Adjustable Robust Optimization for Integrated Power and Water Systems via Equality Constraint Elimination

<p dir="ltr">Water systems and power systems are strongly connected and mutually affect each other. Recently, several studies have suggested leveraging this dependency to enhance the overall efficiency of these systems. However, the uncertainty inherent in both systems has received comparatively less attention. In this study, Robust Optimization (RO) and Adjustable Robust Optimization (ARO) are suggested for co-optimizing the scheduling of generator dispatch and pump scheduling while considering the uncertainty of water demands, power loads, and renewable energy generation. A key challenge in applying RO and ARO to such problems is the presence of equality constraints involving uncertain parameters, which cannot be satisfied under all realizations. To address this, we eliminate the equality constraints by decomposing the decision variables into independent and dependent components, enabling a tractable formulation with only inequality constraints. RO and ARO then offer robust optimal policies against any scenario within uncertainty sets defined by the user. ARO results in a decision rule rather than a fixed policy, allowing the incorporation of real-time information as uncertainty unfolds. In the case of coupled systems, the ARO can adjust decisions in both systems not only based on internal measurements but also in response to the evolving state of the other system. Numerical results highlight a trade-off between cost and robustness, demonstrating ARO’s superiority over RO due to its real-time adaptability.</p><p dir="ltr">This paper was presented at the 21st Computing and Control in the Water Industry Conference (CCWI 2025) at the University of Sheffield (1st - 3rd September 2025).</p>