State of charge (SOC)

The state of charge is the fraction of available charge [Ah] at a given instant, with respect to the capacity. I.e. the (current * time) which you can draw until the battery is empty. Therefore the SOC is varying between 0 (empty battery) and 1 (full charge).

As the capacity is depending on several parameters - mainly the discharge rate - the SOC is not an absolute value: it will depend on the conditions when you will discharge the battery.

The SOC is not directly measurable on the battery. The battery voltage is an indicator, but not always reliable as it highly depends on the current, the temperature, the battery age. In simple controllers, the SOC cannot be used for control decisions, only the voltage is relevant. In complex systems (namely with BMS), the SOC may be evaluated by a calculation (history of currents), but this is never absolute.

During the simulation, we have to evaluate the variations of SOC as a function of the charging or discharging currents or energies. The SOC evolution is evaluated for a specified period, according to the charge or discharge current (without losses):

\(SOCend = SOCbeg + (IBatttery[A] * DTime [h]) / Capacity [Ah]\).

During charging we have to take the Faradic efficiency EfficI into account:

\(SOCend = SOCbeg + (IBatttery[A] * EfficI * DTime [h]) / Capacity [Ah]\).

For the energies, not only the capacity variability, but also the voltage affects the balances. The stored/restored energy is calculated as:

\(ESOCbalance [Wh] = (SOCend - SOCbeg) * Capacity [Ah] * VBattery [V]\)

where the VBattery includes a voltage drop across the internal resistance, depending on the current.