## 5 Simulation Verification
### Overloading  
When ascending a slope of 18\({}^{\circ}\), as calculated previously, the load demand (1535 W) will be higher than the power supply from the HPS. The first simulation we conducted focused on fluctuating DC bus voltages under such overload conditions, which should be maintained well above the rated voltage of the load. In this simulation, the load was increased in steps of 500 W up to a maximum of 3 kW, and each load lasted for 60 s (see Figure 10).  
Initially, with no load applied, the fuel cell power is approximately +32 W (outgoing) and the battery power is approximately \(-\)32 W (incoming), indicating that the power flows from the fuel cell to the battery. This power flow is induced by the voltage difference between the converter and battery. The reference voltage at the output of the converter was set as 25.15 V and the battery open-circuit voltage (OCV) was determined to be 25.129 V at an initial SOC of 50%. With a slight voltage difference of less than 30 mV, a current of 1.3 A corresponding to a power of 32 W charges the battery.  
At 60 s, the load increases to 500 W. Based on the differences in dynamic characteristics between the two power sources, the battery supplies power to the load before the fuel cell. After approximately 6 s, their powers cross each other, and both bear the load equally at a power level of 250 W. Then, approximately 15 s later, the fuel cell power reaches 500 W, meaning the fuel cell can handle the load alone. Immediately thereafter, the fuel cell power  
Figure 10: Simulated (**a**) power, (**b**) voltage, and (**c**) current with SOC of HPS under the overload condition.  
slightly exceeds 500 W, indicating that with this power surplus, the battery is charged. By doing so, the battery can maintain its initial SOC. At all times, the sum of all power flows should be equal to zero. By looking more closely at 60 s, in response to the abrupt load change, the DC bus voltage instantaneously drops to 24.993 V. Since the battery OCV remains at 25.114 V, the voltage difference between them is reversed. In turn, a current close to 13 A begins flowing from the battery to the load.  
At 120 s, the load increases to 1 kW. Again, the battery responds to the load earlier than the fuel cell. However, the fuel cell power is stabilized at approximately 955 W without overshooting and the power shortage (45 W) is covered by the battery. This is because the operating point of the fuel cell is fixed by limiting the reference current at the input of the converter to 30 A. This threshold was set based on the user manual for the selected fuel cell [27], which warns that an over-current (OC) fault will occur if the current exceeds 30 A. Therefore, the operating points at which the maximum output power is extractable are 31.136 V at 30.678 A from the fuel cell (high-side) and 25.095 V at 37.699 A from the load (low-side).  
At 180 s, the load steps up again to 1.5 kW, which overloads the HPS. Under overload conditions, the battery is responsible for excessive power demands as high as 545 W. As the battery continues to discharge at nearly 22 A, 60 s later, its OCV drops to 25.027 V. The DC bus voltage accordingly drops to 24.821 V by deviating from its set point (25.15 V). The DC bus voltage remains greater than the rated voltage of the load (24 V) for 60 s, but it could not be sustained.  
When the load increases to 2 kW at 240 s, the battery covers half of the power demand, so its voltage drop further accelerates. When the load is maximized at 3 kW, it was predicted that the DC bus voltage eventually falls below the rated voltage of the load, thereby failing to meet the voltage requirements.