Ex post conditions for the exactness of optimal power flow conic relaxations
Bibliographic record
Abstract
Convex relaxations of the optimal power flow (OPF) problem provide an efficient alternative to solving the intractable alternating current (AC) optimal power flow. The conic subset of OPF convex relaxations, in particular, greatly accelerate resolution while leading to high-quality approximations that are exact in several scenarios. However, the sufficient conditions guaranteeing exactness are stringent, e.g., requiring radial topologies. In this short communication, we present two equivalent ex post conditions for the exactness of any conic relaxation of the OPF. These rely on obtaining either a rank-1 voltage matrix or self-coherent cycles. Instead of relying on sufficient conditions a priori , satisfying one of the presented ex post conditions acts as an exactness certificate for the computed solution. The operator can therefore obtain an optimality guarantee when solving a conic relaxation even when a priori exactness requirements are not met. Finally, we present numerical examples from the MATPOWER library where the ex post conditions hold even though the exactness sufficient conditions do not, thereby illustrating the use of the conditions. • We consider conic relaxations of the alternating current optimal power flow (AC-OPF). • We present two equivalent ex post conditions guaranteeing the exactness of any conic relaxation of the AC-OPF. • We present a numerical example of the application of these conditions.
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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 | 0.005 | 0.043 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.019 | 0.002 |
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".