## 2 Background and Methodology  
The key for successful fault detection in electrical machines relies on the availability of accurate information from them which allows for the understanding of the machine's condition. Thus, the basis of any fault detection system is precise condition monitoring. It can easily be realized from the name that condition monitoring is an act designed to observe the performance of a device, including electric machines, with the purpose of a maintenance strategy. The reliability of condition monitoring techniques depends upon the best understanding of motor characteristics, including electrical and mechanical characteristics, in both healthy and faulty conditions. In this respect, condition monitoring techniques have continuously been developed over the years, resulting in a range of available methods for failure diagnosis in electrical devices. Condition monitoring techniques presented for broken rotor bar detection in induction machines can be classified into the following categories [4;5]:  
* Acoustic Emission [6];
* Air Gap Torque [7];  
Figure 1: The structure of three phase line start permanent magnet synchronous motors LS-PMSM (four pole). * Motor Current Signature Analysis (MCSA) [8];
* Electromagnetic Field Monitoring [9];
* Instantaneous Angular Speed [10];
* Power [11];
* Motor Circuit Analysis [12];
* Thermal [13];
* Vibration [14];
* Voltage [15]. This section discusses the influence of BRB on the rotor magneto-motive force (MMF) and its effects on the stator current signals. The forward component of this MMF, in a healthy case, rotates at a synchronous speed, \(\omega_{syn}\), with respects to the stator (or \(s\omega_{syn}\) with regard to the rotor). When a bar cracks, there will be no current flow in it, and therefore no magnetic flux is produced surrounding the BRB. As there is no magnetic flux around the BRB, a non-zero backward rotating field is generated, and thus an asymmetry is created in the rotor MMF. It is worth mentioning that the backward rotating field in a healthy rotor is zero. The non-zero backward rotating component produced due to the existence of a BRB conducts an equal but reverse current in the healthy bars. Such a current causes secondary failure. The rotation of non-zero backward MMF as a result of BRB is at a slip speed, which is defined by \(s\omega_{syn}\) with regards to the rotor or by Equation (1) with respect to the stator [16]. \[\omega_{bMMF}=-s\omega_{syn}+\omega_{m}=-s\omega_{syn}+(1-s)\omega_{syn}=(1-2 s)\omega_{syn} \tag{1}\]  
The non-zero backward MMF produces harmonics which are superimposed on the stator currents. These superimposed features can be used as signatures for the detection of BRB in the MCSA technique [17]. Figure 2 shows the effect of BRB faults on the MMF of rotor for a cage with 16 bars per pair of poles. As explained before, broken bars cause harmonic components of \((1-2 ks)f\) in the stator current. Among these components, the main one corresponds to the frequency that has \((k=2)\), called the left sideband harmonic (LSH) and defined as:  
\[f_{LSH}=(1-2s)f \tag{2}\]  
The motor slip changes from one to zero during the start-up; at the beginning of the start-up, the motor slip is one and it goes to zero when the motor reaches the steady state. Accordingly, the frequency of LSH (\(f_{LSH}\)) varies from the value equal to the fundamental frequency to zero and vice versa. The appearance of this harmonic and its particular evolution were also explained [18]. Squirrel-cage bars in LS-PMSM improve start-up operation by allowing the ro  
Figure 2: Effect of a broken bar on the magneto-motive force (MMF) of a rotor [16]. movement. In the stationary region, no current flows in the squirrel-cage bars and thus the value of LSH becomes zero, \(A_{f_{LSH}}\approx 0\). The behavior of the LSH frequency for LS-PMSM during the start-up transient is shown in Figure 3.  
The main idea underlying this methodology is the tracking of the characteristic transient evolution of the fault-related feature from the LSH pattern [19].