正交多项式辨识变压器传递函数及其在绕组变形诊断中的应用

利用变压器绕组频响的实验数据，来拟合其传递函数的解析表示，若使用最小二乘法，会存在病态方程组，影响辨识的准确性，提出利用正交多项式来拟合变压器传递函数，方程的阶次几科是原来的1／2，从而降低了系数矩阵的条件数，避免了病态问题，利用正交伴随矩阵，直接求取传递函数的零、极点。根据零极点分布来诊断变压器绕组变形，反映了绕组特性的本质，比单纯依靠频响曲线有了很大进步。

Transfer Function Identification Using Orthogonal Polynomials and Its Application to Diagnosis of the Transformer Winding Deformation

Methodologies to identify analytical expression of transformer winding's transfer function from frequency response were discussed. When least squares method is used, some factors such as morbid matrix equation group would influence the precision of results. Through the method based on orthogonal polynomials, the condition number of coefficient matrix is minimized and the morbid problem can be avoided. Also, by means of the orthogonal companion matrix, zeros and poles are obtained. At last, the application of the zeros and poles distribution to diagnosis of transformer winding deformations was studied. It reflects the essences of winding's characteristic and makes a great progress from that of only depending on the frequency response curves.