Online dispatch of multi-duration energy storage in low-carbon microgrid with explainable reference learning

This paper proposes an online optimization framework with explainable reference learning for low-carbon microgrid dispatch with battery and hydrogen storage. The core of our framework is an adaptive online convex optimization (OCO) method that incorporates long-term state-of-charge (SoC) reference tracking. To address seasonal temporal coupling in SoC dynamics and hydrogen contracts, we generate the hindsight-optimal SoC trajectories of hydrogen storage in offline training. In the online stage, we employ a nonparametric kernel regression with enhanced feature inputs and optimally tuned hyperparameters to dynamically update the SoC reference. We prove that both long-term and short-term policies achieve sublinear regret bounds, which decrease with more training scenarios and higher tracking penalties. Additionally, we employ a convex approximation model for hydrogen storage, ensuring modeling accuracy and compatibility with the online optimization framework. Simulation results based on synthetic data from Alaska, USA demonstrate that the proposed enhanced kernel regression method improves SoC reference learning accuracy by 32.8%, and the proposed OCO method achieves a 9.7% regret reduction compared with a benchmark model predictive control approach. These benefits scale up with longer hydrogen storage durations, and the method demonstrates resilience to poor forecasts and unexpected system faults.