Development of an Optimal Novel Cascaded 1+TDF^λ/PI^λD^μ Controller for Frequency Management in a Triple-Area Power Grid Considering Nonlinearities and PV/Wind Integration

Continuous decrease in inertia and sensitivity to load/generation fluctuation are significant challenges for present-day power networks. The primary reason for these issues is the increased penetration capabilities of renewable energy sources. An imbalanced load with significant power output has a substantial impact on the frequency and voltage characteristics of electrical networks. Various load frequency control (LFC) technologies are widely used to address these issues. Existing LFC approaches in the literature are inadequate in addressing system uncertainty, parameter fluctuation, structural changes, and disturbance rejection. As a result, the purpose of this work is to suggest a better LFC approach that makes use of a combination of a one plus tilt fractional filtered derivative (1+TDF^λ) cascaded controller and a fractional order proportional–integral–derivative (PI^λD^μ) controller, which is referred to as the recommended 1+TDF^λ/PI^λD^μ controller. Drawing inspiration from the dynamics of religious societies, including the roles of followers, missionaries, and leaders, and the organization into religious and political schools, this paper proposes a new application of the efficient divine religions algorithm (DRA) to improve the design of the 1+TDF^λ/PI^λD^μ controller. A triple-area test system is constructed to analyze a realistic power system, taking into account certain physical restrictions such as nonlinearities as well as the impact of PV and wind energy integration. The effectiveness of the presented 1+TDF^λ/PI^λD^μ controller is evaluated by comparing their frequency responses to those of other current controllers like PID, FOPID, 2DOF-PID, and 2DOF-TID^μ. The integral time absolute error (ITAE) criterion was employed as the objective function in the optimization process. Comparative simulation studies were conducted using the proposed controller, which was fine-tuned by three recent metaheuristic algorithms: the divine religions algorithm (DRA), the artificial rabbits optimizer (ARO), and the wild horse optimizer (WHO). Among these, the DRA demonstrated superior performance, yielding an ITAE value nearly twice as optimal as those obtained by the ARO and WHO. Notably, the implementation of the advanced 1+TDF^λ/PI^λD^μ controller, optimized via the DRA, significantly minimized the objective function to $0.4704\times {10}^{-4}$. This reflects an approximate enhancement of $99.5\%$ over conventional PID, FOPID, and 2DOF-TID^μ controllers, and a $99\%$ improvement relative to the 2DOF-PID controller. The suggested case study takes into account performance comparisons, system modifications, parameter uncertainties, and variations in load/generation profiles. Through the combination of the suggested 1+TDF^λ/PI^λD^μ controller and DRA optimization capabilities, outcomes demonstrated that frequency stability has been significantly improved.