## 3 Multi-Physics Electric Vehicle Modelling and Validation
### Description of the Detected and Simulated Driving Profile  
In order to test the quality of the developed model, both from the component perspective and from the control logics and energy flow management perspective, it is necessary to conduct simulations on speed and altitude profiles in accordance with the typology of types used to define dynamic inputs to the model. The acquisition of this data was performed using an appropriate app that, exploiting the GPS signal of a mobile device, is capable of recording both the speed maintained by the vehicle during data collection along the route and the altitude profile followed. From this perspective, the app in question is equipped with an altimetric profile correction model that exploits a model defined as a Digital Elevation Model (DEM): through the use of a digital model capable of reproducing the Earth's surface, it corrects the position detected by the GPS signal of the employed mobile device. A speed and altitude profile of an urban route taken in the city of Naples was detected and is reported in Figure 5.  
To further explore the dynamic behaviour of the vehicle model, a second driving profile was also acquired and simulated. This additional profile represents the return path along the same urban route previously covered. While the geographical layout is mirrored, the return trip features a different duration compared to the outbound segment due to variations in real-world driving conditions, such as traffic congestion, stop frequency, and vehicle acceleration patterns. The corresponding data--speed and altitude profile--were similarly processed and integrated into the simulation environment. The return route is  
Figure 4: Flow chart of control logics integrated in the vehicle dynamics model for energy flow management. presented in Figure 6, showing the GPS trace, speed profile, and road gradient, as was done for the first segment. To contextualize the results obtained and to underscore the strengths of the proposed simulation approach, a comparison with recent modelling strategies available in the literature is presented. Recent studies in the literature have addressed the modelling of electric vehicles through simulation tools, with differing levels of complexity and fidelity. For instance, ref. [39] proposed a MATLAB/Simulink-based model to analyse energy consumption and battery performance of an electric two-axle vehicle. While the simulation captures  
Figure 5: Map of the city of Naples with the GPS route detected during the driving test and the detected profiles: speed in the upper right and road inclination in the lower right (outbound path). Figure 6: Map of the city of Naples with the GPS route with speed profile in the upper right and road inclination in the lower right (return path). basic vehicle dynamics and SoC evolution, the model architecture relies on simplified representations of traction and braking phenomena, with limited consideration of regenerative braking and component constraints such as battery or inverter limits. Similarly, in the study [40], the authors implemented a model focusing on optimal power flow management in electric vehicles, integrating driving cycles and basic efficiency maps. Although the framework is structured and informative from an energy management standpoint, the vehicle dynamics are treated in a lumped-parameter approach, and detailed interactions among driver behaviour, electric powertrain control, and longitudinal dynamics are not extensively resolved. The model developed in [41] follows a comparable approach, utilizing Simulink for assessing vehicle energy performance under predefined conditions. Regenerative braking is considered, but its implementation remains largely idealized and does not include blended braking strategies or real-time current constraints imposed by the electric components. Even in the study [42], the integration of regenerative braking is described as a system feature, without an in-depth focus on dynamics and regulation.