Robust Optimization Algorithm of Multi-Objective and Multi-Scenario Performance for Uncertain Microgrids Based on Lexicographic Order Method

For microgrids with uncertainties in renewable energy generation and normal load demand, a robust multi-objective and multi-scenario performance optimization algorithm based on lexicographic order is proposed, which considers system economic cost, environmental cost, and user comfort as the objective functions. At first, historical data are processed using K-means clustering to extract typical scenario sequences. In the day-ahead scheduling stage, a lexicographic order method is applied to sequentially optimize the three objectives: economic cost, environmental cost, and user comfort. For each objective, robust optimization is performed by adopting the probability-weighted sum of the cost functions as the objective function. It obtains the optimal solution that ensures superior performance for typical scenarios. Subsequently, a robustness test is conducted under constraints that guarantee normal equipment operation and power balance for all scenarios. In the intraday scheduling stage, measured data of renewable energy and normal load are employed, and deviations in conventional power generation and grid interaction are penalized based on the day-ahead scheduling results. This adjustment improves the economic efficiency of the microgrid operation.