# Sizing Methodology of a Fast Charger for Public Service Electric Vehicles Based on Supercapacitors
## 3 Discussion  
In this section, a practical case of the design of a fast-charging station will be presented. The starting point will be the electric bus Tecnobus Gulliver U500(tm), whose hybrid storage system consists of 72 V and 120 Ah lead-acid batteries and three Maxwell Technologies(tm) 125 V and 63 F SC modules connected in series. The bus has been designed to be used with a fast-charging system for the SCs and uses a pantograph manufactured by Schunk(tm). All the features of both the bus and the charging system can be found in [20]. The charging station proposed here is different from that of the manufacturer. Two strategies for charging SCs are analyzed in [20]: The first one consists of using a single stage where the charging time is 24 s, and the maximum current is 1152 A. The second presents three stages; in each of them the current does not exceed 513 A, but the charging time is extended to 40 s. For the fast-charging station proposed in this paper, the system will be sized to complete the charging in a maximum time of 30 s, in the worst case, and with a maximum peak current of 1 kA. Both the charger and vehicle cells can endure up to 1.9 kA; however, the design current limit shall be set at 1 kA. With this limit, the charging process shall be correctly performed for different initial voltages in the vehicle accumulator, as well as for any degree of cell aging. Each SC module on the bus consists of 48 cells with a rated voltage of 2.7 V. Since the three modules are series connected, the whole accumulator will present a rated voltage (U\({}_{2\text{N}}\)) of 375 V. Following the manufacturers' recommendation to limit the maximum discharge to 50% of its rated voltage, the vehicle's accumulator will discharge up to 187.5 V at most. As for the charger, an initial voltage, U\({}_{01}\), of 400 V will be set in order to optimize energy transference and prevent the cells from reaching too high of a voltage. In addition, to ensure that the final voltage of the SCs is, in all cases, close to U\({}_{2\text{N}}\), the number of U\({}_{02}\) steps, n, will be set to 8. These data are shown in Table 1. The array of SCs installed in the bus presents the rated values shown in Table 2.  
First, the final voltage, U\({}_{0\text{}}\), will be calculated so that the set of capacitors forming the charger will consist of seven identical modules. According to (28), the voltage will be 371.9 V, which will be used when the vehicle arrives with the minimum voltage, 187.5 V. According to (24), the maximum capacitance of the charger will be 137.8125 F. The value of \(\Delta\)V in this case, according to (29), will be 23.4375 V. The modules of capacitance \(\Delta\)C that will form the charger, according to (26), will be of 19.6875 F (there will be 7 identical units). If it is considered that the bus will never arrive at the charging station with a voltage higher than 80% of U\({}_{2\text{N}}\) (300V), in the case where n = 8, the charger can be designed such that U\({}_{02\text{max}}\) = 304.7 V (a very close value to 300 V). There will then be five steps for the voltage U\({}_{02}\) and four steps for the capacitance of the charger so that only four modules of SCs with capacitance \(\Delta\)C will be connected by means of contactors, and three other blocks of the same capacity connected in parallel will not need any kind of switch. For the actual construction of the charger, commercial products should obviously be used, and, with them, it will be necessary to achieve values as close as possible to those \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**U\({}_{2\text{N}}\) [V]** & **U\({}_{02\text{min}}\) [V]** & **U\({}_{01}\) [V]** & **I\({}_{\text{max}}\) [A]** & **t\({}_{\text{charge}}\) [s]** & **n** \\ \hline
375 & 187.5 & 400 & 1000 & 30 & 8 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Initial values of the variables to start the design of the charger.