Online Identification of Differential Order in Supercapacitor Fractional-Order Models: Advancing Practical Implementation

Arsalan Rasoolzadeh (), Sayed Amir Hashemi and Majid Pahlevani ()
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Arsalan Rasoolzadeh: ePower Laboratory, Electrical and Computer Engineering Department, Queen’s University, Kingston, ON K7L 3N6, Canada
Sayed Amir Hashemi: ePower Laboratory, Electrical and Computer Engineering Department, Queen’s University, Kingston, ON K7L 3N6, Canada
Majid Pahlevani: ePower Laboratory, Electrical and Computer Engineering Department, Queen’s University, Kingston, ON K7L 3N6, Canada

Energies, 2025, vol. 18, issue 8, 1-14

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.

Keywords: supercapacitor; fractional-order dynamic model; online identification; least squares error; descent gradient optimization (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2025
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