## 2 Experimental Preparation for Fuzzy Logic Application
### Battery Charging Current  
A factor affecting both the battery capacity and battery life is the determination of the values between which the battery charging current will be. The charging or discharging rates in the batteries are symbolized by C, and this rate is defined as, for example, the ability of a 1 Ah battery to maintain a current of 1 A for 1 h. Discharge processes at different values of the Li-ion battery were performed experimentally. In this way, the limits of the discharge current to be used in the fuzzy logic controller were determined. The batteries used in the experiment are offered to the user at a 30% discharge rate from the factory. Operating between 4.2 V and 2.5 V voltage values, these batteries were first discharged at 1 C and then charged at 1 C. Discharging at different C ratios was performed at 43 \({}^{\circ}\)C with a DL24P discharger capable of discharging between 0.1 A and 30 A. The battery charging  
Figure 4: Battery capacity test at 1C charging current at different temperatures. current experiments were performed at 43 \({}^{\circ}\)C, and the highest capacity was obtained at this temperature (Figure 5). In this test setup, discharges were performed at C/10, C/5, C/3, C/2, C, 2 C, 3 C, and 5 C ratios. The Aspilsan 18650 NMC battery used in this study has a capacity of 2900 mAh. This capacity value of the battery means that it can meet 2.9 A for 1 h. While charging and discharging processes have a positive effect on the battery's capacity at low C rates, at high C rates, some of the energy is converted into heat and causes capacity loss on the battery. The evolution of the capacity as a function of the discharge rate is given in Figure 6.  
Figure 5: Discharge experimental setup at 43 \({}^{\circ}\)C and different C values. Figure 6: Battery capacity test at 25 \({}^{\circ}\)C at different C ratios. The battery capacity decreased by around 5% of its capacity when the C ratios increased from C/10 to 5 C, while the heating increased from 43.2 to 93.6 \({}^{\circ}\)C (Figure 7). The breaking point of the heat increases is observed above 0.5 C. At high C ratios, some of the energy during the charge/discharge process is converted into heat energy, decreasing the battery capacity. In a fuzzy logic controller, the battery parameters used in an EV and the proposed SC parameters are needed to determine the constraints. The EV battery and motor parameters used to determine the constraints are given in Table 1.  
There are 95 series-connected battery cells and 48 parallel-connected battery cells in the EV battery pack. With a motor power of 160 kW, the maximum current to be drawn from the battery cell of the EV is 8.7 A. The maximum current value to be drawn from the battery cell corresponds to the 3 C ratio. Formulas (1)-(4) are calculated for transferring the power gained from regenerative braking to the HESS. (1) is the moment of inertia, (2) is the aerodynamic drag resistance force, (3) is the rolling resistance force, and (4) is the power transferred to the HESS. \[I_{w/t}=m_{w}{r_{w}}^{2}+m_{t}{r_{t}}^{2} \tag{1}\]  
where \(m_{w}\) is the rim weight (kg), \(r_{w}\) is the rim radius (m), \(m_{t}\) is the wheel weight (kg), and \(r_{t}\) is the tire sidewall thickness (m). \[F_{aro}=\frac{1}{2}pC_{d}AV^{2} \tag{2}\]  
where \(p\) is the air density (kg\(\cdot\)m\({}^{3}\)), \(C_{d}\) is the drag coefficient, \(A\) is the vehicle front surface area, and \(V\) is the speed (km/h). \begin{table}
\begin{tabular}{c c} \hline
**EV Parameters** & **Parameter Values** \\ \hline Battery cell voltage & 4.2 V \\ Battery pack voltage & 400 V \\ Battery capacity & 52.4 kWh \\ Battery cell quantity & 4560 \\ Battery weight & 340 kg \\ Engine power & 218 HP \\ Average consumption & 16.9 kWh/100 km \\ \hline \end{tabular}
\end{table} 
Table 1: EV battery and motor parameters. Figure 7: Evolution of the battery temperatures during the isothermal discharge at 43 \({}^{\circ}\)C with different C ratios.