Investigation of the relationship between ill-conditioned power flow and voltage collapse
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Bibliographic record
Abstract
Ill-conditioned power flow problems have been widely investigated and discussed in the literature. Typical approaches are to develop enhanced solution algorithms when a power flow case is found to diverge using the conventional Newton method. It is known that a genuine ill-conditioned problem is caused by the presence of a large condition number in the power flow Jacobian matrix. Since a large condition number is associated with small singular values and the voltage collapse is related to small eigenvalues, we therefore speculate that an ill-conditioned power flow problem is actually a voltage collapse problem. The objective of this letter is to demonstrate the relationship between power flow ill conditioning and voltage instability. Case studies of five classical ill-conditioned cases have confirmed that the ill conditioning of power flow indeed occurs-and only occurs-at the voltage collapse point.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it