Optimal energy storage configuration for multi-energy microgrids based on hybrid multi-stage robust optimization

The source-load uncertainty of a multi-energy microgrid shows markedly different fluctuation characteristics across operating scenarios, which makes an energy storage configuration that balances economy and reliability difficult to obtain. This study proposes an optimal energy storage configuration model for multi-energy microgrids based on hybrid multi-stage robust optimization. An electricity–heat–hydrogen multi-energy microgrid model is first established, and its objective minimizes the sum of the annualized storage investment cost and operation cost. A comprehensive-norm ambiguity set constructed from a 1- and an ∞ -norm constraint then characterizes the uncertainty of the scenario probability distribution, a box uncertainty set with an uncertainty budget characterizes the source-load fluctuation within each scenario, and a min–max–max–min hybrid multi-stage stochastic-robust storage capacity model that accounts for the worst-case scenario probability is formulated. Finally, the column-and-constraint generation (C&CG) algorithm decomposes the model into a master problem and two-level subproblems that are solved iteratively, and the intra-scenario max-min bilevel problem is transformed into an equivalent single-level problem through Karush–Kuhn–Tucker (KKT) conditions. Case studies show that the proposed method hedges against both the source-load output uncertainty and the scenario probability uncertainty, and the configured storage reduces the out-of-sample expected total cost of the microgrid by 6.7% and the worst-case daily cost by 11.3%, and it eliminates the 85.6 kWh daily average loss of load of the storage-free scheme. The conservative nature of the proposed method is tuned flexibly through the uncertainty budget and the confidence level of the comprehensive norm, and a sound balance between economy and robustness is reached.