On the Clique Decomposition Impact to the Optimal Power Flow Semidefinite Relaxation Solve Time
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Bibliographic record
Abstract
Managing intermittent generation in electric power systems with high penetration of renewable sources of energy presents major operational challenges. Faster, more efficient optimization techniques are essential to mitigate this intermittency and ensure grid reliability. Convex relaxations of optimal power flow (OPF) problem offer tractable means of solving the nonlinear, non-convex OPF problem. Specifically, the semidefinite relaxation yields the tightest lower bound for the OPF but require careful exploitation of sparsity to remain computationally viable when scaling to large problem instances. This exploitation can be achieved through clique decomposition of the semidefinite constraint. In this work, we experiment with various clique decomposition algorithms and demonstrate that the resulting OPF solve time is highly sensitive to the choice of decomposition. Our main contribution is showing that the optimal decomposition depends on both the network topology and the demand profile. We find that some networks have a preferred decomposition that performs well across demands, while others require demand-dependent choices, suggesting a learning-based approach to predict the optimal decomposition for minimizing OPF solve time.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.006 |
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 it