Adaptive–based cascaded PI–PID controller for load frequency regulation with real time verification

In order to address Load Frequency Control (LFC) problems in single-area and interconnected two-area power systems, this work proposes a cascaded control scheme that combines PI–PID control with the Set-Membership Affine Projection Algorithm (SMAPA). The proposed approach is evaluated under various practical operating conditions, including step load disturbances, random load variations, wind power fluctuations, and parameter uncertainty. In addition, frequency-domain stability analysis is performed to further assess the robustness of the proposed controller, while real-time validation is conducted for the two-area system to demonstrate its practical effectiveness. The proposed controller is compared with conventional PI controllers tuned using five optimization methods for the single-area system. For the two-area system, its performance is benchmarked against PID controllers designed using three optimization methods and the recently reported SPPI-based approach. The simulation results show that the proposed controller achieves lower overshoot and faster settling time in both configurations. These improvements are attributed to the integration of real-time adaptive parameter updating provided by SMAPA with the favorable dynamic characteristics of the PI–PID control structure. The results demonstrate that the proposed cascaded SMAPA-based PI–PID controller provides robust frequency regulation under different operating conditions and offers promising potential for practical interconnected power system applications.