Boundary-derivative direct method for computing saddle node bifurcation points in voltage stability analysis

Abstract

The Saddle Node Bifurcation (SNB) is the location where equilibrium solutions of one parametric system distinguish when its parameter changes. Load distance between the SNB and the present operation point can reflect the voltage stability of the studied system. At present, Continuous Power Flow (CPF) and Point of Collapse (POC)/Direct Method are main techniques for tracking the point. However, CPF needs multiple power flow calculations, which is not suitable for fast and accurate applications, while POC has problems of large coefficient matrix and initialization of eigenvector. A novel direct method is proposed to calculate the SNB point, titled the Boundary-Derivative Direct Method (BDDM). A one-dimensional boundary condition, which reflects the slope of the equilibrium manifold, is configured to replace the multidimensional conditions of POC. As a result, the dimension of the coefficient matrix is drastically cut and the initialization of eigenvector is avoided. Moreover, we extend the algorithm, considering multi-load growth and general limitations. Several instances on IEEE 9-bus system show the convergence of the proposed algorithm and the cases in IEEE 118-bus system and 2000-Bus Texas System, which contain multi-load increments and reactive power limitations of generators, are used to analyze the effectiveness of the proposed algorithm.