Explicit Solutions for Simple Models of Wind Turbine Interference
Bibliographic record
Abstract
Wind turbine interference - the reduction in output power of a turbine downwind of any others - is a major problem for wind farm optimization and control. With interference, it is well-known for specific cases that co-operative optimization of power output yields more power than does the selfish optimization of individual turbines. This paper develops explicit solutions for simple models of interference for the general case of any number of turbines in line with the wind. For the simplest case of no wake recovery, analytical solutions for co-operative and selfish optimization are derived. They show that co-operative optimization nearly always yields more power and never yields less. Adding a simple form of wake recovery for equally spaced turbines precludes analytical solutions, but numerical solutions are developed to find the power to any required level of accuracy. Again, co-operative optimization is superior in nearly all cases. These simple solutions should be useful for demonstrating the importance of interference and for testing methods for optimizing wind farm layout and operation. It is shown that the maximum benefit from co-operative operation occurs at turbine spacing comparable to that commonly used in wind farms. The analysis is then extended to include topographical effects modeled as changes in wind speed along the line. Explicit solutions are obtained for two turbines in line. Co-operative optimization remains the best strategy. In particular, when the wind speed increases, it quickly becomes optimal to shut down the first turbine.
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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 | 0.000 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".