Stability-Constrained Optimization of a FO(I+PID) Controller for Robust AGC Amid Variable Communication Latency and Hybrid Cyber Threats

The phase lag associated with conventional internal model control strategies for thermal power plants (TPP) with dead time (DT) affects its ability to restore frequency and tie-line power deviations. For the aforementioned reason and foreseen merits of fractional calculus, a robust uni-parametric fractional order integral and proportional integral derivative (FO(I+PID)) controller is proposed for a renewable integrated TPP amid DT. This FO(I+PID) controller is designed based on a frequency-shifted version of the TPP's fractional model, which eliminates the need for phase-lag inducing internal model control filters in conventional designs. The frequency-shifting factor ($\mu$) serves as the only tuning parameter that determines the performance and robustness of the FO(I+PID)-based load frequency control strategy, thereby offering the advantage of simplicity, which is desirable in practice. After applying Pade's approximation and stability considerations (to obtain the upper and lower bounds of$\mu$), its optimal value is obtained using the crayfish optimization algorithm. The efficacy of this scheme is demonstrated through simulations, hardware-in-loop validation, and the IEEE 39-bus system by considering various practical scenarios like step load changes, hybrid cyber attacks, variable communication delay, nonlinearities associated with the TPP, and rigorous sensitivity-based stability/fragility analysis by perturbing TPP model/controller parameters. It outperforms$Max\_{v}$of tie-line power deflection by 70.57% and 72.44% compared to FIMC and TFC, respectively. Moreover, settling time is reduced to 103.2s, outperforming TFC (149.87s), FIMC (114.3s), and PI (131.87s). It confirms the better transient performance of the FO(I+PID) controller over reported techniques.