Novel MINLP formulations for flexibility analysis for measured and unmeasured uncertain parameters

Abstract

In this work, we formulate the extended flexibility analysis, which takes into account two different types of uncertain parameters, measured (θm) and unmeasured (θu), as a rigorous multilevel optimization problem. We recursively reformulate the inner optimization problems by the KKT conditions and with a mixed-integer representation of the complementarity conditions to solve the resulting optimization problem. Special cases are identified, where models are comprised of convex constraints or constraints with monotonic variation of the uncertain parameters. In these cases, a vertex enumeration can be performed to solve the flexibility test. We propose two MINLP reformulations for the more general case yielding to similar results but different model sizes. The formulations are tested and compared in several examples.