An outer approximation of the Minkowski sum of convex conic sets with application to demand response
Bibliographic record
Abstract
Flexible loads can provide services such as load-shifting and regulation to power system operators through demand response. A system operator must know the aggregate capabilities of a load population to use it in scheduling and dispatch routines such as optimal power flow and unit commitment. It is not practical for a system operator to model every single load because it would compromise tractability and require potentially unavailable information. A key challenge for load aggregators is to develop low-order models of load aggregations that system operators can use in their operating routines. In this paper, we develop a simple approximation for loads modeled by linear, second-order cone, and semidefinite constraints. It is an outer approximation of the Minkowski sum, the exact computation of which is intractable. We apply the outer approximation to loads with convex quadratic apparent power constraints and uncertainty modeled with second-order cone constraints.
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How this classification was reachedexpand
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".