15th international conference on Sciences and Techniques of Automatic control & computer engineering - STA'2014, Hammamet, Tunisia, December 21-23, 2014
STA'2014-PID3513-DFC
An Extended Park’s Vector Approach to Detect Broken Bars Faults in Induction Motor S. Bouslimani, S. Drid, L. Chrifi-Alaoui, P. Bussy, M. Ouriagli and L. Delahoche Abstract— In this article, we present a study based on the application of the new approach of the vectors of Park in the two axes ropers to the detection of the defects of bars in the threephase induction machines. In order to simulate the behavior of the motor with defect, we propose the modeling of the diagram multi windings of the induction motor allowing apprehending his behavior in presence or absence of failures. The simulated results suggest that this method is effective and accurate and can be widely used in the induction motor fault diagnosis.
knowledge of the labor in handling the machine [2]. It is necessary to diagnose the fault at the preliminary stage. Because any fault left without finding at the early stage may lead to large losses in man power, profit and the precious time. By modeling an induction motor, the analysis of the machine in faulty and healthy condition is possible; also it gives a choice of creating various faults to analyze the motor under various conditions. There is a considerable demand to reduce maintenance
Keywords— Induction Motor; Condition Monitoring; Park costs and prevent unscheduled downtimes for electrical drive Vector Approach (PVA); Fault Diagnosis. systems, especially ac induction motors. Interestingly,
signatures of all signals are available on electrical terminals (currents) of electric machines including the vibration signals[3].
NOMENCLATURE Nr
Number rotor bars. Stator résistance. Resistance of end ring segment. Rotor bar resistance. cyclic stator inductance. cyclic rotor inductance. inductance of end ring. mutual inductance. speed of the rotor. electrical angle of adjacent mesh’s.
Different faults of induction motors are generally classified as either electrical or mechanical faults. Different types of faults include stator winding faults, rotor bar breakage, misalignment, static and/or dynamic air-gap irregularities and bearing gearbox failures. The most common fault types of these rotating devices have always been related to the machine shaft or rotor. It is estimated that about 38% of the induction motor failures are caused by stator winding faults, 40% by bearing failures, 10% by rotor faults, and 12% by miscellaneous faults. The rotor faults can result in excess heat, decreased efficiency, reduced insulation life, and iron core damage. Therefore, early detection of incipient rotor I. INTRODUCTION faults and appropriate maintenance can avoid more severe The diagnosis of the control of an induction motor, motor failures [4, 5]. became very important, because of the development which Park’s vector approach has been used by different authors knew industrial environment especially for the electric drives. for analyzing different types of individual faults [6],[7],[8] Reliable detection of broken rotor bars must also involve and [9]. Bennett has analyzed the winding failures [10] and the correct identification of current components due to any given the report about that. normal mechanical disturbances of the rotor to avoid an In our paper the induction motor is modeled in stationary incorrect diagnosis [1]. reference frame as well as it is modified to rotor broken bar The failure of the induction motor may be caused because fault and the results are analyzed using Park’s vector of many reasons like manufacturing fault, designing fault of approach. The selected reference frame is a convenient the engineer, overloading, environment and poor technical choice of reference frame, when the supply network is large or complex. Though the induction motor model is readily available in simulation software, for fault diagnosis of S. Bouslimani and S. Drid are with the LSP-IE Laboratory, Department of induction motor, it is more convenient to model the induction Electrical Engineering, Batna University, Algeria (e-mail: motor and simulate it in stationary reference frame. The rotor
[email protected],
[email protected]). fault is diagnosed using Park’s vector approach. The L. Chrifi-Alaoui, P. Bussy and L. delahoche are with the LTI Laboratory, important feature of this paper is, the combined effect of rotor Aisne University Institute of Technology, Cuffies, France (e-mail: is modeled in induction motor and the result is obtained using
[email protected],
[email protected]). Park’s vector approach. This method can be implemented for M. Ouriagli is with Laboratoire d’Informatique Mathématique Automatique et Optoélectronique (LIMAO) Faculté polydisciplinaire de Taza online diagnosis in industrial applications. The software is simpler. Maroc Route d’Oujda, B.P :1223 Taza Maroc Rs Re Rb Lsc Lrc Le Msr ω α
978-1-4799-5906-8/14/$31.00 ©2014 IEEE
411
II. BLOCK DIAGRAM OF INDUCTION MOTOR A. Model Of Rotor Winding For the analytical study of the performances of the induction motor of with rotor dissymmetry’s, we adopted the diagram multi equivalent rolling up which adapts well to the problem arising, because it describes the rotor like a whole of meshs inter-connected between them, each one formed by two adjacent bars and the portions of rings which connect them (fig.1). Starting from traditional assumptions which suppose that the permeability of iron is infinite, that the air-gap and that the stator f.m.m. is with sinusoidal distribution, one is smooth and constant calculates various inductances and mutual insurance companies which intervene in the equations of the circuit. The representation of the dynamics of the machine, with a reference mark binds to the rotor, is given by the following equations: d Φ ds − + ω .φ qs dt d Φ qs − + ω .φ ds dt
V ds = R s . I ds
V qs = R s . I qs
(1) (2)
dφ 0 = Rr .I dr + dr dt 0 = Rr .I qr +
x (t ) = [isd (t ) isq (t ) ird (t ) isq (t )
Lsc 0 − 3 M sr 2 0 0
(4)
dt
−
0
Ir(k-1) Irk
Nr Msr 2 0
Nr Msr 2
0
Lrc
0
0
L rc
0
0
3 Msr 2 0
R
0
Lsc
− ω Lsc
0
T
Rs 0 0 0
0 −
Nr ω Msr 2 S1 S3 0
Ids 0 Iqs d 0 Idr = dt 0 Iqr Ie 0 Le
−
Nr ω Msr 2 0 S2 S4 0
0 0 0 0 Re
I ds I qs I dr I qr I e
where :
Ir(k+1)
Ir(k-2)
Ie (t ) ]
The complete system after the transformation of park is [11], [12] and [13]:
Vds s Vqs ω Lsc 0 − 0 0 0 0
(3)
dφ qr
Where:
Re 2 Re 2 2 + Rb0 + Rb15 cos 0α + 2 Nr + Rb1 + Rb0 cos 1α + L (7) 2 Nr S1 = 16 Re 4 (Rb0 cos0α cos1α ) + (Rb1 cos1α cos 2α ) 2 + 2 + Rb14 + Rb15 cos 15 − α − 16 + L + (Rb15 cos15α cos0α ) Nr
Ie
Re Re 2 Nr + Rb 0 + Rb15 cos 0α sin 0α − 2 Nr + Rb1 + Rb 0 cos 1α sin 1α − L (8) Re + Rb14 + Rb15 cos 15α sin 15α − 2 Nr 2 S2 = − 2 (Rb 0 sin 0α cos1α ) + (Rb1 sin 1α cos 2α ) + 16 + ( ) L + R b 15 sin 15 cos 0 α α 16 (Rb0 cos 0α sin 1α ) + (Rb1 cos1α sin 2α ) + L + 2 16 + (Rb15 cos 15α sin 0α )
Figure 1. Electrical circuits equivalent of a cage rotor
Ir(k-1)
Re/Nr
S1= S4, S2= S3
Le/N
2 Lb(k-1)
1
Irk
Ib Rbk
Rb(k-1) 3
B. Modeling Of The Broken Rotor Bars The Model shown previously, and rewritten below, makes it possible to simulate the broken rotor bars. If one wants to simulate the rupture of a bar or two bars the only values which will change are those of: S1, S2, S3 and S4. The broken rotor bars is one of the most frequent faults in the rotor. Our simulations we will allow to identify the signatures of this defect and to envisage the deteriorations generated in the induction machine.
Lb
Iek Re/N
Le/N
Ie
4
r
Figure 2. Rotor cage topology
412
To illustrate the total break of bar in the model of the five bars. Fig.9, 10, and 11 illustrates the Lissajou forms a machine, we increase the value of the broken bar of 11 times healthy and faulty condition. [11] [14]. When the healthy motor is excited with the balanced sinusoidal supply, corresponding Lissajou’s pattern is a circle C. Extended PVA For Rotor Faults The extended Park’s vector approach in tow axes ropers as shown in Fig. 9. In against part, the presence of faults in the corresponding is easily distinguish the healthy cases from bar occurs by increasing the thickness of the Lissajou forms, defective ones. The detection of rotor faults can be obtained corresponding to one and two broken bars respectively Fig.10 by observing the relative form and thickness of the Lissajou and 11. As against the Park vector in the reference related to the rotor assumes a circular shape in the healthy state and the current. The thickness and the form of Lissajou’s curve changes presence of fault (broken bars) creates a deformation of the circle (Fig.12). because of the harmonics generated by the fault. 3000
5 4 3 2
be ta
1
Iβ
0
Is
Clarke Transform
Iα
Speed (tr/m n)
2500
-1 -2
2 broken bars
1 broken bar
Load
3 broken bars
2000 1500 1000
-3 -4 -5
500 0
Id
4
0.5
1
1.5
2
2.5
3
Tims (s)
3
Figure 4. Speed
2
y
1
Iq
Is
Park Transform
0
healthy 1 broken bar 2 broken bars
0 -1 -2 -3
3100
-4 -4
-3
-2
-1
0
1
2
3
4
Speed (rd/mn)
3000 2900 2800 2 broken bars
1 broken bar
2700
3 broken bars
2600
Figure 3. The proposed methodology for induction motor fault diagnosis
2500
With: Iα , Iβ : Stator current in a reference frame related to the stator. Id , Iq: Stator current in a reference frame related to the Rotor.
2400 0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
Time (s) Figure 5. Zoom Speed
III. SIMULATION AND RESULTS 6
2 broken bars
1 broken bar
Load
3 broken bars
4
Stator C urents (A )
MATLAB/SIMULINK model-based on power system toolbox was developed to examine the proposed control algorithm and the phase-current reconstruction feasibility. The parameters of the induction motor used in this study as follows: U=220/380V; In=4.5/2.6A; Ωn=2850tr/min; Pn=1.1KW; Rs=7.282Ω; J=0.006093Kg.m²; f=0.00725Nm.s/rd; Rayon = 0.03575m; Length = 0.065m; airgap = 0.00025m ; Ns=160; Nr=16; Lsl=0.018H; Rbhealthy=15010-6Ω; Re=72 10-6Ω The model established in this paper can simulate the breaking of rotor bars by a 200-fold increase of its nominal resistance. Fig.4, 5, 6, 7 and 8 shows the evolution of the main characteristics of the multi-winding model, namely: speed, electromagnetic torque, stator current and rotor currents of
2 0 -2 -4 -6 0.6
0.8
1
1.2
1.4
1.6
1.8
Time (s) Figure 6. Stator Current
413
2
2.2
2.4
2.6
18
5
16
4 3
14
2 1
be ta
10 8
1 boken bar
Load
2 boken bars
0
Is
ET (Nm)
12
3 boken bars
-1
6
-2
4
-3
2
-4
0
0
0.5
1
1.5
2
2.5
-5 -5
3
-4
-3
-2
-1
0
1
2
3
4
5
Is alpha
Time (s)
Figure 10. Park’s current vector Isβ = f(Isα)
Figure 7. Electromagnetic Torque
One Broken Bar 5
2000 1500 1000
Ib1
3
Ib2
2
Ib3
1
be ta
Ib4
0
Is
500 0
-1
-500
-2 -3
-1000
-4
-1500 -2000
-5 -5
0
0.5
1
1.5
2
2.5
-4
-3
-2
-1
3
Time (s) Figure 8. Rotor current
0
Is alpha
1
2
3
4
5
Figure 11. Park’s current vector Isβ = f(Isα) Tow broken bar
5 healthy 1 broken bar 2 broken bars
4 4
3 3
2 2
be ta
1
1
0
y
Is -1
Is
Ibk (A )
4
Ib0
0
-2
-1
-3
-2
-4
-3
-5 -5
-4
-3
-2
-1
0
Is alpha
1
2
3
4
-4
5
-4
-3
-2
-1
0
1
2
3
4
Is x Figure 9. Heathly case Park’s current vector Isβ = f(Isα)
Figure 12. Park’s current vector Isq = f(Isd) Healthy, One and tow broken bars
414
Figure 13, 14 and 15 depicts the stator current spectrum of the squirrel cage of healthy motor, one and two broken bars respectively. For nominal loads, we have shown by spectral analysis and monitoring the evolution of characteristic frequencies of a defect present in the stator current could deduce the state of the machine. When broken bar faults exist in an induction motor, the harmonic components appear at the right and left sideband of the fundamental frequency. The corresponding side frequency points are calculated by (1±2ks)fs. The amplitudes of fault-related spectral components increase with the growth of the numbers of adjacent broken bars.
20 0
Stator Current (dB)
-20 -40 -60 -80 -100 -120 -140 -160
0
20
40
60
80
100
Frequancy (Hz)
Figure 15. Stator Current spectrum with tow broken bars 20 0
IV. CONCLUSION
Stator Current (dB)
-20
In this paper, we first presented a model for the asynchronous machine adapted to the simulation breaks the rotor bars: multi-winding model that takes into account the structure of the rotor. Using this model we were able to highlight the phenomena related to the breaking of rotor bars.
-40 -60 -80 -100 -120
Second, an approach to model the rotor faults. We have found out that a bar causes oscillations in the torque, speed and the stator current and at the same time creates an over current in the bar adjacent the bar broken.
-140 -160
0
20
40
60
80
100
Frequancy (Hz)
Figure 13. Stator Current spectrum of Healthy motor
The model is analysed for healthy and faulty conditions using the stator signatures with the help of new Park’s vector. The advantage of this method is that it is based on the stator current which is visible and measurable at the outside of the machine. The display form of the Lissajou vectors current Park, facilitates detection of the fault by observing the shape and increase its thickness.
20 0
Stator Current (dB)
-20 -40 -60
REFERENCES
-80
[1]
-100 -120
[2]
-140 -160
0
20
40
60
80
100
Frequancy (Hz)
Figure 14. Stator Current spectrum with one broken bars
[3]
[4]
[5]
415
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