Battery behavior

The State of Charge (SOC) of a battery indicates the level of charge of a battery relative to the battery capacity. The SOC of a battery can be calculated

(1)\[\text{SOC} = \frac{E_{bat}}{E_{cap}}\]

where, \(\text{E}_{bat}\) is the energy in the battery while \(\text{E}_{cap}\) is the battery capacity.

The energy in the battery is decided based on the amount of power charged or discharged to or from the battery

(2)\[\text{E}_{bat, charge} = E_{bat}+\eta_{charge} \cdot P_{charge} \cdot dt\]

(3)\[\text{E}_{bat, discharge} = E_{bat}-\frac{P_{discharge} \cdot dt}{\eta_{discharge}}\]

here, \(\eta_{charge}\) and \(\eta_{discharge}\) are the charging and discharging efficiency, respectively, \(dt\) is the time increment and \(\text{P}_{charge}\) and \(\text{P}_{discharge}\) are the amount of power charged and discharged, respectively.