Toward Using Surrogates to Accelerate Solution of Stochastic Electricity   Grid Operations Problems
  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. 
Cosmin Safta, Richard L. Chen, Habib N. Najm, Ali Pinar, and Jean-paul   watson
cs.SY