**4. Results**

The values of the performance indicators *PFCnet*, η*sys*, *Fueleff* , and *FuelT* using different dither's frequencies and constant load levels are recorded in Tables 1–4. The values obtained by simulation using the static feed-forward (sFF) strategy [36], which is considered in this study as a reference strategy because it is the most known strategy implemented in commercial FC systems, are mentioned in the first column of these Tables. The differences in the performance indicators will be defined compared to the sFF strategy by using (15):

$$
\Delta P\_{\text{FC.net}} \cong P\_{\text{FC.net}} - P\_{\text{FC.net0}}.\tag{15a}
$$


**Table 1.** FC net power for different dithers' frequencies and constant load levels.


**Table 2.** FC electrical efficiency for different dithers' frequencies and constant load levels.

**Table 3.** Fuel efficiency for different dithers' frequencies and constant load levels.



**Table 4.** Total fuel consumption for different dithers' frequencies and constant load levels.

$$
\Delta \eta\_{\text{sys}} = \eta\_{\text{sys}} - \eta\_{\text{sys0}}.\tag{15b}
$$

$$
\Delta\text{Fuel}\_{eff} = \text{Fuel}\_{eff} - \text{Fuel}\_{eff0\text{\textquotedblleft}}\tag{15c}
$$

$$
\Delta Fuel\_T = \begin{bmatrix} Fuel\_T - \ Fuel\_T \end{bmatrix} \tag{15d}
$$

The differences are recorded in Tables 5–8 and represented in Figures 3–6. Note the multimodal behavior in dithers' frequency for all performance indicators. Also, it is worth mentioning that the optimum's position (maximum of Δ*PFCnet*, Δη*sys*, Δ*Fueleff* , and minimum of Δ*FuelT*) depends on the load level. So, the best value in the frequencies' range could be selected as the frequency where the optimum is obtained for most of load levels, and this seems to be the dither frequency of 100 Hz.


**Table 5.** Differences in FC net power compared to reference.

**Table 6.** Differences in FC electrical efficiency compared to reference.



**Table 7.** Differences in fuel efficiency compared to reference.

**Table 8.** Differences in total fuel consumption compared to reference.


**Figure 3.** Differences in FC net power.

**Figure 6.** Differences in total fuel consumption.

Considering a dither frequency of 100 Hz, the total fuel consumption (*FuelT*) for different values of the parameters *ke*ff and Pload is recorded in Table 9. The values for *ke*ff = 0 (mentioned in the first column of the Table 9) are used as reference values. So, the differences in total fuel consumption (Δ*FuelT*) are estimated in Table 10 and represented in Figure 7.


**Table 9.** Total fuel consumption for different values of the parameters *ke*ff and *Pload*.

**Table 10.** Differences in total fuel consumption compared to *ke*ff = 0.


**Figure 7.** Differences in total fuel consumption for different values of the weighting parameter *ke*ff*.*

The sensitivity analysis of the fuel economy (Δ*FuelT*) highlights the better fuel economy with increase in load level, and this is normal. Also, note the multimodal behavior in the weighting parameter *ke*ff. This is better shown in Figure 8 (where the high values of fuel economy for a load of 7 kW and 8 kW are canceled). Looking to Table 10 (where the optimum, local minimums, and the minimums at *ke*ff = 5 and *ke*ff = 50 are highlighted in different colors: yellow, blue, and gray, respectively), a *ke*ff value in the range of 20 lpm/W to 30 lpm/W seems to give the best fuel economy in the load range of 2 kW to 5 kW. However, note the decrease in fuel economy with the increase in *ke*ff value. So, the recommended value for the entire load range is *ke*ff = 20 lpm/W.

**Figure 8.** The multimodal behavior of the fuel economy Δ*FuelT* in weighting parameter *ke*ff*.*

The effect of a variable energy efficiency of the boost converter on the results obtained at constant energy efficiency will be analyzed and discussed in the next section.
