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Calculation of grounding resistance and earth

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Calculation of grounding resistance and earth

1. 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 EARTH SURFACE POTENTIAL FOR TWO LAYER MODEL SOIL Hatim Ghazi Zaini Taif University, Faculty of Engineering, Electrical department h.zaini@tu.edu.sa ABSTRACT For two layer model soil, the calculation of apparent resistivity is considered very important issue since the absent of a specified method to find it. Some empirical resistivity formula is used in this paper to present the apparent resistivity of the two layer model soil. A current simulation method technique which is a practical technique for calculating the grounding resistance (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 and simulating current sources is used. it is analogous to the Charge Simulation Method. The validation of the method is described by a comparison with the results in literatures. Index terms--Grounding grids, two-layer soil, current simulation method, Computer methods for grounding analysis, System protection. I. NOMENCLATURE Paij= Potential coefficient matrix related to apparent resistivity P1ij, P2ij Potential coefficient matrix related to resistivity of layer 1 and 2 respectively Ij =current source at point j Vi= voltage at evaluation point i ρa =apparent soil reistivity ρ1 =soil reistivity of layer 1 ρ2 =soil reistivity of layer 2 d =distance between current source point and evaluation point in original grid d =distance between current source point and evaluation point in image grid J =current density (A/m2) F =field coefficient zzi & zzj = the dimension of the contour point and current source in z direction respectively Rg=grounding resistance d0 = the depth to the boundary of the zones, 156
2. 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=( ρ2- ρ1)/ ( ρ1+ ρ2))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 earth’s 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 N2 157
3. 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 Dirichlet’s 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 =1 j = N! + N 2 +1N1 N1 + N 2 (1)∑ Pa i, j I j + ∑ P2 i , j I j = V .....i = N A + 1, N1j =1 j = N! +1where, ρa 1 1  ρ 1 1 Pa i , j =  + , P i , j = 1  +  1 4π d d  4π  d d  ρ 1 1 P2 i , j = 2  +  4π 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 2 1 (2)j = N1 +1 j = 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  N1 1 N1 + N 2  − ρ ∑F I − ∑ F2 ⊥ i, j I j +  1 ρ 2  j =1 a ⊥ i , j j ρ 2  j = N ! +1 N1 + 2 N 2 (4) 1 ∑ F1⊥ i , j I j = 0..........i = N1 + 1, N1 + N 2 ρ1 j = N ! + N 2 +1where, 158
4. 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 = ρa (  zz i − zz j + ) ( zzi − zz j   ) ∂z  d3 4π d 3   F1⊥ i , j =− ∂P ij 1 ρ = 1 (  zz i − zz j + ) ( zzi − zz j   ) ∂z 4π  d3 d 3   F2 ⊥ i , j = − ∂P2 ij = ρ2 (  zzi − zz j + ) ( zz i − zz j )  ∂z 4π  d3 d 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, ρa, ρ1 & ρ2 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: V Rg = 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; ρ1ρa = for ρ 2 < ρ1 (6)    1  1 +  ρ1  − 1 1 − e K (d 0 + 2 z )        ρ 2              −1  ρa = ρ2 × 1 +  ρ 2  − 1 1 − e K (d 0 + 2 z )   for ρ > ρ   (7)   ρ1     2 1       where, d0 is the depth to the boundary of the zones, K is the reflection factor (K=( ρ2- ρ1)/ (ρ1+ ρ2)) and z is the top layer depth. 159
5. 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 ρa givenby Eq. 7 tends to ρ2. 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  ρ a = ρ1 × 1 +  ρ 2  − 1 1 − e K (d 0 + 2 z )   forρ > ρ    (8)   ρ1     2 1        For finite h and very large d0, resistivity ρa given by Eq. 8 tends to ρ1, which is incompliance with physical reasoning. When the boundary depth is lower than the grid depth, the apparent resistivity tends to ρ2.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<-0.5 and this shown in Fig.2. If Eq. 8 is modified as in 9 the results by the proposed method are good agreement with theresults in [1].   ρ 2    −1 ρ a = ρ1 × 1 +    − 1 1 − e K (d 0 +15 z )   forρ 2 > ρ1  (9)   ρ1          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 POTENTIAL It 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. 6. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN0976 – 6553(Online) Volume 3, Issue 3, October – December (2012), © IAEME K=0.9 K=0.9-[1] 0.5 K=0.5-[1] 0 K=0-[1] -0.5 K=-0.5-[1] -0.9 K=-0.9-[1] 10 Resistance (ohm) 1 0.1 1 10 100 0.1 0.01 Top layer depth (m) Fig. 2. 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=-0.5 K=-0.5-[1] K=-0.9 K=-0.9-[1] 10 Resistance (ohm) 1 0.1 1 10 100 0.1 0.01 Top 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=-0.5 K=-0.5-[1] K=-0.9 K=-0.9-[1] 10 Resistance (ohm) 1 0.1 1 10 100 0.1 0.01 Top layer depth (m) Fig. 4. Relation between 16 meshes grid resistance and the top layer depth 161
7. 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 80 60 40 20 0 -20 -40 -60 -80 Distance from the grid center (m) Fig. 5. ESP/ GPR for 36 meshes square grid 1.2 ESP/GPR Step Voltage/GPR Touch Voltage/GPR 1 ESP, Step and Touch 0.8 Voltages/GPR 0.6 0.4 0.2 0 80 60 40 20 0 -20 -40 -60 -80 Distance from grid center (m) Fig. 6. ESP, Step and Touch voltages / GPR for 36 meshes square gridV. CONCLUSIONS This 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 Transactions on 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 voltages of 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, IEEE Transactions 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, "Evolutionary Strategy 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 Current Simulation Method with Boundary Element Method for Grounding System Calculations in Case of Multi-Layer Soil, International Journal of Electrical & Computer Sciences IJECS-IJENS Vol:12 No:04, August 2012, pp.17-24.[7] Mosleh Maeid Al-Harthi, Sherif Salama Mohamed Ghoneim, "Measurements the Earth Surface Potential for Different Grounding System Configurations Using Scale Model", 162
8. 8. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN0976 – 6553(Online) Volume 3, Issue 3, October – December (2012), © IAEME International Journal of Electrical Engineering and Technology (IJEET), Volume 3, Issue 2 (July- September 2012) , pp.405-416.[8] F. Navarrina, I. Colominas, “Why Do Computer Methods for Grounding Analysis Produce Anomalous Results?,” IEEE Transaction on power delivery, vol. 18, No. 4, , pp 1192-1201, October 2003.[9] I. Colominas, F. Navarrina, M. Casteleiro, "A Numerical Formulation for Grounding Analysis in Stratified Soils", IEEE Transactions on Power Delivery, vol. 17, pp 587-595, April 2002.[10] F. Dawalibi, N. Barbeito, “ Measurements and computations of the performance of grounding systems buried in multilayer soils”, IEEE Transactions on Power Delivery, Vol. 6, No. 4, pp. 1483-1490, October 1991.[11] F. Dawalibi, J. Ma, R. D. Southey, “ Behaviour of grounding systems in multilayer soils, a parametric analysis”, IEEE Transactions on Power Delivery, Vol. 9, No. 1, pp. 334- 342, January 1994.[12] M. M. A. Salama, M. M. Elsherbiny, Y. L. Chow, "Calculation and interpretation of a grounding grid in two-layer earth with the synthetic-asymptote approach", Electric power systems research, pp. 157-165, 1995.[13] Cheng-Nan Chang, Chien-Hsing Lee, “ Compuation of ground resistances and assessment of ground grid safety at 161/23.9 kV indoor/tzpe substation”, IEEE Transactions on Power Delivery, Vol. 21, No. 3, pp. 1250/1260, July 2006.[14] E. Bendito, A. Carmona, A. M. Encinas and M. J. Jimenez “The extremal charges method in grounding grid design,” IEEE Transaction on power delivery, vol. 19, No. 1, pp 118-123, January 2004.[15] J. A. Güemes, F. E. Hernando “Method for calculating the ground resistance of grounding grids using FEM,” IEEE Transaction on power delivery, vol. 19, No. 2, pp 595-600, April 2004.[16] M. B. Kostic, G. H. Shirkoohi “Numerical analzsis of a class of foundation grounding systems surrounded by two-layer soil,” IEEE Transaction on power delivery, vol. 8, No. 3, pp 1080-1087, July 1993.[17] E. Mombello, O. Trad, J. Rivera, A. Andreoni, "Two-layer soil model for power station grounding system calculation considering multilayer soil stratification", Electric power systems research, pp. 67-78, 1996.[18] J. A. Sullivan, “Alternativ earthing calculatons for grids and rods,” IEE Proceedings Transmission and Distributions, Vol. 145, No. 3, pp. 271-280, May 1998.[19] J. Nahman, I. Paunovic, “Resistance to earth of earthing grids buried in multi-layer soil,” Electrical Engineering (2006), Spring Verlag 2005, pp. 281-287, January 2005.[20] N. H. Malik, “A review of charge simulation method and its application,” IEEE Transaction on Electrical Insulation, vol. 24, No. 1, February 1989, pp 3-20. 163