Modeling electric vehicles adoption for urban commute trips

•This study develops a mixed user equilibrium formulation with electric vehicles (EVs) and gasoline vehicles (GVs).•A new concept called EV charging ratio is introduced to capture EV charging behavior for inner-urban trips.•The formulation with exogenous charging ratio is convex in link flows, stations flows, and EV demands.•The formulation incorporates EV elastic demand, whose utility function is calibrated via a market survey in Hong Kong.•The study observes the property of link flows preservation for a range of EV market penetration. In this paper, a mixed user equilibrium (MUE) model with Electric Vehicles (EVs) and Gasoline Vehicles (GVs) is proposed to account for the charging behavior of EVs in an urban network. The main difference between EVs and GVs lies in that certain EVs with immediate charging need have to traverse a specific station for recharging, while GVs and other EVs without immediate charging need do not have such a requirement. The proportion of EVs with immediate charging need, referred to as charging ratio in this study, is an OD specific endogenous variable, related to their daily commute trip lengths and EV driving ranges, i.e., EVs will need recharging once every few days. The MUE conditions state that EVs with charging need choose the routes via a charging station while en route to their destinations with minimum travel time cost, electricity cost plus charging station cost; whereas GVs and EVs without charging need select the routes with minimum travel cost without having to traverse any charging station. This study also captures the interaction between network design (such as charging station locations) and EV demand which follows a logit model calibrated with an EV market survey conducted in Hong Kong. We formulate the MUE problem first with a nonlinear complementarity (NCP) approach and solve it with a gap function, then we relax the charging ratio to be exogenous and formulate a convex mathematical program for efficient solutions, with the charging ratio iteratively determined. Furthermore, we observe that the resultant link flows exhibit the property of link flow preservation, i.e., the total link flows remain unchanged under a range of EV and GV demands. We first solve the Yang-Bell network to demonstrate its properties, and then solve the Sioux-Falls network to show its solution efficiency.