Determination of stability delay margins for multi-area load frequency control systems with incommensurate time delays through eigenvalue tracing method

This work presents delay-dependent stability analysis using eigenvalue tracing method for multi-area load frequency control (LFC) systems with incommensurate time delays. LFC systems face inevitable communication delays that adversely affect the frequency stability. Time delays exceeding the allowable limit lead to system instabilities. In this study, stability delay margins of a time-delayed LFC system are computed by a simple yet effective frequency-domain method for computing critical eigenvalues and the corresponding delay margins without using the characteristic equation of the system. By tracing eigenvalue loci of a transformation matrix, the method easily determines the critical eigenvalues on the imaginary axis and obtains stability delay margins. Both stability delay margins and the effectiveness of stability regions in the time delay space are confirmed by time domain simulations and the quasi-polynomial mapping-based root finder (QPmR) algorithm. Results indicate that more accurate delay margin values are obtained as compared to ones with Lyapunov stability theory based algorithms.