The continuation power flow: A tool for parametric voltage stability and security analysis

This paper considers a toll for assessing voltage-related instability problems due to slow load variations, based on power flow formulation. Most conventional power flow tools break down when used to analyze voltage stability problems. This paper deals with a class of methods for solving nonlinear equations known as path-following (or continuation) methods, i.e. with a continuation power flow as a robust power flow method capable of dealing with sometimes difficult mathematical problems encountered during the analysis of voltage problems in power systems. In particular, the paper presents a simplified continuation power flow with the next four basic elements: first order polynomial predictor (secant predictor), physical parameterization (bus, area or total system load as a continuation parameter), an ordinary Newton-Raphson solver based on the constant impedance load model and well-conditioned Jacobian matrix in that case throughout solution process, and appropriate step length control. It is well known that constant power load model is the most conservative in voltage stability analyses, and four slightly different algorithms which are combination of the constant power and constant impedance load models during a continuation process, are investigated and presented in the paper. In addition, the application of the proposed continuation power flow to compute the saddle node bifurcation points and security margins in the load parameter space of an electric power system, with appropriate eigenvalue and eigenvector calculations, is also presented in the paper. All examples, included in the report are based on the CIGRE 31-bus Test System which originates from the CIGRE Task Force that investigated voltage collapse indices, and real-life Bosnian Electric Power System (configuration in 1996.).