Physics-Constrained Recursive estimation and load frequency control in renewable-dominated two-area multi-microgrid systems

Abstract The increasing penetration of renewable energy sources in islanded multi-microgrid systems significantly reduces system inertia, making accurate frequency regulation and inertia estimation increasingly challenging. This paper proposes a Physics-Constrained Recursive Maximum Likelihood (PCRML) framework for adaptive load frequency control in renewable-dominated multi-microgrid systems. The proposed method combines recursive parameter estimation with physical system constraints to continuously update the equivalent inertia and enhance frequency stability under varying operating conditions. A two-area islanded renewable microgrid consisting of photovoltaic generation, wind energy, hydro generation, and battery energy storage systems is developed in MATLAB/Simulink to evaluate the proposed approach. Comprehensive simulation studies are conducted under load disturbances, renewable intermittency, measurement noise, and varying renewable penetration levels. Comparative analyses with conventional proportional–integral (PI), proportional–integral–derivative controller, multi-agent deep deterministic policy gradient, and Extended Kalman Filter-based approaches demonstrate that the proposed PCRML framework achieves lower frequency deviations, faster settling, reduced oscillations, and more accurate inertia estimation. Under the considered disturbance scenarios, the proposed method reduced the peak frequency deviation by approximately 46.7%, shortened the settling time by 40%, and improved estimation accuracy by 33% compared with the conventional PI controller. These results demonstrate that the proposed framework provides a reliable and computationally efficient solution for adaptive frequency regulation in low-inertia renewable-integrated multi-microgrid systems.