## 4 Hybridization and Load Sharing Methodology  
As briefly mentioned in the introduction, there are two main topologies to realize a hybrid unit with a high power (HP) storage system which is realized by means of super-capacitor or lithium-ion capacitors and a high energy (HE) storage system which is realized by means of a battery:  
1. active topology [8], and
2. passive topology [8]. There is also a combination of those two methods which is called the semi-active topology [22]. A review article [23] validates the performance and cost efficiency of the semi-active topology in comparison to the passive and fully-active topology. Since the purpose of this study is to investigate the hybridization effect on the lifetime improvement of the energy storage system and to extend the range of the urban electric bus with one fully-charged ESS, a semi-active topology of hybridization is used herein. Some of the semi-active topologies are shown in Figure 9.  
Figure 8: Internal resistance evolution of LiC 2300 F with a heavy-duty load profile. Figure 9: Semi-active hybrid topologies: (**a**) battery semi-active hybrid energy storage topology, (**b**) extended battery semi-active hybrid energy storage topology, (**c**) LiC semi-active hybrid energy storage topology, and (**d**) advanced LiC semi-active hybrid energy storage topology [8]. As the voltage level of the LiC module is different than the LiB module, the selected semi-active topology in this study, as shown in Figure 10, only utilizes a bi-directional DC/DC convertor to adjust the voltage level of the HP source with the voltage level of the HE source. In order to maintain this, a low-complexity control system with less computational demanding is proposed. The simplified diagram of the control unit is shown in Figure 10.  
The controller also aims to limit the LiC current below the maximum value, which is 1200 A, and is given in the datasheet [24]. Moreover, it aims to keep the SoC of the LiC within the acceptable range. The maximum value of the current is also limited by the safety measures to keep the cells' temperature below 70 \({}^{\circ}\)C. The acceptable range of SoC is defined by the control strategy. In this study, the initial SoC of the LiCs is kept at 50% in order to have enough stored energy to deliver to the bus during acceleration, as well as to have free capacity to store energy which goes back to the cell during the regenerative braking. Clearly, the SoC cannot go over 100% or below 0%, however, by limiting the SoC of LiCs to a narrower window (for example, 20% to 80%), LiB-ESS is asked to work with a higher current which, as a result, is imposed to a high-frequency current component. The range of the SoC needs to be defined so as to optimize the cost, size, volume, and lifetime of the entire system. The control system is composed of a high-pass filter which is used to separate the high-frequency current components. These high-frequency components of the load are asked to be delivered by the LiC module. As a consequence, the high-current stress factor is removed from the battery and its lifetime is improved. As it is seen in Figure 2 and is explained in [13], a higher DoD tends to a higher increase in the internal resistance and a faster degradation in the capacity of the cell. By eliminating the high-frequency current components from the LiBs, these cells are imposed to a lower DoD which consequently improves the lifetime. In this study, the high-frequency current component (\(I_{ref}\)) is used as a reference for the LiC control unit. The DC-link voltage is also used as a reference voltage (\(V_{ref}\)) for the LiC controller. Figure 11 shows the LiC and LiB current component for the hybrid bus extracted from the London driving cycles. Figure 10: Simplified diagram of the hybrid battery-LiC power source and the proposed control system [22].