# Sizing Methodology of a Fast Charger for Public Service Electric Vehicles Based on Supercapacitors
## 1 Introduction  
Supercapacitors (SCs) are electrical energy storage devices characterized by their high efficiency and specific power. Both properties are due to the fact that the energy is stored in the form of an electric field, which, together with their low internal resistance, makes them capable of charging and discharging at very high currents. In addition, they endure several orders of magnitude more charging and discharging cycles than other storage systems [1], making them ideal for hybrid systems when combined with batteries or fuel cells [2; 3; 4; 5]. SCs are used in the accumulators of different types of vehicles [7; 8]. Their use is particularly effective in cases where urban journeys with multiple stops are made. In this type of tour, much more energy can be recovered by regenerative braking, and they can be charged extremely quickly compared to electrochemical accumulators. In addition, the high discharge current provides the vehicle with greater acceleration on start-up. On the other hand, SCs are lighter than conventional batteries, thus reducing the overall weight of the vehicle and with it, its energy consumption. The above advantages have made electric urban transport vehicles using SCs an increasingly attractive option [9; 10]. Public transport buses or urban solid waste collection trucks, which follow a fixed route, at slow speeds, with multiple accelerations and decelerations, are the cases where the use of SC-based accumulators is optimal, as long automoines between successive stops are not required [11]. The main drawback of SCs compared to batteries is their lower energy density, which reduces the range of vehicles whose accumulators use them; however, in the case of urbantransport, this disadvantage can be easily solved by installing fast chargers along the route. The time it takes for passengers to get in and out of the vehicle (20-30 s) is more than enough if the charging station is able to supply the necessary current. Recharging at the exit of the stop would then make it possible to reach the next charging station to repeat the process. There are multiple types of electronic converters with different control strategies for fast charging of SCs [12; 13; 14]. However, due to their topologies and the high powers they have to handle, they can cause disturbances in the electrical grid [15], such as voltage drops, voltage dips, flickering, or harmonic distortion, which can only be solved, in some cases, by modifying the grid itself. Therefore, in recent years, several studies have been carried out to develop new technologies for fast-charging stations, [16; 17; 18; 19; 20; 21] that minimize the disturbances mentioned above. One of the most interesting and efficient alternatives is precisely the use of SCs as an energy storage medium [18; 19; 20]. Its operating principle is very simple: a bank of SCs, slowly charged from the grid, can evacuate its energy to the vehicle's accumulator, also built with SCs, very quickly. Once the vehicle has been charged, the SCs in the station are slowly recharged, absorbing a low level of power that does not cause any disturbance. After this slow charging process, the system is ready for the fast charging of the next vehicle arriving at the station. Figure 1 shows a general scheme of the fast-charging station in which the bank of SCs of the charger (C\({}_{1}\), R\({}_{1}\)), that of the vehicle (C\({}_{2}\), R\({}_{2}\)), and the smoothing inductor between them (L, R\({}_{L}\)) are represented. As can be seen, charging is done directly between the two SCs banks without the need for an intermediate DC-DC converter. In addition to the advantages this represents for the grid, the charger is simplified and cheaper, since only one inductor is required between the two sets of SCs to limit the charging current. Later sections will show, in depth, the simplicity of the charging station architecture compared to the use of power converters.