# Online Model Adaption for Energy Management in Fuel Cell Electric Vehicles (FCEVs)
## 2 Methodology
### Model Description  
This study is conducted by modelling an FCEV on GT-Power; a detailed vehicle model is built as a vehicle plant. In the COM, the fuel cell power is modelled as a 1D look-up table using as input the FC current density \(I_{u}\). Figure 5 shows how the COM is organized. The v2021b MATLAB/Simulink interface is where the EMS is implemented. This interface addresses the proposed method of this study and also the standard ECMS applied to control the FCEV. The EMS receives the outputs of different parameters from the vehicle plant from the previous time step, where \(SOC\), \(I_{u}\), \(P_{FC}\), and \(T_{FC}\) represents the battery state of charge, current density, fuel cell power, and fuel cell temperature, respectively. Moreover, the disturbances related to the driving demands at the current time step are taken into consideration, such as \(P_{dem}\), which represents the power demanded by the electric motor to drive the vehicle. Then, the ECMS employs the powertrain model to compute the powersplit between the battery and the fuel cell to fulfil the power demand based on the ECMS strategy, providing as input only the current density for the vehicle plant according to the output power estimated by the 1D table. The GT-Power PEMFC template is used to model the FC according to experimental results. The new FC model shown in Figure 4 is calibrated using the experimental polarization curve as input for the model; this curve represents the output power of a brand-new FC model in steady-state conditions. However, hydrogen consumption is not measured by the vehicle test bench, so hardware design specifications are adjusted to match FC efficiency values found on experimental works developed using the same vehicle [28]. Similarly, the maximum and minimum reported efficiencies regarding hydrogen consumption and FC output power are 65% and 45% at minimum and maximum current densities, respectively. Since the new FC model is calibrated to represent a brand-new FC, this polarization curve was scaled to represent an aged FC close to the end of its lifetime, as shown in the figure. Usually, the failure threshold of a PEMFC is defined as a 10% drop in the voltage performance [29]. So the polarization curve of the new FC model was progressively scaled, reducing the voltage curve by 5% at low- to 10% at high-current densities to represent the aged FC model while maintaining the hardware design and other parameter calibration of the new fuel cell model. Finally, this aged FC model calibration was employed in the FCEV model to evaluate the impact of using a map of a new FC to control an aged one and to develop the proposed adaptive strategy. This paper assumes that the FCEV employs a battery pack and a fuel cell. Figure 1 shows how the powertrain is built and the electrical connections between its components. Figure 5: Representation of the control-oriented model: above, the vehicle model implemented in GT-Power, and below, the EMS implemented in MATLAB. The powertrain integrates these components through a DC bus. A DC/DC converter links the fuel cell and battery, while a DC/AC converter connects to the 120 kW electric motor. Considering 95% efficiency for power losses, the study excludes grid charging. The FCEV is modelled with a Li-ion Battery--62 serial cells and 2 in parallel, totalling 1.5 kWh capacity and 230 V voltage. Its equivalent circuit (RC) considers state-of-charge-dependent open-circuit voltage and resistance. The body specifications are those of the Hyundai Nexo [28] for longitudinal vehicle dynamics and power demand computation. Due to the powertrain architecture considered in the FCEV model, the power demand required by the electric motor to drive the vehicle over the considered driving cycle \(P_{dem}\) must be supplied by the net electrical power of the battery \(P_{batt}\), output power of the fuel cell \(P_{FC}\), or a combination of both, as given by:  
\[P_{dem}=P_{batt}+P_{FC} \tag{1}\]  
So \(P_{dem}\) depends on the progress and conditions imposed by the driving cycle.