Fast QC Relaxation of the Optimal Power Flow Using the Line-Wise Model for Representing Meshed Transmission Networks
Bibliographic record
Abstract
In this paper, we investigate the recently introduced McCormick-based Quadratic Convex (QC) relaxation of the Optimal Power Flow (OPF) where Line-Wise Model (LWM) is used for representing meshed transmission systems (QC-LW OPF) for the sake of decisively determining its relationship to other available convex relaxations in the literature. We also extend the recently introduced convex envelope of the tangent function so it would be suitable for test cases with any voltage angle difference range. A computational study where the recently proposed QC-LW OPF formulation is compared to an equivalent McCormick based QC relaxation of the OPF where Bus Injection Model (BIM) is used for representing meshed transmission systems (QC-BI OPF) is presented in this paper. This computational study was conducted using test cases that belong to different operational categories using 123 test cases from the PGLib-OPF library with a bus size range between 3 up to 6515 buses for the sake of understanding the effect of the change of operating conditions on the quality of solutions obtained using the QC-LW OPF and QC-BI OPF formulations. Results are compared using several metrics that testify to the obtained solution’s quality and the problem’s computational complexity. Comparison of results shows that the QC-LW relaxation neither dominates nor is dominated by the QC-BI relaxation in terms of solution quality. Therefore, it dominates the Second Order Cone (SOC) relaxation and neither dominates nor is dominated by the Semidefinite Programming (SDP) relaxation. Furthermore, it is shown that the QC-LW OPF has reduced the number of relaxed trigonometric functions and McCormick envelopes needed when compared to the QC-BI OPF, leading to a faster solution time for more than 84% of the test cases in the range of 2% up to 67%.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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 source (direct Gemma or distilled Codex), 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".