GIS电场及其逆问题数值计算方法研究
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摘要
随着GIS(Gas Insulated Switchgear)小型化和三相共箱化的发展趋势,GIS内部电场分布变的越来越复杂,选择科学、有效的数值计算方法,对GIS的三维电场进行数值计算来指导绝缘设计是电气设备行业的迫切要求。通过电场的准确计算,有效地优化GIS绝缘结构,使整个场域的电场分布尽可能均匀,对于设计绝缘结构合理的GIS产品具有重要意义。
本文基于有限元法,对GIS电场及其逆问题数值计算方法进行了研究。提出了采用MPCG(Modified Preconditioned Conjugate Gradient)算法求解大型有限元代数方程组的方法,设计了能快速寻址系数矩阵的存储方法,开发了简单易用的电场辅助计算软件,具有工程实际应用价值。最后,引入RBFEM(Reduced-basis FEM)求解GIS电场逆问题。
论文采用有限元法,对三相共箱式GIS的三维电场进行计算,通过计算分析获得了GIS的电场分布规律,影响GIS内部绝缘和表面绝缘的主要因素,以及相关结构参数对电场分布的影响。在此基础上进行电场逆问题求解,实现了绝缘子表面和导体屏蔽均压罩的结构优化设计。从而为GIS的结构设计提供数据支持和理论依据。
针对三维电场剖分后形成的系数矩阵阶数高达几十万阶的特点,论文提出采用MPCG算法求解大型有限元方程组,同时,为了节省程序占用的存储空间,加快存取运算速度,开展了稀疏矩阵存储技术的研究,设计了系数矩阵的快速寻址方法。并用于GIS三维电场有限元方程组的求解。利用该算法可以减少求解时间,具有和ICCG(Incompletely Cholesky Conjugate Gradient)算法相近的收敛速度,非常适合大型有限元方程组求解。
论文基于APDL(ANSYS Parametric Design Language)语言,结合VC,设计并实现了用于GIS电场分布和电压分布的辅助计算软件。软件具有简便的图形用户界面,可以选择不同的工况测试模式,计算相应的电场和电压分布情况,是一种较实用的电场计算软件。
针对随机优化法结合有限元法求解电场逆问题时,需要多次生成有限元网格和重复求解有限元方程导致计算量太大的问题。论文提出了采用基于近似分析的RBFEM快速求解GIS电场逆问题,该算法能够在一次有限元网格剖分的基础上,利用已形成的缩减基矩阵通过插值法来求得新的电位向量,通过降维求解的方式实现电场的快速优化。该方法极大地降低了计算量,提高了优化设计的效率,而且还具有好的精确度。
Along with the structural miniaturization and three-phase-in-one-tank of GIS, electric field distribution becomes more complex in GIS. It is an urgent demand to instruct the insulation design of electrical equipment by using reliable and effective numerical computational method and technology to calculate its three-dimensional electrical field. The electrical field intensity will be more evenly distributed in the whole domain and among phases in GIS through the accurate calculation of electrical field and effective optimization for GIS insulation structure, which is very important to design reasonable insulation structure for GIS.
This thesis focuses working on the numerical computation of electric field and its inverse problem in GIS using the finite element method. We propose a MPCG algorithm to solve large algebraic equations and design a storage method for speeding up addressing coefficient matrix. A software is developed for assistant electrical field calculation which has practical engineering application value. Finally, RBFEM is applied to solve electric field inverse problem in GIS.
Three-dimensional electric field of three-phase-in-one-tank GIS is calculated by FEM. The electric field distribution, the main factors affecting internal insulation and surface insulation of GIS and the effect of related structure parameters on electric field distribution are obtained by analysis of computation results. Based on these results, structure optimization for disk-type insulator is implemented by solving the related inverse problem.
Since the order of coefficient matrix is up to hundreds of thousand after meshed, MPCG algorithm is adopted to solve the large equations. In order to reduce the computation cost and memory storage requirement, a novel mode is designed for coefficient matrix storage. With the algorithm and storage mode, calculation cost is cut down, while the convergence speed is kept close to the ICCG algorithm.
An assistant software is developed to calculate electric field distribution and potential distribution for GIS using VC and ANSYS parametric design language. With this assistant calculation software, engineers or technicians with little FEM knowledge can also compute the three-dimensional electric field distribution and potential distribution for GIS conveniently. The software has compact user graphic interface and can select different working mode.
When solving the inverse problem by combining FEM with random optimization method, there needs to mesh and calculate equations repeatedly, RBFEM is thus adopted to realize fast design optimization of electric field in GIS inverse problem. RBFEM calculate new potential vector by interpolation method based on generating reduced basis matrix with only one mesh. RBFEM provides fast calculation by decreasing matrix dimension and improve optimization efficiency greatly.
本文基于有限元法,对GIS电场及其逆问题数值计算方法进行了研究。提出了采用MPCG(Modified Preconditioned Conjugate Gradient)算法求解大型有限元代数方程组的方法,设计了能快速寻址系数矩阵的存储方法,开发了简单易用的电场辅助计算软件,具有工程实际应用价值。最后,引入RBFEM(Reduced-basis FEM)求解GIS电场逆问题。
论文采用有限元法,对三相共箱式GIS的三维电场进行计算,通过计算分析获得了GIS的电场分布规律,影响GIS内部绝缘和表面绝缘的主要因素,以及相关结构参数对电场分布的影响。在此基础上进行电场逆问题求解,实现了绝缘子表面和导体屏蔽均压罩的结构优化设计。从而为GIS的结构设计提供数据支持和理论依据。
针对三维电场剖分后形成的系数矩阵阶数高达几十万阶的特点,论文提出采用MPCG算法求解大型有限元方程组,同时,为了节省程序占用的存储空间,加快存取运算速度,开展了稀疏矩阵存储技术的研究,设计了系数矩阵的快速寻址方法。并用于GIS三维电场有限元方程组的求解。利用该算法可以减少求解时间,具有和ICCG(Incompletely Cholesky Conjugate Gradient)算法相近的收敛速度,非常适合大型有限元方程组求解。
论文基于APDL(ANSYS Parametric Design Language)语言,结合VC,设计并实现了用于GIS电场分布和电压分布的辅助计算软件。软件具有简便的图形用户界面,可以选择不同的工况测试模式,计算相应的电场和电压分布情况,是一种较实用的电场计算软件。
针对随机优化法结合有限元法求解电场逆问题时,需要多次生成有限元网格和重复求解有限元方程导致计算量太大的问题。论文提出了采用基于近似分析的RBFEM快速求解GIS电场逆问题,该算法能够在一次有限元网格剖分的基础上,利用已形成的缩减基矩阵通过插值法来求得新的电位向量,通过降维求解的方式实现电场的快速优化。该方法极大地降低了计算量,提高了优化设计的效率,而且还具有好的精确度。
Along with the structural miniaturization and three-phase-in-one-tank of GIS, electric field distribution becomes more complex in GIS. It is an urgent demand to instruct the insulation design of electrical equipment by using reliable and effective numerical computational method and technology to calculate its three-dimensional electrical field. The electrical field intensity will be more evenly distributed in the whole domain and among phases in GIS through the accurate calculation of electrical field and effective optimization for GIS insulation structure, which is very important to design reasonable insulation structure for GIS.
This thesis focuses working on the numerical computation of electric field and its inverse problem in GIS using the finite element method. We propose a MPCG algorithm to solve large algebraic equations and design a storage method for speeding up addressing coefficient matrix. A software is developed for assistant electrical field calculation which has practical engineering application value. Finally, RBFEM is applied to solve electric field inverse problem in GIS.
Three-dimensional electric field of three-phase-in-one-tank GIS is calculated by FEM. The electric field distribution, the main factors affecting internal insulation and surface insulation of GIS and the effect of related structure parameters on electric field distribution are obtained by analysis of computation results. Based on these results, structure optimization for disk-type insulator is implemented by solving the related inverse problem.
Since the order of coefficient matrix is up to hundreds of thousand after meshed, MPCG algorithm is adopted to solve the large equations. In order to reduce the computation cost and memory storage requirement, a novel mode is designed for coefficient matrix storage. With the algorithm and storage mode, calculation cost is cut down, while the convergence speed is kept close to the ICCG algorithm.
An assistant software is developed to calculate electric field distribution and potential distribution for GIS using VC and ANSYS parametric design language. With this assistant calculation software, engineers or technicians with little FEM knowledge can also compute the three-dimensional electric field distribution and potential distribution for GIS conveniently. The software has compact user graphic interface and can select different working mode.
When solving the inverse problem by combining FEM with random optimization method, there needs to mesh and calculate equations repeatedly, RBFEM is thus adopted to realize fast design optimization of electric field in GIS inverse problem. RBFEM calculate new potential vector by interpolation method based on generating reduced basis matrix with only one mesh. RBFEM provides fast calculation by decreasing matrix dimension and improve optimization efficiency greatly.
引文
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