Addressing the critical need for intelligent, context-aware energy management in renewable systems, we introduce the OpenCEM Simulator and Dataset: the first open-source digital twin explicitly designed to integrate rich, unstructured contextual information with quantitative renewable energy dynamics. Traditional energy management relies heavily on numerical time series, thereby neglecting the significant predictive power embedded in human-generated context (e.g., event schedules, system logs, user intentions). OpenCEM bridges this gap by offering a unique platform comprising both a meticulously aligned, language-rich dataset from a real-world PV-and-battery microgrid installation and a modular simulator capable of natively processing this multi-modal context. The OpenCEM Simulator provides a high-fidelity environment for developing and validating novel control algorithms and prediction models, particularly those leveraging Large Language Models. We detail its component-based architecture, hybrid data-driven and physics-based modelling capabilities, and demonstrate its utility through practical examples, including context-aware load forecasting and the implementation of online optimal battery charging control strategies. By making this platform publicly available, OpenCEM aims to accelerate research into the next generation of intelligent, sustainable, and truly context-aware energy systems.