Buying random yet correlated wind power

We consider an auction design problem, where an aggregator procures wind power from multiple wind farms. While the realized generation of each wind farm is random, the probability distribution can be learned beforehand as its private information. Since the wind farms are geographically close, the distributions are possibly correlated. We formulate a unified optimization problem to study both the welfare-maximizing and the revenue-maximizing objectives. We show that the aggregator may extract the full surplus by exploiting the correlation among the distributions. We also illustrate, through a numerical example, the case where full surplus extraction is not achievable.