The existence of multiple equilibria in the UPFC power injection model

This letter shows the existence of multiple equilibria that arise from the use of the state model of the unified power flow controller (UPFC). These multiple equilibria can arise from a common power injection model for the same terminal conditions of shunt bus voltage and series active and reactive power injections. The multiple equilibria result in two or more sets of eigen-values, some of which may indicate an unstable operating condition. Therefore, the use of the UPFC power injection model must be used with caution to ensure stable operation of the UPFC.