**Author details**

Complementary, **Figure 14** shows the current pulses in steady state in "m-1 phases" mode. The torque profile is also depicted. It is worth mentioning that increasing the conduction period of the adjacent phases implies overloading both the corresponding power electronics and some of the machine coils from the thermal point of view. Therefore, results from **Figures 13** and **14** could be invalid for long periods of operation (in this sense, angles corresponding to normal mode are a safer choice). However, in this work, current was kept constant for the sake of

**Figure 14.** (a) Current pulses in m-1 phases mode (phase D is disabled) and (b) corresponding torque profile, both at

It is important to notice that degraded mode should be able not only to keep the EV running, but also to start it from any rotor position and from different conditions, such as different road grade values. In this sense, when rotor position implies that a rotor pole is aligned with phase A in **Figure 2** (i.e., *θ* =0° ± *k* ⋅60° ; see **Figure 6**), there is no available torque. In practice, torque is very low in a zone of ±5° around these zero-torque positions (see **Figure 14**), which consti‐ tute the worst situation to start the vehicle. There are at least three possible ways to proceed in

**•** Negative grade (gravitational force helps starting the vehicle): this is the best case, since it is sufficient to release the mechanical brakes and let the vehicle start going down the slope. After 10 mechanical degrees in the motor shaft, which imply barely 7 mm of linear dis‐ placement in this particular case, the motor can already provide enough torque to further

**•** Positive grade (gravitational force opposes vehicle movement in the desired direction): this is the case which requires more torque and therefore the one in which the torque reduction, due to the faulty phase, will be more noticeable during acceleration. However, starting the vehicle is not so difficult, provided that it can move backwards for at least 7 mm. The starting process would comprise two steps: First, mechanical brakes are released and the vehicle reverses, down the slope, until the motor gets out of the low-torque zone, and then it is stopped. Second, high torque is provided by the motor to start the vehicle again, knowing that a torque dip will appear almost as soon as the vehicle starts moving. However, if the

comparison.

118 Modeling and Simulation for Electric Vehicle Applications

3000 rpm and 100% current.

such a case, depending on the road grade:

accelerate the vehicle at reasonable rates.

Pablo Moreno-Torres\* , Marcos Lafoz\* , Marcos Blanco, Gustavo Navarro, Jorge Torres and Luis García-Tabarés

\*Address all correspondence to: pablo.moreno-torres@ciemat.es and marcos.lafoz@ciemat.es

Electrical Engineering Department, CIEMAT (Spanish National Research Centre on Energy, Environment and Technology), Madrid, Spain
