A Novel Rekasius Substitution Based Exact Method for Delay Margin Analysis of Multi-Area Load Frequency Control Systems

Time delays are inevitable in load frequency control (LFC) of the power system, especially in a deregulated system where open communication networks are more favorable than the dedicated ones. However, extensive delays may affect the stability of a system. In this paper, an exact frequency-domain method for calculating the delay margin of LFC systems is presented, which is likely to be used to assess a system's stability caused by time-delays and guide the controller design. Firstly, a dynamic model of load frequency control systems is established, described by delay differential and algebraic equations (DDAEs). The Rekasius substitution is then employed to eliminate the transcendental terms in the characteristic equation without making any approximation. Afterward, an eigenvalue perturbation theory is introduced to transform the problem of calculating the delay margin into solving a series of one-dimensional nonlinear equations. Since only equivalent transforms are involved in the whole process, the delay margins obtained by the proposed method are exact. Finally, a two-area and a three-area deregulated LFC systems are applied to verify the correctness and efficiency of the proposed method.