电路方程的线性变换

Linear transformation of circuit equations

电路分析中的坐标变换和复杂绕组变压器分析中所用的变压器变换都是电路方程的线性变换。根据矩阵理论,对坐标变换和变压器变换进行了统一阐释。坐标变换本质是一个方阵和对角阵的相似变换,变压器变换的本质是新变量对旧变量的表示,当变换矩阵的逆阵等于它的转置(共轭转置)阵时,坐标变换和变压器变换数学表示是相同的。通过对电路方程系数矩阵和三角阵的相似变换,同时得到了三相abc坐标系和任意速度旋转两相dq0坐标系、瞬时值复数分量120坐标系、前进-后退FB0坐标系之间的变换矩阵。这有助于在更加基础的理论层面上揭示和理解电路方程线性变换的本质,也为提出电路方程线性变换的新类型提供了思路。

The coordinate transformation and transformer transformation,which are employed in the circuit analysis and the complex transformer analysis respectively,are all linear transformations of circuit equations. According to matrix theory,a unified interpretation is presented for both coordinate transformation and transformer transformation. The essence of coordinate transformation is the similarity transformation between square matrix and triangular matrix,and the essence of transformer transformation is the expression of old variables by new variables. When the inverse matrix of transformation matrix is equal to its transpose matrix or conjugate transpose matrix,the mathematical expressions of two transformations are same. Through the similarity transformation between circuit equation coefficient matrix and triangular matrix,the transformation matrixes among the three-phase abc coordinate system or arbitrary speed rotating two-phase dq0 coordinate system,the instantaneous value of the plural component 120 coordinate system and the forward backward FB0 coordinate system are obtained simultaneously. It contributes to revealing and understanding the nature of circuit equations linear transformation at more theoretical level and provides a train of thought for the presentation of new type linear transformation.