Stability delay margin computation of multi-area load frequency control system with electric vehicle using critical eigenvalue tracing method

Abstract

This work presents the delay-dependent stability analysis using eigenvalue tracing method for the multi-area load frequency control system that includes both electric vehicles aggregator (LFC-EVs) and incommensurate time delays in each control area. The LFC-EVs systems face inevitable communication time delays that affect the frequency stability. Although communication infrastructures are necessary to maintain system stability and reliability, a large amount of delay exceeding the allowable limit leads to system instability. In this study, stability delay margin values of a time-delayed LFC-EVs system are computed by a simple method finding the critical eigenvalues. By tracing eigenvalue loci of a transformation matrix, the method easily determines critical eigenvalues on the imaginary axis and obtains stability regions in time delay space. Stability delay margins depicted as a stability region in the delay space are determined for various system parameters and verified by time-domain simulations. Results indicate that more accurate stability delay margins are obtained as compared to ones using Lyapunov–Krasovskii Functionals with different linear matrix inequalities.