双绕组电力变压器梯形网络频率响应的矩阵算法

Matrix Algorithm for Ladder Network Frequency Response Analysis of Double-Winding Power Transformer

针对双绕组电力变压器梯形网络的仿真软件建模的非完整性以及现存等效电路频率响应算法多变量求解的低效率,围绕一种电力变压器绕组高频等效模型频率响应的矩阵计算方法开展研究,基于等效电路的拓扑结构,给出了利用阻抗支路矩阵和导纳支路矩阵来完整表示该等效电路的方法。其次,通过矩阵运算,推导了阻抗支路电流、导纳支路电流以及节点电压列向量之间的关系,进而求解节点电压列向量,获得等效电路的频率响应。最后,将矩阵算法与基于电路仿真得到的频响曲线进行比较,结果表明,曲线相关系数较大,吻合程度很高,对于不含高幅值谐振峰(-500dB以上)的曲线,相关系数为10,即两者完全吻合,而矩阵算法的计算耗时少于电路仿真运算。上述分析表明,在保证仿真模型完整性和精确性的同时,提出的矩阵算法由于仅有两次矩阵取逆运算且求取的未知量较少,具有良好的计算效率及计算精度。

To improve the incomplete transformer winding model in the circuit simulation software or the low efficiency of frequency response calculation due to many unknowns in the existing algorithm,a research on a matrix algorithm to calculate the frequency response of the equivalent ladder network for double-winding transformer is conducted.Following the equivalent circuit topology,the model is completely described by the impedance branch matrix and the admittance branch matrix.By means of matrix operation,the relationships of the column vectors of impedance branch current and admittance branch current with nodal voltage are obtained.The frequency response of the equivalent circuit model is calculated by solving the nodal voltage column vector.A comparison between the simulated results of matrix algorithm and those obtained by circuit simulation indicates that the correlation coefficient(CC)becomes greater showing good agreement between them.The curves without high amplitude resonance peaks(above-500 dB)coincide perfectly with a CC of 10.The matrix algorithm takes less calculation time than simulation software.Ensuring the integrality and precision of the simulation model,the proposed algorithm is endowed with good computational accuracy and efficiency due to only twicematrix inversions and less unknowns to be solved.