On the nature of voltage impasse regions in power system dynamics studies

Abstract

This paper presents a fundamental study of voltage collapses that occur on a post-fault trajectory of a stressed power system in seconds after large disturbances. The focus of the study are voltage collapses that are induced by certain load models. Using an n-machine-N-bus power system model, the paper explicitly shows that the voltage collapse is caused by the non-existence of a real, positive solution for a load voltage magnitude in different areas of a relative rotor angle space when the load is of non-linear type. These «areas without voltage solution» are denoted as Voltage Impasse Regions (VIR) and are mathematically characterized as trigonometric functions of (n-1) relative rotor angles. Once the post-fault trajectory enters a VIR, voltage magnitude solutions become complex or negative, the algebraic Jacobian becomes singular and the behaviour of a system becomes undefined. The case study has been carried out using a simple 3-machine-1-load system with static load models. In the study, VIR appeared and enlarged as the non-linear (constant power and constant current) load increased. Furthermore, the non-convergence of time domain solution occurred exactly at VIR, thereby confirming that the problem is of structural nature.