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., fastcharging 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 ε-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.