nternatonal Journal of Electrcal & Computer Scences JECS-JENS Vol: No:4 7 Comparng Charge an Current Smulaton Metho wth Bounary Element Metho for Grounng System Calculatons n Case of Mult-Layer Sol Sherf Salama, EEE member, Salah AbelSattar an Kamel O. Shoush Abstract Grounng gr performance can be measure n terms of grounng resstance, but t s preferable to nclue the strbuton of surface potental an, subsequently, the touch an step voltages over the area above the substaton groun gr an beyon. Two methos are use n ths paper to compute the grounng resstance (R g) an the earth surface potental (ESP) ue to schargng current nto grounng grs. The frst one s the charge (current) smulaton metho (CSM) an the other s the bounary element metho (BEM). or BEM, commercal software TOTBEM by unversty of La Courna, Span s use for computng ESP an R g. The owne ORTRAN coe s prove to calculate the ESP an R g. The sol s assume to multlayer sol. The paper focuses the comparson between these two methos for calculatng ESP an R g. n case of grounng resstance, a comparson between the two methos results an EEE Stanar formula s presente. nex Term-- Grounng grs, Earth surface potental, Step voltage, Touch voltage, Bounary element approach, Charge smulaton metho.. NTRODUCTON Man obectves of the grounng system are ) to guarantee the ntegrty of the equpments an contnuty of the servce uner the fault contons (provng means to carry an sspate electrcal currents nto groun), an ) to safeguar those people that workng or walkng n the surrounngs of the groune nstallatons are not expose to angerous electrcalshocks. Groun grs are consere an effectve soluton for grounng systems for all stes whch must be protecte from lghtnng strokes such as, telecommuncaton towers, petroleum fels, substatons an plants. Groun grs prouce an equ-potental surface an shoul prove very small mpeance but the groun grs are consere complex Ths work was supporte by Taf Unversty, KSA uner grant 73-433-. The Authors are wth the epartment of the Electrcal Engneerng, aculty of Engneerng, Taf Unversty, KSA. ghonem_sherf3@yahoo.com arrangement an many research efforts have been mae to arrangement an many research efforts have been mae to explan the performance of grounng mpeance of ts uner lghtnng an fault contons. Vertcal groun ros s connecte to the gr to have low values of groun resstance when the upper layerof sol n whch the gr s bure, s of much hgher resstvty than that of the sol beneath The aton of the vertcal groun ros to the grounng gr acheve a convenent esgn for grounng system by ecreasng the gr resstance, the step an touch voltage to a safe values for human an publc. The equvalent electrcal resstance (R g ) of the system must be low enough to assure that fault currents sspate manly through the grounng gr nto the earth, whle maxmum potental fferent between close ponts nto the earth s surface must be kept uner certan tolerances (step, touch, an mesh voltages) [,]. n a unform sol, the resstance can be calculate wth an acceptable accuracy usng several smplfyng assumptons []. Touch an step voltages are ffcult to calculate by smplfe metho but t etermne by analytcal expressons [-5]. Recent papers have propose new technques for calculatng the earth surface potental an then knowng the step an touch voltages, one of these methos s A Bounary Element Approach [6]. Ths paper wll present the comparson between two analytcal methos that use for calculatng the grounng resstance an earth surface potental, the frst metho s the Bounary Element Metho that have been mplemente n a computer ae esgn (CAD) system for grounng grs of electrcal substatons calle TOTBEM [6], the secon one s the Charge Smulaton Metho whch s consere a practcal metho for calculatng the fels an from ts smplcty n representng the equpotental surfaces of the electroes, ts applcaton to unboune arrangements whose bounares exten to nfnty an ts rect etermnaton to the electrc fel [7]. The valaton of two methos s explane by comparng ther results wth the results of EEE Gue for 694-7575-JECS-JENS August JENS
nternatonal Journal of Electrcal & Computer Scences JECS-JENS Vol: No:4 8 Safety n AC Substaton Grounng (ANS/EEE St 8- ). gure explans the grounng system wth groune electrcal equpment an shows the very mportant parameters n grounng system esgn.. CHARGE SMULATON METHOD OR ONE-LAYER SOL n the charge smulaton metho, the actual electrc fle s smulate wth a fel forme by a number of screte charges whch are place outse the regon where the fel soluton s esre. potental wll be characterze for beng constant on the grounng grs an ts symmetry [8]. The potental coeffcents wll be as n the followng equaton; P 4 where, s the stance between contour pont an charge pont an s the stance between the contour pont an mage charge pont as shown n gure. As n gure, the fcttous charges are taken nto account n the smulaton as pont charges. The poston of each pont charges an each contour pont are etermne n X, Y an Z coornates where the stance between the contour (evaluaton) ponts are calculate as the followng ; () X X Y Y Z Z g.. llustraton of the grounng system where, X, Y an Z are the mensons of the pont charge an X, Y an Z are the mensons of the contour pont. After solvng equaton to etermne the magntue of smulaton charges, a number of checke ponts locate on the electroes where potentals are known, are taken to etermne the smulaton accuracy. As soon as an aequate charge system has been evelope, the potental an fel at any ponts outse the electroes can be calculate. Values of the screte charges are etermne by satsfyng the bounary contons at a selecte number of contour ponts. Once the values an postons of smulaton charges are known, the potental an fel strbuton anywhere n the regon can be compute easly [7]. The basc prncple of the charge smulaton metho s very smple. f several screte charges of any type (pont, lne, or rng, for nstance) are present n a regon, the electrostatc potental at any pont C can be foun by summaton of the potentals resultng from the nvual charges as long as the pont C oes not rese on any one of the charges. Let Q be a number of n nvual charges an Φ be the potental at any pont C wthn the space. Accorng to superposton prncple n P Q () where P are the potental coeffcents whch can be evaluate analytcally for many types of charges by solvng Laplace or Posson s equatons, Φ s the potental at contour (evaluaton) ponts, Q s the charge at the pont charges. Because of the groun surface s flat, the metho of mages can be use wth the charge smulaton metho an the g.. llustraton of the charge smulaton technque The gr s ve nto equal segments by the pont charges strbuton along the axs of gr conuctors. gure 3 shows the strbuton of the pont charges (ots) for the grounng gr ( mesh), the number of pont charges s strbute on the axs of the gr conuctors equally an also the evaluaton ponts strbute on each conuctor as shown n gure 3. The meshes of the gr are always symmetrcal. 694-7575-JECS-JENS August JENS
nternatonal Journal of Electrcal & Computer Scences JECS-JENS Vol: No:4 9 g. 3. Dstrbuton of pont charges on the gr ( mesh) The charge smulaton technque s use to get the groun resstance (R g ), groun potental rse (GPR) an then the surface potental on the earth ue schargng mpulse current nto groun gr s known. The touch an step voltages are calculate from surface potental. The ualty expresson s use to calculate the groun resstance R g from the next equaton. Q C V R C g n where, V s the GPR that s efne V, Q s the charge of pont charge that use for the calculaton, ρ s the sol resstvty an ε s the sol permttvty. n ths secton, some graphs explan the earth surface potental along agonal profle for the square gr wth fferent number of meshes. The characterstcs of the gr are 5mx5m, the raus of the gr ros ( r ) s 8 mm, the gr epth (h) s.5 m, the resstvty of the sol () s Ω.m, an the total groun potental rse (GPR) s efne as V. gure 4 (a, b) shows the Earth surface potental n 3D an the contour map of ths case. (3) g. 4b. Contour map for 64 mesh gr Usng CSM for one layer sol, the resstvty of the sol s consere very mportant parameter n etermnaton of the grounng resstance value, the earth surface potental an then the step an touch voltages. gure 5 shows that the ecrease of the sol resstvty, the ecrease of the earth surface potental s observe. Also the se length of gr s very effectve parameter n ecreasng the grounng resstance an earth surface potental by esgn a gr wth long se, ths fact s appear n gure 6. 8 6 4 8 6 resstvty= ohm.m 4 resstvty= ohm.m - -5 5 Dstance from the center of gr (m) g. 5. Effect of the sol resstvty n the strbuton of earth surface potental along the gr g. 4a. ESP/GPR for 64 meshes 694-7575-JECS-JENS August JENS
nternatonal Journal of Electrcal & Computer Scences JECS-JENS Vol: No:4 3 5 5 3.5*3.5 55*5 75*75 - -5 5 Dstance from the center of gr (m) As n gure 6, h s the gr epth an z s the epth of top layer sol. n orer to etermne the fcttous current sources, a system of equatons s formulate by mposng the followng bounary contons. At each contour pont on the electroe surface the potental must be equal to the known electroe potental. Ths conton s also known as Drchlet s conton on the electroe surface. At each contour pont on the electrc nterface, the potental an the normal component of flux ensty must be same when compute from ether se of the bounary. g. 6. Effect of the se length n the strbuton of earth surface potental along the gr. CURRENT SMULATON METHOD N TWO-LAYER SOL The representaton of a groun electroe base on equvalent two-layer sol s generally suffcent for esgnng a safe grounng system. However, a more accurate representaton of the actual sol contons can be obtane by usng two-layer sol moel [9]. As n the Current Smulaton Metho, the actual electrc fle s smulate wth a fel forme by a number of screte current sources whch are place outse the regon where the fel soluton s esre. Values of the screte current sources are etermne by satsfyng the bounary contons at a selecte number of contour ponts. Once the values an postons of smulaton current sources are known, the potental an fel strbuton anywhere n the regon can be compute easly [7]. The fel computaton for the two-layer sol system s somewhat complcate ue to the fact that the poles are realgne n fferent sols uner the nfluence of the apple voltage. Such realgnment of poles prouces a net surface current on the electrc nterface. Thus n aton to the electroes, each electrc nterface nees to be smulate by fcttous current sources. Here, t s mportant to note that the nterface bounary oes not correspon to an equpotental surface. Moreover, t must be possble to calculate the electrc fel on both ses of the nterface bounary. n the smple example shown n gure 7, there are N numbers of current sources an contour ponts to smulate the electroe, of whch N A are on the se of sol A an (N - N A ) are on the se of sol B. These N current sources are val for fel calculaton n both sols. At the fferent sol nterface there are N contour ponts (N +,.., N +N ), wth N current sources (N+,..,N +N ) n sol A val for sol B an N current sources (N +N +,..,N +N ) n sol B val for sol A. Altogether there are (N +N ) number of contour ponts an (N + N ) number of current sources. g.7. cttous current source wth contour ponts for fel calculaton by current smulaton metho n two-layer sol. Thus the applcaton of the frst bounary conton to contour ponts to N yels the followng equatons. where, N P N P a, a, N N N! N N N N! P P,, V..., N V... N A A, N a P, P a,, 4 4 P, 4 Agan the applcaton of the secon bounary conton for potental an normal current ensty to contour ponts = N + to N +N on the electrc nterface results nto the followng equatons. rom potental contnuty conton: N N N N P, P... N,, N N! N N N rom contnuty conton of normal current ensty J n : (4) (5) 694-7575-JECS-JENS August JENS
nternatonal Journal of Electrcal & Computer Scences JECS-JENS Vol: No:4 J n Jn for N, N N (6) Eqn. (6) can be expane as follows: where, N N! N, N N a,, P a z P z a, N N... N, N N a 4 4!, N zz zz zz zz zz zz zz zz 3 3 3 3 zz zz zz zz P, 3 3 z 4 where,, s the fel coeffcent n the normal recton to the sol bounary at the respectve contour pont, ρ a, ρ & ρ are the apparent resstvty an resstvtes of sol an respectvely an zz & zz are the menson of the contour pont an current source n z recton respectvely. Equatons to 4 are solve to etermne the unknown fcttous current sources. After solvng 4 to 7 to etermne the unknown fcttous current source ponts, the potental on the earth surface can be calculate by usng Eq. 4. Also, the groun resstance (R g ) can be calculate usng the followng equaton: R g N V where, V s the voltage apple on the gr whch s assume V. The problem for the propose metho s how the apparent resstvty can be calculate. As n [], the apparent resstvty for two sol moel calculates by the followng formula; a (7) (8) K h e (9) for for K h a e () where, s the epth to the bounary of the zones, K s the reflecton factor (K=( ρ - ρ )/ ( ρ + ρ )) an h s the top layer epth. Equatons 9 an are val for the bounary epth greater than or equal the gr epth. But n [], Eq. s mofe because at very large epth of upper sol layer, resstvty a gven by Eq. tens to. Ths s physcally ncorrect f the electroe les n the upper sol layer, as assume n []. Therefore, Eq. s mofe [9] as follows: a K h e for () or fnte h an very large, resstvty a gven by Eq. tens to, whch s n complance wth physcal reasonng. When the bounary epth s lower than the gr epth, the apparent resstvty tens to. Therefore, by usng Eq. 9 an for calculatng the grounng resstance by Current Smulaton Metho, the large fferent between the propose metho results an the results n [] s observe for K<-.5 an ths shown n gure 8. f Eq. s mofe as n the results by the propose metho are goo agreement wth the results n []. a for K 5 h e () gure 9 explans the effect of varaton of layer resstvtes on the earth surface potental. t s seen that when the lower layer resstvty s ecrease, the earth surface potental wll ecrease an then the step an step voltages. The vertcal ros that s connecte to the gr play an mportant roles n ecreasng the grounng resstance ue to t penetrate the sol to reach to the lower sol wth lower resstvty. The effect of vertcal ro length s nvestgate n gures an. A longer vertcal ro, a reucton on ESP s observe. The effect of the top layer epth on ESP s llustrate n gure, when the top layer resstvty s greater that that on lower layer, an ncrease n the top layer epth wll result n an ncrease of the ESP an hence the step an touch voltage. The case stuy of gure s 5m*5m gr wth 6 meshes, / =/ ohm,m, 6m vertcal ro length. gure 8, 9 an are carre out for 5m*5m gr wth 6 meshes. 694-7575-JECS-JENS August JENS
nternatonal Journal of Electrcal & Computer Scences JECS-JENS Vol: No:4 Resstance (ohm ).. K=.9 K=.9-[].5 K=.5-[] K=-[] -.5 K=-.5-[] -.9 K=-.9-[]. Top layer epth (m) g. 8. Relaton between 4 meshes gr resstance an the top layer epth 7 6 5 4 / ohm.m 3 / ohm.m / ohm.m -6-4 - 4 6 Dstance from center of gr (m) g. 9. The effect of varaton of layer resstvtes on the earth surface potental 6 5 4 3 Ver ro length = 6m Ver ro length=3m - -5 5 Dstance from center of gr (m ) g.. The effect of vertcal ro length on the earth surface potental 6 5 4 3 wth ver ro 6m wthout ver ro g.. -6 The effect -4 of presence - of vertcal ro on the earth surface 4potental 7 6 5 4 3 Top layer epth=m Top layer epth=3m -6-4 - 4 6 Dstance from center of gr (m) g.. The effect of top layer epth on the earth surface potental.. V. BOUNDARY ELEMENT METHOD n ths paper a computer ae esgn (CAD) system for grounng grs of electrcal substatons calle TOTBEM [6] s presente to get the grounng resstance an earth surface potental. The effect of the vertcal ros locaton on the earth surface potental an then on V t an V s usng ths technque s presente n ths secton. The characterstcs of the gr are 75m*75m, the number of meshes s 6, the raus of the gr ros (r) s.5m, the gr epth (h) s.5 m, the resstvty of the sol s ohm.m, an the total groun potental rse (GPR) s efne as V. The case uner stuy s shown n gure 3. 694-7575-JECS-JENS August JENS
nternatonal Journal of Electrcal & Computer Scences JECS-JENS Vol: No:4 3 ESP (V) 6 4 8 6 4-5 - -5 5 5 Dstance from the center of gr (m) The ESP for 6 meshes gr usng BEM V. COMPARSON BETWEEN THE BEM AND CSM g. 3: The followng case of stuy s taken to compare between the results by BEM an CSM, the nput ata about the gr confguraton: Number of meshes (N) = 6, se length of the gr n X recton (X) = 75,5, 3.5m, se length of the gr n Y recton (Y) = 75,5, 3.5m, gr conuctor raus = 5 mm, vertcal ro length (Z) = (no vertcal ro), epth of the gr (h) =.5 m, resstvty of the sol (ρ) = an Ω.m an the permttvty of the sol s 9. The followng table explans that the result from the propose metho s close to the other formula n [] an also the values of resstance that calculate by BEM[6]. TABLE GROUNDNG RESSTANCE BETWEEN THE BEM AND CSM AND THE OTHER ORMULAS THAT USED N EEE STANDARDS [] R g ohm Resstvty ohm.m.m 75m*75m 5m*5m 3.5m*3.5m 5m*5m CSM.5 8.45 8.9.9 BEM [6] 3.9.3 3.36.5 Dwght [].8 7.7 8.35.88 Laurent [] 4.48.7 34.7.8 Sverak [] 4.4.5 34.6.7 Schwarz [].7 8.54 8.7.97 gure 4 (a, b) explans that the comparson between CSM an BEM for earth surface potental calculaton. The gure explans that the two methos are close to each other for calculatng the ESP although the two methos have fferent technques. 8 6 4 CSM BEM - -5 5 Dstance from the center of gr (m) g. 4a: Comparson between propose metho an Bounary Element Metho for 6 meshes (5m*5m) gr wthout vertcal ros (=.m) 5 5 5 CSM BEM - -5 5 Dstance from the center of gr(m) g. 4b: Comparson between propose metho an Bounary Element Metho for 6 meshes (5m*5m) gr wthout vertcal ros (=.m) V. CONCLUSONS The vertcal ros play an mportant role for reucng the gr resstance, the step an touch voltages. The propose methos (BEM an CSM) that use to calculate the earth surface potental an grounng resstance ue to schargng current nto grounng gr are effcent. The valaton of these methos s satsfyng by a comparson between the results from t an the results from the formula n EEE stanar. The propose methos gve a goo agreement wth the EEE stanar. The two methos gve the closest results to each other althought the fferent technques are apple n each metho. V. ACKNOWLEDGEMENT The authors gratefully acknowlege the Taf Unversty for ts Support to carryout ths work. t fune ths proect wth a fun number 73-433-. V. REERENCES [] EEE Gue for safety n AC substaton grounng, EEE St.8-. [] J. G. Sverak, Progress n step an touch voltage equatons of ANS/EEE St. 8, EEE Trans. Power Delvery, vol. 3, no. 3, Jul. 999, pp. 76-767. 694-7575-JECS-JENS August JENS
nternatonal Journal of Electrcal & Computer Scences JECS-JENS Vol: No:4 4 [3] J. M. Nahman, V. B. Dorevc, Nonunformty correcton factors for maxmum mesh an step voltages of groun grs an combne groun electroes, EEE Trans. Power Delvery, vol., no. 3, Jul. 995, pp. 63-69. [4] J. M. Nahman, V. B. Dorevc, Maxmum step voltages of combne gr-multple ros groun electroes, EEE Trans. Power Delvery, vol. 3, no. 3, Jul. 998, pp. 757-76. [5] S. Serr Dessouk, S. Ghonem, S. Awa," Groun Resstance, Step an Touch Voltages or A Drven Vertcal Ro nto Two Layer Moel Sol", nternatonal Conference Power System Technology, POWERCON, Hangzhou, Chna, October. [6]. Colomnas,. Navarrna, an M. Castelero, mprovement of the computer methos for grounng analyss n layere sols by usng hgh-effcent convergence acceleraton technques Avances n Engneerng Software 44 (), pp. 8 9. [7] N. H. Malk, A revew of charge smulaton metho an ts applcaton, EEE Transacton on Electrcal nsulaton, vol. 4, No., ebruary 989, pp 3-. [8] E. Bento, A. Carmona, A. M. Encnas an M. J. Jmenez The extremal charges metho n grounng gr esgn, EEE Transacton on power elvery, vol. 9, No., January 4, pp 8-3. [9] Cheng-Nan Chang, Chen-Hsng Lee, Compuaton of groun resstances an assessment of groun gr safety at 6/3.9 kv noor/tzpe substaton, EEE Transactons on Power Delvery, Vol., No. 3, July 6, pp. 5-6. [] J. A. Sullvan, Alternatv earthng calculatons for grs an ros, EE Proceengs Transmsson an Dstrbutons, Vol. 45, No. 3, May 998, pp. 7-8. [] J. Nahman,. Paunovc, Resstance to earth of earthng grs bure n mult-layer sol, Electrcal Engneerng (6), Sprng Verlag 5, January 5, pp. 8-87. []. Dawalb, D. Mukhekar, Parametrc analyss of grounng grs, EEE Transactons on Power Apparatus an Systems, Vol. Pas-98, No. 5, Sep/Oct: 979, pp. 659-668. 694-7575-JECS-JENS August JENS