# Online Model Adaption for Energy Management in Fuel Cell Electric Vehicles (FCEVs)
## 3 Results and Discussion  
The evolution of the map adaptations by the proposed method when the FCEV is covering 15 cycles is shown in Figure 7. This figure shows how the learning map (LM) evolves as the vehicle covers the different driving conditions of the cycles. To expose the method to the worst scenario, at the start of the test, the map of the BM was conditioned as the initial map. In this case there is no information about the ageing level of the FC or operating time that the FCEV has already covered. Due to the warming and low-temperature conditions of the fuel cell, the adaptations are only activated at temperatures above 340 K to avoid corrections during these short periods. Once the fuel cell starts to run and the correction is activated, the adaptation on the maps evolves, and when the FCEV switches off, the map is stored and then used for the next trip and so on. When the FCEV runs again, the map keeps evolving to correct these deviations. According to Figure 7, as the time duration of each cycle is around one hour, higher correction rates are observed during the first driving cycle. So in this case, about 1 h is needed for the algorithm to adapt the map and stabilize it until reaching a condition with lower amplitudes in the map adaptation. Furthermore, one can expect that even if the algorithm strongly adjusts the map in the first hour, the map should maintain a relatively stable map profile during subsequent hours, particularly at high current densities. The ongoing varia  
Figure 6: Flowchart of the proposed EKF adaptative algorithm particularized for the 1D look-up table of the case study. tions observed from medium to high current densities are closely linked to the dynamic responses of the fuel cell. This phenomenon is primarily attributed to rapid changes in the fuel cell operating conditions, often resulting in fuel cell stack temperature fluctuations. For comparison purposes, Figure 8 illustrates the three maps together. In the cases of the AM and BM, these maps remained constant throughout all simulations. In contrast, for the LM case, this map represents the final adaptation achieved after the end of the simulations. Regarding the operating points distributed on the plot, these points represent the output power of the fuel cell as a function of the control input \(I_{u}\) provided by the EMS to the fuel cell over the 15 cycles of the LM case. According to Figure 8, two problems can be underlined when working with COM. First, the differences between the full cell power estimated by the COM (1D look-up table)  
Figure 8: Operating point distribution of the Learning map during the operation of the 15 cycles and the Evaluated maps. Estimations provided by the Actual map, Biased map, and Learning map are shown in black, gray, and blue, respectively. Figure 7: Evolution of the map adaptations by the adaptive method provided during 15 cycles of operation. and the one provided by the plant (GT model) depend on the calibration. However, despite the high calibration effort for mapping the fuel cell used in the AM, this map still shows that it is impossible to cover the region perfectly with the highest operating frequency (red), showing that it is possible to correct and improve the accuracy of the FC models. Second, independent of the model calibration, there will always be deviation in the estimation due to simplification of the system to a 1D look-up table. For this reason, providing a more accurate estimation of the output FC power by the EMS can ensure that the FC will operate closer to optimal conditions and then improve fuel consumption. Moreover, as observed in the map adaptations of Figure 7, it is expected that if the adaptative method can provide quick corrections to the map, the difference between the actual output power the FC provides and the one estimated by the map can be minimized. To some extent, the system dynamic can be considered by the EMS to compute the proper power split, which will be further discussed in this section.