Noncommutative Composite Water-Filling for Energy Harvesting and Smart Power Grid Hybrid System With Peak Power Constraints
Bibliographic record
Abstract
Energy harvesting makes use of energy from the environment. However, since harvesting energy depends on natural conditions, it is not a stable energy source. As a result, the energy from the power grid is often included to serve as a supplementary source to regulate the overall energy supply of the system. Further, the power from the power grid is often subject to the constraints of peak power and the energy budget. These constraints lead to more difficulties in solving optimal power allocation problems. In this paper, we extend our recently proposed geometric water-filling (GWF) and recursive GWF (RGWF) algorithms to solve the throughput maximization problem and transmission completion time minimization problems for this kind of hybrid energy source system. Our investigation shows that the optimal power allocation for throughput maximization is the result of a sequence of water-filling algorithms for smart power grid and harvested energy, in that order, followed by a power adjustment step of the power from the grid. The allocation order is not commutative for an optimal solution due to the specific structure of the target problems. The proposed algorithms can compute the exact (optimal) solutions to the problems via finite computation with low computational complexity. Numerical examples are presented to illustrate the detailed procedures to efficiently obtain the optimal power allocation solutions using the proposed algorithms. The results also illustrate that the composite operation of the two water-fillings is noncommutative.
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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 | 0.001 |
| 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".