采用复指数的频域分解算法及其在三相变压器非对称直流偏磁分析中的应用

Analysis of Three-phase Transformer Under Asymmetrical DC Bias by Using Frequency-domain Decomposition Based on Complex Exponential

采用复指数形式的频域有限元分解算法对三相壳式变压器非对称直流偏磁问题进行研究。考虑场路耦合关系,以磁矢量位及励磁电流为未知量建立频域有限元方程。按照谐波次数将系数矩阵进行分解后,有效地降低了问题求解时所需内存和计算时间。针对三相壳式变压器模型进行不同非对称直流偏置条件下的实验和计算,测量结果和计算结果基本一致,验证了该方法在三相变压器直流偏磁问题分析中的有效性。基于计算结果,分析直流偏磁对三相壳式变压器励磁电流和铁心磁通的影响规律。分析采用复指数的频域分解算法的计算效率,计算精度和收敛性。

The frequency-domain finite element decomposition algorithm using complex exponential was used to study the asymmetrical DC bias of three-phase shell-type transformer. Considering the electromagnetic coupling, the frequency-domain finite element equation was established with the magnetic vector and excitation current as the unknown quantity. The coefficient matrix was decomposed in harmonic domain, which effectively reduces the memory requirement and computational time in problem solving. A three-phase shell-type transformer was tested under DC bias excitation in experiment and the numerical computation was carried out. The calculated results agreed well with the measured one, and that verified the validity of the method in the computation and analysis of the three-phase transformer under DC bias. The exciting current and core flux was analyzed to investigate the influence of DC bias on the three-phase shell-type transformer. The efficiency, accuracy and convergent performance of the frequency-domain decomposition algorithm using complex exponential were analyzed.