# Mathematical modeling of electromagnetic disturbances in railway system

University dissertation from Luleå tekniska universitet

Abstract: By introduction of modern electronics into railway system, new challenges in understanding the electric and electromagnetic behavior of these systems arise. In this thesis, electromagnetic modeling of electric networks above dielectric and perfect electrically conducting surfaces are studied. The approach is based on the Partial Element Equivalent Circuit (PEEC) method for solving Maxwell's equations. The most challenging problem within electromagnetic modeling of large systems is computational speed and for railway systems, modeling of the ground becomes the major bottleneck. The purpose of the thesis is to develop maintenance program for the railway system in the northern Sweden to deal with the failures created by electromagnetic disturbances using mathematical modeling of the electromagnetic phenomena. First, a grid PEEC approach is used to improve the computation time of the original program. This approach utilizes an algorithm to distribute the calculations on computers in a local area network. It is shown that the computation time for large systems can be improved in some stages of the computation process. The second approach to improve the computational efficiency of the PEEC method utilizes the theory of complex images. This results in an appropriate mathematical tool to study and describe the generated electric fields above the earth, as a dielectric- or perfectly electric conducting surface. Different mathematical models are applied to analyze and plot the current distribution on structures and the electric field generated by several structures above a perfect electrical conducting surface. The tests are verified by analytical methods and the traditional PEEC computation method. In the traditional PEEC method, the numerical solution of mathematical modeling of the ground constitutes the major effort due to the large number of unknown variables in the corresponding linear equation system. By using of the complex image methods, where the effect of the ground is approximated, the computational time will clearly be improved in the case studies. This combination of the PEEC method and the method of complex images results into an ultimate linear equation system by a smaller number of unknown variables and therefore a considerable improvement of the computational time. By use of electromagnetic modeling, it will be possible to study the disturbances due to transients and discharges, and also to expand the data bases for artificial intelligence. Defining the problem and determining what can be obtained by using of computational electromagnetic modeling, will be a step towards developing a more appropriate maintenance program for the railway system in the northern Sweden.

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