Decentralized mixed-integer optimization for robust integrated electricity and heat scheduling

Electric power systems (EPSs) and district heating networks (DHNs) are always independently operated and dispatched but also coupled with each other at the interfaces of combined heat and power (CHP) generation, whereas the existing distributed scheduling methods for the integrated electricity and heat system (IEHS) under uncertainty are computationally expensive in practical applications. To handle this problem, this paper proposes a novel decentralized mixed-integer optimization method for robust coordination involving multiple stakeholders. Firstly, a centralized two-stage robust optimization (RO) scheduling model is installed for the IEHS considering the scheduling economy under the nominal scenario and the adjustment feasibility against uncertainty. Secondly, the Fourier-Motzkin elimination equivalently projects the second-stage feasible region of the two-stage RO scheduling model onto the first-stage optimization, thereby producing a concise centralized RO scheduling model in a mixed-integer linear programming (MILP) formulation. Finally, a dual decomposition algorithm derives the decentralized solution to the resulting MILP-type RO model with guaranteed convergence and optimality. This avoids setting up a coordination center for distributed scheduling. Case testing for two IEHSs validates that the computational efficiency of the proposed method is several tens of times speedup than the traditional distributed RO method with guaranteed solution optimality.