Flexible loads and renewable integration: Distributed control and price of anarchy

New sources of uncertainty and variability are being introduced into modern power grids creating new control challenges. Examples include renewable generation from solar and wind generators, electric vehicles, etc. In addition, there is compelling value in reducing the peak electric power demand as that has a direct beneficial impact of reducing the need for new capital investments in overall power sector. Introduction of new sensing, communications and computational elements offers opportunities for novel control solutions. One promising approach to addressing these problems is to exploit the inherent flexibility in many types of electric power loads and use that to accommodate the inherent variability in renewable generation and/or to reduce the peak demand. In this paper, we focus on electric vehicles(EVs) as flexible loads in the context of renewable generation. We take an intra-day time horizon where we assume we have a good prediction of renewable generation. Based on the supply schedule of thermal generators and predicted supply of renewable generation, the charging of the electric vehicles is controlled to minimize the imbalance between generation and consumption using centralized and distributed control algorithms. We develop a pricing scheme based on the proportional allocation mechanism for the distributed case. Assuming individual loads are price takers, we show that there is a time varying price which can be set by the control authority such that it´s objective aligns with the individual´s objective. If the users are price anticipators, the corresponding situation can be formulated in a game-theoretic setting. Distributed algorithms are developed to compute solution in both the cases. We also analyze the “price of anarchy” and show that the worst case loss of efficiency is 0.25.