Advanced Model of Squirrel Cage Induction Machine for Broken Rotor Bars Fault Using Multi Indicators

Squirrel cage induction machine are the most commonly used electrical drives, but like any other machine, they are vulnerable to faults. Among the widespread failures of the induction machine there are rotor faults. This paper focuses on the detection of broken rotor bars fault using multi-indicator. However, diagnostics of asynchronous machine rotor faults can be accomplished by analysing the anomalies of machine local variable such as torque, magnetic flux, stator current and neutral voltage signature analysis. The aim of this research is to summarize the existing models and to develop new models of squirrel cage induction motors with consideration of the neutral voltage and to study the effect of broken rotor bars on the different electrical quantities such as the park currents, torque, stator currents and neutral voltage. The performance of the model was assessed by comparing the simulation and experimental results. The obtained results show the effectiveness of the model, and allow detection and diagnosis of these defects.


Introduction
The squirrel-cage induction machines are widely used and are the most common type of electrical rotating machine used in industry.However, due to the combination of poor working environment and installation, internal faults frequently occur on rotor, such as broken rotor bars, end ring connectors and eccentricities [1].Detection of these faults is an absolute must in any real-life engineering system.Detection of broken rotor bar, particularly at an early stage, is rather difficult than stator faults [2] and [3].This research is important because that even if though broken bars do not cause motor failures initially, they can significantly lower the efficiency and shorten the durability of induction machines.
In order to deal with the problems connected with these failures, a numerical simulation model is usually implemented to improve traditional techniques.In fact, some companies use simulation technique for designing their new product [4].To detect the mechanical or electrical faults in induction machine, multiple methods have been utilized in the literature such as: Fast Fourier Transforms (FFT), Motor Current Signature Analysis (MCSA), Park Vectors, Stator voltages monitoring and recently Neutral Voltage (NV) [5] and [6].Generally, MCSA is the most commonly used technique because it is simple and effective in appropriate conditions.However, this technique has significant limitations due to the increasing complexity of electrical machines and drives [10].In order to reduce these limitations, the neutral voltage signature analysis has been used.This technique focuses on the use of voltage be-tween the stator neutral voltage and an artificial supply neutral voltage [11] and [12].
To demonstrate the performance of the model, a comparison between simulation and experimental results have been verified, the obtained results show the effectiveness of the model, and allow detection and diagnosis of broken rotor bars defects.

Detection of Broken Rotor Bars
Among the widespread failures of the induction machine are the rotor faults, precisely broken rotor bars, end ring connectors and eccentricities.Rotor faults lead to speed fluctuation, torque pulsation, changes of the frequency component in the supplying neutral voltage and current of the motor, temperature increase, arcing in the rotor, and vibration of the machine.These side effects have been utilized in recent years for detecting and diagnosing this type of fault [13] and [14].

Line Current Spectrum Analysis
Motor Current Signature Analysis (MCSA), based on spectrum amplitude, have been widely used to detect broken rotor bars and end ring faults.This technique analyses the anomaly, which corresponds to broken bar faults in motor stator current spectrum, and then predicts the existence of the faults.Considering the speed ripple effect, it was reported that other frequency components of stator current due to rotor asymmetry could be observed around the fundamental at the following frequencies [8]: where s is slip, f s is supply frequency and k = 1, 2, 3, . . .
Other higher harmonic components can be also induced nearby to the rotor slot harmonics in the stator current spectrum: where s is slip, f s is supply frequency, λ is positive integer, N r is number of rotor bars, p is number of pole pairs and k = 1, 2, 3, . . .

Line Neutral Voltage Spectrum Analysis
The proposed approach based on spectral analysis of line-neutral voltage focuses on the use of voltage be-tween the supply and the stator neutrals for broken rotor bars detection.Broken rotor bars causes asymmetries in the mutual inductance of the machine, which gives rise to reveal of additional components in the spectrum of the neutral voltage at frequencies given by the relation: where s is slip, f s is supply frequency and h = 1, 3, 5, . . .
The speed ripple induced additional harmonic components around the previous frequency given by Eq. ( 3), and frequencies of all components can be expressed as follows: where s is slip, f s is supply frequency, k = 1, 2, 3, . . .and h = 1, 3, 5, . . .
The following Tab. 1 presents a summary of frequency components of motor current signature analysis and neutral voltage signature analysis.

Squirrel Cage Induction Motor Model
The model is built considering that both stator and rotor consist of multiple inductive circuits coupled together, and the current in each circuit is considered as an independent variable.We include in this model the most important supply voltage harmonics but also a large number of space harmonics.These harmonic spaces allow obtaining a machine model closer to the real one.However, the main information for the detection of broken bars is at the level of harmonic 3 in this voltage.The model of the induction motor takes into account the following assumptions [13], [14], [16] and [18]: • saturation is neglected, • uniform air gap, • neglecting inter-bar currents, • evenly distributed rotor bars, • neglecting flux coupling between different winding without air gap crossing.

System of Equations
The Stator comprises conventional three phase windings, thus three circuits are required to represent the stator.The rotor consists of N r identical and equally Tab. 1: Frequency components of broken rotor bars motor faults.

Signature analysis Components frequency Harmonic components frequency
Motor Current spaced bars shorted together by two identical end rings [13].Voltage equations for the motor can be written in vector-matrix form as follows: where M sr is the Mutual matrix inductances between the stator and rotor, R s is the Stator resistances matrix, R r is the Rotor resistances matrix, V r is the Rotor voltages vector, V s is the Stator voltages vector, Φ s is the Stator flux vector and Φ r is the Rotor flux vector.The matrix M sr depends on time, which necessitates the inversion of the inductance matrix L s of dimension N r + 4 in each calculation.To make this matrix constant, we apply the Park transformation.The use of the Park transformation bypasses allows obtaining a system of equations with constant coefficients which facilitates their resolution.

Inductances Calculation
It is obvious that the calculation of all inductances is the key to successful simulation of an induction motor.These inductances are conveniently calculated using the Winding Function Approach.According to winding function theory, the inductance between any two windings i and j in any electric machine can be computed by the following equation [7] and [17]: where µ 0 = 4π • 10 −7 H•m −1 , e is the air gap length, θ is the particular rotor angular position, r is the average radius of the air gap, L the active stack length of the motor, ϕ angular position along the stator inner surface, and n i (θ, ϕ), N j (θ, ϕ) is called the winding function of circuit, i and j represent the magnetomotive force distribution along the air gap for the unit current in winding.

Quadrature-Phase Model
The Park transformation is a well-known three-phase to two-phase transformation in machine analysis, consisting of the application of current, voltage and flux, a change of variable by involving the angle between the axis of the windings and the d and q axes.We transform the three-phase windings a, b and c in three orthogonal d, q and o windings, referred to as [13] and [17]: • transverse axis q, • homopolar axis o.
The mathematical model machine equations in the axis system d, q can be written in vector matrix form as follows: and the Electromagnetic torque equation of the machine is defined as follows: where V sd is the Component according to the d axis voltage, V sq is the Component according to the q axis voltage, I sq is the Component of the rotor current along the axis d, I sd is the Component of the stator current on the axis d, I rq is the Rotor current component along the axis q, I rd is the Component of the stator current on the axis q, C em is the Electromagnetic torque, L tr and R tr are global matrices inductors and resistors obtained after the transformation of Park [13]. 3.4.

Line-Neutral Voltage Analysis
The approach of Neutral Voltage Signature Analysis focuses on the use of voltage between the supply and the stator neutrals [9], [11], [12] and [19].This voltage is given by the following mathematical relationship: where R s represents the stator-phase resistance, L a his inductance, I sa is the current passing through it, Ω is the rotation speed, θ is the angular position of the rotor and V supply is simple voltage generated by network supply.
In order to depict the harmonic components related to broken rotor bars defects in the line neutral voltage, it is necessary to explore its theoretical formula.
As the stator windings are star-connected then: and where v os is the zero-sequence component of the supply voltage.
By the summation of the Eq. ( 10) and Eq. ( 13) we get: The mutual inductance as described by Eq. ( 15) presents harmonics with respect to the electrical angle θ, where a = p(2π • N −1 r ) is the electrical angle of a rotor loop.Therefore, the line voltage between neutrals can be written as Eq. ( 16), where V nn is the potential difference between the neutral of star-connected stator and the neutral network in the case of a direct feed or artificial neutral in the case of a supply voltage by inverter results in healthy condition of induction motor.

Simulation Results Analysis
For a squirrel cage induction motor with N r bars, and one end ring current, Eq. ( 7) and Eq. ( 8) can be resolved using the fourth-order Runge-Kutta method.To validate the proposed model, the machine was first simulated under healthy condition.Then, the rotor faults under different broken rotor bars were simulated.The rotor has been presented by all the meshes allowing the representation of various faults, to simulate a broken rotor bar, the resistance of a bar of the cage is increased 40 times its healthy value (R bb = 40 • R b ) in the R tr until the current in the bar is closest to zero.

Simulation and Analysis of Broken Bars Fault in Motor
The motor is simulated at no load for 1 sec and then the motor is loaded with 15 Nm load, at 3 sec a completely broken rotor bars occur in a rotor induction motor.The Fig. 2 The impact of broken rotor bars fault on machine current can be examined through Park vector transformation approach.The current Park's vector for a healthy motor corresponds to a circle, whereas for a faulty one, the shape distorts depending upon the amount of fault level.To decide on the nature of the fault occurred in induction machine, an analysis with the well-known FFT is done to decide on the fault and also its severity.In this case, broken bars related harmonic components are clearly located around the fundamental Fig. 4.
Figure 7 shows a Line neutral voltage comparison between the simulations results (Fig. 7(a) and experiment ones (Fig. 7(b)), we note a match between these results.
Figure 8 shows a line current comparison between the simulations results Fig. 8(a) and experiment ones Fig. 8(b), we note a match between these results.This model is helpful in quantifying the rotor slot harmonics under healthy as well as faulty condition.

Conclusion
In this paper, we presented a mathematical model and simulation of squirrel cage induction motor in healthy case and under defects of The results presented in this paper are promising and clear and thus the future research work should focus on the use of information collected from multiple sensors (indicators), such as current, voltage, torque, vibration, and temperature, to detect and identify motor faults.
Rotor currents.c 2016 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING

Fig. 1 (
Fig. 1(d) and Fig. 1(e) show the simulation results in healthy condition of induction motor.
Zoom of rotor currents.c 2016 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING

Fig. 2 :
Fig. 2: Simulation results of broken bars fault in motor.
Faulty case.
Experimental results.
Broken rotor bars fault in induction machine lead to changes of the frequency component in the supplying neutral voltage and current of the motor, electromagnetic torque and power pulsation.The simulation results are shown in Fig. 1, Fig. 2, Fig. 3, Fig. 4, Fig. 5, Fig. 6, Fig. 7 and Fig. 8.
Figure 1 shows the simulation results of induction machine in healthy case.Figure 1(a): Stator current for no load normal condition, Fig. 1(b): Stator current when the motor is loaded, Fig. 1(c): Rotor currents, Fig. 1(d): Electromagnetic torque and Fig. 1(e): Power.

Figure 4 (
Figure 4(a) Simulation: Normalized FFT spectrum of machine line current of IM with 3 broken rotor bars and Fig. 4(b) show a zoom around the fundamental frequency.
one and three adjacent broken bars.The particularity of the model is that it takes into account the line neutral voltage in the sys-tem equation, and it is based on a detailed modeling of the induction motors, represented by m stator phases and N r rotor bars, which allows detecting and localization of the completely and partially broken rotor bars with multi indicators, without the need to change the model structure.The simulation results show the effectiveness of the model as it adapts with the presented problem and it shows a good match with the theoretical predictions.The accuracy of the simulation results is verified by the experimental results.