AC-OPF-based Joint Optimal Sizing and Siting of Electric Vehicle Charging Stations and Photovoltaic Plants in Coupled Traffic-Power Networks

This work proposes a scheme for the joint optimal sizing and placement of the electric vehicle charging stations (EVCSs) and distributed photovoltaic (PV) plants in power distribution grids accounting for the power grid operation and underlying transportation constraints. The planning tool is formulated to minimize the investment, operational, and maintenance costs and maximize the power distribution grid's self-consumption while satisfying EV users demands and the power grid constraints. The power grid constraints (i.e., the operational limits on the nodal voltages and branches' current flow limits) are modeled via the convex Augmented Relaxed Optimal Power Flow (AR-OPF) model featuring the exact satisfaction of the grid constraints. The traffic constraints consist of EV users driving behavior in a given geographical area during the planning horizon. The EVs driving pattern is converted to its equivalent energy demand by defining the most frequent path taken by the EV user based on historical data. The optimization problem is formulated as a mixed-integer second-order cone program (MISOCP) where the binary variables are used for the optimal siting decisions of EVCSs and PV plants. Thanks to the inherent structure of the proposed optimization problem, it is decomposed via the Benders decomposition, where the master problem deals with the siting problem, and subproblems solve the operational one. The scheme is numerically validated on a coupled electric-transport Nguyen-Dupuis network. The analysis is presented for different electricity prices.