Efficient Representation of Uncertainty for Stochastic Economic Dispatch

TL;DR

This paper introduces Polynomial Chaos and Karhunen-Loeve expansions as efficient methods to represent uncertainties in stochastic economic dispatch, significantly reducing computational costs compared to traditional Monte Carlo sampling.

Contribution

It presents novel uncertainty representation techniques that improve computational efficiency in stochastic economic dispatch models over existing Monte Carlo methods.

Findings

Achieves several orders of magnitude reduction in computational cost.

Provides accurate uncertainty propagation with fewer samples.

Demonstrates effectiveness on renewable energy generation uncertainties.

Abstract

Stochastic economic dispatch models address uncertainties in forecasts of renewable generation output by considering a finite number of realizations drawn from a stochastic process model, typically via Monte Carlo sampling. Accurate evaluations of expectations or higher-order moments for quantities of interest, e.g., generating cost, can require a prohibitively large number of samples. We propose an alternative to Monte Carlo sampling based on Polynomial Chaos expansions. These representations are based on sparse quadrature methods, and enable accurate propagation of uncertainties in model parameters. We also investigate a method based on Karhunen-Loeve expansions that enables us to efficiently represent uncertainties in renewable energy generation. Considering expected production cost, we demonstrate that the proposed approach can yield several orders of magnitude reduction in computational cost for solving stochastic economic dispatch relative to Monte Carlo sampling, for a given target error threshold.