Communications - Scientific Letters of the University of Zilina 2023, 25(1):C13-C23 | DOI: 10.26552/com.C.2023.005

Modeling of Electric Vehicles Fleet's Charging Using Partial Differential Equations

Martina Kajanová ORCID...1, *, Peter Braciník ORCID...1, Michal Kralovič2
1 Faculty of Electrical Engineering and Information Technology, University of Zilina, Zilina, Slovakia
2 Stredoslovenska distribucna, a. s., Liptovsky Mikulas, Slovakia

With an increasing number of electric vehicles, their impact on electrical power systems is starting to be substantial. High deployment of these vehicles can even bring issues such as overloading the power transformers and power lines or loss of stability in the power system. Therefore, a suitable model, able to represent large groups or fleets of electric vehicles, is needed to prepare measures that can prevent these problems. The main contribution of this paper is the definition of a charging model representing a fleet of EVs using partial differential equations. This new approach enables meeting the accuracy of the commonly used battery charging models while significantly decreasing required computation times as shown in simulation results.

Keywords: electric vehicle,  charging,  modeling,  partial differential equations
Grants and funding:

The authors received no financial support for the research, authorship, and/or publication of this article.

Conflicts of interest:

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Received: September 6, 2022; Accepted: October 26, 2022; Prepublished online: November 28, 2022; Published: January 25, 2023  Show citation

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Kajanová, M., Braciník, P., & Kralovič, M. (2023). Modeling of Electric Vehicles Fleet's Charging Using Partial Differential Equations. Communications - Scientific Letters of the University of Zilina, 25(1), C13-23. doi: 10.26552/com.C.2023.005
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    References

    1. CO2 emissions from cars: facts and figures (infographics) - News, European Parliament [online] [accessed 2021-04-25]. Available from: https://www.europarl.europa.eu/news/en/headlines/society/20190313STO31218/co2-emissions-from-cars-facts-and-figures-infographics
    2. Emission from electric vehicles - Alternative Fuels Data Center (U. S. Department of Energy) [online] [accessed 2022-08-26]. Available from: https://afdc.ener gy.gov/vehicles/electric_emissions.html
    3. Vehicle to grid - The mobility house [online] [accessed on 2021-04-25]. Available from: https://www.mobilityhouse.com/int_en/vehicle-to-grid
    4. SORENSEN, A. L., LINDBERG, K. B., SARTORI, I., ANDRESEN, I. Analysis of residential EV energy flexibility potential based on real-world charging reports and smart meter data. Energy and Buildings [online]. 2021, 241, 110923 [accessed 2021-12-27]. ISSN 0378-7788. Available from: https://doi.org/10.1016/j.enbuild.2021.110923 Go to original source...
    5. KAJANOVA, M., BRACINIK, P. Definition of discrete choice models of EV owners based on different socio-demographic aspects. Applied Sciences [online]. 2021, 11, 3679 [accessed 2022-08-26]. eISSN 2076-3417. Available from: https://doi.org/10.3390/app11083679 Go to original source...
    6. CENKY, M., BENDIK, J., ELESCHOVA, Z., BELAN, A., CINTULA, B., JANIGA, P. Probabilistic model of electric vehicle charging demand to distribution network impact analyses. In: 20th International Scientific Conference on Electric Power Engineering EPE: proceedings [online]. IEEE. 2019. ISSN 2376-5623, eISSN 2376-5631, p. 53-58. Available from: https://doi.org/10.1109/EPE.2019.8777973 Go to original source...
    7. TOMASOV, M., KAJANOVA, M., BRACINIK, P., MOTYKA, D. Overview of battery models for sustainable power and transport application. Transportation Research Procedia [online]. 2019, 40, p. 548-555 [accessed on 2020-12-04]. ISSN 2352-1465. Available from: https://doi.org/10.1016/j.trpro.2019.07.079 Go to original source...
    8. LE FLOCH, C., KARA, E. C., MOURA, S. PDE modeling and control of vehicle fleets for ancillary services: a discrete charging case. IEEE Transactions on Smart Grid [online]. 2018, 9(2), p. 573-581 [accessed on 2020-12-30]. ISSN 1949-3053, eISSN 1949-3061. Available from: https://doi.org/10.1109/TSG.2016.2556643 Go to original source...
    9. VARINI, M., CAMPANA, P. E., LINDBERGH, G. A semi-empirical electrochemistry-based model for li-ion battery performance prediction over lifetime. Journal of Energy Storage [online]. 2019, 25, 100819 [accessed on 2020-12-04]. ISSN 2352-152X. Available from: https://doi.org/10.1016/j.est.2019.10081968 Go to original source...
    10. MELENTJEV, S., LEBEDEV, D. Overview of simplified mathematical models of batteries. Talinn: Talinn University of Technology, 2013.
    11. AZAM, S. M. Battery identification, prediction and modelling. Master Thesis. Colorado: Colorado State University [online] [accessed on 2020-12-06]. Available from: https://mountainscholar.org/bitstream/handle/10217/191324/Azam_colostate_0053N_14909.pdf?sequence=1
    12. RAHMAN, M. A., ANWAR, S., IZADIAN, A. Electrochemical model parameter identification of a lithium-ion battery using particle optimization method. Journal of Power Sources [online]. 2016, 307, p. 86-97 [accessed on 2020-12-05]. ISSN 0378-7753. Available from: https://doi.org/10.1016/j.jpowsour.2015.12.083 Go to original source...
    13. RAMADESIGAN, V., NORTHROP, P. W. C., DE, S., SANTHANAGOPALAN, S., BRAATZ, R. D., SUBRAMANIAN, V. R. Modeling and simulation of lithium-ion a systems engineering perspective. Journal of the Electrochemical Society [online]. 2012, 159(3), p. R31-R45 [accessed on 2020-12-06]. ISSN 0013-4651, eISSN 1945-7111. Available from: https://iopscience.iop.org/article/10.1149/2.018203jes/meta Go to original source...
    14. MARRA, F., YANG, G. Y., TRAEHOLT, CH., LARSEN, E., RASMUSSEN, C. N., YOU, S. Demand profile study of battery electric vehicle under different charging options. In: IEEE Power and Energy Society General Meeting: proceedings [online] [accessed on 2021-03-12]. IEEE. 2012. ISSN 1932-5517, eISSN 1944-9925. Available from: https://doi.org/10.1109/PESGM.2012.6345063 Go to original source...
    15. GHAFFARI, A., MOURA, S., KRSTIC, M. PDE-based modeling, control and stability analysis of heterogenous thermostatically controlled load populations [online] [accessed on 2021-02-13]. 2015. Available from: https://ecal.berkeley.edu/pubs/JDSMC-TCL-PDE-Control.pdf Go to original source...
    16. CEROVSKY, B. Impact of a fleet of electric vehicles uncontrolled charging on active power and frequency control / Dopady nekontrolovaneho nabijania flotily elektromobilov na riadenie frekvencie a cinneho vykonu (in Slovak). Master Thesis. Zilina: University of Zilina, 2020.
    17. SEDLACIK, J. Impact of a fleet of electric vehicles uncontrolled charging on distribution transformers overloading / Dopady nekontrolovaneho nabijania flotily elektromobilov na pretazovanie distribucnych transformatorov (in Slovak). Master thesis. Zilina: University of Zilina, 2020.
    18. Tesla Model S 85 charging cost and time calculator [online] [accessed on 2021-04-15]. Available from: https://evcompare.io/cars/tesla/tesla_model_s_85/charging

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