A systematic review of physics-informed machine learning for resilient microgrid control and dynamics

Distribution systems increasingly deploy inverter-dominated microgrids to maintain prioritized service during extreme weather, cyber-physical disturbances, renewable-generation uncertainty, and upstream-grid degradation. Resilient operation depends on feasible transitions among grid-connected operation, islanding, restoration, and reconnection. These transitions must satisfy operating limits, converter constraints, synchronization tolerances, and protection requirements while accounting for resynchronization logic, breaker permissives, topology changes, and post-closing dynamics. Reduced-order models may not capture these constraints when converter limiting, switching events, and protection actions determine system trajectories. Physics-informed machine learning (PI-ML) addresses this limitation by embedding network equations, topology, device constraints, stability conditions, and feasibility mechanisms into learned models and controllers. Existing reviews treat microgrid resilience and PI-ML separately, without auditing transition-feasibility claims. This work presents a systematic, claim-level review of PI-ML for resilient microgrid dynamics and control. Claims are classified by physical content, enforcement pathway, control-layer use, validation fidelity, auditability, and reporting. Current evidence supports the plausibility of physically informed estimation, dynamic modeling, topology-aware monitoring, and safety-aware control support. However, no claim satisfies the admissibility threshold for complete transition feasibility. The main gaps concern violation duration, protection-zone logic, latency compatibility, network assumptions, and reconnection validation. The review defines benchmark specifications and a reporting set for islanding, restoration, and reconnection studies.