The effect of demand response control on stability delay margins of load frequency control systems with communication time-delays

This paper studies the effect of dynamic demand response (DR) control on stability delay margins of load frequency control (LFC) systems including communication time-delays. A DR control loop is included in each control area, called as LFC-DR system and Rekasius substitution is utilized to identify stability margins for various proportional integral (PI) gains and participation ratios of the secondary and DR control loops. The purpose of Rekasius substitution technique is to obtain purely complex roots on the imaginary axis of the time-delayed LFC-DR system. This substitution first converts the characteristic equation of the LFC-DR system including delay-dependent exponential terms into an ordinary polynomial. Then the well-known Routh-Hurwitz stability method is applied to find those imaginary roots and the corresponding stability delay margin known as maximal time-delay. Delay margin results indicate that the inclusion of DR control loop significantly increases stability delay margin and improves the frequency dynamic behavior of the LFC system including time-delays. Theoretical stability margins are confirmed by a proven algorithm, quasi-polynomial mapping-based root finder (QPmR) algorithm and time-domain simulations.