Statistically Feasible Mixed-Integer Programming for Integrated Energy System Scheduling

Integrated energy systems coordinate multiple energy flows to enhance energy efficiency and reduce costs. However, the uncertain and volatile availability of emerging renewable energy generation poses significant challenges to traditional scheduling paradigms of integrated energy systems. To address this issue, we propose a robust sample-driven approach to ensure the statistical feasibility of operational constraints – a notion that is mild conservative and requires no prior knowledge of randomness. We formulate the scheduling problem of an integrated energy system as a statistically feasible mixed-integer program with discrete control characteristics of combined heat and power. To handle the non-linearities from chance constraints, we use shape learning and shape calibration to construct an uncertainty set with a statistical feasibility guarantee. The approach finally employs Benders decomposition to handle the resulting deterministic linear model, offering a rigorous solution to scheduling an integrated energy system under vast uncertainty. We validate our analysis through extensive numerical studies.