## 3 Design and Sizing of the Hydrogen-Battery Hybrid Power System
### Battery Subsystem  
The battery subsystem is made up of three LiPo battery modules (B1, B2, and B3). Each module is composed of 10 cells with a nominal voltage of 3.6 V and a capacity of 2 Ah, with a discharge rate (\(D_{rate}\)) of 1.5C and a 10s1p configuration. The three modules are connected in parallel, which triples the capacity of the battery subsystem (\(C_{bat}\ =\ 6\) Ah) while maintaining a nominal voltage compatible with the DC bus voltage (\(V_{bat}=V_{DCbus}\) = 36 V). Then, the energy stored in the battery subsystem can be identified using Equation (4):  
\[E_{bat}\ =\ V_{bat}.C_{bat} \tag{4}\] \begin{table}
\begin{tabular}{l c} \hline \hline
**Parameter** & **Value** \\ \hline H2 storage volume & 2000 dm\({}^{3}\) \\ Capacity & 3.3 dm\({}^{3}\) \\ Tank weight & 14 kg \\ Pressure recharge & 0.5–3 MPa \\ Certification & CE ISO 16111 [18] \\  & UN 3479 [19] \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Hydrogen tank MyH2-2000: technical characteristics. where:  
\(E_{bat}\) is the energy stored in the battery subsystem (Wh). \(V_{bat}\) is the battery subsystem voltage (36 V). \(C_{bat}\) is the capacity of the battery subsystem (6 Ah). Equation (4) results in \(E_{bat}\) = 216 Wh. Based on the energy stored in the battery, in order to calculate the continuous operating time range of the battery subsystem, it is necessary to determine the power that it must supply to the platform using Equation (5):  
\[P_{Hydrobat}\ =\ P_{FC}+P_{bat} \tag{5}\]  
where:  
\(P_{Hydrobat}\) is the power consumed by the Hygrobot platform (W). \(P_{bat}\) is the power to be provided by the battery subsystem (W). The power consumed by the Hygrobot platform can be determined using Equation (6):  
\[P_{Hydrobat}\ =\ P_{wheel}\cdot n_{wheel}+P_{BoP}+P_{brake} \tag{6}\]  
where:  
\(P_{wheel}\) is the power consumed/wheel (W). \(n_{wheel}\) is the number of wheels (6). \(P_{BoP}\) is the power consumed by the BoP of the PEM fuel cell (W). \(P_{brake}\) is the average power dissipated by the brakes (W). The average power consumed by the wheel is calculated by considering half of the maximum current required by the wheel (maximum current 1.5 A/wheel) at 36 V, where \(P_{wheel}\) = 0.75 A\(\cdot\)36 V = 27 W. The BoP power consumption is obtained from \(P_{BoP}\) = 0.5 A\(\cdot\)36 V = 18 W, while for the rheostatic brake, an activation time of 2% of the platform duty cycle is assumed, resulting in \(P_{brake}\) = 6.4 W. This gives a result of \(P_{Hygrobot}\) = 186.4 W and \(P_{bat}\) = 16.4 W.  
Then, the continuous operating time range of the battery subsystem, \(T_{bat}\), is identified using Equation (7):  
\[T_{bat}\ =\ \frac{E_{bat}}{P_{bat}}\ =\ \frac{V_{bat}\cdot C_{bat}}{P_{bat}} \tag{7}\]  
where:  
\(T_{bat}\) is the continuous operating time of the battery subsystem (h). \(V_{bat}\) is the battery subsystem voltage (36 V). \(C_{bat}\) is the battery subsystem capacity (6 Ah). This results in \(T_{bat}\) = 13.17 h.  
Therefore, the battery and PEM fuel cell subsystems are designed to operate over the same number of hours. Additionally, it should be checked that the maximum power that the hydrogen-battery hybrid power system can deliver is higher than the maximum power required by Hygrobot, \(P_{Hygrobot_{max}}\). Then, \(P_{Hygrobot_{max}}\) can be determined using Equation (8):  
\[P_{Hydrobat_{max}}\ =\ P_{wheel_{max}}\cdot n_{wheel}+P_{BoP}+P_{brake} \tag{8}\]  
where:  
\(P_{wheel_{max}}\) is the maximum power/wheel (\(P_{wheel_{max}}\) = 1.5 A\(\cdot\)36 V = 54 W). Then, \(P_{Hygrobot_{max}}\) = 348.4 W Conversely, the maximum power that the hydrogen-battery-based hybrid system can deliver is determined with Equation (9):  
\[P_{H2-but_{max}}=P_{but_{max}}+P_{FC} \tag{9}\]  
where:  
\(P_{H2-but_{max}}\) is the maximum power provided by the hydrogen-battery hybrid system (W). \(P_{hot_{max}}\) is the maximum power provided by the battery subsystem (W). \(P_{FC}\) is kept at 170 W; the PEM fuel cell is working at \(V_{FC}~{}=~{}V_{DCbus}~{}=~{}36~{}\mathrm{V}\).