## 2 The Analyzed Machine  
This paper deals with a PMa-SynRm, whose main features are summarized in Table 1.  
The analyzed motor has a fault-tolerant winding, since each slot only accommodates a unique phase, as shown in Figure 1. In addition, the combination of the low current design and the large inductances (each slot includes 60 conductors) reduces the risk of high short-circuit currents.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Features** & **Value** \\ \hline Rated power (kW) & 3.5 \\ Rated torque (N-m) & 5.7 \\ Rated speed (rev/min) & 5000 \\ Rated current (ARMS) & 4 \\ Rated voltage (VRMS) & 240 \\ Number of phases & 5 \\ Number of slots & 60 \\ Pole pairs (p) & 12 \\ Slots/pole/phase (q) & 1 \\ Conductors per slot & 60 \\ Layer type & Double layer \\ Airgap width (mm) & 0.3 \\ Permanent magnets & Ferrite HF 30/26 \\ Magnetic steel & M330-35A \\ \(d\)-axis inductance (\(Ld\), mH) & \(59.7_{\text{no\_current}}{-}15.9_{\text{max\_current}}\) \\ \(q\)-axis inductance (\(Lq\), mH) & \(15.2_{\text{no\_current}}{-}11.8_{\text{max\_current}}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Main features of the analyzed fPMa-SynRM.  
Figure 1: _Cont._  
The results presented in this paper are based on a healthy and a faulty machine with a static eccentricity of 40% of the air gap length. It is noted that although this paper analyzes the effects of static eccentricity faults, dynamic eccentricity produces comparable results, and thus similar conclusions apply for both eccentricity types.  
The \(d\) axis is taken as the direction of maximum magnetic flux in the rotor, which is the direction of the magnetic flux in the rotor following the magnetic path. The minimum flux corresponds to the \(q\) axis, corresponding to the direction of the magnetic flux crossing the air barriers, as shown in Figure 2.  
It is noted that the currents in the \(dq\) reference frame (\(i_{d}\)_i\({}_{q}\)) can be calculated from the line currents (\(i_{a}\), \(i_{b}\), \(i_{c}\), \(i_{d}\), \(i_{e}\)) as:  
\[\left[\begin{array}{c}i_{a}\\ i_{q}\end{array}\right]=\frac{q}{5}\left[\begin{array}{cccc}\cos(\theta_{m})& \cos(\theta_{m}-\frac{2\pi}{5})&\cos(\theta_{m}-\frac{4\pi}{5})&\cos(\theta_{ m}+\frac{4\pi}{5})&\cos(\theta_{m}+\frac{2\pi}{5})\\ \sin(\theta_{m})&\sin(\theta_{m}-\frac{2\pi}{5})&\sin(\theta_{m}-\frac{4\pi}{ 5})&\sin(\theta_{m}+\frac{4\pi}{5})&\sin(\theta_{m}+\frac{2\pi}{5})\end{array} \right]\cdot\left[\begin{array}{c}i_{a}\\ i_{b}\\ i_{c}\\ i_{e}\end{array}\right] \tag{1}\]  
and the current angle is calculated as:  
\[\alpha=tg^{-1}\bigg{(}\frac{i_{q}}{i_{d}}\bigg{)} \tag{2}\]  
Figure 1: FEM model of the analyzed machine. (**a**) Layout of the machine. (**b**) Half winding of the five-phase 60-slots machine with a double layer and constant pitch with \(q=1\).  
Figure 2: Direct (\(d\)) and quadrature (\(q\)) axes and the \(mmf\) (magneto-motive force) as a function of the electrical angle of a SynRM.  
Figure 3 shows the five currents and the _mmf_ distribution for a given time instant in both the \(d\) and \(q\) axes.  
The permanent magnets in the rotor are placed in the negative direction of the \(q\) axis, so when the motor is positioned in the \(d\) axis, the net flux through the stator windings due to the permanent magnets is null. This is illustrated in Figure 3a, which shows one pole of a five-phase machine positioned in the \(d\) axis when neglecting the effects of the stator currents. The total flux through the windings is null since the flux in phase A is also null due to the arrangement shown in Figure 3a, whereas phases B and E, and C and D, are complementary, so the net flux is zero.  
It is known that the winding configuration in rotating field machines greatly impacts the power capability and the spectral content of both the _mmf_ and back-_emf_. These effects are reflected in the harmonic composition of the line currents and the ZSVC [21].