From Fig. 4, it is also evident that voltages at different rates of charging and discharging are also different; this is due to internal resistance of the battery [9]. The differences in voltages are not uniform for the whole range of SoC, as the internal resistance is also a non-linear function if the SoC [11]. When the battery is at rest, that is, no current flow takes place, the voltage becomes lower [10]. Polynomial interpolation technique applied in [12] to model the discharge curves of the batteries will be used in this paper. For a given state of charge (SoC), the voltage level when charging is different to that when discharging as shown in Fig. 4. This is due to the fact that some energy used to charge the battery is not recovered when the battery is discharged [13]. This will be considered in modeling the charge and discharge profiles of the battery. The
charge and discharge profiles will be interpolated using polynomial functions.
The charging power of the battery, Pchg, can be obtained from the battery voltage during the charging operation, Vchg, and the charging current Ichg as follows: