Efficient solution algorithms for computing fold points of power flow equations

Techniques for identifying fold points of power flow equations are fundamental to voltage stability analysis. This paper presents efficient methods for computing fold points of power flow equations. The proposed methods make use of two generalized extended systems for determining fold points of nonlinear systems, i.e., the Moore–Spence system and the minimally extended system. Block elimination (BE) techniques are used in the solution procedures for the two systems. Hence, the sparsity of Jacobian matrix of power flow equations can be fully exploited to enhance computational efficiency. Left and right singular vectors corresponding to the zero eigenvalue of Jacobian matrix of nonlinear power flow equations can be obtained simultaneously at the end of the iterations. Numerical examples of Ward & Hale 6-bus system and a real 1620-bus power system in China are presented to validate the methods.