# Online Model Adaption for Energy Management in Fuel Cell Electric Vehicles (FCEVs)
## 2 Methodology  
### Case Study  
The paper focuses on online adjustments to the model to relate the fuel cell current and power in the EMS of an FCEV. This adaptation improves the system control by preventing errors that may propagate to the powertrain caused by the FC system ageing process and drift. In this sense, the plant considered is the FCEV for which the architecture is shown in Figure 1 and for which the main parameters are included in Table 1. To represent the power-split between the battery and the fuel cell, a control-oriented model (COM) is built, for which the complete FCEV model built in the v2020 GT-Power software is used as a vehicle plant. GT-Power is a performance simulation software extensively utilized by leading vehicle manufacturers for vehicle modelling. This versatile tool enables the design and analysis of diverse powertrain topologies, encompassing internal combustion engines, hybrid electric systems, and fuel cell vehicles [27]. With GT-Power, engineers can assess crucial performance metrics such as power output, fuel efficiency, emissions levels, and thermal management. Its comprehensive capabilities make it an invaluable resource for optimizing vehicle design and performance across a wide range of applications in the automotive industry. The GT-Power FC model was calibrated with experimental data, and the FC maps employed in the EMS were obtained through steady-state simulation, as described in Section 2.3.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Weight & 1814 kg \\ Frontal area & 2.73 m\({}^{2}\) \\ Motor power & 120 kW \\ Battery capacity & 1.5 kWh \\ Battery voltage & 230 V \\ FC rated power & 95 kW \\ \hline \hline \end{tabular} Hyundai Nexo specifications.  
\end{table}
Table 1: Description of the FCEV’s main features.  
In order to evaluate the impact of the 1D table accuracy employed in the EMS, three different scenarios are assessed. The first case considers perfect knowledge of the FC state. In this scenario, the GT model is used extensively to create a 1D look-up table relating the FC current with its power, corresponding to the map calibrated by testing the FC in steady-state conditions, represented in Figure 2 as Actual map (AM). In a second scenario, the Biased map (BM) of the FC is considered as the reference. This case aims to estimate the impact of errors in the FC map used for control purposes in the ECMS: a situation that becomes more important as the FC ages and presents a significant performance drop due to the degradation process. This represents the condition where the brand-new FC calibration remains constant for the entire FCEV's useful lifespan.  
To rectify errors that may propagate to the powertrain control due to biased maps, the third case proposes a strategy that involves progressive updating of the BM and eventually improving the results obtained with the FC map obtained by the AM, since the adaption is able to capture, to some extent, the FC dynamics that were not considered in the original scenario. Figure 3 illustrates the driving cycles recorded by a passenger car during its daily journeys, encompassing a wide range of driving conditions, including highway travel and urban routes with varying traffic densities and traffic signals, encompassing a range of driving conditions commonly encountered by vehicles in real-world driving scenarios. These driving cycles are employed in the simulation to evaluate EMS performance considering the three different maps. However, it is important to note that while these daily trajectories represent a specific route, the driving profiles are subject to variations  
Figure 1: Powertrain architecture of the FCEV.  
Figure 2: Maps implemented on the EMS to estimate the fuel cell output power according to the current density input to the vehicle model.  
influenced by driver decisions and the actual traffic conditions, resulting in fluctuations in total travel time.