How to Improve Linear Fuel-Cost Function to Compete with Quadratic and Cubic Functions
Bibliographic record
Abstract
To model the operating cost of thermal generating units, it is common to use polynomial relations between their power output and fuel input. These mathematical relations are known as fuel-cost functions, which are the heart of optimization algorithms. These functions could be modeled as first, second, or third order polynomial equations. The first order or linear equation is weak to explain the variability of units' operating cost. Also, the third order or cubic polynomial equation is rarely used in the literature, because its third element does not have any significant contribution to add. Thus, the second order or quadratic polynomial equation becomes the most popular fuel-cost function. Sometimes, different linear equations grouped as a piecewise function are used to accelerate the computational speed and linear programming algorithms can be directly involved. This study tries to achieve the goal of the last approach without using any piecewise function. That is, improving the preceding single linear equation to be a competitive fuel-cost function.
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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 | 0.001 |
| 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".