A New Hybrid "Park's Vector - Time Synchronous Averaging" Approach to the Induction Motor-fault Monitoring and Diagnosis

Abstract

Induction motors are critical components in industrial processes since their failure usually lead to an unexpected interruption at the industrial plant. The studies of induction motor behavior during abnormal conditions and the possibility to diagnose different types of faults have been a challenging topic for many electrical machine researchers. In this regard, an efficient and new method to detect the induction motor-fault may be the application of the Time Synchronous Averaging (TSA) to the stator current Park's Vector. The aim of this paper is to present a methodology by which defects in a three-phase wound rotor induction motor can be diagnosed. By exploiting the cyclostationarity characteristics of electrical signals, the TSA method is applied to the stator current Park's Vector, allowing the monitoring of the induction motor operation. Simulation and experimental results are presented in order to show the effectiveness of the proposed method. The obtained results are largely satisfactory, indicating a promising industrial application of the hybrid Park's Vector-TSA approach.

1. Introduction

The electrical drives using induction motors are the most common way of converting electrical to mechanical energy within industrial applications. This is mainly due to their robustness, low cost, reasonably small size and capability to operate with an easily available power supply.

However, due to the operating conditions of these motors, with many factors that degrade their performance such as dust, temperature level, humidity, continuous operation and heavy loads, faults can sometimes occur, and the well-functioning of these machines is, consequently, affected [1]. In other words, the appearance of a fault in the drive modifies its operation, and hence affects its performance. Furthermore, most electrical-drive failures interrupt the process, reduce production and can damage other related machinery. Therefore, an effective incipient fault detection technique would be very beneficial for the electrical drive condition monitoring, since it would reduce the maintenance and downtime expenses [2, 3].

In this regard, several diagnosis techniques for the identification and discrimination of the induction motor faults have been proposed. Temperature measurements, infrared recognition, radio frequency emissions, noise monitoring or chemical analysis are some of them [3]. References for coils to monitor the motor axial flux may be found in [4], vibration measurement, in [5], speed fluctuations in [6] and torque sensing in [7]. However, the drawback of these methods is that they require direct access to the machine in order to place transducers for the monitoring.

To overcome this disadvantage, most recent research has been directed toward electrical monitoring of the motor such as: – Spectrum analysis of machine line current, called Motor Current Signature Analysis or MCSA [8-10]: this method is based on sensing the stator current, and utilizing the results of its spectral analysis to identify a failure in the induction motor. – Park’s Vector Approach [11, 12]: It’s based on the identification of a specified current pattern obtained from the transformation of the three-phase stator currents to an equivalent two-phase system. Under ideal conditions, balanced three-phase currents lead to a Park’s vector that is a circular pattern, while under faulty conditions, the Park’s vector pattern becomes elliptic – Extended Park’s Vector Approach: introduced by Cruz and Cardoso [13], this method is based on the spectral analysis of the motor-current Park’s vector modulus.

These methods are the most advantageous since the stator current presents a non-invasive feature.

However, Zhang [14] stated that the characteristic fault components cannot be detected using extended Park’s vector approach when the load is light or nonexistent.

To alleviate this drawback, we’ll develop a method exploiting the cyclostationarity of electrical signals (voltage and current) for the motor condition monitoring. Cyclostationarity is a property that characterizes systems with periodic statistical properties. This term was introduced by Bennett in 1958 [15]. The theory of cyclostationarity was initially developed by Gardner [16] in the field of telecommunication signals. Gardner also establishes the pertinence of the cyclostationarity theory for any physical phenomenon with periodic statistical characteristics (vibration, acoustic signals generated by rotating machines, and so on). Moreover, this theory can bring new solutions to fault detection and diagnosis problems [17]. Indeed, in the case of the cyclostationary signal, each period (or cycle) is considered as the same random process realization. Therefore, if these cycles are superposed, the overall average can be calculated: this average is also called Time Synchronous Average. Time Synchronous Averaging (TSA), is a method developed by McFadden in 1987; it allows the extraction of a deterministic component from a signal. TSA consists of averaging together a series of signal segments each corresponding to one period of a synchronizing signal [18]. Since then, several algorithms have been developed on TSA method [19].

However, nowadays very little work has been done to exploit the electrical-signal cyclostationary characteristics [20, 21].

In this paper, we will present a new approach which uses the cyclostationarity of the electrical signals, in order to determine the TSA of the stator current Park’s Vector components. Then, the spectral analysis of the two-axis residual current components (d-q), evaluated by subtracting the TSA from the current signal, will be performed in order to diagnose the motor defect.

To prove the effectiveness of the proposed approach, two particular cases of failure will be dealt with this paper: an electrical fault, particularly with respect to the rotor defect, where the diagnosis will be made even in the non-loaded motor case, and a mechanical fault, particularly in the case of a load unbalance.

The main novelty of this article stems from the introduction of the notion of “Hybrid TSA – Park’s Vector approach” in order to diagnose induction-motor drive faults, whether they are electrical or mechanical.

The rest of this paper is organized as follows. In Section 2, the MCSA technique is presented. The Park’s Vector theory is developed in Section 3. Sections 4 and 5 are devoted to respectively present the TSA method and the induction motor dynamic model. Then, in Section 6, the proposed model is used for studying the machine behavior under healthy and faulty conditions, using the MATLABSIMULINK software. Section 7 is devoted to the presentation of experimental results performed on the test bench. Finally, conclusions are mentioned in Section 8.

 

2. The MCSA Method

The occurrence of a fault in the drive modifies its operation and affects its performance. The purpose of searching defect kinematic signatures is to characterize the system operation and identify type and origin of each defect. There are several techniques that can be used to detect induction motor defects. The Motor Current Signal Analysis (MCSA) is one of the most popular used methods because of the following reasons. Firstly, it is noninvasive. The stator current can be detected from the terminals without breaking off the drive operating. Secondly, it can be measured online therefore makes online detection possible. Thirdly, most of the mechanical and electrical faults (such as broken rotor bars, short circuit and bearing damage and air gap eccentricity) can be detected by this method [22]. MCSA is based on the spectral decomposition of stator current through the Fast Fourier Transform FFT. In the MCSA method, the current frequency spectrum obtained and specific frequency components are analyzed. These frequencies are related to well-known machine defects. Therefore, after the stator current treatment, it is possible to conclude about the machine’s condition [8, 22]. The frequencies of the signals induced by each fault are calculated as a function of some of the motor’s characteristic data and operating conditions.

In this work, both of electrical and mechanical defects will be studied. We’ll particularly focus on the rotor fault and unbalanced load.

2.1 Rotor fault signature

When a rotor defect appears, the rotor’s impedance exhibits an unbalance. The immediate consequence of such an unbalance is the existence of inverse sequence currents. These currents have a frequency that is equal to the product of the slip s and the supply frequency fs. They generate a magnetic field that turns counter motor rotation-wise, at the speed -sωs, where ωs is the supply pulsation. If translated to stationary co-ordinates, this speed becomes (1-2s). ωs.

It is the interaction of this field with the one descended of stator windings that induces a current in the stator winding at (1-2s)fs. This cyclic current variation causes a speed oscillation at twice the slip frequency (2sfs) and finally, this speed oscillation induces, in the stator current spectrum, an upper component at (1+2s)fs, and so on [23, 24].

where fbb1 and fbb2 are the broken-bar frequencies, fs is the electrical supply frequency and s is the per unit slip.

2.2 Load unbalance signature

Load unbalance produce periodic variations of the load torque or the inertia. These variations often relate to the mechanical rotor position.

Schoen et al. [25] studied the effects of time-varying loads on the stator current and it was demonstrated that a periodic load torque leads to sidebands in the stator current at the following frequencies:

where flo1 and flo2 are the load-unbalance frequencies, fs is the electrical supply frequency, fr is the mechanical rotor speed in Hertz, p is the number of pole pairs and s is the per unit slip.

As shown, given a motor’s characteristic data, its current’s samples and the value of the slip, it is possible to determine the frequencies of the signals induced by each fault.

 

3. Park Vector Theory

The analysis of the three-phase induction motor can be simplified by using the space phasor representation or “Park Transformation”. This concept allows the concentration of the information contained in the three-phase system in a single space phasor [26].

So, a three-phase system xabc(t) can be represented by a Space Phasor given by:

where xabc can be any electrical variable.

Since the connection of three-phase induction motors to the supply does not usually use the neutral, the electrical variables (voltages, currents and fluxes) have no homopolar component. Therefore, a two dimensional representation can be used for describing the machine phenomena, a suitable one being based on the Park’s Vector, defined as:

In the particular case of the stator current, the stator current Park’s Vector is defined as:

 

4. Time Synchronous Averaging

The asynchronous motor operating process and the electric supply fluctuations cause the non-stationary behavior of the stator current signal. However, there has been very little work [20, 21] exploiting the electricalsignal cyclostationary characteristics to identify the faults which occur in an asynchronous-motor drive. The idea is to extend the application of these signal-processing tools to the case of electrical signals. In this work, the first-order cyclostationarity of stator current and voltage will be largely exploited. Furthermore, a rotor fault can be detected by highlighting a stator-current amplitude or phase modulation. However, the modulated-signal weak frequency band makes it too difficult to detect modulation. An alternative to overcome this difficulty is proposed by MacFadden [18]: the Time Synchronous Averaging (TSA) method. It’s a way to reshape the signal before its processing.

The T-period TSA of a signal s(t) is defined as follows:

The TSA method consists of averaging s(t)-signal shifted versions of a whole number of T periods.

This method allows the separation between the excitation sources and, consequently, fault identification. Indeed, consider a signal s(t) sum of T1-period signal s1(t), T2-period signal s2(t) and noise. The application of the TSA method to s(t), at respectively T1 and T2 period allows the separation between s1(t) and s2(t). In fact, we can prove that:

By applying a similar approach, the stator current Park’s Vector can be decomposed as follows:

where Ish(t), Ismec(t) and n(t) are respectively the harmonic current Park’s Vector, the mechanical-structure-related current Park’s Vector and the noise vector.

In fact, the asynchronous motor monitoring consists of supervising the signal harmonic part. So, harmonic frequency (50Hz) which is related to electrical phenomena and mechanical-structure-related frequency must be separated.

For this purpose, the TSA method will be applied to the stator current Park’s Vector. The Th-period TSA of stator current Park’s Vector is done by the following relation, as established in (6) and (7):

where Th=1/fs is the harmonic period and fs =50Hz is the harmonic frequency corresponding to supply frequency.

Note that only the harmonic part of the stator current Park’s Vector Ish(t) corresponding to 50Hz frequency remains in the averaged signal. Thus, the synchronous averaging allows an effective separation between electrical-related and mechanical-related components.

The subtraction between the stator current Park’s Vector and its TSA gives the residual current Park’s Vector where only mechanical-related frequencies remain, as shown in (10):

It’s a very interesting property that will allow conditioning a mechanical-structure-related indicator monitoring an eventual rotor fault.

 

5. Dynamic Model of Induction Machine

The dynamic model of the induction motor can be written in state representation form as follows [27]:

where :

vsa, vsb, vsc, vra, vrb and vrc are respectively the abc stator and rotor voltages; isa, isb, isc, ira, irb and irc are respectively the abc stator and rotor currents; TL is the load torque, Ωr is the rotor angular velocity and θ is the rotor angular position.

[B] and [A] are two 8x8 matrices defined as follows:

where :

rsa, rsb, rsc, rra, rrb and rrc are respectively the abc stator and rotor resistances. Note that in the case of a healthy induction motor, rsa=rsb=rsc and rra=rrb=rrc; but, if a rotor failure occurs, it will cause an electrical imbalance and will induce a change in rotor resistance values that are no longer equal to each other [1]. J is the moment of inertia and f is the friction.

[L] is the inductances matrix given by: where :

ls and lr are respectively the stator and rotor self inductances, msand mr are respectively the mutual inductance between two stator and two rotor coils, msr is the maximal mutual between stator and rotor windings.

The model presented in (11) will be implemented on MATLAB in order to simulate the induction machine operation and the 4th order Runge-Kutta method will be used to resolve this equation.

 

6. Simulation Results

The asynchronous motor operation will be simulated for the three following cases: Healthy case, Electrical defect: Rotor fault, Mechanical defect: Load unbalance.

This simulation will be made for a 10 seconds period (The number of current cycles K = 10s x 50Hz = 500).

Table 1 below summarizes the induction motor parameters used for simulation:

Table 1.Parameters of the simulated Induction Motor

Fig. 1.Simulated d-axis & q-axis current spectra in healthy and rotor-defective cases

Fig. 2.Simulated d-axis & q-axis residual current spectra in healthy and rotor-defective cases

6.1 Rotor fault signature

The rotor failure case will be simulated by adding an extra resistance on one of the rotor phases (i.e. 10% of the rotor resistance value per phase), since this failure generally leads to an increase of a one-phase rotor resistance value [28].

The computed value of per unit slip in the defective case is 1.34%, so the theoretical broken-bar frequencies fbb1 and fbb2 are respectively 48.66Hz and 51.34Hz (1).

As a first step, a spectral analysis to stator current Park’s vector components isd and isq is applied. The predominance of the 50Hz component in the spectrum does not allow detecting the failure: the healthy-case and the faulty-case spectra are combined, as shown in Fig. 1.

The idea is to make the residual current Park’s Vector components iresd and iresq spectral analysis. The faulty d and q residual current spectra present clearly two sidebands at frequencies f1=48.67Hz and f 2=51.33Hz (Fig. 2), while in the healthy case, there was no sideband. These values correspond exactly to the theoretical values fbb1 and fbb2 deduced from (1).

6.2 Load unbalance signature

Load unbalance produce periodic variations of the load torque or the inertia. These variations often relate to the mechanical rotor position.

The mechanical failure (i.e. load unbalance) will be simulated by adding an Ωr-pulsation oscillating torque to the average load torque, so the load torque can be written as: TL(t)=T0+Toscsin(Ωr.t, where T0 is the average torque and Tosc is the amplitude of oscillating torque [29].

The computed value of per unit slip in the defective case is 1.30%, so the theoretical load-unbalance frequencies flo1 and flo2 are respectively 25.33Hz and 74.67Hz (2).

As a first step, a spectral analysis to stator current Park’s vector components isd and isq is applied. The predominance of the 50Hz component in the spectrum does not allow detecting the failure: the healthy-case and the faulty-case spectra are combined, as shown in Fig. 3.

The idea is to make the residual current Park’s Vector components iresd and iresq spectral analysis. The faulty d and q residual current spectra present clearly two sidebands at frequencies f’1=25.33Hz and f’2=74.67Hz (Fig. 4), while in the healthy case, there was no sideband. These values correspond exactly to the theoretical values flo1 and flo2 (2).

Fig. 3.Simulated d-axis & q-axis current spectra in healthy and load unbalance cases

Fig. 4.Simulated d-axis & q-axis residual current spectra in healthy and load unbalance cases

 

7. Experimental Results

The testing ground used includes an industrial threephase wound rotor asynchronous motor of 400V, 6.2A, 50Hz, 3kW, 1385rpm.

The data acquisition system used is DAQLAB 2005 (16- bit, 200 kHz A/D converter) and the sample rate taken is 25 kHz, so the number of samples per average cycle of 50 Hz is 500 (25000/50 = 500).

Supply voltages (vsa, vsb, and vsc) are measured by means of 3 voltage transducers (LEM LV 100-400) while stator currents (isa, isb and isc) are measured by means of 3 current transducers (LEM LT 100-S). The block diagram of Fig. 5 shows the implementation technique adopted during experimental testing

In the experimental test, a problem of cycle drift from one electric cycle to another appears; it’s due to the electrical supply fluctuations. The cyclic statistic rules cannot be directly applied to these signals to extract desired information, except if a way to compensate these fluctuations is proposed.

Fig. 5.Block Diagram of the implemented experimental device

Fig. 6.Superposition of 1000 voltage cycles before and after synchronization

7.1 Signal synchronization

A preliminary stage is needed: the current and voltage signals must be re-sampled according to a reference which “follows” these fluctuations: it’s “the synchronization of the current and voltage signals”.

In previous work [21], we have developed a re-sampling algorithm that allows electrical signals synchronization as illustrated in Fig. 6.

7.2 Rotor fault

The rotor fault has been carried out by adding an extra 40mΩ resistance on one of the rotor phases. The abc stator current and voltage signals are acquired using the data acquisition system and the velocity is measured with an optical tachometer.

The measured value of per unit slip in the defective case is 1.53%, so the theoretical broken-bar frequencies fbb1 and fbb2 are respectively 48.47Hz and 51.53Hz (1).

As in simulation, a spectral analysis to stator current Park’s Vector components isd and isq is applied. The predominance of the 50Hz component in the two spectra does not allow detecting the failure: the healthy and the faulty spectra are quasi combined (Fig. 7)

The idea is, as in simulation, to make the residual current Park’s Vector components iresd and iresq spectral analysis. The faulty d and q residual current spectra present clearly two sidebands at frequencies fexp1=48.56Hz and fexp2=51.44Hz (Fig. 7). These values correspond to the theoretical values fbb1 and fbb2 determined from (1).

To illustrate the hybrid Park’s Vector – TSA approach contribution, Table 2 below presents the comparison between the sideband amplitudes for healthy and rotor-defective cases, deduced from the spectra of Fig. 8. These amplitudes are denoted Ah and Abb respectively.

Fig. 7.Experimental d-axis & q-axis current spectra in healthy and rotor-defective cases

Fig. 8.Experimental d-axis & q-axis residual current spectra in healthy and rotor-defective cases

Table 2.Comparison between the sideband amplitudes in healthy and rotor-defective cases

The Park’s Vector – TSA hybrid method allows therefore an easy rotor-fault diagnosis, since the difference between the sideband amplitudes in defective and healthy cases exceeds 65% for the right sideband ((1+2s)fs) and exceeds 200% for the left sideband ((1-2s)fs).

7.3 Load unbalance

The imbalance was created by addition of an 8g mass at a distance of 48mm from the induction-motor rotation axis. The abc stator current and voltage signals are acquired using the data acquisition system and the velocity is measured with an optical tachometer.

Fig. 9.Experimental d-axis & q-axis current spectra in healthy and load unbalance cases

Fig. 10.Experimental d-axis residual current spectrum in healthy and load unbalance cases

The measured value of per unit slip in the defective case is 1.67%, so the theoretical load-unbalance frequencies flo1 and flo2 are respectively 25.42Hz and 74.58Hz (2).

As in simulation, a spectral analysis to stator current Park’s Vector components isdand isq is applied. The predominance of the 50Hz component in the two spectra does not allow detecting the failure: the healthy and the faulty spectra are quasi combined (Fig. 9).

The idea is, as in simulation, to make the residual current Park’s Vector components iresd and iresq spectral analysis. The faulty d and q residual current spectra present clearly two sidebands at frequencies f’exp1=25.44Hz and f’exp2=74.56Hz (Figs. 10 and Fig. 11). These values correspond to the theoretical values flo1 and flo2 determined from (2).

Table 3 below shows the comparison between the sideband amplitudes for healthy and load unbalance cases, deduced from the spectra of Figs. 10 and Fig. 11. These amplitudes are denoted Ah and Alo respectively.

Fig. 11.Experimental q-axis residual current spectrum in healthy and load unbalance cases

Table 3.Comparison between the sideband amplitudes in healthy and load unbalance cases

As established for the rotor fault, the Park’s Vector – TSA hybrid method allows an unbalance load diagnosis, since the difference between the sideband amplitudes in defective and healthy cases exceeds 100% for the right sideband ((1+(1-s)/p)fs) and exceeds 180% for the left sideband ((1-(1-s)/p)fs).

 

8. Conclusion

In this paper, a new approach applying the TSA method to stator current Park’s Vector in order to diagnose the induction motor faults is presented. Two particular cases were treated: rotor fault and load unbalance.

The proposed method of asynchronous-motor-failure monitoring has two major advantages. First, it is a method which is based on the analysis of the “current” signal. It can therefore be applied even to the inaccessible engines (such as the engines immersed in the motor-driven pump groups), unlike the methods based on the analysis of the accelerometer signal, where a direct access to the engine is necessary to be able to place the sensors there. Besides, the approach is relatively simple: the monitoring of the d and q residual current spectra makes it possible to clearly detect the defective case.

Finally, the MATLAB-SIMULINK software results have been widely validated by the experiment.