shock) is presumed to be applied between the victim hand(s) and remote soil. This assumption is also discussed later.

6. Thepre-existing touch voltage (i.e., the

2.2 Origin of the Derivation of Guide No. 80 Formula

In October 1958, an AIEE Working Group published a Committee Report [7] which laid the foundation of what is now widely known as the ANSI/IEEE Standard 80 [6]. In this report [7], the touch voltage Etouch was defined pictorially as shown in Figure 2.3.

1 Ifault w I. I

I Etouch

The definitions of the elements shown in are as follows.

Fig

Ifaul t is fault human/gFk system current enter

R1tRo is the resistance of the

Rbody is the body resistance

electrode system

re 2.3

ng the

ground

615

Rf is the resistance of the ground immediately under each foot

Several problems arise from this definition of Etouch[7] : o The 1958 AIEE report [7] states that "for

practical purposes,. . . . the resistance R in ohms for each foot can be assumed to be 5 pS [where p s is the local soil resistivity]". At least one of the references cited by the authors of the AIEE report [l], however, describes 3 as the resistance of the soil between the foot and infinity, not simply the resistance of the ground immediately under each foot.

Note that from this pictorial definition of touch voltage (the only one given in the October 1958 version [7]), touch voltage is not the potential difference between a shock victim's hand(s) and feet, but rather the potential difference between his/her hand(s) and some point (Point A in Figure 2.3 [7]) in the earth, separated from the feet by a resistance Rf/2. The location of this point A in the earth is ill-defined, and appears to have become the foot contact point on the earth's surface for just about all subsequent authors and in subsequent revisions of Standard 80. Otherwise Etouch is impossible to measure.

With E as defined ;,n Figure 2.3, the 1958 AIEE [jTuc!tates that any change in the pre-existing voltage by reason of the current diverted through the body can be neglected." Since Point A is not a defined location, and could even, as an extreme example, be taken to be remote soil, this statement may or may not be valid. If Et uc is measured between a human's hands and tie Poot contact point on the earth's surface, this statement becomes patently false.

At present, Etou h is determined in this latter manner. It is tie pre-existing voltage, without the presence of the human, that is used to calculate the current through the body of the human, using the formula derived from Figure 2.3:

Etouch Lbody =

Rbody + Rf'2

where:

Rbody

Ibody

Rf

is the human's body resistance

is the current through the human's body

is the resistance of a human's foot to remote earth (ground resistance of the foot; note corrected definition)

This new definition of R deviates from the circuit model presented in the 1956 AIEE report [7]. If the circuit presented in Figure 2.3 is redrawn with the presently used definition of Eto ch taken into consideration, Figure 2.4 is obtainel. The definition of the elements shown are as follows:

in Figure 2.4

Ifault is the fault current entering the human/gri d

R1 +Ro is the resistance of the ground

electrode system to remote earth (ground grid resistance)

Rbody is the body resistance

is the resistance of a human's foot to remote earth (ground resistance of the Rf foot)

I- - - Figure 2.4 Present touch voltage circuit used in ANSIlIEEE

Standard 80

As noted previously, with Et uch as defined in Figure 2.4, there is no guarantee tlat Etouch with the human present will be equal to the pre-existing potential difference. Furthermore, although values for R RI, and R /2 can be determined to create a !:point networl representing a given foot-grid situation (discussed in Sections 3 and 4), we have found that these values do not agree with the definitions given in Figure 2.4.

From the above discussion, we see that the basis for Equation 2-1 as described in the Standard 80 is not convincing.

In order to find a solid theoretical basis for Equation 2-1 (or a new equation), we designed a series of circuit models. Two intuitive models were developed, tested, and rejected before a third PI-network model and a fourth, simpler, Thevenin model were found to work and provide much insight into the problem.

3. INTUITIVE MODELS

3.1 First Model

A simple PI-network was first used to model a typical human-grid touch voltage situation and is shown in Figure 3.1.

This four port network is defined by terminals A, B, C, and D and by resistors Ra, Rb and Rc in Figure 3.1. The values of Ra, Rb, and Rc are determined by making the appropriate measurements or in this study, computing the appropriate voltage and current values in the actual proposed situations at the network terminal s.

It was hypothesized that Ra could be equated to the grid resistance (to remote earth) and Rc to half the remote foot impedance (touch voltage stress type), leaving Rb to be determined by computer simulations. This hypothesis was made because it is clearly true when the feet and the grid are widely separated. The question to answer is: Is the hypothefis true, when the feet and grid come closer together?

Remote Earth

Figure 3.1 Simple PI-network used to model humadgrid

When the computer simulations were actually performed (using Computer Program MALZ [2],[4],[5]*), and the values of Ra, Rb, and Rc as well as the grid and remote foot impedances determined, it was found that the hypothesis described above was wrong: although R was found to be approximately equal to the gri! resistance in the cases examined, R, varied widely and did not resemble the remote foot impedance. Rb also varied significantly. For example, in one sequence of simulations using a 100 ohm-meters soil and a typical electrode representing the feet in parallel, the value of Rc varied from 299.2 ohms to 2579.8 ohms as the position and number of meshes of the grid was changed, while Rf/2 remained constant at 158.8 ohms.

3.2 Second Model

It was first thought that the hypothesis described in the previous section had failed because it had not taken into account the distributed nature of the soil resistances. The distributed PI-network model shown in Figure 3.2 was therefore developed.

system

Figure 3.2 Distributed PI-network model

The definitions of the elements shown in Figure 3.2 are as follows:

*The accuracy of this program has been verified by extensive computer modeling and field testing: it has been in use by a growing number of major North American utilities for several years. Furthermore, MALZ results in this study have been confirmed by MALT[3], another program which is based on a different algorithm and which has been verified for real world situations and on scale models since the 1970s.

Rg

Rm

Rf ground (i.e. remote foot resistance) When reduced into an equivalent PI-circuit as shown in Figure 3.1, the values of R Rb, and Rc were found to be given by the folfAwing recursive relations:

(3-1) Ra = RL(N) % = RT(N) (3-2)

is the grid resistance (to remote earth)

is an unknown mutual resistance

is the resistance of a humans foot to remote

R,= RR(N) (3-3)

where

and

1

(1-E) + __ k(i) h(i) = E

E

(1 -E) + 3-

k (i- 1)

(1-E) + &)

r = - Rg g N

r = - Rf 2N

r, = n R m

E = rm r m + r f + r g

and where Rg is the grid resistance

(3-7)

(3-9)

(3-10)

(3-11)

(3-12)

(3-13)

Rf

R, N is the number of loops in the circuit o f

This new intuitive distributed PI model also failed: a typical foot/grid/soil configuration was simulated

is the remote foot resistance

is the mutual resistance (to be determined)

Figure 3.2

617

Earth Surface . . . . . . . . . . . -

with the MALZ computer program [4] and the true values of Ra, Rb, and Rc were determined as well as the grid and remote foot resistances. These grid and foot resistances were fed into the above formulas along with a series of values of Rm to obtain the formula-based Ra, Rb, and Rc.

It out that when the value of R, became such that the true and formula-based values of Rb were equal, circuit voltages and currents computed using the model in Figure 3.2 were significantly different from those computed using the MALZ program [4].

4. ACCURATE MODELS

turned

4.1 PI-Model Having rid ourselves of the notion of including grid and remote foot resistances in circuit models, we began once more with a simple PI-model (Figure 3.1). This time we made no assumptions as to the possible values of Ra, Rb, and R , thus ensuring the validity of the resulting mode7. A series of computer si mu1 at i ons with di fferent foot/gri d/soi 1 combinations were made to find typical values of these three resistances. Also, found for each simulation were the grid and remote foot resistances.

From the values mentioned above, obtained from a given simulation, it was possible to calculate the current through a body (represented by a varying resistance Rbody) connected across points A and B of the PI-circuit in Figure 3.1, as well as the potential existing across points A and B with the body not present, i.e., the touch voltage. This touch voltage was then inserted into Equation 2-1 along with the remote foot resistance and body resistance to obtain the ANSI/IEEE version of the body current.

As mentioned in Section 3.1, R was approximately equal to the grid resistance in a h cases studied, whereas Rc and Rb varied independently of the remote foot impedance.

The body current, as computed by the ANSI/IEEE method, diverged from the accurately computed value by as much as 9% for a uniform 1000 ohm-meters soil, a 1000 ohms body resistance, and a 20m x 20m, 16 mesh grid buried 0.5 m below the feet.

Note also that the computer runs vividly illustrated how the presence of the human significantly altered the earth potential values at his/her feet with respect to the pre-existing values in his/her absence. For cases where the human was in the center of a large mesh, the increase in earth potential values approached the product of remote feet resistance (Rf/2) and body current. Since foot resistance is typically a significant proportion of the body resistance (even exceeding it for large soil resistivities), this change in potential can also be on the same order of magnitude as the potential difference across the body (especially for high resistivity soils). For example, for the 20m x 20m mesh and foot described in the Appendix, a 100 ohm-meter soil resistivity, 1000 ohms body resistance, and an assumed fault current of 1000 amperes, the pre-existing foot potential is 2176.13 volts, while the foot potential with the human present is 2281.07 volts (the remote feet resistance is approximately 155 ohms, while the body current is approximately 0.68 amps and the grid potential rise is 2961 volts).

These results confirmed the need for further computer runs to understand which factors cause the Standard 80 approach to err. Because the program (MALZ [4]) used to run the simulations thus far is designed to

rTerminal

Two. Port Network R h d y

-Terminal 1

Figure 4.1 Two-port representation of earth-grid-foot

Terminal 2 is simply a point in the system at the same potential as the grid where the fault current is injected. Terminal 1 is the small area on the earths surface which is in contact with the humans feet. Indeed, if the resistance of the feet themselves are imagined to be in the ankles, this terminal could be the humans feet.

For high voltage systems, the transmission line network supplying fault current to the grounding grid can be approximated by an ideal (or constant) current source (this is because the equivalent network impedance is very large compared to the impedance of the grid). Hence, the two-port network shown in Figure 4.1 consists only of passive elements and an ideal current source. Thevenins Theorem allows us to represent this two-port by the circuit shown in Figure 4.2.

system

O v e q i

TWO - Port

Figure 4.2 Thevenin equivalent circuit of two-port Note that this Thevenin equivalent circuit is valid for a given grid configuration, a given foot size and location, and a given soil resistivity. Note also that ZSystem in Figure 4.1 does not affect any of the

618

Thevenin parameters. lhis implies that all impedances in the two-port are to be found in the soil, consequently, Zeq is proportional to the soil resistivity and can also be taken to be resistive. Hence, Zeq becomes Req. These facts will be useful in examining the effect of soil resistivity on body current. 4.2.1 Computer Modelling

In order to obtain the parameters of the circuit depicted in Figure 4.2 for a given earth-grid-foot configuration, the open-circuit voltage and closed-circuit current are first determined by a computer program such as MALT [3]. For the open-circuit run, the grounding grid alone is injected with current; the foot electrodes (a computer simulated model of each foot made of small wires) are left in the ground, but are not connected to the system in any other way. The open circuit voltage is then taken to be the grid potential rise less the average potential on the foot electrodes lying near the earth's surface.

For the closed-circuit run, the ground bus is shorted to the foot electrodes as if these latter were a part of the grid. The current entering the foot electrodes i s then cal cul ated.

The Thevenin Equivalent circuit parameters are then simply:

'eq = 'opencircuit

R = 'e4

'short circuit

R = 'open circuit

'short circuit eq

(4-1)

(4-2)

(4-3)

4.2.2 Body Current from Thevenin Circuit

From this Thevenin model, it is seen that the true body current through a human with a body resistance Rb, when connected to the two-port, is given by:

(4-4)

where ib-true is the true body current

The value obtained using ANSI/IEEE Guide 80 is given by :

- 'e4 b-IEEE - ____~ i

R,/2 + Rb (4-5)

where

Rf/2

ib-IEEE

is the remote foot resistance of the two feet

is the body current obtained using Standard ANSI/IEEE Guide 80

For these formulas to agree, the following must hold:

Rf Rq = __ 2

(4-6)

This is clearly impossible, since Rf is a quantity which is fixed for a given soil type and foot size, whereas Re can be made to vary under these fixed conditions fiy altering the grid size and location with respect to the feet. It appears that in normal applications, R i s approximately equal to Rf/2. But how does one def!ne "normal"?

4.2.3 For a uniform soil, Rf and Re are both proportional to Soil resistivity, P , ani can, therefore, be expressed as:

Effect of Body Resistance and Soil Resistivity

Rf = 2ap

Rq = PP

(4-7)

(4-8)

- . ~ Req are-used:

PP + Rb Ratio = ____

We see that large body resistivity tend to mask between 6 and o or R resistivities and 1E8 accentuate an inequality, 6 / a or 2 Req/Rf.

Factors which affect body

aP + Rb

The ratio of the ANSI/IEEE body current to the true one is given by ( 4 - 9 ) when these values for Rf and

(4-9)

resistance and low soil the effect of an inequality and Rf/Z. High soil body resistance tend to

but not beyond a ratio of

resistance include the size of the victim and the eiectrical path through the body. If a human is lying down or is in a crouching position or the contact locations are other than the hands and feet, the body resistance is different. Similarly, if the victim is a cow or other four-legged animal with current passing from the mouth to the four hoofs, the body resistance can be significantly lower than that of a standing human (as low as 244 ohms [ll] vs. 1000 ohms for a human). Hence, we see that the significant parameters of the ratio of IEEE current to true current are the grid size, location of the foot, and the soil structure (i.e., uniform, multilayer, etc.). Low soil resistivities and high body resistances only serve to attenuate the effect of the significant parameters listed above. We see then, that in ,,order to answer the question formulated earlier, How do you define 'normal'", it is necessary to study what kinds of conditions can make Req differ greatly from Rf/2. We now know the role that body resistance and soil resistivity play, so these need not be studied any further.

4.2.4 Effects of Soil Structure, Grid Configuration, and Foot

In order to determine the possible effects of soil structure, grid configuration, and foot location, one might ask what conditions maximize the difference between Req (the Thevenin equivalent resistance of the system shown in Figure 4.1) and Rf/2 (the resistance to remote ground of the human's feet).

It is helpful to take another look at Figures 4.1 & 4.2 and realize that R is independent of Ifau t, i .e., for a given foot/grEI/soil configuration, Req is the same for all values of Ifault, including zero. However, Ifau t 0 corresponds to an open-circuit between the $a;lt current source and the ground bus injecting fault current into the grid. The resulting

Location

619

r e s i s t i v i t i e s . Two comparison c a l c u l a t i o n s made f o r t y p i c a l s o i l r e s i s t i v i t i e s and body r e s i s t a n c e f o l l o w f o r h=O. 6:

system f o r I f a u l t = O and corresponding Thevenin equ iva len t c i r c u i t are drawn i n F igu re 4.3.

Th is s i m p l i f i e d system makes i t much e a s i e r t o understand what k i n d o f c o n f i g u r a t i o n s w i l l produce d i f f e r e n c e s between Rf/2 and R q, f o r we see i n t h i s s i m p l i f i e d system t h a t Req i s t l e res i s tance , through ear th , between t h e f e e t and t h e g r i d .

Terminal 2 Terminal 1

Grid r--1 Terminal 2 I O T t - - f ) R b d y ---

Thevcnin Equivalent

Terminal 1 I I L---_I

Figure 4.3 Simplified system with same Thevenin equivalent

4.2.5 Some Examples

One way t o produce a l a r g e d i f f e r e n c e between Rf/2 an:! Reg i s t o min imize Re , w h i l e maximizing Rf/2. Examining a l l p o s s i b l e aays o f do ing t h i s i s beyond t h e scope o f t h i s paper. However, one p o s s i b i l i t y , which cou ld q u i t e e a s i l y occur i n p r a c t i c e , i s t h e example i l l u s t r a t e d i n F igu re 4.4.

resistance as original system

Feet I

Earth Surface t t 0.5m '

Groundins Grid I h "small 8 1

4arge

----- ------- I _--_ Soil Layer Interface

Figure 4.4 Example grounding situation with large R42 and relatively small R

eq

I n t h i s example, t h e f o o t e lec t rodes (computer model of t h e f o o t ) and g r i d are bo th i n a low r e s i s t i v i t y s o i l l a y e r o f v a r i a b l e depth, h. Th i s r e s u l t s i n a low r e s i s t a n c e between t h e f o o t and t h e g r i d . I n o rde r t o f u r t h e r decrease t h i s res i s tance , t h e f o o t e lec t rodes are p laced near t h e co rne r o f t h e g r i d ( a t a nominal depth o f 0.01 m) which increases t h e mutual coupl ing. F i n a l l y , t h e g r i d i s made t o be f a i r l y l a r g e (see Appendix f o r numerical d e t a i l s ) t o f u r t h e r increase t h e mutual coup1 i ng . On t h e o t h e r hand, a second s o i l l a y e r w i t h a h i g h r e s i s t i v i t y l i e s below t h e f i r s t . l a y e r , n o t ve ry f a r below t h e grounding g r i d . Th i s s o i l l a y e r increases t h e ground r e s i s t a n c e o f t h e f e e t much more than t h e mutual r e s i s t a n c e between t h e f e e t and t h e g r i d .

The p l o t i n F igu re 4.5 shows t h e worse case r a t i o o f I E E E body c u r r e n t / t r u e body c u r r e n t ( w i t h Rbody=O) .as a func t i on o f t h e depth o f t h e low/high r e s i s t i v i t y s o i l i n t e r f a c e f o r severa l p o s s i b l e combinations o f s o i l r e s i s t i v i t i e s . I n t h i s example, t h i s r a t i o reaches a minimum o f 60% f o r a h igh/ low s o i l r e s i s t i v i t y r a t i o o f 100 and 72% f o r a r e s i s t i v i t y r a t i o o f 20. Th is means t h a t t h e t r u e c u r r e n t s pass ing through a body i n such s i t u a t i o n s can reach 167% and 139%, r e s p e c t i v e l y , o f those p r e d i c t e d us ing t h e formula suggested i n t h e ANSI/IEEE 80 standard, f o r minimum body r e s i s t a n c e and maximum s o i l

P - low = 100 ohm-meters p - h i = 10000 ohm-meters Rb

R RF72

= 1000 ohms

= 160.09 ohms ( f rom computer r e s u l t s ) = 265.13 ohms ( f rom computer r e s u l t s )

'b-IEEE R + R __ = _ L b - - - 0.91 Rf!2 + R, b-true

Th is means t h a t t h e t r u e body c u r r e n t i s 110% o f t h a t p r e d i c t e d us ing t h e ANSI/IEEE Standard 80 formul a.

P - low = 500 ohm-meters P - h i = 10000 ohm-meters

= 500 ohms Rb

= 784.2 ohms (from computer r e s u l t s ) $2 = 1087.5 ohms ( f rom computer r e s u l t s )

'b-IEEE R + R b - - eq - ._--- R f / 2 + R b = Om8' 'b-me

Th is i n d i c a t e s t h a t t h e t r u e body c u r r e n t i s about 123% o f t h a t p r e d i c t e d by ANSI/IEEE Standard 80 formula.

-- K= 0.98 (100nm/10,000nm) -----_ K= 0.96 (100s" 5,000s" - K= 0.95 (100nmI 2,000s" ---- K- 0.82 (100nm/ 1,000nm) K- 0.67 (1000ml 500nm) -__- K= 0.33 (100s" 200nm)

5 0.51 ", L '2 201 O.b2 0.05 0:l 0:2 3

0:5 1.0 2.b 5.b 10.0 2d.0 50:O lOd.0 h= Tap Layer Height (in meters) 5

Figure 4.5 Plot of the worst case ratio of IEEE body current/ true body current for different top soil layer thicknesses

Th is example showed how Re cou ld be made t o be much sma l le r than Rf/2. Anoaher t h r e e more examples f o l l o w which desc r ibe t y p i c a l grounding s i t u a t i o n s and i n d i c a t e t h e va lue o f t h e Re /(R /2) r a t i o f o r each case. A l l examples use t h e sa le foot /grounding g r i d c o n f i g u r a t i o n descr ibed i n t h e Appendix A.

The examples g i ven i n t h e f o l l o w i n g sec t i ons are n o t n e c e s s a r i l y r e p r e s e n t a t i v e o f a l l s i t u a t i o n s , b u t are c i t e d r a t h e r t o e s t a b l i s h a data p o i n t f o r elach s o i l c o n f i g u r a t i o n . These examples have nolt been c o n t r i v e d t o rep resen t e i t h e r worst cases o r bes t cases from a s a f e t y p o i n t o f view.

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4.2.5.1 Two-Layer Vertical Soil

A two-layer vertical soil model was obtained by equating the resistivity of the soil occupied by most of the grounding grid to 2000 ohm-meters and that of the soil layer where the human is standinq to 1000 ohm-meters (see Figure A.2b). The resulting Req/(Rf/2) ratio is 0.93.

4.2.5.2 Multi-Layer Vertical Soil

A three layer vertical soil was modelled, as illustrated in Figure A.2c. The soil resistivity of the semi-infinite layers is 2000 and 1000 ohm-meters, respectively, and that of the inner layer is 100 ohm-meters. The resulting Req/(Rf/2) ratio is 0.83.

4.2.5.3 Multi-Layer Horizontal Soil

A three-layer horizontal soil model was simulated with a top layer resistivity of 100 ohm-meters, a middle layer resistivity of 2000 ohm-meters, and a bottom layer resistivity of 200 ohm-meters (see Figure A.2d). The layer interfaces lie at 0.6 m and 1.2 m, respectively. The resulting Req/(Rf/2) ratio is 0.84.

5. CONCLUSION

The following conclusions can be drawn from the research described in this paper:

1) This study has shown that the formula presently given by ANSI/IEEE Standard 80 can produce erroneous results when the resistance through earth between a human's feet and the grounding grid varies greatly compared to the remote foot resistance of the human's two feet. Several examples have been given showing how this is the case.

2) It has been demonstrated that when a fault current independent of the presence of a body can be assumed, the formula given by ANSI/IEEE 80 can be applied with Req in place of Rf/2 (Reg is the resistance through earth between a human s feet and the grid, and R /2 is the ground resistance of a human's two feet!.

3)

4)

The divergence between results obtained using the ANSI/IEEE Standard 80 method and true values increases under the following conditions: low body resistance, high soil resistivity, good conductive coupling through earth between feet and the grid (produced by soil structure, proximity of feet to grid, size of feet and grid), and large ground resistance of the feet. This applies particularly to livestock with low body resistance.

The preceding conclusions have been verified only for cases in which the fault current is independent of the presence of a body. This assumption is typically valid for transmission substation grids, which have very low grid impedances relative to the system impedance. This assumption may not be true for distribution systems, or tower and pole grounds. In such cases, a more involved analysis must be performed, which accounts for system source impedances, line impedances, etc.

5) The presence of a human usually significantly alters pre-existing soil potentials at his/her feet when other parts of his/her body are in contact with an energized, grounded metallic structure.

6. ACKNOWLEDGEMENTS The authors wish to thank both Safe Engineering Services & Technologies Ltd. and Pacific Gas & Electric Company for the support and facilities provided during this research effort.

7. REFERENCES [ 11 Pierre Laurent, "General Fundamentals of Electrical Grounding Techniques", Le Bulletin de la Societe Francaise des Electriciens, July 1951.

[2] F. Dawalibi, A. Pinho, "Computerized Anal{sis of Power Systems and Pipelines Proximity Effects IEEE Transactions on Power System Delivery, Vol. bWRD-1 No. 2, April 1986, pp. 40-48.

[3] "Low Frequency Analysis of Buried Conductor Networks - User's Manual for Computer Program MALT", Version 2.15, July 1986, Safe Engineering Services and Technologies Ltd., Montreal, Canada.

[4] "Frequency Domain Analysis of Conductor Networks - User's Manual for Computer Program MALZ", Version 3.4, March 1987, Safe Engineering Services and Technologies Ltd., Montreal, Canada.

[5] F. Dawalibi, R. D. Southey, "Software Methods: State of the Art in Power Line/Pipeline Interference Analysis", CEA Symposium on Joint Right-of-way Use by Oil and Gas Pipelines and Power Transmission Lines, Vancouver, March 1987.

[6] American National Standards Institute, "IEEE Guide for Safety in AC Substation Grounding", ANSI/IEEE Std 80-1986, July 26, 1986 Grounding, IEEE.

[7] AIEE Committee Report, "Voltage Grtdients Through the Ground Under Fault Conditions , AIEE Transactions, October, 1958, pp 669-692, Appendices I & 11.

[8] "Recherche de 1 ' Influence des Chaussures sur 1;s Dangers Presentes par les Tensions de Pas , Certificat No. 162763, Electricite de France.

[9] Biegelmeier, 6.: "Report on the Electrical Impedance of the Human Body and on the Behaviour of Residual Current -Operated Earth- Leakage Circuit-Breakers in Case of Direct Contact for Tensions up to 200 V a.c., 50 Hz", Transactions: Symposium on Electrical Shock Safety Criteria, Toronto 1983. Pergamon Press, Toronto 1984; [lo] M. S. Hammam and R. S. Baishiki, A Range of Body Impedance Values For Low Voltage Low Source Impedance Systems of 60Hz", IEEE Transactions on Power Apparatus and Systems, Vol. PAS-102, No. 5, May 1983.

[ll] T. C. Surbrook, N. D. Reese, and A. M. Icehrle, "Stray Voltage: Sources and Solutions", IEEE Transactions and Industry Applications, Vol. IA-22, No. 2, March/April 1986.

APPENDIX: CONFIGURATION OFTHE BASIC EXAMPLE PROBLEM

The basic problem analyzed in Section 4 consists of the grid and foot (representing two actual feet), a top view of which is depicted in Figure A.l.

Figure A.1 Top view of grid and foot electrodes

All electrode conductors have a radius of 0.006111. The grid is buried at a depth of 0.511 and the foot at 0.01m. Figure A . l shows the grid equivalent foot configuration. Note that the configuration and size of the electrode representing the feet were chosen so that the ground resistance of the feet is about 3 p S . Other sizes and shapes of the electrode would lead to similar results and conclusions. Figure A.,? (parts a, b, c, and d, respectively) shows the soil structures which were studied. Earth Surface

T Ptop Cl0WF-f -----_- - G:id 1

/m

t Soil Interface

P botlom (high)

a) Horizontal %Layers Side View

100 rlm lOOOnm

Grid

/2000nm 1OOnm nterface

b) Vertical 2-Layers Top View

Earth Surface

Y

2000nm Soil Interface 2

200nm Soil

C ) Vertical Multi-Layer d) Horizontal Multi-Layer Top View Side View

Figure A.2 Soil structures examined in Section 4

Dr. Farid Dawalibi (M72 SM82) was born in Lebanon in November 1947. He received the Engineering degrees from St. Josephs University, affiliated to University of Lyon, and the M.Sc.A. and Ph.D. degrees from Ecole Polytechnique, University of Montreal.

Consul ti na Enq

From 1971 to 1976, he was with the Shawinigan Engineering Company, ineers in Montreal, where he

participaied in -numerous projects involving power system analysis and design, railway electrification studies and specialized computer software code

development . He then joined Monte1 -Sprecher & Schuh, manufacturer of high voltage equipment in Montreal as Manager of Technical Services. He was involved in power system design, equipment selection and testing ranging from a few kV to 765kV.

In 1979, he joined Safe Engineering Services & Technologies, a company specializing in soil effects on power networks. Since that time, he is responsible for the engineering activities of the company including the development of specialized software code relating to power systems applications.

Dr. Dawalibi is the author of more than 50 papers on power system grounding, soil resistivity analysis, safety, and electromagnetic interference. He is also the author of several research reports on behalf of CEA and EPRI.

Dr. Dawalibi is a corresponding member of various IEEE Comnittee Working Groups and a Senior Member of the IEEE Power Engineering Society and the Canadian Society for Electrical Engineering. Dr. Dawalibi is a registered Professional Engineer in the Province o f Quebec.

Mr. Robert Southey (M87) was born in Shawinigan, Quebec, Canada, on April 26, 1964. He graduated from McGill University, Montreal, in December 1985 with a B. Eng. (Honors) degree in El ectr 1 cal Engineering.

From that time to the present, he has worked for Safe Engineering Services Technologies as an el ectr i c power engineer

speci a1 i zing in software devel opment . He was extensively involved in an EPRI research project investigating electrical interference between pipelines and transmission lines as well as a CEA project studying Canadian distribution grounding practices.

Mr. Southey has coauthored several papers on grounding and related subjects. Mr. Southey is a registered Junior Professional Engineer in the Province of Quebec.

Mr. Rod S. Baishiki (S63 M67 SM77) was born in Buffalo, NY, on August 12, 1945. He received a B.S. degree in Electrical Engineering with honors from California State Polytechnic University, San Luis Obispo, CA, and a M.S. degree in Electrical Engineering from Stanford University, Stanford, CA, in 1967 and 1972, respectively.

He is presently a Consulting Electrical Engineer in the Technical Systems Analysis Group of the Electrical Engineering Department of Pacific Gas b Electric Company, San Francisco, CA, where he has worked since 1967.

Mr. Baishiki is a Senior Member of IEEE, a member of the Power Engineering Society, IEEE AC Fields Working Group, Magnetic Coupling Effects Task Force and Radio Noise Working Group, CIGRE, BENS, Tau Sigma, Tau Beta PI, Blue Key, and Whos Who Historical Society, and a Registered Professional Electrical Engineer in the State of California.

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Discussion

A. P. Sakis Meliopoulos, (School of Electrical Engineering Georgia Institute of Technology Atlanta, Georgia 30332): The subject of this paper is very important in safety assessment of grounding systems and the authors should be commented for opening the discussion on this matter.

The purpose of this discussion is twofold: (a) the authors are asked to clarify the interpretation of Figure 2.4 and (b) to present the basis of the IEEE Std 80 on the subject of body current calculations.

In my opinion, Figure 2.4 of the paper represents a misinterpretation of the ANSIlIEEE Std 80. For comparison purposes, Figure 6 of the guide is repeated here. Note that the touch voltage is shown to be not across the human body resistance but across the series combination of Rf/2 and Rb. In other words, the Std 80 states that the touch voltage is the Thevenin equivalent voltage and Rf/2 is the Thevenin equivalent resistance of the soil at the points of contact. A tutorial explanation of Figure 6 of the Std 80 was given in the EPRI report EL-2682 and it is repeated here for convenience.

The computational procedure for body currents consists of computing a Thevenin equivalent circuit connected to the points of contact of the human body with the ground field (i.e., points A and B in Fig. lb). The Thevenin voltage source, and (b) the equivalent resistance. The voltage source equals the open-circuit voltage, meaning in this case the voltage at the points of contact when the human being is not touching. This voltage will be the touch voltage. The equivalent internal resistance between the points of contact can be accurately computed with numerical techniques (1).

For fast but approximate computations, the human foot can be modeled as a plate touching the surface of the earth. The resistance of the plate to remote earth is approximately

where p is the resistivity of the earth and b is the radius of the plate. The human foot definitely is not a circular plate. However, it has been observed with scale models and numerical studies that the area of the foot in touch with the earth is the determining variable. For this reason, b can be approximated with

b=d :

where A is the area of the foot in touch with the earth. For an adult with large feet, the area A of the persons feet is approximately 200 cmz. Thus the value of b is computed to be

b z 0.08 m

In this case the resistance of one foot touching the earth is

where p is expressed in ohm.meters. Thus, approximately, the equivalent resistance in Fig. lb, where the resistances of the two feet to soil are connected in parallel, is

The equivalent resistance, rq, in Fig. lb, should also take into account the resistance of the grounding system. However, for practical grounding systems, this resistance is typically small compared to the resistance 1.5 p , and thus omitted. In my opinion, cases in which the effect of the grounding system resistance can account for more than 5 % are of academic importance only.

Once the Thevenin equivalent circuit has been computed, the electric current through the human body, ih, is computed from

i b = V e q req + rb

where rb is the resistance of the human body between the points of contact. It is this reasoning which leads to the equations in the IEEE Std 80. The

accuracy of the approximate equation for reg has been checked by the discusser using sophisticated computer models (Reference 1, pages 2-12 through 2-17.) and found acceptable for all practical applications.

(b) Fig. 1. to a touch voltage.

Definition of equivalent circuit for the computation of body currents due

A 4

R A = Rs + ~ ( R F + RMF)

Fig. 6 . Touch Voltage Circuit

Reference

1. EPRI Report EL-2682, Analysis Techniques for Power Substation Grounding Systems, Volume 1, Methodology and Tests, October 1982.

Manuscript received Feb. 19, 1989.

Abdul M. Mousa, D. A. Jensen and R. M. Rockwell (BC Hydro, Vancouver, Canada): The 1986 Edition of the IEEE substation grounding guide differs from both the earlier 1976 edition and the 1958 AIEE Committee Report regarding the definitions of the touch voltage and the resistance of the foot Rf. The following physical facts are presented to put the definition and calculation of Rf into perspective: The dimensions and the material of the physical resistor which corresponds to the resistance of the feet vary from case to case. Parts A and B of Fig. 1 show the case of a transferred potential situation with a large separation between the man and the injection point of the fault current If. In this case, the body current I h

623

flows from the feet to infinity and is governed by pa which is the effective resistivity from the surface of the earth to infinity. The corresponding foot resistance Rfm can be calculated assuming the pattern of the flow of Ib to be unaffected by the flow of If. If the foot is taken as a circular plate having a radius r = 0.08 m, then,

Rfm=p,,/4r s 3p, (1) Parts C and D of Fig. 1 show the case of a transmission tower using

concentrated grounding which can be represented by an equivalent hemisphere (designated 0). The fault current flows in radial lineslconical surfaces (labelled 1, 2, 3...), and the hemispheres shown by dotted lines (labelled 0, P, Q, R, ...) become equipotential surfaces. Let point A (the location of the mans feet at the ground surface) be on the equipotential surface P, and let the intersection of surface P with current flow line No. 1 (which is the one closest to the surface of the ground) be point A. Point A is separated from point A by a small vertical distance AH. Note that the body current is a negligible fraction of the fault current. Hence the potential distribution and current flow lines shown in Fig. 1C apply regardless of the existence of the man on the site. When the hand contact takes place, the body current flows in almost vertical lines over the short distance AH, then it joins current flow surface No. 1. Hence the resistance R,., (subscript t denotes the tower) can be taken to be that of a parallel plate resistor having a length AH and a cross section equal to the area of the foot. Takmg AH = 0.06 m, which is physically reasonable, and r = 0.08 m as above gives:

(2) where p. is the resistivity of only the surface layer of the earth. Although a numerical similarity exists between (1) and (2), they are completely different from each other because each is expressed in terms of a different resistivity.

Parts E and F of Fig. 1 show the case of a substation. In this case, the driving voltage is taken as the mesh voltage rather than the voltage corresponding to 1 m reach which is used in the case of a transmission tower. Here there is no significant fault current flowing in the layer (usually 0.5 m thick) separating the ground mat from the surface of the earth. The body current flows from the feet to the ground mat, as shown by the dotted lines in Fig. 1E. Hence Rk (subscript s denotes the substation) is equivalent to a parallel plate resistor having a length equal to 0.5 m and an effective cross section significantly larger than that of the foot. Let this cross section be a circular plate of radius rl . In the typical case, the 0.5 m burial depth of the mat consists of two layers: a thin surface layer of resistivity p s (crushed rock) followed by native soil of variable resistivity p , . If the whole burial depth is covered by a single material of resistivity p , , then,

Rn = AH . p , / d = 3p,

Rfs =0.5p1/?rr: (3) The 1958 AIEE report and the 1976 edition of the Standard use eqn. (2)

to calculate Rf . This is not appropriate because it corresponds to the case of transmission towers rather than the case of substations for which the Standard is intended. The method used in the 1986 edition of the Standard is also not appropriate since it corresponds to Fig. 1A which is not a touch voltage situation at all. On the other hand, section 4.2.4 of this paper correctly identifies the subject resistance as the resistance, through earth, between the feet and the grid. The numerical examples given in Section 4 .2 .5g iveG = 160Qforpl = 100QmandQ = 784Qforp, = 5 0 0 Q m. Noting that:

%q = 0.5Rh, (4)

Rfs E 36% ( 5 )

the above numerical values are approximately given by:

Comparing (3) and (5) gives:

r1 = 0.23 m (6) which is physically reasonable. Note that the above numerical values are based on a ground mat consisting of a single 20 m x 20 m mesh and without a crushed rock layer. Obviously, this is not a typical design case.

Other comments on the paper and the IEEE Standard follow.

1. Assume the fault current to be flowing and the man to be standing next to the structure but not yet touching it. This is indicated in Figs. 1D and 1F by switch S. The touch voltage should be logically defined as the difference in voltage between the structure and the hand of the man in the above situation. This is the definition used in both the 1958 AIEE Report and the 1976 edition of the Standard, as per Fig. 2.3 of the paper. After the hand contact is established, a fraction of the touch voltage appears across the mans body, and that portion should be rather called

0.5 Rfs Ro If G Rb

* (A) ( 8 ) TRANSFERRED POTENTIAL SITUATION

H

(C ) (D) CASE OF TRANSMISSION TOWERS

2.

(GPR -Emesh) 9 (E) (F)

CASE OF SUBSTATIONS

Fig. 1. Definition of Rf for the different cases.

the BODY VOLTAGE (Eb). (There is a need to specify this quantity because some jurisdictions tend to legislate safety in terms of voltage rather than body current). In a survey done by one of the discussers covering a large number of points of a 230 kV/69 kV substation, the measured values of the ratio (Eb/EfoUch)were found to be 0.2 or less. The body current is given by:

(7)

I b = (8)

The 1986 edition of the Standard defines &ouch as given in Fig. 2.4 which is not appropriate. Having done so, Ib should be calculated using the form of eqn. (8). Instead, the Standard uses a form similar to (7) [eqn. (25) on p. 461 which is incorrect. This confusion would be cleared up by using two different terms: Touch Voltage and Body Voltage. When measuring the touch voltage, the mans body is replaced by a high impedance instrument as shown by the dotted lines in Figs. 1D and 1F. Since this draws a negligible current, the voltage drop across the resistance (0.5 Rf) is also negligible. Hence the instrument records the correct value of the touch voltage without requiring access to point A in the mound.

I b = &ouch/(% i- 0.5 R d

Y

3. The ultimate fault current upon which the design of the ground mat of a HV substation is based, is usually in the range 5-50 kA. For the ground mat to meet safety requirements, it must limit the body current to a fraction of an ampere: about 0.2 A for the typical case of a 0.3 second fault duration. Without restoring to calculations, it is obvious that the diversion of such a negligible fraction of the total fault current into a different path (the mans body) cannot change the voltage distribution in the ground. With Etouch properly defined as in Fig. 2.3, the assumption that the touch voltage is practically the same regardless of the existence of the man at the site must be valid. Of course, preliminary design work may include grounding configurations which turn out to be inadequate and hence are dropped. For some of those preliminary design cases, the body current may be excessive enough to invalidate the above

624

assumption. This, however, is not important because those cases do not represent a solution which meets the IEEE guidelines and will not appear in design documentations. The numerical example in Section 4.1 gives a body current equal to 0.68 A for an assumed fault current of only 1OOO A. That case violates IEEE guidelines even though it is based on a fault current which is too low to be realistic. Hence it is not appropriate to use that example to study the change in the pre-existing voltage. The data in Fig. 4.5 appear to be misleading since it is based on the unrealistic case of a zero body resistance. Note that the error in calculating the body current, reported in the two examples in Section 4.2.5, would be practically eliminated if Rf is correctly defined as per Fig. lE, and eqn. (5) is used to calculate it. It would be appreciated if the authors provide numerical values for KS based on realistic data regarding total size of the ground grid, grid spacing, the existence of a thin surface layer of crushed rock, and the filling of the balance of the burial depth of the ground grid by a native soil of variable resistivity.

Manuscript received February 25, 1988.

Donald N. Laird, (Los Angeles Department of Water and Power Los Angeles, California): There appears to be a misunderstanding by the authors of the method used by the guide (IEEE-80-1986) to allow for the computation of body current. In statement 2.1.6, they refer to the voltage between the victims hand and remote soil. The voltage that causes the body current to flow is the voltage between the victims hand and the victims feet. The victims feet are not touching remote soil but are in close proximity to his hands. If the victims feet were on remote soil, the victim might experience transfer potential.

The authors Figure 2.4 should also show E touch as being the voltage across the combined resistance of R body and Rf/2. Perhaps this misunderhanding has led to some questioning of the methodology used in the guide. In the case analyzed by the authors of soil with no high resistivity rock layer, this difference in the understanding of the definition of touch voltage may not be too significant.

Rewriting Equation 26 of the guide gives the body current as the touch voltage divided by (1,OOO + 1.5C S) where C is a reduction factor which takes into account the thickness of the rock layer (here taken as 0) and a reflection factor (also 0). If the soil resistivity was 100 ohm-meter, then the resistance limiting body current would be: [(l,OOO + 1.5(100)] or 1,150 ohms. In this case, the 150 ohms is taken to be the contact resistance to the earth at this point of contact.

In many substations, a rock layer is needed to further reduce the body current. If a six-inch layer of 1,OOO ohm-meter gravel is used, the total resistance would be [(1,OOO + 1.5(0.73)(1,OOO)] or 2,095 ohms. In this case, the 1,095 ohms is the combined contact resistance and effect of the six-inch layer of rock. The touch voltage is the voltage between the interference between the soil and rock, and the grounding grid or grounded object.

I hope this discussion will be beneficial to the understanding of the methodology used in the guide. In general, I would disagree with the authors conclusions. The guide presents a reasonable method of allowing for the beneficial effect of a thin layer of gravel without the use of a complex computer program. For additional discussion of this, please refer to Chapter 5, IEEE Tutorial Course Text Practical Applications of ANSI/ IEEE Standvd 80-1986, 86 EH0253-5-PWR.

Manuscript received February 22, 1988.

F. P. Dawalibi, R. D. Southey, and R. S . Baishiki

The discussers have made quite a few interesting comments and we thank them for their input. In the following, we would like to respond to each discusser separate1 y . Mr . Me1 i opoul os : We thank the discusser for his comments. In our opinion, it is the discusser who is misinterpreting the ANSI/IEEE Std. 80. As far as Figure 2.4 of our paper is concerned, we are aware that it i s not the touch voltage circuit illustrated in recent releases

of the present standard; however, it is certainly the touch voltage circuit defined by the following passage fro; Chapter 6, Section 1 of the present standard: touch voltage: the potential difference between the ground potential rise (GPR) and the surface potential at the point where a person is standing, while at the same time having his hands in contact with a grounded structure. No reference is made, in this definition, of open circuit voltage or foot resistance. The intent of our Figure 2.4 was to indicate the lack of a comprehensive definition and a sol id theoretical basis to the present standards body current equation, and we still believe that we have succeeded.

Also, contrary to the discussers claims, there is no explicit nor implicit reference to Thevenin voltages or impedances in the standard. As far as EPRI Report EL-2682 is concerned, it is not part of Std. 80 and it is not a standard. Therefore, its contents reflect the perspective of its authors. In the same way as another EPRI report written by one of the authors of this paper reflects his perspective (EPRI EL 2699).

Furthermore, the discusser does not appear to understand the nature of the Thevenin equivalent resistance in the touch voltage situation discussed. The discusser goes into detail describing how to approximate a foot by a circular plate and how to calculate its resistance to remote earth, but never mentions why he is concerned with the resistance between foot and remote earth, when, according to his own Fig. 1 b Thevenin model, he should be concerned with the resistance between foot and grid.

As an afterthought, the discusser mentions that the Thevenin equivalent resistance should account for the resistance of the nearby grounding system. Now, our paper shows that in cases where a foot is well coupled to a nearby grounding grid, proceeding incorrectly by measuring the resistance from foot to remote earth, produces in equivalent resistance that can be much bigger than the resistance determined (correctly) between foot and grid. It is precisely grounding systems which have low resistances which permit good coupling with nearby feet and therefore afford the greatest potential for error. Yet Mr. Meliopoulos declares that the low resistance of a grounding system is a good reason for ignoring its presence! This is simply in contradiction with scientific evidence.

If it is true, as stated by the discusser, that it is this reasoning Yhich leads to the equations in IEEE Standard 80 , and we suspect that it is in part, then we suggest that it is all the more urgent that the standard be revised to correctly describe the concepts and approximations behind the present equations.

We understand the discusser has felt the need using sophisticated computer models to verify the adequacy of the IEEE approach in a manner similar to the methodology developed in this paper. However, we regret his study was not published to reassure other potentially concerned colleagues.

Mr. Laird:

In the first paragraph of his discussion, Mr. Laird summarizes the authors view point of the fundamental problem with the present IEEE-80-1986 Standard: In computing the resistance of the body current path through the earth, the present standard places the body resistance in series with the resistance of the earth between the foot and remote ground: as if a

625

t r a n s f e r p o t e n t i a l were causing t h e shock. Our suggested remedy, which i s h i n t e d a t by e a r l y i n v e s t i g a t o r s o f touch v o l t a g e shocks, such as P i e r r e Laurent (Reference [ l ] o f our paper), i s t o rep lace t h e remote f o o t r e s i s t a n c e by t h e r e s i s t a n c e through e a r t h between t h e f e e t and t h e g r i d .

I n h i s d iscuss ion o f g rave l layers , M r . L a i r d i n s i s t s upon des ignat ing th; e a r t h p a t h r e s i s t a n c e as t h e "contac t r e s i s t a n c e . T h i s widespread misunder- s tand ing must be c l a r i f i e d . The f o o t r e s i s t a n c e represents a d i f f u s e r e s i s t a n c e produced by t h e mass o f e a r t h between t h e f o o t and t h e g r i d ; i t i s i n no way conf ined s t r i c t l y t o t h e f o o t con tac t p o i n t .

F i n a l l y , we must agree t h a t t h e guide presents an adequate s i m p l i f i e d method f o r c a l c u l a t i n g f o o t r e s i s t a n c e i n most t y p i c a l t ransmiss ion subs ta t ion cases, b u t we m a i n t a i n t h a t i t i s impor tan t t o i n d i c a t e under which c o n d i t i o n s problems w i l l occur, and t o p resent t h e c o r r e c t concept behind t h e t r u e body c u r r e n t equat ion which i s approximated by ANSI/IEEE Standard 80.

M r . Mousa e t a l . :

We note t h a t t h i s d iscuss ion under l ines our p r i n c i p a l asser t ion : t h a t t h e ANSI/IEEE Standard 80 equat ion can o n l y be made accurate i f f o o t r e s i s t a n c e i s de f ined as " res is tance, through ear th , between t h e f e e t and g r i d " , r a t h e r than t h e present i m p l i c i t d e f i n i t i o n which i s " t h e r e s i s t a n c e through e f r t h , between t h e f e e t and i n f i n i t y (remote ear th ) . I n o ther words, t h e present standard neg lec ts t h e f o o t - g r i d p r o x i m i t y e f f e c t when c a l c u l a t i n g t h e f o o t r e s i s t a n c e va lue t o use i n t h e body c u r r e n t equat ion.

The d iscussers have under1 i n e d t h a t t h e examples we have presented do n o t represent t y p i c a l design cases. We must emphasize t h a t , i n e x p l o r i n g t h e e f f e c t s o f var ious parameters on t h e importance o f t h e g r i d - f o o t p r o x i m i t y e f fec t , we have chosen designs which are n o t o f t e n encountered i n t y p i c a l t ransmiss ion subs ta t ions i n o rder t o o b t a i n s i g n i f i c a n t r e s u l t s . I n so doing, we have under l ined t h e s i g n i f i c a n t parameters, c l e a r l y i l l u s t r a t e d t h e i r . p o s s i b l e e f f e c t s i n a conceptual and q u a n t i t a t i v e manner, and shown t h a t i n "normal" t ransmiss ion subs ta t ion grounding s i t u a t i o n s , p r o x i m i t y e f f e c t s can be neglected.

The d iscussers p o i n t o u t t h a t no case has been examined i n which, as i s t y p i c a l l y t h e case f o r t ransmiss ion subs ta t ions , a l a y e r o f crushed r o c k covers t h e e a r t h ' s surface. The e f f e c t o f such a layer , assuming t h a t i t s r e s i s t i v i t y i s g r e a t e r than t h a t o f t h e s o i l below, w i l l be t o d i m i n i s h t h e importance o f t h e g r i d - f o o t p r o x i m i t y e f f e c t . To see t h i s , remember t h a t t h e g r i d - f o o t p r o x i m i t y e f f e c t i s g r e a t e s t when t h e r e s i s t a n c e through e a r t h between t h e f e e t and t h e g r i d i s small compared t o t h e r e s i s t a n c e through e a r t h between t h e f e e t and i n f i n i t y (remote ground). A crushed r o c k l a y e r diminishes t h i s d i f f e r e n c e , and hence d imin ishes f u r t h e r t h e p o s s i b l e inaccurac ies generated by t h e present ANSI/IEEE method. It i s , however, impor tan t t o no te here, t h a t t h e sur face cover ing m a t e r i a l in t roduces o t h e r d i f f i c u l t i e s , which are n o t r e l a t e d t o t h e problem discussed i n t h i s paper; t h i s sub jec t i s p r e s e n t l y under i n v e s t i g a t i o n and research r e s u l t s w i l l be communicated as soon as they become a v a i l a b l e .

I n d e s c r i b i n g t h e c u r r e n t conduct ion mechanism i n t h e s o i l , t h e d iscussers have r e s o r t e d t o d e s c r i b i n g var ious types o f p a r a l l e l p l a t e r e s i s t o r s , imaginary

l i n e s o f c u r r e n t , and an a r i b i t r a r y depth d e l t a H which i s remin iscent o f t h e 1958 AIEE Committee Report p i c t o r i a l d e f i n i t i o n o f touch vo l tage. S t r i c t l y speaking, we cannot agree w i t h these exp lanat ions which a r t i f i c a l l y c o n f i n e t h e f o o t r e s i s t a n c e t o c y l i n d r i c a l clumps o f e a r t h below t h e feet, and conf ine c u r r e n t f l o w t o imaginary l i n e s of cur ren t . One statement i n p a r t i c u l a r , " t h e bofy c u r r e n t f l o w s from t h e f e e t t o t h e ground mat , r e q u i r e s c o r r e c t i o n : body c u r r e n t f lows from t h e fee t t o remote ground ( o r t h e remote genera t ing ground) a long every p o s s i b l e path, b u t tends t o avo id t h e ground mat; t h i s l a t t e r behaves as a competing e lec t rode which a l s o i n j e c t s c u r r e n t i n t o t h e ground. Also, f o o t r e s i s t a n c e i s t h e r e s i s t a n c e o f t h e mass o f e a r t h separa t ing t h e f e e t f rom t h e grounding g r i d , and n o t any k i n d o f c y l i n d e r . The p i c t o r i a l d e s c r i p t i o n o f t h e d iscussers i s use fu l t o some ex ten t because i t he lps i n v i s u a l i z i n g t h e problem on an i n t u i t i v e l e v e l .

We must i n s i s t t h a t t h e vo l tage d i s t r i b u t i o n a t t h e ear th 's sur face near t h e f e e t o f t h e human s u b j e c t i s d i s t u r b e d as soon as t h e s u b j e c t i s connected t o r e c e i v e an e l e c t r i c shock, however smal l , and t h a t t h e change i n t h e p o t e n t i a l a t t h e f o o t con tac t p o i n t , when t h e shock begins, i s independent o f t h e magnitude o f t h e ( p o s s i b l y very smal l ) c u r r e n t passing through t h e body, f o r a g iven p r e - e x i s t i n g touch vol tage: i t i s a f u n c t i o n o f t h e body res is tance and f o o t - t o - g r i d r e s i s t a n c e (and p r e - e x i s t i n g touch vo l tage) on ly . Admit tedly, t h e ex ten t o f t h e e a r t h mass which experiences a s i g n i f i c a n t change i n vo l tage due t o t h e connect ion o f t h e human i n t h e c i r c u i t can be very smal l , and decreases w i t h decreasing body c u r r e n t ; b u t Mousa e t a l ' s Body Vol tage t o Touch Vol tage r a t i o o f 0.2 conf i rms t h e conc lus ions (about vo l tage d i s t r i b u t i o n near t h e f e e t ) d e r i v e d from o u r s tud ies .

I f tough v o l t a g e i s d e f i n e d as t h e d i f f e r e n c e i n p o t e n t i a l between a p o s s i b l e ( o r a c t u a l ) hand contac t p o i n t and a p o s s i b l e ( o r a c t u a l ) f o o t con tac t p o i n t on t h e e a r t h ' s surface, and i f t h e f o o t - t o - g r i d r e s i s t a n c e i s a s i g n i f i c a n t f r a c t i o n o f t h e body res is tance, then c l e a r l y , t h e touch vo l tage w i l l change s i g n i f i c a n t l y f rom t h e case i n which no human i s p resent t o t h e case where t h e human i s present, even i f t h e body c u r r e n t i s 0.2 A on ly .

i s f a r as F igure 4 . 5 i s concerned, we l a b e l l e d i t wors t case r a t i o o f I E E E body c u r r e n t / t r u e body

c u r r e n t " i n o rder t o u n d e r l i n e i t s t r u e s i g n i f i c a n c e and thus avo id mis lead ing anybody; we c l e a r l y p o i n t ou t i n Sec t ion 4 . 2 . 5 and on t h e p l o t i t s e l f , t h a t t h i s r a t i o a p p l i e s f o r Rbody = 0 ( o r h i g h s o i l r e s i s t i v i t i e s ) . We f u r t h e r presented 2 examples t o i l l u s t r a t e t h e r e s u l t s when t h e c o r r e c t approach i s app l ied t o t y p i c a l cases, and t o show t h a t these r e s u l t s d i f f e r f rom those ob ta ined from t h e wors t case scenar io.

I n conclusion, t h i s whole i ssue b o i l s down t o one quest ion: p r e s e n t l y ANSI/IEEE Standard 80 performs body c u r r e n t c a l c u l a t i o n s us ing a f o o t r e s i s t a n c e which assumes a t r a n s f e r r e d p o t e n t i a l s i t u a t i o n as i l l u s t r a t e d by F igure 1 A o f Mousa e t a l ; i . e . , t h e e f f e c t o f mutual c o u p l i n g between a sub jec t ' s fee t and a nearby g r i d i s completely ignored. Our ques t ion was: how much d i f f e r e n c e does t h i s make - i n any s i t u a t i o n : w i t h o r w i t h o u t g rave l , f o r var ious 1 i k e l y and u n l i k e l y body res is tances , f o r var ious s o i l s t r u c t u r e s ? Our research i n d i c a t e s t h a t , i n general, p r o x i m i t y e f f e c t s a re minimal f o r t y p i c a l t ransmiss ion s u b s t a t i o n grounding s i t u a t i o n s . We have descr ibed, however, circumstances under which

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inaccuracies can occur, and what order of magnitude such inaccuracies can atain. This is important for grounding situations which iannot be labelled "typical transmission substation. We have stated clearly what conceptual model must be used to understand what the foot resistance truly represents in the body current equation. Manuscript received July 20, 1988.