CVaR-Guided Decision-Focused Learning and Risk-Triggered Re-Optimization for Two-Stage Robust Microgrid Operation

Microgrid operation is highly vulnerable to short-term load uncertainty, while conventional predict-then-optimize pipelines cannot fully align probabilistic forecasting quality with downstream robust scheduling performance. This paper proposes a CVaR-guided decision-focused learning and risk-triggered re-optimization framework for two-stage robust microgrid operation. A probabilistic load forecasting model first generates multi-quantile outputs, which are converted into prediction intervals to parameterize the load uncertainty set of the downstream two-stage robust optimization (TSRO) model. To improve forecasting reliability under difficult and high-risk operating conditions, a CVaR-guided forecasting objective is introduced to emphasize tail-sensitive samples. To further close the forecast-decision gap, a convex regularized surrogate TSRO model and a smooth regret loss are developed, enabling downstream operational feedback to be propagated to the forecasting model through KKT-based implicit differentiation. For online deployment, a risk-triggered re-optimization mechanism selectively re-solves the remaining-horizon TSRO only when the schedule mismatch becomes significant, avoiding unnecessary online computation. Case studies on modified IEEE 33-bus and 69-bus microgrids demonstrate superior probabilistic forecasting accuracy, operational economy, and tail-risk mitigation over benchmark methods, while preserving near-full-re-optimization performance with less than 0.5% higher operating cost and up to 91% lower daily solution time.