# Analysis of a Supercapacitor/Battery Hybrid Power System for a Bulk Carrier
## 3 Proposed Hybrid Power System
### Cargo Loading/Unloading Mode  
In this mode, the onboard deck cranes were the heaviest loads, and they needed repetitive peak power while unloading or loading cargo. These cranes were generally required to perform three functions, namely, to hoist/lower, to luff and to slew. * Hoisting (lowering) is bringing up (down) a crane wire while a crane jib remains in a constant position. * Luffing is the raising or lowering of a crane jib. * Slewing is the swinging round (or rotation) of a crane. Among these crane operations, the biggest load is the hoist motor, which raises and lowers cargo. When lowering the cargo, the motor drive must be capable of handling the inverse power by feeding it back to the onboard main power grid. The specifications of the selected deck crane are shown in Table 7.  
The power demand for hoisting or luffing is dependent on the weight required to carry the cargo by a crane, as shown in the below equation. The crane jip weight (m\({}_{\text{j}}\)) is only applied to the luffing operation [28; 29]:  
\[\text{P}_{\text{hoist}}=\left(\text{m}_{\text{h}}\times\text{v}_{\text{h}} \right)/\left(6.12\times\eta\right)=\left(\left(\text{m}_{\text{load}}+\text{m} _{\text{g}}+\left(\text{m}_{\text{j}}\right)\right)\times\text{v}_{\text{h}} \right)/\left(6.12\times\eta\right)\left(\text{k}\text{W}\right), \tag{3}\]  
where, m\({}_{\text{h}}\) (t) is the hoisting weight, m\({}_{\text{load}}\) (t) is the cargo load weight, m\({}_{\text{g}}\) (t) is the grab weight, v\({}_{\text{h}}\) (m/min) is the hoisting speed, and \(\eta\) is the mechanical efficiency. In this study, m\({}_{\text{load}}\) was set to the maximum load of 30 t, m\({}_{\text{g}}\) was assumed to be 5 t, m\({}_{\text{j}}\) was 10 t, and \(\eta\) was 0.85. The power demand for slewing was also dependent on the weight required to turn the load by a crane, as shown below:  
\[\text{P}_{\text{slew}}=\left(\text{m}_{\text{s}}\times\text{v}_{\text{h}} \right)/\left(6.12\times\eta\right)=\left(\left(\text{m}_{\text{load}}+\text{ m}_{\text{st}}\right)\times\text{R}_{\text{S}}\times\text{v}_{\text{s}}\right)/\left(6.12 \times\eta\right)\left(\text{k}\text{W}\right), \tag{4}\] \begin{table}
\begin{tabular}{c c} \hline \hline
**Category** & **Specification** \\ \hline Target terminal voltage & 355 V \\ Configuration & 2 strings \(\times\) 4 modules in series \\ Usable energy & 80 kWh \\ Total weight (8 modules) & 720 kg \\ Total size (8 modules) & 0.5642 m\({}^{3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Specifications of the selected LIB pack. \begin{table}
\begin{tabular}{c c} \hline \hline
**Classification** & **Specifications** \\ \hline Crane type & Electric-driven type \\ \hline Hoisting max. capacity & 30 t \\ Max. lifting height & 40 m \\ Crane weight & 45 t \\ Hoisting/slewing speed & 20 m/min (full load) 40 m/min (no load) \\ Luffing speed & 10 m/min (full load) \\ \hline Motor rated power & Hoisting & 145 kW \\ Luffing & 90 kW \\ Slewing & 40 kW \\ Grab & 20 kW \\ \hline Motor drive type & AFE (bi-directional) type \\ Electric voltage & AC 440 V \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Specifications of the selected deck crane. where, m\({}_{\rm s}\) (t) is the slewing weight, m\({}_{\rm st}\) (t) is the weight of the slewing structure, R\({}_{\rm s}\) is the resistance to slewing, v\({}_{\rm s}\) (m/min) is the slewing speed, and \(\eta\) is the mechanical efficiency. In this study, it was assumed that m\({}_{\rm st}\) was 10 t, \(\eta\) was 0.85 and R\({}_{\rm s}\) was 0.2. The regenerative power rate was assumed to be 50% according to similar cases [7; 24; 25] as mentioned in Section 3.1. There are ten (10) steps for a deck crane operation, and the expected power demands for one cycle are assumed, as shown in Table 8, based on the empirical evidence from crews. Then, the minimum energy of the SC pack (E\({}_{\rm sc\_min}\)) was obtained through the demand energy (E\({}_{\rm sc\_demand}\)), aging factor (k\({}_{\rm a}\)), safety factor (k\({}_{\rm s}\)), and the system efficiency of (k\({}_{\rm e}\)).