Analysis of a Network of Non-Identical Parallel-Connected Supercapacitors
Bibliographic record
Abstract
Supercapacitors are widely used in various applications ranging from wind turbine pitch control systems to regenerative braking in electric and hybrid vehicles. This is due to their unique properties including high power density, scalability, high reversibility, and long operational lifetime. Although it is well-known that associating non-identical supercapacitors in parallel increases the equivalent capacitance of the network at a constant voltage, their dynamic behavior in the time domain remains under-explored. However, this cannot be simply done using the models of ideal capacitors, because supercapacitors exhibit a combined resistive-capacitor, dispersive nature. In this work, we analyze the behavior of supercapacitors connected in parallel (two or more different devices) in both the time and frequency domains using the constant phase element (CPE) as the building model. The CPE has a fractional impedance of the form z ( s ) = ( C α s α ) − 1 with C α a positive constant representing a pseudocapacitance, and α a dispersion coefficient that takes values between zero and one. From our theoretical analysis we obtain explicit expressions for the power-law-like voltage response of the supercapacitor network under constant current excitation in terms of the generalized Mittag-Leffler function. The derived formlæ are validated by experimental time and frequency-domain data of real commercially-available devices.
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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 | 0.001 |
| 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 | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".