Using optimization models and techniques to implement electricity auctions
Bibliographic record
Abstract
Optimization models and techniques for two different bid format auctions are analyzed in this paper. The first model is the simple-bids auction in which participants only submit the offered power quantity and its unitary price. The second model deals with a multi-part bids auction in which bidders submit both a startup and variable cost coefficient. An optimization model that describes the simple-bids auction is formulated and the conditions under which multiple primal solutions exist are described. Using duality theory, the authors prove that Lagrange multipliers can be used to set the market price and that, in the absence of degeneracy, they reflect marginal pricing. They briefly describe the pros and cons of using simplex and interior-point methods to solve the optimization model. For the multi-part bids auction, they find that, in the absence of duality gap, Lagrange multipliers used as market prices lead to the recovery of all the costs submitted by the scheduled bidders. When a duality gap exists, the dual variables do not recover all the costs; even more, the cost not recovered is equal to the magnitude of the duality gap. The authors describe the conditions under which certain type of multiple primal solutions can be identified. The use of a direct and a Lagrangian-relaxation based technique to solve the auction are also briefly discussed.
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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 | 0.002 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.005 | 0.002 |
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".