Adaptive distributed cascade control using fuzzy-explainable neural networks for frequency stability in microgrids

Abstract The increasing penetration of renewable energy sources (RES) and plug-in hybrid electric vehicles (PHEVs) has introduced significant frequency instability in interconnected microgrid (MG) systems, necessitating adaptive and robust control strategies for reliable operation. This paper proposes a fuzzy-explainable neural network (FxNN)-based distributed fractional-order PID (FOPID) controller for active frequency regulation in interconnected microgrids. The control problem is formulated within a Lyapunov-based optimization framework, where system stability is ensured through a recursively updated energy function and differential learning dynamics of the explainable neural network. The proposed cascaded FxNN-FOPID controller is evaluated under varying load disturbances and intermittent renewable power. Simulation results demonstrate superior dynamic performance compared with conventional single-loop FxNN and PSO-GSA-based controllers. The proposed controller achieves a minimum settling time of 3.0 s, representing improvements of 14.3% and 30.2%, respectively. Furthermore, the integral absolute error (IAE) is reduced to 0.6292 × 10 −3 , 0.5929 × 10 −3 , and 0.6000 × 10 −3 for MG1, MG2, and MG3, respectively, while the integral time absolute error (ITAE) is reduced by up to 93.6%. The controller also minimizes frequency oscillations with a peak magnitude of 0.0003 p.u. and achieves improved Integral of Squared Error (ISE) 0.1040 × 10 −5 and Integral of Time-weighted Squared Error (ITSE) 0.9918 × 10 −3 values. Owing to its adaptive gain tuning capability, the proposed controller maintains robust performance without requiring manual retuning under varying operating conditions. Comparative analysis confirms that the proposed cascaded FxNN-based distributed FOPID controller provides faster dynamic response, improved disturbance rejection, and superior low-frequency oscillation damping, making it an effective solution for reliable frequency regulation in renewable-energy-integrated microgrid systems. Furthermore, the proposed framework supports Sustainable Development Goals (SDG 7: Affordable and Clean Energy, SDG 9: Industry, Innovation and Infrastructure, and SDG 13: Climate Action) by facilitating resilient microgrid operation, enhancing renewable energy integration, and promoting low-carbon power systems.