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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.

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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