Coulomb Counting and its limitations

Coulomb Counting is one of the simplest and most widely used methods for estimating the State of Charge (SoC) of a battery. The method is based on the principle of charge conservation, where the amount of charge entering or leaving the battery is accumulated over time.

As the battery discharges, electrical charge is removed and the estimated SoC decreases. During charging, charge is added to the battery and the estimated SoC increases. By continuously integrating the battery current, the remaining charge can be estimated throughout battery operation.

The SoC at any time can be calculated using

$${\mathrm{SoC}}_k={\mathrm{SoC}}_{k-1}-\frac{I_k\mathrm{\Delta }t}{3600Q}$$

where

• ${\mathrm{SoC}}_k$ is the estimated State of Charge at the current time step.
• ${\mathrm{SoC}}_{k-1}$ is the estimated State of Charge at the previous time step.
• $I_k$ is the measured battery current.
• $\mathrm{\Delta }t$ is the sampling interval.
• $Q$ is the rated battery capacity in ampere-hours (Ah).
• The factor 3600 converts ampere-seconds into ampere-hours.

Limitations

Although simple and easy to implement, the method has several limitations. Since the battery current is continuously integrated, even small measurement errors accumulate over time, causing the estimated SoC to gradually drift from its actual value.

The primary sources of estimation error include:

• Uncertainty in the initial SoC.
• Current sensor offset and measurement noise.
• Battery capacity variation due to aging and temperature.
• Sampling and numerical integration errors.

Because these errors continuously accumulate, Coulomb Counting alone cannot provide reliable long-term SoC estimation. A correction mechanism is therefore required to periodically compensate for the accumulated drift.

One effective approach is to use a mathematical model of the battery together with measurable quantities such as terminal voltage. This enables the estimated SoC to be continuously corrected, significantly improving estimation accuracy.