Stability Analysis Of Multi Area Power System Using Lyapunov Function

Abstract

Lyapunov function has emerged as a powerful tool of control theory and used in newlinestability analysis of nonlinear dynamical systems. However, the use of Lyapunov function is newlinea complex issue and further exploration is needed to fully understand their potential and newlinelimitations. One particular area of application of Lyapunov function is in the context of newlinecomplex power systems, where the dynamic interactions between different components can newlinegive rise to a wide range of stability challenges. In this research, the aim is to develop a newlineLyapunov-based method that can capture the dynamics of the power system and can be applied newlineto improve its performance. To achieve this goal, the research involves construction of newlineLyapunov functions that incorporate synchronous machine dynamics, network dynamics, and newlinecontrol signals to capture the interactions between the different components of the power newlinesystem. The suitability of the Lyapunov-based method is tested on different power systems, newlinewhere the performance and stability of the system are evaluated under different operating newlineconditions and disturbances. Specifically, the proposed Lyapunov function is tested on a single newlinemachine infinite bus power system, a two-machine infinite bus power system, and an IEEE 9- newlineBus test system. In addition to evaluating the performance of the proposed Lyapunov function newlineon these test systems, the research presents an approach to identify a group of generators newlineresponsible for system separation and transient instability. This study includes critical machine newlineidentification, critical clearing time calculation, and other related analyses. To carry out this newlineanalysis, the power system is modeled and simulated, and the rotor angles and speeds of the newlinegenerators are recorded. The identification of critical machines is performed by analyzing the newlineaverage instantaneous rotor accelerating powers, while coherency is measured based on the newlinerotor angles and speed characteristics during fault. The pre- and post-fault rotor angles are newlineutilized to identify the disturbed machin