The State of Charge Estimation of Lithium-Ion Batteries Based on a Proportional-Integral Observer


With the development of electric drive vehicles (EDVs), the state-of-charge (SOC) estimation for lithium-ion (Li-ion) batteries has become increasingly more important. Based on the analysis of some of the most popular model-based SOC estimation methods, the proportional-integral (PI) observer is proposed to estimate the SOC of lithium-ion batteries in EDVs. The structure of the proposed PI observer is analyzed, and the convergence of the estimation method with model errors is verified. To demonstrate the superiority and compensation properties of the proposed PI observer, the simple-structure RC battery model is utilized to model the Li-ion battery. To validate the results of the proposed PI-based SOC estimation method, the experimental battery test bench is established. In the validation, the urban dynamometer driving schedule (UDDS) drive cycle is utilized, and the PI-based SOC estimation results are found to agree with the reference SOC, generally within the 2% error band for both the known and unknown initial SOC cases.


  1. Battery
  2. Electric vehicle
  3. Lithium-ion (Li-ion) battery
  4. Proportional-integral (PI) observer
  5. Sliding-mode observer
  6. State of charge (SOC)



Fig. 1. Block diagram of different observer-based SOC estimation methods for Li-ion batteries. (a) Block diagram of the common structure. (b) Block diagram of a PI observer.


 Fig. 2. Identification results.

Fig. 3. UDDS current profile.

Fig. 4. SOC estimation results when the initial SOC is given.

Fig. 5. SOC estimation results when the initial SOC is unknown.


A battery SOC estimation algorithm based on a PI observer has been proposed for Li-ion batteries. Acceptable accuracy has been verified by experiments on battery bench testing for both known and unknown initial SOC. The PI-based SOC estimation has a simple structure and is easy to implement. The compensation properties of the PI observer demonstrate that a simple RC model can be utilized to model the Li-ion battery. The estimated SOC with the PI observer converges to the reference SOC quickly, and the SOC estimation errors are maintained in a small band. Most of the errors of the PI-based SOC estimation method are confined to 2% when compared with the reference SOC that is based on Coulomb counting with known initial SOC.


[1] B. Pattipati, C. Sankavaram, and K. Pattipati, “System identification and estimation framework for pivotal automotive battery management system characteristics,” IEEE Trans. Syst., Man, Cybern. C, Appl. Rev., vol. 41, no. 6, pp. 869–884, Nov. 2011.

[2] K. Kutluay, Y. Cadirci, Y. S. Ozkazanc, and I. Cadirci, “A new online state-of-charge estimation and monitoring system for sealed lead-acid batteries in Telecommunication power supplies,” IEEE Trans. Ind. Electron., vol. 52, no. 5, pp. 1315–1327, Oct. 2005.

[3] M. Charkhgard and M. Farrokhi, “State-of-charge estimation for Lithiumion batteries using neural networks and EKF,” IEEE Trans. Ind. Electron., vol. 57, no. 12, pp. 4178–4187, Dec. 2010.

[4] L. Xu, J.Wang, and Q. Chen, “Kalman filtering state of charge estimation for battery management system based on a stochastic fuzzy neural network battery model,” Energy Convers. Manag., vol. 53, no. 1, pp. 33–39, Jan. 2012.

[5] X. Hu, F. Sun, and Y. Zou, “Estimation of state of charge of a Lithium-ion battery pack for electric vehicles using an adaptive Luenberger observer,” Energies, vol. 3, no. 9, pp. 1586–1603, 2010.


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