# Electrification of a Class 8 Heavy-Duty Truck Considering Battery Pack Sizing and Cargo Capacity
## 2 Methodology
### Battery Cell Characterization  
The second-order equivalent circuit model is used for the mathematical modelling of each battery pack shown in Figure 2. For this purpose, the SONY VTC6 cylindrical battery cells were tested in a High Voltage Energy Storage (HVES) lab at Oxford Brookes University. The HPPC tests were performed for characterization of the battery cells in the lab at a temperature of 25 \({}^{\circ}\)C. In HPPC tests, the battery cell underwent a discharge test at 1.5 C, which provided a picture of voltage at various SOC, as well as the transient response to current pulses. The cell has a maximum voltage of 4.2 V, and a capacity of  
Figure 4: The (**a**) velocity profiles and (**b**) road inclination variations in the Long-haul driving cycle [26,27].  
3000 mAh. As an approximation, 1.5 C was chosen as a typical discharge rate seen for commercial automobiles [17; 18; 28; 29]. The cell was placed in a testing chamber to hold the temperature constant (Figure 5). A clamping apparatus which utilizes spring force was used to provide firm contact between the cell terminals and the power supply. Voltage across the cell was measured by clipping leads to metal at each plate, while current was recorded using an Arbin battery tester (ARBIN LBT21084). Thermocouples were used to obtain the temperature of the cell, and the experiment was conducted at 25 \({}^{\circ}\)C to gain an understanding of behavior at average ambient temperature.  
After data was obtained from the HPPC tests, a second-order ECM was developed in MATLAB Simulink to characterize the cell behavior for use in pack modelling with AVL CRUISE M. The model uses a battery block, which is controlled by defining parameters such as internal resistance, dynamic time constants and resistances, capacity, and cell voltage. Current is controlled through the \"Current Source\" block, which received the same input current as the experimental tests. The \"Voltage Sensor\" block outputs cell voltage, while the \"SOC\" block outputs the state of charge (Figure 6). The model received parameter values from a separate MATLAB workspace, and it sends outputs and input current to the parameter estimate module as well as the workspace.  
\begin{table}
\begin{tabular}{l c c} \hline \hline
**Case** & **Number of Cell Rows** & **Cargo Capacity [\%]** \\ \hline R35L10 & 35 & 10 \\ \hline R40L10 & 40 & 10 \\ \hline R45L10 & 45 & 10 \\ \hline R35L50 & 35 & 50 \\ \hline R40L50 & 40 & 50 \\ \hline R45L50 & 45 & 50 \\ \hline R35L100 & 35 & 100 \\ \hline R40L100 & 40 & 100 \\ \hline R45L100 & 45 & 100 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Case scenarios for parametric study performed.  
Figure 5: Sony VTC6 cell experimental setup.  
Each parameter can be expressed as an array of values, each value being defined at a specific SOC. In this particular case, 16 discharge pulses were conducted experimentally to take the cell from 4.2 V to 3.4 V, so all parameter arrays had 16 items.  
Simulink's built-in parameter estimator was used to determine parameter values which matched experimental results. The varied parameters were voltage, first and second dynamic resistances, first and second-time constants, and static resistance. The Levenberg-Marquardt algorithm was used to iteratively find parameters that resulted in minimizing the least-squares difference from the experimental results. The parametrization resulted in closely matching voltage vs SOC graphs, with an R\({}^{2}\) value of 99% (Figure 7).  
Figure 6: MATLAB model used for cell parameter estimation.  
Figure 7: Cont.