Quadratic performance of primal-dual methods with application to secondary frequency control of power systems
Bibliographic record
Abstract
Primal-dual gradient methods have recently attracted interest as a set of systematic techniques for distributed and online optimization. One of the proposed applications has been optimal frequency regulation in power systems, where the primal-dual algorithm is implemented online as a dynamic controller. In this context however, the presence of external disturbances makes quantifying input/output performance important. Here we use the H2system norm to quantify how effectively these distributed algorithms reject external disturbances. For the linear primal-dual algorithms arising from quadratic programs, we provide an explicit expression for the H2 norm, and examine the performance gain achieved by augmenting the Lagrangian. Our results suggest that the primal-dual method may perform poorly when applied to large-scale systems, and that Lagrangian augmentation can partially (or completely) alleviate these scaling issues. We illustrate our results with an application to power system frequency control by means of distributed primal-dual controllers.
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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 | 0.004 | 0.009 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| 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".