An interval Type-2 fuzzy Fractional-Order PD-PI controller for frequency stabilization of islanded microgrids optimized with CO algorithm

Frequency control in microgrids (MGs) during islanded operation faces significant challenges due to load fluctuations and the intermittent nature of renewable energy sources (RESs). To address this challenge, this study proposes an interval type-2 fuzzy fractional-order PD-PI (IT2FFOPD-PI) controller with the capability to reduce frequency deviations. Additionally, optimizing the controller parameters in dynamic systems is another critical issue, where traditional algorithms such as genetic algorithm (GA), particle swarm optimization (PSO), and sine cosine algorithm (SCA) often struggle with premature convergence and suboptimal solutions. To overcome these limitations, the cheetah optimizer (CO) is employed, for its superior global search capability, ability to avoid local optima, and simplicity, as it does not rely on complex mathematical formulations. Different scenarios are considered in which the effect of the proposed controller on network frequency changes has been compared with two other controllers, i.e., interval type-2 fuzzy fractional-order tilt integral derivative (IT2FFOTID) and interval type-2 fuzzy fractional-order proportional integral derivative (IT2FFOPID) using several optimization methods. Simulation results demonstrate approximately 58.6% and 54.3% improvement in integral time absolute error (ITAE) compared to other two controllers, respectively, in a combined scenario. The CO algorithm also achieves an optimal ITAE objective value of 0.0001092, outperforming other optimization techniques.