# An Optimal Sizing Design Approach of Hybrid Energy Sources for Various Electric Vehicles
## 4 Simulation Results and Discussion
### Parameters and Specifications of Energy Sources  
The performance indices of three energy storage devices (SC, LTO, and Li3 battery) needed to be searched in advance. Note that though the costs of materials of batteries were similar, the labor cost and management cost widely vary, which causes large differences in the final costs and influences the key indices. For the viewpoint of this purely academic research, we only retrieved the data from research papers rather than focusing on specific market areas or specific time periods. However, to avoid the large difference of a specific index, three data-cancellation rules were set to judge and delete the extreme values: (1) the maximum value is more than or equal to two times the minimum values; (2) the difference of average values before and after deleting the maximum or minimum value is more than 10%; (3) from the normal distribution, the Z score (standard score) is higher than 1.23.  
In Table 1, for supercapacitors, the averaged value of specific power was 7.3 (kW/kg) [24; 25; 26], the value of specific price [24] was 10,000 (USD/kWh), the averaged value of specific energy at constant volume was 0.0085 (kWh/L) [27], and the averaged value of specific energy at constant mass was 0.00484 (kWh/kg) [24; 27; 28]. The specific price and specific power was relatively high. Note that not all data-cancellation rules were satisfied (e.g., for specific power, the maximum value was two times the minimum value and the average values before and after deleting 10 were 7.3 and 5.95 (an 18.50% difference); however, the Z-score was 1.069, which was below 1.10, so all data were used for calculation).  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** & **Average** \\ \hline \multirow{3}{*}{Specific power (kW/kg)} & 5 [24] & \\ \cline{2-3}  & 10 [25] & 7.3 \\ \cline{2-3}  & 6.9 [26] & \\ \hline Specific price (USD/kWh) & 10,000 [24] & 10,000 \\ \hline Power density (kWh/L) & 0.0085 [27] & 0.0085 \\ \hline \multirow{3}{*}{Specific energy (kWh/kg)} & 0.0065 [27] & 0.00484 \\ \cline{2-3}  & 0.00302 [28] & \\ \hline \hline \end{tabular}
\end{table}
Table 1: The performance indices of supercapacitors.  
In Table 2, for LTO batteries, the average value of specific power was 2.763 (kW/kg) [2,17,29,30]; the value of specific price was 578.66 (USD/kWh) [2,29,31]; the average value of specific energy at constant volume was 0.138 (kWh/L) [30,31,32]; and the average value of specific energy at constant mass was 0.0635 (kWh/kg) [2,17,30,31,32]. Note that concerning the data-cancellation rules, for specific energy, the maximum value was nine times the minimum value, the average values before and after deleting 0.011 were 0.056 and 0.0635 (a 13.39% difference), and the Z-score was 1.62, which is higher than 1.10, so the data point 0.11 was deleted.  
In Table 3, for NCM (Li3) batteries, the average value of specific power was 0.416 (kW/kg) [2,17]; the value of specific price was 397.5 (USD/kWh) [2]; the averaged value of specific energy at constant volume was 0.400 (kWh/L) [31,32,34]; and the average value of specific energy at constant mass was 0.201 (kWh/kg) [2,17,30,31,34,35]. The values of specific energy at constant volume and specific energy at constant mass were relatively high. Note that concerning the data-cancellation rules, for specific power, the maximum value was 6.35 times the minimum value; the average values before and after deleting 2.3 were 0.887 and 0.416 (a 41.63% difference); and the Z-score was 1.49, which is higher than 1.10, so the data point 2.3 was deleted. From Tables 1-3, these performance indices were used for calculations.