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Fractional techniques to characterize non-solid aluminum electrolytic capacitors for power electronic applications

  • Xi ChenEmail author
  • Lei Xi
  • Yunning Zhang
  • Hui Ma
  • Yuehua Huang
  • Yangquan Chen
Original paper
  • 79 Downloads

Abstract

Non-solid aluminum electrolytic capacitors are one type of reliability-critical components, and they are widely adopted in power electronic converters. The capacitance and equivalent series resistance of these components have significant effects on the performance and reliability of power electronic systems. In this work, by exploring the electrochemical principles of aluminum electrolytic capacitors, the fractional-order (FO) characteristics of the capacitors are revealed, according to which the frequency-dependent parameters of this kind of components are expressed by FO models, while the parameters of the models are estimated by a multi-objective optimization algorithm. Under the same conditions such as the number of arguments supplied and optimization algorithm, the proposed models perform better. Additionally, to show further applications of fractional techniques, a brief example on the output ripple analysis of DC–DC converters is offered, in which one of the proposed FO models of the capacitor is adopted. The effectiveness and superiority of the techniques for predicting the states of the converters are confirmed by comparison with traditional models.

Keywords

Aluminum electrolytic capacitors Fractional order (FO) Multi-objective optimization algorithm DC–DC converters 

Notes

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. 1.
    Yang, S., Bryant, A., Mawby, P., Xiang, D., Ran, L., Tavner, P.: An industry-based survey of reliability in power electronic converters. IEEE Trans. Ind. Appl. 47(3), 1441–1451 (2011)CrossRefGoogle Scholar
  2. 2.
    Zhu, B., Zeng, Q., Chen, Y., Zhao, Y., Liu, S.: A dual input high step Up DC–DC converter with ZVT auxiliary circuit. IEEE Trans. Energy Convers. 34(1), 161–169 (2019)CrossRefGoogle Scholar
  3. 3.
    Xi, L., Chen, J., Huang, Y., Yanchun, X., Liu, L., Zhou, Y., Li, Y.: Smart generation control based on multi-agent reinforcement learning with the idea of the time tunnel. Energy 153, 977–987 (2018)CrossRefGoogle Scholar
  4. 4.
    Both, J.: The modern era of aluminum electrolytic capacitors. IEEE Electr. Insul. Mag. 31(4), 24–34 (2015)CrossRefGoogle Scholar
  5. 5.
    Nichicon: General description of aluminum electrolytic capacitors. [Online]. https://www.nichicon.co.jp/english/products/pdf/aluminum.pdf. Accessed Apr 2017
  6. 6.
    Rubycon: Manufacture of alumunim electrolytic capacitor. [Online]. http://www.rubycon.co.jp/de/products/alumi/pdf/Process.pdf. Accessed Sept 2017
  7. 7.
    Bard, A.J., Faulkner, L.R., Methods, E.: Fundamentals and Applications, 2nd edn. Wiley, New York (2000)Google Scholar
  8. 8.
    Imam, A.M.: Condition monitoring of electrolytic capacitors for power electronics applications. Ph.D. dissertation, Georgia Institute of Technology (2007)Google Scholar
  9. 9.
    Malek, H., Dadras, S., Chen, Y.: Fractional order equivalent series resistance modeling of electrolytic capacitor and fractional order failure prediction with application to predictive maintenance. IET Power Electron. 9(8), 1608–1613 (2016)CrossRefGoogle Scholar
  10. 10.
    Cheng, K.-Y., Yu, F., Lee, F.C., Mattavelli, P.: Digital enhanced \(V^2\)-type constant on-time control using inductor current ramp estimation for a buck converter with low-ESR capacitors. IEEE Trans. Power Electron. 28(3), 1241–1252 (2013)CrossRefGoogle Scholar
  11. 11.
    Sundararajan, P., Sathik, M.H.M., Sasongko, F., Tan, C.S., Tariq, M., Simanjorang, R.: Online condition monitoring system for DC-link capacitor in industrial power converters. IEEE Trans. Ind. Appl. 54(5), 4775–4785 (2018)CrossRefGoogle Scholar
  12. 12.
    Hammam Soliman, H., Blaabjerg, W.F.: A review of the condition monitoring of capacitors in power electronics converters. IEEE Trans. Ind. Appl. 52(6), 4976–4989 (2016)CrossRefGoogle Scholar
  13. 13.
    Xu, N., Riley, J.: Nonlinear analysis of a classical system: the double-layer capacitor. Electrochem. Commun. 13(10), 1077–1081 (2011)CrossRefGoogle Scholar
  14. 14.
    Simon, P., Gogotsi, Y., Dunn, B.: Where do batteries end and supercapacitors begin? Science 343, 1210–1211 (2014)CrossRefGoogle Scholar
  15. 15.
    Costentin, C., Porter, T.R., Savéant, J.-M.: How do pseudocapacitors store energy? Theoretical analysis and experimental illustration. ACS Appl. Mater. Interfaces 9(10), 8649–8658 (2017)CrossRefGoogle Scholar
  16. 16.
    Forse, A.C., Merlet, C., Griffin, J.M., Grey, C.P., Savéant, J.-M.: How do pseudocapacitors store energy? Theoretical analysis and experimental illustration. J. Am. Chem. Soc. 138(18), 5731–5744 (2016)CrossRefGoogle Scholar
  17. 17.
    Prehal, C., Koczwara, C., et al.: Quantification of ion confinement and desolvation in nanoporous carbon supercapacitors with modelling and in situ X-ray scattering. Nat. Energy 2(3), 16215 (2017)CrossRefGoogle Scholar
  18. 18.
    TDK: Aluminum electrolytic capacitors: general technical information. [Online] (2017). https://www.tdk-electronics.tdk.com/download/530704/5f33d2619fa73419e2a4af562122e90c/pdf-generaltechnicalinformation.pdf. Accessed July 2018
  19. 19.
    Cheng, K.Y., Yu, F., Mattavelli, P., Lee, F.C.: Digital enhanced V2-type constant on-time control using inductor current ramp estimator for a buck converter with small ESR capacitors. In: 2010 IEEE Energy Conversion Congress and Exposition, Atlanta, GA, pp. 508–513 (2010)Google Scholar
  20. 20.
    Leyva-Ramos, J., Ortiz-Lopez, M.G., Diaz-Saldierna, L.H.: The effect of ESR of the capacitors on modeling of a quadratic boost converter. In: 2008 11th Workshop on Control and Modeling for Power Electronics, Zurich, pp. 1–5 (2008)Google Scholar
  21. 21.
    Bao, B.C., Yang, J., Xu, J.P., Zhang, X., Zhou, G.H.: Effect of output capacitor ESR on dynamic performance of voltage-mode hysteretic controlled buck converter. Electron. Lett. 49(20), 1293–1294 (2013)CrossRefGoogle Scholar
  22. 22.
    Braham, A., Lahyani, A., Venet, P., Rejeb, N.: Recent developments in fault detection and power loss estimation of electrolytic capacitors. IEEE Trans. Power Electron. 25(1), 33–43 (2010)CrossRefGoogle Scholar
  23. 23.
    Abdennadher, K., Venet, P., Rojat, G., Retif, J.-M., Rosset, C.: A real-time predictive-maintenance system of aluminum electrolytic capacitors used in uninterrupted power supplies. IEEE Trans. Ind. Appl. 46(4), 1644–1652 (2010)CrossRefGoogle Scholar
  24. 24.
    Zhao, K., Ciufo, P., Perera, S.: Rectifier capacitor filter stress analysis when subject to regular voltage fluctuations. IEEE Trans. Power Electron. 28(7), 3627–3635 (2013)CrossRefGoogle Scholar
  25. 25.
    Kieferndorf, F.D., Forster, M., Lipo, T.A.: Reduction of DC-bus capacitor ripple current with PAM/PWM converter. IEEE Trans. Ind. Appl. 4(2), 607–614 (2004)CrossRefGoogle Scholar
  26. 26.
    KEMET: Surface mount capacitors. [Online]. http://www.dialelectrolux.ru/files/file/Kemet/f3102.pdf. Accessed July 2018
  27. 27.
    CDM Cornell Dubilier: Aluminum electrolytic capacitor application guide. [Online]. http://www.cde.com/resources/catalogs/AEappGUIDE.pdf. Accessed July 2018
  28. 28.
    Parler, S.G.: Improved spice models of aluminum electrolytic capacitors for inverter applications. IEEE Trans. Ind. Appl. 39(4), 929–935 (2003)CrossRefGoogle Scholar
  29. 29.
    Podlubny, I.: Fractional Differential Equations. Academic Press, London (1998)zbMATHGoogle Scholar
  30. 30.
    Elwakil, A.S.: Fractional-order circuits and systems: an emerging interdisciplinary research area. IEEE Circuits Syst. Mag. 10(4), 40–50 (2010)CrossRefGoogle Scholar
  31. 31.
    Petrás̆, I.: Fractional-Order Nonlinear Systems. Springer, Berlin (2011)CrossRefGoogle Scholar
  32. 32.
    Si, G., Zhu, J., Diao, L., Ding, Z.: Modeling, nonlinear dynamic analysis and control of fractional PMSG of wind turbine. Nonlinear Dyn. 88, 1608–1613 (2016)Google Scholar
  33. 33.
    Chen, X., Chen, Y., Zhang, B., Qiu, D.: A modeling and analysis method for fractional-order DC–DC converters. IEEE Trans. Power Electron. 32(9), 7034–7044 (2017)CrossRefGoogle Scholar
  34. 34.
    Westerlund, S., Ekstam, L.: Capacitor theory. IEEE Trans. Dielectr. Electr. Insul. 1(5), 826–839 (1994)CrossRefGoogle Scholar
  35. 35.
    Mark, E.: Orazem Bernard Tribollet, Electrochemical Impedance Spectroscopy, Chapter 13: Time-Constant Dispersion. Wiley, London (2008)Google Scholar
  36. 36.
    Sabatier, J., Cugnet, M., Laruelle, S., Grugeon, S., Sahut, B., Oustaloup, A., Tarascon, J.M.: A fractional order model for lead-acid battery crankability estimation. Commun. Nonlinear Sci. Numer. Simul. 15(5), 1308–1317 (2010)CrossRefGoogle Scholar
  37. 37.
    Jun, X., Mi, C., Cao, B., Cao, J.: A new method to estimate the state of charge of lithium-ion batteries based on the battery impedance model. J. Power Sources 233, 277–284 (2013)CrossRefGoogle Scholar
  38. 38.
    Wang, B., Liu, Z., Li, S.E., Moura, S.J., Peng, H.: Fractional modeling and SOC estimation of lithium-ion battery. IEEE Trans. Control Syst. Technol. 25(1), 3–11 (2017)CrossRefGoogle Scholar
  39. 39.
    Hao, M., Xiong, R., Zheng, H., Chang, Y., Chen, Z.: A novel fractional order model based state-of-charge estimation method for lithium-ion battery. Appl. Energy 207, 384–393 (2017)CrossRefGoogle Scholar
  40. 40.
    Bertrand, N., Sabatier, J., Briat, O., Vinassa, J.M.: Embedded fractional nonlinear supercapacitor model and its parametric estimation method. IEEE Trans. Ind. Electron. 57(12), 3991–4000 (2010)CrossRefGoogle Scholar
  41. 41.
    Kumar, M.R., Ghosh, S., Das, S.: Frequency dependent piecewise fractional-order modelling of ultracapacitors using hybrid optimization and fuzzy clustering. J. Power Sources 335, 98–104 (2016)CrossRefGoogle Scholar
  42. 42.
    Reichbach, N., Kuperman, A.: Recursive-least-squares-based real-time estimation of supercapacitor parameters. IEEE Trans. Energy Convers. 31(2), 810–812 (2016)CrossRefGoogle Scholar
  43. 43.
    Leyden, K., Goodwine, B.: Fractional-order system indentificaiton for health monitoring. Nonlinear Dyn. 92, 1317–1334 (2018)CrossRefGoogle Scholar
  44. 44.
    Allafi, W., Zajic, I., Uddin, K., Shen, Z., Marco, J., Burnham, K.: Design of delayed fractional state variable filter for parameter estimation of fractional nonlinear models. Nonlinear Dyn. 94(4), 2697–2713 (2018)CrossRefGoogle Scholar
  45. 45.
    Price, K.V., Storn, R.M., Lampinen, J.A., Evolution, D.: A Practical Approach to Global Optimization. Springer, Berlin (2005)zbMATHGoogle Scholar
  46. 46.
    Wang, W., Yang, S., Lin, Q., Zhang, Q., Wong, K.-C., Coello, C.A.C., Chen, J.: An effective ensemble framework for multi-objective optimization. IEEE Trans. Evol. Comput. 23(4), 645–659 (2019)CrossRefGoogle Scholar
  47. 47.
    Coello, C.A.C.: Theoretical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art. Comput. Methods Appl. Mech. Eng. 191(11), 1245–1287 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  48. 48.
    Erickson, R.W., Maksimovic, D.: Fundamentals of Power Electronics. Springer, New York (2001)CrossRefGoogle Scholar
  49. 49.
    Diethelm, K., Ford, N., Freed, A.: A predictor–corrector approach for the numerical solution of fractional differential equations. Nonlinear Dyn. 29, 3–22 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  50. 50.
    Rubycon: Radial lead aluminum electrolytic capacitors: PX series. [Online]. http://www.rubycon.co.jp/en/catalog/e_pdfs/aluminum/e_px.pdf. Accessed July 2018
  51. 51.
    Li, M., Zhang, B., Qiu, D., Zhang, G.: Sneak circuit phenomena in a DCM boost converter considering parasitic parameters. IEEE Trans. Power Electron. 32(5), 3946–3958 (2017)CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.College of Electrical Engineering and New EnergyChina Three Gorges UniversityYichangChina
  2. 2.School of EngineeringUniversity of CaliforniaMercedUSA

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