Optimizing Multi-Microgrid Frequency via Takagi–Sugeno FOPID Controller-Based ESC Algorithm

The increasing replacement of synchronous generation by converter-interfaced renewable energy sources, particularly photovoltaic (PV) systems, has significantly diminished the effective inertia of interconnected power networks, making frequency regulation increasingly challenging under uncertain operating conditions. To tackle this challenge, this paper proposes an implementation-oriented Takagi–Sugeno fuzzy-weighted modified fractional-order PID (TS-FOPID) controller for load-frequency control (LFC). ESC determines the optimal controller gains and fractional orders, λ and μ, offline, whereas the online TS fuzzy mechanism blends the error-dependent outputs of preconfigured Nipid elements to realize the optimized fractional actions. This structurally transparent architecture avoids the repeated online execution of ESC. Unlike predefined time fuzzy tracking methods, the proposed controller suppresses frequency deviations in both areas and the tie-line power deviation under load and photovoltaic disturbances using the same optimized parameters. The proposed TS-FOPID controller is validated using a multi-area thermal power grid consisting of two interconnected areas and compared with TS-FOTID, TS-FOPD, and TS-FOTD controllers under five test scenarios encompassing step-load disturbances, photovoltaic integration, sequential disturbances, random load variations, and combined photovoltaic and wind disturbances. Controller performance is assessed using both time-domain specifications and quantitative error indices, including the integral absolute error (IAE) and root mean square deviation (RMSD). Across the investigated scenarios, the proposed TS-FOPID controller consistently outperforms the three TS controllers. For a 1% step-load disturbance, the settling time of the Area 1 frequency deviation is reduced to 1.70 s compared with 3.12 s for TS-FOTID, 16.00 s for TS-FOPD, and 17.76 s for TS-FOTD. In addition, the proposed controller achieves aggregate IAE reductions of up to 95.94% compared with the other TS-based fractional-order controllers across the considered operating conditions, including photovoltaic integration, multiple sequential disturbances, and random load variations. Overall, these results demonstrate faster settling, lower regulation errors, and improved disturbance rejection, supporting the robustness and potential practical applicability of the proposed controller for secondary load-frequency control in renewable-integrated interconnected power systems.