Capacity optimization of a transportation-power coupled network based on elastic traffic demand user equilibrium using a multi-step evolutionary algorithm

With the rapid proliferation of electric vehicles and the development of dynamic wireless charging (DWC) technology, the coupling between the transportation network (TN) and the power distribution network (PDN) has intensified, posing significant challenges to the capacity and operation optimization of the transportation-power coupled network (TPCN). This study proposes a multi-objective bi-level program to optimize the capacity of the TPCN. The upper level is a multi-objective optimization problem that takes the capacity of the TPCN as the decision variable, aiming to minimize the integrated cost, carbon emissions, and dependence degree of the PDN. The lower level addresses the coordinated optimization between the TN and the PDN. In the coordinated operation of the TPCN, the PDN determines the charging prices based on the capacity of devices provided by the upper level and transmits them to the TN. Considering the charging prices and elastic traffic demand, the traffic assignment problem of the TN is established as a user equilibrium (UE) model. Then, this paper transforms the UE model into variational inequalities (VIs) and designs a projection algorithm to address VIs. Subsequently, the DWC systems convert the traffic flow under UE into charging loads and transmit them to the PDN. Based on charging loads and the demand response from residential loads, the PDN scheduling is solved to minimize the operating cost of the PDN. Furthermore, a multi-step evolutionary algorithm consisting of a multi-step operator, a genetic operator, and an environmental selection is developed to handle the multi-objective bi-level program. The numerical experiments have verified the effectiveness of the proposed models and algorithms in solving the capacity and operation optimization of the TPCN.