Improved EAD Algorithm to Estimate Domains of Attraction of Power Systems Including Induction Motors for Transient Voltage Stability Analysis

Transient voltage stability analysis (TVSA) of power systems is one of the most computationally challenging tasks in dynamic security assessment. To reduce the complexity of TVSA, this paper proposes an improved expanding annular domain (improved EAD) algorithm to estimate the domain of attraction (DA) of power systems containing multiple induction motors (IMs), whose improvements are concerned with relaxing the restriction on critical value and simplifying iteration steps. The proposed algorithm can systematically construct Lyapunov function for lossy power systems with IMs and their slip constraints. First, the extended Lyapunov stability theory and sum of squares (SOS) programming are presented, which are powerful tools to construct Lyapunov function. Second, the internal node model of IM is developed by an analogy with that of a synchronous generator, and a multi-machine power system model by eliminating algebraic variables is derived. Then, an improved EAD algorithm with SOS programming is proposed to estimate the DA for a power system considering the slip constraint of IM. Finally, the superiority of our method is demonstrated on two modified IEEE test cases. Simulation results show that the proposed algorithm can provide a better estimated DA and critical clearing slip for power systems with multiple IMs.