Federated Learning-Based Distributed Frequency Control of Networked Microgrids Under PMU Failures Using Fuzzy Neural Network FOPID Controller

Abstract

Modern power systems, with the large-scale integration of renewable energy (RE) and distributed energy resources (DERs), have evolved into networked microgrid systems (NMGSs). While this transition aligns with sustainable development goals, it also introduces significant reliability challenges, including frequency instability caused by low system inertia, slow stochastic variations in load demand, communication time delays, and cyber–physical disturbances. Such scenarios make traditional centralized control strategies ambiguous, as system performance can drop significantly even in a simple case of communication disruption. To overcome these issues, a new distributed control framework for NMGS is developed based on federated learning fuzzy neural network (NN) optimized fractional-order PID (FLFNN FOPID). It is a federated architecture in which agents exchange only parameter updates, not raw operational data. This strategy preserves data confidentiality, reduces communication overhead, and enables control of synchronization frequency among DER. The proposed controller is then rigorously validated across normal load conditions, random disturbances, and phasor measurement unit (PMU) failure cases, while its practical implementation feasibility is additionally ascertained via hardware-in-the-loop (HIL) experiments on an OPAL-RT real-time simulator. Compared to the NN FOPID baseline, the proposed FLFNN FOPID reduces integral absolute error (IAE) by more than 69% for <inline-formula> <tex-math notation="LaTeX">$\Delta $ </tex-math></inline-formula>f1, with its value (<inline-formula> <tex-math notation="LaTeX">$2.4235\times 10^{-3}$ </tex-math></inline-formula>) compared with that of NN FOPID’s (<inline-formula> <tex-math notation="LaTeX">$0.7313\times 10^{-3}$ </tex-math></inline-formula>), while keeping track of improvement in almost similar ratios for each <inline-formula> <tex-math notation="LaTeX">$\Delta $ </tex-math></inline-formula>f2 and <inline-formula> <tex-math notation="LaTeX">$\Delta $ </tex-math></inline-formula>f3 independently too. It is important to note that the integral time absolute error (ITAE) in <inline-formula> <tex-math notation="LaTeX">$\Delta $ </tex-math></inline-formula>f2 decreased by almost 93% from <inline-formula> <tex-math notation="LaTeX">$0.1513\times 10^{-5}$ </tex-math></inline-formula> to <inline-formula> <tex-math notation="LaTeX">$0.0099\times 10^{-5}$ </tex-math></inline-formula>, which demonstrates a much-improved transient behavior. In all three MGs, integral squared error (ISE) and integral time-weighted squared error (ITSE) are also minimized, indicating reduced oscillatory behavior and improved system stability. Settling time reduced from 6.2 to 6.6 s under NN FOPID to 3.5–3.9 s under the proposed controller, corresponding to faster stabilization of about ~44%. Additionally, reductions in peak magnitude, rise time, peak time, and absolute error collectively indicate improved steady-state accuracy. These results have made the proposed FLFNN FOPID framework a powerful, privacy-preserving, and communication-friendly solution for frequency regulation of next-generation NMGSs under various circumstances.