Said Drid
Mohamed-Said Nait-Said
Abdesslam Makouf
Mohamed Tadjine
L.S.P.I.E
Laboratory,
Electrical
Engineering Department. Rue Chahid
M. E. H Boukhlof, Batna University.
s_drid@yahoo.fr
J. Electrical Systems 2-2 (2006): 103-115
Regular paper
Doubly Fed Induction Generator
Modeling and Scalar Controlled
for Supplying an Isolated Site
JES
Journal of
Electrical
Systems
This paper deal with the scalar control of the doubly fed induction generator, (DFIG), supplying an
isolated site and using the wind power. The DFIG is more adapted for this application, because even if it
receives a variable speed on its rotor shaft, due to variable wind speed, a voltage wave with constants
magnitude and frequency can be produced. If the injected rotor currents with the specific
voltage/frequency ratio according to rotor variable speed and the fixed frequency and magnitude stator
voltage are the known problems, than to solve these latter, a simple scalar control method is proposed
taking into account the variable speed condition. Experimental results are given in this work so as to attest
the feasibility and the simplicity of our method.
Keywords: Double Fed Induction Generator, Variable Speed, Isolated Site Voltage Supplying, Stator
Voltage Constant Key-Parameters, Scalar Control, Modeling.
Nomenclature
x
: Variable complex such as:
x = ℜe [ x ] + j .ℑm [ x ] with j =
: It can be voltage u , current i or flux φ
x
x*
−1
: Complex conjugate
Rs , Rr : Stator and rotor resistances
Ls , Lr
M
: Stator and rotor inductances
: Mutual inductance
θ : Absolute rotor position
P : Number of pairs poles
δ : Torque angle
θs , θc
: Stator and rotor flux absolute positions
ω : Mechanical rotor frequency (rd/s)
Ω : Rotor speed (rd/s), with: Ω = ω / P
ωs
: Stator voltage frequency (rd/s)
ωc
: Injected rotor current frequency (rd/s)
T e, T m
: Electromagnetic and motor torque
DFIG
: Doubly Fed Induction Generator
Initial version of this paper was presented at the Second
International Conference on Electrical Systems ICES’06, May 0810, 2006 Oum El Bouaghi Algeria.
Copyright © JES 2006 on-line : journal.esrgroups.org/jes
S. Drid et al: Doubly Fed Induction Generator Modeling and Scalar Controlled for Supplying...
1. INTRODUCTION
The differential heating of terrestrial surface by the sun involves the displacement of
important masses of air on the earth, i.e. the wind. The conversion systems of the wind
power transform the kinetic energy of the wind into electricity or other forms of energy.
The wind power is one of the most important sources of renewable energy in the world; it
knew an extraordinary expansion during the last decade, because this energy is recognized
as being a means ecological and economic to produce electricity. At the same time, there
was a fast development relating the wind turbine technology [1-3].
With regard to the generation, it is necessary to conceive a system which produces the
electric power at constant frequency and which adapts to the variable speed [1], [3]. This
can be carried out using the synchronous generators provided that a static frequency
converter is used to connect the machine to the grid. Another interesting solution consists to
use a double fed induction generator (DFIG) where the produced stator energy can be
controlled from the injected power on its rotor as illustrated on the Figure 1. Hence, the
DFIG using causes the increasing attention for the wind power generation [1-3]. Among the
DFIG’s advantages, that on the rotor side the reduced power converter can be sufficiently
employed to control the power-factor and the energy flow. The offered possibilities to
produce an electrical energy with unit power-factor might to reduce substantially the cost of
the hard implementation system [1-3].
It is more important to well understand the behavior of such generator especially in open
loop control, i.e. to be interested of its modeling. The DFIG is connected, at the same time,
like the synchronous machine and the asynchronous machine from which its magnetizing
system is given from both armatures (stator and rotor) contribution. There are two
distinguished DFIG cases: the first one where the stator is directly connected to the
powered grid and the second one where the same stator supplies an isolated load [1-6].
Load
Switch
Sensor Voltage LV-25-P
Variable
Speed
ω *r
ω *s
+
ω̂ s
V r*
PI _ ω s
PI _ V s
+
-
V s*
Estimation ωs
Soft Control
Figure 1: Double fed induction generator for wind turbine system
From the modeling point view, the imposition of the frequencies in both DFIG
armatures generates an additional difficulty for the use of the common conventional
reference frames in order to create an efficient control system. Consequently, without
taking into account of the existing angle between the stator and rotor mmf’s (magneto
motive force) conducts to appear the oscillations on the normally continuous (no
alternating) quantities such torque and speed. That is the different case of that the squirrel
cage induction machine, so the reference frames relativity must taking more attention in the
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J. Electrical Systems 2-2 (2006): 103-115
DFIG system [7] and [9]. The previous angle is called torque angle, like in the synchronous
machine, and of which it is necessary to take into account in the conventional Park
transformations rotation in order to guarantee DFIG-system stability.
Thus this work is registered respecting to the DFIG space vector modeling with it’s the
scalar using the separate reference frames. The experiment and digital simulation are
carried out 0.8 kW laboratory machine will be shown an interesting results for future use of
the DFIG-control-system on the serious wind powered region for supplying an isolated site
on electric energy.
2. MACHINE MODELING
The voltage stator and rotor space vector equations, presented in complex notation, of an
induction machine are given by the following system [7-9]:
(s )
⎧⎪ (s )
⎪⎪ us = Rs is (s ) + d φs
dt
⎪⎨
⎪⎪
d φ (r )
⎪⎪ ur(r ) = Rr ir(r ) + r
⎪⎩
dt
(1)
Flux equations:
⎧⎪ φs(s ) = Ls is (s ) + M ir(r )e j θ
⎪⎪
⎨ (r )
⎪⎪ φr = Lr ir(r ) + M is (s )e − j θ
⎪⎩
(2)
From (1) and (2), the model is written like
dis (s )
di (r )
+ M .e j θ ( r + j ω.ir(r ) )
dt
dt
(r )
di
di (s )
+ Lr r + M .e − j θ ( s − j ω.is(s ) )
dt
dt
us(s ) = Rs is (s ) + Ls
ur(r )
= Rr ir
(r )
(3)
Superscripts (s) and (r) indicate that the variables are measured in the respective reference
frames carrying these indices (s: stator, r: rotor). s : Derivative Laplace operator; θ :
Absolute rotor position, as indicated in Figure2, illustrating the relativity of the reference
frames. Note the presence of the particular torque angle δ defined between both armatures
mmf’s. Moreover each mmf is located by its position such as we can write the following
expressions:
θ = P ∫ Ωdt
∫ ωcdt
= ∫ ωsdt
θc =
θs
(4)
The system (1) can be schematized by the circuit given in the Figure 3.
When the DFIG is connected to the powered grid, this one imposes its magnitude voltage
and its frequency (generating no autonomous) then the injected rotor currents will have as a
role of the flow control of active and reactive power between the machine and the grid.
For an autonomous generator (isolated supplying system) the problem becomes more
complex, because it is necessary to control the stator magnitude and frequency voltage in
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S. Drid et al: Doubly Fed Induction Generator Modeling and Scalar Controlled for Supplying...
order to maintain their rated values recommended for the usually electrical load. For DFIG
mode, the system must be adopted by respecting the followed sign convention of currents
such as:
is → −is : generator (stator)
(5)
ir → ir : receiver (rotor)
The stator m.m.F.
ωs
The rotor m.m.F.
θs
δ
Rotor
θc
P.Ω
θ
Stator
Figure 2: m.m.f presentation in the
ur
M
di r
R r .i r
dt
d (i s .e
− jθ
R s .i s
)
M
dt
Ls
d (i r .e
di s
To Load
dt
jθ
)
dt
DFIG Voltage
Lr
us
Figure 3: The DFIG equivalent circuit coupled to the load
If ur is a control voltage, us , iset ir appear like state variables. The system (3) with the
condition (5) cannot admit a unique solution because the number of variables is higher than
the number of equations. Thus, the equation of the load (6) removed this indetermination.
The load parameters R, L and C are subscripted by load.
us = Rload is + Lload
dis
1
+
dt
C load
∫ is .dt
(6)
The electromagnetic torque developed by the generator and which is opposed to the drive
system (wind turbine) is given by:
*
Te = P .M ℑm ⎢⎡ is ( ire j θ ) ⎥⎤
⎣
⎦
The frequency of the induced stator voltage is given by:
fs =
106
PΩ
± fr
2π
(7)
(8)
J. Electrical Systems 2-2 (2006): 103-115
The sign ± explains that the DFIG mmf’s rotations can be in the same or in the opposition
direction.
2.1 Simulation Diagram
Figure 4 presents the simulation diagram of the DFIG in the separate reference frames with
the rotor voltage ur and the speed like inputs. This diagram is built from the equations (37). Each physic measurement must be effected in its appropriate referential without any
transformations. Figure 5 and 6 represents the stator voltage and current simulation results
respectively without and with load.
Load
Circuit
(R_L_C)
(s )
In the stator
frequency
is
Switch
Rs
∑
−
d
Ls
dt
Torque
+
Te
(s )
us
d
M .e
− jθ
dt
θ
Variable Speed
∫
P
d
θ
dt
In the injected
rotor frequency
(r )
−
jθ
ir
(r )
ir
Tr
+
ur
M .e
Figure 4: DFIG Simulation diagram.
1
2
0.5
0
-0.5
-1
0
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Time (sec.)
Figure 5: Simulation results of the stator voltage
(1) and stator current (2), 1600 rpm without
load.
Stator voltage (V)
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
1
150
0
--150
-300
0
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
1
Stator current (A)
0
-150
-300
0
300
1
150
Stator current (A)
Stator voltage
300
2
0.5
0
-0.5
-1
0
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Time (sec.)
Figure 6: Simulation results of the stator voltage
(1) and stator current (2), 1600 rpm with load
Rload=312 ohm.
2.2 Experimental tests
The figures 7 and 8 illustrate respectively, the experimental and the simulation results of the
stator voltage and the stator current after and before loaded machine (Rload =312Ω). This
operation has been achieved at 1600 rpm.
107
150 V
S. Drid et al: Doubly Fed Induction Generator Modeling and Scalar Controlled for Supplying...
1
0.5 A
0.05 sec
2
0.05 sec
0.05 sec
1
0.5 A
150 V
Figure 7: Experimental results of the stator voltage (1) and stator current (2), 1600 rpm without load.
2
0.05 sec
Figure 8: Experimental of the stator voltage (1) and stator current (2), 1600 rpm with load Rload =312.
ohm
2.3 Rotor-stator voltages transfer function
From (3), we can rewritten the stator voltage equation as follows
us(s ) = Rs is (s ) + Ls
dis(s )
+ Es(s )
dt
(9)
where Es is the electromotive force (emf) which depending of injected rotor current and it
is expressed as
Es(s ) = M
dir(r ) j θ
e + jM .ω.ir(r ) .e j θ
dt
(10)
From (1), we can also present the rotor voltage equation as follows:
vr(r ) = ur(r ) − Er(r ) = Rr ir(r ) + Lr
dir(r )
dt
(11)
where Er(r ) is the rotor emf which depending of stator current, or load current, and it is
expressed as:
Er(r ) = M
108
dis (s ) − j θ
− jM .ω.is (s ).e − j θ
e
dt
(12)
J. Electrical Systems 2-2 (2006): 103-115
We consider that this rotor emf as a voltage disturbance because it depends of the stator
current is (s ) , varying with load, and rotor speed, varying with wind speed. So this rotor emf
disturbance is considered such as the stator voltage must be maintained or regulated to its
rated value. Consequently, the used control strategy must be designed in such manner that
this considered disturbance is simply rejected.
Using (10) and (11), we can write the cause-effect transfer function between rotor and
stator voltage as
Es(s )
⎛M
= ⎜⎜
(r ) j θ
⎝
Rr
vr
e ⎞⎟ s + j ω
⎠⎟⎟ Tr s + 1
(13)
vs(s )
As mentioned above, the stator current must assumed too as disturbance, because the stator
voltage must be maintained as constant for any electric load. So the regulation process
conducts to realize that:
vs(s ) = us(s ) ≅ Es(s )
(14)
where
vs(s ) = us(s ) − Δus (is ) = Es(s )
(15)
with,
di (s )
Δus (is ) = (Rs is (s ) + Ls s )
dt DL = Disturbance
(16)
Load
With the previous assumptions, (13) becomes simply
H (s ) =
vs(s )
⎛M
= ⎜⎜
⎝ Rr
vr(s )
⎞⎟ s + j ω
⎠⎟⎟ Tr s + 1
(17)
If the numerator s-operator of (17) is replacing by the direct calculation of the rotor current
derivative from (11), then we can give another simply bloc diagram of the same transfer
function (17), so-called DFIG transfer function, as done in figure 9.
j.ω
Δu s (is )
1
Tr
v r(s )
−
1
Lr
+
×
+
M
+
v s(s )
− us
+
Figure 9: DFIG transfer function
Figure 9 shows that, evidently, speed and stator voltage droop caused by the stator current,
are assumed, as mentioned previously, like disturbances. Hence we can see clearly that the
rotor voltage control the stator voltage.
In steady state operation one can take s = jωr, in this case (17) will be rewritten as follows:
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S. Drid et al: Doubly Fed Induction Generator Modeling and Scalar Controlled for Supplying...
vs(s )
⎛M
= ⎜⎜
⎝ Rr
vr(s )
⎞⎟
j ωs
⎠⎟⎟ j ωrTr + 1
(18)
Where,
ωs = ωr + ω
(19)
40
70
30
60
50
10
0
ω = 50 rd/sec.
Imag(Es /ur)
Real (Es /ur )
20
-10
-20 ω = 100 rd/sec.
-30
-40
-80
ω = 150 rd/sec.
-40
30
ω = 150 rd/sec.
20
ω = 100 rd/sec.
10
ω = 200 rd/sec.
-60
ω = 200 rd/sec.
40
-20
0
20
40
60
80
ωr (rd/sec.)
Figure 10: Real part of DFIG transfer function.
0
-80
ω = 50 rd/sec.
-60
-40
-20
0
20
40
60
80
ωr (rd/sec.)
Figure 11: Imaginer part of DFIG transfer
function.
The simulation of complex transfer function (18) according to the injected rotor
frequency variation for each step of rotor speed, allows to gives the followed results
illustrated by the figures 10 and 11. Theses figures present respectively the real part and the
imaginary part of (18). From theses results, it can be clearly observed that if we need to
produce the high level of stator power using DFIG, the rotor must be rotates highly, i.e. with
speed value exceeds the rated one. In fact, that constitutes a serious problem expressly
when the DFIG rotor is acted by wind turbine which can receive a non satisfactory level of
wind speed. Consequently, in order to generate an electric stator power respecting the stator
key-parameters (fixed frequency and magnitude of stator voltage), the DFIG must be closed
loop controlled and the rotor speed and stator current will be assumed as disturbance. In
this work, the simpler scalar will be used as presented in the followed section.
3. SCALAR CONTROL
3.1 Voltage scalar control implementation
As exposed above, the stator voltage may be controlled trough the rotor injected voltage
such its magnitude and frequency must be maintained at constants. The stator voltage
magnitude is directly measured such as
U s = us2α + us2β
(20)
uˆ
From the stator voltage position θˆs = arccos( sα ) , the estimated frequency can be derived
ˆ
Us
d θs
ωˆs =
(21)
dt
The equations (20) and (21) provide the feedback controlled variables. Figure 12 presents
the DFIG scalar control implementation where two PI controllers are used.
110
J. Electrical Systems 2-2 (2006): 103-115
Laod
Stator Voltage Sensors
LV-25 P
Us and ωs Computing
Eq(20) and eq (21)
DC
Motor
Variable Speed
Ur
Controllers
ω sref
ωr
Scalar
Control and
PMW
Inverter
U s , ωs
U sref
DFIG
DC Voltage
Figure 12: Voltage scalar control DFIG implementation.
3.2 Experimental results open loop
200 V
Since that any system electric energy supplied can work under its nominal conditions, its
magnitude and frequency voltage may be maintained within the tolerated limits defined by
the hardware designer, for example ± 5%. We consider that our isolated site works
normally at 150V and 50 Hz. The wind speed variation is simulated in laboratory that we
can assume the rotor rotates at the followed different values of speed: 1800 rpm, 2400 rpm
and 1000 rpm. Figures 13, 14 and 15 represent the DFIG induced voltage as well as the
current injected into the rotor circuit, these same figures show clearly that we can maintain
constant the stator voltage and frequency by a judicious choice of the voltage and frequency
injected in the rotor.
1
4A
0.05 sec
2
0.05 sec
200 V
Figure 13: Experimental results of the stator voltage (1) and rotor current (2), speed 1000 rpm.
1
4A
0.05 sec
2
0.05 sec
Figure 14: Experimental results of the stator voltage (1) and rotor current (2), speed 1800 rpm.
111
200 V
S. Drid et al: Doubly Fed Induction Generator Modeling and Scalar Controlled for Supplying...
1
4A
0.05 sec
2
0.05 sec
Figure 15: Experimental results of the stator voltage (1) and rotor current (2), speed 2400 rpm.
3.3 Experimental results for closed loop
Figure 16 and 17 show the control block diagrams of the linear equivalent model control.
PI regulators are used to regulate the magnitude and frequency of the stator voltage in order
to achieve zero steady-state error.
Voltage drop
jω
ΔU s
U s*
+
PI
−
Ur
− Us
H (s )
+
1
Tload s + 1
Is
Figure 16: Stator voltage control loop.
jω
ω*s
+
−
PI
θr
∠( H ( s ))
θs
ω̂ s
d
dt
Estimation
Figure 17: Stator frequency control loop.
The test induction machine rated values are given in appendix. To validate our approach,
the experimental tests will be defined the adopted reference speed profile given in figure
18. In this figure we can note that after 1.25 s speed starting of the unloaded (1200 rpm), a
load of (Rload = 150 Ω and Lload = 0.1H) is applied. Then after 2.2 s, at the same load, the
speed is increased at 1600 rpm. The stator voltage magnitude and frequency are
respectively maintained by feedback control during this test at 314 rd/s and 100v as shown
in figures 19 and 20; respectively.
3.4 Obtained results
Successively, we can show the obtained results like presented on the following figures.
Also figures 19 and 20 illustrate the frequency and the stator rms voltage versus time
evolution. Figures 21, 22 and 23 shows, respectively, the stator currents, the rotor voltages
and the rotor measured on theirs respective reference frames. Note that for an increase of
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J. Electrical Systems 2-2 (2006): 103-115
the rotor speed induces tolerable transients in the frequency and the magnitude of stator
voltage. This can be explained that the two PI controllers are solicited to intervene to
maintain the key-parameters at their rated values. In fact the speed increasing in open loop
control causes the increase of both key-parameters and the role of the PI controllers is that
to reduce this increasing in reducing the amplitude and the frequency of stator voltage. The
PI acting is incarnate by the rotor voltage time evolution as given by figure 22. We can
observe that the magnitude of the rotor current is related to the stator load and it increase
with the stator current increasing; this is illustrated by figure 23. We can see also that the
rotor frequency decreases if the rotor increases as shown in the same figure, this can be
explained by the fact that when the rotor speed increases if we must maintain a same stator
power level the rotor frequency must be decreases.
1600
1400
Speed (rpm)
1200
1000
800
600
400
200
0
0
1
2
3
Time (sec.)
4
5
Figure 18: Reference speed profile.
100 (rd/s)/ div
20 V/ div
0.5 s/ div
0
0.5 s/ div
0s
0 sec.
0
Figure 19: Experimental results of the rms stator
voltage.
Figure 20: Experimental results of the estimated
stator frequency ωs
1 A/ div
10 V/ div
0.2 s/ div
0.5 s/ div
0
0
1s
3s
Figure 21: Experimental results of the stator
current.
0 sec.
Figure 22: Experimental results of the rotor
voltage.
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S. Drid et al: Doubly Fed Induction Generator Modeling and Scalar Controlled for Supplying...
4 A/ div
0.5 s/ div
0
0 sec.
Figure 23: Experimental results of the rotor current.
4. CONCLUSION
Simulation and experimentation results of the proposed model show clearly the
capacities of the DFIG to operate as a normal autonomous generator. The DFIG is initially
involved with opened rotor, and then it is started by injection of rotor current. It appears
that the experimental tests confirm largely the proposed DFIG modeling based on the space
vector model described in the separate reference frame.
In this paper, it is initially shown the interest to model the double fed induction machine
in its generating operations in the separate reference frames. The experimental results attest
favorably the suggested modeling. In the second place, an aspect of regulation by the rotor
parameters (voltage, frequency) is also illustrated which indicates the possibility of
operation of the DFIG on an isolated site (no connected to the grid) where we must
maintain the voltage and the frequency of the stator to their rated values. This is a criterion
of standardization of exploitation of an energy source. The DFIG can be fed and controlled
from the rotor with the reduced power converter. The used scalar control for DFIG system
which supplying an isolated site gives a sufficient robustness against the disturbances
caused by the speed wind and the stator load current. The suggested control shows the
interesting performances obtained through the various experimental and simulation results.
References
[1]
J. B. Ekanayake et al, Dynamic Modeling of Doubly Fed Induction Generator Wind Turbines,
IEEE Transaction on Power systems, Vol.18, N°. 2, May 2003, pp 803-809.
[2]
R. Datta. and V. T. Ranganathan, Variable-Speed Wind Power Generation Using Doubly Fed
Wound Rotor Induction Machine—A Comparison With Alternative Schemes, IEEE
Transaction on energy conversion, vol.17, N°. 3, September 2002, pp 414-421.
[3]
A. Tapia et al, Modeling and Control of a Wind Turbine Driven Doubly Fed Induction
Generator, IEEE Transaction on energy conversion, vol. 18, N°. 2, June 2003 pp 194-204.
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M. Djurovic et al, Double Fed Induction Generator with Two Pair of Poles,” Electrical
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[5]
C. Keleber, W. Schumacher, Adjustable Speed Constant Frequency Energy Generation with
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[6]
C. Keleber, W. Schumacher, Control of Doubly fed induction Machine as an Adjustable
Motor/Generator, Proceedings of the European Conference Variable Speed in Small Hydro,
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[7]
S. Drid, M-S. Nait-Said, M. Tadjine, The Doubly Fed Induction Machine Modeling In The
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[8]
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[9]
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Separate Reference Frames for an Exploitation in an Isolated Site with Wind Turbine,” Third
IEEE International Conference on Systems, Signals & Devices SSD'05, March 21-24, 2005,
Sousse - Tunisia
Appendix
Rated Data of the Induction motor with wound rotor
• Rated values: 0.8 kW ; 220/380 V-50 Hz ; 3.8/2.2 A
•
Rotor-star connected: 3×120 V; 4.1 A ; 1420 rpm
115