## 2 Simulation Model
### Fuel Cell Degradation Model  
The purpose of establishing the degradation model is to quantify and predict the voltage decay issue in fuel cell operation that was not considered in the original fuel cell model. The degradation model used in the paper is based on reference [24]. To apply this model in both real-world and simulation scenarios, two implementation methods are provided. The first method involves analyzing the degradation and its influencing factors of the fuel cell under specific operating conditions by acquiring the fuel cell's operational data. The second method involves incorporating the degradation model in parallel with the aforementioned fuel cell model, enabling the real-time optimization of the fuel cell's output state. This approach can also be applied in practical applications.  
In practical applications, the degradation behavior of a fuel cell is primarily reflected in its voltage. Therefore, when calculating the actual output voltage of the fuel cell at the same current density, the equation should be as follows:  
\[V_{a}=V_{fc,int}(1-\delta) \tag{6}\]  
To calculate the degradation rate of the fuel cell, a semi-empirical and semi-physical approach is proposed, combining empirical models and physical methods based on previous research on fuel cell degradation models. This approach combines the empirical knowledge and physical understanding of fuel cell degradation, providing a more comprehensive and accurate estimation of the degradation rate.  
The degradation of a fuel cell's voltage output is influenced by activation polarization, ohmic polarization, and concentration polarization. Therefore, the degradation of the fuel cell's voltage is divided into low-power degradation, high-power degradation, and moderate-power degradation (natural degradation). According to reference [24], the degradation trends for moderate-power and high-power degradation are consistent, so they are unified as normal power degradation. When the operating conditions of a fuel cell change, there is also a significant impact on the stack [25]. Therefore, it is necessary to separately analyze the effects of load changes and start-stop operations on fuel cell voltage degradation. However, voltage is only a result of fuel cell operation, and it requires analysis of deeper influencing factors. The operating temperature of the fuel cell, relative humidity of hydrogen/air, current density, and other factors can affect the voltage output of the fuel cell. The commonly defined performance output characteristics of a fuel cell are represented by polarization curves, where the dependent variable is the current density. Therefore, defining the load variation in a fuel cell based on the intensity of the current density is more scientifically accurate. In the proposed model, based on four operational conditions of the fuel cell, the analysis of fuel cell degradation is divided into three layers: reference degradation rate, electrochemical changes, and physical factor changes. The overall calculation of fuel cell degradation can be determined using the following equation:  
\[\delta=k_{lp}\delta_{lp}+k_{np}\delta_{np}+k_{lc}\delta_{lc}+n_{ss}\delta_{ss} \tag{7}\]