  Real-time dispatch practices for operating the electric grid in an economic
and reliable manner are evolving to accommodate higher levels of renewable
energy generation. In particular, stochastic optimization is receiving
increased attention as a technique for handling the inherent uncertainty in
wind and solar generation. The typical two-stage stochastic optimization
formulation relies on a sample average approximation with scenarios
representing errors in forecasting renewable energy ramp events. Standard Monte
Carlo sampling approaches can result in prohibitively high-dimensional systems
for optimization, as well as a poor representation of extreme events that
challenge grid reliability. We propose two alternative scenario creation
strategies, importance sampling and Bayesian quadrature, that can reduce the
estimator's variance. Their performance is assessed on a week's worth of 5
minute stochastic economic dispatch decisions for realistic wind and electrical
system data. Both strategies yield more economic solutions and improved
reliability compared to Monte Carlo sampling, with Bayesian quadrature being
less computationally intensive than importance sampling and more economic when
considering at least 20 scenarios.
