Online Identification of Differential Order in Supercapacitor Fractional-Order Models: Advancing Practical Implementation
Bibliographic record
Abstract
Supercapacitors (SCs) are increasingly recognized as a reliable energy storage solution in various industrial applications due to their high power density and exceptionally long lifespan. SC-powered systems demand precise parameter identification to enable effective energy management. Although various approaches exist for the offline identification of SCs, some parameters depend on factors such as state of health (SoH), aging, temperature, and their combination. Consequently, the variation in parameter values under different conditions highlights the importance of online identification based on a dynamic model structure. Among various SC models proposed in the literature, fractional-order models offer greater accuracy, making them a superior choice for SC modeling. However, the conventional formulation in these models requires a very long window of samples and coefficients for filter implementation. Additionally, due to the several orders of magnitude difference in the elements of matrices, numerical instability can arise, leading to errors and drift in the final calculations. In this paper, a novel online identification approach is introduced for differential order estimation in fractional-order SC models. The proposed method significantly shortens the long window while maintaining accuracy, making it feasible for implementation in low-cost microcontrollers and a viable solution for real-world applications. In addition, the proposed method addresses the drift error by applying online least squares error estimation that aligns it with its offline estimated value.
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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 | 0.001 | 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 | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".