Analysis of the load flow behaviour near a Jacobian singularity
Bibliographic record
Abstract
New theoretical results above the behavior of the load flow solution near a Jacobian singularity are presented. The principal result is the derivation of an analytic closed-form relation between the specified injections and the resulting voltages in the neighborhood of a singularity. This result is a companion to the conventional load flow sensitivity analysis which is valid only if the operating point is not at a Jacobian singularity. The new closed-form relation derived is theoretically important since it can predict and explain the main load flow phenomena observed through simulation analysis near a singularity. These are: the nonexistence of solutions for certain injection changes, the bifurcation of the voltages into two nearby solutions, the sudden collapse of voltages for small injection changes, and the nature of the collapse, that is, which buses are more susceptible to the collapse. Numerical simulations support the validity of the theoretical result by comparing the closed-form analytic relation near a singularity with exact load flow simulations.>
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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 | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.003 | 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".