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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.