Local blackout and global power system wide blackout are caused by non‐linear negative damping
Bibliographic record
Abstract
Local blackout occurs when the transient stability limit is exceeded after a transmission line fault. As to global blackout, a recording of the 10 August 1996‐WECC blackout shows that it was accompanied negative damping. A turbine‐generator swinging against an infinite bus is used to approximate the dynamics leading to the WECC blackout. There is no analytic solution when non‐linearity is included. Small‐signal linearisation shows that negative damping can occur but cannot produce the waveform recorded in the WECC blackout. Therefore, the graphical phase‐plane method, which is easy to use, is resorted to. The study shows that the kernel of non‐linearity consists of the gradients which produce limit cycles. Positive or negative damping is produced by shifting the gradients of the limit cycles to the right or left in the direction of the trajectory. The study makes a contribution by showing that phase plane can be used to study the impact of multiple independent controllers. A worked example shows when transient stability limit is exceeded, local blackout occurs. The swing equation of local blackout is applied to the WECC blackout. As proof that negative damping was due to non‐linearity, a waveform having the frequency of the recorded WECC blackout is presented.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| 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".