Machine Learning-Guided Metaheuristic Optimization for PID Design in Load Frequency Control of a Two-Area PV–Thermal Power System

The problem of load frequency control (LFC) becomes more severe with the extensive integration of photovoltaic (PV) generation owing to the intermittent nature of the source. In this study, a machine learning approach is developed to design the proportional–integral–derivative (PID) controller of a two-area PV–thermal LFC system, extending a prior proportional–integral (PI) benchmark to full PID action. A Random Forest model is trained to predict the relationship between the six PID gains and the closed-loop integral of time-multiplied absolute error (ITAE), yielding an accurate performance model (test R2 = 0.933) that is subsequently searched by a metaheuristic optimizer to determine the controller gains; the resulting controller is termed ML-PID. The novelty of the approach lies in employing the learned model not as a controller or a physical-quantity predictor, as in existing ML-based LFC studies, but as a reusable performance model that maps the controller gains directly to the closed-loop index and guides the PID design. To isolate and quantify the contribution of the learned model, the same three optimizers, namely the Cheetah Optimizer (CO), the Grey Wolf Optimizer (GWO), and Particle Swarm Optimization (PSO), are also applied directly to the plant, yielding purely metaheuristic controllers (CO-PID, GWO-PID, and PSO-PID) that are compared against the machine learning-assisted designs under identical algorithms and computational budget, with CO selected on the basis of the Friedman and Wilcoxon tests. The proposed ML-PID-CO controller attains the minimum ITAE under a step-load disturbance, approximately 70% lower than that of the reference SCHO-PI controller and comparable to the directly optimized controllers, with reduced control effort. Under a simultaneous variation in the plant time constants, it is the most robust of all controllers, exhibiting the smallest Δf1 undershoot and a performance that degrades about 4.2 times less than that of the reference. The results show that a learned performance model provides a good and reusable basis for PID design. It can be searched over repeatedly once built and reduces the per-design simulation burden relative to direct metaheuristic tuning, while the design is largely independent of the optimizer used.