电场计算的快速多极子预条件高阶边界元法

Fast multi-pole preconditioned GMRES high order boundary element method for power frequency electric field of multi-medium

针对多介质工频电场计算中低阶边界元法及预条件(GMRES)法的计算精度低及计算成本高的不足,在低阶边界元法基础上引入高阶边界元和快速多极子法,提出了一种用于求解三维电场分布的快速多极子预条件GMRES高阶边界元法。建立了三维电场计算高阶边界元模型,阐述了快速多极子预条件GMRES高阶边界元法基本原理和具体实现方法;通过双介质实验模型进行了方法验证,并基于500kV变电站部分关键设备的三维电场计算,表明该方法在电场计算精度及在内存消耗和计算时间上均比预条件GMRES法有明显的优势。最后将计算结果与实际测量值进行了比较,该方法的计算结果与测量值最大相对误差为8.65%,该方法更适合于分析变电站这种大尺度多介质环境下的工频电场分布。

In order to improve the computational accuracy and cost for multi-medium power frequency electric field （PFEF） solved by low order boundary element method （BEM） and preconditioned generalized minimal residual （GMRES）,a hybrid technique combining the high order BEM and fast multi-pole （FM） method has been introduced to low order BEM. The FM preconditioned GMRES high order BEM is proposed to solve three dimension electric field distribution. The high order BEM model for three dimension electric field distribution is built, and the basic principles and implemen＇tation steps of the FM preconditioned GMRES high order BEM are given. The higher accuracy has verified in two medium test models. Part key devices in 500 kV substation is carried out to demonstrate that FM preconditioned GMRES high order BEM is much faster and more efficient than the preconditioned GMRES BEM in the computational cost and the storage of computer. The simulation values of this method are compared with measured values in 500 kV substation. It is found that the max relative error is 8.65%, so this method is suggested for use in large scale and multi-medium PFEF problems.