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Stochastic economic dispatch models address uncertainties in forecasts ofrenewable generation output by considering a finite number of realizationsdrawn from a stochastic process model, typically via Monte Carlo sampling.Accurate evaluations of expectations or higher-order moments for quantities ofinterest, e.g., generating cost, can require a prohibitively large number ofsamples. We propose an alternative to Monte Carlo sampling based on PolynomialChaos expansions. These representations are based on sparse quadrature methods,and enable accurate propagation of uncertainties in model parameters. We alsoinvestigate a method based on Karhunen-Loeve expansions that enables us toefficiently represent uncertainties in renewable energy generation. Consideringexpected production cost, we demonstrate that the proposed approach can yieldseveral orders of magnitude reduction in computational cost for solvingstochastic economic dispatch relative to Monte Carlo sampling, for a giventarget error threshold.

Efficient Representation of Uncertainty for Stochastic Economic Dispatch