Diagnosis and Detection of Eccentricity Faults in a Doubly-Fed Induction Generator
(Full text in English)
Hichem MERABET1, Tahar BAHI2
1Research Centre in Industrial Technologies CRTI, P.O. Box 64, Cheraga, Algeria
2Electrical Department, Faculty of Science Engineering. University of Annaba, Algeria
Abstract
Doubly-fed induction generators are being used extensively in wind energy conversion systems. Efforts are being made to effectively adopt existing condition monitoring and fault diagnostic techniques for these systems. We consider in this paper to take account of the specificities and characteristics of the doubly-fed induction generator, for develop an analytical model that describes as precisely as possible the machine performance in healthy and machine with different eccentricity faults types.
In this paper, we propose a method for the eccentricity diagnosis fault based on the stator current analysis during the start-up using this wavelet method enables faults eccentricity detection and isolation of this fault in rotor by analysing the frequency spectrum. This study showed that the application of this technique offered reliable and acceptable results for diagnosis detection and faults.
Keywords: diagnosis, detection, faults, doubly-fed induction generator, eccentricity, modelling, Simulation.
Received: April, 01, 2016
1. Introduction
The development of wind turbine system is becoming very powerful, in terms of power quality and very interesting for environmental protection. However, their potential is considerable in the world, the wind energy sources have drawn more and more attention all over the world recent years to improve the serious environment problems and deal with the shortage of fossil fuels in recent years [1].
The doubly-fed induction generator (DFIG) is one of essential part of wind turbine system and has dominated in the field of electromechanical energy conversion system because of robustness and low cost [2].
So, for a substantial profit, the diagnosis should be properly developed to ensure a production system more make safe. Production systems must be provided with reliable protection systems as any failure can lead to inevitable damage [3]. The occurrence of different faults can be completely in damage this machine type and inevitably cause the process to stop, resulting in loss of production consequently [4].
Therefore, it is necessary to develop a model machine allow to detect the presence of the faults. Wind turbine is prone many failures and because of their size and localization, it is very costly to repair or emplace their component. In generally, mechanical faults are the most encountered in wind turbines systems at the gearbox.
These faults can occur at the level of ball, inner and outer race bearings, and flanges of the machine shaft. In scientific research tasks shows that rotor faults are more frequent breakdowns, [5, 6]. In this paper we are interested to study the rotor eccentricity faults types [7].
The DFIG in this type of faults can be subjected to counteract between the centre of rotation of the shaft and the centre of the rotor resulting the oscillations in the electromagnetic torque, uneven distribution of the currents in the rotor and the unbalance of stator current.
This phenomenon is called static or dynamic
eccentricity, and both at the same time creates the fault mixed eccentricity, whose origin may be related to incorrect positioning of the bearings during assembly or bearing failure [8, 9].
Several methods of diagnosis are based on spectral analysis of the electromagnetic quantities, using the magnetic flux, stator current and the neutral voltage vibration signal analysis and especially the stator current, which requires only a current sensor [10, 11]. Therefore, most of the recent research has benne directed towards non-invasive techniques such as stator current and vibration signal analysis, motor signature analysis with wavelet, courant envelope, Artificial Intelligence such as Neural Network, Fuzzy Logic and Fuzzy Neural Network.
The analysis of the stator currents in the frequency domain remains the most commonly used because the spectrum results contains a source of information on the majority of electric, mechanical faults and magnetic properties can appear in the machine [12, 13].
In this paper, we present tow methods for detection and isolation the eccentricity faults in a doubly-fed induction generator (DFIG). The first method uses the stator current signature based in fast Fourier transform, we demonstrate that spectral analysis can detect in case of faults [14, 15]. We also show that the use of this technique allows the surveillance during the transitional and permanent regime for monitoring. The second method is based on packet wavelet decomposition [16- 18].
In this paper, the investment interest in wind turbine conversion system based on DFIG is presented. Then, we focus on the study of their designs and the development of a global model for doubly-fed generator in case of rotor eccentricity faults. Finally, in order to validate the considered method, the proposed model has been simulated and validated by numerical simulations using Matlab/Simulink.
2. Modelling of double-fed induction generator in healthy case
Modelling an electric machine is an important phase of faults diagnosis. The progress of engineering software, have achieved reliable modelling and optimization to consider the electric machines. Modelling can guide the development of the qualification events. In addition, it is a valuable contribution because it renders an image of what may have observed experimentally and shows most diverse behaviour than the experimental observation.
The development of a diagnostic procedure based on analytical models of DFIG, covers problems number of synthesis methods describing the behaviour generator.
This accurately incorporating some parameters to describe more precisely possible the performance of the machine [19].
2.1. Voltage Equations
The stator and rotor voltages equations are given by (1) and (2) respectively:
+
=
sc sb sa
sc sb sa
sc sb sa
sc sb sa
dt d i i i
r r r
V V V
ϕ ϕ ϕ
.0 0
0 0
0 0
(1)
+
=
rc rb ra
rc rb ra
rc rb ra
rc rb ra
dt d i i i
r r r
V V V
ϕ ϕ ϕ .
0 0
0 0
0 0
(2)
2.2. Flux equations
The stator flux equation is given by:
+
=
rc rb ra sr abc sc sb sa s abc sc
sb sa
i i i L i i i
L
_.
_.
ϕ ϕ ϕ
(3)
T
he rotor flux equation is given by:
+
=
rc rb ra rs abc rc rb ra r abc rc
rb ra
i i i L i i i
L _ . _ .
ϕ ϕ ϕ
(4)
with
+
−
−
− +
−
−
− +
=
ms ls ms ms
ms ms
ls ms
ms ms
ms ls s abc
L L L L
L L
L L
L L
L L L
5 . 0 5
. 0
5 . 0 5
. 0
5 . 0 5
. 0
_ (5)
+
−
−
− +
−
−
− +
=
ms lr ms ms
ms ms
lr ms
ms ms
ms lr r abc
L L L L
L L
L L
L L
L L L
5 . 0 5
. 0
5 . 0 5
. 0
5 . 0 5
. 0
_ (6)
=
A L C L B L
B L A L C L
C L B L A L L
m m
m
m m
m
m m
m sr abc
cos cos
cos
cos cos
cos
cos cos
cos
_ (7)
with
A=cos
( )
θrB=
+ 3 cos θr 2π
C=
−
3
cos 2π
θr
abcsr t
abcrs
L
L =
In
ductances Lms, Lmr and Lm are given respectively by the following relationships:0 0 2
. . . . . µ rle p
Lms Ns π
= (8)
0 0 2
. . . . . µ rle p
Lmr Ns π
= (9)
0 0. .. . .
. µ rle
p N p
Lm Ns r π
= (10)
where:
e0: air-gap width;
µ0: magnetic permeability;
l: lenght of machine;
r: radius of machine;
Ns: number of the stator turns;
Nr: number of the rotor turns;
Lls: stator leakage inductance;
Llr: rotorleakage inductance;
P: poles number.
2.3. Electromagnetic torque
The electromagnetic torque equation is given by:
[ ]
=
r abc
s abc r rs abc tabc
sr abc s abc r r abc s abc
em
i
i L L
L L d i d i T
_ _ _ _
_ _ _
_
. .
2 1
θ
(11)3. DFIG in Faults eccentricity cases
The theory of fault eccentricity is presented by figure 1, where D: centre of dynamic eccentricity and S:
centre of static eccentricity.
Figure 1. Fault eccentricity
To address the lack of eccentricity, we must use an expression of the air gap that reflects this type fault. The air gap comes in the form (12), [20].
(
s r)
e a( )
s a(
s r)
eθ ,θ = 0− 1.cos θ − 2.cos θ −θ (12) where
θs: nangular position of a fixed air gap relative to the stator;
θr: rotor position.
a1: eps e0, and a2= epd e0
a1: static eccentricity quantity;
a2: dynamic eccentricity quantity.
eps: static eccentricity percentage;
epd: dynamic eccentricity percentage.
3.1. Static Eccentricity
The position of minimum radial air-gap length is fixed in space. In this case the quantity of dynamic eccentricity null (a2=0).
It can be caused by oval stator cores or by the incorrect positioning of the stator or rotor.
( )
s e a( )
se
θ
= 0− 1.cosθ
(13)3.1. Dynamic Eccentricity
The centre of rotation and the centre of the rotor are not the same. In this case the quantity of static eccentricity null (a1=0). It can be caused by misalignment of bearings, a bent rotor shaft, wear of bearings, etc.
(
s r) e a (
s r)
e θ , θ =
0−
2. cos θ − θ
(14)3.2. Mixed Eccentricity
This fault is the combine of two previous faults (a1≠0 and a2≠0).
4. Faults detection methods
4.1. Fault detection with stator current analysis
The stator analysed of the currents in the spectral field is the method most usually used because the resulting spectrum contains a source of information on the majority of the electric and magnetic fault, which can appear within the electric machine [21].
4.2. Wavelet packet method
4.2.1. Decomposition of wavelet packet
The wavelet packet is a generalization of the decomposition in discrete wavelet which a richer range of the possibilities for the signal analysis.
In the analysis in wavelet, a signal is decomposed into approximation and detail.
The approximation itself is then decomposed into approximation and detail of second level, and the process is repeated. For n-level decomposition, there are (n+1) manners possible to decomposed or code the signal.
In the wavelet packet analysis, the details as well as the approximation can be decomposed. This report over (22n+1) of various signals decompositions.
The decomposition tree wavelet packets signal is shown in the Figure 2 [22, 23].
Figure 2. Decomposition of wavelet packet
In the same mode that the decomposition in wavelets, the original signal in the wavelet packet decomposition is
estimated by the sum of the approximation signals and detail at each level.
+ +
+ +
+ +
=
+ +
+
=
=
+
=
=
) ( 3 ) ( 3 ) ( 3
) ( 3 ) ( 3 ) ( 2 ) ( 3 , 3
) ( 2 ) ( 2 ) ( 2 ) ( 2 ) ( , 2
) ( 1 ) ( 1 ) ( , 1
n DDD n DAD n AAD
n DDA n ADA n DAA n AAA i
n DD n AD n DA n AA n f i
n D n A n f i
(15)
The wavelet packets decompose the original signal is stationary or non-stationary in independent frequency bands, there is no redundant information in decomposed frequency bands, it is an effective approach to analysis based on multi -resolution and can be proposed as a default diagnostic method.
The multilevel decomposition of the stator current is carried out by using the mother wavelet (Daubechies 44) and the decomposition level necessary is calculated according to the following relation:
( )
) 2 2 log(
int log +
= s e
ls
f
N f (16)
with
f
s:
fundamental frequency;f
e:
sampling frequency.In this case, fs = 50 Hz and fe = 10 Khz thus then the Decompositions lavels is:
( )
levels
Nls 2 9
) 2 log(
50 10000
int log + =
= (17)
4.2.2. Energy Level of the wavelet decomposition The fault diagnosis is based on observation and comparison of the decomposition levels, which contain the fault information for various machines to diagnose.
When the fault of the rotor bars and stator short- circuit in the asynchronous machine appears and the defect information from the stator current signal is included in each frequency band resulting from the wavelet decomposition or wavelet packet. By calculating the energy associated with each level or each node of decomposition can be constructed a diagnostic tool very effective
The proper values V of decomposition energy levels have the signals information in the induction machine, the plot of these values can be used to diagnose faults in the doubly-fed induction generator (DFIG) and can identify the degree of defect. The deviation of certain inherent value indicates the severity of faults [24].
The proper value of energy of each frequency band is defined by:
) (
1 2
,
n
D E
n k
k k j
j
∑
==
=
(18)where j is the level of decomposition. Based on the eigen value of energy, the vector is given by:
=
−E E E
E E
V E
0,
1,...,
2m1(19) Such as:
1 2 2
∑
=0−=
jmE
jE
(20)5. Simulation of results
The stator and rotor currents magnitudes of the doubly-fed induction generator are shown for the healthy
case, static, dynamic eccentricity, and mixed case.
Figures 3.a) and 3.b) illustrate the three stator phases currents "Isa, Isb, Isc", and the three rotor currents phases
"Ira, Irb, Irc" with Zoom in the healthy function cases. Zooms on parts, are presented to show the balance of these currents of the static eccentricity faults causes a disturbance on the magnutid of the machine.
Figure 3. Machine healthy case
One notices light oscillations on stator currents "Isa, Isb
and Isc" (Figure 4.a)). As well, the appariation of the fast oscillations is noted and approximate among them on the
rotor level of the currents of the phases "Ira, Irb, Irc" these oscillations are very visible between the healthy case and the case of defects of static eccentricity (Figure 4.b)).
Figure 4. Machine in 50 % static fault case
Figures 5.a and 5.b present the three currents of the stator phases "Isa, Isb, Isc", the three currents of the rotor phases "Ira, Irb, Irc" at the time of the presence of a dynamic eccentricity fault. In this case, the oscillations are
appeared homogeneous envelopes and very clear on the three currents of the stator phases the rotor "Isa, Isb, Isc"
and currents are unbalanced.
Figure 5. Machine in 50 % dynamic fault case
One notices on the figures 6.a) and 6.b) the
combination between the two phenomena appear in two defects (statics and dynamics) this type of defects and called mixed defect of eccentricity.
Figure 6. Machine in mixted fault case
The spectral analysis of the stator current in phase "Ias"
when the machine is operational, one notices that the fundamental frequency paired only (Figure 7.a)).
The static eccentricity reveals additional components from the fundamental as shown in Figure 7.b).
Figure 7. Spectral analysis of the stator current in the eccentricity faults cases
These frequencies correspond to the fault frequency according to the following expression:
s sta
ecc
n f
f
_= .
(21)where: n=1, 3, 5....
Dynamic fault eccentricity also appears to frequencies above the fundamental frequency. We distinguish new frequencies corresponding to the faults frequencies as shown in the figures 7.c, these faults frequencies according to the following expression:
= ±
r s s dyn
ecc n f m f
f f n
. . .
_ (22)
where: n=1, 3, 5... and m=2, 4, 6...
In the case of mixed fault eccentricity. We noticed the appearance of the new frequencies, which appear at the time of the fault statics and fault dynamics eccentricity as show the 7.d, more of the frequencies correspond to the
frequencies of the fault type according to the following expression:
±
±
=
r s
r s
s mix
ecc
f i f n
f m f n
f n f
. .
. .
.
_ (23)
where:
n=1, 3, 5....
m=2, 4, 6....
i=1, 3, 5....
where:
n≠i
In the multilevel decomposition of the stator current, we used Daubechies 44 like wavelet mother.
One represented in the figure 8 the signals details (d1, d2… , d7, d8, d9) and the signal of approximation (a9).
Figure 8. Multi-level decomposition of stator current in healthy case
One starts with the healthy case to compare it with
the failing cases. In figure 9, one notes clearly in the approximation a9
and the details d9 and d8 of the new forms of disturbance.
Figure 9. Multi-level decomposition of stator current in static fault case In figure 10, the analysis using wvelet decomposition of stator current at the time of the presence of a dynamic faul eccentricity shows one observes a disturbance in the
amplitude of the signal a9, d9 and d9 corresponds to the time of fault creation.
Figure 10. Multi-level decomposition of stator current in dynamic fault case
In Figure 11, we clearly see the A9 approximation and the details and d9 d8 new disturbance forms.
Figure 11. Multi-level decomposition of stator current in mixed faulty case Figure 12 presents the variation of dcomposition
energy level of wavelet in the 16 frequency bands for healthy function case and in the presence of fault eccentricity cases in the doubly-fed induction generator.
Figure 12. Variation of the energy levels in the frequency bands In the figure 13, we are presented the variation of the energy in the 7th band frequency according to the percentage of static, dynamic and mixed eccentricity faults.
Figure 13. Variation of the energy in the band 7
6. Conclusions
In this paper, we introduced in the first part, the modeling and simulation of the doubly-fed induction generator using Matlab/Simlink in the healthy case. This result is taken as reference. In second part we interested for study three types of fault static eccentricity and dynamic eccentricity and the combine of the two previous types of eccentricity faults (static and dynamic). For each case, we presented the curves of simulations of the stator and rotor magnitudes, In the third part, we applied tow methods, the first besed in frequency analysis by fast Fourier transform on the stator current spectrum of phase "a". Only the fundamental appears for healthy cases, against when eccentricities additional frequencies appear as fault, the appear of these frequencies helps us to detect the fault types. Furthermore, analysis of the stator current was conducted in healthy cases and in the presence of defects, the second method of fault detection in this work,is based on the analysis of magnitude of of the wavelet packet decomposition and energy level of decomposition for diagnosis and detection of different severity levels of eccentricity faults in the rotor of DFIG.
7. Acknowledgment
This work is realised in the Research Centre in Industrial Technologies CRTI, Algeria, in framework of validation the results of my PHD thesis “Diagnosis of electromagnitic and mechanical faults in wind turbine besed on douby-fed induction generator”.
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8. Biography
Hichem MERABET received the Engineering degree in electrical engineering in 2006 and the Magister degree in electrical engineering in 2009, both from the University of Badji Mokhtar University, Annaba, Algeria.
His main research fields include the control of electric machines, fault diagnosis, system electro-energy and Renewable Energy.
Correspondence address: Research Center in Industrial Technologies CRTI, P.O. Box 64, Cheraga, Algeria E-mail: h.merabet@csc.dz
Tahar BAHI received the Engineering, Magister and Doctorate degrees in electrical engineering from Badji Mokhtar University, Annaba, Algeria in 1983, 1986 and 2006, respctively.
Since 1983, he has been with the Department of Electrical of the University of Annaba, Algeria where he is currently a Professor of electrical engineering. His main research fields include the control of electric machines, power electronic applications and Renewable energy.
Correspondence address: Electrical Department, Faculty of Science Engineering. University of Annaba, Algeria
E-mail: tbahi@hotmail.com
