Computation of Stability Delay Margin of Time-Delayed Generator Excitation Control System with a Stabilizing Transformer

This paper investigates the effect of time delays on the stability of a generator excitation control system compensated with a stabilizing transformer known as rate feedback stabilizer to damp out oscillations. The time delays are due to the use of measurement devices and communication links for data transfer. An analytical method is presented to compute the delay margin for stability. The delay margin is the maximum amount of time delay that the system can tolerate before it becomes unstable. First, without using any approximation, the transcendental characteristic equation is converted into a polynomial without the transcendentality such that its real roots coincide with the imaginary roots of the characteristic equation exactly. The resulting polynomial also enables us to easily determine the delay dependency of the system stability and the sensitivities of crossing roots with respect to the time delay. Then, an expression in terms of system parameters and imaginary root of the characteristic equation is derived for computing the delay margin. Theoretical delay margins are computed for a wide range of controller gains and their accuracy is verified by performing simulation studies. Results indicate that the addition of a stabilizing transformer to the excitation system increases the delay margin and improves the system damping significantly.