4. An Optimal and Distributed Control Strategy for Charging Plug-in Electrical Vehicles in the Future Smart Grid

In this chapter, we propose an optimal and distributed control strategy for plug-in electric vehicles’ (PEVs) charging as part of demand response in the smart grid. We consider an electricity market where users have the flexibility to sell back the energy stored in their PEVs or the energy generated from their distributed generators. The smart grid model in this chapter integrates a two-way communication system between the utility company and consumers. A price scheme considering fluctuation cost is developed to encourage consumers to lower the fluctuation in the demand response by charging and discharging their PEVs reasonably. A distributed optimization algorithm based on the alternating direction method of multipliers is applied to solve the optimization problem, in which consumers need to report their aggregated loads only to the utility company, thus ensuring their privacy. Consumers update the scheduling of their loads simultaneously and locally to speed up the optimization computing. We also extend the distributed algorithm to the asynchronous case, where communication loss exists in the smart grid. Using numerical examples, we show that the demand curve is flattened after the optimal PEV charging and load scheduling. We also show the robustness of the proposed method by considering estimation uncertainty on the overall next day load, and also the renewable energy. The distributed algorithms are shown to reduce the users’ daily bills with respect to different scenarios, thus motivating consumers to participate in the proposed framework.