**Hong Gao 1, Kai Liu 1,\*, Xinchao Peng <sup>1</sup> and Cheng Li <sup>2</sup>**


Received: 23 March 2020; Accepted: 14 April 2020; Published: 16 April 2020

**Abstract:** With the rapid development of electric vehicles (EVs), one of the urgent issues is how to deploy limited charging facilities to provide services for as many EVs as possible. This paper proposes a bilevel model to depict the interaction between traffic flow distribution and the location of charging stations (CSs) in the EVs and gasoline vehicles (GVs) hybrid network. The upper level model is a maximum flow-covering model where the CSs are deployed on links with higher demands. The lower level model is a stochastic user equilibrium model under elastic demands (SUE-ED) that considers both demands uncertainty and perceived path constraints, which have a significant influence on the distribution of link flow. Besides the path travel cost, the utility of charging facilities, charging speed, and waiting time at CSs due to space capacity restraint are also considered for the EVs when making a path assignment in the lower level model. A mixed-integer nonlinear program is constructed, and the equivalence of SUE-ED is proven, where a heuristic algorithm is used to solve the model. Finally, the network trial and sensitivity analysis are carried out to illustrate the feasibility and effectiveness of the proposed model.

**Keywords:** electric vehicles; public charging station; bilevel model; range constraint
