Skip to main content

Advertisement

SpringerLink
Log in

Investigation of Voc and SoH on Li-ion batteries with an electrical equivalent circuit model using optimization algorithms

  • Original Paper
  • Published:
Electrical Engineering Aims and scope Submit manuscript

Abstract

Many significant parameters show the performance of batteries used in important fields such as biomedical systems, energy storage units, electric vehicle technologies, and advanced space studies. Two essential indicators among these parameters are open-circuit voltage and state of health. In this study, it is tried to estimate open-circuit voltage and state of health with high accuracy by applying optimization methods on the Thevenin electrical equivalent circuit model of batteries. The parameter values obtained by examining the discharge tests of the Li-ion battery cell with 2A constant current during the 150 charge/discharge cycle time at 25 °C are transferred to the electrical equivalent circuit model. Curve-fitting method, artificial bee colony, particle swarm optimization, dragonfly algorithm, and genetic algorithm have been studied in the prediction operation of open-circuit voltage and state of health which is defined based on state of charge, number of cycles, rated current capacity, and time. Comparisons are made considering the absolute error values, the smallest value of the sum of the squares of the errors, the response speed of the methods, and the correct estimation ability. Ultimately, it is aimed to obtain the most suitable method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Availability of data and material

The methods and data used are shared obviously.

Code availability

Not applicable.

Abbreviations

a :

Alignment weight for DF

c :

Cohesion weight for DF

c 1, c 2 :

Cognitive and social coefficients

C n :

Rated current capacity

C N :

Number of cycles

C p :

Transient condition capacitor

C r :

Crossover rate for GA

C ref :

Current supply capacity at the starting

e :

Enemy factor for DF

E i :

Enemy’s distraction motion

F :

Food factor for DF

F i :

Attraction of the food

f it :

Fitness value of the objective function

I L :

Charge/discharge current

j :

Iteration number for PSO

j + 1 :

Next iteration value for PSO

k :

Random factor and its range is within [-1, number of nutrients]

M r :

Mutation rate for GA

N n :

Number of neighbors in the swarm

N ij :

Food source for ABC

N new :

New food source for ABC

p :

Probability of choosing the ith solution for ABC

p best :

Best of the particle

R max :

Maximum number of iterations

R p :

Transient condition resistor

R t :

Current (present) iteration

R T :

Response time

R Ω :

Internal resistance

s :

Separation weight for DF

S i :

Separation motion of ith individual

s best :

Best of the swarm

SoC:

State of charge

SoH:

State of health

t :

Time

T eb :

Total number of worker bees

t s :

Sample time

v ij :

Ith particle velocity at jth iteration

V oc :

Open-circuit voltage

V p :

Voltage drop caused by polarization

V T :

Output terminal voltage

w :

Inertia coefficient for PSO

x :

Position vector

X :

Current position of the dragonfly

X + :

Position of the food source for

X − :

Enemy’s position for DF

λ 1 , λ 2 :

Random factor within [0, 1]

ϕ :

Random factor within [0, 1]

φ :

Random factor within [− 1, 1

References

  1. Sparacio AR, Reed FG, Kerestes JR, Grainger MB, Smith TZ (2012) Survey of battery energy storage systems and modeling techniques. In: Proceedings of IEEE Power and Energy Society General Meeting, pp 1–8. https://doi.org/10.1109/PESGM.2012.6345071

  2. Bhangu BS, Bentley P, Stone DA, Bingham CM (2005) Nonlinear observers for predicting state of charge and state of health of lead acid batteries for hybrid electric vehicles. IEEE Trans Veh Technol 54(3):783–794. https://doi.org/10.1109/TVT.2004.842461

    Article  Google Scholar 

  3. Carkit T, Alci M (2020) Comparison of some electrical equivalent circuit models used in battery-based energy storage systems. In: Proceeding of 2nd International GAP Renewable Energy and Energy Efficiency Congress, pp 64–67. https://gapyenev2020.harran.edu.tr/wp-content/uploads/2021/01/GapYenev2020.pdf. Accessed 23 June 2007

  4. Qays Q, Buswing Y, Anyi M (2019) Active cell balancing control method for series connected lithium-ion battery. Int J Innov Technol Explor Eng 8(9):2424–2430. https://doi.org/10.35940/ijitee.i8905.078919

    Article  Google Scholar 

  5. Shaheen AM, Hamida MA, El-Sehiemy RA, Elattar EE (2021) Optimal parameter identification of linear and non-linear models for li-ion battery cells. Energy Rep 7:7170–7185. https://doi.org/10.1016/j.egyr.2021.10.086

    Article  Google Scholar 

  6. Yang F, Li E, Li C, Miao Q (2019) State-of-charge estimation of lithium-ion batteries based on gated recurrent neural network. Energy 175:66–75. https://doi.org/10.1016/j.energy.2019.03.059

    Article  Google Scholar 

  7. Singh KV, Bansal HO, Singh D (2020) Hardware-in-the-loop implementation of ANFIS based adaptive SoC estimation of lithium-ion battery for hybrid vehicle applications. J Energy Storage 27:101–124. https://doi.org/10.1016/j.est.2019.101124

    Article  Google Scholar 

  8. Gao L, Liu S, Dougal RA (2002) Dynamic lithium-ion battery model for system simulation. IEEE Trans Compon Packaging Technol 25(3):495–505. https://doi.org/10.1109/TCAPT.2002.803653

    Article  Google Scholar 

  9. Chiasson J, Vairamohan B (2005) Estimating the state of charge of a battery. IEEE Trans Control Syst Technol 13(3):465–470. https://doi.org/10.1109/TCST.2004.839571

    Article  Google Scholar 

  10. Barbarisi O, Vasca F, Glielmo L (2006) State of charge Kalman filter estimator for automotive batteries. Control Eng Pract 14:267–275. https://doi.org/10.1016/j.conengprac.2005.03.027

    Article  Google Scholar 

  11. Miyamoto H, Morimoto M, Morita K (2007) On-line SoC estimation of battery for wireless tram car. In: Proceedings of IEEE 7th international conference on power electronics and drive systems, pp 1624–1627. https://doi.org/10.1109/PEDS.2007.4487927

  12. Tremblay O, Dessaint LA (2009) Experimental validation of a battery dynamic model for EV applications. World Electric Vehicle J 3:289–298. https://doi.org/10.3390/wevj3020289

    Article  Google Scholar 

  13. Liu YH, Luo YF (2010) Search for an optimal rapid-charging pattern for Li-ion batteries using the Taguchi approach. IEEE Trans Industr Electron 57(12):3963–3971. https://doi.org/10.1109/TIE.2009.2036020

    Article  Google Scholar 

  14. Reddy T B, Linden D (2011) Handbook of batteries. 4th Edition, Published by The McGraw Hill Companies, New York USA. https://www.accessengineeringlibrary.com/binary/mheaeworks/31e81714f2ef35b8/18612c103589dd483a7998835a510d00c04a47cd69e7c232c8724c0df672a86f/book-summary.pdf. Acce-ssed 24 June 2021

  15. Hussein AAH, Batarseh I (2011) An overview of generic battery models. In: Proceedings of IEEE Power and Energy Society General Meeting. https://doi.org/10.1109/PES.2011.6039674

  16. Huria T, Ceraolo M, Gazzarri J, Jackey R (2012) High fidelity electrical model with thermal dependence for characterization and simulation of high power lithium battery cells. In: Proceedings of IEEE international electric vehicle conference, pp 1–8. https://doi.org/10.1109/IEVC.2012.6183271

  17. Hu X, Li S, Peng H (2012) A comparative study of equivalent circuit models for li-ion batteries. J Power Sour 198:359–367. https://doi.org/10.1016/j.jpowsour.2011.10.013

    Article  Google Scholar 

  18. Petzl M, Danzer MA (2013) Advancements in OCV measurement and analysis for lithium-ion batteries. IEEE Trans Energy Convers 28(3):675–681. https://doi.org/10.1109/TEC.2013.2259490

    Article  Google Scholar 

  19. Sarikurt T, Ceylan M, Balikci A (2014) A hybrid battery model and state of health estimation method for lithium-ion batteries. In: Proceedings of IEEE international energy conference, pp 1349–1356. https://doi.org/10.1109/ENERGYCON.2014.6850598

  20. Li SE, Wang B, Peng H, Hu X (2014) An electrochemistry-based impedance model for lithium-ion batteries. J Power Sour 258:9–18. https://doi.org/10.1016/j.jpowsour.2014.02.045

    Article  Google Scholar 

  21. Vo TT, Chen X, Shen W (2015) New charging strategy for lithium-ion batteries based on the integration of taguchi method and state of charge estimation. J Power Sour 273:413–422. https://doi.org/10.1016/j.jpowsour.2014.09.108

    Article  Google Scholar 

  22. Wang SC, Liu YH (2015) A PSO based fuzzy controlled searching for the optimal charge pattern of li-ion batteries. IEEE Trans Industr Electron 62(5):2983–2993. https://doi.org/10.1109/TIE.2014.2363049

    Article  Google Scholar 

  23. Mesbani T, Khenfri F, Rizoug N, Chaaban K, Bartholomeüs P, Moigne PL (2016) Dynamic modeling of li-ion batteries for electric vehicle applications based on hybrid particle swarm nelder mead (PSO-NM) optimization algorithm. Electric Power Syst Res 131:195–204. https://doi.org/10.1016/j.epsr.2015.10.018

    Article  Google Scholar 

  24. Liu K, Li K, Yang Z, Zhang C, Deng J (2016) An advanced lithium ion battery optimal charging strategy based on a couple thermoelectric model. Electrochimi-ca Acta 225:330–344. https://doi.org/10.1016/j.electacta.2016.12.129

    Article  Google Scholar 

  25. Chen WJ, Tan XJ, Cai M (2017) Parameter identification of equivalent circuit models for li-ion batteries based on tree seeds algorithm. IOP Conf Ser: Earth and Environ Sci 73:1–8. https://doi.org/10.1088/1755-1315/73/1/012024

    Article  Google Scholar 

  26. Wang Q, Wang J, Zhao P, Kang J, Yan F, Du C (2017) Correlation between the model accuracy and model based SoC estimation. Electrochim Acta 228:146–159. https://doi.org/10.1016/j.electacta.2017.01.057

    Article  Google Scholar 

  27. Kollimalla SK, Manandhar U, Ukil A (2017) Optimization of charge/discharge rates of battery using two stage rate limit control. IEEE Trans Sustain Energy 8:516–529. https://doi.org/10.1109/TSTE.2016.2608968

    Article  Google Scholar 

  28. Min H, Sun W, Li X, Guo D, Yu Y, Zhu T, Zhao Z (2017) Research on the optimal charging strategy for li-ion batteries based on multi-objective optimization. Energies 10(5):709–724. https://doi.org/10.3390/en10050709

    Article  Google Scholar 

  29. Zhang C, Jiang J, Gao Y, Zhang W, Liu Q, Hu X (2017) Charging optimization in lithium ion batteries based on temperature rise and charge time. Appl Energy 194:569–577. https://doi.org/10.1016/j.apenergy.2016.10.059

    Article  Google Scholar 

  30. Lei Y, Zhang C, Gao Y, Li T (2018) Charging optimization of lithium ion batteries based on capacity degradation speed and energy loss. Energy Procedia 152:544–549. https://doi.org/10.1016/j.egypro.2018.09.208

    Article  Google Scholar 

  31. Meng J, Luo G, Ricco M, Swierczynski M, Stroe DI, Teodorescu R (2018) Overview of lithium-ion battery modeling methods for state of charge estimation in electrical vehicles. Appl Sci 8(5):1–7. https://doi.org/10.3390/app8050659

    Article  Google Scholar 

  32. Boadu JMA, Elie AG, Sinencio ES (2018) The impact of pulse charging parameters on the life cycle of lithium ion polymer batteries. Energies 11(8):1–15. https://doi.org/10.3390/en11082162

    Article  Google Scholar 

  33. Kai H, Fang GY, Gang LZ, Cheng LH, Ling LL (2018) Development of accurate lithium-ion battery model based on adaptive random disturbance PSO algorithm. Math Probl Eng 2018:1–13. https://doi.org/10.1155/2018/3793492

    Article  Google Scholar 

  34. Hemi H, Sirdi NM, Naamane A, Ikken B (2018) Open circuit voltage of a lithium ion battery model adjusted by data fitting. In: Proceedings of 6th international renewable and sustainable energy conference, pp 1–5. https://doi.org/10.1109/IRSEC.2018.8702860

  35. Shekar AC, Anwar S (2019) Real-time state-of-charge estimation via particle swarm optimization on a lithium-ion electrochemical cell model. Batteries 5(4):1–17. https://doi.org/10.3390/batteries5010004

    Article  Google Scholar 

  36. Ruba M, Nemeş R, Ciornei S, Martiş C (2020) Parameter identification modeling and testing of li-ion batteries used in electric vehicles. In: Applied electromechanical devices and machines for electric mobility solutions, pp 1–19. https://doi.org/10.5772/intechopen.89256

  37. Li L, Hu M, Xu Y, Fu C, Jin G, Li Z (2020) State of charge estimation for lithium-ion power battery based on H-infibity filter algorithm. Appl Sci 10(18):6371–6389. https://doi.org/10.3390/app10186371

    Article  Google Scholar 

  38. Andreev AA, Vozmilov AG, Kalmakov VA (2015) Simulation of lithium battery operation under severe temperature conditions. Procedia Eng 129:201–206. https://doi.org/10.1016/j.proeng.2015.12.033

    Article  Google Scholar 

  39. Ahmed M (2016) Modeling lithium-ion battery chargers in PLECS. PLEXIM Corpus Publishing pp 1–9. https://www.plexim.com/sites/default/files/plecs_lithium_ion_adv.pdf. Accessed 25 June 2021

  40. Bratton D, Kennedy J (2007) Defining a standard for particle swarm optimization. In: Proceedings of IEEE swarm intelligence symposium, pp 120–127. https://doi.org/10.1109/SIS.2007.368035

  41. Chiaradonna S, Giandomenico FD, Murru N (2020) On enhancing efficiency and accuracy of particle swarm optimization algorithms. Int J Innov Comput Inform Control 11(4):1165–1189

    Google Scholar 

  42. Nickabadi A, Ebadzadeh M, Safabakhsh R (2011) A novel particle swarm optimization algorithm with adaptive inertia weight. Appl Soft Comput 11(4):3658–3670. https://doi.org/10.1016/j.asoc.2011.01.037

    Article  Google Scholar 

  43. Jiang X, Ling H, Yan J, Li B, Li Z (2013) Forecasting electrical energy consumption of equipment maintenance using neural network and particle swarm optimization. Math Probl Eng 2:1–8. https://doi.org/10.1155/2013/194730

    Article  Google Scholar 

  44. Chen CL, Lin YL, Fu WY (2015) Effects of battery energy storage system on the operating schedule of a renewable energy based tou rate industrial user under competitive environment. J Mar Sci Technol 23(4):541–550. https://doi.org/10.6119/JMST-015-0521-1

    Article  Google Scholar 

  45. Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Global Optim 39(3):459–471. https://doi.org/10.1007/s10898-007-9149-x

    Article  MathSciNet  Google Scholar 

  46. Kaya B, Eke İ (2020) Developments in artificial bee colony algorithm and the results. J Product 1:99–115

    Google Scholar 

  47. Rahman CM, Rashid TA (2019) Dragonfly algorithm and its applications in applied science survey. Comput Intell Neurosci 2019:1–21. https://doi.org/10.1155/2019/9293617

    Article  Google Scholar 

  48. Reynolds CW (1987) Flocks, herds and schools: a distributed behavioral model. Comput Graph 21(4):25–34. https://doi.org/10.1145/37402.37406

    Article  Google Scholar 

  49. Mirjalili S (2016) Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems. Neural Comput Appl 27(4):1053–1073. https://doi.org/10.1007/s00521-015-1920-1

    Article  Google Scholar 

  50. Zhang N, Yang X, Zhnag M, Sun Y, Long K (2017) A genetic algorithm-based task scheduling for cloud resource crowd-funding model. Int J Commun Syst 31(5):1–10. https://doi.org/10.1002/dac.3394

    Article  Google Scholar 

  51. Hassanat A, Almohammdi K, Alkadaween E, Abunawas E, Hammouri A, Prasath VBS (2019) Choosing mutation and crossover ratios for genetic algorithms-A review with a new dynamic approach. Information 10(12):1–36. https://doi.org/10.3390/info10120390

    Article  Google Scholar 

  52. National Aeronautics and Space Administration (2021) Li-ion battery aging datasets. NASA’s Open Data Portal NASA Publishing. https://data.nasa.gov/dataset/Li-ion-Battery-Aging-Datasets/uj5r-zjdb. Accessed 22 June 2021

  53. Carkit T, Alci M (2021) Investigation of electrical equivalent circuit model simulation data for li-ion battery by comparing with experimental discharge test results. In: International conference & exposition on modern energy and power systems, pp 11–16. http://www.icmeps.com/wp-content/uploads/2020/08/Conference-Proceedings-ICMEPS2021-1.pdf

Download references

Funding

The authors did not receive support from any organization for the submitted work. The authors have no relevant financial or non-financial interests to disclose.

Author information

Authors and Affiliations

  1. Department of Electrical and Electronics Engineering, Kırklareli University, Kırklareli, Turkey

    Taner Çarkıt

  2. Department of Electrical and Electronics Engineering, Erciyes University, Kayseri, Turkey

    Mustafa Alçı

Authors
  1. Taner Çarkıt
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mustafa Alçı
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

The contributions of the authors are given in the article. All authors contributed to the study conception and design. Material preparation, data collection, and analysis were performed by Taner ÇARKIT and Mustafa ALÇI. The first draft of the manuscript was written by Taner ÇARKIT, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Taner Çarkıt.

Ethics declarations

Conflicts of interest

Competing interests: There is no conflict of interest between the authors and the journal referees. The authors declare they have no financial interests. The authors have no conflicts of interest to declare that are relevant to the content of this article.

Ethics approval

Not applicable.

Consent to participate

Approval given.

Consent for publication

Release granted.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Çarkıt, T., Alçı, M. Investigation of Voc and SoH on Li-ion batteries with an electrical equivalent circuit model using optimization algorithms. Electr Eng 106, 1781–1792 (2024). https://doi.org/10.1007/s00202-021-01484-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00202-021-01484-2

Keywords

Search

Navigation