## 3 Materials and Methods
### Split City Port Study Case--Ferry Fleet Energy Demand Analysis
The total heating power \(H\) is calculated according to the formula:  
\[H=H_{g}\times m \tag{2}\]  
The total heating power of the fuel used on an annual basis is 590,567 GJ. Therefore, the total heating power is the equivalent of 164 GWh. In accordance with the efficiency of the diesel engines observed in this analysis, a lower efficiency limit of 30% was taken for calculation according to the formula; annual energy needs are calculated according to:  
\[E_{\text{{Annual~{}Needs}}}=\frac{P_{\text{{Energy~{}DLIivered~{}to~{}the~{}Shaft~{} LINE}}}}{P_{\text{{Total~{}Energy~{}contained~{}in~{}fuel}}}} \tag{3}\]  
Based on a previous formula, the annual energy needs amount to 49.2 GW/h. Furthermore, the question arises whether the required power of an electrified fleet of ferries would be equal to the needs of the existing fleet. First of all, it depends on the design requirements and the specifics of the waterway. However, observing the maximum speed of the electrified ferries from Table 1 in comparison with the existing ferries that maintain the considered lines, a decrease in the average peak speed can be observed from 14.13 to 12.8 kt (the difference is 1.33 kt). The regression curve connecting the required propulsive power \(P_{p}\) and the speed of the ship \(v\) can be defined as a power function with added estimated parameters of the thrust functions \(a\) and \(c\). \[P_{p}=a\times v^{c} \tag{4}\]  
Using data from the World Register of Ships database for ferries sailing on the Croatian side of the Adriatic Sea, parameter \(a\) is 0.0757, parameter \(c\) is equal to 3.987, while the \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**No.** & **Ship Name** & **Length (m)** & **Max. Speed (kt)** & **Passenger No.** & **Vehicles No.** & **Line No.** & **Fuel 2023.** \\ \hline
1 & M/V Biokovo & 87.6 & 13 & 1200 & 138 & 636 & 984,713 \\
2 & M/V Faros & 105 & 14 & 650 & 170 & 635 & 1,072,720 \\
3 & M/V Hrvat & 87.6 & 13 & 1200 & 138 & 631 & 674,235 \\
4 & M/V Korčula & 101.4 & 16 & 685 & 150 & 604 & 4,064,960 \\
5 & M/V Marjan & 87.6 & 12.3 & 1200 & 130 & 631 & 663,506 \\
6 & M/V Petar & 91.8 & 15.5 & 1080 & 120 & 602 & 2,183,173 \\
7 & M/V [PERSON] & 98.3 & 14 & 1000 & 200 & 631 & 1,100,000 \\
8 & M/V Valun & 81.2 & 13 & 730 & 60 & 631 & 866,232 \\
9 & M/V Zadar & 116 & 17.5 & 1109 & 280 & 635 & 4,107,502 \\  & Average/Total & 92.13 & 14.13 & 935.4 & 143 & & 15,717,041 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: List of ferries maintaining state ferry lines that use the city port of Split. correlation factor \(R^{2}=0.91\)[59]. Considering the correlation factor, it can be concluded that there is a strong connection, i.e., that the model is representative. However, the almost insignificant reduction in peak speed in the amount of 9.5% results in a reduction of the required propulsive power by 32.6%. The mentioned saving is not only reflected in fuel consumption but also in the reduction of the required installed power of the propulsion system, which significantly reduces investment costs. Furthermore, the introduction of new technologies in the optimization of the hull and ship's propeller and the use of ship coatings contribute to the reduction of fuel consumption. Certainly, in the case of electrification of ferries, all the mentioned methods of reducing energy consumption would be applied. However, for the sake of objectivity, in this energy analysis, possible savings in energy consumption will not be considered in order to make the analysis as objective as possible. Losses of the shaft line and propeller were not considered because they are common to both versions of the propulsion system. As with internal combustion engines, losses also occur with electromotive systems. The chemical energy contained in the batteries needs to be converted into electricity, and then the electricity into mechanical work, which is transferred to the shaft transmission line. The efficiency of modern high-voltage electric motor drives in favorable conditions can be over 98% [60].