Sample average approximation and stability tests applied to energy system design

Abstract

This paper uses confidence intervals from sample average approximation (SAA) and stability tests to evaluate the quality of the solution of a long-term energy system model with stochastic wind power production. Using poorly designed scenarios can give stochastic model results that depend on the scenario representation rather than the actual underlying uncertainty. Nevertheless, there is little focus on the quality of the solutions of stochastic energy models in the applied literature. Our results demonstrate how too small a sample size can give a poor energy system design and misrepresent the value of the stochastic solution (VSS).We demonstrate how to evaluate the number of scenarios needed to ensure in-sample and out-of-sample stability. We also show how replication and testing of many candidate solutions using SAA iterations can provide a solution with a satisfactory confidence interval, including when the samples contain fewer scenarios than required for stability. An important observation, though, is that if SAA repeatedly solves the model with a sample size that satisfies in-sample and out-of-sample stability, the confidence interval is narrow, and the solutions are of high quality in terms of providing a tight bound for the optimal solution.

Empirical Analysis of the Optimal Capacity Investment Solutions in Distribution Grids

“…In rest of this subsection, we describe the metrics to evaluate the investment solution's quality and stability. We will use the sample-average approximation (SAA) method, [16] for approximating the problem (22).…”

“…Stochastic programming is a mathematical framework that lets capturing the uncertainty of power production from nonconventional renewable sources [14], [15]. It has been proposed in [16] to use Sample Average Approximation (SAA) to generate scenarios in the planning problem with stochastic parameters. Nevertheless, scenario generation techniques are limited because they are an approximation (discrete scenarios) of real distribution.…”

Spatio-temporal smoothing and dynamics of different electricity flexibility options

“…In this paper, we use methods that can generate distributionally consistent artificial data that satisfactorily fit historical data of production and demand based on [BP18;BCR21]. A good representation of production distribution is particularly important for intermittent renewable generation [ST21]. We want to evaluate the impact of spatial and temporal smoothing via electricity transmission and storage, studying their interaction and benefits [RAG12; Rod+14]: electricity storage allows transferring renewable production in time; transmission allows taking advantage of the different renewable energy potentials across space and that contemporaneous weather conditions can differ from one location to the next.…”