Coordination in Markets With Nonconvexities as a Mathematical Program With Equilibrium Constraints—Part II: Case Studies
Bibliographic record
Abstract
This paper is the second of a two-paper series. It is concerned with the numerical study of the solution procedure derived in to solve the coordination problem that arises in a new equilibrium model , which for the purpose of this presentation applies to a static (no-time coupling costs or constraints) electricity pool market with price inelastic demand and no network. The new equilibrium model has the following main properties: i) every scheduled generator satisfies its minimum surplus (or bid profit) condition; ii) the energy price is a system marginal cost (a Lagrange multiplier associated with the power balance constraint in the related economic dispatch problem where all of the discrete variables are fixed to their optimal values); iii) the power balance and all of the generators' technical constraints are satisfied. We present some numerical results based on three test systems: a simple three-generating unit system that can be solved by hand, a 32-generating unit system that consists of piecewise linear offer curves, and a large system of 768 generating units with monotone and nonmonotone, piecewise linear offer curves, some of which are set as must-run units. The results demonstrate that the proposed procedure is more efficient than a heuristic approach, both in terms of solution quality and computational efficiency.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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".