## 2 System Model Description
### Vehicle Longitudinal Dynamic Model  
The hybrid power system in this study consists of a PEMFC and a Li battery. A DC-DC converter regulates the current output from the FCS to the DC bus, which is connected in parallel with the Li battery, ensuring a stable power distribution. The DC power is then converted into AC power to drive the electric motor, providing vehicle propulsion. Figure 2 presents a schematic of the system architecture, highlighting the energy flow and the key components of the hybrid system.  
During the operation of the FCHV, it is essential to satisfy the dynamic equations governing the driving process. The input conditions must be converted into the required power for the vehicle using Equation (1).  
\[P_{vehicle}(t)=v(t)\bigg{[}m_{v}g(sin\theta+fcos\theta)+\frac{1}{2}C_{d}\rho Fv( t)^{2}+m_{v}\frac{dv(t)}{dt}\bigg{]} \tag{1}\]  
where \(v(t)\) is the velocity at the current time, \(m_{v}\) is the vehicle mass, \(g\) is gravitational acceleration, \(\theta\) is the road grade, \(\mu\) is the rolling resistance coefficient, \(C_{d}\) is the drag  
Figure 1: The structure of weighted multi-objective optimization.  
coefficient, \(\rho\) is the air density, and \(F\) is the frontal area of the vehicle. The vehicle mass can be expressed as follows in Equation (2):  
\[m_{v}=m_{v,b}+\frac{P_{fc,max}}{\gamma_{fc}}+\frac{Q_{bat}U_{bat}}{\beta_{bat}} \tag{2}\]  
where \(m_{v,b}\) is the basic vehicle mass (excluding energy sources), \(P_{fc,max}\) is the maximum output power of the fuel cell, \(Q_{bat}\) represents the rated capacity of the battery, \(Q_{bat}\) is the voltage value of the battery, \(\gamma_{fc}\) is the power-to-weight ratio of the fuel cell, and \(\beta_{bat}\) is the specific energy of the battery.  
Since the battery can recover energy during braking, when the power requirements are negative, this is considered as charging the battery. Additionally, due to losses in the motor and converter, the energy provided by the power sources must exceed the power demand of the operating conditions. Therefore, the demand power is represented as follows in Equation (3):  
\[P_{req(t)}=\left\{\begin{array}{ccc}&\frac{P_{vehicle}(t)}{\eta}&P_{vehicle}(t)\geq 0\\ &\eta\cdot\eta_{recovery}\cdot P_{vehicle}(t)&P_{vehicle}(t)<0\end{array}\right. \tag{3}\]  
where \(\eta=\eta_{GB}\eta_{m}\eta_{dcac}\) accounts for the losses in the motor and converter, \(\eta_{GB}\), \(\eta_{m}\), and \(\eta_{dcac}\) are the efficiencies of the transmission, motor, and DC-AC converter, respectively, and \(\eta_{recovery}\) is the regenerative braking efficiency. These parameters are all considered as fixed constants. The total power demand from the power sources can be expressed as follows in Equation (4):  
\[P_{req(t)}=P_{bat}+\eta_{fc\_dcdc}P_{fcnet} \tag{4}\]  
where \(P_{bat}\) represents the output power of the battery, \(P_{fcnet}\) represents the output power of the FCS, and \(\eta_{fc\_dcdc}\) represents the conversion efficiency of the fuel cell's DC-DC converter, responsible for regulating and boosting the power delivered to the vehicle.  
The key parameters of the FCHV are listed in Table 1. The parameters of the power sources, including the rated power of the FCS and the energy capacity of the battery pack, need to be matched and optimized.  
Figure 2: Fuel cell electric vehicle powertrain.