## 3 Materials and Methods
### Split City Port Study Case--Ferry Fleet Energy Demand Analysis
Losses of the battery system depend on the state of charge, the technology used, and other different parameters. Losses occur during charging, storage, and discharging of the battery. According to a study [61], the efficiency of the entire process of the battery system is 81%. The amount of energy required to drive the state ferry fleet on the shaft line is 49.2 GW/h. Considering the efficiency of the electric drive and the battery, the required energy delivered from the shore connection to the ship is calculated according to the formula:  
\[E_{\text{SC}}=P_{\text{ENERGY}}  
Due to the sailing schedule, which is adapted to the needs of the island's population, the sailing profile is extremely unfavorable in terms of the available time for charging electric batteries. Figure 6 shows the operational navigation profile for the observed ferry fleet. In the figure, the time the ship spends on navigation is marked blue, while the time the ship is available for charging in the City Port of Split is marked in green. The period that is not shaded refers to the rest of the ship outside the City Port of Split. For example, if observing state line 636 maintained by the ferry Biokovo and connecting the island of Solta with the City Port of Split, it is evident that the only available time for charging is between 2:00 p.m. and 4:15 p.m. The remaining time the ship sails, maintaining the line with a break of 15 min, which is necessary for the operation of disembarking and loading passengers and vehicles. At right, the ship is stationed at the port of Rogac (Solta island). The availability of an individual ferry for charging is an important factor from the aspect of optimizing the charging process. However, an even more important factor is the amount of energy needed in the time available to charge the ship's battery storage of electricity. Table 4 shows the daily energy needs of the ferry fleet, the percentage share of each ship in total consumption, the available time for charging, and the necessary continuous power of the connection for each ship during the charging process. \begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Ship**} & **Daily Energy Needs (MWh)** & **Percentage Share (\%)** & **Time Available (h)** & **Constant Power (MW)** \\ \hline M/V Biokovo & 0.71737 & 6.26526 & 2.25 & 0.318831964 \\ M/V Faros & 0.78149 & 6.8252 & 3 & 0.260495259 \\ M/V Hrvat & 0.49119 & 4.28983 & 17.66 & 0.027813478 \\ M/V Korčula & 2.96136 & 25.8634 & 1.5 & 1.974238959 \\ M/V Marjan & 0.48337 & 4.22157 & 15.17 & 0.031863536 \\ M/V Petar & 1.59046 & 13.8905 & 2.5 & 0.636184148 \\ Hektorović & 0.80136 & 6.99877 & 15.42 & 0.051968839 \\ M/V VanU & 0.63106 & 5.51142 & 15.6 & 0.040452403 \\ M/V Zadar & 2.99235 & 26.1341 & 5.75 & 0.520408809 \\ \hline \end{tabular}
\end{table} 
Table 4: Energy needs of the ferry fleet. Figure 5: The average annual number of sailings by month on line 604 [48]. Figure 6: Daily operational profile of the observed fleet of ships. In relation to the land-based power system, the energy needs of the ferry fleet are represented as a variable consumer of electricity in a 24-h time interval, which is called a daily energy load diagram. The amount of energy consumed by the \(E_{CON}\) is defined by the expression:  
\[E_{CON}=\int_{t_{1}}^{t_{2}}P_{CON}(t)dt=\int_{t_{1}}^{t_{2}}u(t)\cdot i(t)dt \tag{6}\]  
where \(P_{CON}\) indicates the instantaneous power with which the consumer group loads the network, \(u(t)\) the instantaneous network voltage, and \(i(t)\) the instantaneous current of the consumer group, while t represents time.