a simplified method for calculating the impulse resistence of vertical grounding rods

Proceedngs of /EEE TENCON02

A SIMPLIFIED METHOD FOR CALCULATING THE IMPULSE RESISTANCE OF VERTICAL GROUNDING RODS

" ZHANG Xiaoqing . (Departmeni of Electric Eiigiiieering, Nodiem Jiaotong Uiuversity. Beijiiig 160044. China)

Email: [email protected]~n

Abstract: A simplified inethod is proposed for calculating the impulse resistance, of vertical grounding. rods. The analytic formula is first derived to determine the low current resistance and then the calculation procedun: is developed 10 estimate the impulse resistance. In Ure procedure, a noillinear relationship is introduced to characterize the electric field .and current density in the ionization zone surrounding the grounding rod. The effective radius of the grounding rod is evaluated according to the nonlinear relationslup. The impulse resistance is calculated by substituting tlic cffcctivc radius into thc analytic formula of the low current resistance. Finally. a comparison is made between calculated and measured risulls in coifinnation of tlie validiF of the proposed niethod. Key words: grounding rod. impulse rcsistance. ground potential rise.

1. Introduction Thc impulse pcrfomiaicc of grounding clcctrodcs is

important for the lightiiing protection design of civil buildings aid electric substations. An appropriate choice of protection measures against lightning overvoltage dcpcnds to a largc dcgrcc on thc knowledgc of thc inipnlsc behavior of gromidiiig electrodes during lightning current dissipation. One of the basic parameters describing the impulse behavior is the impulse resistance, by which the p d potential rise level can be evaluated conveniently 'I, As tlie simplest fonu. of groundiug electrodes, verticjll

grouuding rods are widely used in practical grounding systeiiis. The impulse resistance of vertical groiiiiding rods has been shrdied for many years. Althoiiph a few calculation methods were presented by differelit authors

. their modeling for soil brealidow is still a problem. 12-11

These previoiis methods usually utilized a linear relatioilship to characterize the electnc field and curreut densih in the ioiiization zoue siirroimdiog the. grouiiding rod. In fact, tlic relationship has pronounced nonlinearity. for @pica1 kinds of soil in terms of the esperiniental investigation '*I. The nonlinear relationship should be taken into accoimt in order to perrorm more accurate calcnlation of the impulse resistance.

The aioi of this paper is to propose an eEcieiit method for calculating tlie impulse resistance of verhcal grounding

rods. The grounding rods under consideration are assumed to be not quite long and their inductaxe and capacitance may be neglected. The proposed. method utilizes the nonlinear characteristic to represent the relatioilship between the electric field and curreut density in the ionization zone. A reasonable simplification is made for the soil brealtdown. Based,on the simplified treatment, the calculatioii procedure is developed to determine tlie effective,radins of the grounding rod. Then: the effective radios is used to calculate tlie impulse resistance. Validity of thc proposcd iilctbod ievcrificd by comparing calculated and measured results.

2. Low Current Resistance Whcn a low ciirrcnt I with low frcqucncy is injected

into a vertical grounding rod and iiisuficient to initiate soil brealidowi, the relatioilship between the electric field and corrent density in the soil is linear. i.e.

where E is the electric field intensity, P the soil resistivity and J . the ciurent density. The equipotential surface surroundiug the groimding rod is approximately represented by a cylindrical portion. and a semispherical portion[2,61, as sbown in Fig. I . Correspoiidingly, the

E = p J (1)

Fig. 1 Low current resistance model free of soil breakdown I -vertical grounding rod. 2-equipotential surface

ciirrent density can be expressed as

I ~

~

I .I =

2 K d + 2 K r Z 2 K r(r + I )

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Snbstimting cqn. 2 into eqii. 1, thc clcctric ficld intensity can be written as

E = (3) 2n r ( r + I ) The ground poteutial rise U generated by the grounding rod is derived from the integration for eqn. 3

Therefore. the low current resistance of the grounding rod call be found

(5)

The above expression is identical to Liew's expression ['I which was obtained by other method. As a numerical example, values of rc, 1 and P are taken to be 0.025m, Im and 42.3 Q . 111, respectively. The resistance & calculated by eqn. S is 21.3 Q .. while its measiued is 23.2Q. Obviously, h e former is conformable to the latter.

3. Impulse Resistance For a high impulse current with crest value Im:

representative of lightning, the impulse resistaxe of the grounding rod is defined as a ratio of the crest value of impulse ground potential rise to Im. When the electric field intensit? 011 the surface of the grounding rod exceeds the critical value E, of soil ionization gradient, the breakdown will occur. This process is illustraled in Fig. 2. As the current increases, streamers are developed and in turn arcs are generated. Within the streamer and an: zones,

Fig. 2 Impulse breakdown of soil surrounding a vehcal grounding rod I -arc zone. 2 -streamer zone, 3 - sciiuconductivc zonc. 4 -constant rcsistivity mnc

the resistivih decreases from its original valne to a limit of approaching conductor. In addition, there is a semiconductive zone behveen the streamer zone and the

constant rcsistivity zonc. For simplicity, this process can be described by a simplified modelr91shown in Fig.3. In the simplified model, the semiconductive 7mie is neglected since it is small, while the streamer and arc zones are modeled as an ionization zone. The border of the ionization zone is delimited by the critical value &. A nonlinear relationship is introduced to characterize the electric field and current density in the ionization zone. The nonlinear relationship is denoted in the following

E = a J " (6) and b are constants that were given for typical

Substituting eqn. 2 into eqn. 6: the where kinds of soil in ref. 8.

........... ................. ! ! ................ I I p-.".." ................

I ................. I .......................... I

, ................ 1 , ................ I ~.~.~,~.~.~.'.'.'.'.','.~!

................. .............. , .................. 7 I ~ ....................................... ........................... ................ j ..................

......... ......... ._ ..... -. 7

I I Fig. 3 Simplified model of ionization zone

electric field intensity is rewritten as

I b 1 E = </L

(2n)b r b ( r ( 7;

. . On the border of the ionization zone: E should satisfy the boundary condition

Thus, the boundary radius of the ionization zone can be dcrivcd from cqns. 7 and 8

y = -I+= 2 H

where

The soil breakdown is basically equivalent to an increase in the dimension of the grounding rod. This increase can be represented by an effective radius re of the grounding rod, as shown in Fig.4. The voltage between the grounding rod and the border of the ionization zone is

where

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Fig. 1 Sketch for evaluation of the effective radius 1-ionization zone. 2-constant resistivity P zone

The voltage betweeu lhe equivalent grounding rod aud Uie equipotential surface with radius r . ~ is

250

200

?.

150 I -

p 100

Because 11, and U, mist be equal, the effective radius re cai be detenniued by equs. 9 aud 11

rIi I re =

where -I =exp( U ) aud rH ( A - I)+ /z I

a l l b - '

. . - Measured - ..._.. -/

,-

r- -

-

w = D p(2ir)b.'

As Lhe iiitegratioii oC eqn. 10 is dillicull to be calculated analytically, a nunierical computation procedure is implemented to obtaiu D

1 + D = - k [ Ar. ~~ 1

2 k=l 'i.' 'i-' + I ) b r;" (r, + I ) b where A I' is the radial step aud

- '0 a=- A I .

By replacing r.<, with re in eqn 5 : the impulse resistance R,,, cm bc g h i

27r I In eqn 12, since the effective radius r, varies with the current crest value I,2,, the impulse resistance Ri,, is dependetit 011 Also: tbe crest value 1hnz of impulse groiuid potential rise cau be evaluated as follows

U;,, = R,, I , (13)

4. Comparison of Calculated and Measured Results To check the validity of the proposed method, a

comparison is made between calculated and measured .results. In the comparison, the first set of data are: r0=0.0127ni, 1=3.05m, P =87.2 . Q . m , &=~27kv/lil: ~ 3 0 9 4 . 6 , b=0.5 1. The impulse resistances at differeut current crest values are calculated by eqn.12, which are shown in Fig. 5 together with the measured result [lo'

The secoud set of data are: r'o=0.025nI, I=lm. , 0 4 3 . 5 0 . m; Ec=350kV/m, 0=219.05, h=0.82. The crest valuesof impulse ground potential rise calculated by

Measured Calculatcd

._.... 20

16 .. h

c y 12 4:

0 J

0 4 8 12 16 20 24 28 32 . I , (kA)

Fig. 6 Calculated and measured crest values of impulse

5. Conclusion A simplified method for calculating the impulse

.1883


resistaiice'of vertical~grouiiding rods has been proposed in this paper. 'For a vertical grounding rod dissipating high '

iinpolse current, tlie soil breakdowi process is niodeledPy an ioiiization zone snrrounding it. In the ionization zone, a nonlinear relationship is introduced to ,characterize the electric field aiid current density instead of the traditional linear relationship used in the previous methods. The effective radius of tlie grounding rod is estimated in tenns of~the nonlinear relationship. Then, the impulse resistance is obtained by means of the effective radius and the ground potential rise level is also evaluated from the impulse resistance aiid current crest. The calculated results have been coinpared with the measured ones and a better agreement. appears between them, which verifies the validity of the proposed method.

Acknowledgement This work is financially supported by University Key

Teacher Foundation of Education Ministry and Natural Science Foitndation of Beijing.

Reference 1 GB 50057-94. Desinii Code for Protection of Structures

a&& Lightning (National Code of China), 2000

impulse characteristics of concentrated earth," Pmc. IEE.Vo1.121: pp.123 - 135,Feh. 1974

3. R.Velazquez and D. Mukhedkar, " Analytical iiiodeling of grounding electrodes transient behavior," IEEE Puns. Power Appurutirs ant Systems,

'Vol.PAS-103, pp.1314-1322$ Jmi. 1984 4. E. Garbagiiati >.A. Gcri and, G Sartorio and G M.Veca,

"Non-linear behavior of ground electrodes under lighining surge currents: computer modeling and comparison with experimental results", IEEE Puns. Mugnetics, Vol. 28: pp.1442-1445, Mar. 1992

5 . Z. Stojkovic: + The soil ionization influence 011 lighhiing . perfoniiruice of transmission lines", Electrical Ezgineering ,Vol. 82: pp.49-58, Nov. 1999

6. A. Geri, '. Behavior of groiiiidiiig systems excited by impulse currents: the iiiodel and its validation", IEEE % m s . P ~ ~ ~ D e l i ~ e i y , Vol. 14, pp.1008-1017, Jul. 1999

7. B. P. Laionov, "Lightning protection (Part 11 )", E/ecfr.ichesh;o (in Russian), No.7, pp.64 - 68, Feh.1999

8. A . ~ Z. Puyenkov, '' The Volt-Ampere characteristic of soil under lightning surge cnrrents", Electrichestvo (in Russian), No. 2, pp.57-60, 1986

9. A. R. Hilemai. Iiisulation Coordination for Power Systems, Marcel Dekker hc. , 1999

10. P. L.' Bellaschi, R. E. Aniiington and A. E. Snowden, "lmpulse and 60 cycle characteristics of driven grounds-I1 'I_ Puns. Ani..lnst. Elec. Eng., Vol. 61, pp. 349 - 363,1942

2. A. C. Liew and M. Darveniza, 'Dynamic model of

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a simplified method for calculating the impulse resistence of vertical grounding rods

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