Energy efficiency of supercapacitors in hybrid energy storage systems

• Autorzy: Lewandowski Mirosław , Orzyłowski Marek , Maciołek Tadeusz

Identyfikatory

DOI

10.24425/bpasts.2025.153841

• Języki publikacji: EN

Abstrakty

EN

The supercapacitor supports the main energy source of the hybrid electrical energy storage system. In short periods, it supplies additional energy or absorbs braking energy. The paper addresses the issue of energy losses in supercapacitors used in such a pulsed mode of operation. Commonly used first-order RC capacitor impedance models are not a good basis for accurate calculation results of energy losses in supercapacitors. The article presents fractional-order supercapacitor impedance models based on the Cole-Cole relaxation equation. The following part presents the results of measurements of energy losses in real supercapacitors in comparison with simulation calculations using both above-mentioned supercapacitor impedance models. The article also discusses the problem of using the equivalent series resistance (ESR) values in RC impedance models, called AC ESR and DC ESR, specified by different supercapacitor manufacturers. It shows that the simulation results using the presented fractional impedance model are the closest to reality. The use of the other discussed models leads to even a several-fold underestimation of energy losses in supercapacitors used in electric energy storage systems.

Słowa kluczowe

EN

supercapacitor; storage system; energy loss; fractional calculus; impedance model

PL

superkondensator; system magazynowania; straty energii; rachunek różniczkowy niecałkowitych rzędów; impedancyjny model

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2025
• Tom: Vol. 73, nr 4
• Strony: art. no. e153841
• Opis fizyczny: Bibliogr. 33 poz., rys., tab., wykr.

Twórcy

autor

Lewandowski Mirosław

• Electrical Power Engineering Institute of the Warsaw University of Technology, Warsaw, Poland

autor

Orzyłowski Marek

• Electrical Power Engineering Institute of the Warsaw University of Technology, Warsaw, Poland

autor

Maciołek Tadeusz

• Electrical Power Engineering Institute of the Warsaw University of Technology, Warsaw, Poland

• https://orcid.org/0000-0001-6955-558X

Bibliografia

• [1] S. Sharma and P. Chand, “Supercapacitor and electrochemical techniques: A brief review,” Res. Chem., vol. 5, p. 1000885, 2023, doi: 10.1016/j.rechem.2023.100885.
• [2] J. Zhang, M. Gu, and X. Chen, “Supercapacitors for renewable energy applications: A review,” Micro Nano Eng, vol. 21, Dec. 2023, doi: 10.1016/j.mne.2023.100229.
• [3] M. Lewandowski, M. Orzylowski, and M. Wieczorek, “Application of supercapacitors in electric traction storage systems,” MATEC Web Conf., vol. 180, pp. 4–9, 2018, doi: 10.1051/matecconf/201818002002.
• [4] M. Lewandowski and M. Orzylowski, “Novel Time Method of Identification of Fractional Model Parameters of Supercapacitor,” Energies (Basel), vol. 13, no. 11, p. 2877, Jun. 2020, doi: 10.3390/en13112877.
• [5] L. Shi and M.L. Crow, “Comparison of ultracapacitor electric circuit models,” IEEE Power and Energy Society 2008 General Meeting: Conversion and Delivery of Electrical Energy in the 21st Century, PES, Jun. 2008, doi: 10.1109/PES.2008.4596576.
• [6] A. Sahin, M.E. Blaaberg, F. Snagwongwanich, “Modelling of Supercapacitors Based on Simplified Equivalent Circuit,” CPSS Trans. Power Electron. Appl., vol. 6, no. 1, pp. 31–39, 2021.
• [7] H. Miniguano, C. Fern, P. Zumel, and L. Antonio, “A General Parameter Identification Procedure Used for the Comparative Study of Supercapacitors Models,” Energies (Basel), vol. 12, p. 1776, 2019, doi: 10.3390/en12091776.
• [8] K.S. Cole and R.H. Cole, “Dispersion and absorption in dielectrics I. Alternating current characteristics,” J. Chem. Phys., vol. 9, no. 4, pp. 341–351, 1941, doi: 10.1063/1.1750906.
• [9] R.H. Cole and W. Davidson W., “Dielectric relaxation in glycerol, propylene glycol, and n-propanol,” J. Chem Phys., vol. 19, no. 12, pp. 1484–1490, Dec. 1951.
• [10] A. Dzieliński, D. Sierociuk, and G. Sarwas, “Some applications of fractional order calculus,” Bull. Pol. Acad. Sci. Tech. Sci., vol. 58, no. 4, pp. 583–592, Dec. 2010, doi: 10.2478/v10175-010-0059-6.
• [11] M. Lewandowski and M. Orzyłowski, “Fractional-order models: The case study of the supercapacitor capacitance measurement,” Bull. Pol. Acad. Sci. Tech. Sci., vol. 65, no. 4, pp. 449–457, 2017, doi: 10.1515/bpasts-2017-0050.
• [12] U. Mehta, R. Prasad, and K. Kothari, “Various Analytical Models for Supercapacitors: a Mathematical Study,” Resour.-Effic. Technol., vol. 1, pp. 1–15, 2020, doi: 10.18799/24056537/2020/1/218.
• [13] M. Lewandowski and M. Orzyłowski, Wybrane zagadnienia modelowania i zastosowania superkondensatorów. Warszawa: Oficyna Wydawnicza Politechniki Warszawskiej, 2021.
• [14] A. Allagui, H. Benaoum, A.S. Elwakil, and M. Alshabi, “Non-Debye impedance and relaxation models for dissipative electrochemical capacitors,” IEEE Trans. Electron Devices, vol. 69, no. 10, pp. 5792–5799, Oct. 2022, doi: 10.1109/TED.2022.3197384.
• [15] T.J. Freeborn, B. Maundy, and A.S. Elwakil, “Fractional-order models of supercapacitors, batteries and fuel cells: A survey,” Mater. Renew. Sustain. Energy., vol. 4, no. 3, pp. 1–7, 2015, doi: 10.1007/s40243-015-0052-y.
• [16] Q. Zhang and K. Wei, “A comparative study of fractional-order models for supercapacitors in electric vehicles,” Int. J. Electrochem. Sci., vol. 19, no. 1, Jan. 2024, doi: 10.1016/j.ijoes.2023.100441.
• [17] C.A. Monje, Fractional-Order Systems and Controls, Fundamentals and Applications. Springer London Dordrecht Heidelberg New York, 2010. doi: 10.1007/978-1-84996-335-0.
• [18] A. Rufer, Energy Storage: Systems and Components, CRC Press, 2018.
• [19] International Standard IEC 62391-1:2022 “Fixed electric double-layer capacitors for use in electronic equipment, Part 1: Generic Application,” International Electrotechnical Commission, Oct. 2022.
• [20] J.L. Déjardin and J. Jadzyn, “Determination of the nonlinear dielectric increment in the Cole-Davidson model,” J. Chem. Phys., vol. 125, no. 11, p. 114503, 2006, doi: 10.1063/1.2346378.
• [21] R. Kopka, “Estimation of Supercapacitor Energy Storage Based on Fractional Differential Equations,” Nanoscale Res. Lett., vol. 12, p. 636, 2017, doi: 10.1186/s11671-017-2396-y.
• [22] J. Sung and C. Shin, “Recent studies on supercapacitors with next-generation structures,” Micromachines, vol. 11, p. 1125; Dec. 2020, doi: 10.3390/mi11121125.
• [23] P. Galek, A. Slesinski, K. Fic, and J. Menzel, “Peculiar role of the electrolyte viscosity in the electrochemical capacitor performance,” J. Mater. Chem. A Mater., vol. 9, no. 13, pp. 8644–8654, Apr. 2021, doi: 10.1039/d0ta11230e.
• [24] L. Kexue and P. Jigen, “Laplace transform and fractional differential equations,” Appl. Math. Lett., vol. 24, no. 12, pp. 2019–2023, Dec. 2011, doi: 10.1016/j.aml.2011.05.035.
• [25] J. Sabatier and C. Farges, “Initial value problems should not be associated to fractional model descriptions whatever the derivative definition used,” AIMS Math., vol. 6, no. 10, pp. 11318–11329, 2021, doi: 10.3934/math.2021657.
• [26] X.D. Chen and I. Petras, “Fractional Order Control – A Tutorial,” Proceedings of 2009 American Control Conference, pp. 1397–1411, 2009.
• [27] IOXUS, “Representative Test Procedures for Customer Evaluations,” no. 7–105, 2015. [Online] available at: https://www.rellpower.com/wp/wp-content/uploads/2015/07/Ioxus-Test-Procedures-for-Customer-Evaluations.pdf
• [28] LS Mitron, “TEST METHOD 1) Capacitance 2) DC ESR 3) Leakage Current 4) Self-Discharge.” [Online] available at: https://www.lsmaterials.co.kr/_common/download.asp?menucat=upYDsKYx&fname=fHTxgHXyfmj5kI4zg003g1cVeLUIsE
• [29] CAP-XX, “GA109 / GA209 Supercapacitor,” October, pp. 2–9, 2015. [Online] available at: https://www.cap-xx.com/wp-content/uploads/datasheets/CAP-XX-GA109-GA209-Datasheet.pdf
• [30] Skeleton Technologies, “Instructions for Testing of Skeleton Technologies’ Ultracapacitors,” [Online] available at: https://www.skeletontech.com/downloads
• [31] Maxwell, “Test Procedures for Capacitance, ESR, Leakage Current and Self-Discharge Characterizations of Ultracapacitorse,”2015.
• [32] G. Xiong, A. Kundu, and T.S. Fisher, Thermal Effects in Supercapacitors. Springer, 2015, doi: 10.1007/978-3-319-20242-6.
• [33] E. Pameté et al., “The Many Deaths of Supercapacitors: Degradation, Aging, and Performance Fading,” Adv. Energy Mater.,vol. 13, no. 29, p. 2301008, Aug. 2023, doi: 10.1002/aenm.202301008.

Uwagi

We would like to thank the Warsaw University of Technology for partial support of this work with a grant in the discipline of Automation, Electronics, Electrical Engineering, and Space Technologies entitled “Research on the energy efficiency of supercapacitors – proper selection of parameters in the energy storage”.