An Elastic Demand Model for Locating Electric Vehicle Charging Stations

In this study, we aim to optimally locate multiple types of charging stations, e.g., fast-charging stations and slow-charging stations, for maximizing the covered flows under a limited budget while taking drivers' partial charging behavior and nonlinear demand elasticity into account. This problem is first formulated as a mixed-integer nonlinear programming model. Instead of generating paths and charging patterns, we develop a compact formulation to model the partial charging logic. The proposed model is then approximated and reformulated by a mixed-integer linear programming model by piecewise linear approximation. To improve the computational efficiency, we employ a refined formulation using an efficient Gray code method, which reduces the number of constraints and binary auxiliary variables in the formulation of the piecewise linear approximate function effectively. The epsilon-optimal solution to the proposed problem can be therefore obtained by state-of-the-art MIP solvers. Finally, a case study based on the highway network of Zhejiang Province of China is conducted to assess the model performance and analyze the impact of the budget on flow coverage and optimal station selection.