Risk limiting dispatch in congested networks

Increased uncertainty due to high penetration of renewables imposes significant costs to the system operators. The added costs depend on several factors including market design, performance of renewable generation forecasting and the specific dispatch procedure. Quantifying these costs has been limited to small sample Monte Carlo approaches applied specific dispatch algorithms. The computational complexity and accuracy of these approaches has limited the understanding of tradeoffs between different factors. In this work we follow a different approach by considering a two-stage stochastic economic dispatch problem, where the optimal dispatch is called risk limiting dispatch. First we consider an uncongested network and derive the price of uncertainty, a number that characterizes the intrinsic impact of uncertainty on the integration cost of renewables. Then we extend the results to a two bus network where a transmission line may become congested. We demonstrate the existence of the price of uncertainty even in this case, under mild assumptions. We show that risk limiting dispatch is given by a set of deterministic equilibrium equations. The dispatch solution yields an important insight: congested links do not create isolated nodes, even in a two-node network. In fact, the network can support backflows in congested links, that are useful to reduce the uncertainty by averaging supply across the network.