A Primal-Dual based Approach to Social Welfare problem for Electric Vehicle Charging

The simultaneous charging of Electric Vehicles (EVs) put extra burden on the distribution grid. The necessity of coordinated charging and discharging of EVs is very vital. This brings the EV owner and utility to act together to maximize their profits without affecting the grid from load congestion, voltage instability, and transformer overloading. In this paper, we formulate the benefits of utility and EV owner as a social welfare problem. The objective is to maximize the problem taking into account the generation costs and the battery charging costs. The optimization problem is casted as a dynamics problem using a primal-dual approach. The simulation results are presented to demonstrate the feasibility of the proposed solution and the optimal energy management during the peak load for Time of Use (ToU) pricing.