Flexibility analysis using boundary functions for considering dependencies in uncertain parameters

In this work, we present a novel approach for considering dependencies (often called correlations) in the uncertain parameters when performing (deterministic) flexibility analysis. Our proposed approach utilizes (linear) boundary functions to approximate the observed or expected distribution of operating points (i.e. uncertainty space), and can easily be integrated in the flexibility index or flexibility test problem. In contrast to the hyperbox uncertainty sets commonly used in deterministic flexibility analysis, uncertainty sets based on boundary functions allow subsets of the hyperbox which limit the flexibility metric but in which no operation is observed or expected, to be excluded. We derive a generic mixed-integer formulation for the flexibility index based on uncertainty sets defined by boundary functions, and suggest an algorithm to identify boundary functions which approximate the uncertainty set with high accuracy. The approach is tested and compared in several examples including an industrial case study.