# Estimation algorithm research for lithium battery SOC in electric vehicles based on adaptive unscented Kalman filter

## Abstract

The state of charge (SOC) is a significant part of energy management for electric vehicle power battery, which has important influence on the safe operation of power battery and the judgment of driver’s operation. Because the battery SOC cannot be measured directly, many researchers use various estimation methods to obtain accurate SOC values. But the SOC is affected by the temperature, current, cycle life and other time-varying nonlinear factors, which make difficult to construct prediction model. The key problem of battery SOC estimation is the change rule of battery capacity. The Peukert equation is a good method for calculating the battery capacity. The traditional Peukert equation without considering the influence of temperature, but the differences of temperature lead to changes in the constants n and K of the Peukert equations. In this paper, the Peukert equation based on temperature, current change and cycle life is established to estimate the battery capacity. And the battery model state equation is established for estimation and measurement equations of charge and discharge parameters $$\left\{ {C_{\text{e}} ,R_{\text{e}} ,C_{\text{d}} ,R_{\text{d}} ,R_{0} } \right\}$$ and $$V_{\text{OC}}$$ by using the ampere-hour method and the second-order RC model. And the dynamic estimation of charge state of battery is realized by AUKF. The results show that the accuracy of the lithium battery SOC estimation algorithm based on the temperature, current and cycle life of the modified Peukert equation is about 8% higher than that of the traditional KF ampere-hour method.

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## References

1. 1.

Cheng KWE, Divakar BP, Wu H et al (2011) Battery-management system (BMS) and SOC development for electrical vehicles. IEEE Trans Veh Technol 60(1):76–88

2. 2.

Lawder MT, Suthar B, Northrop PWC et al (2014) Battery energy storage system (BESS) and battery management system (BMS) for grid-scale applications. Proc IEEE 102(6):1014–1030

3. 3.

Lim GJ, Choi SS, Lee YJ et al (2010) Battery management system (BMS) and driving method thereof: US, US 7680613 B2[P]

4. 4.

Lee J, Nam O, Cho BH (2007) Li-ion battery SOC estimation method based on the reduced order extended Kalman filtering. J Power Sources 174(1):9–15

5. 5.

Hu Y, Yurkovich S (2012) Battery cell state-of-charge estimation using linear parameter varying system techniques. J Power Sources 198(1):338–350

6. 6.

Yuan Z, Hu X, Ma H et al (2015) Combined state of charge and state of health estimation over lithium-ion battery cell cycle lifespan for electric vehicles. J Power Sources 273:793–803

7. 7.

Dong G, Wei J, Chen Z (2016) Kalman filter for onboard state of charge estimation and peak power capability analysis of lithium-ion batteries. J Power Sources 328:615–626

8. 8.

Liu C, Liu W, Wang L et al (2016) A new method of modeling and state of charge estimation of the battery. J Power Sources 320:1–12

9. 9.

Dai H, Wei X, Sun Z et al (2012) Online cell SOC estimation of Li-ion battery packs using a dual time-scale Kalman filtering for EV applications. Appl Energy 95(2):227–237

10. 10.

Xiong R, Gong X, Mi CC, Sun F (2013) A robust state-of-charge estimator for multiple types of lithium-ion batteries using adaptive extended Kalman filter. J Power Sources 243:805–816

11. 11.

Chen Q, Jiang J, Liu S, Zhang C (2016) A novel sliding mode observer for state of charge estimation of EV lithium batteries. J. Power Electron 16:1131–1140

12. 12.

Wang Y, Zhang C, Chen Z (2015) A method for state-of-charge estimation of LiFePO4, batteries at dynamic currents and temperatures using particle filter. J Power Sources, 279(ISSN):306–311

13. 13.

Shen Y (2014) Hybrid unscented particle filter based state-of-charge determination for lead-acid batteries. Energy 74(5):795–803

14. 14.

Wu T, Chen X, Xia F et al (2011) Research on SOC hybrid estimation algorithm of power battery based on EKF. In: Asia-Pacific power and energy engineering conference. IEEE Computer Society, pp 1–3

15. 15.

Jiang C, Taylor A, Duan C et al (2013) Extended Kalman filter based battery state of charge (SOC) estimation for electric vehicles. In: Transportation electrification conference and expo. IEEE, pp 1–5

16. 16.

Hu C, Youn BD, Chung J (2012) A multiscale framework with extended Kalman filter for lithium-ion battery SOC and capacity estimation. Appl Energy 92(4):694–704

17. 17.

Zhao Y, Zhou X, Liu Y (2015) SOC estimation for Li-ion battery based on extended Kalman particle filter. China Mech Eng 26(3):394–397

18. 18.

He H, Xiong R, Zhang X et al (2011) State-of-charge estimation of the lithium-ion battery using an adaptive extended Kalman filter based on an improved Thevenin model. IEEE Trans Veh Technol 60(4):1461–1469

19. 19.

Zhang C, Jiang J, Zhang W et al (2012) Estimation of state of charge of lithium-ion batteries used in HEV using robust extended Kalman filtering. Energies 5(4):1098–1115

20. 20.

Xia B, Wang H, Tian Y et al (2015) State of charge estimation of lithium-ion batteries using an adaptive cubature Kalman filter. Energies 8(6):5916–5936

21. 21.

He H, Xiong R et al (2011) Evaluation of lithium-ion battery equivalent circuit models for state of charge estimation by an experimental approach. Energies 4(4):582–598

22. 22.

Yu Z, Huai R, Xiao L (2015) State-of-charge estimation for lithium-ion batteries using a Kalman filter based on local linearization. Energies 8(8):7854–7873

23. 23.

He Z, Gao M, Wang C et al (2013) Adaptive state of charge estimation for li-ion batteries based on an unscented Kalman filter with an enhanced battery model. Energies 6(8):4134–4151

24. 24.

Tang X, Liu B, Gao F et al (2016) State-of-charge estimation for Li-ion power batteries based on a tuning free observer. Energies 9(9):675

25. 25.

Gomez J, Nelson R, Kalu EE et al (2011) Equivalent circuit model parameters of a high-power Li-ion battery: thermal and state of charge effects. J Power Sources 196(10):4826–4831

26. 26.

Sepasi S, Ghorbani R, Liaw BY (2014) A novel on-board state-of-charge estimation method for aged Li-ion batteries based on model adaptive extended Kalman filter. J Power Sources 245(1):337–344

## Acknowledgements

This project is supported by the National Natural Science Foundation of China (Grant No. 51705220), the Jiangsu Province Higher Education Natural Science Research Project (17KJD580001), the Jiangsu Provincial Higher Education Natural Science Research Major Project (17KJA580003), Foundation for Jiangsu Province ‘‘333 Project’’ Training Funded Project (BRA2015365).

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Correspondence to Shaoyi Bei.

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Li, B., Bei, S. Estimation algorithm research for lithium battery SOC in electric vehicles based on adaptive unscented Kalman filter. Neural Comput & Applic 31, 8171–8183 (2019). https://doi.org/10.1007/s00521-018-3901-7