Journl of Electromgnetic Anlysis nd Applictions, 03, 5, 3-37 http://dx.doi.org/0.436/jem.03.58050 Published Online August 03 (http://www.scirp.org/journl/jem) Mohmed Nyel Electricl Engineering Deprtment, Assiut University, Assiut, Egypt. Emil: m niel@yhoo.com Received April 8 th, 03; revised My 5 th, 03; ccepted July st, 03 Copyright 03 Mohmed Nyel. This is n open ccess rticle distributed under the Cretive Commons Attribution License, which permits unrestricted use, distribution, nd reproduction in ny medium, provided the originl work is properly cited. ABSTRACT Four-electrode method is one of the well-known methods in mesuring ground resistivity. But, most fults currents nd lightning currents hve high frequencies components. It is proposed to develop this method to study ground frequency chrcteristics. A step like current ws injected into ground to mesure the ground impednce. The ground impednce is ssumed to be frequency dependent prllel resistnce/cpcitnce. Two equtions were proved to estimte ground resistivity nd permittivity from four-electrode method. An nlyticl model ws proposed to model studied cses. The four electrodes re divided to equl spheres nd complex imge method hd been used to stisfy the boundry conditions nd penetrtion depth effects. The clculted results show good greement with the mesured results. Keywords: Ground; Trnsient; Four Electrode Method; Frequency; Impednce. Introduction When designing grounding system for specific performnce objective, it is necessry to ccurtely mesure the ground resistivity of the site where the ground is to be instlled. Grounding system design is n engineering process tht removes the guesswork nd rt out of grounding. It llows grounding to be done right, the first time. The result is cost svings by voiding chnge orders nd ground enhncements []. The ground impednce frequency chrcteristic plys n importnt role in understnding nd designing grounding systems. To investigte this issue, smples of ground re tested in lbortories [,3]. The chrcteristics of these smples will be chnged due to ground excvtion, temperture nd humidity. There re other methods used in prediction of ground prmeters nd it depends on electromgnetic wve trnsmitted nd reflected from ground or grounding system nlysis [4,5]. Grounding resistivity mesuring methods depend on injecting current through the ground vi the probe electrodes. The current flowing through the ground ( resistive mteril) develops voltge/potentil difference. There re different methods [6,7] such s, four electrode method, deep electrode method nd two electrode method to mesure nd obtin ground resistivity. The most ccurte method in prctice of mesuring the verge resistivity of lrge volumes of undisturbed erth is the four-electrode method. The electrode configurtions commonly used for ground resistivity mesurements re the Wenner nd Schlumberger, illustrted in Figures () nd (b), respectively. Approximting the current electrodes by hemispheres, the pprent soil resistivity ρ pp cn be computed using the following Equtions []: Wenner Method: R () Schlumberger Method: Rcc d d () When the djcent current nd potentil electrodes re close together, the mesured ground resistivity is indictive of surfce ground chrcteristics. When the electrodes re fr prt, the mesured ground resistivity is indictive of verge deep ground chrcteristics throughout much lrger re. This pper studies the frequency dependence of ground impednce by injecting step like current in outer electrode of four electrodes method. By using successive imge method, four electrodes re modeled in ground with permittivity nd conductivity prmeter of ground. The ground impednce by the proposed method is studied for different ground prmeters nd different frequencies.. Experimentl Setup The ground resistivity nd permittivity is obtined from mesured voltge nd current wveforms due to wve propgtion in the ground to study the effect of frequency.
33 () (b) () Figure. Four electrodes configurtions: () Wenner Method; (b) Schlumberger Method. Figure () illustrtes n experimentl setup of four electrode method for ground impednce mesuring. A step-like current of 0 nsec rise time is injected from pulse genertor (PG) of 500V. The pulse genertor injects the current s chrge/dischrge cble, so, the injected current is not equl to return current. The four electrode method needs to inject current in outer electrode nd return the sme current from the other side outer electrode. To overcome the unblnce of pulse genertor nd connection cble blnce trnsformer. Figure (b), is used to convert unblnce current/voltge to blnce current/voltge t high frequency. The blnce trnsformer is connected t the end of connected cble to the pulse genertor s shown in Figure (). The current is mesured by CT (Peson model 877, bndwidth from 300 Hz to 00 MHz), nd recorded by digitl oscilloscope (Tektronix TDS 3054 m, bndwidth 500 MHz). Trnsient voltges were mesured by voltge probe (TEKTRONIX P639A, bndwidth 500 MHz). The field mesurements were crried out in Doshish University yrd site. The current rise time 0 ns is injected for different distnces between electrodes. Four electrodes re buried in the ground, s shown in Figure (), ll t depth 0. m nd spced (in stright line) t intervls m between the inner electrodes nd 4 m between the outer electrodes. 3. Mesured Results A current, s shown in Figure 3, is injected in electrode (C) nd collected from the outer electrodes (C) nd the two voltges of the two inner electrodes (P nd P), s shown in Figure 4, re recorded with the oscilloscope. The ground impednce is obtined from the mesured voltges nd currents (C, C, P, P). The four electrode method t low frequency is used to obtin the grounding resistnce by dividing the potentil difference (b) Figure. Experimentl setup of four electrode method: () Experimentl setup; (b) Blnce trnsformer. Figure 3. Injected current wveform. Figure 4. Mesured voltge wveforms for non-equl four electrodes method.
34 between two inner electrodes by the injected current t the outer electrodes s follows: Vp Vp RG (3) I Finlly, complete content nd orgniztionl editing before formtting. Plese tke note of the following items when proofreding spelling nd grmmr: Define bbrevitions nd cronyms the first time they re used in the text, even fter they hve been defined in the bstrct. Abbrevitions such s IEEE, SI, MKS, CGS, sc, dc, nd rms do not hve to be defined. Do not use bbrevitions in the title or heds unless they re unvoidble. In the sme mnner the ground impednce t different frequencies Z G (f) is obtined. The current t injected points to ground (C, C) is distorted due to the induced voltge between ground nd connection wires. The voltge wveforms t ny frequency (f) t inner electrodes re reformed to be s result of current I by multiplying them V p nd V p by I/I C nd I/I C s follows: Vp f I f Vp f I f ZG f I f IC f I f IC f (4) Vp f Vp f ZG f I f I f C C The ground impednce is ssumed to be consists of prllel resistnce R G (f) nd cpcitnce C G (f). From the obtined ground impednce Z G (f) the ground resistnce nd cpcitnce re obtined. The ground resistivity is obtined for non-equl four electrode method by the following eqution: f c c d R f d (5) As RC the ground permittivity cn be obtined. dcg f r f (6) c c d G 0 Figure 5 shows the clculted ground impednce obtined from the mesured results by using Eqution (4) nd clculted impednce by proposed model in next section. It shows good greement between mesured nd clculted results nd the dependence of grounding impednce on frequency. 4. Numericl Model 4.. Penetrtion Depth Effect Assume wve trvels into conducting medium [8]. Eqution (7) is solution of the wve eqution for plne wve trveling in the x direction in the conducting medium. Jy x J e e j x 0 (7) Figure 5. Grounding impednce vs frequency obtined by four electrodes method. where: = penetrtion depth m. It gives the vrition of E y or J y in both mgnitude nd phse s fuction of x. The electric field E y or current density J y deceses to /e (36.8%) of its initil vlue, while the wve penetrtes to distnce clled penetrtion depth [8]. (8) f where: f = frequency Hz, µ = ground permebility, = ground conductivity. Figure 6 shows the decy of the electric field E y or currrent density J y s function of penetrtion depth, bsed on the mgnitude of Eqution (7). Integrting the bsolute vlue of Eqution (7) from x = 0 to results in E 0 / or J 0 /. Ares under step functionl nd exponentil curve re equl when step function width is equl to the penetrtion depth [8] s shown in Figure 6. It is ssumed tht ll of injected current pss in the re of /e depth nd the ground resistivity below the penetrtion depth is proposed to be infinity [9]. The successive imge method shown in Figure 7 is proposed to consider the penetrtion depth in homogenous ground. To mke sure tht ll current pss in the re of /e depth, two lyer ground is ssumed with top lyer of ground resistivity, permitivitty nd depth equl to penetrtion depth. The bottom lyer is ssumed with resistivity =, permitivity = 0 nd extended to infinity. The refliction coefficinet between the ground nd ir is ssumed k j 0 j 0. The bottom lyer is ssumed with resistivity =, permitivity = 0 nd extended to infinity nd its refliction coefficient with ground is ssumed unity. The nlyticl method used to clculte the surfce potentil profile of the four electrodes nd grounding resistnce/cpcitnce ssumed ech electrode driven into
35 Z nn p p k k 4 j (0) r p p p Figure 6. Electric field E or current density J (=E) s function of depth of penetrtion [5]. Figure 7. Imge mp for 4 electrodes t homogenous ground. the ground s sphere. As electrode length is very short, ech electrode is considered s equipotentil surfce. The reltionship between the voltge nd current cn be written s: V Z Z Z3 Z4 I V Z Z Z3 Z 4 I (9) V 3 Z3 Z3 Z33 Z 34 I 3 V Z 4 4 Z4 Z43 Z44 I4 where I j is the current of the j th electrode (j = ; ; 3; 4), V i is the voltge of the j th electrode, Z mn is the mutul impednce element (i.e., mutul impednce between electrode number m nd electrode number n), Z nn is the self-impednce of the n th sphere. The elements of the impednce mtrix re clculted s equl to: Z mn p p p k k k () 4 j rmn p rmnp rmnp rmnp 3 where r mn is the distnce between m th electrode nd n th electrode, r mnp,,3,4 re the distnces between the m th electrode nd the imge of the n th sphere nd equl to: r x x y y p mnp m n m n r x x y y p mnp m n m n mnp3 mnp4 m n m n r r x x y y p Figure 8 shows the vrying of pprent ground impednce for r = 0 nd 50 nd ( = m, = 000 Ωm) with frequency. The pprent ground impedce decreses more shrbly s the ground reltive permittivity increses. This is due to the decrese of the cpcitive prt of pprent ground impednce with the increse of pprent reltive permittivity. Figure 9 shows the vrying of pprent ground impednce for = 000 nd 500 Ωm nd ( = m, r = 0) with frequency. The pprent ground impednces decreses s the ground resistivity decreses. This is due to the decrese of the decrese of gound resistnce. Figure 0 shows the vrying of pprent ground impednce for = nd 5 m nd ( r = 0, = 000 Ωm) with frequency. The pprent ground impednce decreses s the spce between electrodes increses. Figures 8-0 show tht, t high frequency until the frequency rech MHz, The pprent ground impednce t low frequency hs no chnge fter tht it decreses s the frequency increses. This is due to the decrese of cpcitive prt of ground impednce with frequency. 4.. Ground Chrcteristics The pprent resistnce clculted from four electrodes buried in homogenous ground with tking into ccount the effect of penetrtion depth is ssumed to be s follows. 4 () n n 4 n where : first lyer depth; : ground resistivity m; distnce between elecrodes Figure shows the vrying of pprent resistivity with frequency. The pprent resistnce hs no chnge
36 Figure 8. Clculted pprent impednce for r = 0 nd 50 nd ( = m, = 000 Ωm) vs frequency obtined by four electrodes method. Figure. Apprent resistivity vs frequency. until the frequency rech MHz, fter tht it is incresed s the frequency increses. This increses in pprent resistnce due the decrese of the re tht the current pss in due to the decrese of penetrtion depth. The chnge in pprent resistnce increses s the distnce between electrodes increses. The ground cpcitive prt is frequency dependent by the following eqution: X Cg fc (3) In ddition of tht the penetrtion ffect on the cpcitive impednce which cn presented s chnge in penetrtion depth nd pprent reltive permittivity s follows: Figure 9. Clculted pprent impednce for = 500 nd 000 Ωm nd ( = m, r = 0) vs frequency obtined by four electrodes method. Figure 0. Clculted pprent impednce for = nd 5 m nd ( = 000 Ωm, r = 0) vs frequency obtined by four electrodes method. 4 (4) n n 4 n where : first lyer depth; : ground reltive permittivity, distnce between elecrodes From Eqution (4), s the frequency increses, the penetrtion depth decreses nd pprent permittivity decreses. The pprent reltive permitivity pu clculted from 4 electrodes buried in homogenous ground with tking into ccount the effect of penetrtion depth is ssumed to be s follows. Figure shows the vrying of pprent ground reltive permittivity (pu) with frequency. The pprent reltive permittivity hs no chnge t low frequencies. At high frequency bove MHz, the ground reltive permittivity (pu) decreses s the frequency increses. This decrese in ground pprent reltive permittivity is coming from the decrese of the re tht the current pss in due to the decrese of penetrtion depth.
37 Figure. Apprent reltive permitivity vs frequency. 5. Conclusion The four-electrode method is used successfully to mesure the ground resistivity nd permittivity by injecting step like current into ground. The blnced trnsformer is used to solve the problem of chrge/dischrge cble s source. The mesured results show the effects of frequency dependence on ground resistivity. The penetrtion depth effects on the mesured results nd cn be considered by the proposed equtions to estimte the ground resistivity nd permittivity. The proposed clcultion model proves physiclly the ground resistivity effects nd penetrtion depth effects on the mesured results. The chrge simultion method is used successfully in resistive/cpcitive problem t high frequency. The proposed clcultion model results gree successfully with the mesured results. The pprent ground resistivity increses s the frequency increses. The pprent ground permittivity decreses s the frequency increses. Erth Surfce Potentils of Grounding System, IEEE Stndrds 8-983, 0. [] N. M. Nor, A. Hddd nd H. Griffiths, Performnce of Erthing Systems of Low Resistivity Soils, IEEE Trnsctions on Power Delivery, Vol., No. 4, 006, pp. 039-047. doi:0.09/tpwrd.006.874656 [3] B. Anggoro, N. I. Sinisuk nd P. M. Pkphn, Resistivity nd Dielectric Constnt Chrcteristic of Soil If re Treted by Wter, Slt nd Crbon, 8th Interntionl Conference on Properties nd Applictions of Dielectric Mterils, Bli, June 006, pp. 893-896. [4] S. Viscro nd R. Alipio, Frequency Dependence of Soil Prmeters: Experimentl Results, Predicting Formul nd Influence on the Lightning Response of Grounding Electrodes, IEEE Trnsctions on Power Delivery, Vol. 7, No., 0, pp. 97-935. doi:0.09/tpwrd.0.79070 [5] A. G. Pedros, M. A. O. Shroeder, M. M. Afonso, R. S. Alípio, S. de Cstro Assis, T. A. S. Oliveir nd A. R. Brg, Trnsient Response of Grounding Electrodes for the Frequency-Dependence of Soil Prmeters, 00 IEEE/PES Trnsmission nd Distribution Conference nd Exposition: Ltin Americ (T&D-LA), So Pulo, 8-0 November 00, pp. 839-845. [6] I. F. Gonos, A. X. Moronis nd I. A. Stthopulos, Vrition of Soil Resistivity nd Ground Resistnce during the Yer, 8th Interntionl Conference on Lightning Protection, Knzw, 7- September 006, pp. 740-744. [7] IEEE Power & Energy Society, IEEE Guide for Sfety in AC Substtion Grounding, ANSI/IEEE Stndrd 80-000, 000. [8] F. Krus, Electromgnetics with Applictions, 5th Edition, McGrw-Hill, New York, 999. [9] M. Nyel, Investigtion of Wve Propgtion Penetrtion Depth in Multi-Lyer Ground, IEEJ Trnsctions on Power nd Energy, Vol. 3, No. 8, 0, pp. -6. doi:0.54/ieejpes.3.78 REFERENCES [] IEEE Power & Energy Society, IEEE Drft Guide for Mesuring Erth Resistivity, Ground Impednce, nd