Optimal Day-Ahead Dispatch of a Grid-Connected Microgrid with Energy Storage under Time-of-Use Pricing and Load Uncertainty

Microgrid energy management must balance a time-of-use electricity purchase plan against battery storage dispatch so that the total purchase cost is minimised while all physical constraints on state of charge and charge/discharge power are satisfied. Existing studies rely onnonlinear economic model predictive control orrolling-horizon optimisation, which restore feasibility online but do not guarantee a global optimum, and onprice-arbitrage battery scheduling that treats the tariff in isolation. Model constructs a two-stage framework that first partitions the tariff into three tiers by partitioning-around-medoids clustering with a silhouette coefficient of 0.772 and then solves a deterministic day-ahead dispatch with linear programming and an equivalent big-M mixed-integer program, which yields a globally optimal schedule with zero simultaneous charge/discharge slots. Day-ahead uncertainty is absorbed by a quantile safety margin plus penalised emergency purchase. The deterministic scheme lowers the daily purchase cost from 48,052.05 to 35,126.95 yuan, a 26.90% saving, and the annual two-stage cost is 14,066,913.87 yuan. Compared with online controllers, the model offers a global optimum guarantee, an explicit three-tier price interpretation, and atractable safety margin.