Scenario Reduction for the Two-Stage Stochastic Unit Commitment Problem

TL;DR

This paper reviews and compares scenario reduction methods for the two-stage stochastic unit commitment problem, demonstrating that a specific cost function can effectively select representative scenarios with high accuracy and computational efficiency.

Contribution

It introduces a novel formulation of the cost function for scenario reduction and proves its optimality in selecting the best scenario from a sample.

Findings

A specific cost function improves scenario selection accuracy.

Approximation with around 2% of scenarios maintains near-optimal solutions.

The method is computationally efficient on a standard power system test case.

Abstract

The two-stage stochastic unit commitment problem has become an important tool to support decision-making under uncertainty in power systems. Representing the uncertainty by a large number of scenarios guarantees accurate results but challenges the solution process. One way to overcome this is by using scenario reduction methods, which aim at finding a distribution supported on fewer scenarios, but leading to similar optimal first-stage decisions. In this paper, we recap the classical scenario reduction theory based on the distance of probability distributions and the optimal mass transportation problem. We then review and compare various formulations of the underlying cost function of the latter used in the literature. Using the Forward Selection Algorithm, we show that a specific formulation of the cost function can be proven to select the best possible scenario from a given sample on the first draw with respect to the Relative Approximation Error. We demonstrate this result and compare the quality of the approximation as well as the computational performance of the different cost functions using a modified version of the IEEE RTS 24-Bus System. In many cases, we find that the optimal solution of the two-stage stochastic unit commitment problem with 200 scenarios can be approximated with around 2% scenarios when using this cost function.