Optimal Planning of Charging Stations in Coupled Transportation and Power Networks Based on User Equilibrium Conditions

In this article, we propose a new bi-level approach for the location and sizing of charging stations (CSs) based on the integration of power distribution and traffic networks. At the lower level, the user choices and the energy demands are modeled through the user equilibrium (UE) traffic assignment conditions that are derived for the case of electric vehicles (EVs). At the higher level, an optimization problem is formalized for the optimal planning of locations, sizes, and unit prices of a set of new charging stations in a territory, which embeds the UE conditions and the power flow model as constraints. The main novelties lie in the integration of traffic and electric networks, the optimization problem formalization, and the inclusion of detailed electrical issues [such as the complete alternating current (AC) power flow equations and the modeling of CSs with different phases]. The developed model has been applied to a case study in the Genoa Municipality. Note to Practitioners - In the past decade, particular attention has been posed on EVs and renewable resources to reduce pollutants' emissions. Critical issues regard the setting of adequate recharging infrastructure and the integration of huge distributed and intermittent loads and production into the electrical grid. This article aims to provide a bi-level optimization model that can be used by companies or public administrations that want to install charging stations in a territory. In particular, the transportation and the electrical networks are integrated: at a lower level, the UE traffic assignment conditions are derived to represent users' choices and to assess the energy demand. At the upper level, an optimization problem is formalized, to minimize costs of installation and power losses and to maximize benefits, which embeds as constraints the UE conditions for the case of EVs and the model of the electrical grid (load flow equations, bounds over-voltage, apparent power, etc.).