Fractional-Order General Type-2 Fuzzy Control with Adaptive Type-Reduction for Load Frequency Control in Multi-Area Renewable-Based Power Systems with Communication Delays

Abstract

This study investigates a Load Frequency Control (LFC) framework for a three-area renewable-based power system interconnected through tie-lines and subject to communication delays. The proposed framework integrates an open-loop dynamic model, an α-plane-based General Type-2 Fuzzy inference System (GT2FS), three type-reduction approaches (Nie–Tan (NT), Karnik–Mendel (KM), and a causal fractional-order post-filter) and a delay-dependent selection strategy. The framework further incorporates multi-objective parameter optimization and closed-loop performance evaluation. The baseline system comprises three interconnected areas arranged in a ring topology and accounts for Governor Dead Bands (GDBs), soft constraints on the turbine power rate of change, and five distinct communication delay values. The numerical accuracy of the type-reduction methods was assessed against benchmark results. The fractional-order post-filter reproduced the NT output with a reported maximum absolute error of zero, while the iterative KM algorithm achieved an exact match based on direct identification of the switching points. Multi-Objective Particle Swarm Optimization (MOPSO) produced a Pareto archive containing seven solutions, from which a compromise solution was selected, yielding an Integral of Time-weighted Absolute Error (ITAE) of 81.722190, an Integral of Squared Error (ISE) of 0.6906788, and a Total Variation (TV) of 25.089462. However, closed-loop simulations indicate that the performance of the proposed controller, under the current parameter calibration, is not uniformly superior to that of the benchmark configurations. Specifically, the ITAE of the FOGT2-Adp controller exceeded that of the FOGT2-b1 variant in all four evaluated scenarios. Moreover, the frequency-deviation constraint was violated in the Photovoltaic (PV) scenario, and none of the controllers maintained stability at communication delays of 150 and 200 ms. Linearized pole analysis indicated that four controller configurations, excluding the Proportional–Integral–Derivative (PID) controller, satisfied the stability criterion used in the analysis. Nevertheless, this result does not, by itself, establish the stability of the nonlinear closed-loop system under communication delays and actuator saturation. Overall, the findings support the numerical consistency of the evaluated type-reduction implementations and demonstrate the functional role of fractional-order memory within the proposed framework. However, they do not establish the universal superiority of the adaptive controller or its robustness to substantial communication delays.