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Fig 1. Wind turbine connection to grid with DFIG and converters
speed operation of the wind turbine by decoupling the powersystem electrical frequency and the rotor electrical frequency.
A. Mechanical Part ModelingWind energy is captured by the blades, transformed by the
gearbox to a higher speed at the generator shaft, and then intoelectrical energy by the generator [6]. The turbine model must
take into account the behavior of the blades, the shaft on both
sides of the gearbox, and the gearbox itself. At two next partsaerodynamic and gearbox model is investigated.
a) Aerodynamic ModelThe aerodynamic model of a wind turbine is determined by
its power speed characteristics. For a horizontal axis wind
turbine, the mechanical power output op that a turbine can
produce in steady state is given by:
),(...2
1 3 po CvAp = (1)
The factor pC is called the power coefficient of the rotor orthe rotor efficiency. It is depends on the tip speed ratio ( )
and the blade angle ( ). One way to get pC is by using a
look up table [6]; another way is by approximating pC by
using a non-linear function [9, 11]. In this paper second
method is used because it gives more accurate results and is
faster in simulation. is expressed as (2).
v
Rt.= (2)
Nonlinear function used for calculation of pC is obtained as
follow [9]:)0,(
54321 6)(
Cx
p eCCCCCC
= (3)
In above equation 5431 ,,, CCCC and are constant but 2C
and 6C are defined as follow:
=
=
T
T
vC
vC
/17.0
/
6
2
(4)
In the case of turbines without pitch control, the blade angle
is constant and pC depends only on [6].
Fig 2. Two mass model of wind turbine.
b) Gearbox ModelGearbox can be modeled in two ways: two-mass model and
simplified model. At the first method turbine and generator
angular speeds aren't equal but at the simplified model these
are equal.
Two-mass Model:
A lumped model is presented in Fig.2. Three different
damping components are present on the mechanical model: the
turbine self damping ( TD ), the generator self damping
( GD ) and the mutual damping (Dm ). The aerodynamic
resistance take place in the turbine blade, the generator self
damping represents mechanical friction and windage and themutual damping represents balancing dynamics, which occurs
because of different speed between the generator rotor and theturbine shaft [6]. The mechanical equations of the two-mass
model neglecting the turbine and the generator mutual
damping are given as follow:
dt
dJDKT T
TTTGTshT
= )(
(5)
dt
dJDTK GGGGGGTsh
= )( (6)
)( GTshsh KT = (7)
These parameters are referred to the generator side and can
be applied directly to model a directly driven wind turbine (i.e.without gear box).
Simplified Model:
The gearbox model can be simplified by removing shaft
stiffness. Hence, there is only a single inertia which is the sum
of the generator rotor and the turbine inertia. Themathematical equation of this model can be expressed as
follow [6]:
GTG
GT TTdt
dHH =+
)( (8)
This simplified model assumes that T and G are equal,
that is to say, the torsional oscillations of the shaft are
neglected.
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B. Electrical Part ModelingDFIGmodeling is presented in this section. At first variation
in the stator and rotor leakage inductances due to saturation in
the leakage flux path is ignored (unsaturated model). Then,saturation effect is considered using variable leakage
inductance.
a) Unsaturated Induction Generator Model
In this section the unsaturated model for DFIG is given. The
dand q axis component of the stator and rotor voltage in per-
unit can be expressed as a function of flux linkages. The
voltage equations for the induction generator are given below,
where all quantities except the angular frequency, b , are in
pu.
dt
diRu ds
bqsdssds
1+= (9)
dt
diRu
qs
b
dsqssqs
1= (10)
dtdiRu dr
bqrrdrrdr
1)1( += (11)
dt
diRu
qr
bdrrqrrqr
1)1( = (12)
Using these equations, a model for both the squirrel cage and
wound rotor generators can be developed. The difference
between these two generators lies in the rotor: the first one hasshort circuited winding, so rotor voltage is zero, and the
second one has these winding fed by a converter, responsible
of controlling the generator [6]. Flux linkage used in previous
equation, is obtained from (13) and (14):
+=
+=
drmdssds
qrmqssqs
iXiX
iXiX
(13)
+=
+=
drrdsmdr
qrrqsmqr
iXiX
iXiX
(14)
The electromagnetic torque is calculated by
dsqsqsdsG iiT _= (15)
b) Saturated Induction Generator ModelFor better representation of the induction machine under
transient condition, saturation effect should also include thevariation in the stator and rotor leakage inductances due to
saturation in the leakage flux path. The effect of saturation inleakage flux path is considered by modifying the unsaturated
stator and rotor leakage reactance's with saturation factor satK
[8]. satK is introduced as follow [7]:
>+
= sat
sat
sat II
II
K )1)1
((tan2
1
1
(16)
0 5 10 15 20 25 300
0.2
0.4
0.6
0.8
1
current(pu)
saturation
factor
Fig. 3. Saturation factor characteristic
Where is equal to the ratio between current at which the
saturation begins, satI , to the current through the leakage
reactance. The saturation factor characteristic is shown inFig.3.
TABLE I
DIFFERENT STATES WHICH IS SIMULATEDTwo-mass model Saturation
First state (a) ignore Ignore
Second state (b) consider Ignore
Third state (c) ignore Consider
Fourth state (d) consider Consider
IV. STATORCURRENT TRANSIENT OF DFIGIn this section the performance of doubly fed induction
generator has been investigated by considering a grid
connected wind driven doubly fed induction generator under
various power system transients. These transients are
interruption due to short circuit in terminal of DFIG and
voltage sag. The transient performances have been simulated
for four states. These four states are defined in table I.
A. Voltage SagShort duration under voltages are called "voltage sags" or
"voltage dips". The latter term is preferred by the IEC. Within
the IEEE, the term voltage sag is used. According to the IEC, a
supply voltage dip is a sudden reduction in the supply voltage
to a value between 90% and 1% of the declared voltage,
followed by a recovery between 10 ms and 1 minute later. For
the IEEE a voltage drop is only a sag if the during sag voltage
is between 10% and 90% of the nominal voltage [12]. In this
paper a 50% voltage sag is considered for simulation. At t =5s, a voltage sag happens. Then, at t =7s the voltage is
restored to its presage value, i.e. 1pu. Stator current after
voltage sag occurrence and after voltage restoration for
different states was simulated in Fig.4. The machine used for
simulation was a 2 MW, 690 V wind turbine and machine
parameters are given in appendix.
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5 5.1 5.2 5.3 5.4 5.50
1
2
3
4
5
Time (s)
Sta
tor
current(pu)
(a)
(b)
(c)
(d)
7 7.1 7.2 7.3 7.4 7.50
1
2
3
4
5
Time (s)
Stator
current(pu)
(a)
(b)
(c)
(d)
Fig. 4. Stator transient current due to 50% voltage sag comparison among
different states
B. InterruptionInterruptions, according to the IEEE Std.1159-1995, are
classified into there categories [12]:
i. Momentary interruption: between 0.5 cycles and 3seconds
ii. Sustained interruption: longer than 3 secondsiii. Temporary interruption: between 3 seconds and 1
minute.
In this investigation, it was presumed that the pre-fault value
of the terminal voltage is 1 pu. At t=5s, a momentary
interruption occurs then at t=7s the voltage is restored to itspre-fault value. The effect of various states on short circuitcurrent transient of DFIG is shown in Fig. 5.
The following results can be seen from above simulations for
both voltage sag and interruption:
i. The maximum of stator current increases when thesaturation effect is considered.
ii. Effect of saturation in steady state is negligible, butits effect is important during transient state.
iii. Because satI is equal to 2.5 p.u, stator transientcurrent has step change in this value.
iv. Considering or ignoring of two mass model doesn'thave significant effect on maximum of stator
transient current.
5 5.05 5.1 5.15 5.2
0
2
4
6
8
10
Time (s)
Stat
or
current(pu)
(a)
(b)
(c)
(d)
7 7.1 7.2 7.3 7.4 7.5
0
2
4
6
8
10
Time (s)
Stator
current(pu)
(a)
(b)
(c)
(d)
Fig. 5. Stator transient current due to voltage interruption comparison among
different states
v. Two-mass model is caused that stator transientcurrent has low frequency oscillations.
vi. Two-mass model influence in steady state isnegligible.
V. STATOROVER-CURRENT DUE TO VOLTAGE SAGThe abrupt drop of the grid voltage causes over-voltages and
over currents in the rotor and stator windings that could even
destroy the converter if no protection element is included. In
[13] the factors that affect over-current were investigatedmathematically. In this paper the effect of these fctors is
simulated considering an accurate model. For all simulation in
this section fifth-order model considering saturation effect and
two-mass model is used.
A. Crowbar ResistanceThe first factor is rotor resistance. If the stator resistance is
neglected, the amplitude of over-current is proportional to 1/Rr
[13]. So the solution to protect converter is to short circuit the
rotor windings with the so-called crowbar resistance [2]. The
crowbar circuit used in real scheme consists of three phase full
controlled converter bridge that inserts a resistance cbR in the
rotor circuit during fault as shown in Fig.6 [9].
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DFIG
Rotor
side converter
Fig. 6. Crowbar connection
5 5.02 5.04 5.06 5.08 5.1
0
1
2
3
4
5
Time (s)
Stat
or
current(pu)
Rcb=0
Rcb=0.2 pu
Rcb=0.3 pu
Rcb=0.4 pu
Fig. 7. Stator over-current due to 50% voltage sag for different crowbar
resistance value.
In this paper, when the fault occurs the crowbar resistance is
added to rotor resistance.
There are two main requirements that give an upper and a
lower limit to the resistance:
1) On one hand, the resistance should be high to limitthe short circuit current [14]. This limit takes intoaccount the rotor heating due to the rotor winding
joule losses [15].
2) On the other hand, it should be low to avoid a toohigh voltage in the rotor circuit [12].
A too high voltage can result in breakdown of the isolation
material of the rotor and the converter. Fig.6 shows a
simulation that uses crowbar resistance in series with rotor
resistance as a solution to reduce stator over-current.
Simulation was done for different value of crowbar. When the
voltage sag occurs the crowbar resistance is added to rotor
resistance.
As shown in Fig.7, the more the value of crowbar resistance,the less the maximum of rotor current. Table II shows themaximum of stator current while the crowbar resistance
changes.
TABLE IIMAXIMUM OF ROTOR CURRENT WHILE THE CROWBAR CHANGES
)(cbR 0 0.02 0.03 0.04
)(max AIr 4.994 4.385 4.242 4.019
Fig. 8. Voltage divider model for voltage sag
B. Depth of Voltage DipThe second factor is depth of voltage dip. In fact, the more
severe of a voltage drop, the bigger of the rotor current
amplitude was. To quantify sag magnitude in radial systems,
the voltage divider model, shown in Fig.8, can be used. The
voltage at the DFIG terminals can be found from (17).
EZZ
ZV
FS
Fsag
+= (17)
Any fault impedance should be included in the feeder
impedance FZ .
It's seen from (17) that the sag becomes deeper for faultselectrically closer to the DFIG (when FZ becomes smaller),
and for systems with a smaller fault level (when SZ becomes
larger). In (17) E=1 pu and lzZF = , with z the impedance
of the feeder per unit length and l the distance between the
fault and the pcc (Point of Common Coupling), leading to
(18).
zlZ
zlV
S
sag+
=
(18)
The sag magnitude as a function of the distance to the fault
has been calculated for a typical 11 kV overhead line, resulting
in Fig.9.
The fault level is used to calculate the source impedance at thepcc. In this paper, 11 kV overhead line, and 200MVA fault
level is considered. The impedance of overhead line is 0.117 +
j0.315 per km. Simulations are done for different distance
between fault and pcc.
Fig.10 shows that the distance between fault and terminal ofDFIG is an important factor for maximum amplitude of rotor
0 10 20 30 40 500
0.2
0.4
0.6
0.8
1
distance to the fault (km)
sagmagnitude(pu)
750MVA
200MVA
75MVA
Fig. 9. Sag magnitude as a function of the distance to the fault, for faults on an11 kV, overhead line.
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5 5.05 5.1 5.150
2
4
6
8
Time (s)
Stator
current(pu)
Vsag=0.847 pu,dis=10 km
Vsag=0.735 pu,dis=5 km
Vsag=0.357 pu,dis=1 km
Vsag=0.217 pu,dis=0.5 km
Fig. 10. Rotor over-current due to voltage sags for different distance between
fault and PCC.
current. For example when it is 500m, rotor maximum currentis 7.57A, while it is 10km, rotor maximum current is 1.363A.
VI. CONCLUSIONStator transient current of DFIG considering or ignoring
saturation effect and two-mass model was compared. Then
some parameters that affect rotor over-current due to voltage
sag were simulated. The main findings can be summarized in
the following points:
1. The stator and rotor current of DFIG calculated byconsidering the saturation effect are significantly higherthan the ones that ignores it.
2. It's crucial to incorporate the saturation effect to study thetransient performance of DFIG, but it's not important for
steady state study.
3. Two-mass model imposes low frequency oscillations tostator transient current.
4. Two-mass model doesn't affect maximum of stator overcurrent and steady state too.
5. Crowbar resistance is used in series with rotor resistanceto reduce the maximum of the stator and rotor over
current and protects the converters due to power systemtransient.
6. In the case of strong voltage sags and interruptions, thereappear over-current whose amplitude depends on the
depth of the dip, the machine parameters, and the
protection element.
APPENDIX
Wind turbine data
TR 37.5 m
TJ 4 s
shK 1.5 radpu /
Gear box ratio 1:94
1hv 4 sm /
1h 1 m
Number of blades 3
DFIG data
GJ 0.6 s
Number of pole 4
sr 0.048 pu
rr 0.018 pu
sX 0.075 pu
rX 0.12 pu
mX 3.8 pu
f 50 Hz
REFERENCES
[1] Mukund R.Patel, Wind and solar power systems, U.S. MarchantMarine Academy Kings point, New York.
[2] J. Lopez, P. Sanchis, X. Roboam, and L. Marroyo, "Dynamicbehavior of the doubly fed induction generator during three-phasevoltage dip", IEEE Trans on energy conversion, Vol.22, No.3,
Sept. 2007.
[3] J.B.Ekanayake, L.Holdsworth, and N.Jenkins, "Comparison of 5thand 3rd order machine models for doubly fed induction generator
(DFIG) wind turbines", Electric Power Systems Research 67(2003), pp.207-215.
[4] Andres Feijoo, Jose Cidras, and Camilo Carrillo, "A third ordermodel for the doubly-fed induction machine", Electric PowerSystems Research 56 (2000), pp.121-127.
[5] Z. Miao, and L, Fan, "The art of modeling and simulation ofinduction generator in wind generation applications using high
order model", Simulation Modeling Practice and Theory, 2008.
[6] M. Garcia, M. P. Conech, J. Sallan, and A. Llombart, "Modelingwind farms for grids disturbance studies", Renewable Energy33(2008), pp.2109-2121.
[7] H. M.Jabr, and N. C.Kar, "Effect of main and leakage fluxsaturation on the transient performances of doubly-fed wind driveninduction generator",Electric Power Systems Research 77 (2007),
pp.1019-1027.
[8] H. M. Jabr, and N. C. Kar, "Leakage flux saturation effects on thetransient performance of wound rotor induction motors", Electric
Power Systems Research 78(2008) 1280-1289.[9] A.A.El-Sattar, N.H.Saad, M.Z.Shams El-Dein, "Dynamic response
of doubly fed induction generator variable speed wind turbine
under fault", electric power system research 78(2008), pp.1240-
1246.
[10] Janaka B. Ekanayake, Lee Holdsworth, XueGuang Wu, NicholasJenkins, "Dynamic modeling of doubly fed induction generator
wind turbines", IEEE transactions on power systems, Vol. 18, No.2, May 2003.
[11] Siegfried heier, Grid integration of wind energy conversion sytems,kassel university,germany, 1998.
[12] M. H. J. Bollen, Understanding power quality problems, ChalmersUniversity of Technology Gothenburg, Sweden, 2000.
[13] A. Han, Z. Zhang, and X. Yin, "Study of factors affected therotor over-current of DFIG during the three phase voltage dip",
DRPT2008, 6-9 April 2008.
[14]
Johan Morren, Sjoerd W.H. de haan,"short circuit current of windturbines with doubly fed induction generator", IEEE transaction on
energy conversion, Vol 22, No 1, March 2007.
[15] D.santos-Martin, S.Arnaltes, J.L.Rodriguez Amenedo, "Reactivepower capability of doubly fed asynchronous generators", electrical
power system research 78(2008), pp.1837-1840.
Vsag=0.217 pu , dis=0.5km
Vsag=0.357 pu, dis=1 km
Vsag=0.735 pu, dis=5 km
Vsag=0.847 u, dis=10 km
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