Integration Of Electric Vehicles Into Smart Grids With Optimal Distributed Charging Control

Charging a large amount of Plug-in Electric Vehicles(PEVs) could seriously endanger grid stability and energy security. On the other hand, if PEV charging is managed properly, it could bring significant flexibility into the grid, thus allowing for enhanced energy efficiency, more integration of distributed energy production, deferral investment in grid reinforcement etc. Shifting PEV charging load to off-peak periods(mostly at nighttime) is often referred to as valley-filling. This paper studies the valley-filling problem within the portfolio of a Demand Response(DR) Aggregator. We consider two separate problems: real-time welfare maximization combined with dynamic pricing on one side(also called the intraday problem) and the valley-filling problem on the other side(also called the day-to-day problem). We use Lagrange Relaxation to formulate the decentralized version of the real-time welfare maximization problem, which leads to a decentralized charging control algorithm. Then, using control theory, we study the steady-state conditions for the charging control algorithm and arrive to the conclusion that welfare maximization used with concave utility function cannot lead to the optimal valley-filling solution when combined to dynamic pricing(this being due to the monotony of the real-time willingness to pay, a quantity proportional to the first derivative of the utility according to the real-time state of charge). On the other hand, we show that the control architecture(obtained from the decentralized formulation of the welfare maximization) can advantageously be adapted. Indeed, we show that using charging flexibility to define the real-time willingness to pay is a solution that respect the convergence criteria(i.e. solvability condition for the valley-filling problem) and can even allow a generalization of the model to better fit real market mechanisms. Simulation results show significant Peak-Valley Difference reduction with minimal charging cost, without jeopardizing the final State of Charge. The proposed procedure requires no communication between vehicles, and ensures full charging to the level required by the user. It offers a minimal amount of centralized computation that does not suffer from curse of dimensionality as no vehicle specific information is required.