## 4 In-Loop Testing of the Control Model
### Comparative Analysis of Energy Management Strategies  
All the above three control strategies can meet the supply of demand power. On this premise, to compare the control effects of different energy management strategies, three items of output power fluctuation of the hydrogen fuel cell, hydrogen fuel cell efficiency, and hydrogen consumption are selected as evaluation indexes. From the comparison of Figures 11, 13 and 17, it can be seen that the output power of the hydrogen fuel cell under the multi-layer decoupled control strategy based on the wavelet rule has the smoothest variation, which can effectively improve the service life of the hydrogen fuel cell and is easier to control. From Figure 19, it can be seen that the hydrogen fuel cell operating points under the wavelet rule-based multi-layer decoupling control strategy are more intensive and close to the optimal power point of the efficiency curve compared to the power-following and fuzzy control strategies. Table 2 compares the hydrogen fuel cell's average power points and efficiency with different control strategies. In the experimental cycle, compared with the power-following and fuzzy control strategies, the average efficiency of the PEMFC under the wavelet rule-based multi-layer decoupling control strategy is the highest, with an increase of 2.87% and 1.2%, respectively. Figure 17: (**a**) The power output of each energy part; (**b**) The power output of the hydrogen fuel cell; (**c**) The power output of the LiFePO4 battery; (**d**) The power output of the ultracapacitor. Figure 18: The actual working point of the hydrogen fuel cell. Some studies have proved that excessive power fluctuation will affect the life of the PEMFC system and accelerate its degradation of the PEMFC system. The larger the output power fluctuation, the faster the system aging when the output power is in the same order of magnitude [10; 11; 12; 13; 14]. The study of the life of the PEMFC system is a complicated work, nowadays more complex and multi-objective objectives are being worked on [46; 47; 48; 49; 50; 51; 52; 53], but only the output power fluctuation is analyzed in this paper. To observe the output power fluctuation of the PEMFC system under different control strategies more directly, the method mentioned in Formula (18) was adopted. The sampling interval was 1 s, taking the absolute value of the result, and the fluctuation rate of the output power of the PEMFC system under different control strategies is shown in Figure 20.  
It can be seen that the maximum fluctuation ratio of output power per second of the power-following control, fuzzy control, and haar-wavelet control strategy is 14.3%, 10.7%, and 6.8%, respectively. The output power fluctuation rate of the PEMFC system under the haar-wavelet control strategy is the lowest, that is, its output is the smoothest which reflects from the side that it can prolong the service life of the PEMFC. Table 3 compares the average fluctuation ratio of output power per second and the maximum power fluctuation per second under different control strategies. Obviously, \begin{table}
\begin{tabular}{c c c} \hline \hline
**Types of Control Strategies** & \
\begin{tabular}{c} **Average Power Point of the** \\ **Hydrogen Fuel Cell/kW** \\ \end{tabular} &
\begin{tabular}{c} **The Average Efficiency of** \\ **the Hydrogen Fuel Cell/\%** \\ \end{tabular} \\ \hline power-following & 18.5 & 57.52 \\ fuzzy control & 16.12 & 58.45 \\ multi-layer decoupling control & 16.57 & 59.16 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of the efficiency of hydrogen fuel cells with different control strategies. Figure 20: Comparison of the output power fluctuation rate of the PEMFC with different control strategies. the multi-layer decoupling control strategy based on the haar-wavelet rules effectively suppresses the power output fluctuation of the PEMFC system. Figure 21 shows the variation curve of hydrogen consumption with time for each control strategy.