Limitations of assigning general critical values to voltage stability indices in Voltage-Stability-Constrained optimal power flows
Bibliographic record
Abstract
The representation of system stability in Optimal Power Flow (OPF) models is a challenging task, which, in some cases, might render such representation impractical. The use of Voltage Stability Indices (VSIs) to monitor how close a system is to voltage collapse may be a very straightforward approach to overcoming those difficulties. However, when the voltage collapse is associated with a single generator encountering one of its reactive power generation limits, VSIs are difficult to be predicted. Nevertheless, assigning a general critical value to VSIs could be considered. Thus, this paper proposes the analysis of such consideration by modeling and solving a Voltage-Stability-Constrained OPF (VSC-OPF) problem in the context of electricity markets. The Voltage Stability Constraint (VSC) was implemented by means of the Minimum Singular Value (MSV), which is based on the Singular Value Decomposition (SVD) of the power flow Jacobian matrix, and the Tangent Vector Norm (TVN), which is based on the Tangent Vector (TV) to the bifurcation manifold of the power flow equations. The consideration of assigning an absolute critical value to these VSIs was verified with a small 6-bus test system. Results show that such consideration is too conservative, which may lead to inadequate price signals in the context of VSC-OPFs applied to electricity market clearing.
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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 | 0.007 | 0.028 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 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".