*4.1. Fuel Cell Range Extenders*

The first type of truck we decided to target is a medium-duty or class 4 pickup or delivery van. It has a cargo mass of 2800 kg, just like the conventional baseline. As mentioned above, FCREx is battery-dominant and similar to a series hybrid electric vehicle that uses a fuel cell instead of an internal combustion engine. Figure 2 shows the configuration of the FCEV in Autonomie. This fuel cell connects to the battery for charging. As the battery becomes fully charged, an electric motor runs the vehicle using electrical energy. When it runs on the electrical energy and uses hydrogen with the fuel cell system while its battery sustains a certain charge state, this is called charge sustaining mode. FCRExs often use power from both the battery and the fuel cell when they need the large amounts of wheel power demanded for energy management control strategies. Table 2 shows vehicle

specifications. We do not expect much change in fuel cell power or motor power, because the vehicle should still meet all performance requirements.

**Figure 2.** Configuration of fuel cell electric vehicle (FCEV) in Autonomie.



Above all, the optimization technique needs to be verified against parameter sweeps for the test cases. For example, there are class 4 FCREx optimization results. The optimization is 4 times faster than parameter sweeps and yields better results. Figure 3a,b show feasible points for grade and range tests, respectively. Figure 3c shows sums the feasible ranges of Figure 3a,b. The right square magnified shows the related results. Blue circles are feasible points and red crosses are surrounding points. Red and blue stars are the estimated and POUNDERS results, respectively. Squares are POUNDERS tracking points. Each number next to a point is an RCO value. Some variables do not coincide exactly with the optimal value because the POUNDERS results can be one of the local optimums. We found the estimated optimal value by using the minimum value from the fixed grid data, which can reveal the optimal battery capacity, hydrogen mass, and fuel cell power. However, the estimated value missed the optimal point because of low resolution, 7 by 7. The lowest RCO is located on the left side and bottom of Figure 3c. Therefore, the bottom left values within the feasible section are optimal, closer to the POUNDERS result. If the resolution for the estimated results rise to explore more points the current estimate did not identify, the new optimal point may be closer to the POUNDERS result. POUNDER uses fewer iterations and smaller step sizes to arrive at a better solution.

**Figure 3.** Feasible values of (**a**) range and (**b**) grade for 100 kW of fuel cell power, and (**c**) relevant ownership cost (RCO) results for the estimate and POUNDERS.

Optimized FCRExs have component size that are similar to FCHEVs, as shown in Figure 4. The FCREx can have the same hydrogen tank as FCHEV, but the different driving strategies of both vehicles increase the FCREx battery to achieve the same performance as FCHEV. Table 3 summaries optimization results and compares them with rule-based component sizes. There is tradeoff between fuel mass and battery capacity. The optimized vehicle has lower battery capacity and higher hydrogen mass. Some performance results are lower than those for the rule-based sizing, but they still meet performance requirements. The 0–97 km/h acceleration time increases, but it is still better than that of the conventional vehicle. Grade speed drops, because the battery is no longer assisting the fuel cell during grades. The total vehicle mass remains largely unchanged, although there is a small reduction of 76 kg. These results are independent of fuel cell cost, because fuel cell power remains the same in both cases. In this case, 100 kW of power is necessary to cruise at highway speeds. Therefore, the fuel cell cannot be further downsized.

**Figure 4.** Summary of optimized hydrogen tank and battery pack for class 4 fuel cell vehicles; the #1 case assumes a hydrogen cost of \$4/gge (gasoline gallon equivalent) and #2 assumes a hydrogen cost of \$12/gge.


**Table 3.** Comparison between the rule-based and optimized results. FCREx: fuel cell range extenders.

In addition, the optimum solution changes as hydrogen cost increases. We assume \$12 per gge of hydrogen, not \$4 per gge. Table 4 shows the optimized results, comparing hydrogen costs of \$4 and \$12. We observe larger battery capacity and reduced hydrogen fuel use as hydrogen cost increases. Figure 5 shows the RCOs for different hydrogen costs. The manufacturing cost rises with a larger battery and the energy cost increases. The RCO increased by about \$20,000 because of the increased energy cost. The overall component design remains fuel cell dominant.

**Table 4.** Optimized results according to hydrogen price.

