Methods For Soc Estimation; Figure 19. Equivalent Circuit - STMicroelectronics AEK-POW-BMS63EN User Manual

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Methods for SOC estimation

The state of charge (SOC) of a cell indicates the energy stored by a cell, defined as the ratio of the charge
quantity of a cell in a given moment and its total capacity.
The traditional calculation method is the coulomb counting.
According to this method, a charging/discharging current I(t) is integrated in time to calculate the residual energy
quantity of the cell itself.
SOC(t) in a specific instant is calculated as the sum of the SOC related to the previous instant SOC(t-1) and the
quantity of energy removed/added to that specific instant, as shown in the following formula:
where:
• SOC(t) is the state of charge of the cell in the instant (t)
• SOC(t-1) is the state of charge of the cell in the previous instant (t-1)
• Q is the total capacity of the cell
• η is the cell efficiency
This method does not consider the speed, and hence the dynamics of the cell charge/discharge, temperature,
hysteresis of charge/discharge and especially the cell age, which directly influences efficiency.
Moreover, this method is not accurate due to the error of integration and to the initial SOC estimation, and to the
eventual inaccuracy of the cell current measurement.
Other issues are related to the difficult estimation in case the cell undergoes an open circuit voltage variation
(OCV with no load voltage) that is not significant in relation to the actual SOC (for example, in case LFP batteries
are used).
The Kalman filter represents a promising alternative approach, which allows overcoming these obstacles through
a higher effort in terms of computational resources.
This filter is based on a non-linear model of a cell through an equivalent circuit.
In our approach, we have used a first-grade equivalent circuit, as shown in the image below.
In this circuit:
• Vo is the no-load voltage
• Vt is the voltage at the battery poles
• R0 represents the ohmic behavior of the cell
• R1C1 takes into account the dynamic behavior during charge and discharge
The equations that define the model are:
UM3185 - Rev 1
I t ∙ η
t
SOC t = SOC t − 1 ∙ ∫ t − 1
Q n
Figure 19. Equivalent circuit
dSOC i
= −
dt
3600AH T
Methods for SOC estimation
∙ dt
UM3185
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