Power System Transient Stability Study by Involving Higher Order Corrections in Improved Quadratic Lyapunov Function for Singular Perturbed Model of Synchronous Generator

Abstract

The assessment of transient stability of multi-machine power system, in a post-fault scenario, is a very challenging task due to highly non-linear nature of the system equations. In this work, the physical concept of maximum relative acceleration of a machine at a fault scenario is related with the boundary of stability region. This approach is extended to develop a quadratic Lyapunov function using singular perturbed modelling. Unlike the conventional energy function methods, this Lyapunov function candidate is a more general energy function and has a decaying nature around an equilibrium point. Moreover, with higher order corrections, an improved Lyapunov function candidate is presented with simulation results of power system examples. The decaying nature of Lyapunov function candidate remains similar even without higher order corrections. However, the relevance of inclusion of higher order corrections is brought out in the cases of faults occurring at other than generator buses. Also, the upper bound of singular perturbation parameter in the model is within allowable limits and ensures the accuracy of results.