Articles
A fractional operator model to describe the supercapacitors dynamic
Rodrigo Correa
Published 2020-05-11
Keywords
- supercapacitors,
- conformable derivative,
- equivalent circuit,
- experimental validation,
- conformable operator
How to Cite
Mendoza Contreras, D. S., Solano, J., & Correa, R. (2020). A fractional operator model to describe the supercapacitors dynamic. Revista UIS Ingenierías, 19(3), 79–86. https://doi.org/10.18273/revuin.v19n3-2020008
Copyright (c) 2020 Revista UIS Ingenierías
This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.
Abstract
This paper proposes a new equivalent circuit to model supercapacitors. The proposed circuit is an array of RC branches described by differential conformable fractional derivative equations. A parameter identification algorithm based on experimental data is implemented. Validation results using experimental data show that the proposed equivalent circuit can be used to model the real behavior of the supercapacitors.
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References
[1] C. Abbey, G. Joos, “Supercapacitor Energy Storage for Wind Energy Applications,” IEEE Transactions on Industry Applications, vol. 43, no. 3, pp. 769-776, 2007, doi:
10.1109/TIA.2007.895768
[2] J. Pegueroles-Queralt, F. D. Bianchi, O. Gomis-Bellmunt, “A Power Smoothing System Based on Supercapacitors for Renewable Distributed Generation,” IEEE Transactions on Industrial Electronics, vol. 62, no. 1, pp. 343 - 350, 2015, doi: 10.1109/TIE.2014.2327554
[3] N. R. Tummuru, M. K. Mishra, S. Srinivas, “Dynamic energy management of renewable grid integrated hybrid energy storage system,” IEEE Transactions on Industrial Electronics, vol. 62, no. 12, pp. 7728–7737, 2015, doi: 10.1016/j.energy.2018.08.016
[4] J. S. Martínez, J. Mulot, F. Harel, D. Hissel, M.C. Pera, R. I. John, M. Amiet, “Experimental validation of a type-2 fuzzy logic controller for energy management in hybrid electrical vehicles,” Engineering Applications of Artificial Intelligence, vol. 26, no. 7, pp. 1772–1779, 2013, doi: 10.1016/j.engappai.2012.12.008
[5] W. Lhomme et al., “IEEE VTS Motor Vehicles Challenge 2019 - Energy Management of a Dual-Mode Locomotive,” 2018 IEEE Vehicle Power and Propulsion Conference (VPPC), Chicago, IL, 2018, pp. 1-6, doi: 10.1109/VPPC.2018.8605044
[6] A. Lahyani, P. Venet, A. Guermazi, A. Troudi, "Battery/Supercapacitors Combination in Uninterruptible Power Supply (UPS),” IEEE Transactions on Power Electronics, vol. 28, no. 4, pp. 1509-1522, 2013, doi: 10.1109/TPEL.2012.2210736
[7] L. Zubieta, R. Bonert, “Characterization of double-layer capacitors (DLCs) for power electronics applications,” Conference Record of 1998 IEEE Industry Applications Conference. Thirty-Third IAS Annual Meeting (Cat. No.98CH36242), St. Louis, MO, USA, 1998, pp. 1149 - 1154 vol. 2, doi: 10.1109/IAS.1998.730292
[8] J. Solano, D. Hissel, M. Pera, “Modeling and Parameter Identification of Ultracapacitors for Hybrid Electrical Vehicles,” 2013 IEEE Vehicle Power and Propulsion Conference (VPPC), Beijing, 2013, pp. 1-4, doi: 10.1109/VPPC.2013.6671692
[9] J. Tian, R. Xiong, Q. Yu, “Fractional-Order Model-Based Incremental Capacity Analysis for Degradation State Recognition of Lithium-Ion Batteries,” IEEE Transactions on Industrial Electronics, vol. 66, no. 2, pp. 1576-1584, 2019, doi: 10.1109/TIE.2018.2798606
[10] L. Martinez, J. Rosales, C. Carreño, J. Lozano, “Electrical circuits described by fractional conformable derivative,” International Journal of Circuit Theory and Applications, vol. 46, no. 5, pp. 1091–1100, 2018, doi: 10.1002/cta.2475
[11] V. Morales-Delgado, J. Gómez-Aguilar, M. TanecoHernandez, “Analytical solutions of electrical circuits described by fractional conformable derivatives in liouville-caputo sense,” AEU-International Journal of Electronics and Communications, vol. 85, pp. 108–117, 2018, doi: /10.1016/j.aeue.2017.12.031
[12] E. C. de Oliveira, J. A. T. Machado, “A review of definitions for fractional derivatives and integral,” Mathematical Problems in Engineering, vol. 2014, pp. 1–6, 2014, doi: 10.1155/2014/238459
[13] G. S. Teodoro, J. T. Machado, E. C. de Oliveira, “A review of definitions of fractional derivatives and other operators,” Journal of Computational Physics, vol. 388, pp. 195 - 208, 2019, doi: 10.1016/j.jcp.2019.03.008
[14] M. Caputo, M. Fabrizio, “A new definition of fractional derivative without singular kernel,” Progr. Fract. Differ. Appl, vol. 1, no. 2, pp. 1–13, 2015, doi: 10.12785/pfda/010201
[15] R. Khalil, M. Al Horani, A. Yousef, M. Sababheh, “A new definition of fractional derivative,” Journal of Computational and Applied Mathematics, vol. 264, pp. 65–70, 2014, doi: 10.1016/j.cam.2014.01.002
[16] A. Pandolfo, A. Hollenkamp, “Carbon properties and their role in supercapacitors,” Journal of power sources, vol. 157, no. 1, pp. 11–27, 2006, doi: 10.1016/j.jpowsour.2006.02.065
10.1109/TIA.2007.895768
[2] J. Pegueroles-Queralt, F. D. Bianchi, O. Gomis-Bellmunt, “A Power Smoothing System Based on Supercapacitors for Renewable Distributed Generation,” IEEE Transactions on Industrial Electronics, vol. 62, no. 1, pp. 343 - 350, 2015, doi: 10.1109/TIE.2014.2327554
[3] N. R. Tummuru, M. K. Mishra, S. Srinivas, “Dynamic energy management of renewable grid integrated hybrid energy storage system,” IEEE Transactions on Industrial Electronics, vol. 62, no. 12, pp. 7728–7737, 2015, doi: 10.1016/j.energy.2018.08.016
[4] J. S. Martínez, J. Mulot, F. Harel, D. Hissel, M.C. Pera, R. I. John, M. Amiet, “Experimental validation of a type-2 fuzzy logic controller for energy management in hybrid electrical vehicles,” Engineering Applications of Artificial Intelligence, vol. 26, no. 7, pp. 1772–1779, 2013, doi: 10.1016/j.engappai.2012.12.008
[5] W. Lhomme et al., “IEEE VTS Motor Vehicles Challenge 2019 - Energy Management of a Dual-Mode Locomotive,” 2018 IEEE Vehicle Power and Propulsion Conference (VPPC), Chicago, IL, 2018, pp. 1-6, doi: 10.1109/VPPC.2018.8605044
[6] A. Lahyani, P. Venet, A. Guermazi, A. Troudi, "Battery/Supercapacitors Combination in Uninterruptible Power Supply (UPS),” IEEE Transactions on Power Electronics, vol. 28, no. 4, pp. 1509-1522, 2013, doi: 10.1109/TPEL.2012.2210736
[7] L. Zubieta, R. Bonert, “Characterization of double-layer capacitors (DLCs) for power electronics applications,” Conference Record of 1998 IEEE Industry Applications Conference. Thirty-Third IAS Annual Meeting (Cat. No.98CH36242), St. Louis, MO, USA, 1998, pp. 1149 - 1154 vol. 2, doi: 10.1109/IAS.1998.730292
[8] J. Solano, D. Hissel, M. Pera, “Modeling and Parameter Identification of Ultracapacitors for Hybrid Electrical Vehicles,” 2013 IEEE Vehicle Power and Propulsion Conference (VPPC), Beijing, 2013, pp. 1-4, doi: 10.1109/VPPC.2013.6671692
[9] J. Tian, R. Xiong, Q. Yu, “Fractional-Order Model-Based Incremental Capacity Analysis for Degradation State Recognition of Lithium-Ion Batteries,” IEEE Transactions on Industrial Electronics, vol. 66, no. 2, pp. 1576-1584, 2019, doi: 10.1109/TIE.2018.2798606
[10] L. Martinez, J. Rosales, C. Carreño, J. Lozano, “Electrical circuits described by fractional conformable derivative,” International Journal of Circuit Theory and Applications, vol. 46, no. 5, pp. 1091–1100, 2018, doi: 10.1002/cta.2475
[11] V. Morales-Delgado, J. Gómez-Aguilar, M. TanecoHernandez, “Analytical solutions of electrical circuits described by fractional conformable derivatives in liouville-caputo sense,” AEU-International Journal of Electronics and Communications, vol. 85, pp. 108–117, 2018, doi: /10.1016/j.aeue.2017.12.031
[12] E. C. de Oliveira, J. A. T. Machado, “A review of definitions for fractional derivatives and integral,” Mathematical Problems in Engineering, vol. 2014, pp. 1–6, 2014, doi: 10.1155/2014/238459
[13] G. S. Teodoro, J. T. Machado, E. C. de Oliveira, “A review of definitions of fractional derivatives and other operators,” Journal of Computational Physics, vol. 388, pp. 195 - 208, 2019, doi: 10.1016/j.jcp.2019.03.008
[14] M. Caputo, M. Fabrizio, “A new definition of fractional derivative without singular kernel,” Progr. Fract. Differ. Appl, vol. 1, no. 2, pp. 1–13, 2015, doi: 10.12785/pfda/010201
[15] R. Khalil, M. Al Horani, A. Yousef, M. Sababheh, “A new definition of fractional derivative,” Journal of Computational and Applied Mathematics, vol. 264, pp. 65–70, 2014, doi: 10.1016/j.cam.2014.01.002
[16] A. Pandolfo, A. Hollenkamp, “Carbon properties and their role in supercapacitors,” Journal of power sources, vol. 157, no. 1, pp. 11–27, 2006, doi: 10.1016/j.jpowsour.2006.02.065