Scenario Reduction With Submodular Optimization

TLDR

Stochastic programming for renewable generation relies on scenario sets whose size and accuracy affect cost and reliability, yet existing reduction methods require a user‑defined number of scenarios. We propose a scenario‑reduction algorithm that uses submodular optimization to automatically determine and rank the optimal number of scenarios. The algorithm selects representative scenarios by optimizing a submodular objective and is evaluated qualitatively and quantitatively against the fast forward selection baseline.

Abstract

Stochastic programming methods have been proven to deal effectively with the uncertainty and variability of renewable generation resources. However, the quality of the solution that they provide (as measured by cost and reliability metrics) depends on the accuracy and the number of scenarios used to model this uncertainty and variability. Scenario reduction techniques are used to manage the computational burden by selecting representative scenarios. The common drawback of existing scenario reduction techniques is that the number of representative scenarios is a user-defined parameter. We propose a scenario reduction algorithm based on submodular function optimization to endogenously optimize the number of scenarios as well as rank these scenarios. This algorithm is compared, both qualitatively and quantitatively, with the state-of-the-art fast forward selection algorithm.