HDE-CGWO-Based Optimal Load Frequency Control for Nonlinear Power Systems

In modern power-system load frequency control (LFC), proportional–integral–derivative (PID) controllers are widely used because of their simple structure and ease of implementation. However, the combined effects of communication delay and nonlinear constraints can degrade control performance. To address this issue, this paper proposes a model-constraint-aware optimal PID tuning method based on a Hybrid Differential Evolution–Chaotic Grey Wolf Optimizer (HDE-CGWO). First, a nonlinear LFC model incorporating data sampling, communication delay, governor deadband (GDB), and generation rate constraint (GRC) is established, and a PID-based LFC model is formulated. Next, an objective function based on the integral of time-weighted absolute area control error (ACE), namely ACE-based integral of time-weighted absolute error (ITAE), is constructed. Accordingly, quasi-opposition-based learning (QOBL), chaotic warm-up, Lévy flight, and differential evolution (DE) are incorporated into the standard Grey Wolf Optimizer (GWO) to develop an HDE-CGWO-based PID design scheme for LFC under sampled-data delay and nonlinear unit constraints. Finally, simulation studies are carried out on a multi-area LFC system. The resulting time-domain responses and statistical results show that, compared with standard GWO in the single-area test, HDE-CGWO reduces the ACE-based ITAE by about 43.3%. In the three-area system, the ACE-based ITAE is reduced by about 3.0% under step disturbances and about 1.4% under random disturbances compared with the warm-up Grey Wolf Optimizer (WGWO), indicating that the proposed method can reduce frequency deviations, attenuate post-disturbance oscillations, and accelerate the dynamic recovery process under the considered disturbance conditions.