Effects of algebraic singularities on the voltage dynamics of differential‐algebraic power system model

Abstract

AbstractVoltage stability analysis of differential‐algebraic equation (DAE) power system model is more complicated than for systems described by ordinary differential equations (ODEs). In addition to unstable equilibria, algebraic singularity plays a crucial role in assessing the voltage stability. This paper explores the algebraic structure and singularities of the DAE model to investigate its influence on the voltage stability. Singular points are identified at various load levels and are illustrated together with the equilibria using nose curves. Then, at a given load level, the constraint manifold is decomposed into the voltage casual regions and singular points connecting them. Time‐domain simulations initiated in the vicinity of singular points are performed to determine how singular points affect system dynamics. It is shown that depending on the relative location of initial points with respect to singular points, trajectories of bus voltages may settle to an infeasible low voltage stable equilibrium point, which may cause a further disturbance in the system leading a voltage stability problem. Copyright © 2007 John Wiley & Sons, Ltd.