The rapid integration of renewable energy resources into modern power systems has significantly improved energy sustainability while simultaneously introducing operational uncertainties associated with intermittency, bidirectional power flow, and dynamic load behavior. Existing energy management strategies predominantly rely on deterministic optimization or data-driven models that often fail to maintain robust performance under rapidly changing operating conditions. This study proposes a novel physics-informed digital twin framework for adaptive energy management in renewable-rich microgrids by integrating first-principles electrical system models with real-time machine learning prediction and multi-objective optimization. Unlike conventional digital twins that primarily provide system visualization or offline analysis, the proposed framework continuously synchronizes physical system states with virtual models to predict equipment degradation, optimize distributed energy resource dispatch, enhance voltage stability, and improve operational resilience against renewable generation fluctuations. The framework incorporates photovoltaic generation, battery energy storage, flexible demand response, and intelligent inverter coordination within a unified decision-making architecture capable of simultaneously minimizing operating cost, reducing carbon emissions, and maintaining power quality. Simulation-based evaluation under varying renewable penetration levels and stochastic load conditions demonstrates improved energy utilization, reduced voltage deviation, faster fault recovery, and enhanced system reliability compared with conventional energy management approaches. The proposed methodology provides a scalable solution for future smart grids and community microgrids where increasing renewable penetration requires adaptive, predictive, and self-optimizing control mechanisms. The research contributes a new direction for intelligent energy systems by combining physics-based modelling with artificial intelligence to bridge the gap between operational reliability and sustainable energy management, thereby supporting resilient low-carbon electricity networks for future power infrastructure.