Computation of time delay margins for stability of a single-area load frequency control system with communication delays

Abstract

Time delays have become unavoidable in power systems since communication links are extensively used for sending and receiving control signals. This paper investigates the effect of time delays on the stability of a single-area load Frequency Control (LFC) system. A direct and exact method to compute delay margins is presented. The delay margin is the maximum amount of the time delay that the system can tolerate before it becomes unstable for a given operating point. The proposed method starts with the determination of all possible purely imaginary characteristic roots for any positive time delay. To achieve this, Rekasius substitution is first used to convert the transcendental characteristic equation of the LFC system into a polynomial. Then, Routh stability criterion is applied to determine the critical root, the corresponding oscillation frequency and the delay margin for stability. For a wide range of controller gains, delay margins of LFC system are determined to find out the qualitative effect of controller gains on the delay margin. Finally, theoretical delay margin results are verified by using the time-domain simulation capabilities of Matlab/Simulink.