  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 consider a two-stage stochastic economic dispatch problem. Our goal is to
provide an analytical quantification and an intuitive understanding of the
effects of uncertainties and network congestion on the dispatch procedure and
the optimal cost.} We first consider an uncongested network and calculate the
risk limiting dispatch. In addition, we 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 network where
one link can become congested. Under mild conditions, we calculate price of
uncertainty even in this case. 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. We demonstrate the performance of our approach in standard IEEE
benchmark networks.
