# Multiport Energy Management System Design for a 150 kW Range-Extended Towing Vessel
## 2 EMS Model for RETV
### ESS Model
#### 2.2.3 Bidirectional Buck-Boost Converter Model  
The bidirectional DC-DC converter is the conversion device between DC voltages. As shown in Figure 3, it can enable bidirectional energy transfer while maintaining the voltage polarity on both the input and output sides. A non-isolated bidirectional buck-boost DC-DC converter was employed for the multiport EMS. This type of converter facilitates bidirectional power flow and voltage adjustment catering to ESS [36]. The non-isolated DC-DC converter had a simple structure and a small volume because there was no isolation transformer. It can realize highly efficient bidirectional power conversion in the ESS composed of battery and supercapacitors [37; 38]. According to the current flow directions, the converter mainly worked in buck and boost modes. As shown in Figure 4, the \(U_{1}\) was connected to the lithium battery that supplied power to the external load. The load was connected in parallel with the output capacitor \(C_{2}\), and the positive pole of the output voltage \(U_{2}\) was downward. In this case, \(S_{1}\) was the main switching tube and \(S_{2}\) was the synchronous switching tube. Assuming \(D_{1}\) is the duty cycle of \(S_{1}\), \(T=1/f_{S}\) is the switching period, where \(f_{S}\) is the switching frequency, and \(L\) is the inductance of the inductor \(L_{1}\). The working principle of the boost mode can be explained as follows. First, when \(0<t<D_{1}T\), the switch \(S_{1}\) is turned on, and the switch \(S_{2}\) is turned off. The inductor voltage \(U_{L}=U_{1}\), and the inductor current is  
\[i_{L}(t)=\frac{1}{L}\int_{0}^{t}U_{L}\mathrm{d}t+i_{L}(0)=\frac{U_{L}}{L}t+i_{ L}(0) \tag{5}\]  
Bringing \(t=D_{1}T\) into the Equation (6), the peak value of the AC component of the inductor current is obtained as  
\[\Delta i_{L}=i_{L}(D_{1}T)-i_{L}(0)=\frac{U_{L}D_{1}}{f_{S}L} \tag{6}\]  
where the drain-source voltage is 0 for the switch \(S_{1}\) (\(U_{DS1}=0\)), the drain-source current is \(I_{L}\) (\(I_{D1}=I_{L}\)), the drain-source voltage is \(U_{1}+U_{2}\) for the switch \(S_{2}\) (\(U_{DS2}=U_{1}+U_{2}\)), and the drain-source current is 0 (\(I_{D2}=0\)). \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Lithium battery’s nominal voltage & 600 V \\ Lithium battery’s rated capacity & 1000 Ah \\ Lithium battery’s initial state of charge & 75\%/15\% \\ Supercapacitors’ rated capacitance & 700 F \\ Supercapacitors’ rated voltage & 700 V \\ Supercapacitors’ initial state of charge & 100\% \\ Supercapacitors’ number of series capacitors & 200 \\ Supercapacitors’ number of parallel capacitors & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of the ESS. Figure 4: An equivalent circuit of the bidirectional DC–DC buck–boost converter in the boost mode. Figure 3: Energy flow diagram for a bidirectional DC–DC converter. Second, when \(D_{1}T<t<T\), the switch \(S_{1}\) is turned off and \(S_{2}\) is turned on. The inductor voltage \(U_{L}=-U_{2}\), and the inductor current is  
\[i_{L}(t)=-\frac{U_{2}}{L}(t-D_{1}T)+i_{L}(D_{1}T) \tag{7}\]  
Other relevant voltages and current values are as follows. \[\Delta i_{L}=i_{L}(D_{1}T)-i_{L}(0)=\frac{U_{2}(1-D_{1})}{f_{S}L} \tag{8}\]  
\[U_{DS1}=U_{1}+U_{2},\ I_{D1}=0,\ I_{DS2}=0,\ I_{D2}=I_{L}\]  
The ideal DC voltage conversion ratio in the discharge state is  
\[M_{U}=\frac{U_{2}}{U_{1}}=\frac{D_{1}}{1-D_{1}} \tag{9}\]  
Figure 5 shows an equivalent circuit diagram for the bidirectional DC-DC buck-boost converter in buck mode. As shown, \(S_{2}\) was the main switch, \(S_{1}\) was used as the synchronous switch, and \(D_{2}\) was the duty ratio of \(S_{2}\). \(U_{2}\) charged the lithium battery pack in this case. Third, when \(0<t<D_{2}T\), switch \(S_{2}\) is turned on and \(S_{1}\) is turned off.