Performance Study Of Grounding Grids In Complex Soil Based On Boundary Element Method

In order to ensure the safe operation of the substations, it’s very important to establish proper soil model to research the performance of grounding grids. Except for the multi-layer soil model in which grounding grids lie, there are also hemispherical layered soil model, cylindrical layered soil model, massive texture soil model and composite soil model and so on. In this paper, the performance of grounding grids are researched based on boundary element method, which includes three main parts, namely traditional boundary element method research in massive ground soil structure, application of fast boundary element method in grounding problems in layered soil model and soil with massive texture, and the study of grounding problems in composite layered soil model. The main research work is as follows:(1) This paper deduces the mathematical soil model of grounding with massive texture using the direct boundary element method and the indirect boundary element method. At the same time, this paper uses the CDEGS software to verify the validity of the programming algorithm. The programing codes based on the two kinds of boundary element method are used to do the contrastive research in aspect of influence that the massive soil boundary subdivision number have on the grounding grids performance. The results of the study show that:in the same subdivision method, when using the two kinds of boundary element method to get the solution of the grounding resistance of grounding grids in the same soil with massive texture, the direct boundary element method needs less subdivision units, and with the decreasing of thickness of the massive soil, the direct boundary element method has more obvious advantage in subdivision number, especially when grounding grids are in area of narrow massive soil. The computing results of the direct boundary element method are more stable than that of the indirect boundary element method. In the same subdivision method, direct boundary element method has an advantage on the solution performance over software CDEGS based on indirect boundary element method. The advantage of direct boundary element method in number of the boundary element subdivision of massive soil grounding model, provides the possibility for further research of grounding grids in more complex soil with massive texture.(2) A preconditioned method of Krylov subspace-GMRES iterative algorithm is proposed. The coefficient matrix will become large-scale linear equations of asymmetrical full array when using boundary element method to solve the problems of grounding grids in the soil with massive texture, in which large amount of subdivision units are needed. And the solving inefficiency problem exists when using direct methods such as Gaussian elimination to solve the problems. Therefore, this article attempts to propose a method to solve these problems. In solving an example of a typical soil with massive texture grounding problem, GMRES iterative algorithm performs significantly better than the direct method such as Gaussian elimination in aspect of computing time, and the iteration performance of GMRES that has been preconditioned is obviously better than that has not.(3) This paper proposes a fast multi-pole boundary element method to solve the grounding problem of layered soil. The fast multi-pole boundary element method is dedicated to solve the problem that traditional boundary element method requires a great number of memory space when it is used to calculate the parameters of large grounding grids, which means it can’t be used in ordinary computer because of memory limit. Based on the traditional boundary element method, this method uses the fast multi-pole boundary element method and builds adaptive quadtree storage structure instead of the traditional storage schema to make coefficient matrix implicitly stored. It uses the interaction between the square nodes instead of the traditional units, which largely reduces the amount of memory and computation. In this paper, a small scale grounding model in soil with massive texture is calculated and the comparison with the results of traditional boundary element method is made. Comparing the ground resistance calculation results of this method with software CDEGS, the validity of this method is verified. And the comparison of the memory space and computation time between these two methods shows the high efficiency of the new method.(4) The fast multi-pole boundary element method for the calculation of the grounding grids parameters in soil with massive texture is proposed to make up for the defect that huge amount of memory and computation is needed for the traditional boundary element method. This method uses an adaptive octree storage structure instead of the traditional storage schema to make coefficient matrix implicitly stored. It uses the interaction between the cubic nodes instead of the traditional units, which largely reduces the amount of memory and the computation. In this paper, a small scale grounding model in soil with massive texture is calculated and the accuracy as well as the efficiency of this method is verified by the comparison with traditional boundary element method and CDEGS. An example shows that the fast multi-pole boundary element method can solve grounding problems of large scale soil with massive texture in a single ordinary computer, which is impossible for the traditional boundary element method and CDEGS because of the limit of memory. The method proposed in this paper provides a direction for the further study of more complex grounding problems in soil with massive texture.(5) The unity of direct boundary element method and moment method for solving the grounding problem of layered soil is proved in this paper. Taking the grounding problem of the uniform soil or two-layer soil for example, the fundamental solution of the direct boundary element method is studied in detail, which shows that the form of boundary integral equations will vary with the different fundamental solutions. The model of the same layered soil is derived with appropriate fundamental solution using the moment method and the direct boundary element method separately, in which only subdivision of grounding grids is needed, and a unanimous conclusion formula is concluded, which shows the uniformity of direct boundary element method and moment method in solving the grounding problem in layered soil. More importantly, subdivision at the interface of the layered soil can be effectively avoided when direct boundary element method is employed with appropriate fundamental solution, thus solving the problem that the traditional direct boundary element method requires additional subdivision at the interface of different soil.(6) A new direct boundary element method is proposed to solve complex layered soil grounding model.the integral calculation on the horizontally layered soil interface can be avoided by selecting the fundamental solution. The method only needs to make subdivision on the interface of the soil with massive texture and the grounding grids, which can largely reduce the amount of subdivision units and avoid solving large-scale full matrix, so the efficiency of the computation is improved and the required memory for solving the equation is greatly reduced. Meanwhile, this method makes up for the defect that large numbers of subdivision units, large amount of memory and the computation is needed when using traditional direct boundary element method to make subdivision on layered soil interface, massive soil interface and grounding grids. In comparison with traditional direct boundary element method and calculation results of CDEGS, the accuracy and efficiency of the algorithms as well as the programming principle is verified.(7) By introducing node voltage method, grounding grids are considered as unequal potential. Combined with the new direct boundary element method, grounding grids in layered soil containing massive texture are further studied, and models for both grounding grids and massive texture in any layered soil are detailedly derived. It makes the new direct boundary element method more general in solving the soil model. By comparing the calculation example and the traditional boundary element method in which unequal potential is considered as well as the calculation results of CDEGS, the validity and the efficiency of the algorithm is verified. At the same time, when solving unequal potential grouding models in composite soil, novel direct boundary element method has an advantage on the solution performance over software CDEGS that needs equivalence.