双绕组变压器集总等效电路频率响应的电路矩阵算法研究

Research on Circuit Matrix Algorithm for Calculation of FRA Results of Lumped Equivalent Circuit of Two-Winding Transformer

为准确、高效地计算含线饼数量较多的双绕组电力变压器集总参数等效电路的频率响应,对电路方程的矩阵算法展开研究。根据双绕组等效电路结构和各支路所接元件特点,建立了等效电路的广义支路,并据此构建了等效电路的支路电压、电流矩阵;通过选择节点、独立回路和独立割集,基于基尔霍夫电压、电流定律,推导了等效电路频率响应的节点电压、独立回路电流与独立割集电压方程的矩阵算法;特别地,提出了等效电路的独立割集选取方法,避免了选择基本割集时需要选定电路图的树支与连支这一复杂步骤;基于Multisim电路仿真软件验证了所提算法的正确性。从电路方程矩阵的装配时间、方程求解时间以及总计算时间对3种算法进行了对比,结果表明:对于含线饼数量较多的双绕组变压器,独立割集电压方程矩阵算法具有最高的计算效率;若考虑前期的独立割集选择时间,节点电压矩阵算法则更具优势。

To accurately and efficiently calculate the FRA results of the lumped parameter equivalent circuit of a two-winding power transformer with a large number of discs,this paper studies the circuit equation matrix algorithm.First,according to the structure of the two-winding equivalent circuit and the characteristics of the components in each branch,a generalized branch of the equivalent circuit is established,and the branch voltage and branch current matrices are constructed;then,by selecting nodes,independent loops,and independent cut sets,matrix algorithms of the node voltage,loop current,and cut-set voltage equations are derived for frequency response of the circuit based on the KVL and KCL;in particular,the independent cut-set selection method for the equivalent circuit is proposed to avoid the complicated step of selecting the tree branch and the link branch of the circuit diagram when the fundamental cut-set is used;second,the accuracy of the three methods is verified by Multisim;finally,the three methods are compared in terms of the assembly time of the circuit equation matrix,the equation solving time and the total calculation time.The results show that the cut-set voltage equation matrix algorithm has the highest efficiency.However,if the selection time of the independent cut set in the early stage is considered,the node voltage matrix algorithm has more advantages.