Optimal strategic coordination of distribution networks and interconnected energy hubs: A linear multi-follower bi-level optimization model

Energy hub systems have been developed in energy systems to provide sufficient flexibility in satisfying energy demands. In an energy hub system connected to distribution network (DN), input energy carriers can be converted into different energies like electricity, and heat to support the energy hub's operator in supplying various types of energy demands and dealing with other competitive operators of similar energy hubs who seek to have cost-effective performance of their operating system. In this paper, a multi-follower bi-level optimization framework is developed for optimal interaction of energy hubs and DN in which total operation cost of DN is minimized subject to network's constraints in the upper level problem while the total cost of each energy hub being connected to DN is minimized in the lower level problem. It is noteworthy that in addition to the DN, each energy hub is capable of exchanging power with other energy hubs to supply energy demand. The proposed model determines the optimal power exchange strategies between the energy hubs and DN in order to minimize the total operation cost associated with energy hubs and DN. The proposed bi-level model for optimal coordination of energy hubs and DN is a non-linear problem in which Karush-Kuhn-Tucker (KKT) optimality conditions are taken into account. The proposed model is linearized through applying linear constraints and then studied regarding the IEEE 33-bus test system and the strategic optimization results are analyzed to approve the efficiency of the proposed optimization model.