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Implementation of discharging/charging current sensorless state-of-charge estimator reflecting cell-to-cell variations in lithium-ion series battery packs

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This paper offers novel insights to the design and implementation of an innovative state-of-charge (SOC) estimator for the lithium-ion (Li-Ion) series battery pack. The most interesting feature of this approach is that it can utilize information from each filtered terminal voltage of the Li-Ion cells connected in series for SOC estimation of the battery pack. Without actual sensing each discharging/charging current (DCC) applied to the Li-Ion cells, it is possible to extract each DCC estimation from the corresponding filtered terminal voltages with an equivalent electrical circuit model (EECM) identification of all Li-Ion cells in the battery pack. There are two advantages to SOC estimation of the battery pack with this approach. First, the proposal can be implemented simply and effectively, reducing the computational steps required for SOC estimation. By reducing computational steps, the proposal is expected to be more cost-effective. Second, the approach guarantees an improved SOC performance, even if the battery pack results in inevitable cell-to-cell variation among Li-Ion cells. Accordingly, there are fewer differences to previously estimated DCCs among Li-Ion cells. Specifically, all values from the estimated DCCs are properly compensated for by simultaneous parameter modification according to each cell’s electrochemical characteristics. Experimental results clearly demonstrate that our DCC sensorless SOC estimator provides robust SOC performance for the battery pack. This approach considered an experimental battery pack (12S1P) connected in series using 2.6 Ah LiCoO2 cells produced by Samsung SDI.

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electric vehicle


hybrid electric vehicle


battery management system




discharging/charging current


estimated current equalizer


equivalent electrical circuit model


open-circuit voltage


constant current




constant current–constant voltage

C :

equivalent capacitance of RC battery model, F

C i :

equivalent capacitance of i-th cell in a series battery pack, F

C n :

nominal capacity of battery, As

C n,i :

nominal capacity of the i-th cell, As

C n,pack :

nominal capacity of a series battery pack, As

G C,i :

relative proportion of the i-th cell’s equivalent capacity

G R,i :

relative proportion of the i-th cell’s equivalent resistance

G R,i(–):

a priori G R,i at time k

I :

estimated current of RC battery model, A

I i :

estimated current of the i-th cell, A

K I :

PI observer gain

k :

discrete time

R :

equivalent resistance of RC battery model, W

R i :

equivalent resistance of the i-th cell, W

SOCi :

SOC of the i-th cell in a series battery pack

SOCpack :

SOC of a series battery pack

T :

operational period of the ECE, s

T s :

sampling time, s

V t :

terminal voltage of battery, V

V t,i :

terminal voltage of the i-th cell, V

Q i :

total charge during period T of the i-th cell, As

T s :

sampling time, s

α :

smoothing factor


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Correspondence to J. Kim.

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Chun, C.Y., Cho, B.H. & Kim, J. Implementation of discharging/charging current sensorless state-of-charge estimator reflecting cell-to-cell variations in lithium-ion series battery packs. Int.J Automot. Technol. 17, 909–916 (2016).

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Key words

  • Battery pack
  • Cell-to-cell variation
  • Filtered terminal voltage
  • Lithium-ion batteries
  • State estimation
  • State-of-charge (SOC)