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Artificial intelligence is increasingly used for real-time decision support and control in cyber-physical smart grids. However, the growing reliance on data-driven control creates a need for methods that are both explainable to human operators and consistent with electrical-network physics. This review proposes a two-dimensional classification scheme for AI methods in smart-grid control. The scheme combines an explainability dimension with a physics-informed dimension and applies the resulting framework to voltage regulation, congestion management, and microgrid control. A systematic literature search identified 25 peer-reviewed journal articles published between 2017 and 2025. The selected studies were classified according to their explainability mechanism, degree of physical-knowledge integration, application domain, and relevance to cyber-physical grid operation. The review shows that most studies emphasize either explainability or physical consistency, while methods combining both remain limited. Voltage regulation is dominated by reinforcement-learning and safety-constrained control studies, whereas microgrid control contains a broader variety of AI methods. The proposed classification provides a structured basis for analysing trustworthy AI in smart-grid control. It highlights methodological gaps and identifies under-developed combinations of explainability, physics-informed learning, and operational deployment.

Microgrids are increasingly relied upon to maintain supply during disruptions, but their resilience depends on timely islanding, accurate renewable forecasts, and efficient battery dispatch. Digital twins offer a platform to integrate these functions into a coordinated control environment. Existing microgrid control architectures often treat islanding, forecast uncertainty, and battery recovery as separate problems. An integrated conceptual framework that unifies them within a digital-twin environment is therefore needed. This article proposes a conceptual framework for digital-twin-assisted microgrid control that coordinates resilience-oriented islanding, renewable forecast error handling, and battery dispatch recovery. The framework is intended as a design-oriented contribution rather than an experimental validation. The framework is developed through conceptual synthesis of digital twin architectures, microgrid resilience theory, forecasting uncertainty modeling, and battery storage control. No experiments, simulations, field measurements, or empirical results are reported. The framework describes a multi-layered control architecture that continuously assesses resilience, triggers islanding under forecast uncertainty, and manages battery dispatch for post-islanding recovery. Four tables summarize digital twin functions, forecast error types, control architecture, and resilience indicators. The framework provides a design blueprint for resilient microgrid controllers that leverage digital twins. It can guide future simulation studies, hardware-in-the-loop testing, and field validations.