Co-Estimation of State of Charge and Capacity for Lithium-Ion Batteries with Multi-Stage Model Fusion Method

Abstract

Lithium-ion batteries (LIBs) have emerged as the preferred energy storage systems for various types of electric transports, including electric vehicles, electric boats, electric trains, and electric airplanes. The energy management of LIBs in electric transports for all-climate and long-life operation requires the accurate estimation of state of charge (SOC) and capacity in real-time. This study proposes a multistage
model fusion algorithm to co-estimate SOC and capacity. Firstly, based on the assumption of a normal distribution, the mean and variance of the residual error from the model at different ageing levels are used to calculate the weight for the establishment of a fusion model with stable parameters. Secondly, a differential error gain with forward-looking ability is introduced into a proportional–integral observer
(PIO) to accelerate convergence speed. Thirdly, a fusion algorithm is developed by combining a multistage model and proportional–integral–differential observer (PIDO) to co-estimate SOC and capacity under a complex application environment. Fourthly, the convergence and anti-noise performance of the fusion algorithm are discussed. Finally, the hardware-in-the-loop platform is set up to verify the performance
of the fusion algorithm. The validation results of different aged LIBs over a wide range of temperature show that the presented fusion algorithm can realize a high-accuracy estimation of SOC and capacity with the relative errors within 2% and 3.3%, respectively.

Keywords

State of charge / Capacity estimation / Model fusion / Proportional–integral–differential observer / Hardware-in-the-loop

References

[[1]] Xiong R, Ma S, Li H, Sun F, Li J. Towards a safer battery management system: a critical review on diagnosis and prognosis of battery short circuit. iScience 2020;23(4):101010.

[[2]] Eddahech A, Briat O, Vinassa JM. Determination of lithium-ion battery state-ofhealth based on constant-voltage charge phase. J Power Sources 2014;258:218–27.

[[3]] Xiong R, Pan Y, Shen W, Li H, Sun F. Lithium-ion battery aging mechanisms and diagnosis method for automotive applications: recent advances and perspectives. Renew Sustain Energy Rev 2020;131:110048.

[[4]] Verma MKS, Basu S, Patil RS, Hariharan KS, Adiga SP, Kolake SM, et al. On-board state estimation in electrical vehicles: achieving accuracy and computational efficiency through an electrochemical model. IEEE Trans Veh Technol 2020;69 (3):2563–75.

[[5]] Xiong R, Yang R, Chen Z, Shen W, Sun F. Online fault diagnosis of external short circuit for lithium-ion battery pack. IEEE Trans Ind Electron 2020;67 (2):1081–91.

[[6]] Zheng Y, Ouyang M, Han X, Lu L, Li J. Investigating the error sources of the online state of charge estimation methods for lithium-ion batteries in electric vehicles. J Power Sources 2018;377:161–88.

[[7]] Waag W, Fleischer C, Sauer DU. Critical review of the methods for monitoring of lithium-ion batteries in electric and hybrid vehicles. J Power Sources 2014;258:321–39.

[[8]] Wang Y, Gao G, Li X, Chen Z. A fractional-order model-based state estimation approach for lithium-ion battery and ultra-capacitor hybrid power source system considering load trajectory. J Power Sources 2020;449:227543.

[[9]] Xu J, Mi CC, Cao B, Deng J, Chen Z, Li S. The state of charge estimation of lithium-ion batteries based on a proportional–integral observer. IEEE Trans Veh Technol 2014;63(4):1614–21.

[[10]] Hu X, Sun F, Zou Y. Estimation of state of charge of a Lithium-ion battery pack for electric vehicles using an adaptive Luenberger observer. Energies 2010;3 (9):1586–603.

[[11]] Chen X, Shen W, Cao Z, Kapoor A. A novel approach for state of charge estimation based on adaptive switching gain sliding mode observer in electric vehicles. J Power Sources 2014;246:667–78.

[[12]] Zhu Q, Li L, Hu X, Xiong N, Hu GD. H1-based nonlinear observer design for state of charge estimation of lithium-ion battery. IEEE Trans Veh Technol 2017;66(12):10853–65.

[[13]] Wang Y, Chen Z. A framework for state-of-charge and remaining discharge time prediction using unscented particle filter. Appl Energy 2020;260: 114324.

[[14]] Xu J, Cao B, Cao J, Zou Z, Mi CC, Chen Z. A comparison study of the model based SOC estimation methods for lithium-ion batteries. In: Proceeding of 2013 IEEE Vehicle Power and Propulsion Conference (VPPC); 2013 Oct 15–18; Beijing, China; 2013.

[[15]] Hu X, Feng F, Liu K, Zhang L, Xie J, Liu B. State estimation for advanced battery management: key challenges and future trends. Renew Sustain Energy Rev 2019;114:109334.

[[16]] Xiong R, Li L, Tian J. Towards a smarter battery management system: a critical review on battery state of health monitoring methods. J Power Sources 2018;405:18–29.

[[17]] Li Y, Abdel-Monem M, Gopalakrishnan R, Berecibar M, Nanini-Maury E, Omar N, et al. A quick on-line state of health estimation method for Li-ion battery with incremental capacity curves processed by Gaussian filter. J Power Sources 2018;373:40–53.

[[18]] Wang L, Pan C, Liu L, Cheng Y, Zhao X. On-board state of health estimation of LiFePO4 battery pack through differential voltage analysis. Appl Energy 2016;168:465–72.

[[19]] Bartlett A, Marcicki J, Onori S, Rizzoni G, Yang XG, Miller T. Electrochemical model-based state of charge and capacity estimation for a composite electrode lithium-ion battery. IEEE Trans Control Syst Technol 2016;24(2):384–99.

[[20]] Xiong R, Tian J, Shen W, Sun F. A novel fractional order model for state of charge estimation in lithium ion batteries. IEEE Trans Veh Technol 2019;68 (5):4130–9.

[[21]] Pan H, Lü Z, Wang H, Wei H, Chen L. Novel battery state-of-health online estimation method using multiple health indicators and an extreme learning machine. Energy 2018;160:466–77.

[[22]] Petit M, Prada E, Sauvant-Moynot V. Development of an empirical aging model for Li-ion batteries and application to assess the impact of vehicle-to-grid strategies on battery lifetime. Appl Energy 2016;172:398–407.

[[23]] Wang J, Xiong R, Li L, Fang Y. A comparative analysis and validation for doublefilters-based state of charge estimators using battery-in-the-loop approach. Appl Energy 2018;229:648–59.

[[24]] Li S, Pischinger S, He C, Liang L, Stapelbroek M. A comparative study of modelbased capacity estimation algorithms in dual estimation frameworks for lithium-ion batteries under an accelerated aging test. Appl Energy 2018;212:1522–36.

[[25]] Shen P, Ouyang M, Lu L, Li J, Feng X. The co-estimation of state of charge, state of health, and state of function for lithium-ion batteries in electric vehicles. IEEE Trans Veh Technol 2018;67(1):92–103.

[[26]] Tian J, Wang Y, Chen Z. Sensor fault diagnosis for lithium-ion battery packs based on thermal and electrical models. Int J Electr Power Energy Syst 2020;121:106087.

[[27]] Yu Q, Xiong R, Yang R, Pecht MG. Online capacity estimation for lithium-ion batteries through joint estimation method. Appl Energy 2019;255:113817.

[[28]] Wei Z, Zou C, Leng F, Soong BH, Tseng KJ. Online model identification and state-of-charge estimate for lithium-ion battery with a recursive total least squares-based observer. IEEE Trans Ind Electron 2018;65(2):1336–46.

[[29]] Wang Y, Liu C, Pan R, Chen Z. Modeling and state-of-charge prediction of lithium-ion battery and ultracapacitor hybrids with a co-estimator. Energy 2017;121:739–50.

[[30]] Ludovico CS, Bermudez JCM. A recursive least squares algorithm robust to lowpower excitation. In: Proceeding of 2004 IEEE International Conference on Acoustics, Speech, and Signal Processing; 2004 May 17–21; Montreal, QC, Canada; 2004.

[[31]] Li W, Jia Y, Du J, Zhang J. Distributed multiple-model estimation for simultaneous localization and tracking with NLOS mitigation. IEEE Trans Veh Technol 2013;62(6):2824–30.

[[32]] Lin C, Mu H, Xiong R, Cao J. Multi-model probabilities based state fusion estimation method of lithium-ion battery for electric vehicles: state-of-energy. Appl Energy 2017;194:560–8.

[[33]] Cheng X, Wang S, Yao L. Li-ion battery pack state-of-charge estimation disturbed by colored noises. Energy Procedia 2017;105:4104–9.

[[34]] Wei Z, Zhao J, Zou C, Lim TM, Tseng KJ. Comparative study of methods for integrated model identification and state of charge estimation of lithium-ion battery. J Power Sources 2018;402:189–97.

[[35]] Dai K, Wang J, He H. An improved SOC estimator using time-varying discrete sliding mode observer. IEEE Access 2019;7:115463–72.

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

[[37]] Meng J, Boukhnifer M, Diallo D, Wang T. A new cascaded framework for lithium-ion battery state and parameter estimation. Appl Sci 2020;10(3):1009.