Bald Eagle Search Optimized Cascade PID Controller for Frequency Regulation of Renewable Based Microgrid System with Virtual Inertia Support

Frequency control has emerged as a significant challenge in microgrid systems due to the increasing penetration of renewable energy sources. To address this issue, a virtual inertia (VI) based control scheme is proposed. A cascaded PID (C-PID) controller which consists of a first stage PD controller with derivative filter followed by a second stage one plus a PI controller is used in the VI control scheme to improve the frequency regulation. The recently proposed Bald Eagle Search (BES) algorithm is employed to optimize the controller parameters. Initially, the PI controller is considered, and the results of BES are compared with the Genetic Algorithm (GA) and Particle Swarm Optimization (PSO). It is demonstrated that the objective function value with BES is decreased by 25.15% and 26.1% compared to GA and PSO, respectively. In the next stage, PID and C-PID controllers are considered, and controller parameters are tuned by the BES algorithm. The efficacy of C-PID is evaluated with PID and PI for different cases like constant and variable load, solar and wind power. It is shown that the percentage improvements in integral of squared error (ISE), integral of time-weighted absolute error (ITAE),integral of time weighted-squared error( ITSE), integral of absolute error(IAE), and mean squared error( MSE) are 97.75%, 89.35%, 98.12%, 88.55%, and 98.27%, respectively, compared to the BESoptimized PI controller, and 81.42%, 65.84%, 84.89%, 62.06%, and 85.71%, respectively, compared to the BES-optimized PID controller under simultaneous variations in solar power, wind power, and load demand. Sensitivity analysis, stability analysis, effect of nonlinearities and comparison with recent control schemes of proposed approach is also performed. Finally, real-time validation through Open Platform for Advanced Laboratory-RealTime(OPAL-RT) is done.