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<ul><li>1.INTERNATIONAL JOURNAL OF ELECTRICAL0976 6545(Print), ISSN International Journal of Electrical Engineering and Technology (IJEET), ISSN ENGINEERING 0976 6553(Online) Volume 3, Issue 3, October December (2012), IAEME& TECHNOLOGY (IJEET)ISSN 0976 6545(Print)ISSN 0976 6553(Online)Volume 3, Issue 3, October - December (2012), pp. 156-163 IJEET IAEME: www.iaeme.com/ijeet.asp IAEMEJournal Impact Factor (2012): 3.2031 (Calculated by GISI)www.jifactor.com CALCULATION OF GROUNDING RESISTANCE AND EARTHSURFACE POTENTIAL FOR TWO LAYER MODEL SOILHatim Ghazi ZainiTaif University, Faculty of Engineering, Electrical departmenth.zaini@tu.edu.saABSTRACTFor two layer model soil, the calculation of apparent resistivity is considered very importantissue since the absent of a specified method to find it. Some empirical resistivity formula isused in this paper to present the apparent resistivity of the two layer model soil. A currentsimulation method technique which is a practical technique for calculating the groundingresistance (Rg) as well as the Earth Surface Potential (ESP) of the grounding grids in two-layer model soil which based upon the apparent resistivity of the two layer soil andsimulating current sources is used. it is analogous to the Charge Simulation Method. Thevalidation of the method is described by a comparison with the results in literatures.Index terms--Grounding grids, two-layer soil, current simulation method, Computer methodsfor grounding analysis, System protection.I. NOMENCLATUREPaij= Potential coefficient matrix related to apparent resistivityP1ij, P2ij Potential coefficient matrix related to resistivity of layer 1 and 2 respectivelyIj =current source at point jVi= voltage at evaluation point ia =apparent soil reistivity1 =soil reistivity of layer 12 =soil reistivity of layer 2d =distance between current source point and evaluation point in original gridd =distance between current source point and evaluation point in image gridJ =current density (A/m2)F =field coefficientzzi & zzj = the dimension of the contour point and current source in z direction respectivelyRg=grounding resistanced0 = the depth to the boundary of the zones,156</li></ul><p>2. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 6545(Print), ISSN0976 6553(Online) Volume 3, Issue 3, October December (2012), IAEMEK = the reflection factor (K=( 2- 1)/ ( 1+ 2))z = the top layer depthGPR=Ground potential rise (V)Vtouch= touch voltageII. INTRODUCTIONThe knowledge of the grounding systems impulse characteristics has a great significance fora proper evaluation of substation equipment stresses from lightning over-voltages andlightning protection evaluation. As it is stated in the ANSI/IEEE a safe grounding design hastwo objectives: the first one is the ability to carry the electric currents into earth under normaland fault conditions without exceeding operating and equipment limits or adversely affectingcontinuity of service. The second is how this grounding system ensures that the person in thevicinity of grounded facilities is not exposed to the danger of electric shock. To attain these targets, the equivalent electrical resistance (Rg) of the system must be lowenough to assure that fault currents dissipate mainly through the grounding grid into theearth, while maximum potential difference between close points into the earths surface mustbe kept under certain tolerances (step, touch, and mesh voltages). Analysis of substationgrounding systems, including buried grids and driven rods has been the subject of manyrecent papers [1- 4]. Several publications [5-19] have discussed the analytical methods used when uniform andtwo-layer soils are involved.This paper uses a practical method to calculate the grounding resistance as well as theearth surface potential for grounding grids which buried in uniform and two-layer soil. Thismethod is Current Simulation Method (CSM). The Current Simulation Method is analogousto Charge Simulation Method. The validation of a proposed method is explained by comparison between the results fromthe proposed method and the other that formulated in [1].III. CURRENT SIMULATION METHOD IN TWO-LAYER SOIL The representation of a ground electrode based on equivalent two-layer soil is generallysufficient for designing a safe grounding system. However, a more accurate representation ofthe actual soil conditions can be obtained by using two-layer soil model [13]. As in the Current Simulation Method, the actual electric filed is simulated with a fieldformed by a number of discrete current sources which are placed outside the region where thefield solution is desired. Values of the discrete current sources are determined by satisfyingthe boundary conditions at a selected number of contour points. Once the values andpositions of simulation current sources are known, the potential and field distributionanywhere in the region can be computed easily [20].The field computation for the two-layer soil system is somewhat complicated due to thefact that the dipoles are realigned in different soils under the influence of the applied voltage.Such realignment of dipoles produces a net surface current on the dielectric interface. Thus inaddition to the electrodes, each dielectric interface needs to be simulated by fictitious currentsources. Here, it is important to note that the interface boundary does not correspond to anequipotential surface. Moreover, it must be possible to calculate the electric field on bothsides of the interface boundary. In the simple example shown in Fig. 1, there are N1 numbers of current sources andcontour points to simulate the electrode, of which NA are on the side of soil A and (N1- NA)are on the side of soil B. These N1 current sources are valid for field calculation in both soils.At the different soil interface there are N2 contour points (N1 +1,.., N 1+N2), with N2157 3. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 6545(Print), ISSN0976 6553(Online) Volume 3, Issue 3, October December (2012), IAEMEcurrent sources (N1+1,..,N 1+N2) in soil A valid for soil B and N2 current sources (N1+N2+1,..,N1 +2N2) in soil B valid for soil A. Altogether there are (N1+N2) number of contourpoints and (N1 + 2N2) number of current sources. As in Fig. 1, h is the grid depth and z is the depth of top layer soil. In order to determinethe fictitious current sources, a system of equations is formulated by imposing the followingboundary conditions. At each contour point on the electrode surface the potential must be equal to the known electrode potential. This condition is also known as Dirichlets condition on the electrode surface. At each contour point on the dielectric interface, the potential and the normal component of flux density must be same when computed from either side of the boundary. Thus the application of the first boundary condition to contour points 1 to N1 yields thefollowing equations.N1 N1 + 2 N 2 Pa i, j I j +P i , j I j = V .....i = 1, N A 1j =1j = N! + N 2 +1N1N1 + N 2 (1) Pa i, j I j + P2 i , j I j = V .....i = N A + 1, N1j =1j = N! +1where, a 1 1 1 1 Pa i , j = +, P i , j = 1 +1 4 d d 4 d d 1 1 P2 i , j= 2 + 4 d d Again the application of the second boundary condition for potential and normal currentdensity to contour points = N1+1 to N1+N2 on the dielectric interface results into thefollowing equations. From potential continuity condition:N1 + N 2 N1 + 2 N 2 P2 i , j I j P i , j I j = 0....i = N1 + 1, N1 + N 21(2)j = N1 +1j = N! + N 2 +1From continuity condition of normal current density Jn:J n1 (i ) J n 2 (i ) = 0 for i = N1 + 1, N1 + N 2 (3)Eqn. (3) can be expanded as follows: 1 1 N11 N1 + N 2 F I F2 i, j I j + 1 2 j =1 a i , j j 2 j = N ! +1 N1 + 2 N 2(4)1 F1 i , j I j = 0..........i = N1 + 1, N1 + N 2 1j = N ! + N 2 +1where, 158 4. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 6545(Print), ISSN0976 6553(Online) Volume 3, Issue 3, October December (2012), IAEMEFa i , j = Pa ij= a ( zz i zz j + ) (zzi zz j )z d3 4d 3 F1 i , j = P ij 1 = 1 ( zz i zz j+) ( zzi zz j )z4 d3 d 3 F2 i , j = P2 ij = 2 ( zzi zz j + ) ( zz i zz j ) z 4 d3d 3 Fig.1. Fictitious current source with contour points for field calculation by current simulation method in two-layer soil.where, F,ij is the field coefficient in the normal direction to the soil boundary at therespective contour point, a, 1 & 2 are the apparent resistivity nd resistivities of soil 1 and 2respectively and zzi & zzj are the dimension of the contour point and current source in zdirection respectively. Equations 1 to 4 are solved to determine the unknown fictitious currentsources. After solving 1 to 4 to determine the unknown fictitious current source points, the potentialon the earth surface can be calculated by using Eq. 1. Also, the ground resistance (Rg) can becalculated using the following equation: VRg = N1(5) I j =1where, V is the voltage applied on the grid which is assumed 1V. The problem for the proposed method is how the apparent resistivity can be calculated. Asin [18], the apparent resistivity for two soil model calculates by the following formula;1a =for 2 < 1(6) 1 1 + 1 1 1 e K (d 0 + 2 z ) 2 1 a = 2 1 + 2 1 1 e K (d 0 + 2 z ) for > (7) 1 2 1 where, d0 is the depth to the boundary of the zones, K is the reflection factor (K=( 2- 1)/ (1+ 2)) and z is the top layer depth. 159 5. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 6545(Print), ISSN0976 6553(Online) Volume 3, Issue 3, October December (2012), IAEME Equations 6 and 7 are valid for the boundary depth greater than or equal the grid depth. Butin [19], Eq. 7 is modified because at very large depth of upper soil layer, resistivity a givenby Eq. 7 tends to 2. This is physically incorrect if the electrode lies in the upper soil layer, asassumed in [18]. Therefore, Eq. 7 is modified [19] as follows: 1 a = 1 1 + 2 1 1 e K (d 0 + 2 z ) for > (8) 1 2 1 For finite h and very large d0, resistivity a given by Eq. 8 tends to 1, which is incompliance with physical reasoning. When the boundary depth is lower than the grid depth, the apparent resistivity tends to 2.Therefore, by using Eq. 6 and 8 for calculating the grounding resistance by CurrentSimulation Method, the large different between the proposed method results and the results in[1] is observed for K 1(9) 1 Figures 3 and 4 present the comparison of the results calculated by the proposed methodwith the results reported in [1] for a square 30m*30m, 4 and 16 meshes grids buried at 0.5 mdepth in various two layer structures. It is noticed from Figs. 3 and 4 that the proposedmethod gives a good agreement with the results in [1].IV. GROUNDING RESISTANCE AND EARTH SURFACE POTENTIALIt is clear that the Ground Potential Rise (GPR) as well as distribution of the Earth SurfacePotential (ESP) during flow the impulse current into the grounding system is importantparameters for the protection against electric shock. The distribution of the Earth SurfacePotential helps us to determine the step and touch voltages, which are very important forhuman safe.The maximum percentage value of Vtouch is given by: GPR _ VminMax Vtouch % = 100(10) GPRwhere, GPR is the ground potential rise, which equal the product of the equivalent resistanceof grid and the fault current and Vmin is the minimum surface potential in the grid boundary. The maximum step voltage of a grid will be the highest value of step voltages of thegrounding grid. The maximum step voltage can be calculated by using the slope of the secantline. Figure 5 explains the Earth Surface Potential per Ground Potential Rise (ESP/GPR) whenthe case is square grid, 36 meshes, grid dimension 60m*60m, vertical rod length that connectto grid 6m, grid conductor radius 0.005m, grid depth 0.7m, the top layer to lower layerresistivity 1000/100 ohm.m and the top layer depth 3m. Fig. 6 illustrates that the maximumtouch voltage occurs at the boundary of the grid near the corner mesh but the maximum stepvoltage occurs outside the boundary of the grid near the edge of it. 160 6. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 6545(Print), ISSN0976 6553(Online) Volume 3, Issue 3, October December (2012), IAEMEK=0.9K=0.9-[1]0.5K=0.5-[1]0K=0-[1]-0.5 K=-0.5-[1]-0.9 K=-0.9-[1]10Resistance (ohm)10.1 1101000.1 0.01 Top layer depth (m) Fig. 2. Relation between 4 meshes grid resistance and the top layer depthK=0.9K=0.9-[1]K=0.5K=0.5-[1]K=0K=0-[1]K=-0.5 K=-0.5-[1]K=-0.9 K=-0.9-[1]10Resistance (ohm)1 0.11 101000.1 0.01Top layer depth (m) Fig. 3. Relation between 4 meshes grid resistance and the top layer depth K=0.9 K=0.9-[1] K=0.5 K=0.5-[1] K=0 K=0-[1] K=-0.5K=-0.5-[1] K=-0.9K=-0.9-[1]10Resistance (ohm)10.1 1101000.1 0.01 Top layer depth (m)Fig. 4. Relation between 16 meshes grid resistance and the top layer depth161 7. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 6545(Print), ISSN0976 6553(Online) Volume 3, Issue 3, October December (2012), IAEME 1.2 1 0.8 ESP/GPR 0.6 0.4 0.2 0 806040200 -20 -40-60-80 Distance from the grid center (m)Fig. 5. ESP/ GPR for 36 meshes square grid 1.2 ESP/GPRStep Voltage/GPR Touch Voltage/GPR 1 ESP, Step and Touch 0.8Voltages/GPR 0.6 0.4 0.2 080604020 0 -20-40-60 -80 Distance from grid center (m)Fig. 6. ESP, Step and Touch voltages / GPR for 36 meshes square gridV. CONCLUSIONSThis paper aims to calculate the Earth Surface Potential due to discharging current intogrounding grid in two-layer soil by using a traditional but practical method which is theCurrent Simulation Method. The validation of the method is satisfying by a comparisonbetween the results from the method and the results in [1]. It is seen that a good agreementbetween the proposed method results and the results in [1].VI. REFERENCES[1] F. Dawalibi, D. Mukhedkar, Parametric analysis of grounding grids, IEEE Transactionson Power Apparatus and Systems, Vol. Pas-98, No. 5, pp. 1659-1668, Sep/Oct: 1979.[2] J. Nahman, and S. S Kuletich, Irregularity correction factors for mesh and step voltagesof grounding grids, IEEE Transactions on Power Apparatus and Systems, Vol. Pas-99,No. 1, pp. 174-179, Jan/Feb: 1980.[3] Substation Committee Working Group 78.1, Safe substation grounding, Part II, IEEETransactions on Power Apparatus and Systems, Pas-101, pp. 4006/4023, 1982.[4] IEEE Guide for safety in AC substation grounding, IEEE Std.80-2000.[5] Elsayed M. Elrefaie, Sherif Ghoneim, Mohamed Kamal, Ramy Ghaly, "EvolutionaryStrategy Technique to Optimize the Grounding Grids Design", The 2012 IEEE Power &Energy Society General Meeting, July 22-26, 2012, San Diego, California, USA.[6] Sherif Salama, Salah AbdelSattar and Kamel O. Shoush, "Comparing Charge and CurrentSimulation Method with Boundary Element Method for Grounding System Calculationsin Case of...</p>

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