## Author

## Date

State of charge (SoC) of a battery is a measure of the amount of charge (a reasonable proxy for energy) in a battery. Since it is typically expressed as a percentage, it is a measure of the amount of charge in a battery relative to its full capacity.

SoC is not a directly measurable parameter of a battery and must be estimated using other measured parameters such as current and voltage. Knowing the right SoC is highly critical for most battery applications – to estimate the remaining range for electric vehicles, to optimally schedule charge-discharge cycles in stationary storage systems

This makes accurate SoC estimation one of the most important tasks for battery management systems or energy management systems working with batteries.

There are a few ways in which SoC is estimated today –

**Open Circuit Voltage Method:**

When the battery is not connected and has had sufficient time to rest, there exists a known relation between the battery voltage (open circuit voltage or OCV) and the SoC, which depends on the cell chemistry. This relation is approximately linear for lead acid batteries, but significantly non-linear for Li-ion batteries.

SoC at rest for an open-circuit battery can be accurately estimated from the OCV (at a given temperature), however, this is a rare scenario for a battery that is in use. When the battery is connected and charging or discharging, the voltage measured at the battery terminals varies from the OCV due to the various internal resistances and capacitances of the battery cells. This results in an inaccurate measure of SoC as shown below.

**Coulomb Counting Method:**

THe Coulomb counting method is a widely used method for battery SOC estimation since it is easy to implement. In this method, as the term suggests, the amount of charge entering (charging) or exiting (discharging) the battery is measured and summed over time. The total charge in the battery at any time (t) is calculated as the total charge at a previous time (t-1) plus the amount of charge flowing in that interval.

SOC(t) = SOC(t-1) – ŋ*∫ i(t) dτ, ŋ = 1/(3600*battery capacity)

This method works reasonably well for some use cases, but suffers from a few important shortcomings. Since the accuracy of the current measurement is not always great, there is always some small error in the SoC estimation. Moreover, since this method calculates the current SoC from the previous SoC, the error in estimation accumulates over time and cannot be easily corrected.

**Extended Kalman Filter Method:**

The Extended Kalman Filter (EKF) is a mathematical method to estimate physical states from data given by inaccurate sensors. In the case of SoC estimation using EKF, the method incorporates both the coulomb counting method as well as the OCV method to arrive at a much better estimate of the correct SoC.

Often, Battery management systems are built with significant computing constraints and are unable to incorporate complex algorithms such as EKF into their battery estimation. In such cases, the supervisory energy management system (EMS) can do the heavy lifting and give a better estimate of SoC to optimize battery schedules and increase battery life.