# Analysis of a Supercapacitor/Battery Hybrid Power System for a Bulk Carrier
## 3 Proposed Hybrid Power System
### Port In/Out Mode  
In this mode, the mooring and windlass winches were the heaviest loads unless bow thrusters were installed onboard. The combined windlass/mooring winch, which is used to handle both anchors and mooring ropes together, is typically installed towards the fore side of a ship, and mooring winches are installed towards the aft side. The specifications of the selected winches are described in Table 3. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Classification** & **Specification** \\ \hline \multirow{2}{*}{Rated motor capacity} & **Type** & **Electric-Driven Type** \\ \cline{2-3}  & Combined windlass/mooring winch & 100 kW \(\times\) 2 (Forward) (one is standby) \\  & Mooring winch & 50 kW \(\times\) 3 (AFT) (one is standby) \\ \hline \multirow{2}{*}{Rated pulling force} & Combined windlass/mooring winch & 300 kN \\  & Mooring winch & 150 kN \\ \hline \multirow{2}{*}{Motor drive type} & Active front-end (bi-directional) type \\ \hline \multirow{2}{*}{Electric voltage} & AC 440 V \\ \cline{2-3}  & & \\ \end{tabular}
\end{table} 
Table 3: Specifications of windlass/mooring winches. Figure 5: Docking/undocking procedure of a ship in the proposed system. The regenerated power rate when lowering an anchor was difficult to define due to various factors such as the inertia of the motor, angular speed, rotation speed, and mechanical loss, etc. [23]. Therefore, regenerated power rate was assumed to be about 50%, according to similar cases [7; 24; 25]. The power demands for one operation cycle were assumed, as shown in Table 4, based on empirical evidence from crews. In this study, the instantaneous peak braking and initial starting power were not taken into consideration for simulation simplification. Based on the battery manufacturer's datasheet, the specifications of the selected LIB modules are shown in Table 5.  
The minimum capacity of the LIB is calculated as shown below [27]:  
\[\mathrm{C_{min}=(E_{d}\times k_{a})\,/\,(V_{dc}\times k_{DoD}\times k_{e})\,(Ah),} \tag{1}\]  
where \(\mathrm{C_{min}}\) (Ah) is the minimum battery capacity, \(\mathrm{E_{d}}\) (VAh) is the demanded energy, \(\mathrm{V_{dc}}\) (V) is the nominal battery voltage, \(\mathrm{k_{DoD}}\) is the battery depth of discharge (DoD), \(\mathrm{k_{a}}\) is the battery aging factor, \(\mathrm{k_{e}}\) is the system efficiency, and other factors are not considered. In this case, \(\mathrm{k_{e}}\) was set to 0.9, \(\mathrm{k_{a}}\) was set to 1.2, and \(\mathrm{k_{DoD}}\) was set to 0.8, assuming that the operating range of the state of charge (SOC) was 10%-90%. The output voltage of the SC pack was determined to be DC 355 V, which was achieved by arranging four (4) battery modules in series. Moreover, two (2) parallel strings were required to meet the demanded energy capacity. Therefore, \(\mathrm{C_{min}}\) was calculated to be about 196.0 Ah, and the designed battery capacity (\(\mathrm{E_{LIB\_design}}\)) was calculated to be about 76.5 kWh, incorporating a 10% safety margin (\(\mathrm{k_{s}}\)) as below. The specifications of the selected LIB pack are shown in Table 6. This LIB pack was split into two sets with the same capacities, and installed at different places for safety reasons. \[\mathrm{E_{LIB\_design}=C_{min}\times V_{dc}\times k_{s}=196.0\,\,Ah\times 355 \,V\times 1.1\cong 76.5\,\,(kWh)<80\,\,(kWh).} \tag{2}\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & & **Operation Mode** & **Time (min)** & **Power (kW)** & **Energy (kWh)** \\ \hline \multirow{3}{*}{**Port-in**} & \multirow{3}{*}{\(\Sigma\)} & 1 & Lowering (heaving up) an anchor & 5 & \(-\)50 & \(-\)4.15 \\  & & & 10 & 200 1 & 33.40 \\  & & **Total** & **15** & - & **29.25** \\ \hline \multirow{3}{*}{Port-out} & \multirow{3}{*}{\(\Sigma\)} & 3 & Pulling (hoisting) an anchor & 10 & 100 & 16.70 \\  & & & 10 & 150 2 & 25.05 \\  & & **Total** & **20** & - & **41.75** \\ \hline \hline \end{tabular}  
* Combined windlass/mooring winch (50 kW \(\times\) 1), mooring winch (50 kW \(\times\) 2).  
\end{table}