Coordinated Deployment and Pricing of Mobile and Fixed Charging Stations

Abstract

As fixed charging stations (FCSs) approach saturation, mobile charging stations (MCSs) have emerged as a flexible complement. This study proposes a bi-level optimization framework that integrates dynamic siting of MCSs with coordinated pricing for both MCSs and FCSs. The upper level maximizes the operator’s total net profit by jointly deciding MCS deployment and spatio-temporal prices, while the lower-level models EV users’ charging choices via cost minimization. The bi-level problem is reformulated as a single-level mathematical program with equilibrium constraints (MPECs) by replacing the lower-level with Karush–Kuhn–Tucker (KKT) optimality and complementarity conditions. The nonconvexities are addressed using the Big-M method, auxiliary variables, and piecewise linearization. This reformulation converts the problem into a mixed-integer linear program (MILP). The case studies show that the proposed coordinated strategy substantially improves the operator’s total net profit compared with the fixed sitting benchmark. This improvement is mainly achieved by allowing the MCSs to respond to spatiotemporal demand variations. Compared with the MCS-only optimization benchmark, the increase in total net profit is marginal under the tested scenario. This result suggests that coordinated MCS–FCS pricing mainly improves the investor’s portfolio-level outcome by reducing internal competition between MCSs and FCSs, rather than by increasing the standalone profit of the MCSs. The proposed framework provides an optimization approach for coordinated MCSs and FCSs operation in saturated charging networks.