# Analysis of Hybrid Ship Machinery System with Proton Exchange Membrane Fuel Cells and Battery Pack
## 2 Methodology  
The numerical model was conceptually developed as shown in Figure 1 and later implemented in the commercial software AVL CRUISETM M 2023.1 with a balance of plant system. The conceptual model consists of three main components. the first main component is the PEMFC stack with 300 kWe, and the second is the battery pack with unknown required power that must ensure enough power for the required load profile shown on Table 1. The last component consists of two asynchronous electric motors with a maximum power requirement of 300 kW each (600 kW in total). The required amount of hydrogen with tank capacity is unknown, and simulation was calculated based on the current generated by the fuel cell system. Additionally, ship resistance was modelled with a longitudinal dynamic model to ensure realistic acceleration and velocity of the vessel; the propeller type is B series, which has a numerical background from the Wageningen B series tests [22]. Torque on the propellers, which generate load on electric motors (EM), ensures a realistic load on the power system. Balance of plant (BoP) includes the regulation of mass flow rates at the cathode and anode side in the sub-system of the PEMFC, which consists of a compressor at the cathode side with a mass flow of up to 0.3 kg/s and air pumping up to 4 bar from external pressure, which is cooled and circulated through a humidifier before the PEMFC stack \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Position** & **Distance** & **Velocity** & **Time** & **Propulsion Power** & **Distance Crossed** \\ \hline
**Unit** & **nm** & **kts** & **min** & **kW** & **nm** \\ \hline Port of Split—start of route & 0 & 0 & 3 & 0 & 0 \\ \hline Port of Split—starting maneuver & 0.5 & 6 & 5 & 100 & 0.5 \\ \hline Port of Split—sailing ferry to Port Resnik & 5.7 & 12 & 28.5 & 600 & 6.2 \\ \hline Approach maneuver of ferry to Port Resnik & 0.3 & 6 & 3 & 80 & 6.5 \\ \hline Ferry in Port Resnik & 0 & 0 & 3 & 0 & 6.5 \\ \hline Boarding of passengers & 0 & 0 & 20 & 0 & 6.5 \\ \hline Departure of ferry from Port Resnik & 0 & 0 & 3 & 0 & 6.5 \\ \hline Ferry port Resnik—departure maneuver & 0.3 & 6 & 3 & 80 & 6.8 \\ \hline Ferry Port Resnik & 5.7 & 12 & 28.5 & 600 & 12.5 \\ \hline Approaching maneuver to Port of Split & 0.5 & 6 & 5 & 80 & 13 \\ \hline Ferry in Port of Split & 0 & 0 & 3 & 0 & 13 \\ \hline Boarding of passengers & 0 & 0 & 20 & 0 & 13 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Voyage route with details of catamaran distance, velocity, time, and required propulsion power for calculation. Figure 1: Main components for the numerical model of a hybrid vessel energy system. to ensure proper humidity for the membrane. Pressure and airflow are controlled via two PID controllers for the compressor and control of the backpressure valve. The power consumption of compressor is defined as linear and dependent on the PEMFC stack load with maximal consumption compared and upscaled from Toyota Mirai PEMFC stack testing [23]. The anode side consists of a large hydrogen tank that stores hydrogen at a pressure of 700 bar and has enough fuel for six voyages; the injection model manages the mixing of hydrogen with water vapor via fuel cell current demand. Recirculation of the unused humid hydrogen is also present, which feeds it back to the system through a Venturi injector, where excess water is removed with a water separator to maintain constant humidity. Pressure is controlled with a PID controller, which controls the Venturi injector's opening. Additionally, to address nitrogen buildup due to crossover through the membrane, a purge valve is periodically opened and releases some of the gas into the surroundings. Some unused hydrogen is lost during the process, but in typical operating conditions, the loss does not exceed 2% of total fuel consumption. Removal of excessive heat is required to maintain a stable temperature of 65 \({}^{\circ}\)C in the PEMFC stack, which is managed with a pump that is controlled with PID control and dependent on the load from the PEMFC stack.