  This paper considers a security constrained dispatch problem involving
generation and line contingencies in the presence of the renewable generation.
The uncertainty due to renewables is modeled using joint chance-constraint and
the mismatch caused by contingencies and renewables are handled using reserves.
We consider a distributionally robust approach to solve the chance-constrained
program. We assume that samples of the uncertainty are available. Using them,
we construct a set of distributions, termed ambiguity set, containing all
distributions that are close to the empirical distribution under the
Wasserstein metric. The chance constraint is imposed for all distributions in
the ambiguity set to form the distributionally robust optimization problem.
This problem is nonconvex and computationally heavy to solve exactly. We adopt
a two-step approach to find an approximate solution. In the first step, we
construct a polyhedral set in the space of uncertainty that contains enough
mass under all distributions in the ambiguity set. This set is constructed by
solving several two-dimensional distributionally robust problems. In the second
step, we solve a linear robust optimization problem where the uncertain
constraint is imposed for all uncertainty values lying in the polyhedral set.
We demonstrate the scalability and robustness of our method using numerical
experiments.
