# An Optimal Sizing Design Approach of Hybrid Energy Sources for Various Electric Vehicles
## 4 Simulation Results and Discussion
### GSA Results and Discussion
#### 4.2.2 Case Study of Five Types of EVs  
In this Section, the GSA developed in Section 2.2 and the vehicle performance requirements and constraints in Section 3 were simulated. Table 4 demonstrates the optimal sizing of the electric sedan. The vehicle performance requirements (constraints) were listed in Section 3.1. Table 4 shows that the case of LTO/Li3 combination was the best solution due to the lowest cost (33,111 USD) compared to that of the SC/Li3 case (33,842 USD). For the electric capacity, the optimal sizing was that the capacity of the LTO battery (as the high-power source) was 7.459 kWh, where the capacity of the Li3 battery (as the high-energy source) was 67.541 kWh. The size ratio was 9.9:0.1 where the total required capacity was 75 kWh. With the optimal sizing, the maximum output power of the LTO battery was 324.5 kW, while that of the Li3 battery was 139.8 kW. Figure 6: The performance indices of LTO/Li3 HEES with respect to size ratio and total price: (**a**) mass, (**b**) stored energy, (**c**) volume, and (**d**) output power. The combined power exceeded the required power of 464 kW. The HEES mass (453 kg) was slightly higher than that of the SC/Li3 case (416 kg). Similarly, the occupied volume (222L) was slightly more than that of the SC/Li3 (212 L) case. The optimal position of the DC/DC converter was at the high-energy (Li3 battery) side. To prove that the GSA searched the optimal results in the electric sedan case, we manually and randomly selected cases that satisfied the physical constrains. For LTO/Li3 optimization, as the electric capacity was 7.55 and 67.45 kWh, respectively, the total price was calculated to be 33,151 USD. It increased by 0.12% compared to the GSA optimal result. The case with the highest price that satisfied the physical constraints was 33,181 USD, which was increased by 0.21%. In the case of SC/Li3 hybridization, the electric capacity was 0.33 and 74.64 kWh, respectively, where the price increased to 35,968 USD, which was increased by 6.3%. The case with the highest price that satisfied the physical constraints was 38,206 USD, which was increased by 12.89%. Figure 8: The performance indices of the LTO/Li3 HEES with respect to size ratio and electric capacity: (**a**) total cost, (**b**) volume, (**c**) mass, and (**d**) output power. Figure 7: The performance indices of SC/Li3 HEES with respect to size ratio and electric capacity: (**a**) total cost, (**b**) volume, (**c**) mass and (**d**) output power. Table 5 demonstrates the optimal sizing of the electric forklift [36]. The case of SC/Li3 combination was the best solution, as the case of LTO/Li3 was unable to satisfy the required maximum output power. The HEES cost was calculated to be 24,973 USD. For the electric capacity, the optimal sizing was that the capacity of the SC module (as the high-power source) was 1.357 kWh, where the capacity of the Li3 battery (as the high-energy source) was 28.643 kWh. The size ratio was 4.52:95.48, where the total required capacity was 30 kWh. With the optimal sizing, the maximum output power of the SC was 2046 kW, while that of the Li3 battery was 59.3 kW. The combined power exceeded the required power of 2000 kW. The HEES mass was 422 kg, while the occupied volume was 231 L. The position of the DC/DC converter was at the SC side. To prove that the GSA was useful in the electric forklift case, we manually selected cases that satisfied the physical constrains. For SC/Li3 hybridization, as the electric capacity was 1.5 and 28.5 kWh, respectively, the total price was 26,347 USD. It increased 5.5% compared to the GSA optimal result. In the case that the electric capacity was 2 (SC) and 28 (Li3) kWh, respectively, the price was 31,154 USD, which was increased by 24.75%. Table 6 demonstrates the optimal sizing of the long-distance electric bus. No matter LTO/Li3 or SC/Li3 cases, only using the Li3 battery was the best solution because of the long travelling distance. In this case, the Li3 battery cost was calculated to be 39,750 USD.