Modelling, Faults Detection and Diagnosis of Squirrel Excited Induction Generator
* Industrial Technology Research Unit Annaba,
**Department of Electrical Engineering,
Abstract – The condition monitoring of the s Self-Excited Induction Generator (SEIG) significantly reduce the costs of maintenance, the unscheduled downtimes and
maintenance decisions for isolated Wind Energy Conversion Systems (WECS). On the other hand, growing attention has been paid to fractional calculus theory in practical control field for many industrial applications. In this paper, an on
procedure for stator and rotor faults in the squirrel SEIG of isolated wind energy conversion system is presented. This diagnostic procedure is based on stator current analysis by FFT. A generalized model of the squirrel-cage SEIG is developed to simulate both the rotor and stator faults taking iron loss,
cross flux saturation into account. Additionally, a new control strategy is proposed for the fixed operation of the wind turbine, based on fractional PIλcontrollers.
Keywords – Squirrel Cage SEIG, Fractional Control, Fault Detection and Diagnosis, FFT, Modelling
I. INTRODUCTION The use of induction machines in of applications like in isolated conversion system (WECS) justifies
of the supervision of their normal operations. Fault diagnosis allows the detection and the identification of any deviation of the operating parameters of these machines from its normal values
faults can occur within induction
normal operation of the wind systems. Several, such as rotor cage malfunctions or stator phase unbalance can result in a complete breakdown of the energy conversion system if the progress of the fault is not detected.
A dynamic model of the SEIG incorporating the effect of different defects studied is necessary to simulate the operation of the isolated wind system closed loop operating conditions under faulty conditions in order to test the diagnosis method.
emulate a stator fault, the simplest method
an additional resistance in series to one phase stator winding [2], [3] to provoke a stator phase unbalance.
While, to emulate a rotor fault, the classical model is takes into account the individual conductors in the rotor cage using R-L series circuits, with current loops defined by two adjacent rotor bars connected by
ing, Faults Detection and Diagnosis of Squirrel
Excited Induction Generator for Isolated Wind Energy Conversion System
I. Atoui* and A. Omeiri**
Research Unit URTI/CSC, BP 1037, university site of Badji Mokhtar, Chaiba Annaba, Algeria, Email: [email protected]
Department of Electrical Engineering, Annaba University, Email: omeiri.amar@univ
he condition monitoring of the squirrel-cage enerator (SEIG) can reduce the costs of maintenance, prevent and make the best isolated Wind Energy ystems (WECS). On the other hand, growing attention has been paid to fractional calculus for many industrial an on-line diagnostic procedure for stator and rotor faults in the squirrel-cage SEIG of isolated wind energy conversion system is diagnostic procedure is based on stator generalized model of the to simulate both the rotor and stator faults taking iron loss, main flux and . Additionally, a new control strategy is proposed for the fixed-speed operation of the wind turbine, based on fractional-order
Fractional Control, Fault Modelling.
in almost all types isolated wind energy justifies the importance normal operations. Fault diagnosis allows the detection and the identification of any deviation of the operating parameters of these machines from its normal values [1]. A variety of hin induction machines during normal operation of the wind systems. Several, such stator phase unbalance can result in a complete breakdown of the wind if the progress of the fault A dynamic model of the SEIG incorporating the effect of different defects studied is necessary to isolated wind system in closed loop operating conditions under faulty conditions in order to test the diagnosis method. For emulate a stator fault, the simplest method is to insert an additional resistance in series to one phase stator a stator phase unbalance.
the classical model is dual conductors in the series circuits, with current loops defined by two adjacent rotor bars connected by
portions of the end ring. Therefore,
complex and computer simulation becomes very long.
In this paper, a new modelling method based on a coupled magnetic circuit theory [
the effect of saturation of the magnetic circuit and iron loss which takes into account the stator and the rotor asymmetries due to the faults, is
For a healthy machine, the rotor loops
resistances are identical and have the same parameters that make this model similar to the classical model, but when a rotor and/or stator
some rotor loops and/or stator resistances
In this condition, the equivalent resistance of the stator and/or the rotor in the two axes
not diagonal, making this model more generalized than the classical d-q model.
In this work, the combination of maintaining a constant rotational speed, system stability and robustness are the control objectives specified for the wind turbine. A new control strategy
fractional-order PIλ controllers
a turbine model about an operating point is proposed for the fixed-speed operation of wind turbines by adjusting the blade-pitch angle.
The most popular methods of condition monitoring utilize the steady components of the current quantities current spectral components are used to faults of SEIG.
Fig. 1 SEIG witch a capacitor excitation system driven by a wind turbine
II. MODELLING OF THE SYST A. Modelling of the squirrel-cage SEIG
The generalized two axes model of a self-excited induction generator
rotor and stator faults taking iron loss, cross flux saturation into account
[ ] [ ][ ] [ ] [ ]
idt L d i R
v = T + T
ing, Faults Detection and Diagnosis of Squirrel-Cage Self- for Isolated Wind Energy Conversion
university site of Badji Mokhtar, Chaiba 2300, [email protected]
portions of the end ring. Therefore, this model is quite complex and computer simulation becomes very long.
In this paper, a new modelling method based on a theory [4], [5] incorporating the effect of saturation of the magnetic circuit and iron loss which takes into account the stator and the rotor asymmetries due to the faults, is presented.
For a healthy machine, the rotor loops and stator are identical and have the same parameters that make this model similar to the classical d-q and/or stator fault occurs, resistances are affected.
In this condition, the equivalent resistance of the the rotor in the two axes d-q model are not diagonal, making this model more generalized bination of maintaining a constant rotational speed, system stability and robustness are the control objectives specified for the new control strategy based on controllers consists of linearizing a turbine model about an operating point is proposed speed operation of wind turbines by
pitch angle.
The most popular methods of induction machine condition monitoring utilize the steady-state spectral quantities [6], [7]. These current spectral components are used to diagnose
SEIG witch a capacitor excitation system driven by a wind turbine
ODELLING OF THE SYSTEM cage SEIG
The generalized two axes model of a squirrel-cage excited induction generator to simulate both the stator faults taking iron loss, main flux and cross flux saturation into account is presented by:
] [
+ GT][ ]
i (1) LoadThe matrices of (1) are defined as:
[v] = [-Vds -Vqs Vdr Vqr]T, [i] = [ids iqs idr iqr]T, [RT] = [Rsdq Rrdq]T,
[ ]
+ +
+ +
=
NEW NEW
NEW NEW
NEW NEW
NEW NEW
NEW NEW
NEW NEW
NEW NEW
NEW NEW
q r dq q
dq
dq d
r dq d
q dq
q s dq
dq d
dq d
s
T
M l M
M M
M M
l M
M
M M
M l M
M M
M M
l L
[ ]
( )
( )
( ) ( )( )
( ) ( )( )
+
−
−
+
−
−
−
− +
− +
−
=
0 0
0 0
0 0
0 0
mNEW s r s mNEW
r s
mNEW s r s mNEW
r s
mNEW s mNEW
s s
mNEW s mNEW
s s
T
L l L
L l L
L L
l
L L
l G
ω ω ω
ω
ω ω ω
ω
ω ω
ω ω
where
p L R M R M
m m
m dq
dqNEW = +
,
p L R M R M
m m
m d
dNEW = +
,
p L R M R M
m m
m q
qNEW = +
,
p L R L R L
m m
m m
mNEW = +
The RSDQ is the equivalent resistance matrix, it’s given by:
( )
( )
+
−
+
−
=
=
= −
3 cos 2 3 cos 2 cos
3 sin 2 3 sin 2 sin 3 , 2
1
θ π θ π
θ
θ π θ π
θ
s qs sdq
sdq ds s s s
SDQ P
R R
R P R R P R
(2)
The (d-q) components of the magnetizing current [im]123 system taking iron loss into account satisfy:
( )
(sq rq )
m m
m mq
rd sd m m
m md
ki s i
L R i R
ki s i
L R i R
+ +
= + +
=
(3)
and
(
2 2)
/ 22
mq md
m i i
i = + (4) Rm represents the iron lossor core loss in the SEIG model. The variation in Rm is modeled by the following curve fit [8].
950
3 +
= ph
m V
R (5) where Vph is the phase RMS voltage across Rm in parallel with Lm.
The majority of the models for rotor fault simulation in the squirrel-cage induction machines are made by rotor decomposition.
R is the equivalent rotor loop resistance matrix; its expression is given by:
+ +
−
−
− + +
−
− + +
−
−
− + +
=
−
−
−
−
) ( ) 1 ( ) 1 ( )
(
) ( ) ( ) 1 ( ) 1 (
2 1 2 1
) ( 1
) ( 1
2 ...
0 0
...
...
...
...
...
...
...
...
...
...
...
...
0 ...
2 0
0 ...
0 2
...
0 0 2
r r r r
r r
N b e N b N b N
b
k b k b e k b k b
b b e b b
N b b
N b e b
R R R R R
R R R R R
R R R R R
R R
R R R
R
(6)
Rb and Re are: the bar resistance and the end-ring segment resistance, respectively.
The expression of rotor resistance:
=
= −
qr rdq
rdq dr
r r
RDQ R R
R K R
R K
R 1
(7) where
( )
( )
− − −
− −
− − −
− −
=
2 1 sin 2
...
sin 2
2 1 cos 2
...
cos 2 2
r r
s r
r s
r r
s r
r s
r
r p p j
j p p
K N
θ α α θ
θ θ
θ α α θ
θ θ
with αr = 2π/Nr and θs ,θr is the two axes reference angular velocity.
In simulation of broken rotor bars, it is sufficient to increase the resistance of the broken rotor bar to eliminate the current which circulates in this bar [9].
B. Modeling of the load (RL) and fixed capacitor bank Assume that the load is RL (per phase value) series circuit connected across winding. The voltage and current equations in this case will be given by
( )
( )
( )
( )
−
−
=
−
−
=
+
−
=
+
−
=
dch s qL L qs ch qL
ds s qL qs qs
qL s dL L ds ch dL
qs s dL ds ds
i i
R L V
dt i d
V i
C i dt V
d
i i
R L V
dt i d
V i
C i dt V
d
ω ω
ω ω
1 1 1
1
(8)
where iqL and idL are the q- and d-axis load currents.
C. Model of wind turbine
The mathematic expressions of wind turbine are expressed as follows [10, 11]:
( ) R w t p
mec w t w g
aer GT P GP C
T = = Ω= Ω = , Α /Ω
2 / 1
/ λβρ υ3 (9)
( ) 116 0.4 -5 e 0.0068
0.5176
, i
21 -
i
λ λ β
β
λ λ +
−
p = C
(10)
1 0.035 08 -
. 0
1 1
3 +
= +
β β λ
λi
(11)
w tR
λ = Ωυ (12) where Pw is the aerodynamic power captured from wind; ρ is the density of air; AR is the area that the wind power can be obtained; Cp is the power coefficient; νw is the wind speed; λ is the tip speed ratio (TSR); β is the pitch angle; Ωt is wind turbine mechanical angular velocity; Taer is the wind turbine output torque; Tg is the driving torque of the generator, G is the gear ratio and Ωmec is the generator mechanical angular velocity.
Because the torque coefficient is related to the power coefficient, CP, through the following relation:
(λ,β ) λ q(λ,β )
p C
C = (13) Manipulation of the torque coefficient using λ and β will result in manipulation of the power produced by the turbine.
The fundamental dynamics of the variable-speed wind turbine are captured with the following simple mathematical model:
dt J d T
Tw − SEIG = t Ω t (14)
D. Model of actuator
The actuator turbine blade adjustment, which may be represented by the block diagram shown in Fig.(2) where βa(s) and βo(s) are the Laplace transform of the pitch angle input and output respectively.
( ) ( )
( ) m Ls
m a
p e t
K s
s s
G −
= +
= 1
0
β
β
(15) Km is the gain constant, tm is the time constant and L is the time delay parameter (L = 0.01 in our study).
E. Model linearization of wind turbine
An approach to design used linear controllers such as PIα, requires that the non-linear turbine dynamics be linearized about a specified operating point.
Linearization of the turbine (6) would yield:
β δ υ ξ
γ∆Ω + ∆ + ∆
= Ω
∆ t t w
Jt
. (16) Where the linearization coefficients are given by:
( )
t op p t wop R op t t op t
t
m C
A T J
Ω Ω
∂
= ∂
Ω
Ω
∂
= ∂ Ω
∂
=∂ λ β
υ ρ
γ 0.5 3 ,
.
(17)
( ) [ p w]op
top R op t t op w
m J A C
T . 3
* 1 ,
5 .
0 ρ υ λβ υ
υ ξ υ
ω
ω ∂
∂
= Ω
Ω
∂
= ∂
∂
=∂
( )
[ p ]op top
wop R op t t op
m J A C
T β λ β
ρ υ β
δ β 0.5 ,
. 3
∂
∂
= Ω
Ω
∂
= ∂
∂
= ∂
where
wop top op
R
λ = υΩ (18) Here, ∆Ω, ∆νw, and ∆β represent deviations from the chosen operating point, Ωtop, νwop, and βop. Selection of the operating point is critical to preserving aerodynamic stability in this system. The rotational speed operating point, ωtop, was selected to be the desired constant speed of the turbine, 450 rpm (47.1 rad/sec). The blade-pitch and wind speed operating points were selected as (βop = 7° and νwop = 6.4 m/s).
After Laplace Transformation, (16) becomes:
( )
ss
Jt ∆Ω t = γ∆Ω t +ξ∆υω +δ∆β (19) Let
Jt
D = γ
The turbine rotor shaft speed can be represented as
( ) ( )
D s p
s J
Jt t
t −
∆ + ∆
=
∆Ω ξ υ δ β 1
ω (20)
III. CONTROL SYSTEM
The system of the studied device included control blocs (speed control) is shown in Fig. 2.
Fig. 2 Simulation block diagram
Assuming that the gain crossover frequency is ωc
and the phase margin is φm , for the system stability and robustness, three specifications concerned with the phase and the gain of the open-loop transfer function are proposed as follows[12], [13].The procedure of the FOPI controller design used is proposed in [14], [15].
Using Laplace transforms the transfer function of the fractional-order PIλ is given by:
( )
+
= pλi
K
K p 1
p C
(21) The fractional-order PIλ controller is more flexible than the classical PI controller, because it has one more adjustable parameter, which reflects the intensity of integration.
In this work, this function is approximated by a rational function [16].
IV. DIAGNOSIS PROCEDURE
The implementation procedure of the rotor unbalance fault detection and diagnosis in rotating machinery can be illustrated with the flowchart in Figure 3.
Fig. 3 Flowchart of the diagnosis procedure
V. RESULTS AND INTERPRETATION
We present the simulation, using Matlab/Simulink, of the system connected to the load RL. The results of simulations are obtained for rotational speed (ωr-ref = 0).
Fig. 4 show, respectively, the rotor voltage waveform Vas, the current waveform ias, the magnetizing current waveform Im and load current waveform iaL for different value of resistance RL.
N Y
End
Move the temporal window T
Y N
Data vector
Measured stator current data x(t)
for T=1s
ASTFT is computed on the
current data x(t)
Fault component detection
Fault components detection at frequencies equal to
k*fs (stator faults) and/or (1+- 2k s) for
rotor faults.
Begin
FFT computation
Faulty (Stator and/or rotor)
Activate Alarms/Warnings
Healthy
Operator Control Shutdown Equipment
Ωr Non- Linear Turbine
+ SESG
Actuator
∆β + +
Reference Pitch (ββββref)
Pitch Angle Limit
- s
+
∆Ωr PIα Controller
Ωr-ref
Wind Speed
>
= Ω
=
≤
<
= Ω
=
≤
<
= Ω
=
≤
≤
= Ω
=
s t L
R
s t s L
R
s t s L
R
s t s H L R
ch L
ch L
ch L
ch L
12 3H
- 200e ,
600
12 8
3H - 200e ,
300
8 6
3H - 200e ,
400
6 0
0 ,
0
(22)
Fig.5 presents some differences between the rotational speed of the SEIG and its reference. The SEIG rotational speed component follows its reference perfectly.
Fig. 4 Rotor voltage Vas,stator current ias, magnetizing current Im and load current iaL waveforms in healthy
operating conditions.
Fig. 5 Simulation block diagram
The rotor voltage waveform Vas, the current waveform ias, the magnetizing current Im and load current iaL are being shown in Fig. 6 for stator fault at t=8s, and are also being shown in Fig. 7 for rotor fault at t=8s.
Fig. 2 Rotor voltage Vas,stator current ias, magnetizing current Im and load current iaL waveforms in faulty operating
conditions (stator fault at t=8s).
Fig. 6 Rotor voltage Vas,stator current ias, magnetizing current Im and load current iaL waveforms in faulty operating
conditions (rotor fault at t=8s).
Fig.7 shows the stator current FFT in healthy conditions and the harmonic components (k*fs or (1- k*s)*fs) are negligible. While as the Fig.8 shows the FFT of the stator current in case of stator unbalance. It is evident the presence of the fault component at frequency k*fs. Also Fig.9 shows the FFT of the stator current in case of rotor unbalance. It is evident the presence of the fault component at frequency (1- k*s)*fs. Fig.10 shows the FFT of the stator current in case of rotor and stator unbalance. It is evident the
0 2 4 6 8 10 12 14 16 18 20
-400 -200 0 200 400
V a s ( V )
T i m e ( s )
0 2 4 6 8 10 12 14 16 18 20
-4 -2 0 2 4
i a s ( A )
T i m e ( s )
0 2 4 6 8 10 12 14 16 18 20
0 1 2 3
I m ( A )
T i m e ( s )
0 2 4 6 8 10 12 14 16 18 20
-1 0 1
i a L ( A )
T i m e ( s )
0 2 4 6 8 10 12 14 16 18 20
0 50 100 150 200 250 300 350
w r ( r a d / s )
T i m e ( s )
2 3 4 5 6 7 8 9 10
-300 -200 -100 0 100 200 300
V a s ( V )
T i m e ( s )
2 3 4 5 6 7 8 9 10
-4 -2 0 2 4
i a s ( A )
T i m e ( s )
3 4 5 6 7 8 9 10
0 1 2 3
I m ( A )
T i m e ( s )
3 4 5 6 7 8 9 10
-1 -0.5 0 0.5 1
i a L ( A )
T i m e ( s )
0 1 2 3 4 5 6 7 8 9 10
-200 0 200
V a s ( V )
T i m e ( s )
0 1 2 3 4 5 6 7 8 9 10
-4 -2 0 2 4
i a s ( A )
T i m e ( s )
0 1 2 3 4 5 6 7 8 9 10
0 1 2 3
I m ( A )
T i m e ( s )
0 1 2 3 4 5 6 7 8 9 10
-1 -0.5 0 0.5 1
i a L ( A )
T i m e ( s )
presence of the fault component at frequency (1- k*s)*k*fs and k*fs.
Fig. 7 FFT of the stator current in healthy conditions.
Fig. 8 FFT of the stator current for a stator unbalance produced by an additional resistance of stator phase.
Fig. 9 FFT of the stator current for a rotor unbalance.
Fig. 10 FFT of the stator current for stator and rotor unbalances.
V. CONCLUSION
In this paper an isolated wind energy conversion system based on a squirrel-cage self-excited induction generator was modelled and controlled in Matlab Simulink. Stable operation of the system was achieved by means of a fractional control technique.
The machine current signals can be utilized for diagnostic purposes, providing interesting possibilities for the detection of electrical faults. In fact, their harmonic content has suitable features to be used for the diagnosis of stator and rotor asymmetries, providing a reliable diagnostic index. The simulation results presented in this paper validate the component models, the chosen diagnostic method and the proposed control scheme.
V. REFERENCES
[l] D. Zhen, T.Wang, F.Gu, A.D.Ball, "Fault diagnosis of motor drives using stator current signal analysis based on dynamic time warping", Mechanical Systems and Signal Processing, Vol. 34, August 2012, pp.191–202.
[2] Y. Zhao, T.A. Lipo: Modeling and Control of a Multi- phase Induction Machine with Structural Unbalance, IEEE Trans. on Ener. Conv., Vol. 11, No. 3, Sep. 1996, pp. 570-577.
[3] A. Stefani, A. Yazidi, C. Rossi, F. Filippetti, D.
Casadei, G.A. Capolino. Doubly fed induction machines diagnosis based on signature analysis of rotor modulating signals. IEEE Trans. Ind. Appl. 44 (6) (2008) 1711–1721.
[4] A.R. Munoz, T.A. Lipo, "Complex Vector Model of the Squirrel-cage Induction Machine Including Instantaneous Rotor Bar Currents", IEEE Trans. Ind.
Appl, Vol. 35, No. 6, Nov/Dec 1999, pp. 1332-1340.
[5] S.N. Mahato, S.P. Singh, M.P. Sharma, "Dynamic behavior of a single-phase self-excited induction generator using a three-phase machine feeding single- phase dynamic load", Electrical Power and Energy Systems 47 (2013) 1–12.
[6] A. Lebaroud, A. Medoued, "Online computational tools dedicated to the detection of induction machine faults", Electrical Power and Energy Systems 44 (2013) 752–
757.
[7] K. Bacha, S. B. Salem, A. Chaari, "An improved combination of Hilbert and Park transforms for fault detection and identification in three-phase induction motors", Electrical Power and Energy Systems 43 (2012) 1006–1016.
[8] T. F. Chan, “Analysis of Self-Excited induction generators using an iterative method”, IEEE Transaction on EC, Vol. 10, No.3, 1995, pp.502-507.
[9] A.Sadeghian, Y.Zhongming, W.Bin, “Online detection of broken rotor bars in induction motors by wavelet packet decomposition and artificial neural networks”, IEEETrans.Instrum.Meas.58(2009)2253–2263.
[10] S. P. Singh, B. Singh, and M. P. Jain, “Steady state analysis of self-excited pole changing induction generator,” J. Inst. Eng., vol. 73, pp.137–144, Aug.
1992.
[11] H. Siegfried, “Grid integration of wind energy conversion systems,” Willy; 1998.
[12] G.Franklin,J. Powell and A.Naeini, “Feedback control of dynamic systems,” Reading, MA: Addison-Wesley;
1986.
[13] Y. Q.Chen and K. L. Moore, “Relay feedback tuning of robust PID controllers with isodamping property,”
IEEE Transactions on Systems, Man, and Cybernetics, Part B, 35(1); 2005, p. 23–31.
[14] HS. Li, Ying Luo, and YQ. Chen, “A Fractional Order Proportional and Derivative (FOPD) Motion Controller:
Tuning Rule and Experiments,” IEEE Transactions on control systems technology, Vol. 18, No. 2; March 2010, p. 516-520.
[15] Y. Luoand all, “ Tuning fractional order proportional integral controllers for fractional order systems,”
Journal of Process Control 20 ; 2010, p. 823–831.
[16] A. Charef, H.H. Sun, Y.Y. Tsao and B. Onaral,
“Fractal system as represented by singularity function, ” IEEE Transactions on Automatic Control, Vol. 37, n9, pp 1465-1470, 1992.
0 50 100 150 200 250 300 350 400
-90 -80 -70 -60 -50 -40 -30 -20 -10
F r e q u e n c y [ H Z ]
S p e c t r a l d e n s i t y ( d B )
0 200 400 600 800 1000
-90 -80 -70 -60 -50 -40 -30 -20 -10
F r e q u e n c y [ H Z ]
S p e c t r a l d e n s i t y ( d B )
20 30 40 50 60 70
-80 -70 -60 -50 -40 -30 -20 -10
F r e q u e n c y [ H Z ]
S p e c t r a l d e n s i t y ( d B )
0 50 100 150 200 250 300
-90 -80 -70 -60 -50 -40 -30 -20 -10
F r e q u e n c y [ H Z ]
S p e c t r a l d e n s i t y (d B )
