Nonlinear negative damping caused August 10, 1996-WECC blackout
Bibliographic record
Abstract
This paper shows that the August 10, 1996-WECC blackout originated from negative damping arising from sin6 nonlinearity. The proof is based on keeping the nonlinearity in the dynamic equation of a turbine-generator swinging against an infinite bus. Small signal perturbation linearization can predict the occurrence of negative damping. But the linear approach cannot produce the negatively damped waveform of the WECC blackout. Therefore, the graphical Phase Plane method is resorted to. As MatLab, MATHEMATICA, Wolfram MathWorld, etc. offer software plotters, the phase plane method is not difficult to use. Phase portraits show that the “Swing Equation” has stable and unstable regions. The WECC blackout happened because the initial states fell in the unstable region. Although dismissed as being limited to two-dimensions, the paper makes a contribution by showing that phase plane can be used to study the impact of 3 independent controllers. A worked-example shows when the independent controllers (turbine torque, the generator counter-torque and the damping torque) cannot meet the Transient Stability Limit after a line short circuit fault, local blackout occurs. The global WECC blackout is considered to be a scaled up local blackout. Instead of a turbine-generator swinging against an infinite bus, the last stage of the August 10, 1996-WECC blackout is assumed to be the Seattle-area swinging against the California-area. A phase portrait is found in the unstable region whose trajectory unravels in several cycles. Time-domain simulation shows a waveform oscillating with same number of cycles, which qualitatively matches the waveform of the August 10, 1996-WECC blackout.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 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".