Alternative LP and SOCP Hierarchies for ACOPF Problems
Bibliographic record
Abstract
The alternating current optimal power flow (ACOPF) problem optimizes the generation and the distribution of electric energy taking into account the active and the reactive power generation limits, demand requirements, bus voltage limits, and network flow limits. The ACOPF problem can be formulated as a nonconvex polynomial program that is generally difficult to solve due to the nonlinear power flow constraints. A recently proposed approach to globally solve the ACOPF problem is through the formulation of a hierarchy of semidefinite programs that are computationally challenging to solve for large-scale problems. In this paper, we explore a solution approach that alleviates this computational burden by using hierarchies of linear and second order cone programs and by exploiting the network structure of the transmission grid. Furthermore, we show that the first level of the second order cone hierarchy is equivalent to solving the conic dual of the approximation that was recently proposed in the literature, which provides the optimal solution of the ACOPF problem for special network topologies.
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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 | 0.002 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.010 | 0.001 |
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".