Optimal Pricing of Electric Vehicle Charging on Coupled Power-Transportation Network based on Generalized Sensitivity Analysis

In the last decade, charging service providers are emerging along with the prevalence of electric vehicles. These providers need to strategically optimize their charging prices to improve the profits considering operation conditions of the coupled power-transportation network. However, the optimal pricing problem generally involves the user equilibrium model, which leads to a mathematical program with equilibrium constraints. As a result, the pricing problem is non-convex and computationally intractable especially for large-scale network. To address this challenge, we propose a generalized sensitivity analysis approach for optimal pricing of electric vehicle charging on coupled power-transportation network. Specifically, we adopt a sensitivity analysis to capture the best response of charging demand to charging price in the gradient form. Consequently, charging service providers can make pricing decisions based on the gradient information instead of the conventional KKT conditions of the user equilibrium model. We then propose a tailored gradient descent algorithm to solve the whole pricing problem. The mathematical proof of validity is given and the time complexity of the proposed algorithm is theoretically polynomial. Numerical experiments on different scales of networks verify the computational efficiency of the proposed algorithm, indicating its potential in evaluating the impact of the optimal pricing on the operational performance of large-scale coupled power-transportation network.