  Stochastic unit commitment models typically handle uncertainties in forecast
demand by considering a finite number of realizations from a stochastic process
model for loads. Accurate evaluations of expectations or higher moments for the
quantities of interest require a prohibitively large number of model
evaluations. In this paper we propose an alternative approach based on using
surrogate models valid over the range of the forecast uncertainty. We consider
surrogate models based on Polynomial Chaos expansions, constructed using sparse
quadrature methods. Considering expected generation cost, we demonstrate the
approach can lead to several orders of magnitude reduction in computational
cost relative to using Monte Carlo sampling on the original model, for a given
target error threshold.
