## 3 Components Modeling of Proposed Design
### Dc-dc Sepiic Converter  
The second DC-DC converter used is a single-ended primary inductive converter (SEPIC). A SEPIC is a non-inverting, bidirectional converter capable of working in DCM. The advantage of the SEPIC converter over others is that its output has the same polarity as the input. It has minimal active components. It has an inductor at the input which reduces the switching harmonics experienced by the source. In the proposed system, the SEPIC converter regulates the voltage coming out of the SC. The voltage from the SC is then used to recharge the battery pack. The SC is charged with the help of a regenerative braking system which converts kinetic energy to electrical energy. A comparison of different types of converters and all the features are given in Table 4. Among these, the SEPIC converter was selected because it is best suited for EV application. The circuit diagram for the SEPIC converter can be seen in Figure 4. \begin{table}
\begin{tabular}{c c} Input Voltage (V\({}_{i}\)) & 230 V \\ Inductor (L) & 3.3 mH \\ Capacitor (C) & 1.7 mF \\ Load Resistance (R\({}_{\text{L}}\)) & 38 \(\Omega\) \\ Output Voltage (V\({}_{\text{o}}\)) & 400 V \\ Output Current (I\({}_{\text{o}}\)) & 10.5 A \\ Inductor Current (I\({}_{\text{L}}\)) & 18.3 A \\ Output Power (P\({}_{\text{o}}\)) & 4.2 KW \\ Frequency (F\({}_{\text{S}}\)) & 20 kHz \\ Time Period (T) & 50 \(\upmu\)s \\ \end{tabular}
\end{table} 
Table 3: Boost Converter Parameters. When the converter operates in steady-state, Volt-sec balance of inductor \(L_{1}\)  
\[\frac{1}{T_{s}}\int_{0}^{T_{s}}v_{L_{1}}dt\ =\ \frac{1}{T_{s}}\biggl{(}\int_{0}^{DT_{s}}v_{L_{ 1}}dt+\int_{DT_{s}}^{T_{s}}v_{L_{1}}dt\biggr{)}=\ 0 \tag{13}\]  
\[V_{o}+V_{C_{1}}=\frac{V_{i}}{1\ -\ D} \tag{14}\]  
where \"\(D\)\" is the duty cycle of the SEPIC converter and \"\(T_{s}\)\" is the total time period. Volt-sec balance of inductor \(L_{2}\). \[\frac{1}{T_{s}}\int_{0}^{T_{s}}v_{L_{2}}dt\ =\ \frac{1}{T_{s}}\biggl{(}\int_{0}^{DT_{s}}v_{L_{ 2}}dt+\int_{DT_{s}}^{T_{s}}v_{L_{2}}dt\biggr{)}=\ 0 \tag{15}\]  
\[V_{o}+V_{C_{1}}=\ \frac{V_{o}}{D} \tag{16}\]  
Combining (15) and (16), the transfer ratio is obtained as:  
\[\frac{V_{o}}{V_{i}}=\frac{D}{1\ -\ D} \tag{17}\]  
The average voltage across capacitor \(C_{1}\) is  
\[V_{C_{1}}=\frac{(1\ -\ D)V_{i}}{1\ -\ D}=\ V_{d} \tag{18}\] \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Features** & **SEPIC** & **Boost** & **Buck-Boost** & **CUK** & **References** \\ \hline Input Current & Continuous & Continuous & Pulsating & Non-Pulsating & [2] \\ Output Voltage Polarity & Non-Inverting & Non-Inverting & Reverse & Reverse & [7] \\ Output Current & Continuous & Pulsating & Pulsating & Continuous & [8] \\ Switching Voltage & Grounded & Floated & Floated & Floated & [8] \\ Output to Input voltage & Greater/Lesser & Higher & Lesser/Greater & Lesser/Greater & [9] \\ Magnitude & Low & High & Low & Low & [9] \\ Switching Losses & Medium & Medium & Medium & Medium & [10] \\ Cost & High & Low & Low & Medium & [11] \\ Efficiency & Higher rating & High Load and & Nearly Matched & Same rating & \\ Application & battery and & Low module & battery—Voltage & battery and & [8, 12, 13] \\  & module voltage & Voltage & module & voltage module & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of Different Types of Converter. Figure 4: Circuit diagram of SEPIC converter. The average voltage across capacitor \(C_{2}\) is  
\[V_{C_{2}}=\ V_{o} \tag{19}\]  
The relation between the input and output power can be expressed as:  
\[V_{i}I_{i}=\ V_{o}I_{o} \tag{20}\]  
To calculate the ripple current across the inductor, we will use the expression in Equation (21).