Automatic Design of Insulation Structure In Power Transformer

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This chapter presents the procedure, which can be used in the automatic design of the insulation structure in power transformer. It explains the use of the multidimensional Hermite polynomial, differing to the Taylor polynomial approximation, to approximate the objective function to replace the finite element computation in optimization. Dr. Coulomb proposed a Taylor polynomial approximation of the objective function with respect to both physical and geometric parameters for the magnetic field problem. In their approximation, based on the finite element meshing only once, the objective function is expressed as a Taylor polynomial and it is used for the optimization of the objective function for electromagnetic apparatus. In this algorithm, once the Taylor polynomial is built, there is no need to do repeated finite element meshing and solving in the optimization. The Hermit polynomial helps to construct an approximation of the objective function in which its values and derivatives are specified at the given points of the parameters. Thus, whole region of the parameters is divided into several small subregions and apply the Hermit polynomial to the approximation of the objective function in every subregion. Based on the finite element method, a new algorithm for evaluating the sensitivity of electric field intensity to geometric parameters is presented. By means of this algorithm, the sensitivity can be evaluated such as the nodal potential solution. Numerical results show that Hermit polynomial approximation is very effective and can be used in the automatic design of the insulation structure in high-voltage and big-volume power transformer.