# An Optimal Sizing Design Approach of Hybrid Energy Sources for Various Electric Vehicles
## 4 Simulation Results and Discussion
### GSA Results and Discussion  
#### 4.2.1 Optimization of Energy Sources  
To fundamentally analyze four performance indices (mass, electric capacity, volume, and output power) with respect to size ratio and total price or electric capacity of the HESS, the GSA without the vehicle performance requirements (Equations (13)-(16)) was evaluated. There are two possible combinations: SC/Li3 and LTO/Li3 HESS. Figure 5 illustrates the performance of SC/Li3 with respect to total price and size ratio. In Figure 5a, at a fixed price, if the size ratio increases (more SC), the mass increases due to the high specific cost of the SC. In Figure 5b, at the fixed price, the electric capacity decreases as the SR increases due to the low energy density of the SC. In Figure 5c, at a fixed price, the volume increases \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** & **Average** \\ \hline \multirow{4}{*}{Specific power (kW/kg)} & 3.2 [29] & \multirow{4}{*}{2.7625} \\ \cline{2-3}  & 2.25 [30] & \\ \cline{2-3}  & 2.4 [17] & \\ \cline{2-3}  & 3.2 [2] & \\ \hline \multirow{4}{*}{Specific price (USD/kWh)} & 432 [29] & \multirow{4}{*}{578.66} \\ \cline{2-3}  & 899 [2] & \\ \cline{2-3}  & 405 [31] & \\ \hline \multirow{4}{*}{Power density (kWh/L)} & 0.09 [30] & \multirow{4}{*}{0.138} \\ \cline{2-3}  & 0.147 [31] & \\ \cline{2-3}  & 0.177 [32] & \\ \hline \multirow{4}{*}{Specific energy (kWh/kg)} & 0.085 [33] & \multirow{4}{*}{0.0635} \\ \cline{2-3}  & 0.042 [30] & \\ \cline{1-1} \cline{2-3}  & 0.0715 [31] & \\ \cline{1-1} \cline{2-3}  & 0.046 [2] & \\ \cline{1-1} \cline{2-3}  & 0.0464 [17] & \\ \cline{1-1} \cline{2-3}  & 0.09 [32] & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The performance indices of LTO battery. due to the low power density at the constant volume. In Figure 5d, at a constant price, the output power increases as the SR increases due to the high power density of the SC. Another example is the LTO/Li3 HEES case. In Figure 6a, at a fixed price, if the size ratio increases (more LTO battery), the mass increases due to the lower specific energy at constant mass of the LTO battery referred to in Tables 2 and 3. In Figure 6b, at the fixed price, the electric capacity decreases as the SR increases due to the lower energy density of the LTO compared to Li3 batteries. In Figure 6c, at a fixed price, the occupied volume increases due to the lower specific energy at the constant volume. In Figure 6d, at a constant price, the output power increases as the SR increases because of the higher power density of the LTO batteries. Figure 5: The performance indices of SC/Li3 HEES with respect to size ratio and total price: (**a**) mass, (**b**) stored energy, (**c**) volume, and (**d**) output power. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** & **Average** \\ \hline \multirow{3}{*}{Specific power (kW/kg)} & 0.433 [2] & \multirow{3}{*}{0.416} \\ \cline{2-3}  & 0.362 [2] & \\ \cline{2-3}  & 0.454 [17] & \\ \hline \multirow{3}{*}{Specific price (USD/kWh)} & 362 [2] & \multirow{3}{*}{397.5} \\ \cline{2-3}  & 433 [2] & \\ \hline \multirow{3}{*}{Power density (kWh/L)} & 0.37 [32] & \\ \cline{2-3}  & 0.493 [31] & \\ \cline{2-3}  & 0.339 [34] & \\ \hline \multirow{3}{*}{Specific energy (kWh/kg)} & 0.174 [30] & \multirow{3}{*}{0.201} \\ \cline{2-3}  & 0.214 [31] & \\ \cline{2-3}  & 0.241 [17] & \\ \cline{2-3}  & 0.144 [2] & \\ \cline{2-3}  & 0.241 [2] & \\ \cline{2-3}  & 0.24 [35] & \\ \cline{2-3}  & 0.153 [34] & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The performance indices of the NCM (Li3) battery. From another view point, to investigate the relationship of multidimensional performance indices, we chose the electric capacity as the \(y\)-axis variable. In Figure 7a, at a fixed capacity, if the size ratio increases (more SC modules), the total cost increases due to the extremely high specific cost of the SC referred to in Tables 1 and 3.