Efficient Frequency Response Calculation for Transformer Windings Using Relaxation Method

变压器绕组变形故障的快速诊断对保障电力系统稳定运行至关重要。频率响应分析(Frequency Response Analysis, FRA)为故障检测提供了有效手段，因此建立等效电路并快速实现频率响应计算就成为研究的首要任务。本文针对高阶双绕组变压器等效电路，提出了一种基于松弛法的频率响应计算方法。首先，建立n阶双绕组变压器集总参数等效电路模型，明确其拓扑结构与参数分布；其次，在节点电压法的基础上，合理选取松弛因子与初始值，迭代求解节点电压，从而实现等效电路的频率响应计算；最后，基于Multisim平台构建仿真模型，对比所提算法与Multisim仿真、传统方法的偏差。结果表明曲线最大偏差低于0.25 dB，验证了算法的准确性。此外，为进一步验证算法在复杂网络中的适用性，本研究在高阶等效电路中进行了仿真，频率响应计算结果表明，松弛法与稀疏矩阵法、撕裂算法及节点电压法的结果具有高度一致性。The rapid diagnosis of transformer winding deformation faults is crucial for ensuring the stable operation of power systems. Frequency Response Analysis (FRA) provides an effective means for fault detection. Thus, establishing equivalent circuits and rapidly computing frequency responses have become critical research priorities. In this paper, a frequency response computation method rooted in the relaxation method is proposed for the equivalent circuit of high-order two-winding transformers. First, an n-order dual-winding transformer lumped-parameter equivalent circuit model is established, clarifying its topological structure and parameter distribution. Second, the node voltage equations derived from the node voltage method are iteratively solved using the relaxation method, with optimized strategies for selecting the relaxation factor and initial values. Finally, a simulation model is constructed on the Multisim platform to compare the deviations between the proposed algorithm, Multisim simulations, and traditional methods. The results demonstrate a maximum deviation of less than 0.25 dB in the frequency response curves, validating the algorithm’s accuracy. Furthermore, to verify the algorithm’s applicability in complex networks, simulations are conducted on high-order equivalent circuits. The frequency response calculations reveal high consistency between the relaxation method and results from the sparse matrix method, tearing algorithm, and node voltage method, confirming the method’s robustness in intricate scenarios.