an approach for the modeling of an autonomous induction generator[1]
TRANSCRIPT
Volume 4, Issue 1 2005 Article 1052
International Journal of EmergingElectric Power Systems
An Approach for the Modeling of anAutonomous Induction Generator Taking Into
Account the Saturation Effect
Dr. Rekioua Djamila, Department of ElectricalEngineering, University of Bejaia, (Algeria)
Pr. Rekioua Toufik, Department of Electrical Engineering,Univeristy of Bejaia, (Algeria)
Idjdarene Kassa Jr., Department of Electrical Engineering,Univeristy of Bejaia, (Algeria)
Dr. Tounzi Abdelmounaim , LaboratoireD’Electrotechnique et D’Electronique de Puissance de Lille,
L2EP (France)
Recommended Citation:Djamila, Dr. Rekioua; Toufik, Pr. Rekioua; Kassa, Idjdarene Jr.; and Abdelmounaim , Dr.Tounzi (2005) "An Approach for the Modeling of an Autonomous Induction Generator TakingInto Account the Saturation Effect," International Journal of Emerging Electric Power Systems:Vol. 4 : Iss. 1, Article 1052.Available at: http://www.bepress.com/ijeeps/vol4/iss1/art1052DOI: 10.2202/1553-779X.1052
©2005 by the authors. All rights reserved. No part of this publication may be reproduced, storedin a retrieval system, or transmitted, in any form or by any means, electronic, mechanical,photocopying, recording, or otherwise, without the prior written permission of the publisher,bepress, which has been given certain exclusive rights by the author. International Journal ofEmerging Electric Power Systems is produced by Berkeley Electronic Press (bepress).
An Approach for the Modeling of anAutonomous Induction Generator Taking Into
Account the Saturation EffectDr. Rekioua Djamila, Pr. Rekioua Toufik, Idjdarene Kassa Jr., and Dr. Tounzi
Abdelmounaim
Abstract
This paper deals with a model to simulate the operating of an autonomous inductiongenerator. The model used is a diphase one obtained by the application of the Park transform. Thismodel permits, when adopting some simplifying hypothesis, to take account of the saturationeffect. This is achieved using a variable inductance function of the magnetising current. The nonlinearity is then based on the approximation of the magnetising inductance with regards to thecurrent. In our case, we use a polynomial function, of 12th degree to perform it. This approach issimple and very accurate. The developed model has been used to study the operating of aninduction machine when a capacitive bank is connected to the stator windings. The simulationcalculation was achieved using MATLAB®-SIMULINK® package. This paper presents transientanalysis of the self-excited induction generator. In order to simulate the voltage build-up processand the dynamic behaviour of the machine, we first establish the machine's model based on a d-qaxis considering the machine’s saturation effect. Secondly, effect of excitation capacitors or loadimbalances on voltage build-up process is investigated. Simulations results for a 5.5 kW inductiongenerator are presented and discussed. Several experimentations are presented to validatesimulations and verify the effectiveness of the developed model.
KEYWORDS: Autonomous induction generator, Saturation effect, Modelisation, Magnetisinginductance
1. INTRODUCTION
It is well known that induction machines may generate power if sufficient
excitation is provided [1, 2]. The squirrel induction machines are widely used in
the wind energy conversion in the case of isolated or faraway areas from grid
distribution [3, 4, 5]. Theses structures have a lot of advantages. They are robust,
need few maintenance and do not cost so much. When operating as an
autonomous generator, the induction machine has to be magnetised by an external
supply [6]. The simple way to achieve this consists in connecting its stator
windings to a capacitive bank in parallel to the load. Hence, for a given rotation
speed, the remaining magnetic flux yields a low electromotive force. Then when
the capacitances are well designed, the magnetising current through the capacitive
bank yields the built up of the electromotive force and its increase to an useful
value.
A lot of works dealt with the study of the autonomous induction generator.
They concerned the calculation of the required capacitance value or the
performances of the device using the equivalent monophase model [7, 9] taking
into account the saturation effect. These last twenty years, different authors use
models to study also the transient operating of the device [10, 13]. These models
take account of the non linearity of the magnetic material by different approaches
more or less accurate and easy to implement. Hence, in references [12] and [13], a
variable magnetising inductance, using the saturation degree function, permits to
the saturation phenomena to be taken into consideration. However, this method,
which is very accurate, needs the knowledge of the linear and saturated
components of the magnetising flux. Besides, others authors do not use the
approximation of the magnetising inductance but utilise determination techniques
of the parameters (voltage, current…) to achieve the study of the induction
generator [1, 14].
In our approach, the model used is a diphase one obtained by the application of
the Park transform. This model permits, when adopting some simplifying
hypothesis, to take account of the saturation effect. In this case, the non linearity
is based on the approximation of the magnetising inductance with regards to the
current. We use a polynomial function, of 12th
degree [15, 16] to achieve this
approximation. This approach is simple and very accurate. In this case, we can
apply easily control methods in closed loop.
1
Djamila et al.: An Approach for the Modeling of an Autonomous Induction Generator
Published by Berkeley Electronic Press, 2005
In this paper, the developed model is used to study the autonomous generator
running of an induction machine. First, we present the machine which has been
used as an experimental test bench. Then, we perform calculation as no load and
when the generator is loaded. For both cases, we compare the simulation results to
the experiment.
2. PROPOSED STUDIED SYSTEM
Figure 1. shows the three-phase connection diagram of the self-excited induction
generator (SEIG).
Fig. 1: Proposed structure.
To analyse the behaviour of the SEIG under several asymmetrical conditions, the
dynamic equations of generator must be established.
2.1 Induction machine model
The linear model of the induction machine is widely known and used. It yields
results relatively accurate when the operating point studied is not so far from the
conditions of the model parameter identification. This is often the case when the
motor operating, at rated voltage, is studied. As the air gap of induction machines
is generally narrow, the saturation effect is not negligible in this structure. So, to
improve the accuracy of simulation studies, especially when the voltage is
variable, the non linearity of the iron has to be taken into account in the machine
model.
This becomes a necessary condition to study an autonomous induction generator
because the linear model is not able to describe the behaviour of the system. Thus,
only approaches, which take account of the saturation effect, can be utilized. This
effect is not easy to yield with using three phase classical models. So, we usually
SEIG
Ca Cb Cc Load
Capacitive bank
2
International Journal of Emerging Electric Power Systems, Vol. 4 [2005], Iss. 1, Art. 1052
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adopt diphase approaches to take globally account of the magnetic non linearity.
This evidently supposes some simplifying hypotheses. Indeed, the induction is
considered homogenous in the whole structure. Moreover, the use of diphase
model supposes that the saturation effect is considered only on the first harmonics
and does not affect the sinusoidal behaviour of the variables.
In our approach, we adopt the diphase model of the induction machine expressed
in the stator frame. The classical electrical equations are written as follows:
dt
di
dt
di
dt
di
dt
di
i
iLLl
i
iiLl
i
iiL
i
iLLll
i
iLL
i
iiLl
i
iiL
i
iLLl
i
i
i
i
RLlRl
LlRlR
LRl
LlR
v
v
mq
md
sq
sd
m
mq
mmr
m
mqmd
mr
m
mqmd
m
m
md
mmrr
m
mq
mm
m
mqmd
ms
m
mqmd
m
m
md
mms
mq
md
sq
sd
rmrrrrr
mrrrrrr
mssss
mssss
sq
sd
.
..
.0
...0
..
.0
...0
.
).(.
).(.
0..
.0.
0
0
2
''
'
2
'
2
''
'
2
'
(1)
Where Rs, ls, Rr and lr are the stator and rotor phase resistances and leakage
inductances respectively, Lm is the magnetizing inductance and .p
Besides, Vsd, isq , Vsq and isq are the d-q stator voltages and currents respectively,
imd and imq are the magnetizing currents, along the d and q axis, given by:
rdsdmd iii (2)
rqsqmqiii (3)
Where ird and irq are the d-q rotor currents
isd and isq are the d-q stator currents.
Thus, the saturation effect is taken into account by the expression of the
magnetizing inductance Lm with respects to the magnetizing current im defined as:
22
mqmdm iii (4)
To express Lm in function of im, we use a polynomial approximation, of degree
12 [15, 16].
3
Djamila et al.: An Approach for the Modeling of an Autonomous Induction Generator
Published by Berkeley Electronic Press, 2005
n
j
j
mjm
mm
mm
n
j
j
mjmm
iajifid
d
id
dLL
iaifL
0
1'
0
..
.
(5)
2.2 Load model
The stator windings of the induction machine are connected to a star capacitive
bank connected in parallel to a resistive load. Hence, at no load, the diphase stator
voltages and currents are linked by the following expression:
ds
qs
qs
ds
qs
ds
V
V
i
i
C
C
V
V
dt
d.
0
0
.1
0
01
(6)
This takes, when the induction generator is loaded, this other writing:
ds
qs
qchqs
dchds
qs
ds
V
V
ii
ii
C
C
V
V
dt
d.
0
0
.1
0
01
(7)
Where:
idch and iqch are the current through the equivalent diphase resistive load R. They
can be expressed, from the stator voltages (Fig.2.).
Fig.2: Induction machine model.
The dynamic model of a three-phase balanced resistive load in the q-d axis
arbitrary reference frame is given by
qchqs
dchds
iRV
iRV
.
. (8)
Induction
machine
model
ichd, ichd
C Load
R
isd, isq
vsd, vsq
iCd, iCq
4
International Journal of Emerging Electric Power Systems, Vol. 4 [2005], Iss. 1, Art. 1052
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2.3 The global system
The global differential system to solve is then written as follows:
dt
di
dt
di
dt
di
dt
di
i
iLLl
i
iiLl
i
iiL
i
iLLll
i
iLL
i
iiLl
i
iiL
i
iLLl
i
i
i
i
RR
RR
LpRlp
LplpR
v
v
mq
md
sq
sd
m
mq
mmr
m
mqmd
mr
m
mqmd
m
m
md
mmrr
m
mq
mm
m
mqmd
ms
m
mqmd
m
m
md
mms
mq
md
sq
sd
rr
rr
mss
mss
sq
sd
.
..
.0
...0
..
.0
...0
.
00
00
0..
.0.
0
0
2
''
'
2
'
2
''
'
2
'
(9)
To take into account the non linearity of the resolution, we use Runge Kutta
algorithm to solve the system (7) and system (9) together.
3. RESULTS AND DISCUSSION
The developed model is used to study the autonomous generator running of an
induction machine. First, we present the machine which has been used as an
experimental test bench. Then, we perform calculation at no load and when the
generator is loaded. For both cases, we compare the simulation results to the
experiment.
Fig 3: im versus the phase applied voltage.
Phas
e ap
pli
ed v
olt
age
vs
(V)
Magnetizing current im (A)
0
50
100
150
200
250
300
350
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
5
Djamila et al.: An Approach for the Modeling of an Autonomous Induction Generator
Published by Berkeley Electronic Press, 2005
3.1 The experimental machine
Experimental results were obtained from the implementation of the structure
presented in Fig.1. using an induction machine of 5.5 kW (table.1) manufactured
by CEN (Constructions Electriques -Nancy) (figure 4.). [16].
Fig 4: The experimental bench.
Parameter Value Parameter Value
PN 5.5 kW J 0,230 kg.m²
UN 230/400 V f 0,0025 N.m/rads-1
IN 23,8/13,7 Rs 1,07131
f 50 Hz Rr 1,29511
NN 690 rpm p 4
Table1. Machine parameters [16].
Then, from these data and the active power absorbed by the machine, one can
determine the evolution of the magnetising inductance in function of i0. The
obtained curve is drawn in figure 5-a. Lastly, to avoid the problem due to the
absence of experimental inductance values outside the magnetising current range
identification, we drawn a complementary part. This yield the evolution given in
figure 5-b.
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International Journal of Emerging Electric Power Systems, Vol. 4 [2005], Iss. 1, Art. 1052
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a: Measurement result b: Simulation result
Fig.5: Magnetizing Curve.
3.2 No load tests.
The experimental device is shown in figure 6. In this section, experimental and
computed results are presented.
Fig.6: The experimental device studied.
The model introduced in the precedent paragraph has been used in the
MATLAB SIMULINK environment to study the performance of the autonomous
Mag
net
izin
g i
nd
uct
ance
Lm
(H
)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
0.11
0.12
0.13
a
b
Magnetizing current im(A)
7
Djamila et al.: An Approach for the Modeling of an Autonomous Induction Generator
Published by Berkeley Electronic Press, 2005
induction generator. The parameter of the model used are the ones of the
experimental machine when the magnetizing inductance is the one given above,
expressed by a proposed polynomial function. To simulate the remaining voltage,
we take a non low initial value for the phase voltages.
3.2.1. Voltage build-up process under balanced conditions
In order to validate the model of the induction generator, we study firstly the
built up process of the stator voltage when the rotor of the induction machine is
driven at 780 rpm under no-load conditions. The value of each self excitation is
fixed to 100 µF [16].
Time [sec].
a: Simulated results.
Time [sec].
b: Experimental results.
Fig. 7: A phase voltage built up process under no-load conditions.
For the same conditions, the evolution of a phase voltage calculated and
measured is shown in the figure 7 (a and b respectively). We can notice the good
agreement between both curves. We can observe that the voltage value before the
Phas
e v
olt
age
Va
[V]
0.14 0.2 0.42 0.56 0.70 0.84 0.980.00
-400
-300
-200
-100
0
100
200
300
400
Phas
e vo
ltag
e V
a [V
]
100 V/div
0.14s/div
8
International Journal of Emerging Electric Power Systems, Vol. 4 [2005], Iss. 1, Art. 1052
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built-up is different for experimental test and for simulation. This is due to the
initial conditions. The voltage build-up process is due to remaining field in the
machine which can be different after every utilisation of the machine.
We show also the calculation results related to a phase current (Fig.8) and the
magnetizing current (Fig.9.)
Time [sec]
Fig.8: Evolution of a phase current.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
2
4
6
8
10
t (s)
i0 (A)
Time [sec]
Fig.9: Evolution of the magnetising current.
3.3 Other operating points.
Other tests have been performed. The first one studies the effect, on the phase
voltage, when the generator is loaded. In the figure 10a and b we show the
simulated and measured evolution of a phase voltage respectively when the
generator is connected to a resistive load of 50 per phase.
Phas
e cu
rren
t ia
[A
]
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-8
-6
-4
-2
0
2
4
6
8
Mag
net
isin
g c
urr
ent i 0
[A]
9
Djamila et al.: An Approach for the Modeling of an Autonomous Induction Generator
Published by Berkeley Electronic Press, 2005
Time [sec].
a: Computed results.
Time [sec].
b: Measured results.
Fig.10: Evolution of a phase voltage when the generator is loaded (100 F–780
rpm) and R from to 50 .
Once more, the results are in good agreement. The connection of the load yields
a decrease of the phase voltage magnitude and a low variation of its frequency.
Lastly, tests have been carried out to determine the evolutions of the phase
voltage with regards to the capacitance, the speed rotation and the load values.
Hence, for two capacitance values 100 µF and 110 µF, we drawn the curves V(R)
for 3 values of the rotation speed (720, 750 and 780 rpm).
In figure 11a and b, we give the simulation and experimental results
respectively when the capacitance value is 100 µF. Figures 12a and b give the
same evolutions for a capacitance of 110 µF.
Sta
tor
vo
ltag
e V
a [V
]
100 V/div
0.14 s/div
1.42 1.5 1.58 1.66 1.74 1.82 1.9
-400
-300
-200
-100
0
100
200
300
400
Sta
tor
volt
age
Va
[V]
10
International Journal of Emerging Electric Power Systems, Vol. 4 [2005], Iss. 1, Art. 1052
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R[ ]
a: Simulation results.
R[ ]
b: Experimental results
Fig.11: Evolution of the rms phase voltage with respects to the R for 3 speed
rotation values (100µF).
Ph
ase
volt
age
Vef
f [V
] P
has
e v
olt
age
Vef
f [V
]
0
50
100
150
200
250
300
050100150200250300350400450
780 rpm
750 rpm
720 rpm
50
100
150
200
250
300
050100150200250 300350400450
780 rpm
750 rpm
720 rpm
11
Djamila et al.: An Approach for the Modeling of an Autonomous Induction Generator
Published by Berkeley Electronic Press, 2005
R[ ]
a: Simulation results
R[ ]
b: Experimental results
Fig.12: Evolution of the rms phase voltage with respects to the R for 3 speed
rotation values (110µF).
As we could expect, the magnitude of the phase voltage is an increasing
function of both the capacitance and the speed rotation values. Furthermore, when
the generator is highly loaded, the magnitude voltage decreases quickly. This well
known characteristic, and problem, of the autonomous induction generator when
connected to a simple capacitance bank in parallel.
We drawn the evolution of the phase voltage with regards to the current (Fig.13,
Fig14, Fig.15.) for three rotation speed values (780, 750 and 720 rpm) and two
different values of capacitance (100µF, 110µF).
Ph
ase
vo
ltag
e V
eff
[V]
Phas
e vo
ltag
e V
eff
[V]
0
50
100
150
200
250
300
050100150200250300350400450
0
50
100
150
200
250
300
050100150200250300350400450
780 rpm
750 rpm
720 rpm
780 rpm
750 rpm
720 rpm
12
International Journal of Emerging Electric Power Systems, Vol. 4 [2005], Iss. 1, Art. 1052
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Current phase ia[A]
C=100µF C=110µF
a: Simulation b: Measurement
Fig. 13: Variation of terminal voltage with current phase at constant speed
(780 rpm).
Current phase ia[A]
C=100µF C=110µF
a: Simulation, b: Measurement
Fig.14: Variation of terminal voltage with current phase at constant speed.
(750 rpm).
0
100
200
300
1 2 3
ab
01 2 3 4 5
ab
01 2 3 4 5 6 7
ab300
200
100
300
200
100
0 1 2 3 4 5 6
ab
100
200
300
Phas
e vo
ltag
e V
eff
[V]
Phas
e volt
age
Vef
f [V
]
13
Djamila et al.: An Approach for the Modeling of an Autonomous Induction Generator
Published by Berkeley Electronic Press, 2005
Current phase ia[A]
C=100µF C=110µF
a: Simulation b: Measurement
Fig. 15: Variation of terminal voltage with current phase at constant speed.
(720 rpm).
As we note, more the capacitance value increases and more the induction machine
provides a constant voltage for a load current. We will find the same results for
the two other speed values N. The curves have all the same shape of hook. We
can add that more the rotor speed increases and more the stator voltage is high.
Finally, all the curves are in the shape of hook. The higher capacity is the more
one has a good behavior in voltage for a higher current. It will be necessary to
choose the excitation capacity adapted for a given use of the induction machine.
3.4. Sudden disconnection of one capacitor
We suddenly disconnected one of the excitation capacitors (C=100 F), the
corresponding simulated transient results are shown respectively on figures 16a, b
and c. This test shows the good accuracy of the machine and the load model.
0
100
200
300
0 1 2 3 4 5 6 7
ab
0 1 2 3 4 5
ab
100
200
300
Phas
e v
olt
age
Vef
f [V
]
14
International Journal of Emerging Electric Power Systems, Vol. 4 [2005], Iss. 1, Art. 1052
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3 4 5 6 7 8
-200
-150
-100
-50
0
50
100
150
200
Time [sec].
a: Phase a.
3.9 4.1 4.3 4.5
-200
-150
-100
-50
0
50
100
150
200
Time [sec].
b: Phase a, b and c.
3.98 4 4.02 4.04 4.06 4.08 4.1
-250
-200
-150
-100
-50
0
50
100
150
200
250
Time [sec].
c: Zoom on phase a, b and c.
Fig. 16: Effect of a sudden disconnection of one capacitor (C=100 F) on stator
voltage.
Naturally the transient behaviour of the SEIG will depend on the resulting
remaining equivalent excitation capacitor. In fact, if the initial values of the
capacitors are high, the voltage will not fall down under sudden disconnection of
Phas
e vo
ltag
e V
a[V
] P
has
e v
olt
age
Vab
c[V
] P
has
e vo
ltag
e V
abc[
V]
15
Djamila et al.: An Approach for the Modeling of an Autonomous Induction Generator
Published by Berkeley Electronic Press, 2005
one capacitor. It will drops a little during transient and then return to a new
steady-state operation point. The line current variation (Fig.17.) is similar to the
one of voltage (Fig.16.).
3 4 5 6 7 8
-8
-6
-4
-2
0
2
4
6
8
Time [sec].
a: Phase a.
3.9 4.1 4.3 4.5
-8
-6
-4
-2
0
2
4
6
8
Time [sec].
b: Phase a, b and c.
3.98 4 4.02 4.04 4.06 4.08 4.1
-8
-6
-4
-2
0
2
4
6
8
Time [sec].
c: Zoom on phase a, b and c.
Fig. 17: Effect of a sudden disconnection of one capacitor (C=100 F) on stator
current.
Cu
rren
t phas
e
ia(A
) C
urr
ent
ph
ase
ia
bc(
A)
Curr
ent
ph
ase
ia
bc(
A)
16
International Journal of Emerging Electric Power Systems, Vol. 4 [2005], Iss. 1, Art. 1052
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3.4 Influence of capacitor bank imbalance
In order to show the influence of the capacitor bank imbalance (C=160 F), we
present respectively in figure 18. and figure 19. the variations of the stator voltage
and current .
3 4 5 6 7 8
-300
-200
-100
0
100
200
300
Time [sec].
a: Phase a.
3.9 4.1 4.3 4.5
-300
-200
-100
0
100
200
300
Time [sec].
b: Phase a, b and c.
3.98 4 4.02 4.04 4.06 4.08 4.1
-300
-200
-100
0
100
200
300
Time [sec].
c: Zoom on phase a, b and c.
Fig. 18: Influence of capacitor bank imbalance (C=160 F) on Stator voltage.
Volt
age
ph
ase
va(
V)
Vo
ltag
e p
has
e v
abc(
V)
Volt
age
ph
ase
v
abc(
V)
17
Djamila et al.: An Approach for the Modeling of an Autonomous Induction Generator
Published by Berkeley Electronic Press, 2005
3 4 5 6 7 8
-15
-10
-5
0
5
10
15
Time [sec].
a: Phase a.
3.9 4.1 4.3 4.5
-15
-10
-5
0
5
10
15
Time [sec].
b: Phase a, b and c.
3.98 4 4.02 4.04 4.06 4.08 4.1
-15
-10
-5
0
5
10
15
Time [sec].
c: Zoom on phase a, b and c.
Fig. 19: Influence of capacitor bank imbalance (C=160 F) on Stator current.
3.6. Influence of a sudden disconnection of the load
We can notice that the disconnection of a purely resistive load, involves a voltage
variation but the steady-state is reached after a delay of about 1 s. The same
Cu
rren
t p
has
e ia
(A)
Cu
rren
t p
has
e ia
(A)
Curr
ent
ph
ase
ia
(A)
18
International Journal of Emerging Electric Power Systems, Vol. 4 [2005], Iss. 1, Art. 1052
http://www.bepress.com/ijeeps/vol4/iss1/art1052DOI: 10.2202/1553-779X.1052
phenomenon can be observed on stator currents. Simulation results show the
validity of the adopted modelling approach.
3 4 5 6 7 8
-300
-200
-100
0
100
200
300
Time [sec].
a: Phase a
3.9 4 4.1 4.2 4.3 4.4 4.5
-300
-200
-100
0
100
200
300
Time [sec].
b: Phase a, b and c.
3.98 4 4.02 4.04 4.06 4.08 4.1
-200
-150
-100
-50
0
50
100
150
200
Time [sec].
c: Zoom on phase a, b and c.
Fig. 20: Stator voltages of phases a, b and c under
unbalanced load conditions.
Vo
ltag
e p
has
e
vab
c(A
) V
olt
age
phas
e v
abc(
A)
Vo
ltag
e p
has
e va(
A)
19
Djamila et al.: An Approach for the Modeling of an Autonomous Induction Generator
Published by Berkeley Electronic Press, 2005
3.9 4 4.1 4.2 4.3 4.4 4.5
-10
-5
0
5
10
Time [sec].
a: Phase a, b and c.
3.98 4 4.02 4.04 4.06 4.08 4.1
-10
-8
-6
-4
-2
0
2
4
6
8
10
Time [sec].
b: Zoom on phase a, b and c.
Fig.21: Stator currents of phases a, b and c under
unbalanced load conditions.
3.7. Influence of an unbalanced load.
The aim of this test is to show the resistive load unbalance effect on the behaviour
of the stator voltages and currents. The resistive load parameters are Ra=Rb=50 ,
Rc=80 and each excitation capacitors is equal to 100 µF. The obtained results
are presented respectively on figures 22 and 23.
Cu
rren
t p
has
e ia
bc(
A)
Cu
rren
t p
has
e ia
(bcA
)
20
International Journal of Emerging Electric Power Systems, Vol. 4 [2005], Iss. 1, Art. 1052
http://www.bepress.com/ijeeps/vol4/iss1/art1052DOI: 10.2202/1553-779X.1052
4 4.02 4.04 4.06 4.08 4.1
-200
-100
0
100
200
Time [sec].
Fig. 22: Stator voltages of phases a, b and c under
unbalanced load condition.
4 4.02 4.04 4.06 4.08 4.1
-8
-6
-4
-2
0
2
4
6
8
Time [sec].
Fig. 23: Stator current of phases a, b and c under
unbalanced load condition.
The influence on stator voltage is negligible while the chosen load imbalance
induces a consequent variation of the peak current value.
4. CONCLUSION
The paper examines the dynamic performances of an autonomous induction
generator, taking the saturation effects into account, by the means of a variable
magnetising inductance, has been presented. This magnetising inductance is
expressed, using a polynomial function, of degree 12, as a function of the
magnetising current. The proposed model has been used, in a MATLAB
SIMULINK simulation environment to study an induction machine in
autonomous generator operating.
Vo
ltag
re p
has
e v
abc(
A)
Curr
ent
ph
ase
ia
bc(
A)
21
Djamila et al.: An Approach for the Modeling of an Autonomous Induction Generator
Published by Berkeley Electronic Press, 2005
Obtained results of the SEIG under voltage build-up process, balanced or
unbalanced network load side conditions are presented and compared. Excessive
conditions like disconnection of one self-excitation capacitor or sudden
disconnection of the load are also analysed.
The analysis presented is validated by experimental results. The comparison of
all these results shows a very good agreement between the experimentation and
simulation. The amplitudes of the signals, their shapes as their duration present
practically the same values for both simulation and experimentation. The
coherence between computed and measured results is very good as well for
dynamic conditions as for steady state. This concordance between the
experimentation and simulation confirms the validity of the developed model.
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International Journal of Emerging Electric Power Systems, Vol. 4 [2005], Iss. 1, Art. 1052
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Djamila et al.: An Approach for the Modeling of an Autonomous Induction Generator
Published by Berkeley Electronic Press, 2005