Izvestiya of Saratov University.

Physics

ISSN 1817-3020 (Print)
ISSN 2542-193X (Online)

For citation:

Anishchenko V. S., Ebeling W., Hass E., Plath P., Shimansky-Geier L., Strelkova G. I. Modeling battery systems – problems of nonlinearity, efficiency, aging, coupling, and network setup. Izvestiya of Saratov University. Physics , 2022, vol. 22, iss. 4, pp. 288-309. DOI: 10.18500/1817-3020-2022-22-4-288-309, EDN: GLCHRL

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
30.11.2022
Full text:
download
(downloads: 101)
Language: 
English
Heading: 
Radiophysics, electronics, acoustics
Article type: 
Article
UDC: 
621.354.36
DOI: 
10.18500/1817-3020-2022-22-4-288-309
EDN: 
GLCHRL

Modeling battery systems – problems of nonlinearity, efficiency, aging, coupling, and network setup

Autors: 
Anishchenko Vadim Semenovich, Saratov State University
Ebeling Werner, Humboldt University of Berlin
Hass Ernst-Christoph, University of Bremen
Plath Peter, Fritz-Haber-Institut der Max-Planck-Gesellschaft
Shimansky-Geier Lutz, Humboldt University of Berlin
Strelkova Galina Ivanovna, Saratov State University
Abstract: 

We discuss several problems of batteries and fuel cells from the point of view of nonlinear dynamics and review some earlier work on modeling this class of systems as well as new developments. We consider batteries and fuel cells as active nonlinear electrochemical circuits with properties depending on many factors as load, age, load history etc. We show that most satisfactory battery regimes are reached by coupling of an odd number of circuits in opposite phases. Specific points of discussion are types of dynamic regimes and the efficiency of the conversion of chemical into electrical energy in dependence on the work load, the life cycles of batteries, including installation, work under load, aging and decay. Further we discuss specific properties of managing battery networks, in particular the cycle of replacing of old batteries by fresh ones including the optimization of this cycle. The last part of this work is merely a list of open tasks to be elaborated.

Key words: 
battery
load
aging
battery networks
nonlinearity
efficiency
Acknowledgments: 
The authors thank U. Erdmann, R. Feistel, B. Lindner, P. Romanczuk and F. Schweitzer for basic common work about active dynamical systems and E. Hildebrandt as well as I. Sokolov for discussions about fractional dynamical models and references.
Reference: 
  1. Hass E.-C., Knicker K., Sydow U., Schulz M., Plath P.-J. Battery – determination and forecast via Synergetics. In: Müller S. C., Plath P. J., Radons G., Fuchs A., eds. Complexity and Synergetics. Springer International Publishing AG, 2018, pp. 139–153. https://doi.org/10.1007/978-3-319-64334-2_12
  2. Arena P., Caponetto R., Fortuna L., Porto D. Nonlinear Noninteger Order Circuits and Systems – An Introduction. World Scientific, Singapore, 2000. 212 p. https://doi.org/10.1142/4507
  3. Anishchenko V. S., Astakhov V., Vadivasova T., Neiman A., Schimansky-Geier L. Nonlinear Dynamics of Chaotic and Stochastic Systems. Springer, 2007. 449 p. https://doi.org/10.1007/978-3-540-38168-6
  4. Newman J. S. Electrochemical Systems. 2nd edition. Englewood Cliffs, Prentice Hall, NJ, 1991. 560 p.; Newman J. S., Thomas-Alyea K. E. Electrochemical Systems. 3rd edition. Englewood Cliffs, Prentice Hall, NJ, 2004. 648 p.
  5. Chaturvedi N., Klein R., Christensen J., Ahmed J., Kojic A. Algorithms for advanced battery management systems. IEEE Control Systems Magazine, 2010, vol. 30, no. 3, pp. 49–68. https://doi.org/10.1109/MCS.2010.936293
  6. Romanczuk P. Bär M., Ebeling W., Lindner B., Schimansky-Geier L. Active Brownian Particles. From Individual to Collective Stochastic Dynamics. Eur. Phys. J. Special Topics, 2012, vol. 202, no. 1, pp. 1–162. https://doi.org/10.1140/epjst/e2012-01529-y
  7. Bachmann J. E. Fuel Cells. https://wiki.uiowa.edu/display/greenergy/Fuel+Cells
  8. Rychcik M., Skyllas-Kazacos M. Characteristics of a new all-vanadium redox flow battery, J. of Power Sources, 1988, vol. 22, iss. 1, pp. 59–67. https://doi.org/10.1016/0378-7753(88)80005-3
  9. Ebeling W., Feistel R. Energy conversion in isothermal nonlinear irreversible processes – struggling for higher efficiency. Eur. Phys. J. Special Topics, 2017, vol. 226, no. 9, pp. 2015–2030. https://doi.org/10.1140/epjst/e2017-70014-2
  10. Joeriseen L., Garche J., Fabjan Ch., Tamozic G. Possible use of vanadium redox-flow batteries for energy storage in small grids and stand-alone photovoltaic systems. J. of Power Sources, 2004, vol. 127, iss. 1, pp. 98–104. https://doi.org/10.1016/j.jpowsour.2003.09.066
  11. Gupta S., Lim T. M., Mushrif S. H. Insights into the solvation of vanadium ions in the vanadium redox flow battery electrolyte using molecular dynamics and metadynamics. Electrochimica Acta, 2018, vol. 270, pp. 471–479. https://doi.org/10.1016/j.electacta.2018.03.008
  12. Afif A., Radenahmad N., Cheok Q., Shams S., Kim J. H. Ammonia-fed fuel cells: A comprehensive review. Renewable and Sustainable Energy Reviews, 2016, vol. 60, iss. C, pp. 822–835. https://doi.org/10.1016/j.rser.2016.01.120
  13. Wang S., Fernandez C., Chunmei Y., Yongcun F., Wen C., Stroe D.-I., Chen Z. Battery System Modeling. Elsevier, 2021. 347 p. https://doi.org/10.1016/C2020-0-03232-9
  14. Eckert M. Modellbasierte Identifikation fraktionaler Systeme und Ihre Anwendung auf die Lithium-Ionen-Zelle. KIT Scientific Publishing, Karlsruhe, 2017. 258 S. https://doi.org/10.5445/KSP/1000071542
  15. Wang B., Liu Z., Li S. E., Moura S. J., Peng H. State-of-Charge estimation for Lithium-Ion batteries based on a nonlinear fractional model. IEEE Transactions on Control Systems Technology, 2017, vol. 25, iss. 1, pp. 3–11. https://doi.org/10.1109/TCST.2016.2557221
  16. Ebeling W., Schweitzer F., Tilch B. Active Brownian motion with energy depots modeling animal mobility. Biosystems, 1999, vol. 49, no. 1, pp. 17–29. https://doi.org/10.1016/s0303-2647(98)00027-6
  17. Tilch B., Schweitzer F., Ebeling W. Directed motion of Brownian particles with internal energy depot. Physica A, 1999, vol. 273, iss. 3–4, pp. 293–314. https://doi.org/10.1016/S0378-4371(99)00247-2
  18. Li D., Sun Y., Yang Z., Gu L., Chen Y., Zhou H. Electrochemical oscillation in Li-ion batteries. Joule (Cell Press), 2018, vol. 2, pp. 1265–1277. https://doi.org/10.1016/j.joule.2018.03.014
  19. Schweitzer P., Ebeling W., Tilch B. Complex Motion of Brownian Particles with Energy Depots. Phys. Rev. Lett., 1998, vol. 80, pp. 5044. https://doi.org/10.1103/PhysRevLett.80.5044
  20. Erdmann U., Ebeling W., Schimansky-Geier L., Schweitzer F. Brownian particles far from equilibrium. Eur. Phys. J. B, 2000, vol. 15, pp. 105–113. https://doi.org/10.1007/s100510051104
  21. Romanovsky Yu. M., Kargovsky A., Ebeling W. Models of Active Brownian Motors Based on Internal Oscillations. Eur. Phys. J. Special Topics, 2013, vol. 222, pp. 2465–2479. https://doi.org/10.1140/epjst/e2013-02030-y
  22. Kolomeisky A. B., Fisher M. E. Molecular Motors: A Theorist’s Perspective. Annual Rev. of Phys. Chem., 2007, vol. 58, pp. 675–695. https://doi.org/10.1146/annurev.physchem.58.032806.104532
  23. Ebeling W., Gudowska-Nowak E., Fiasaconaro A. Statistical distribution for Hamiltonian systems coupled to energy reservoirs and applications to molecular energy conversion. Acta Phys. Pol. B, 2008, vol. 39, no. 5, pp. 1251–1272.
  24. Toyabe S., Muneyuki E. Experimental thermodynamics of single molecular motor. Biophysics, 2013, vol. 9, pp. 91–98. https://doi.org/10.2142/biophysics.9.91
  25. Nishiyama M., Higuchi H., Yanagida T. Chemomechanical coupling of the forward and backward steps of single kinesin molecules. Nature Cell Biol., 2002, vol. 4, pp. 790–797. https://doi.org/10.1038/ncb857
  26. Harada T. Phenomenological energetics for molecular motors. Europhys. Lett., 2005, vol. 70, no. 1, pp. 49–55. https://doi.org/10.1209/epl/i2004-10456-2
  27. Richter P. H., Ross J. The efficiency of engines operating around a steady state at finite frequencies. J. Chem. Phys., 1978, vol. 69, pp. 5521–5531. https://doi.org/10.1063/1.436546
  28. Lipowsky R. Universal aspects of the chemomechanical coupling for molecular motors. Phys. Rev. Lett., 2000, vol. 85, pp. 4401. https://doi.org/10.1103/PhysRevLett.85.4401
  29. Feistel R., Ebeling W. Physics of self-organization and evolution. Wiley-VCH, Weinheim, 2011. 517 p. https://doi.org/10.1002/9783527636792
  30. Schweitzer F. Brownian agents and active particles. Springer, 2003. 420 p. https://doi.org/10.1007/978-3-540-73845-9
  31. Balmer R. T. Modern Engineering Thermodynamics. Academic Press, Elsevier, 2011. 827 p. https://doi.org/10.1016/C2009-0-20199-1
  32. Barbosa R. S., Tenreiro Machado J. A., Vinagre B. M., Calderon A. J. Analysis of the van der Pol oscillator containing derivatives of fractional order. J. of Vibration and Control, 2007, vol. 13, iss. 9–10, pp. 1291–1301. https://doi.org/10.1177/1077546307077463
  33. Ebeling W., Engel A., Feistel R. Physik der Evolution-sprozesse. Akademie-Verlag, Berlin, 1990. 371 S.
  34. Ebeling W., Feistel R. Studies on Manfred Eigen’s Model for the Self-Organization of Information processing. Eur. Biophys. J., 2018, vol. 47, pp. 395–401. https://doi.org/10.1007/s00249-018-1287-1
  35. Ebeling W., Schimansky-Geier L., Poeschel T., Asselmeyer T., Beule D., Buchholtz V., Erdmann U., Kappler C., Lieske R., Militzer B., Neiman A., Rose H. Rosenkranz D., Schautz F., Tilch B., Zamparelli M. Evolutionary algorithms, EVOAL G. Foundations and applications of evolutionary algorithms. Final report, BMBF 01IB403B. https://hdl.handle.net/10068/153803(1998)
  36. Ebeling W., Rechenberg I., Schwefel H.-P., Voigt H.-M., eds. Parallel Problem Solving from Nature. PPSN IV, vol. 1141. Springer, 1996. 1076 p.
  37. Bäck T., Heistermann T., Kappler C., Zamparelli M. Evolutionary Algorithms Support Refueling of Pressurized Water Reactors. Conference Paper, Research Gate, 1996. https://doi.org/10.1109/ICEC.1996.542342
  38. Grolleau S., Delaille A., Gualous A. Lithium-ion battery aging. 27th Int. Electric Vehicle Symp. Barcelona, 2013.
  39. Romanovsky Yu. M., Stepanova N. V., Chernavsky D. Mathematical Biophysics. Moscow, Nauka Publ.,1984. 304 p. (in Russian).
  40. Ebeling W., Engel A., Mazenko V. G. Modeling of selection processes with age-dependent birth and death rates. Biosystems, 1986, vol. 19, iss. 3, pp. 213–221. https://doi.org/10.1016/0303-2647(86)90040-7
Received: 
10.07.2022
Accepted: 
12.09.2022
Published: 
30.11.2022
  • 658 reads