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GROUNDING RESISTANCE CALCULATIONS Isa \u0130lisu - Electrical Engineer It is known that grounding systems play an important role in electrical energy systems in terms of safety and the technical expectations of the network. Increased sensitivity to the danger of electric shock for living beings necessitates more careful sizing of grounding systems. Various electrode types have been used in grounding systems. While rod electrodes are commonly preferred in our country, network grounding systems are predominantly preferred in foreign sources. Again, while importance is given to the spreading resistance of the grounding system in our country, the calculation of touch voltage is preferred in foreign sources. This article will attempt to provide information on the calculation of soil spreading resistance. Soil spreading resistance depends on the shape and dimensions of the grounding system and the specific resistance of the soil. The soil layer at the location of the grounding system can consist of layers with different specific resistances in both the vertical and horizontal directions. Various researchers have developed different calculation methods based on analytical calculations for calculating soil spreading resistance. These formulas and calculation methods yield suitable results for regions with a maximum of two vertical layers. With the development of computer systems, computer programs using the "Finite Element Method" have also been developed. Comparing analytical methods and computer programs shows that the margin of error between the two systems does not exceed 10%. Therefore, using expensive computer programs for small-scale projects is not recommended. Among analytical methods, the Sverak and Schwarz methods stand out, while the Thapar-Gerez method is also noteworthy. The IEEE publication, IEEE Guide for Safety in AC Substation Grounding, Std 80-2000, provides explanations of the Sverak and Schwarz methods. It also includes numerical calculation examples for different network structures. It has been observed that the calculations were performed using the Sverak method. Both methods are explained below. Sverak Method: Adding the network depth to the formula given by Laurent and Niemann, the Sverak method gives the spreading resistance of a grounding system constructed in a network as follows: Here, L: Total length of buried conductor (m) (including rods) A: Area covered by the network (m\u00b2) h: Depth of burial of the network (m). Schwarz Method: In this method, the resistances of horizontal conductors and vertical rods, and the mutual resistances between them are taken into account. The system resistance is given as follows: R: System resistance (\u03a9) R1: Ground resistance of the network conductor group (\u03a9) R2: Ground resistance of the rod group (\u03a9) Rm: Mutual resistance between the two groups (\u03a9). The total grounding resistance of the network conductors is R1, where \u03c1: Soil resistivity (\u03a9.m), LC 2a h A: Total length of horizontal conductors in the network (m), : Conductor diameter (m), : Network burial depth (m), : Area covered by the network (m2), \u03c1: Soil resistivity (\u03a9.m), k1,k2: Coefficients to be taken from the table below, R: Spreading resistance (\u03a9). The total resistance of the rods is calculated as R2, where LR: Length of a rod (m), 2b: Rod diameter (m), nR: Total number of rods. The mutual resistance between the rods and the network conductors is Rm. The coefficients k1 and k2 depend on the mesh's length\/width ratio (\u03b1), the mesh's burial depth (h), and the area covered by the mesh (A). The table for calculating k1 and k2 coefficients is provided below. Applications: Example-1: In a 3m x 6m soil environment with a uniform resistivity of 100 \u03a9.m, a foundation ground electrode is buried to a depth of 0.5 m. 2 m long, 2.5 cm diameter stakes are driven into the four corners of this ground electrode. Additionally, a second ring ground electrode is routed around the foundation at a distance of 1 m. The soil spreading resistances calculated using both methods given above for various situations are compared below. Figure Ring (\u03a9) Network (\u03a9) Sverak (\u03a9) Schwarz (\u03a9) Basic grounding Outer ring addition Intermediate branches addition Rods addition 13.91 11.83 \u201c \u201d \u2019 16 9.28 9.01 9.01 8.82 14.27 10.51 8.42 8.15 7.87 7.73 7.36 7.26 7.01 6.98 h 0 1\/10 1\/6 k1 k2 Middle section addition - 0.04\u03b1+1.41 0.15\u03b1+5.50 -0.05\u03b1+1.20 0.10\u03b1+4.68 -0.05\u03b1+1.13 -0.05\u03b1+4.40 Example-2 As seen in the table, the k1 and k2 coefficients are given depending on the network area. Finding the coefficients for a specific network depth After obtaining values related to the network area, coefficients should be found by interpolating these values with the actual network depth value. As can be seen, the Schwarz method requires quite lengthy calculations. Both methods can be easily used if organized in an EXCEL file. No studies have been found in foreign publications regarding which method is more reliable. It is planned to construct a 40m x 50m network with a 90mm\u00b2 cross-section conductor at a depth of 0.5m in a soil medium with a specific resistance of 100 \u03a9.m, and for the network to consist of meshes spaced 10m apart. The resistance of the network was examined for cases with and without rods, and the results are given below. Case Without rods 8 rods 30 rods 4m length, 30 rods Sverak (\u03a9) Schwarz (\u03a9) 1.18 1.17 1.16 1.14 1.20 1.20 1.19 1.15 As can be seen The effect of rods used in homogeneous environments such as those mentioned above on grounding resistance is very small. Calculations for two-layered soils and touch voltage calculations in mesh holes will be the subject of another article. 88 Electrical Engineering, Issue 438, March 2010 Electrical Engineering, Issue 438, March 2010 89 The output for the rod case for example-1 is given in Appendix A. Appendix A General formula Approximate formula VARIOUS GROUNDING RESISTANCE CALCULATION METHODS RING GROUNDING IRON Rg=\u03c1.Ln(2\u03c0.D\/d)\/(\u03c02.D) Rg=2.\u03c1\/(3.D) D=1.13\u221a(A) NETWORK GROUNDING IRON Conductive plate on soil h = 0 Rg=\u03c1\/4.\u221a(\u03c0\/A) Laurent addition* max resistance h = 0.25 * Formula given in the grounding regulations Sverak approach For depths of 0.25-2.5 m, the sum of the mesh conductors + rod lengths is calculated as follows: LT Rg = \u03c1\/4.\u221a(\u03c0\/A) + \u03c1\/L Rg = \u03c1(1\/LT + 1\/\u221a(20A)(1 + 1\/(1 + h.\u221a(20\/A))) 58 m 11.83 \u03a9 9.33 \u03a9 7.15 m 7.01 \u03a9 9.01 \u03a9 7.87 \u03a9 CALCULATION OF SPREADING RESISTANCE OF NETWORK GROUNDERS ACCORDING TO THE SCHWARZ METHOD ** Given: Specific resistance around the electrode at depth h Total length of conductors in the mesh Average length of rods in the mesh Network burial depth (d1.h) 1\/2 Short side length Long side length Mesh area ab Number of rods Mesh conductor diameter Rod diameter Interpolated values for 0.50 m Length \/ Width b\/a \u03c1 L l2 h h' a b A n d1 d2 K1 K2 x 100 \u03a9.m 50 m 2 m 0.5 m (d1.h)1\/2 5 m 8 m ab 4 pieces 0.0107 m 0.021 m Network conductor resistance Rod resistance Network and rod-to-rod mutual resistance (\u03c1\/\u03c0L)(Ln(2L\/h')+K1(L\/A1\/2)-K2) (\u03c1\/2n\u03c0l2)(Ln(8l2\/d2)-1+2K1(l2\/A1\/2)(n1\/2-1)2) R1 R2 R12 (\u03c1\/\u03c0L)(Ln(2L\/l2)+K1(L\/A1\/2)-K2+1) Total resistance ** Taken from IEEE Std 80 -2000. Calculation of coefficients K1 and K2: Rg (R1R2-R12 2)\/(R1+R2-2R12) K1=-0.04x+1.41 K1=-0.05x+1.20 K1=-0.05x+1.13 K2=0.15x+5.50 K2=0.1x+4.68 K2=-0.05x+4.40 h=0 h=1\/10.A1\/2 h=1\/6.A1\/2 h K1 1.35 1.12 1.05 K2 5.74 4.84 4.32 0 0.63 1.05 0.50 Interpolated values for m 1.17 5.03 90 Electrical Engineering, Issue 438, March 2010 Calculations 0.07 m 40.0 m2 1.17 5.03 1.60 7.27 \u03a9 12.68 \u03a9 5.80 \u03a9 7.01 \u03a9\n<<\/pre>\n
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