analysis of complex grounding systems by the program package FIELD GS
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1 The FEM analysis of complex grounding systems by the program package FIELD GS M. Trlep, A. Hamler, B. Hribernik University ofmaribor, Faculty ofelectrical Engineering and Computer Science, Smetanovaul 7, 2000Maribor, Slovenia Abstract This paper shows the practical use of the software package FIELD_GS for the analysis of complex grounding systems (GS) in the protection of power and industrial systems. In order to get an accurate field calculation the finite element method (FEM) with isoparametric second order finite elements was applied. The automatic discretization of the soil domain was performed with 20-node 3D finite elements, while the GS domain was carried out using 3-node ID finite elements. In the program solution a spatial transformation of the "semi-infinite space" into thefinitespace was applied. The FIELD_GS is suitable for any GS configuration and for isotropic or anisotropic soil properties. Introduction There are two basic approaches to the analysis and calculation of grounding systems: the integral approach e.g. Kurtovic [4], Dawalibi [5], and the differential approach e.g. Cardoso [6], Trlep [7]. The first one enables the calculation of the electric potential by using the integral equation for the line current. The calculation is relatively fast and practically independent of the configuration of the grounding system. But a larger number of domains with different conductivities cannot be taken into account, unless parallel layers of soil with different conductivities are assumed, and this is the main weakness of the approach. Generally, models with two layers are used, but often they do not correspond to the real conditions. In cases when we change the soil conductivity
2 244 Software for Electrical Engineering Analysis and Design artificially only in the proximity of the grounding system this approach cannot be used at all. These weaknesses can be overcome only with the differential approach using FEM. With this approach it is very easy to take into account the characteristics of the heterogeneous soil in the calculation domain. Since the calculation of GS represents an open boundary problem, the spatial transformation of the "semi-infinite space" suggested by Stochniol [2], is used. It enables a precise treatment of boundary conditions and reduces drastically the number of unknowns in the FEM system. 2 FEM model of grounding system A grounding system can be in general composed of grounding grids,ringsfor designing the potential, vertical rods and fence. All elements (electrodes) are electrically interconnected or unconnected. The current field in the stratified anisotropic soil is defined by the electric scalar potential (p and expressed by Poisson's equation eqn () and boundary conditions eqn (2). V([a]Vq>) = 0 () /g (p(oo) = o, (in earth surface) = 0 (%) By applying Galerkin's formulation of FEM and the additional transformation of the "semi-infinite space", the finite element equation is obtained. The equation of the 3D finite element in the non-transformed soil domain is given by, 20 #,(0, P) /= where: q>,[a], N and O^ are the electric scalar potential, the tensor of soil conductivity, the interpolation function and the volume of the 20-node 3D finite element of the second order in the non-transformed domain. In the transformed soil domain thefiniteelement equation is similar to eqn (3), only the transformed values q>', [a'], N' in O^ have to be taken into account. The equation of the ID finite element in the grounding system domain is: Z#.(py (4) 7=
3 Software for Electrical Engineering Analysis and Design 245 where: SID, /ID and a^ are the cross-section, the length and the conductivity of the grounding system element, and N is the interpolation function of the 3-node IDfiniteelement. The final form of the FEM equation of the grounding system problem is: MM= (5) First we solve eqn (5) by assuming the potential, for example IV, on the GS. For this potential we calculate the current (/) that flows from the GS, and then by means of eqn (6) and the known injected current (I\) we calculate the absolute values of nodal potentials in the entire calculation domain: (6) 3 Software package FIELD GS The software package FIELDJ3S is an interactive graphic program designed for 3D current field calculations of the grounding system. It is composed of three modules: GENJ3S, FEMJ3S and PROCJ3S. In thefirstmodule GEN_GS the following grounding system input data are defined: the geometry of the grounding system, the electric properties (conductivity) of the soil and the injected current. Any GS geometry can be obtained. In order to speed up data preparation the standard grounding system elements are included: the grounding grid, rings and vertical rods, and to support the processing of results, also the fence. The GS can have any number of rods, but not more than two grounding grids and two grounding rings. The basic shape of the grounding element is a rectangle defined by the following data: width, length and depth of the element, the number of conductors in the width direction, the distance between conductors in the width direction, the number of conductors in the length direction, the distance between conductors in the length direction. In Fig. we can see the initial GS shape determined by the data shown in Table. Table. Data of grounding grid and grounding rings. GS element width of GS element (m) length of GS element (m) depth of GS element (m) number of conductors in width direction distance between conductors in width d. (m) number of conductors in length direction (m) distance between conductors in length d. (m) grid , 8, 8,9,9, 8,8, 8 7 8, 8, 9, 9, 8, 8 ring ring
4 246 Software for Electrical Engineering Analysis and Design \ \ I Figure. Initial geometry of grounding system. Each grounding element can be transformed into any desired shape by adding data in the first two lines. Three data are needed to describe a corner: the shortening of the length and width of an element and the form of the corner. No special order of succession is prescribed for the data that define individual corners since each corner is marked by a sign when shortening the length and width of a element. Figure 2 shows the transformation of a GS with one grounding grid and two rings from the initial to the final shape. - n= l Tl L - J: 'j Figure 2. Final geometry of grounding system.
5 Software for Electrical Engineering Analysis and Design 247 If the final GS shape is like the one shown in Fig. 2, we must add three data for each changed corner, which is presented in Table 2. In the interactive work we can cut away or add a part of the grounding grid (see Fig. 2). Table 2. Data for correction of grounding elements corners. width of grid length of grid width of ring length of ring width ofring2 length ofring upper -6,0 6,0-6,0 6,0-6,0 6,0 Left corner lower -0,0-6,0-0,0-6,0-0,0-6,0 Right comer upper lower 8,0 6,0 8,0 6,0 8,0 6,0 The individual parts of the grounding system may or may not be electrically interconnected. Also, the electrical properties of soil are defined in this module: any number of layers or only parts of the discussed domain can be defined by different isotropic or anisotropic properties, which enables the simulation of various conditions in the soil surrounding the grounding system. With these data it is possible to discretize automatically the discussed half-space with 20- node isoparametric finite elements and the grounding system with 3-node finite elements. Figure 3 shows the discretization (2D) only in the earth surface above the grounding system. :f± S :::::;::::: i Figure 3. Discretization in the earth surface above the GS.
6 248 Software for Electrical Engineering Analysis and Design In the second module FEM_GS the 3D current field in the soil of the given injected current is calculated by FEM Equation (5) is used to calculate the value of the electric potential in all nodes of the discretization space, the potential on the grounding system under the assumption of no potential drops, and finally the grounding resistance. The method ICCG was used in the solution of eqn (5). The third module PROC_GS is used to process the calculated values in the earth surface. Four levels of displaying are possible:. the display of the numerical values of the potential, the step voltage and the touch voltage in any point, 2. the drawing of the values of the potential, the step voltage and the touch voltage on any line, 3. the drawing of equipotential lines of the potential and the touch voltage on the entire earth surface, 4. the display of the step voltage and touch voltage in the colour scale on the entire earth surface. In order to reduce the duration of interactive work needed for the calculation, simulation and design of GS, the program offers a special option which enables a fully automated calculation and processing of results at a minimum number of input data. The processing is carried out in the earth surface above the GS and in its direct vicinity which is automatically defined for the GS configuration at the start of the module PROC_GS. For example: to draw the values of the potential, the step voltage and the touch voltage of the GS shown on Fig. 2, we get the automatically generated lines shown in Fig. 4. F -5 LHzzz: Figure 4. The lines for automatic processing of FEM results.
7 Software for Electrical Engineering Analysis and Design 249 All the results of processing, numerical values, graphs and drawings are stored during the execution of the program so that the user's presence is not necessary. Later, the user can analyse them with the aid of the option "MOVIE", which displays all the results of automatic processing in the order of appearance or directly includes them in the project documentation. 4 Application of program package FIELD GS The use of the program is demonstrated on the example of the GS shown in Fig. 2. When designing the GS, the values of the step voltage ( /,) and the touch voltage ( /,) must be within the prescribed limits. In case of a properly chosen grounding grid these requirements can be easily satisfied in the earth surface above the grounding grid domain, but difficulties arise in the earth surface above the grid border. To be able to lower the (7, and (7, values in the discussed domains we must use grounding rings in addition to grounding grids because they affect the potential profile and thus indirectly cause (7, and /, to decrease. Included is an analysis of the impact of grounding rings on the potential, 7, and 7, profiles in the earth surface above the GS at the injected current of 000 A. Three possible GS configurations have been analysed: I. The GS consists of a grounding grid at the depth of 0.8 m, II. A grounding ring at the depth of m is added to the GS described in I, III. Another grounding ring at the depth of.2 m is added to the GS described in II. The currentfieldcalculation using the software package FEELD_GS was carried out by 2992 finite elements of second order and nodes. A two-layer soil model was used; the electric conductivity in the first layer was O.OlS/m, and 0.005S/m in the second layer. In Table 3 we can see the values of the earth grounding resistance and the potential on the GS. It is clearly seen that the addition of grounding rings decreases the earth grounding resistance, which is very important in view of the desired lowest possible values. The difference in the grounding resistance between I. and III. is about 8%. Table 3. Potential on the GS and earth resistance Configurations I II III q>os(v) R (0) Figure 5 shows the equipotential lines in the earth surface above the GS for the configuration III. Its comparison with the first two configurations reveals that changes in the potential profile are noticeable only in the domains in the earth surface above the GS border, while the values of the potential differ throughout the domain.
8 250 Software for Electrical Engineering Analysis and Design QXS)(o)(o)(Q Figure 5. Equipotential lines in the earth surface above the grounding system. Further on we can see the potential, (7, and [/, profiles on the line 4 in the earth surface. Figure 6 shows the potential profile. The highest potential values are observed with the GS configuration I, and the smallest with the GS configuration III. The potential profiles of all three configurations are alike, except in the earth surface above the border of the grounding grid, where the grounding rings slow down the local potential drop j config. config,n Figure 6. Potential profile on the line 4 in earth surface.
9 Software for Electrical Engineering Analysis and Design 25 In this way a direct lowering of [/, is achieved, which was the purpose of adding grounding rings (see Fig. 7). The maximum [/, value of the GS configuration I (350 V) drops to 25 V in case of the configuration III. Similar relations are obtained if the [/, of all GS configurations are compared (Fig. 8). Again, the GS configuration III yields the lowest C/, and C/, values. ccnfigl caifig.n ccnfig.ni Figure 7. Step voltage profile on the line 4 in earth surface. oonfig.l -< config.fl -*-cx)nfig.lll Figure 8. Touch voltage profile on the line 4 in earth surface.
10 252 Software for Electrical Engineering Analysis and Design In order to get a complete estimation of the influence of grounding rings on the potential, 7, and Ut profiles and values, the entire domain above the grounding grid border should be studied. The comparison of local dependences of the potential, C/, and [/, on the remaining lines leads to similar results. It can therefore be concluded that grounding rings usually solve the problem of too high Us and Ut values in the earth surface above the grounding grid border and that they simultaneously lower the grounding resistance and the potential of the GS. 5 Conclusion The proposed procedure for the calculation of grounding systems by the FEM has proved to be a very accurate and simple way of analyzing and designing grounding systems, especially in case of different local soil properties and arbitrary shapes and combinations of grounding system elements. The program FDELDJ3S was tested on many cases and the comparison of obtained results shows good agreement with all reference results, which confirms the correctness of our program solution to the discussed problems. References. Silvester, P.P. & Ferrari, R.L., Finite Element for Electric Engineers, Cambridge University Press, Cambridge, Stochniol, A., A general transformation for open boundary finite element method for electromagnetic problems, IEEE Transsaction on Magnetics, vol. 28, no. 2, pp , Konrad, A. & Graovac M., An application of line elements embedded in 2D or 3D finite element mesh, IEEE Transsaction on Magnetics, vol. 32, no. 3, pp , Kurtovic, M. & Vujevic, S., Numerical modelling of the earthing grid, Computational Methods in Engineering, Advance and Applications, vol., pp , Dawalibi, F. & Mukhedkar, D., Optimum design of substation grounding in a two layer eart structure, part II, IEEE Transsaction on Power Apparatus and Systems, vol. PAS-94, no. 5, pp , Cardoso, J.R., FEM modelling of grounded systems with unbounded approach, IEEE Transsaction on Magnetics, vol. 30, no. 5, pp , Trlep, M., Hamler, A. & Hribernik, B., The analysis of complex grounding systems by FEM, IEEE Transsaction on Magnetics, vol. 34, no. 5, pp , 997.
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