6.2.3. Bat/HFC/SC Sizing

The Bat/SC/HFC hybrid configuration allows for the integration of three energy sources, each utilized in different flight mission segments. During the take-off and landing segments, where the power demand is highest, the supercapacitor is employed. The battery is utilized during hovering segments, while the hydrogen fuel cell is utilized during the cruise segment. The battery power, the supercapacitor power, and the hydrogen fuel cell power are related to the motor power by

$$\begin{cases} P\_{\text{bat}} = \mathbf{x} \cdot P\_{\text{mot}}, \\ P\_{\text{SC}} = \mathbf{y} \cdot P\_{\text{mot}}, \\ P\_{\text{HFC}} = (1 - \mathbf{x} - \mathbf{y}) \cdot P\_{\text{mot}}. \end{cases} \tag{53}$$

where *x* and *y* are, respectively, the hybridization coefficient of the battery power to the motor power and the supercapacitor power to the motor power. From Equations (15), (23) and (25), the flight time is given by

$$t\_{flight} = \left(\frac{m\_{\rm SC} \cdot \rho\_{\rm SC} \cdot \eta\_c \cdot \eta\_{\rm SC}}{\chi} + \frac{m\_{\rm bat} \cdot \rho\_b \cdot \eta\_c \cdot \eta\_b}{\mathcal{Y}} + \frac{m\_{\rm Il\_2} \cdot LHV \cdot \eta\_c \cdot \eta\_{\rm FC}}{1 - \chi - \mathcal{Y}}\right).$$

$$\left(\frac{\eta\_{\rm MP}}{(m\_{\rm SC} + m\_{\rm bat} + m\_{\rm HFC} + m\_{\rm others}) \cdot \mathcal{Z}}\right).\tag{54}$$

In this case, the flight time depends on five parameters, namely supercapacitor mass *mSC*, battery mass *mbat*, hydrogen fuel cell mass *mHFC*, and hybridization coefficients *x* and *y*. Figure 18a–c presents the flight time evolution for the three cases.

As the hydrogen fuel cell (HFC) mass increases (Figure 18a), the flight time shows a tendency to increase when considering the battery and supercapacitor masses. This can be attributed to the improved energy density of the energy storage system resulting from the increased hydrogen mass. Furthermore, the cruise phase typically constitutes the longest segment in a flight mission.

Regarding the effect of the SC mass on the evolution of the flight time in terms of the HFC and battery masses, as seen in Figure 18b, it is remarkable that the flight time has a tendency to decrease. This can be explained by the lower value of the SC energy density in comparison to FCs and batteries. In addition, the take-off and landing segments, where the SC is utilized, have a relatively short duration in the overall flight mission.

**Figure 18.** Flight time evolution in terms of the battery mass *mbatt*, the supercapacitor mass *mSC*, and the hydrogen fuel cell mass *mHFC*.

The effect of the battery mass on the evolution of the flight time, as a function of the mass of the hydrogen fuel cell and the mass of the supercapacitor, as seen in Figure 18c, remains similar to the case in Figure 18b. The flight time in this case tends to decrease as the battery mass increases. This can be attributed to the battery's low energy density and the relatively short duration of the hovering segment during which the battery is used.

In this case, the optimization process involves finding an optimal solution in terms of the three masses, with the objective of maximizing the flight time for a given level of hybridization. The optimization problem is given by

$$\begin{cases} \max(t\_{flight}) = \min(-t\_{flight}),\\ 0 < m\_{lat} + m\_{SC} + m\_{HFC} \le GTOW - m\_{other}. \end{cases} \tag{55}$$

Figure 19 presents an optimization example for hybridization coefficients *x* = 10%, and *y* = 6%. In this case a, the multirotor aerial vehicle achieved a flight time of *tflight* = 62.93 min. The sizing process for each component, in this case, follows a similar approach as in the previous cases. The optimized parameters for each component are presented in Table A7.

**Figure 19.** Example of a flight time optimization in the Bat/SC/HFC configuration case.

#### 6.2.4. Flight Time Comparison

The flight times obtained for each energy storage system configuration in the multirotor aerial vehicle are shown in Figure 20. It is remarkable that the energy storage system configuration based on Bat/SC/HFC achieved the best flight time with a value of more than *tflight* = 62 min, followed by the Bat/HFC configuration with a flight time of more than *tflight* = 56 min. Both the battery-based and Bat/SC configurations achieved similar flight times on the order of *tflight* = 14 min. The supercapacitor in this configuration does not have a significant influence on the flight time due to the shorter duration of the segments in which it is used. The HFC-based configuration allowed for a flight time of *tflight* = 30 min. Despite the increase in the complexity of control and energy management in the Bat/SC and Bat/SC/HFC configurations, they remain the best solution for maximizing flight time.

**Figure 20.** Flight time comparison for each energy source configuration.

6.2.5. Multirotor Aerial Vehicle *GTOW* Estimation

In this section, the multirotor aerial vehicle *GTOW* estimation is described. Regression models presented in Section 3 are utilized to estimate the masses of the propeller, motor, and ESC components. The masses of the payload and fuselage, on the other hand, are fixed. The mass of the energy storage part is computed for each configuration:


Figure 21 presents the distribution of *GTOW* for each energy storage configuration. The optimized gross take-of weight is given by GTOW = 14.9747 kg.

**Figure 21.** Multirotor aerial vehicle mass distribution.
