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 more and more important. Based on the analysis of some of the most popular model-based SOC evaluation methods, the proportional-integral (PI) observer is planned to estimate the SOC of lithium-ion batteries in EDVs.


The structure of the planned PI observer is consider, and the union of the evaluation method with model errors is verified. To display the superiority and compensation properties of the planned PI observer, the simple-structure RC battery model is applly to model the Li-ion battery. To validate the results of the planned PI-based SOC evaluation method, the experimental battery test bench is traditional.


In the validation, the urban dynamometer driving schedule (UDDS) drive cycle is apply, and the PI-based SOC evaluation 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 evaluation algorithm based on a PI observer has been planned 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 evaluation has a simple structure and is easy to implement. The compensation properties of the PI observer display that a simple RC model can be apply to model the Li-ion battery. The evaluation SOC with the PI observer converges to the reference SOC quickly


and the SOC evaluation errors are maintained in a small band. Most of the errors of the PI-based SOC evaluation method are confined to 2% when compared with the reference SOC that is based on Coulomb counting with known initial SOC.


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