基于本征正交分解的换流变压器极性反转电场降阶模型

A Reduced Order Model via Proper Orthogonal Decomposition for Polarity Reverse Electric Fields in Converter Transformers

为了解决在求解换流变压器极性反转瞬态电场过程中计算时间过长,占用存储空间过大的问题,该文基于本征正交分解(proper orthogonal decomposition,POD)方法构建了求解换流变压器极性反转瞬态电场的低阶有限元模型。首先,应用传统伽辽金有限元法计算部分时刻的场域电位组成样本数据,并对样本数据组成的矩阵进行特征值分解得到一组POD正交基,最后通过生成的POD正交基构建准静态电场方程的降阶模型。应用所提出的POD降阶模型,分析了一台?500k V换流变压器在极性反转情况下绕组端部电场随时间的变化情况。计算结果表明:POD降阶模型的计算结果与全阶模型(传统伽辽金有限元模型)的计算结果较吻合,验证了POD降阶模型的准确性。同时,应用降阶模型计算换流变压器瞬态电场的计算时间远小于全阶模型的计算时间,说明了降阶模型的高效性。

To solve the problem of prohibitively consuming of computation time and storage space for obtaining the polarity reverse transient electric field distribution in converter transformers, the low order finite element model based on proper orthogonal decomposition（POD） method was developed. This paper firstly achieved sample data of field potential on some discrete time-in-point calculated by the traditional Galerkin finite element method. Then, a group of POD orthogonal basis was obtained through eigenvalue decomposition for the matrix formed by the sample data. Finally, a reduced order model of quasi-static electrical field was constructed via the generated POD basis. The electrical field distribution in the winding end of a type of ±500k V converter transformers on the polarity reverse condition was computed used the POD reduced order model. It shows that the computed result of the POD reduced order model is in very good agreement with that of the full order finite element model（traditional Galerkin finite element model）, and it verifies the accuracy of the proposed POD reduced order model. Meanwhile, the computation time of the reduced order model is much smaller than the time of the full order model, and it shows the high efficiency of the reduced order model.