3.3.1. Electric Drive

The dynamic model of the electric drive was made of 3 main subsystems: the Electronic Control Unit (ECU), the Electronic Power Unit (EPU), and the brushless electric model. The model of the Electronic Power Unit made use of a functional description of the PWMmodulated inverter. It received the commands from the ECU, which was responsible for the motor current control in the d-q-0 axis and modulated the electric power exchanged

with the motor. The d-q axis control featured PI regulators receiving as input the current command and the filtered current feedback subject to Park's transformation. The output of the controllers was then transformed back to the 3-phase system and used inside a PWM modulator based on a triangular bipolar wave carrier that generated the digital control signal for each of the 3 commutation poles, thus modulating the DC-link tension and generating the 3 motor phase voltages as per [27]. The motor model was derived from that adopted in [16]. As depicted in Figure 4, it was based on the representation of the 3-phase dynamics through a lumped parameters representation, where each electrical parameter is a variable as a function of the windings' temperature, itself computed at each time step as a function of the thermal power generated through the Joule effect and commutation losses and the external temperature according to a simplified first-dynamic order model of the motor's thermal dynamics. The introduction of faults within the model was achieved according to the literature models. In particular, the occurrence of a turn-to-turn short was described according to [2], where the fault process caused the progressive decrease of 1 phase resistance, auto-inductance, and mutual inductance.

**Figure 4.** Schematics of the Electric-Drive model.

Such a failure mode was mainly caused by the progressive degradation of the insulating material separating the coils from each other. Such a degradation process was mainly driven by thermal issues and was modeled according to a modified Arrhenius Law as proposed by [28]. As evidenced in Figure 5, its occurrence caused asymmetric behavior between the 3-phase currents and increased a common node current which is not present under nominal health conditions. Similar considerations can be performed for the other considered failure modes. The progressive degradation of the motor permanent magnets was simulated by progressively reducing its magnetic flux term, while the occurrence of eccentricity was represented by changing the flux term according to the expected gap size variation as a function of the rotor angular position.
