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A Graphical Method for Safety Assessment of Grounding SystemsA. P. Sakis Meliopoulos, Fellow, IEEESchool of Electrical and ComputerEngineeringGeorgia Institute of TechnologyAtlanta, GA, U.S.A.

Department of Electrical EngineeringI-Shou UniversityKaohsiung, Taiwan, R.O.C.

Rowland I. JamesEntergy Transmission639 Loyola Avenue 70113P. 0.Box 61000New Orleans, LA 70161

Abstract: This paper presents a graphical method for safetyassessment of grounding systems. For a grounding system to besafe, the maximum touch and step voltages should not exceedpostulated safety criteria. The method presented in this paper isapplicable to the safety criteria of the IEEE Standard 80as wellas the 1EC-479-1. Both standards define safety criteria in termsof allowable body current. The allowable body current is thentranslated into the allowable touch and step voltages. Thus,safety assessment of a grounding system is referred to aprocedure by which the actual maximum touch and stepvoltages are computed and compared to the maximumallowable (safe) touch and step voltages. Since the IEC-479-1safety criteria are nonlinear, a graphical method ispresented forsafety assessment.Keywords: Safety Assessment, Touch voltage, Step voltageIntroductionWith ever increasing fault current levels in todaysinterconnected power systems, there is renewed emphasis onsafety [1-23. Since the early days of the electric power industry,safety of personnel in and around electric power installationshas been a prime concern. A mechanism by which safety ofpersonnel is affected is the ground potential rise of groundedstructures during electric power faults and the possibility ofhumans touching grounded structures and, therefore, subjectmgthemselves to voltages. A human body coming in contact withan energized grounding system will be normally subjected to avoltage (touch or step). The amount of current through herhisbody will depend on the body resistance, and the parameters ofthe system at the point of contact. A 50 or 60 Hz electriccurrent conducted through a human body as a result of anaccidental conduct with a grounded structure, under adverseconditions, should be of magnitude and duration below thosethat cause ventricular fibrillation.

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Safety assessment of grounding systems is a procedure thatdetermines whether the maximum touch and step voltagescomputed meet the postulated safety criteria. The safetycriterion in IEEE Standard 80 and IEC-479-1 is defined interms of the allowable body current, that is, the value ofelectric current that the average person can withstand withoutdanger of electrocution (or the possibility of sufferingventricular fibrillation). The allowable body current is thentranslated into the allowable touch and step voltages. Inother words, safety can be assessed in terms of he touch andstep voltages instead of the body current. The aim of thispaperis to describe a graphical method for determining allowabletouch and step voltages.The paper is organized as follows: first the electric shockmodel is presented, and all relevant parameters are defined.Then, a graphical method to determine the allowable touch andstep voltages is described in detail and followed by an example.Finally, conclusions are drawn in Section4.

2016

The Electric Shock ModelElectric shock may occur when an individual touches agrounded structure during a fault (touch voltage), walks in thevicinity of a grounding system during a fault (step voltage),touches two separately grounded structures during a fault(metal to metal touch voltage), etc. While each condition canbe exarmned separately and in detail, in order to keep the sizeof this paper short, we will discuss both conditions but we willpresent the graphical method for touch voltage only.The electric shock models are shown in Figs. 1and 2, whichillustrate a human being in the vicinity of a substation groundmat subjected to touch and step voltages, respectively. Theelectric shock model is the circuit that determines the flow ofelectric current in the human body. The human body may comeinto contact with a ground or soil either at three points (handand two feet) or at two points (two feet) as illustrated in Figs.l(a) and 2(a). The grounding system and soil are representedby a Thevenin equivalent at the points of contact. Figure l(a)illustrates the equivalent resistances between any pair ofcontactpoints,B, A 1, andA2,he groundmat and remote earth.When a fault occurs, voltages will appear between any pair of,points of contact, B, Al, and A2. Similarly, Figure 2(a)illustrates equivalent resistances between Al, A2, round and

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remote earth. The Thevenin equivalent in this case is a threeterminal circuit (terminals B, Al, and A2). Similarly, theThevenin equivalent in Fig. 2(a) is a two terminal circuit(terminals A1 and A2). The Thevenin equivalent can becomputed using proper analysis methods. The Theveninvoltage source V, equals the open-circuit voltage, meaning inthis case the voltage at the points of contact when the human isnot touching. The equivalent intemal resistance, as shown inFigs. I@) and 2@), between the points of contact, can beaccurately computed with numerical techniques [3], [4], [ 5 ] orwith the approximate equations provided in Table 1. For theelectric shock model of Figs. le)and 2@), the followingdefinitions apply:

Touch Resistance (or Thevenin Equivalent Resistance): Theresistanceof the soil between the point of contact of the humanbody with the soil (points A1 and A2) and the groundingsystem, i.e., reS.Body Current:The electric current through the human body.

/ I f \/ - /

n

@)Figure 1. Definition of the Electric Shock ModelParameters-Touch Voltage.

Touch Voltage (or Thevenin Equivalent Voltage): The opencircuit potential difference between a grounded structure (pointB) and the surface potential at the point where a person isstanding (pointsA1 and A2).Step Voltage (or Thevenin Equivalent Voltage): The opencircuit potential difference between two feet at the point wherea person is standing (points A1 and A2) without contacting anyother grounded object.Body Voltage: The voltage across the human body when theelectric shock circuit is closed.Body Resistance: The resistance of the human body betweenthe points ofcontact, i.e., in the case ofFig. 1,between pointBandpointsA 1 and A2 (hand to tw o feet) or in the case of Fig. 2,between points A1 and A2 (foot to foot). It depends on manyfactors, such as size, skincondition, pressure at contact, etc.

Figure2. Definitionof theElectric Shock ModelParameters-Step Voltage.Table 1. Electrical Shock Model Differences between IEEEStd 80 and IEC-479-1

IEEEStd 80 IEC 479- 1Voltage Dependent1000ohms and Path Dependent(Figs. 3 and 4)BodyResistance

Thevqnin I .sc,p, for touch voltageEquiv'l~lent 6.0Cspsfor step voltageResistanceTheveninEquivalent Simplified Equationski k,L Ior use of computer models isVoltage suggested

no guidance

no guidanceS-curves independentof human size(Fig. 5 )0.157A / f i for 70kg personCurrent

Note: C, is the reduction factor, ps is the resistivityof the surface

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material (0-m),nd t is the duration of lectric shock (sec).

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The described electric shock model is inherent in both IEEEStd 80 and IEC 479-1 [ l ] , [2]. However, the two documentsdiffer in their application of the electric shock model. Table 1provides an overview of the differences between the twodocuments with reference to the electric shock model. The IEC479-1 provides data for body resistance as a finction of bodyvoltage, which are illustrated in Figure 3, and data for bodyresistance as a function of path, which are illustrated in Figure4. In Figure 3, the 5 % curve indicates body resistance valueswhich were not exceeded by 5% of the population, the 50%curve indicates body resistance values which were notexceeded by 50 % of the population, etc. All the values inFigure 3 are for hand-to-hand resistance. IEC 479-1 alsoprovides values of permissible body current versus electricshock duration as shown in Figure 5. The space of body currentand shock duration diagram is separated into different zones bytwo curves. As an example, Zone 4 represents all thecombinations of body current and shock duration that will leadto ventricular fibrillation with probability more than 50%.

-B2 000.::-$ 3000.a6

2000

1000.

'OO01

-95 % Body Resistance Values50% Body Resistance Values5% m a y Resistance ues

5000ooois

01 ' 8 1 ' ' 1 " I0 200 400 600 800 1000 1200 1400 1600 1800 2000Body Voltage 01)

Figure3. Human Body Resistance as a Functionof BodyVoltage.The Proposed ApproachThis section summarizes the proposed method for determiningallowable touch and step voltages.The basic concept which-determines allowable touch and stepvoltages is that of the Allowable Body Current Limi t . Theallowable body current in the IEEE standard 80 [l] is definedwith equation:

0.116 A-lb,allowable --;where t is the electric shock duration in seconds, while theallowable body current in the IEC-479-1 is defined with the topcurve of Figure 5. Because the IEEE Std 80 uses a constant1000 ohm resistance for the body resistance, the computationof the allowable touch (or step) voltage is straightforward. TheIEC-479-1 uses a nonlinear body resistance that makes thiscomputation complicated.

nResistanceto One Hand(Resistance to Both Hands)

Figure4. Internal Impedanceof the Human Body as aFunctionof the Current Path [Data from IEC 479-11.1

one 4

r . . . . . . . . # . . . . . . . . . . . . LIO' IO' lo3 IO'

Duration of currmc-flow (ms)Note: Zone 2 - Usually no harmful physiological effects,Zone 3 - Usually no organic damage tobe expected,

Zone 4 - Likely ventricular fibrillation.Figure5. Permissible Body Current per IEC 479-1 [Datafrom IEC 479-11.

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The proposed procedure to determine the allowable touch (orstep) voltage, per IEC-479-1, consists of three simple steps:STEP 1: Compute the equivalent foot resistant, r,. Thisresistance is to be computed with the equation of Table 1orwith computer based methods, for example references [ 6 ] , 7].

Note: The proposed procedure requires a graph of curve 1,Figure 6, i.e. a graph of the body voltage versus body current.This graph can be easily generated from the data in theIEC-479-1.

IC03 1STEP 2: For a given (or computed) touch (or step) voltageand equivalent resistance r from step 1, the actual bodycurrent is computed using a smple graphical method which isshown in Fig. 6. Specifically, the actual body current isdetermined by simultaneous solution of the following twoequations:

eq.

where the function rb = f(Vb) represents the nonlinearcharacteristics of the body resistance as a function of bodyvoltage (See Appendix A). Note that Equation (2) represents anonlinear fimction that is illustrated in Fig. 6as curve 1. Thiscurve depends on the assumed body resistance,rb, versus bodyvoltage, VI,, (i.e., the voltage across the human body). Thefollowing is suggested: For touch voltage applications use 75%of the average body resistance given in IEC-479-1. For stepvoltage applications use 100% of the average body resistancegiven in IEC-479-1.Equation (1) is a straight line in the coordinate system Vb vs Ib.This line is constructed as follows. For a given touch voltage,VmUch,his line will pass through he point ( 0 , V ~ " c h ) . This pointis shown as point A in Fig. 6.Also the line will pass fIom point(V,dr,, 0). This point is shown as point B in Fig. 6. Thegraphical construction consists of drawing a straight linethrough points A andB. The intersection of this line with curve1 determines the actual body current for the specified touchvoltage, as shown in Fig. 6.STEP 3: Compute the allowable body current with Eq. (1)and compare it to the actual body current. If the actual bodycurrent is below the allowable body current, then the giventouch voltage is below the allowable value. The allowabletouch voltage, Vtouch,allow&le, can be determined with anadditional simple graphical procedure. For this purpose, avertical line must be drawn at the allowable body current as isshown in Figure 6.This line intersects curve 1 at point D asshown in Figure 6.Next a line parallel to the line AB must bedrawn as shown in Figure 6.The intersection of this line withthe voltage axis determines the allowable touch voltage,vrouch,allowablc*The above simple three steps determine whether a computedtouch voltage is allowable or not allowable. The procedure fordetermining the allowable step voltage parallels the procedurefor computing the allowable touch voltage. A simple exampleis given next.

ib ib&abbFigure6. Graphical methodfor computing the actual bodycurrent.Example: The grounding of a substation consists of an 8 x 8mesh ground mat buried in a 105 ohm.meter soil. A 4 inchgravel layer of 2000 ohmmeter resistivity covers the substationarea. The actual touch voltage has been computed to be 390volts. The maximum fault duration is 24 cycles (0.40 seconds).Determine whether the voltage is below allowable, perIEC-479-1. Also determine the maximum allowable touchvoltage. Compute the maximum allowable touch voltage perIEEE Std 80, 1986 edition and compare to the value computedusing IEC-479-1.Solution: First the following quantities are computed:

k = (p-p,)/(p+p,) =-0.90h = 4 inches = 0.1 metersc, = 0.572 (fkom the present guide)res= 1.5csp, = (1.5)(0.572)(2000) = 1716ohms

ib,alhwable 0.150 Amperes (from Figure 5, probability 0.5%)The coordinates of points A andB (see Fig. 7) are

A = (O,V,,*) = (0,390 volts) andB = ( V d r - , 0)= (390/1716,0.0)=(0.227A, 0.0).

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The straight line through the points A and B intersects curve 1at point C, which provides the following values for the bodyvoltage and body current:

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Since ib < ballownble, the touch voltage of 390 volts is below theallowable touch voltage.Next the allowable touch voltage is determined as follows: Avertical line is constructed at & = 150 mA (the allowable bodycurrent). This line intersects curve 1 at point D. rom point D,a straight line parallel to the line AB is constructed as shown inFigure 7.This ine intersects the voltage axis at point E. Point Edetermines the allowable touch voltage which in th is case is453 volts:

The allowable touch voltage per IEEE Std 80, 1986 iscomputedas follows:Vwl&,dh,bk,,9&j=O.l16(1716+1000)/fi = 498 volts.The above allowable voltage is shown in Figure 7.Note that inthiscase, the allowable touch voltage per IEEE Std 80, 1986 ishigher than the one computed with the proposed method. Thismeans that in this case, the IEC-479-1 is more conservativethan heIEEE Std 80.

5fN-l .

0 k I0 50 100 150 200 250123mA B(227,O)

Figure7. Graphlcal methodfor computing the allowbletouch voltage.Body Current(mA)

Summary and ConclusionsThispaper presents a graphical method for safety assessment ofgrounding systems. The safety assessment is based on thecomputation of allowable touch and step voltages. Thesevoltages are depended upon the allowable body current and thebody current is a function of body resistance. The proposed

method involves a simple graphical procedure when the bodyresistance is a nonlinear function ofbody voltage (IEC-479-1).The IEEE Std 80uses a fixed 1000ohm body resistance and agraphical solution is not necessary. An example has beenpresented that compares the two standards. Finally, the paperpresents an analytical expression of the nonlinear bodyresistance as a function of body voltage.ReferencesANSI / lEEE Std 80-1986. IEEE Guide for Safety in AC SubstationGrounding, 1986.International Electrotechnical Commission IEC Report, Effects ofCurrent Passing Through the Human Body, Part 1: General Aspects,Magda S.Hammam, Rod S.Baishiki, A Range of Body ImpedanceValues for Low Voltage, Low Source Impedance Systems of 60 Hz,IEEE Transaction on Pow er Apparatus and System , Vol. PAS-102, No.5, pp. 1097-1105, May 1983.EPRI Report EL2682, Analysis Techniques for Power SubstationGrounding System, Volume 1, Methodology and Tests, October 1982.A. P Sakis Meliopoulos, Power System Gtvuding and Transients: AnIntroduction. New York,Marcel Dekker, Inc., 1988.Baldev Thapar, Victor Gerez,h alakrishnan, and Donals A.Blank, Evaluation of Ground Resistance of a Grounding Grid of AnyShape, IEEE Transaction on Power Delivery, Vol. 6, No. 2, pp.Baldev Thapar, Victor Gerez and Vijay Singh, Effective GroundResistance of the Human Feet in High Voltage Switchyrads, IEEEikunsaction on Power Delivery, Vol. 8, No. 1, pp. 7-12, January 1993.

479-1, IEC 1984.

640-647, April 1991.

BiographiesChien-Wing Lee (M 94) was born in Taiwan on June 13, 1967. Hereceived the Diploma of Electrical Engineering from NationalKaohsiung Institute of Technology, Taiwan, he B.S. degree inelectrical engineering from Arizona State University, Tempe, AZ in1987 and 1993, respectively; the M.S.E.E. and Ph.D. degrees fiom theGeorgia Institute of Technology in 1995 and 1998, respectively. He isan assistant professor at I-Shou University in Taiwan. His researchinterests are power system grounding analysis, power system transientmodeling, power quality, and applications of wavekt theory in powersystems.A. P.Sakis Meliopoulos (M 76, SM 83, F 93) was born in Katerini,Greece, in 1949. He received the M.E. and E.E. diploma from theNational Technical University of Athens? Greece, in 1972; theM.S.E.E. and Ph.D. degrees from the Georgia Institute of Technologyin 1974 and 1976, respectively. In 1971, he worked for WestemElectric in Atlanta, Georgia. In 1976, he joined the Faculty ofElectrical Engineering, Georgia Institute of Technology, where he i spresently a professor. He is active in teaching and research in thegeneral areas of modeling, analysis, and control of power systems. Heha s made significant contributions to power system grounding,harmonics, and reliability assessment of power systems. He is theauthor of the books,Power Systems Grounding and Transients, MarcelDekker, June 1988, Ligthning and Overvoltage Protection, Section 27,Standard Handbook or Electrical Engineers, M a w ill, 1993, andthe monograph, Numerical Solution Methodsof Algebraic Equations,EPFU monographseriris.Dr. Meliopoulos is a member of the HellenicSociety of Professional Engineering and the SigmaXi.

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Appendix A: Analytical Expressions of BodyResistance vs Body Voltage

The coefficients al, bl, CIand vo or the vector X=[al, bl, CI, O]and the coefficients az, bl, c2 and or the vector X=[az, bz, CZ,io]will be different for each one of the three sets of data. Foreach data set, the unknownvector x = [a, bl c1 vo 1 and x = [a2 a2b2bz cz 1 are computed by the Weighted Least Squares Method, cz

This Appendix presents analytical expressions for the voltagedependent body resistance that closely match the IEC 479-1data. These formulae can be used in lieu of the tabular data ofthe IEC 479-1. Table A.l presents a reproduction of bodyresistance data in the IEC 479-1. The table contains three setsof data, corresponding to the statistical values of 5%, 50% and95% of population [2]. Each one of the sets can beapproximated withone analytic function of the form

5% of the 50% of the 95% of thepopulation population population140.6 63.1 77.80.6 1o 1.4-130.1 -50.5 -68.0

A.2 and A.3. The accuracy of the derived analytic expressionsas compared to the IEC 479-1 data is illustrated in Table A.4and Table AS. For all practical purposes, the analyt~cexpressions can be used in lieu of data of Table A. 1.

i.e. by solving the following optimization problem io 241.1 48.1

TableA2. Computed Coefficientsof the AnalyticExpressions for Body Resistance5% ofthe 50%of the 95% of theulation o ulation ulation668.38 1 1080.021 1427.2967751.063 73049.270

C I 515.588 2552.197 2119.462va 3 11.673 80.182 13 .727

Table A3. Computed Coefficientsof the AnalyticExpressionsfor BodyVoltage.

26.9mi=l

Minimize J = wirf = rWrwhere r = rb,d - b,& (X)- the weight for the residual riW a diagonalmatrixof weightswiTable A I. Total Body impedance, per IEC 479-1 [Data fromIEC479-1 (1984))

ulation ulation

1250 2200 3500100 1200 1875 3200

Table A4. Comparisonof the Proposed Formula forResistance to the IEC479-1 DataI Values for the total body mpedance(n that arenot exceededfor a percentage(p&tild rank) f

SO??of the 95% ofheulation ulation ulationouch 5% of the, 479-1 Formula 479-1 Formula 479-1 Formula25 1750 1758.0 3250 3258.6 6100 6102.3plo002000 1450125012001125lo00750700677- 1414.41278.31195.91136.4992.7744.9704.6668 4338.33600.73 49.82832.22158.31542.11501.41427.0125 1125 1625 2875 Table115. Comparbonof the Proposed Formula for BodyCurrent vs Body Voltage to the IEC 479-1 Data.

lo00 700 1050 15002000 677 1084 1464The solution to above nonlinear estimation problem isobtainedwith the following a l g o r i h

100125220700

I 2000The computed analytic expression for the three sets of datausing above algorithm with wi=l.O for all i are listed in Table

Values for the body voltage (V) that arenot exceeded for a I5% of he

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