## 3 Energy Management Strategy of FCHEV
### Da-Ecms  
The ECMS converts the electrical energy consumption of the battery into an equivalent hydrogen consumption by setting an equivalence factor, which in turn calculates the total hydrogen consumption rate minimum at each moment. The instantaneous total hydrogen consumption rate \(\dot{m}_{eqv}(t)\) of the FCHEV can be expressed as:  
\[\dot{m}_{eqv}(t)=\dot{m}_{fc}(t)+s(t)\dot{m}_{bat}(t), \tag{37}\]  
where \(\dot{m}_{fc}(t)\) is the fuel cell instantaneous hydrogen consumption rate and \(s(t)\) is the equivalence factor. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Category** & **Driving Condition** & **Value of the Optimal Covariate** \\ \hline
1 & Urban congestion & \(-\)201.4 \\
2 & Urban smooth & \(-\)218.2 \\
3 & Suburban & \(-\)224.4 \\
4 & High speed & \(-\)237.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Optimal covariate. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Numerical Value** \\ \hline Input number of nodes in layer & 4 \\ Number of hidden layers & 1 \\ Number of hidden layer nodes & 14 \\ Output number of nodes in layer & 4 \\ Learning rate & 0.0001 \\ Maximum number of training cycles & 500 \\ Lot size & 30 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Selected hyperparameters of optimal covariate predictor. The optimization objective of the ECMS is to minimize the instantaneous total hydrogen consumption rate. Thus, the optimization objective function is defined as:  
\[J=\min\big{[}m_{eqv}(t)\big{]}. \tag{38}\]  
\(\dot{m}_{bat}(t)\) can also be expressed as a function of \(\dot{SOC}(t)\):  
\[\dot{m}_{bat}(t)=\frac{P_{bat}(t)}{LHV}=-\frac{U_{decv}\dot{SOC}(t)Q_{bat}}{LHV}. \tag{39}\]  
The relationship between the covariates and the equivalence factors can be derived as:  
\[s(t)=-\frac{LHV}{U_{ccv}Q_{bat}}\lambda(t). \tag{40}\]  
The speed prediction model and the optimal covariate predictor constructed in the previous section are combined with the ECMS to construct an A-ECMS. Compared to the fixed equivalence factor of the ECMS, the equivalence factor of the A-ECMS can vary with the change of the operating conditions. The performance degradation of the fuel cell and the battery is incorporated into the optimization objective of the A-ECMS, in which case the total instantaneous hydrogen consumption rate considering performance degradation \(\dot{m}_{eqq}(t)\) of the FCHEV can be expressed as:  
\[\dot{m}_{eqq}(t)=\dot{m}_{fc}(t)+s(t)\dot{m}_{bat}(t)+\dot{m}_{d_{-}fc}(t)+ \dot{m}_{d_{-}bat}(t), \tag{41}\]  
where \(\dot{m}_{d_{-}fc}(t)\) is the equivalent hydrogen consumption rate of the fuel cell performance degradation and \(\dot{m}_{d_{-}bat}(t)\) is the equivalent hydrogen consumption rate of the battery performance degradation. The objective function of the DA-ECMS is defined as:  
\[J=\min\Big{[}\dot{m}_{eqq}(t)\Big{]}. \tag{42}\]  
Compared to the A-ECMS, the DA-ECMS considers the performance degradation of the energy sources. The fuel cell stack was considered to have failed when its performance degradation reached 10%. The ideal output voltage of the fuel cell stack is 300 V in this study. \(\dot{m}_{d_{-}fc}(t)\) can be expressed as:  
\[\dot{m}_{d_{-}fc}=\frac{\Delta\phi_{fc}M_{fc}}{10^{9}\omega_{H_{2}}}, \tag{43}\]  
where \(\Delta\phi_{fc}\) is the fuel cell stack performance degradation rate, \(M_{fc}\) is the fuel cell stack price, and \(\alpha_{H_{2}}\) is the hydrogen price. The battery is considered to have failed when its performance degradation reaches 20%. \(\dot{m}_{d_{-}bat}\) can be expressed as:  
\[\dot{m}_{d_{-}bat}=\frac{Q_{loss}M_{bat}}{20^{9}\omega_{R_{H_{2}}}}, \tag{44}\]  
where \(M_{bat}\) is the battery price. In this optimization problem, the fuel cell stack output power \(P_{fc}\), the battery output power \(P_{bat}\), and SOC should satisfy the following constraints:  
\[\left\{ \begin{array}{l}P_{dem}=P_{fc}+P_{bat}\\ 0\leqslant P_{fc}(t)\leqslant P_{fc_{-}max}\\ P_{bat_{-}min}\leqslant P_{bat}(t)\leqslant P_{bat_{-}max}\\ SO\bar{C}_{\min}\leqslant SOC(t)\leqslant SOC_{\max}\end{array}