Modeling and control of a pitch-controlledvariable-speed wind turbine driven by a DFIG with

frequency control support in PSS/E

Mikel de Prada Gil∗ Andreas Sumper ∗†‡ Oriol Gomis-Bellmunt∗†‡mdeprada@irec.cat asumper@irec.cat ogomis@irec.cat

∗IREC Catalonia Institute for Energy Research, Jardins de les Dones de Negre 1, 2a.

08930 Sant Adria de Besos, Barcelona (Spain)†Centre d’Innovacio Tecnologica en Convertidors Estatics i Accionaments (CITCEA-UPC),

Departament d’Enginyeria Electrica, Universitat Politecnica de Catalunya EU d’Enginyeria Tecnica Industrial de Barcelona,

C. Comte d’Urgell, 187, Pl. 1. 08036 Barcelona, Spain†Centre d’Innovacio Tecnologica en Convertidors Estatics i Accionaments (CITCEA-UPC),

Departament d’Enginyeria Electrica, Universitat Politecnica de Catalunya ETS d’Enginyeria Industrial de Barcelona,

Av. Diagonal, 647, Pl. 2. 08028 Barcelona, Spain

Abstract—In recent years, due to the rising penetration of windenergy conversion systems (WECS) into the electricity networks,increasingly comprehensive studies and accurate dynamic modelsare required to analyze its behavior under grid faults. A completemodel of a pitch-controlled variable-speed wind turbine driven bya doubly fed induction generator (DFIG) and its control schemeare implemented. All encompassed subsystems, such as windturbine, pitch actuator, two-mass drive train model, DFIG model,converters and protections are modeled in FORTRAN usingthe power system simulation software PSS/E. A cascade controlstructure is used where the outer control loop concerns the speedcontrol and the inner control loop is responsible for the electricalcontrol. Additionally, a frequency control support is developed inorder to accomplish with the Grid Codes requirements enhancingthe grid power quality. The model performance under varioussystem disturbances is tested by means of simulations.

I. INTRODUCTION

W IND energy has become one of the most important

and promising sources of renewable energy all over

the world, mainly due to its contribution for a low-carbon

society and its economical viability. The increasing size of

the turbines and the rising penetration of the wind energy

conversion systems (WECS) into the grid have encouraged the

use of power electronic converters [1], in order to address the

potential concerns of transmission systems operators (TSO) in

terms of power quality [2] and fault ride-through capability [3].

Detailed models of wind turbines and their associated controls

and protections are required for grid integration studies both

for analysis of the wind turbine under grid faults [4] and for

power system stability studies [5].

Many comprehensive studies have been carried out regard-

ing modeling and control of a DFIG-based wind turbine,

and several models have been developed by researchers using

different softwares, such as MATLAB-Simulink [3], [6], [19],

PSCAD [7], [8] or DigSilent [9].

In this paper, an accurate user-model consisting of a pitch-

controlled variable-speed wind turbine driven by a doubly fed

induction generator (DFIG) and modeled in FORTRAN using

PSS/E is presented. A frequency support controller is also

implemented with the aim of accomplish with the Danish Grid

Code requirement [10].

II. MODELING

A schematic diagram of the overall WECS is illustrated in

Figure 1. It consists of four main functional blocks, namely

the aerodynamic (wind turbine model), mechanical (drive train

model), electrical (DFIG and power converter model), and

pitch servo subsystems. All these blocks and its controls

are written in FORTRAN using the power system simulation

software PSS/E.

Wind Wind Turbine Model

Drive Train Model

Doubly Fed InductionGenerator

Model

Grid

Converter and control ModelPitch angle

controller

- Speed Control- Electrical Control- Frequency Control

Windspeed

Pitch angle

Low speed shaft velocity

Low speed shaft torque

High speed shaft

torque High speedshaft

velocity

Voltageand

frequency

Voltageand

frequency

Active and reactive power

Torque and reactive power set points

Rotorvoltages

Fig. 1. General structure of the pitch-controlled variable-speed wind turbinedriven by a DFIG model.

A. Wind Turbine Model

The power generated by a wind turbine, Pwti, comes from

the kinetic energy of the wind and depends on the power

coefficient, CP , according to the following expression

978-1-4673-1130-4/12/$31.00 ©2012 IEEE

Pwti = CPPwind =1

2CP ρAv3w (1)

where Pwind is the air stream kinetic power, ρ is the air

density, A = πR2 is the surface covered by the wind wheel of

radius R and vw is the average wind speed at the hub height.

This CP power coefficient is unique for each turbine and can

be written as [11] [12]:

CP (λ, θpitch) = c1

(c2

1

Λ− c3θpitch − c4θ

c5pitch − c6

)e−c7

1Λ

(2)

where θpitch is the pitch angle, and λ is the so-called tip speed

ratio defined as:

λ =ωtR

vw(3)

and

1

Λ=

1

λ+ c8θpitch− c9

1 + θ3pitch(4)

where [c1 . . . c9] are characteristic constants for each wind

turbine and ωt is the low speed shaft angular velocity.

B. Drive Train Model

The drive train of a WECS transfers the aerodynamic torque

on the blades to the generator shaft. It encompasses the rotor,

the low- and high-speed shafts and the gearbox. In this paper, a

two-mass representation of the drive train is used. This model

is described by the following equations [13]:

2HMdωM

dt = TM −KSθS −DMωM

2HGdωG

dt = KSθS − TE −DGωG

dθSdt = ω0(ωM − ωG)

(5)

where θS is the torsional twist, KS is the shaft stiffness,

H is the inertia constant, T is the torque, D is the damping

coefficient, ω is the rotational speed and ω0 denotes the electric

system speed. The subscripts G and M and E stand for wind

turbine rotor, generator mechanical and generator electrical,

respectively.

C. Pitch System Model

As it is shown in Figure 2, the pitch system model is

divided into two blocks: the pitch controller and the pitch angle

actuator. The former determines the pitch angle reference,

βref , from the difference between the measured and the

desired rotor speed and is explained in Section III-B. The

latter consists of an actuator that rotates all the blades to a

certain pitch angle, β, equal to the desired one.

The pitch actuator is a nonlinear servo that can be modeled

in closed loop as a first-order dynamic system with saturation

in the amplitude and derivative of the output signal [14]. Figure

3 shows a block diagram of the first-order actuator model. The

�ref���

Fig. 2. Basic configuration of the pitch system model.

dynamic behaviour of the pitch actuator operating in its linear

region is described by the following differential equation

β = − 1

τpitchβ +

1

τpitchβref (6)

where τpitch is the time constant. Typically, β ranges from

−2◦ to 30◦ and varies at a maximum rate of ±10◦/s [14].

ref� �1

actuator s�

�

�

+ -

Fig. 3. Model of the pitch angle actuator.

D. DFIG Model

The DFIG dq equivalent circuit, shown in Figure 4, is

obtained from the following machine voltage equations [15]:

vsd = Rsisd − ωdλsq + Llsddt isd + Lm

ddt (isd + ird)

vsq = Rsisq + ωdλsd + Llsddt isq + Lm

ddt (isq + irq)

(7)

vrd = Rrird − ωdAλrq + Llrddt ird + Lm

ddt (isd + ird)

vrq = Rrirq + ωdAλrd + Llrddt irq + Lm

ddt (isq + irq)

(8)

where Lls and Llr are the stator and rotor leakage induc-

tances, Lm is the mutual inductance between stator and rotor

windings, Rs and Rr are the stator and rotor resistance and ωd

and ωdA are the dq-axis relative rotational speed with respect

to the stator and rotor, respectively. In this paper, a dq reference

frame rotating at synchronous speed, ωs, is used and, therefore,

ωd = ωs and ωdA = ωs −ωm = ωslip, being ωs the electrical

angular speed at the stator of the machine.

DC

DC

DC

DC

(a) d-axis

(b) q-axis

+

-

-

-

-

+

+

+

+

+

+

- -

- -

+

sR

sR rR

rRlsL

lsL lrL

lrL

sqdtd � rqdt

d �

rddtd �sddt

d � mL

mL rqvsqv

sdv rdv

sqd��

sdd��

sdi

rqi

rdi

sqi

rddA��

rqdA��

Fig. 4. DFIG dq-axis equivalent circuit.

The electromagnetic torque and the stator reactive power,

which are the variables to be controlled by the rotor side

converter, can be expressed as [15]:

Γm =3

2pLm(isqird − isdirq) (9)

Qs =3

2(vsqisd − vsdisq) (10)

where p is the number of pole pairs.

E. Converter Model

The converter model consists of an IGBT voltage source

back-to-back power converter used as an interface between the

AC grid and the rotor windings. As it can be seen in Figure 5,

it is composed by two independent converters connected to a

common DC-bus. In order to consider that the applied voltages

by the converter fit in with the voltages set points (v∗rsc ≈ vrscand v∗gsc ≈ vgsc), it is assumed that the switching frequency

of the SVPWM is high (usually over 1 kHz) and the high-

frequency components of the voltage signals generated by the

inverters are filtered by the low pass nature of the machine and

the grid-side circuit [16]. In addition, the electronic switching

are considered to be ideal and without losses.

The DC-bus voltage, E, is calculated from an active power

balance in the back-to-back converter (see Figure 5). Thus,

in the case that the dc-chopper is switch on, the equation is

described as

Pgsc − Prsc = PDC + PChopper (11)

being

Pgsc =32 (vgscdild + vgscqilq)

Prsc =32 (vrscdird + vrscqirq)

PDC = 12C

ddtE

2

Pchopper = E2

Rchopper

(12)

���� ����

����� ���

��� ���

Fig. 5. Active power balance in the back-to-back converter.

The voltage equation of the grid side electrical circuit, given

by the space vector form, can be written as

vaz − vagsc = rgscial + Lgsc

d

dtial (13)

where vaz and vagsc are the voltage space vectors of the grid

and the AC side of the converter, respectively,ial is the current

space vector and rgsc and Lgsc are the resistance and the

inductance of the circuit. The superscript “a” indicates that

the space vectors are expressed as complex numbers with the

stator a-axis chosen as the reference axis with an angle of 0◦.

III. CONTROL SCHEME

The main control objectives in a WECS are to improve

efficiency and quality of power conversion, ensuring that the

turbine is kept within its safe operating region. These goals

are usually represented as the so-called ideal power curve

shown in Figure 6. It can be noted two different regions

with distinctive generation objectives. In partial load region

(I), which corresponds to wind speeds lower than the rated

speed, the aim is to maximize the energy capture from the

wind. Otherwise, at hight wind speeds (region II or full load

operation mode), the control goal is to limit the generated

power below its rated value to avoid overloading.

]/[ smvw

NP

][KW

Power

NVCut-in Cut-out

Partial load operation Full load operation

Fig. 6. Ideal power curve of a typical wind turbine.

To achieve these objectives, the control system is divided

into two levels (see Figure 7): a high-level control or speed

control and a low level control or electrical control. The

former gives the proper torque (Γ∗m), square dc voltage ((E2)∗)

and reactive powers (Q∗s and Q∗

z) set points to the converter

as function of the wind speed, the low speed shaft angular

velocity and the grid voltage. The latter, regulates the incoming

reference signals computing the appropriates voltage set points

to the back-to-back power converter.

Apart from this control system, if the machine is operating

in the full load region, pitch control is activated in order to

keep the extracting power at its nominal value.

DFIG

Gearbox

wv GRID

pitch�

RSC controller GSC controller

High-level controlwv

*sQ

*zQ2 *( )E*

m

t�

*rscv

*gscv

zv

Fig. 7. Control design of the system.

A. Speed Control

Depending on the region where the wind turbine is operat-

ing, two different control strategies are used. In the partial

load region, the main goal is to extract all the available

power from the wind. In this paper, a Maximum Power Point

Tracking (MPPT) strategy with only a rotation speed sensor

required, is used. The advantage of this method is to avoid

the measurement of the wind speed and, consequently, its

stochastic nature.

According to [16], the maximum CP and, therefore, the

maximum power generation for a single wind turbine, is

guaranteed to match the generator electrical torque with

KCP optω2t .

where KCP optis a constant parameter that depends on the

geometry of the turbine and is expressed as follows

KCP opt=

1

2

(c1c2c7

)e−

c6c7c2

−1ρAR3

( c2c7c2c9c7+c6c7+c2

)3(14)

The control strategy changes in the full load region. In this

case, the torque reference signal (Γ∗m) is fixed whereas the

pitch control is activated to limit the captured power to its

nominal value.

B. Pitch Control

The pitch controller is sketched in Figure 8. It consists

in regulating the rotational wind turbine speed by means

of a Gain Scheduling function block (GAINS) and a PI-

controller, resulting a pitch angle reference (βref ) to the pitch

actuator described above in Section II-C. Gain Scheduling is a

technique commonly used in the control of nonlinear systems

[14], [17]. In the case of Figure 8, the gain scheduled controller

is implemented as a PI control and a gain depending on the

pitch angle [14].

PIGAINS+ -

*t�

t�

ref�

Fig. 8. Pitch controller design.

To evaluate the effectiveness of the pitch control method,

Figures 9 and 10 are shown. In Figure 9, the rotational wind

turbine speed step response to a sudden increase in wind speed

from 12 to 15m/s is simulated. It can be observed as the turbine

speed increases due to the sudden change in wind speed, and

then it is regulated by the pitch control system, returning to its

rated value. In Figure 10, the pitch angle actuator behavior is

presented. As it can be noted, the pitch angle reference (βref ,

green) changes at 20 seconds due to the pitch control and

the pitch angle (β, blue) follows it according to a first-order

system with saturation in the amplitude and rate of change,

as it is modeled. The pink line represents the pitch angle βexpressed in degrees.

C. Electrical Control

The electrical control or low level control is divided into

two subsystems: the rotor side converter (RSC) control and the

grid side converter (GSC) control . Both inner control loops

are assumed to be ideal since the WT electric system time

Fig. 9. Wind turbine speed response (green) when the wind speed is increasedin one step from 12 to 15m/s at 20 seconds. Values are in SI untis.

Fig. 10. Pitch angle actuator response. Pitch angle reference, βref (green),pitch angle in radians, β (blue) and pitch angle in degrees (pink).

responses are much faster than the outer speed control loop

or high level control [16]. Thus, it is possible to dissociate

both control loops and to define a cascade control structure

where the inner control loop concerns the back-to-back power

converter and the outer control loop concerns the speed

control.

Besides the RSC and GSC controls, the dc-chopper is

implemented in order to dissipate the excess of energy that

cannot be evacuated to the grid during a fault. The system

control also includes the voltage and currents limits according

to the capacity of the generator and the rating of the converters.

1) Rotor Side Converter Control: The RSC objective con-

trol is to regulate both the generator torque and the stator

reactive power. In order to do so, a vector control approach

is deployed. A synchronously rotating dq-axis frame with the

q-axis oriented along the stator flux vector position is chosen

(λsd = 0). This enables a decoupled control of the torque and

the stator reactive power, which can be expressed as a function

of the direct and quadrature components of the rotor current

references, respectively, as follows [3]

i∗rd =2LsΓ

∗m

3pLmλsq(15)

i∗rq ≈ λsq +2Q∗

sLs

3vsd

Lm(16)

The rotor current control is implemented by the following

state linearization feedback [3]:

vrscd = vrscd − ωdAλrq

vrscq = vrscq + ωdAλrd(17)

where the vrscd and vrscq are the output voltages of the dq-

axis rotor currents controller. Thus, replacing the equation 17

in 8 and neglecting the stator current transients, the following

decoupled system is obtained

idqr (s) =

[ 1Rr+Lrs

0

0 1Rr+Lrs

]︸ ︷︷ ︸

G(s)

vdqrsc(s) (18)

The PI controllers are designed according to the Direct

Synthesis methodology detailed in [18], with the desired close

loop transfer function, M(s), and the plant, G(s), as

M(s) = ird(s)i∗rd(s)

=irq(s)i∗rq(s)

= 1δs+1

G(s) = Kτs+1 =

1Rr

sLrRr

+1

(19)

being

Kp =τ

Kδ=

Lr

δy Ki =

1

Kδ=

Rr

δ(20)

To sum up, the generator torque control loop and the stator

reactive power control loop are shown in Figures 11 and 12,

respectively.

PIsqm

msrd pL

Li�3

2 **

rqmsqssq iLiL ��

*m *

rdi ��

rdi

� �

_ ( )·( )rscd comp d m m sq r rqV L i L i� � � � �sqirqi

^

rscdV

_rscd compV

SVPWM*rscdV

sq�sqirqi

RSC

Fig. 11. Block diagram of the generator torque control loop.

PI

*sQ

sq�

*rqi

��

rqi

� �

_ ( )·( )rscq comp d m m sd r rdV L i L i� � � �sdirdi

_rscq compV

rscqV

SVPWM*rscqV

rqmsqssq iLiL ��sqi

rqim

sd

sssq

rq LVLQ

i 32 *

*�

�

sdV*rqi

RSC

Fig. 12. Block diagram of the stator reactive power control loop.

2) Grid Side Converter Control: The objectives of the GSC

are to keep the DC-link voltage constant and to control the

grid side reactive power, by means of regulating the dq-axis

currents (idql ) and appying the proper voltages to the grid side.

Using a vector control approach, with a synchronously rotating

dq-axis frame and aligning the d-axis of the reference frame

along the stator-voltage vector position (vsq = vzd = 0),

enables a decoupled control between the DC-voltage and the

reactive power.

In the case of the reactive power control loop, the current

reference is directly computed as

i∗lq = − 2Q∗z

3vzd(21)

However, the calculation of the d-axis grid side current

reference (i∗ld) becomes more complex and some assumptions

need to be considered [19]. A cascade control structure is

implemented, where the outer control loop is responsible for

regulating the square dc voltage and the inner control loop

consist in controling the grid side currents (see Figure 13). It

is considered that the current response is much faster than the

dynamics of the outer loop due to the slow response of the

capacitors. Furthermore, the dc-chopper is not considered in

the control design.

As in the RSC case, PI parameters are tuning according to

the Direct Synthesis methodology, with M(s) equals to a first

order transfer function and

G(s) =E2

P ∗DC

=2

c · s (22)

Thus, as can be seen in the equation 23, a proportional

controller (P) is only needed for tuning the controller R(s)

R(s) =M(s)

G(s)(1−M(s))=

1δs+1

Ks (1− 1

δs+1 )=

1

Kδ(23)

being

Kp =1

Kδ=

C

2δ(24)

Aligning the d-axis of the reference frame along the stator-

voltage position, the d-axis grid side current reference (i∗ld)

can be written as

i∗ld =2P ∗

gsc

3vzd(25)

A similar analysis for the control of the dq-axis rotor

currents can likewise be done for the control of the dq-axis

grid side currents. Therefore, the following state feedback is

used to linearize the current dynamics.

vgscd = − ˆvgscd + vzd + ωdLgscilq

vgscq = − ˆvgscq − ωdLgscild

(26)

where the vgscd and vgscq are the output voltages of the

dq-axis grid side currents controller. The decoupling leads to

idql (s) =

[1

rgsc+Lgscs0

0 1rgsc+Lgscs

]︸ ︷︷ ︸

G(s)

vdqgsc(s) (27)

Finally, using the Direct Synthesis methodology, the result-

ing PI parameters are computed as

Kp =τ

Kδ=

Lgsc

δy Ki =

1

Kδ=

rgscδ

(28)

Analogously to the RSC case, both the square dc voltage

and the grid side reactive power control loops are shown in

Figures 13 and 14, respectively.

_gscd compV

SVPWM*gscdV

_gscd comp zd d gsc lqV V L i� �zdVlqi

ldi

*ldi

** 2

3gsc

ldzd

Pi

V PI�

��

PI��

� �

GSC

2E

2*)(E

rscP

*DCP

*gscP

^

gscdV �

Fig. 13. Block diagram of the square dc voltage control loop.

PI*lqi �

�

lqi

�

ldi

_gscq compV

gscqV

SVPWM*gscqV*

zQ

zdV

** 2

3z

lqzd

QiV

�

_gscq comp d gsc ldV L i� �

�

GSC

Fig. 14. Block diagram of the grid side reactive power control loop.

IV. FREQUENCY CONTROL

Due to increased wind penetration into the grid, a potential

concern of transmission system operators is the capability of

wind farms to provide dynamic frequency support if a sudden

event occurs and the grid frequency deviates from its nominal

value.

Hence, in recent years, the various national Grid Codes have

imposed some frequency and active power requirements on

wind farms. In this paper, a frequency control is proposed

according to the Danish Grid Code [10]. In Figure 15, this

frequency and active power requirements are shown. Between

49.9 and 50.1Hz (deadband), no special requirement is needed

since frequency is in the acceptable operating range to ensure

power quality. From 50.1 to 51Hz the active power output

of individual wind generators should be limited according

to a slope, Kfrec, depending on whether the wind turbine

operates at full (black line) or partial (blue line) capacity of

its available power from the wind. Finally, if the frequency

drops below 49.9Hz, due to either a loss of generation or a

increased demand, the wind generators should provide more

power output. However, this is only possible if the wind

turbine fix its set point power below its maximum and a

percentage of reserve power is available (blue line).

5150,1

50

0

100

49,9

80

Frequency [Hz]

% Activepower Deadband

Fig. 15. Frequency and active power requeriments according to the DanishGrid Code.

Previous research work has investigated different method-

ologies for contributing to frequency support of DFIG-based

wind farms [20]–[22]. In this paper, the proposed frequency

support controller consists of an additional control loop that

adapts the torque set point, calculated previously in Section

III-A, as a function of the grid frequency deviation, Δf (see

Figure 16).

+ -

*_ totalm Converter

control

*m

+ - freqKf�

gridf

reff P�

�

t�

t�

*m

t�

Fig. 16. Block diagram of the frequency support controller.

Thus, a proportional controller is activated when the grid

frequency exceeds certain limits (deadband). The proportional

gain constant, Kfreq , is given by the following equation

Kfreq = −ΔP/Mbase

Δf/fbase(29)

where fbase is nominal frequency of the system (50Hz) and

Mbase is the nominal apparent power of the machine (3MVA).

V. SIMULATION RESULTS

With the aim to evaluate the behavior of the system under

grid faults conditions, some simulations are carried out using

PSS/E. To that purpose, the equivalent grid shown in Figure

17 and provided by Asociacion Empresarial Eolica (AEE)

is chosen [23]. The parameters of the lines, transformers,

generators and loads, shown in Figure 17, are expressed in per

unit with Sbase equal to 100MVA. The 3MW wind generator

used for this study is connected to the 0.69kV busbar (501).

20 kV

TR22500MVA

X= 0.004 pu

PCC

GS2

R=0.003 puX=0.03 puG

S1

TR32000MVA

X=0.006 pu

R=0.001 puX=0.01 pu

P=1700 MWQ=500 MVAr

PV GenP=1.600 MWV=1.035 p.u.

B=0.4 pu B=0.133 pu

1 101 201

301 401

G3 MW

TR13.5MVA

X=0.06 pu501

0.69 kVSlack Gen

V=1.035 p.u.

Fig. 17. Equivalent electrical grid provided by Asociacion Empresarial Eolica(AEE) [23].

A. Fault ride-through

In order to evaluate the fault ride-through capability of the

model and check the overall system behavior, a symmetrical

three-phase voltage sag is introduced at PCC (bus 201).

The simulation results are compared with the requirements

established by the operation procedure P.O.12.3 developed by

REE (Red Electrica de Espana) [24]. This procedure is one of

the standards for grid connection in Spain and is addressed

to answer requirements for voltage dips in electrical wind

installations. The characteristic parameters of the simulation

are shown in table I.

TABLE ICHARACTERISTIC PARAMETERS OF THE SIMULATION

Parameter Value UnitVbase 690 VSbase 100 MVADepth of the voltage sag 0.105 puInstant when it appears 40 sDuration dip 550 msShort-circuit impedance 0.02 ΩWind speed 12 m/sQ∗

s 0 kVArQ∗

z 0 kVAr

As can be seen from Figures 18 and 19, the wind turbine

remains connected to the grid during the fault according to

the requirements specified in the P.O.12.3 [24]. In addition,

the active power generated and the electromagnetic torque

drops rapidly down to zero during the fault and recovers

its nominal values once the fault is cleared. The settling

time of both signals are 30ms. This reduction implies the

wind turbine speed increase as is shown in Figure 19. Once

the electromagnetic torque returns to its nominal value, the

machine begins to decrease its angular speed until it reaches

the rated one, according to equation 5 described in the drive

train model. Finally, the reactive power exchanged with the

grid at bus 501 (sum of Q∗s and Q∗

z) is zero before and after

the voltage dip, as expected.

B. Frequency response

In the last case of study, simulations are done to show the

ability of wind turbines to support primary frequency control.

In Figure 20, the wind turbine step response is analyzed when

Fig. 18. RMS terminal voltage (pink), active power (green) and reactivepower (blue) during a three-phase fault in the PCC. Values are in per unit.

Fig. 19. Wind turbine speed (green) and electromagnetic torque (blue) duringa three-phase fault in the PCC. Values are in SI units.

the grid frequency is increased from 50 to 50.55Hz as a result

of a sudden load decrement in the system. As is explained

in Section IV, the Danish Grid Code is used as a reference,

in order to compare the established requirements with the

obtained machine response.

As can be observed in Table II, when the frequency of the

system is stepped-up from 50 to 50.55Hz, the active power

generated should be halved.

It can be noticed in Figure 20 the proper response of the

wind turbine to the frequency increase, being reduced the

100% of its active power generated (which corresponds to

1,34 MW for a 9m/s wind speed) to only the 50% of its power

TABLE IICHARACTERISTIC PARAMETERS OF THE SIMULATION

Parameter Value UnitInitial frequency 50 HzFinal frequency 50.55 HzInitial active power capacity 100 %Desired final percentage of active power 50 %Wind speed 9 m/s

output capacity (670kW).

Fig. 20. Power output response (green) when the frequency is increased inone step from 50 to 50.55Hz (blue). Wind speed at 9m/s.

VI. CONCLUSION

A complete user-model consisting of a pitch regulated

variable speed wind turbine driven by a DFIG is presented.

The implemented control scheme is based on two levels: a

high control level or speed control and a low control level or

electrical control. A vector control approach is used to regulate

both rotor and grid side converters. The operating voltages

and current limits are considered, as well as the inclusion

of dc-chopper protection under fault ride through situations.

The performance of the overall system is evaluated under grid

faults by means of simulations carried out using PSS/E. In

order to improve the grid stability, a frequency control support

is implemented and analyzed. Satisfactory results are obtained

accomplishing with the Grid Codes requirements.

ACKNOWLEDGMENT

This work was supported by the Ministerio de Ciencia e

Innovacion under the project ENE2009-08555.

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