基于Grbner基的特征值/向量法在潮流计算中的应用

Application of Eigenvalue/Eigenvector Methods in Power Flow Calculation Based on Grbner Basis

基于Grbner基理论,将潮流计算这个多项式方程组问题转化为等价的矩阵特征值和特征向量问题。该方法的求解能力和求解精度均优于已有的消元法(目前唯一的求解潮流方程全部解的方法),不仅能解决潮流方程的多解问题,还从原理上避免了雅可比矩阵的奇异性问题。文中以消元法难以求解的2机5节点系统为例,得到潮流方程的8个解,在潮流计算基础上绘制得到了相比连续潮流法更为完整的PV曲线,验证了该方法的可行性。

Based on the theory of Grobner basis, a power flow problem, which is a polynomial equation system problem, is converted into an equivalent eigenvalue/vector problem. The effectiveness and accuracy of the proposed method is better than an elimination method, which is the only method available so far. The proposed method can yield all solutions of the system without any singular matrix problem. A two-machine five-bus system never before solved by elimination methods is studied as an example, whose eight solutions are obtained and the PV curves, which are more complete than those obtained by a continuous power flow method, are described to demonstrate the effectiveness of the proposed method.