 Open Access
 Total Downloads : 477
 Authors : Ashok Singroly, Deepak Pandey
 Paper ID : IJERTV1IS6225
 Volume & Issue : Volume 01, Issue 06 (August 2012)
 Published (First Online): 30082012
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Fault Detecting In Induction Machine By Sinusoidal Pulse Width Modulated Inverter
Ashok singroly, Deepak Pandey
With Electrical & Electronics Dept., IES College of Technology Bhopal
ABSTRACT: Most commonly used variable speed drive in industries is inductionmachines.80 % of industrial application are based on induction machine because of its variable speed, robust and simple design. If motor fails, deterioration can be detected in early stage than plant safety and reliability can be improved economically. Many paper have been published on the method of fault detection and analysis of broken rotor bars in electrical machine supplied directly on line but fewer efforts are made for induction motor drives fed by pulse width modulated inverter which is most commonly used drive in industry. In this paper sinusoidal pulse width modulation (SPWM) technique is used in inverter based on spectral analysis of stator currents to detect broken rotor bars fault in the rotor. It can be seen by the obtained results that it is possible to extract signs to locate and detect fault.
q Number rotor bars.
Rs Stator phase rÃ©sistance o axis stationary frame quantities.
Re Ring resistance
Rb Rotor bar resistance Lcb Rotor bar inductance Lce Rotor ring leakage
inductance
P Number of pole pairs
J Moment inertia
Lrii Proper inductance of the mesh i
Lrij mutual inductance between
i and j rotor mesh
Rotor angular
Te Electromagnetic torque
Tl Load torque

Introduction:
The development of interdisciplinary research in the context of surveillance, security and diagnostics of electric drives is growing rapidly in recent years due to the growing interest of industry for the maintenance of electrical drive. The asynchronous motor constitutes the core of these systems because of the simplicity of its implementation, its compactness, its better output and its excellent reliability. In spite of the qualities which this motor presents, it can be the subject of various order defects. The fault analysis cannot ask problem if we know its characteristics. The most difficult problem is to ignore the existence of the incident until it damages the systems. Therefore, it is beneficial and even required to early detect and diagnose a fault in a cautions manner in order to avoid technical and economical consequences which are invaluable. In the systems for variable speed the induction motor is supplied by an inverter based on IGBT (Insulated Gate Bipolar Transistor) fed by sinusoidal pulse width modulation inverter. The principal function of this inverter is the variation speed. The strong evolution of this function was based, on the one hand, on the development of solidstate components entirely commendable and rapids, and on the other hand, on the quasigeneralized use of the techniques of Pulse Width Modulation (PWM) [3] .In these industrial processes, the multiple failures can occur in the induction motor. They can be predictable, unintended, mechanical,
electrical, magnetic, or even hybrids. Their causes are diverse. Indeed, the most common drive in the industry is that with a VSI and induction motor .SPWMVSI induction motors are usually more reliable than those supplied directly online. This paper presents a method analysis for broken rotor bars in induction motor fed by a voltage source inverter based on the spectral analysis of a stator phase current (MCSA; Motor Current Signature Analysis). This method showed that the application of this technique offered reliable and satisfactory results has several advantages. Among these advantages two are more interesting: the first is that the implementation of this method has only currents sensors and a spectrum analyzer, the second is that the detection and the localization can be carried out during the systems operation in real time. A study by simulation was presented. This study showed that the application of this technique offered reliable and satisfactory results for this defects diagnosis.

System and Mathematical Model
The three phase voltage inverter is based on three cells of commutation as shown in Fig. 1. Where Vd is the DC voltage inverter input and presents the logic state corresponding to the conducting. In a three phases system, the vector components are separate from each other by an angle of 120Â°. Each commutation cell can be regarded as a phase of the inverter. The considered system is a threephase inverter controlled by a Sinusoidal Pulse Width Modulation (SPWM) generator module feeding one induction motor. The command of the complementary switch of the same cell is initially assumed unchanged. Based on this command, a mean variable voltage is applied to the motor at each commutation period. We study the rotor broken bars when the induction motor is fed from SPWM voltage source inverter.
We consider that the machine consists of a stator winding back and a rotor squirrel cage. The proposed model is based on an approximation of magnetically coupled circuits where the current in each mesh in the rotor cage is an independent variable [5, 6]. This approach offers a compromise in terms of model accuracy and computational time. In addition, this type of model can take into account a number of electromagnetic faults such as broken bars and eccentricity faults. Each bar of the rotor cage is modeled by a resistance Rb [7, 8, 9] in series with a leakage inductance Lb and each portion of the ring of short circuit with a resistance Re in series with a leakage inductance Le, as shown in Fig. 2.
The application of Kirchoff's law on a grid gives us:
For the stator, it is assumed that it is composed of three phases each consisting of coils placed in series, regularly distributed in slots on its entire bore. We'll develop an analytical model of induction machine from the general equations we calculate different
inductance of the machine. For this purpose, it suffices to consider the mechanical angle (sisj) in the calculation of flux. This angle represents the angular difference between the phase i and phase j stator. The equation expresses the electrical functioning of the cage induction machine is:
With voltage and current stator are:
The resistance and inductance matrices are respectively represented by the following general form (8):
The mutual inductance matrix between stator phases and rotor mesh is of the order (m, Nb):
The rotor resistance matrix is:
With:
F R, resistance matrix F L, inductance matrix
Frs Fsr =0, for considered resistance matrix
With:
These electrical equations must be added to the following mechanical equation:
The matrix of inductances of stator phases expressed by the relationship (9) is of the order (m, m), with m=3:
With:
Lsii if (i=j): The proper inductance of the phase i;
Lsij if (ij) : Mutual inductance between i and j stators phases.
The order matrix of rotor inductance is (q+1, q+1).
The electromagnetic torque is calculated by using the basic principle of energy conversion. The torque developed by the machine Te can be obtained by considering the change in coenergy (Wco) of the system produced by a small change in rotor position when the currents are held constantly deriving the latter expression with respect to the position taken by the rotor towards the stator. The expression of electromagnetic torque is ultimately determined by the relationship below:
It follows that the electromagnetic torque can be expressed as:
Where,[Ls ] , [Lr ] et[Lsr ] , [Lrs ] are respectively the matri of proper and mutual inductances of stator and rotor windings.
Multi meshes model rotor broken bars: The modeling of a broken bar or a ring segment of a short circuit occurs (see Fig. 3.) by increasing the value of its resistance so that the current crossing is the most close as possible to zero in steady state.
This is introduced in the matrix of resistances by the addition of the matrix of the rotor resistance [Rr] with the default matrix [Rd]. In our study, the method of modeling by increasing the resistance of the broken bar, the value of this resistance is multiplied by a factor of M = 103.

Simulations and interpretation
The realized simulations with the model proposed are designed in order to analyze the behavior of induction motor with rotor fault when the motor is fed by a voltage inverter controlled by pulse width modulation. The obtained simulation results are illustrated in Fig. 4 and 5. Remember that, according to the work [12]
this type of fault is characterized by appearance of frequency lines according to the following: f1, 2 = (1 Â± 2sk) fs. In case, where the machine is powered by a purely sinusoidal voltage. However, we know that using a pulse width modulation voltage source inverter, shows the natural frequencies identified in [13]. The first family is centered on the frequency mfs and includes the term of rank m, the pair harmonics of rank m 2 and m +2, m4 and, m+4. The second family is centered on the frequency 2mfs and includes a pair of harmonics of rank 2m1 and 2m +1, 2m3 and 2m +3… The third family is focused on 3mfs and includes the harmonic rank 3m, and includes 3m2 and 3m +2, 3m4 and 3m+4 … .However; the interest of our tests and thus this work is to decide if this relationship is still valid. Fig. 4a, b, c and d, respectively represent speed, stator currents, torque and the first four rotor meshes These are calculated when you start the machine powered by a voltage inverter without load and apply torque load of 3 (N.m) at time
0.5 seconds. At time 1.5 seconds simulates the breaking of the first bar we do follow the second to 2.5 seconds. In Fig. 4d, we show moments of the two zoom breaking bars. We note at these moments currents of the bar considered void. When applying the failure, envelopes appear on the ends of the current. Fig. 5a, b, c and d, illustrate the result of frequency analysis of current phases (Fig. 4b) before breaking bars (healthy machine) when the motor has a single broken bar and two broken bars (Fig. 5c). At the end, Fig. 5d shows the superposition spectra of the three cases studied. Thus, we note that for the healthy machine that is fed by a voltage inverter with modulation index (m = 9), the appearance of the frequencies of 50,150, 250 and 350 (Hz) as shown in the first row of table 1. The frequency analysis is the case of one broken bar (Fig. 5b) shows that for each previous detected frequency there are two other ones that appear on both sides. Or that the spectrum
for the case of two breaks of bars (Fig. 5c) there are four pics, two correspond to the first broken bar and two others at the second (see zoom in Figure 5c). So, the frequency analysis shows that corrections must be reported as a result of f1, 2 = (1 Â± 2sk) fs+2 (k1) fs, where k has the order of the families of harmonics created by the inverter voltage. This correction must be made in order to assess the failure of the break of the bar. Finally, the analysis frequencies of healthy motor and broken bars motor are superposed (see Fig. 5 d).

Conclusion
The Breaking or rupture of the bars is one of the most common faults in the rotor. It reduces the average value of electromagnetic torque and increases the amplitude of oscillations, which themselves cause oscillations in the speed of rotation and also causing mechanical vibrations and thus, abnormal functioning of the machine .The large amplitude of these oscillations accelerate deterioration of the machine. In this work, the model mesh for modelling rotor was used. This model has enabled the detection of broken bars even if the induction motor is fed by a voltage inverter controlled by pulse width modulation. We only note that the known conventional relation used for diagnosis of broken bar when the motor is powered by the network is no longer valid in case the induction motor is fed by a voltage inverter. The expression in question must be corrected with an additional term in the initial expression or (2.k – 1) fs.
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