Forecasting and Optimization in Low‐Carbon Microgrids: A Hybrid LLM–Based Approach With Synthetic Data and Prophet–XGBoost Baselines

Control and energy management of microgrids with increasing distributed energy resources (DERs) necessitate accurate renewables, load, and price forecasting. However, the creation of a cohesive and dependable forecasting‐optimization framework capable of managing multisource data, nonlinear interdependencies, and operational uncertainties continues to be a research challenge. This paper introduces a hybrid framework combining large language models’ (LLMs) contextual reasoning with baseline time‐series models such as Prophet, extreme gradient boosting (XGBoost), and long short–term memory (LSTM) to bridge the gap between data‐driven forecasting and dispatch optimization in microgrids. The framework is complemented by a carefully crafted synthetic data pipeline simulating weather‐affected time‐series of load, wind, solar, and price to capture real‐world operating scenarios. After synthesizing the dataset, the hybrid forecast method leverages the LLM’s contextual sequence learning in combination with baseline priors, and the predictions are input into a CVXPY‐based mixed‐integer linear program (MILP) optimizer to solve least‐cost, low‐carbon power dispatch subject to demand and operational limitations. The results show that the proposed hybrid‐LLM forecasting method provides superior results to conventional frameworks. Specifically, the LLMXGBoostProphet configuration attains mean absolute percentage errors (MAPEs) of 3. 68% in load, 9. 86% in solar, 11. 30% in wind, and 4. 94% in price, with LSTM‐based configurations realizing moderate boosts when supported by fallback baselines. The optimization phase limits grid imports to 100 kW and achieves an 83. 6% combined contribution from renewables and storage while maintaining a carbon intensity of 0. 091 kg CO 2 /kWh. The results indicate the potential of utilizing hybrid‐LLM forecasting together with CVXPY‐based MILP optimization to form a robust decision‐support system for modern low‐carbon power systems.