Comparison of touch and step voltages between IEEE Std 80 and IEC 4791.pdf
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Comparison of touch and step voltages between IEEE Std 80 and IEC 4791 C.H.Lee and A.l?Sakis Meliopoulos
Abstract: A comparison of the safety criteria of two widely accepted standards, i.e. the IEEE Std 80 and the IEC 4791 is proposed. The two standards differ in their definitions of permissible body current and body resistance. Another difference is that the IEC 4791 does not provide guidance on human feeusoil contact impedances. It tacitly assumes that these impedances are computable by the designer. A comprehensive study of permissible touch and step voltages by these two standards is included for a wide range of conditions, which enables a direct comparison of the two standards. It is shown that differences exist and these differences are quantified.
1
Introduction
Since the early days of the electric power industry, safety of personnel in and around electric power installations has been a prime concern. A mechanism by which the safety of personnel is affected is the ground potential rise of grounded structures during electric power faults, and the possibility of humans touchng grounded structures and therefore subjecting themselves to voltages. The 50 or 60Hz electric current conducted through a human body as a result of an accidental conduct with a grounded structure, under adverse conditions, should be of magnitude and duration below those that cause ventricular fibrillation. Over the years, and after many investigations of electric current effects on humans, safe limits have been established
safety. On the other hand, globalisation of national economies provides an interest towards harmonisation of standards. The first step in this endeavour is the technical comparison of various standards addressing the same issue. This paper provides a technical comparison of two standards that address the safety of electrical installations.
and standards have been developed which provide permis
sible values of body currents to avoid electrocution. Two such standards are the IEEE Std 80 and the IEC 479 1. The IEEE Std 80 has seen three editions (1961, 1976 and 1986); it is being currently revised, and has been in use in the USA and several other countries. The IEC 4791 was released in 1984. The premise of both standards is to establish safe (permissible) body currents. The underlying assumption is that the designer of grounding systems will make sure that these values are not exceeded under adverse conditions of accidental contact of humans with grounded structures. The phdosophcal difference between the two documents is that while the IEC 4791 does not address all relevant computational issues that may be 'necessary in the design process (such as feethoil resistance, etc.), the IEEE Std 80 does address most computational issues and provides procedures and guidance for assessing safety of a grounding system [l]. With ever increasing fault current levels in today's interconnected power systems, there is renewed emphasis on OIEE, 1999 ZEE Proceedings online no. 19990586 DOL lO.l049hpgtd:19990586 Paper received4th May 1999 C.H.Lee is with the Departmentof Electrid Engineering, IShou Univmity, Kaohsiung, Taiwan, Republic of China A.P. Sakis Meliopoulos is with the School of Elatrid and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 303320250, USA IEE Proc.Gener. Transm. Distrib., Vol. 146, No. 5, September 1999
Fig. 1 Defmitwn of electric shock mdeljnirameters  touch voltage
A2
Fig. 2
2
h& equivalent circuit
Electric shock model
Electric shock may occur when an individual touches a grounded structure during a fault (touch voltage), walks in the vicinity of a grounding system during a fault (step voltage), or touches two separately grounded structures during a fault (metal to metal touch voltage), etc. While each condition can be examined separately and in detail, we shall only focus on touch voltages. The electric shock model is shown in Figs. 1 and 2, which dlustrate a human standing near the middle point of a ground mesh and subjected to touch voltage. The electric shock model is the circuit which determines the flow of electric current in the human body. 593
The human body may come into contact with a ground or soil at three points (hand and two feet), as illustrated in Fig. 1. The grounding system and soil are represented with a Thevenin equivalent at the points of contact. Fig. 1 illustrates the equivalent resistances between any pair of the contact points, B, Al, and A2. When a fault occurs, voltages will appear between any pair of the points of contact B, Al, and A2. The Thevenin equivalent in this case is a three terminal circuit (terminals B, Al, and A2), and can be computed with proper analysis methods [2]. A typical simplification is to assume that the voltage at points AI and A2 are practically the same, in whch case the Thevenin equivalent is simplified to that of Fig. 2. The Thevenin voltage source Veq equals the open circuit voltage, in this case the voltage at the points of contact when the human is not touching. The equivalent internal resistance, as shown in Fig. 2 between the points of contact, can be accurately computed with numerical techniques [ 2 4 . For the electric shock model of Fig. 2, the following definitions apply: Touch voltage (or Thevenin equivalent voltage): The open circuit potential difference between a grounded structure (point B) and the surface potential at the point where a person is standing (points A1 and A2). Body voltage: The voltage across the human body when the electric shock circuit is closed. Body resistance:The resistance of the human body between the points of contact, i.e., in the case of Fig. 1 between point B and points A1 and A2 (hand to two feet). It depends on many factors such as size, skin condition, pressure at the contact, etc. Touch Resistance (Thevenin equivalent resistance): The resistance of the soil between the point of contact of the human body with the soil (points A1 and A2) and the grounding system, i.e. req. Body current:The electric current through the human body. The described electric shock model is inherent in both documents. However, the two documents differ in the application of the electric shock model. Table 1 provides an overview of the differences between the two documents with reference to the electric shock model. In subsequent paragraphs, a more detailed discussion of the safety criteria adapted in the two documents will be presented, followed by a comparison.
3
Safety criteria  IEEE Std 80
The IEEE Std 80 is based on a simplified electric shock model. The parameters of the electric shock model are shown in the second column of Table 1. This model is usually translated into permissible touch (or step) voltages. As an example, the permissible touch, VTPerm,and step, Vs,perm, voltages for a 50kg person are
0.116
VT,peTm
0.116
VS,perm
h
Additional comments and observations regarding the IEEE Std 80 are given below. The permissible body current has been selected from statistical data and represents a 0.50/0probability of ventricular fibrillation. It is believed that the approximate formulae for the Thevenin equivalent resistance in IEEE Std 80 were derived as follows. The human foot can be modelled as a circular plate touchng 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 is definitely not a circular plate. However, it has been observed with scale models and numerical studies that the area of the foot in contact with the earth is the most important variable. For this reason, b can be approximated with
where A is the area of the foot in contact with the earth. For an adult with large feet, the area A of the person’s feet is approximately 200cm2.Using this value, the radius is b = 0.08m and the resistance of one foot touchng the earth is
where p is expressed in Qm. The IEEE Std 80 further assumes that the mutual resistance between the two feet (see Figs. 1 and 2) has negligible effect, and thus the equivalent resistance is simply the parallel combination of the two feet to soil resistances
The equivalent resistance, req, in Fig. 2 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 1.5p, and is thus omitted. Cases in which the effect of the grounding system resistance can account for more than 2% are of academic importance only. The above equations for req apply to the case of uniform soil and neglect the effect of grounding system proximity or mutual resistance between feet. For nonuniform soil or for soil with a cover layer of high resistivity, the IEEE Std 80 provides a correction factor c,(h,, k). Specifically, the equivalent resistance req is given by
+
~ ~ ~ = ( 1 . 5 ~1000)
h
+
= ( 6 . 0 ~ 1000) ~ ~ ~
r e q= 6.0cs(hs,k ) p s Teq
= 1.5cS(h,, k ) p s
for step voltage
(3)
for touch voltage
(4)
Table 1: Electrical shock model differences between IEEE Std 80 and IEC 4791
594
IEEE Std 80
IEC 4791
Body resistance
100052
Voltagedependent and Pathdependent (Figs. 5 and 6 )
Thevenin equivalent resistance
1.5cgSfor touch voltage 6.0c8,for step voltage
no guidance
Thevenin equivalent voltage
Simplified equations k; k, L l o r use of computer models is suggested
no guidance
Permissible body current
O.116Adtfor 50kg person 0.157Adtfor 70kg person
Scurves (Fig. 7) independent of human size IEE P r o c G e n e r . Tmnsm. D u t r i b . , Vol. 146, No. 5, September I999
where = (P

Ps)/(P
+
(5)
P S I
Note that the region of greatest discrepancy is for layers of 1 4 in (or 0.02540.1016 m) thck, which is the usual case.
py = resistivity of the upper layer, p = resistivity of the soil below the upper layer, h, = thickness of the upper layer, c, = reduction factor for derating the nominal value of the
surface layer resistivity determined as follows: (1) c, = 1.04 for uniform soil, and (2) for nonuniform soil, the IEEE Std 80 provides a graph (Fig. 3 of the standard) for the graphical determination of c, from k and h,y. Investigation with computer models revealed that the IEEE Std 80 approximate formulae are accurate for all practical purposes for uniform soil only. For soil with an upper layer of high resistivity stone the correction factor cs(hs,k) is in error, especially for the practical case of upper layer thickness of 14 in (0.02544.1016m).
0.12 0.18 layer thickness, m Reduction factor comparison of IEEE Std SO andprogrm SGSYS 0
Fig. 4
0.06
IEEEStd 80
~
4 4  SGSYS computed
4
i8
4.0
Safety criteria  IEC 4791
.
3.5
0
Fig.3
1.o
2.0
D Feet to soil resistances as a fwzction of feet separation and gravel
thickness
= 3925Rm. pyclt/ = 2108m, D = feet separation. ft
The computerbased method for evaluation of the correction factor c,(h,, k ) consists of computing an equivalent voltage source connected to the points of contact of the human body with the ground field as indicated in Figs. 1 and 2. The points of contact of the human feet with the earth’s surface are modelled with two metallic plates placed at the location of the feet. The shape and dimensions of the plates are shown in Fig. 3. The grounding system together with the contact model is then viewed as a system with multiple grounds. This system has three terminals Al, f i 2 , and B. The elements of the equivalent circuit are computed with the method of moments [2,4]. Standard network techniques are then employed to compute the Thevenin equivalent parameters veq, req, as illustrated in Fig. 2. It is important to note that modelling the feet as two plates (surface electrodes) provides a realistic analysis model. The correction factor c,(h,, k) is then computed from equation
7000 
6000 t C: 5000 ai
5
4000

req
c s ( h s , k )= 1.5Ps
The value of reg, and therefore cs(h,, k), depends on foot size and spacing between feet. Using a foot model as shown in Fig. 3, the IEEE Std 80 model is matched exactly for uniform soil and assuming feet separation of D = 2 ft. Fig. 3 also illustrates the effect of the mutual resistance between the two plates representing the two feet. Note that for the usual standing position D = 12 ft, the effect of the mutual resistance is negligible. However, as the feet come closer than 1 ft, the effect of the mutual resistance is such as to increase the value of req. The computed values of c,(h,, k) are given in Fig. 4 superimposed on the present values of the IEEE Std 80. IEE Proc Gener Trunsm Distrib , Vol 146, No 5, September 1999
The data of IEC 4791 can be utilised in two ways: (a) actual body currents can be computed for an individual subjected to a touch or step voltage in a specific system and specific conditions, and (b) permissible touch and step voltages can be computed for a specific system. 595
a
Fi .6 Internal i m p e k e
Pa'
of the human
bo& as a fiction of the current
Numbers in brackets indicate current paths between both hands and corresponding part of the body. Numbers without brackets indicate impedance of several paths in the body as percentage of hand to hand impedance. Data from IEC 4791 (1984).
3L zone 4
a
10
E
zone2
10
'.
Figs. 5 and 6. req,T is the feet to soil resistance for touch voltage, i.e. the two feet to soil resistances are in parallel. reqSis the feet to soil resistance for step voltage, i.e. the two feet to soil resistances are in series. The IEC 4791 does not provide any data for r e , , or req,* For this reason, we shall use the data of IEEE Std 80, i.e. Eqns. 3 and 4. Note that application of above equations to obtain the permissible touch and step voltages is straightforward and involves the following steps: Step 1: For a given electric shock duration t and assumed probability of ventricular fibrillation, determine the value of permissible body current, ib,penn(t), from Fig. 7. Step 2 For the current ib,penn(t), determine the body resistances RbT and Rbs from the data of Figs. 5 and 6. For touch voltage it is expedient to assume that the path will be one hand to two feet (75% of the body resistance given in Fig. 5), and for step voltage the path is foot to foot (100% of the body resistance given in Fig. 5). Step 3: Compute req,Tand reqSfor IEEE Std 80. Step 4: Compute permissible touch and step voltages using eqns. 6 and 7 For comparison purposes with the IEEE Std 80, the permissible body current ib,pem(t) is computed for probability 0.5'1/0 of ventricular fibnllation by proper interpolation between the curves C1 and C2 of Fig. 7.
4.2 Computation of actual body current For a given touch or step voltage, the computation of the body current using the IEC data requires the solution of a set of nonhear equations. This solution can be obtained iteratively or with a graphical method described below. Step 1: Compute the Thevenin equivalent resistance, req, of the electrocution circuit. Step 2 For a given (or computed) touch (or step) voltage and equivalent resistance re from step 1, the actual body current is computed with t i e graphical method shown in Fig. 8. Specifically, the actual body current is determined by the simultaneous solution of the following two equations: &ouch
1
2
10
3 10
10
duration of currentflow, ms
Fig.7
Ib
Permissible bo4 currentfor IEC 4791
4. I Permissible touch and step voltage IEC 4791 The permissible (or allowable) touch, VTa,and step, Vf, voltages are computed from the following equations
v$ = i b , p e r m ( t ) v:
[RF ( i b , p e r m ( t ) ) $ r e q , ~ ] (6)
= i b , p e r m ( t ) [Rf
( i b , p e r m ( t ) ) $ Teq,S]
= V b / r b = T/b/f(Vb)
(9)
where the function rb = V b ) represents the nonlinear characteristics of the body resistance as a function of body voltage determined with the data of Fig. 5. Note that eqn. 9 represents a nonlinear function whch is illustrated in Fig. 8 as curve 1.
r1
350
(7)
where ibgem(t) is the permissible body current for IEC 4791 for an electric shock duration t. This current is obtained from the data of Fig. 7. &T(ib,pem(t)) is the body resistance for the path specified by the touch voltage (typically hand to two feet) and for a body current equal to ibpem(t). This value can be obtained from the data of Figs. 5 and 6. R,,s(ib,pem(t)) is the body resistance for the path specified by the step voltage (foot to foot) and for a body current equal to ibgem(t). This value can be obtained from the data of 596
(8)
v b $ r e q i b
4
10
CUNe 1
50 B(Vtouch/req, 0)
0
0
50
I
1
100 150 200 250 300 350 400
body current, mA
Fig.8 Graphical methodof computing a c t d b o r f v current IEE ProcCener. Transm. Distrib., Vol. 146, No. 5, September 1999
Table 2: Permissible touch voltages per IEEE Std 80,1986 edition 50kg person, probability of ventricular fibrillation 0.5% Shock
Soil resistivity
duration
50Qm
100Qrn
200Qrn
500Qm
1000Qrn
3000Qm
0.05s
526.9V
559.2V
599.7V
680.6V
923.4V
1328.0V
2946.6V
0.10s
372.5V
395.4V
424.0V
481.3V
652.9V
939.1V
2083.6V
0.15s
304.2V
322.9V
346.2V
393.0V
533.1V
766.7V
1701.2V
0.20s
263.4V
279.6V
299.8V
340.3V
461.7V
664.0V
1473.3V
0.25s
235.6V
250.1V
268.2V
304.4V
413.0V
593.9V
1317.8V
0.30s
215.1V
228.3V
244.8V
277.9V
377.0V
542.2V
1202.9V
0.35s
199.1V
211.4V
226.7V
257.3V
349.0V
502.0V
1113.7V 1041.8V
0.40s
186.3V
197.7V
212.0V
240.6V
326.5V
469.5V
0.45s
175.5V
186.4V
199.9V
226.9V
307.8V
442.7V
982.2V
0.50s
166.6V
176.8V
189.6V
215.2V
292.0V
420.0V
931.8V
Table 3: Permissible step voltages per IEEE Std 80,1986 edition, 50 kg person, probability of ventricular fibrillation 0.5% Shock
Soil resistivity
duration
50Qm
100Qm
200Qm
500Qm
1000Qm
3000Qm
0.05s
551.1V
680.6V
842.5V
1166.2V
2137.3V
3755.9V
10230.1V
0.1os
389.7V
481.3V
595.7V
824.6V
1511.3V
2655.8V
7233.8V
0.15s
318.2V
393.0V
486.4V
673.3V
1234.0V
2168.5V
5906.4V
0.20s
275.6V
340.3V
421.2V
583.1V
1068.7V
1877.9V
5115.0V
0.25s
246.5V
304.4V
376.8V
521.5V
955.8V
1679.7V
4575.0V
0.30s
255.0V
277.9V
343.9V
476.1V
872.6V
1533.3V
4176.4V
0.35s
280.3V
257.3V
318.4V
440.8V
807.8V
1419.6V
3866.6V
0.40s
194.9V
240.6V
297.9V
412.3V
755.7V
1327.9V
3616.9V
0.45s
183.7V
226.9V
280.8V
388.7V
712.4V
1252.0V
3410.0V
0.50s
174.3V
215.2V
266.4V
368.8V
675.9V
1187.7V
3235.0V
Table 4 Permissible touch voltages per IEC 4791,5% body resistance values, probability of ventricular fibrillation 0.5%, hand to two feet Shock
Soil resistivity
duration
10Qm
50Qm
lOOQm
200Qrn
500Qm
1000Qm
3000Qm
0.05s
342.4V
375.8V
417.6V
501.2V
751.8V
1169.6V
2840.9V
0.1os
319.0V
349.3v
387.1V
462.7V
689.6V
1067.7V
2580.2V
0.15s
287.5V
313.8V
346.7V
412.5V
609.9V
938.9V
2254.9V
0.20s
256.7V
279.5V
308.1 V
365.1V
536.1 V
821.2V
1961.6V
0.25s
222.2v
241.3V
265.2V
313.1V
456.6V
695.9V
1652.9V
0.30s
187.9V
203.7V
223.4V
262.7V
380.9V
577.8V
1365.3V
0.35s
148.8V
160.9V
176.0V
206.2V
296.9V
448.2V
1053.0V
0.40s
121.7V
131.0V
142.7V
166.1V
236.1V
352.9V
820.1V
0.45s
101.1V
108.5V
117.9V
136.6V
192.6V
286.1V
660.0V
0.50s
88.9V
95.3V
103.4V
119.5V
167.8V
248.2V
570.1V
IEE ProcGener. Transm. Distrib., Vol. 146. No. 5. September 1999
591
Table 5: Permissibletouch voltages per IEC 4791,50% body resistancevalues, probability of ventricular fibrillation 0.5%, hand to two feet Shock
Soil resistivity
duration
108m
508rn
1009rn
2008rn
5008m
10008rn
0.05s
449.4V
482.8V
524.6V
608.2V
858.8V
1276.7V
2947.9V
0.10s
415.5V
445.7V
483.6V
559.2V
786.1V
1164.2V
2676.6V
30008rn
0.15s
374.5V
400.9V
433.8V
499.6V
697.0V
1026.0V
2342.0V
0.20s
334.6V
357.4V
385.9V
442.9V
614.0V
899.1V
2039.5V 1720.4V
0.25s
289.6V
308.8V
332.7V
380.6V
524.1V
763.4V
0.30s
245.1V
260.8V
280.5V
319.9V
438.OV
634.9V
1422.4V
0.35s
193.8V
205.9V
221.0V
251.2V
341.9V
493.2V
1098.0V
0.40s
152.9V
162.2V
173.9V
197.3V
267.3V
384.1V
851.3V
0.45s
128.8V
136.3V
145.6V
164.3V
220.4V
313.9V
687.7V
0.50s
116.0V
122.5V
130.5V
146.6V
194.9V
275.4V
597.3V
Table 6: Permissible step voltages per IEC 4791,5% body resistance values, probability of ventricular fibrillation 0.5%, hand to two feet Shock
Soil resistivity
duration
108rn
50Bm
1008m
200Bm
5008m
10008rn
3000Qrn
0.05s
367.5V
501.2V
668.3V
1002.5V
2005.3V
3676.5V
10361.5V
0.10s
341.7V
462.7V
614.0V
916.4V
1823.9V
3336.4V
9386.2V
0.15s
307.2V
412.5V
544.1V
807.3V
1596.9V
2913.0V
8177.1V
0.20s
273.8V
365.1V
479.1V
707.2V
1391.4V
2531.8V
7093.2V
0.25s
236.5V
313.1V
408.8V
600.2V
1174.4V
2131.5V
5959.6V
0.30s
199.7V
262.7V
341.5V
499.0V
971.5V
1759.1V
4909.3V
0.35s
157.8V
206.2V
266.7V
387.7V
750.6V
1355.4V
3774.8V
0.40s
128.7V
166.1V
212.8V
306.2V
568.5V
1053.6V
2922.3V
0.45s
106.7V
136.6V
174.0V
248.7V
473.1V
846.9V
2342.4V
0.50s
93.7v
119.5V
151.7V
216.1V
409.2V
731.1V
2018.7V
Table 7: Permissible step voltages per IEC 4791,50% body resistance values, probability of ventricular fibrillation 0.5%. hand to two feet Shock
Soil resistivity
duration
109m
0.05s
474.5
608.2
0.1os
438.2
559.2
0.15s
394.3
499.6
0.20s
351.7
442.9
0.25s
304.0
0.30s
50Qm
1008rn
2008rn
5008m
775.3
1109.5
2112.3
3783.5
10468.5
710.4
1012.9
1920.4
3432.9
9482.7
631.2
894.4
1684.0
3000.0
8264.2
557.0
785.1
1469.3
2609.6
7171.1
380.6
476.3
667.7
1241.9
2198.9
6027.1
256.9
319.9
398.6
556.1
1028.7
1816.2
4966.4
0.35s
202.8
251.2
311.7
432.7
795.6
1400.4
3819.8
0.40s
159.9
197.3
244.0
337.4
617.7
1084.9
2953.5
0.45s
134.4
164.3
201.7
276.5
500.8
874.7
2370.1
0.50s
120.9
146.6
178.8
243.2
436.3
758.2
2045.8
Figs. 912 provide the data of Tables 27 in graphical form. The coordinates are the permissible touch or step voltages of the two standards, respectively. Each point represents permissible voltages, as allowed by the two standards computed for the same parameters of soil resistivity and shock duration. By construction, then, each point on the diagonal of the graph represents a case where the two standards yield the same permissible voltages. Points above the diagonal represent cases where the IEC 4791 is more conservative than the IEEE Std 80, whde points below the 598
1000Qm
30008m
diagonal represent cases where the IEEE Std 80 is more conservative than the IEC 4791. Note that the points are about evenly distributed around the diagonal. Finally, Figs. 13 and 14 compare the body resistance value used for the computation of the permissible touch and step voltages with the two standards. Note that for the usual shock durations 0.250.5s, the 5% body resistance of the IEC 4791 standard is near 100052 or higher. Ths is useful information for persons questioning the use of 100OQ in the IEEE Std 80. IEE Proc.Gener. Transm. Distrib., Vol. 144, No. 5, September 1999
1600 1400 
IEC 4791 more
1200 
d 5
1000 
c
.I
p! A
600 
13
400
U
IEEE Std 80 more conservativethan

800
Fi 9 Permissible touch voltages er IEEE Std 80 against IEC 4791; 5% bog resistunce values, probability ofvenntricular fibrillation 0.5% hand to two
feet
11 10
01 0
A
1 2 3 4 5 6 7 8 9 1011 permissible step voltage, kV (IEC 4791)
Fig. 10 Permissible step voltages per IEEE Std 80 vs IEC 4791; 5% body resistme values, probubility of ventriculrufbrilhtion 0.596, hund to two feet
r
3.0 2.5 2.0
IEC 4791 more conservativethan IEEE Std EO

SQ
1.5
2g .g 2
1.0

x x
’/
,LEE Std 80 more Conservativethan IEC 4791
0.5
0.5 1.0 1.5 2.0 2.5 3.0 permissible touch voltage, kV (IEC 4791)
Fi .I1 Permissible touch voltagesper IEEE Std 80 ugaht IEC 4791; 50% b a resistance values, probability of ventricular fbrilhtion 0.5%, hand to two feet
600 400
1
0
I
’
‘
I
0.50
IEEE Std 80
0.10 0.20 0.30 0.40 electric shock duration, s
0.50
Fi . I 4 Body resistance aguinst electric shock h a t i o n at mm permissib!! t a c h voltage; 50Y( I body resistance values, hand to twofeet
6
c’o
’
IEC 4791
IEEE Std 80 more conservativethan IEC 4791
2
6
’
touch voltage; 5% body resistance values, hund to two@et
x5
B ’m
I
Fi . I 3 Body resistance against electric shock duration at mwcimm permis
sib!
g” 1000 2 800
86
I
0.10 0.20 0.30 0.40 electric shock duration, s
IEC 4791 more
3
IEEEStd 80

200 0.5 1.0 1.5 2.0 2.5 3.0 permissible touch voltage, kV (IEC 4791)


Summary and conclusions
The safety criteria of the IEC 4791 and IEEE Std 80 have been compared and their differences have been quantified. There are cases in whch the IEEE Std 80 is more conservative than the IEC 4791 and vice versa. The IEC 4791 safety criteria are rather complex, while the safety criteria of IEEE Std 80 are simplified. The opinion of the authors is that simplicity is important. Given the fact that the safety criteria include comfortable safety margins, one can conclude that the simplicity of the IEEE Std 80 does not compromise safety in grounding system design. Another major difference is that the IEC 4791 does not address all relevant computational issues, while the IEEE Std 80 provides approximate equations and formulas which are useful to a designer. The IEEE Std 80 also provides useful procedures for grounding systems safety assessment. References
11 IEC 4791 more conservativethan IEEE Std 80 7 6 5 t
/ x
IEEE Std 80 more conservativethan IEC 4791 1 2 3 4 5 6 7 8 9 10 11 permissible step voltage, kV (IEC 4791)
Fi .I2 Peimirsible step voltages er IEEE Std 80 against IEC 4791; 50% bo!y resistance values, probability of ventricularfibrillation 0.5%, hund to two feet IEE Proc.Gener. Transm. Distrib., Vol. 146, No. 5, September 1999
\
ANSVIEEE Std 801986: ‘IEEE guide for safety in AC substation grounding’. 1986 SAKIS MELIOPOULOS, A.P.: ‘Power system grounding and transients: an introduction’ (Marcel Defier, Inc., New York, 1988), pp. 119133 International Electrotechnical Commission IEC Report: ‘Effects of current passing through the human body, part 1: general aspects’. 4791, IEC 1984 SAKIS MELIOPOULOS, A.P., XIA, F., JOY, E.B., and COKKINIDES, G.J.: ‘An advanced computer model for grounding system analysis’, IEEE Trans. Power Deliv., 1993, 8, (l), pp. 1%23
Appendix: Analytical expressions of body resistance vs. body voltage
This Appendix presents analytic expressions for the voltagedependent body resistance which closely match the IEC 4791 data. These formulae can be used in lieu of the 599
Table 8 Total body impedance, per IEC 4791 (data from IEC 4791 (1984)) Values for the total body impedance (9)that are not
Touch
exceeded for a percentage (percentile rank) of
voltage (v)
5% of the population
50% of the population
95% of the population
25
1750
3250
6100
tabular data of the IEC 4791. Table 8 presents a reproduction of body resistance data in the IEC 4791. The Table contain three sets of data corresponding to the stafistical values of 5%, 50% and 95% of population (see IEC 4791). Each one of the sets can be approximated with one analytic function of the form Rb,model(Z)
50
1450
2625
4375
75
1250
2200
3500
100
1200
1875
3200
125
1125
1625
2875
220
1000
1350
2125
700
750
1100
1550
1000
700
1050
1500
2000
677
1084
1464
&,model
50% of the population
668.381
1080.02 1
1427.296
bl
15344.426
7751.063
73049.270
C1
515.588
2552.197
21 19.462
Vn
311.673
80.182
131.727
( ~ 2b ,2 ~ 2 ~ 2 0 )
bzib
k C2
*
The coefficients a l , bl, c1 and vo or the vector X = [al, bl, c1, vo] and the coefficients q,b2, c2 and i,, or the vector X = [a2,b2, c2, io] will be different for each one of the three sets of data. For each data set, the unknown vectors x = [al, bl, c1, volT and x = [a2, b2, c2, &IT are computed by the weighted least squares method, i.e. by solving the following optimisation problem. m
Minimise J =
95% of the population
a1
(z)= &,model = U 2 k
Table 9: Computed coefficients of the analytic expressions for body resistance 5% of the population
= R b , m o d e l (a1> b l >c 1 , 210)
wir: = rTWr i= 1
where r =  Rb,mode,(~), w iis weight for the residual ri, and W is a diagonal matrix, the diagonal elements being the weights w i The solution to the above nonlinear estimation problem is obtained with the following algorithm
Table IO: Computed coefficients of the analytic expressions for body voltage
5""
= X u  (HTWH)lWTWIRb,modei(Zu)  b]
where b = Rb,mpanued, Rb(xV+') R&")
+ H.(x"+~  x"), and
H = dRb(X)/aXIX=XO 5% of the population
50% of the population
a2
140.6
63.1
9
0.6
1.o
95% of the population
The computed analytic expression for the three sets of data, using the above algorithm with wi = 1.0 for all i, are listed in Tables 9 and 10. The accuracy of the derived analytic expressions as compared to the IEC 4791 data is illustrated in Tables 11 and 12. For all practical purposes, the analytic expressions can be used in lieu of the data of Table 8.
77.8 1.4
Q
130.1
50.5
68.0
io
241.1
48.1
26.9
Table 11: Comparison of the proposed formula for resistance to the IEC 4791 data Values for the total body impedance (a)that are not exceeded for a percentage (percentilerank) of Touch voltage
..
5% of the population
50% of the population
95% of the population
IVI
IEC 4791
600
Proposed formula
IEC 4791
Proposed formula
IEC 4791
Proposed formula 6102.3
25
1750
1758.0
3250
3258.6
6100
50
1450
1414.4
2625
2603.1
4375
4338.3
75
1250
1278.3
2200
2185.0
3500
3600.7 3149.8
100
1200
1195.9
1875
1890.8
3200
125
1125
1136.4
1625
1678.9
2875
2832.2
220
1000
992.7
1350
1279.4
2125
2158.3
700
750
744.9
1100
1091.5
1550
1542.1
1000
700
704.6
1050
1087.8
1500
1501.4
2000
677
668
1084
1080.0
1464
1427.0
IEE ProcGener. Transm. Distrib., Vol. 146, No. 5, September 1999
Table 12: Comparison of the proposed formula for body current vs. body voltage to the IEC 4791 data Values for the body voltage (V) that are not exceeded for a percentage (percentile rank) of
5% of the population Body current (mA)
14.3 34.5 60.0 83.3 111.1
IEC 4791
25 50 75 100
95% of the population
50% of the population Proposed formula
26.5 48.6 75.2 98.7 125.4 220.8 677.7
Body current (mA)
7.7
IEC 4791
19.0 34.1
25 50 75
53.3 76.9 163.0 636.4
100 125 220 700
220.0 933.3 1428.3
125 220 700 1000
1000.1
952.4
1000
2954.2
2000
1913.1
1845.0
2000
IEE Proc.Gener. Transm. Distrib.. Vol. 146, No. 5, September 1999
Proposed formula
27.7 47.9 71.9 99.2 128.9 222.5
Body current (mA)
4.1 11.4 21.4 31.3 43.5
IEC 4791
25 50 75 100 125 220
Proposed formula
25.1 49.1 76.7 99.7 124.3
692.2
103.5 451.6
700
219.4 701.8
1004.6 1908.1
666.7 1366.1
1000 2000
998.9 1990.3
60 1
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