## 4 Dynamics Simulation and Experimental Results
### Comparison of Simulation and Experimental Results  
Figure 9 compares the temperatures of PEMFC and the battery. According to the constructed simulator from Figure 4, and with the waste heat commands from Figure 8c,d, the simulated temperature profiles of the battery system and the PEMFC were plotted. Meanwhile, after the experimental platform was constructed in Figure 6, the experimental temperature profiles were plotted. It shows that for the battery temperature profiles, the simulated one reached the target temperature (40 \({}^{\circ}\)C) at the 771 st second, while the experimental temperature reached the target at the 876 th second. For the PEMFC temperature profiles, the simulated profile reached the target temperature (55 \({}^{\circ}\)C) at the 842 nd second, while the experimental temperature reached the target at the 684 th second. The average simulation-experiment temperature error of the battery was 0.898 \({}^{\circ}\)C; the average simulation-experiment temperature error of the PEMFC was 4.839 \({}^{\circ}\)C. The average temperature error is defined in Equations (17) and (18):  
\[e_{bat}=\frac{\sum_{k=1}^{k=N}\abs{T_{bat,sim}(k)-T_{bat,\text{exp}}(k)}}{\text {N}} \tag{17}\]  
\[e_{fc}=\frac{\sum_{k=1}^{k=N}\abs{T_{fc,sim}(k)-T_{fc,\text{exp}}(k)}}{\text {N}} \tag{18}\]  
where \(e\), N represent error, nth sampling time, respectively. Figure 10 is the simulation/experiment comparison of the mode-switch timing. Mode 1 and mode 2 were in the inner-loop structure, while mode 3 and mode 4 were in the outer-loop structure. For the experimental data, as temperatures of dual sources were under their target values, it was in mode 1. At the 688 th second, as investigated from Figure 9 where \(T_{bat,a}<T_{bat,g}\) and \(T_{fc,a}\geq T_{fc,g}\), the mode was switched to mode 3. After the 1169 th second, the system was majorly switched from mode 2 to mode 4. By appropriate mode switch, the system temperatures tracked the targets well. In simulation results, at the 737 th second from Figure 9, the battery reached the target temperature while the PEMFC did not, so that  
Figure 8: Driving Scenarios with the emulated variables: (**a**) WLTP class 1 driving cycles; (**b**) required power of two energy sources; (**c**) waste heat of emulated PEMFC; (**d**) waste heat of emulated lithium battery.  
mode 2 was switched. As the PEMFC reached the goal at the 776 th second as well, the mode was switched to mode 4, and the system continuously tracked the targets to the end of the simulation.  
Figure 11 demonstrates the control signals of key components (proportional valve voltage, coolant pump voltage and radiator voltage) for the simulation/experiment comparison. In the beginning of the experiments, as in mode 1, the voltages of proportional valve, coolant pump, and radiator were 1.98 V, 1.7 V, and 0 V, respectively. At the 873 rd second, both temperatures of dual energy sources reach targets, so that the voltages of proportional valve, coolant pump, and radiator were changed to 2.2 V, 3.83 V, and 5 V, respectively, where the targets were tracked well. In the simulation, the initial voltages of actuators were the same as those in the experiments. At the 843 rd second, both temperatures of dual energy sources reach targets where there was a 30 s difference between the simulation and the experiment cases.  
Figure 10: Simulation/experiment comparison of the mode-switch timing.  
Figure 9: Simulation/experiment comparison of coolant temperature variations of two energy sources.  
From the above, it shows that the simulator is able to represent the experimental platform for further application such as: performance evaluation of system performance, thermal management system designs for various power/energy sources and advanced control strategy development for thermal management systems.  
Figure 11: Simulation/experiment comparison of the control signals of key components: (**a**) proportional valve voltage; (**b**) coolant pump voltage; (**c**) radiator voltage.