Adaptive Finite Element Analysis Of Electromagnetic Field Problems In Transformers

Power transformers are massively used in electrical power systems. Along with the construction of UHV (Ultro-High-Votage) AC and DC projects, the voltage level of transformers has been rised up to 1,000kV in China. The effective analysis of the electromagnetic field in transformers is significant for reducing the transformer cost, enhancing the transformer performance and developing the new product with high voltage and large capacity. This thesis conducts systematic research to the application of the adaptive finite element method in transformer electromagnetic flied computation, gives a series of new algorithms aiming at the key problems of adaptive finite element analysis method such as a posteriori error estimation, adaptive iterative process control and mesh generation, and successfully develops the adaptive finite element analysis software for transformer electromagnetic field computations, which can be incorperated into the codes of transformer optimization design as well as can be used independently.The conducting current field analysis is needed in the dielectric structure design of high-voltage DC converter transformers, for which the expressions of finite element discretization are deduced considering the anisotropy and nonlinearity of the dielectric materials. Besides, the computation method of the transient conducting current fields is researched in this thesis.A posteriori error estimation is the key link of the adaptive finite element analysis. The residual method and average method applied to electromagnetic field problems are investigated detailedly. The calculating expressions are given, and the CIL and CAL methods which are both better than the classical average method are proposed by the author. For the issue of how to apply the a posteriori error estimation to the mesh refinement control, the thesis also presents its own method.The process of adaptive finite element analysis is just the process of continuous mesh optimization. This thesis researches the generating method of the initial mesh and refining mesh, and proposes a complete scheme of mesh generation, which is suitable to the analysis of the electromagnetic field in transformers. Based on this research, the software of adaptive finite element analysis is developed for the computation of static electric fields, static magnetic fields, conducting current fields and eddy current fields in transformers, by which the properties of cross-platform and data-motive portability are achieved, and it can be incorporated into the electromagnetic computation of transformers easily.A few TEAM workshop problems and the examples of transformer electromagnetic field analysis are used, by which validity of the theoretic and computational results in this thesis is verified.