Distributed Optimization for Day-Ahead Stochastic Scheduling of Integrated Electricity and Heat Systems Based on FW-PH Algorithm

To cope with wind power uncertainty, the day-ahead scheduling of integrated electricity and heat systems can be formulated based on the two-stage stochastic mixed-integer linear programming (SMILP) model. This paper focuses on developing a distributed solution for the SMILP model. However, the inclusion of binary integer variables in the unit commitment renders the model nonconvex, posing challenges for traditional progressing hedging algorithms in achieving global convergence. To enhance the convergence of distributed optimization, this paper employs the Frank-Wolfe (FW) algorithm within the progressive hedging (PH) framework to convexify the feasible region. The original problem is divided into multiple sub-problems according to the scenario, and the FW-PH algorithm is used to solve each sub-problem. Two heuristic acceleration strategies, the scenario bundle method, and the integer variable convergence criterion method, are proposed to speed up the algorithm convergence and reduce computational time, respectively. Finally, the effectiveness of the FW-PH algorithm is verified based on the modified IEEE-6 bus system in terms of solution accuracy and computational efficiency. The engineering practicability of the acceleration strategies is verified on a large-scale system in Northeast China.