Piecewise Mixed Decision Rules Based Multi-Stage Distributionally Robust Unit Commitment for Integrated Electricity-Heat Systems

This letter presents a multi-stage distributionally robust unit commitment (DRUC) optimization method for integrated electricity-heat systems (IEHSs) considering wind power uncertainty. To respect the non-anticipativity of uncertain optimization, a multi-stage framework for DRUC is developed. Then, a novel decision rule for continuous and binary variables to fill the limitations of typical continuous recourse is proposed, namely, piecewise mixed decision rules, which leverages the flexibility and scalability of nonlinear and binary decision rules. On this basis, the multi-stage DRUC problem is reformulated into a tractable form using dual theory. The proposed method can significantly reduce the total cost of IEHSs under wind uncertainty.