Distributionally Robust Optimization for Vehicle-to-grid with Uncertain Renewable Energy

Recent years have seen the wide applications of renewable energy sources and plug-in electric vehicles in smart grids. However, their inherent uncertainties may lead to serious voltage deviations, load fluctuations and power losses. In this paper, we formulate a distributionally robust optimization (DRO) for vehicle-to-grid considering the uncertainties of solar power and PEVs. We utilize conditional value at risk to quantify the risk of violating inequalities containing uncertainties and the Wasserstein metric to reformulate the DRO problem into a tractable convex optimization problem. The DRO is implemented under a model predictive control framework to further reduce the uncertainties of PEVs and RESs. Numerical experiment results validate the efficiency of our method.