Interactive Equilibrium of Electricity-Gas Energy Distribution System and Integrated Load Aggregators Considering Energy Pricings: A Master-Slave Approach

Integration of electricity and gas distribution networks improves energy utilization and alleviates environmental pollution. In order to obtain a reasonable energy prices and optimize the day-ahead scheduling scheme under the premise of considering the interests of both supply and demand, an interactive equilibrium model considering electricity-gas energy distribution system and integrated load aggregators is established in this paper. In the upper level, the integrated energy distribution network (IEDN) maximizes the profit via solving the day-ahead optimal energy flow considering energy prices changing in the next day. In the lower level, integrated load aggregators (ILA) minimize charging costs, thus optimizing energy distribution based on integrated demand responses. By using the Karush-Kuhn-Tucker (KKT) optimality conditions and the duality theorem of linear programming, the master-slave game model is transformed into a single layer optimization problem. To solve this problem, second-order cone programming (SOCP) and penalty convex-concave procedure (PCCP) are used to deal with the non-convex functions of electricity-gas distribution system. Therefore, the proposed model is approximated by a mixed-integer second-order cone programming problem. Finally, case studies verify the effectiveness of the proposed model and method.