Optimal Water–Power Flow Solutions Using Polyhedral and Conic Relaxations
Bibliographic record
Abstract
Water distribution systems (WDSs) and power grids are vital infrastructures that support daily human activities. Substantial research has focused on optimizing the operation of each system individually. However, the power consumption of WDS creates interdependence between these systems, leading to the need for optimizing their conjunctive operation, also known as the optimal water and power flow (OWPF) problem. Combining the WDS optimal operation problem with the optimal power flow (OPF) problem results in a non-convex mixed integer nonlinear programming (MINLP) problem, presenting significant mathematical and computational challenges. Previous studies have used various approximation methods to make the problem convex and obtain feasible solutions. However, these methods often converge to local optima and lack theoretical guarantees of global optimality. Failing to guarantee global optima or provide an optimality gap may result in inconsistent and untrustworthy results for decision makers. This study introduces a tailored solution method for optimizing the conjunctive operation of WDS and power grids. The method uses polyhedral relaxations of the non-convex hydraulic constraints, along with conic relaxations to address nonlinearities in the OPF problem. By using convex relaxations, the method provides optimality gaps for the computed solutions. To validate its effectiveness, the method is tested on two sample applications and its performance is compared with that of an off-the-shelf nonlinear solver.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".