变压器电磁场问题的自适应有限元分析方法研究
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摘要
变压器是电力系统大量应用的重要装备之一,随着交直流特高压输电项目的建设,变压器的电压等级也达到了百万伏级。变压器内电磁场问题的有效分析对于降低变压器制造成本、提高变压器性能指标及高电压大容量新产品开发具有重要意义。本文对自适应有限元分析方法在变压器电磁场问题中的应用进行了系统化的研究,针对后验误差估计、自适应迭代过程控制及网格生成等自适应有限元分析的关键环节给出了一系列新的算法,并成功开发了既可用于变压器优化设计程序又可单独运行的变压器电磁场问题自适应有限元分析程序。
高压直流输电换流变压器绝缘结构设计要求进行传导电流场分析,本文推导了考虑绝缘材料各向异性及非线性特性的有限元离散化公式,并研究了瞬态传导电流场的计算方法。
后验误差估计是自适应有限元分析的关键环节。本文详细研究了余量法、平均法针对电磁场问题的实现方法,给出了在涡流场分析时的计算公式,提出了计算优于经典平均法的CIL与CAL方法。对于如何应用后验误差估计进行网格加密控制,也给出了自己的实现方法。
自适应有限元分析的过程就是网格不断优化改进的过程。本文研究了初始网格及加密网格的生成方法,给出了适合变压器电磁场问题分析的完整网格生成解决方案。在此基础上,开发了可以进行静电场、静磁场、传导电流场及涡流场分析的变压器电磁场自适应有限元分析程序,该程序具有跨平台、数据驱动及可以结合进变压器电磁计算程序等特点。
TEAM WORKSHOP问题及变压器电磁场问题分析实例验证了本文研究成果的正确性和有效性。
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.
高压直流输电换流变压器绝缘结构设计要求进行传导电流场分析,本文推导了考虑绝缘材料各向异性及非线性特性的有限元离散化公式,并研究了瞬态传导电流场的计算方法。
后验误差估计是自适应有限元分析的关键环节。本文详细研究了余量法、平均法针对电磁场问题的实现方法,给出了在涡流场分析时的计算公式,提出了计算优于经典平均法的CIL与CAL方法。对于如何应用后验误差估计进行网格加密控制,也给出了自己的实现方法。
自适应有限元分析的过程就是网格不断优化改进的过程。本文研究了初始网格及加密网格的生成方法,给出了适合变压器电磁场问题分析的完整网格生成解决方案。在此基础上,开发了可以进行静电场、静磁场、传导电流场及涡流场分析的变压器电磁场自适应有限元分析程序,该程序具有跨平台、数据驱动及可以结合进变压器电磁计算程序等特点。
TEAM WORKSHOP问题及变压器电磁场问题分析实例验证了本文研究成果的正确性和有效性。
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.
引文
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