# Combination of LiCs and EDLCs with Batteries:
## 2 Proposed Hybrid Energy Storage System
### The Multiple Input Converter Implementation  
Figure 4a,b presents the conventional and the proposed energy storage hybridisation topologies, respectively. The conventional hybridisation topology involves the use of a three-input DC-DC converter, having one input port for each energy storage, while the hybridisation topology proposed in this research involves having SC and HC connected directly in parallel, thus requiring only a two-input converter, as shown in Figure 4b. The multiple input converter that was used to implement the proposed hybridisation topology as presented in Figure 4b was first proposed by the authors of [41; 42]. The converter can operate in Modes A and B and C and D, as described by the switching patterns presented in Table 2, when the energy storage devices (battery and SC and HC, respectively) are supplying energy and when the DC link is supplying energy to the storage devices, for example during regenerative braking, respectively. Specifically, in Mode A, the battery alone is supplying energy to the EV, while in Mode B, only SC and HC are supplying energy to the EV load. Conversely, in Mode C, energy is being transferred from the DC link of the EV to the battery, while in Mode D, energy is being transferred from the DC link to SC and HC. The steady state waveforms of the converter operation in the modes described above is presented in Figure 5. More detail about the steady-state waveform and other possible modes of the converter operation were adequately addressed in reference [42]. The relationship between the battery voltage and DC bus voltage in Modes A and D is presented in Equations (1) and (2), while the relationship between the DC bus voltage and the parallel arrangement of SC and HC is given by Equations (3) and (4) for Modes B and C, respectively, where \(V_{DC}\) is the average output voltage, \(D\) is the duty ratio, \(T_{1}\) is the ON time, while \(T_{2}\) is the total OFF time, and \(V_{B}\), \(V_{SC}\), and \(V_{HC}\) is the battery, SC, and HC voltage, respectively [42]. Figure 4: The implementation circuit of (**a**) the conventional hybridisation topology using a three-input converter; (**b**) the proposed hybridisation topology having SC and HC directly connected in parallel; and (**c**) the experimental implementation of the converter high side and low side switches with the MOSFET driver. \[V_{\text{DC}}=\frac{T1}{T2+T3}\cdot V_{B}=\frac{D}{1-D}\cdot V_{B} \tag{1}\] \[V_{B}=\frac{T1}{T2+T3}\cdot V_{\text{DC}}=\frac{D}{1-D}\cdot V_{ \text{DC}}\] (2) \[V_{\text{DC}}\;V_{\text{DC}}=\frac{T1}{T2+T3}\cdot\frac{1}{2}\;(V _{\text{SC}}+\;V_{\text{HC}})=\;\frac{D}{1-D}\cdot\frac{1}{2}\;(V_{\text{SC}}+ \;V_{\text{HC}})\] (3) \[\frac{1}{2}\;(V_{\text{SC}}+\;V_{\text{HC}})=\frac{T1}{T2+T3}\cdot V _{\text{DC}}=\;\frac{D}{1-D}\cdot\frac{1}{2}V_{\text{DC}} \tag{4}\]  
Taking a look at the converter in Figure 4b, it can be seen that when each input is considered individually, it is simply an H-bridge DC-DC converter without isolation, therefore having high side and low side switches, just like the conventional H-bridge converter. The high side switch in simple \begin{table}
\begin{tabular}{c c c} \hline
**Mode** & \(\mathbf{T_{1}}\) & \(\mathbf{T_{2}}\) \\ \hline A & \(S_{3}\;S_{2}\) & \(S_{1}\;S_{4}\) \\ B & \(S_{5}\;S_{2}\) & \(S_{1}\;S_{6}\) \\ C & \(S_{1}\;S_{4}\) & \(S_{2}\;S_{3}\) \\ D & \(S_{1}\;S_{6}\) & \(S_{2}\;S_{5}\) \\ \hline \end{tabular}
\end{table} 
Table 2: Conduction of devices for the operating modes of the multiple input converter. Figure 5: Steady-state waveforms of the operation of the multiple input converter for the proposed energy storage hybridisation topology. terms refers to the switching arrangement of having the switch connected between the positive (high) side of the power supply and the load, like Switch S\({}_{3}\) in Figure 4b; while the low side refers to having the switch connected between the ground (low side) and the load, like Switch S\({}_{4}\) in Figure 4b.