# SoC Estimation by Coulomb Counting

SoC Estimation by Coulomb Counting is based on the measurement of the current and integration of that current over time.

The State of Charge (SoC) of a battery cell is required to maintain it’s safe operation and lifetime during charge, discharge and storage. However, SoC cannot be measured directly and is estimated from other measurements and known parameters. This leads to errors in the estimated SoC and that means it is not possible to fully exploit the full capability of the cell.

Coulomb counting gives a relative change in SoC and not an absolute SoC. If you measure the current over a given time step you have a measure of the number of Ah that have left or been received by the battery.

where:

• SoC(t) = estimated State of Charge at time, t
• SoC(t-1) = previous State of Charge at time t-1
• I(t) = charging or discharging current at time, t
• Qn = battery cell capacity
• Δt = time step between t-1 and t

If you want to know the absolute SoC you need to know the starting SoC of the cell, SoC(t-1) as given in the equation. One option is to fully charge the cell to a known voltage. Charging to maximum cell voltage and SoC can be used as a reset and known point.

There are a number of sources of error with the coulomb counting method:

• Starting SoC accuracy
• Current measurement accuracy
• Current integration error
• Uncertainty in battery capacity
• Timing error

In order to define the accuracy you need it is important that you firstly look at what the SoC is used for.

• capacity of the cell that is remaining (fuel gauge on your phone or electric vehicle)
• an input to estimate the available charge and discharge power capability of the battery
• used in the calculation of State of Health

The accuracy required for these values will determine the accuracy that is required for the inputs to the SoC algorithm. This will impact the selection of:

• components for cell voltage measurement
• voltage sense wires, connectors and connection locations
• current sensor or sensors
• voltage and current measurement channel accuracy
• timing circuit

The references below give a good overview of the errors associated with Coulomb Counting along with methods to improve them.

#### References

1. Movassagh, K.; Raihan, A.; Balasingam, B.; Pattipati, K., “A Critical Look at Coulomb Counting Approach for State of Charge Estimation in Batteries“, Energies 2021, 14, 4074.
2. Analog Devices, “A Closer Look at State of Charge (SOC) and State of Health (SOH) Estimation Techniques for Batteries“, Technical Article

This post is designed to give an introduction to the subject. If you would like to write a post expanding on this or any other subject please drop us a line nigel@batterydesign.net