rse043113 final published

Small-signal analysis of a fully rated converter wind turbine

Nolan D. CaliaoMindanao University of Science and Technology, Lapasan,Cagayan de Oro City, Misamis Oriental 9000, Philippines

(Received 3 January 2011; accepted 8 July 2011; published online 8 August 2011)

Small signal analysis of the fully rated converter wind turbine connected to a large

power system was undertaken. The dynamic behaviour of the fully rated converter

wind turbine was investigated using eigenvalue analysis. Eigenvalue analysis was

undertaken to determine the influence of the network short circuit level on the

networks dominant eigenvalues. It was shown that the strength of the transmission

system does not influence the dynamic behaviour of the generator of the fully

rated converter wind turbine. VC 2011 American Institute of Physics.

[doi:10.1063/1.3618744]

I. INTRODUCTION

The integration of wind power into the grid is now increasing at a significant pace which

poses new challenges for power system operators. As a result, there are revisions of grid code

requirements (GCRs). In these grid codes, fault ride through is of primary concern. The reason

for this is that when large proportion of wind energy is supplying the grid, they have to contin-

uously supply power during fault to avoid large frequency deviation.

There is even a bigger challenge of wind power technology. That is to bear the same

responsibilities for contribution to power system management as conventional synchronous gen-

erators does. This is a huge challenge, considering that wind power generation differs funda-

mentally from conventional generation in various ways.

Figure 1 shows the increase in size of wind turbines. In the 1980s, wind turbines were 15 m in

diameter and generating about 50 kW. In the 1990s, wind turbines increased to over 100 m in di-

ameter generating an average of 3 MW. The Enercon E-126 has a rotor diameter of 126 m. It can

generate 7 MW, enough to power about 5000 four-person households in Europe.1,2 Also, Vestas

announced recently to develop V164 7MW by 2012. The machine is designed for offshore appli-

cation and will have a full converter topology with a permanent magnet machine.

Fault ride through is primary requirements of the many grid codes, before wind turbines

can be connected to the network. During a network fault, the wind turbine should remain con-

nected to the network. Figure 2 shows the voltage sag versus duration curve of the GB grid

code. A wind farm has to remain connected to the GB transmission system (operating at super-

grid voltages) during a sag of zero retained voltage that lasts up to 140 ms. A wind farm has to

remain connected and transiently stable for supergrid voltages above the heavy black line in

Figure 2. Supergrid voltages are voltages greater than 200 kV.3,4

Modern variable speed wind turbines are able to meet fault ride through requirements and

as discussed in a number of studies. Other grid code requirements include active power and re-

active power support.4–9

This paper will demonstrate the dynamic behaviour of the fully rated converter wind tur-

bine (FCWT) was investigated using eigenvalue analysis. Eigenvalue analysis was undertaken

to determine the influence of the network short circuit level on the networks dominant eigenval-

ues. It was shown that the strength of the transmission system does not influence the dynamic

behaviour of the generator of the fully rated converter wind turbine.

II. WIND TURBINE TECHNOLOGIES

Presently, large wind turbines are usually in the range 3–5 MW operating at variable speed.

However, smaller wind turbines utilise the Danish concept. These wind turbines are at a fixed

1941-7012/2011/3(4)/043113/13/$30.00 VC 2011 American Institute of Physics3, 043113-1

JOURNAL OF RENEWABLE AND SUSTAINABLE ENERGY 3, 043113 (2011)

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http://dx.doi.org/10.1063/1.3618744

http://dx.doi.org/10.1063/1.3618744

speed and are usually connected to the distribution system. The drive train consists of a low-

speed shaft connecting the aerodynamic rotor to the gearbox, a 2- or 3-stage speed-increasing

gearbox, and a high-speed shaft connecting the gearbox to the generator. The generators of

these wind turbines are typically induction and operate at 690 V (AC).

The advantages of fixed speed induction generator (FSIG) wind turbines are that they are

simple and reliable and the concept is well proven. Current fixed speed wind turbines are the

Vestas V82 1.65 MW, Siemens SWT-1.3-62 1.3 MW, and Suzlon S.64 1.25 MW.

Variable speed wind turbines are used increasingly because they can meet most grid code

requirements. The doubly fed induction generator (DFIG) wind turbines and the fully rated con-

verter wind turbines are the most common designs. Commercial DFIG wind turbines include

Gamesa G80 2 MW, GE WE1.5s 1.5 MW, Vestas V80-2.0 2 MW, and Siemens SWT-2.3-82

VS 2.3 MW. FCWT include GE 2.5xl 2.5 MW and Clipper Liberty 2.5 MW.

FIG. 1. Increase in size of wind turbines in recent years (Ref. 1).

FIG. 2. Required ride through capability of wind farms for supergrid voltage sags of more than 140 ms duration under the

GB grid code (Ref. 3).

043113-2 Nolan D. Caliao J. Renewable Sustainable Energy 3, 043113 (2011)


Both DFIG and FCWT use power electronic converters to control the generator. For the

DFIG wind turbines, a pair of IGBT-based (IGBT-insulated gate bipolar transistor) voltage

source converters is connected to the rotor circuit.5,14,25 For the FCWT, a diode rectifier can be

used in the generator as in the case of the Enercon E-70 2.3 MW and E-82 2 MW wind tur-

bines. The Enercon E-70 2.3 MW and E-82 2 MW wind turbines have direct drive (with no

gearbox) and with electrically excited synchronous generators.

A. Fixed speed wind turbines

In a fixed speed wind turbine, the generator is directly connected to the network (Figure 3).

The frequency of the grid determines the rotational speed of the generator and thus of the rotor.

The low rotational speed of the turbine rotor is translated into high mechanical speed of the

generator through the gearbox. The generator speed depends on the number of pole pairs of the

generator and the grid frequency.

The fixed speed wind turbine design has the advantage of being simple. The disadvantages

of induction generators are high starting currents, which usually are smoothed by a thyristor con-

trolled soft starter, and their demand for reactive power. The wind fluctuations are directly trans-

lated into mechanical torque fluctuations and consequently into electrical power fluctuations in

the grid. These can lead to voltage fluctuations at the connection point and reduce the power

quality in weak grids. The frequency of these wind induced power fluctuation is about 1 Hz.18

B. Variable speed wind turbines

1. Limited variable speed wind turbines

This variable speed wind turbine uses wound rotor induction generator. In this design,

additional variable resistors are used to control the slip of the induction generator (Figure 4).

When the rotor resistance is varied, the torque-speed characteristic is changed, thus altering

the slip of the machine. For example, doubling the rotor resistance approximately doubles

the slip (Figure 5).18,19

This wind turbine is commercially known as OptiSlip. The external resistor is controlled

optically. Thus, slip rings and brushes are avoided thus reducing maintenance. These wind tur-

bines operate with speed range between 0% and 10% above synchronous.18,19

2. Doubly fed induction generator wind turbines

The block diagram of DFIG is shown in Figure 6. This machine uses wound rotor induc-

tion machine with two connections from the grid via the stator windings and via two back-to-

back converters to the rotor windings. Typically, a DFIG has a speed range between �40% and

þ30% of the synchronous value.21,22

FIG. 3. Block diagram of fixed speed induction generator wind turbine (FSIG).

043113-3 Small-signal full wind turbines J. Renewable Sustainable Energy 3, 043113 (2011)


DFIG has gained wide spread interest because of some advantages. One of its advantages

is its ability to control reactive power and to decouple active and reactive power control by in-

dependently controlling the rotor excitation current. Its drawback is its need for slip rings.

In a DFIG, a crowbar is used to protect the rotor side converter during network faults.

Because of the stiff grid code requirements, wind turbines nowadays are expected to support

the grid with respect to voltage control, reactive power support, and frequency support and are

equipped with fault ride through capability. Current DFIG wind turbines are capable of provid-

ing these ancillary grid requirements.7–12,20

DFIG wind turbines inject a variable voltage into the rotor at the slip frequency. As shown

in Figure 7, DFIG can operate from super-synchronous whereby it generates and delivers power

to the network to sub-synchronous where it absorbs power from the network. Curve 1 of Figure

7 shows the torque-speed characteristic when the injected rotor voltage is zero (short-circuited

rotor windings). When the injected rotor voltage is positive, the induction machine operates at

sub-synchronous speed (Point A in the torque-speed curve 2). When the injected rotor voltage

is negative, the induction machine operates at super-synchronous speed (point B in the torque-

speed curve 3).

FIG. 4. Limited variable speed wind turbine.

FIG. 5. Torque-speed (slip) curves with varying rotor resistance.



The rotor side converter is used for both speed control and to provide power factor control

whilst the supply side converter is responsible for transmitting active power. The induction

machine converter is controlled in a synchronously rotating dq reference frame with the d-axis

oriented along the stator flux vector position. This ensures decoupling control of stator-side

active and reactive power flows into the grid.

3. Fully rated converter wind turbines

Recently, there has been interest in wind turbine equipped with fully rated back to back

converters. The back to back converters are either connected to a squirrel-cage induction genera-

tor of a synchronous generator (Figure 8). The gearbox is designed so that maximum rotor speed

corresponds to rated speed of the generator. Synchronous generators or permanent-magnet syn-

chronous generators can be designed with multiple poles in which no gearbox is needed.

If the generator is a synchronous machine, the generator side converter can be a diode rec-

tifier. However for an induction generator, an IGBT-based generator side converter is used as it

FIG. 6. Doubly fed wind turbine.

FIG. 7. Effect of rotor injected voltage on DFIG torque-speed characteristics.



supplies current for the magnetisation of the windings. There is more freedom to control both

the generator and the grid-side converter independently because of the decoupling of the gener-

ator and the grid by the DC-link. Thus, this topology offers many options for network

support.5,13,23,24

Figure 9 shows the block diagram of a FCWT with a squirrel-cage induction generator.

The generator is fed through back-to-back power converters via the stator windings. These con-

verters, which are IGBT-based voltage source converters, are linked by a capacitor. The con-

verters perform an AC=DC=AC conversion which decouples the generator from the grid. The

generator side controller is based on rotor flux oriented control. The grid side controller is

based on load angle control or vector control.14–16

4. The generator side converter controller

Table I provides the dynamic equations of an induction generator which represent the full-

order model (5th order model). The 3rd order model was used in this chapter. The inertia con-

stant in the swing equation represents the total inertia constant of the wind turbine generating

system. This is equivalent to the sum of the inertia constants of wind turbine and the induction

generator referred to the high speed shaft. The total inertia constant used is 4.8 s.18

III. SMALL-SIGNAL ANALYSIS OF FULLY RATED CONVERTER WIND TURBINE

CONNECTED TO A LARGE POWER SYSTEM

“Small signal stability is the ability of the power system to maintain synchronism when

subjected to small disturbances.” The disturbance is considered small if the equations that

describe the system response can be linearised. The disturbance can be a fault or changes in

load. There are two forms of instability that may arise from the disturbance. The instability

may be a steady increase in the generator rotor angle due to lack of synchronising torque or

rotor oscillations of increasing amplitude due to lack of damping torque.17,26

FIG. 8. Fully rated converter wind turbines.

FIG. 9. Block diagram of a fully rated converter wind turbine based on induction generator.



In time-domain studies, the outputs are provided directly and the system dynamic behaviour is

shown visually. Small signal analysis complements time domain results by identifying and quantifying

the cause and nature of these dynamics.17 Small-signal analysis of a fully rated converter wind turbine

connected to a large system was performed. Both eigenvalue analysis and participation factors were

used to determine the influence of the generator controller gains on various modes. The influence of

the damping and synchronising power coefficient on the network’s dominant eigenvalues were inves-

tigated. Eigenvalue analysis was also used to investigate the influence of the transmission line react-

ance on the dominant eigenvalues of the network. A participation factor study was conducted to mea-

sure the influence of each state variable on the modes of oscillation.

A. Differential and algebraic equations of grid connected FCWT

The power system is modelled as a set of differential and algebraic equations given by

dx

dt¼ f ðx; uÞ; (3.1)

0 ¼ gðx; uÞ; (3.2)

where x represents the state variables, z represents the algebraic variables, and u represents the

control inputs. In small signal studies, Eqs. (3.1) and (3.2) are linearised around an operating point

by Taylor series expansion. The Taylor series represents a function as an infinite sum of terms

TABLE I. Voltage, flux, electromagnetic torque, and swing equation of an induction generator (Ref. 15).

Voltage equations Flux equations

�vds ¼ � �Rs�ids � �x �wqs þ

d

d�t�wds (2.1)

�wds ¼ ��Lss�ids þ �Lm

�idr (2.5)

�vqs ¼ � �Rs�iqs þ �x �wds þ

d

d�t�wqs (2.2)

�wqs ¼ ��Lss�iqs þ �Lm

�iqr (2.6)

�vdr ¼ �Rr�idr � s �x �wqr þ

d

d�t�wdr (2.3)

�wdr ¼ �Lrr�idr � �Lm

�ids (2.7)

�vqr ¼ �Rr�iqr þ s �x �wdr þ

d

d�t�wqr (2.4)

�wqr ¼ �Lrr�iqr � �Lm

�iqs (2.8)

Here; �Lss ¼ �Ls þ �Lm and �Lrr ¼ �Lr þ �Lm

Torque equation Swing equation

�Te ¼ �wdr�iqr þ �wqr

�idr (2.9)2H

d �xr

dt¼ �Tm � �Te (2.10)



calculated from the values of its derivatives at a single point. For small perturbations, the second

and higher orders terms are neglected. Therefore, the linearised forms of Eqs. (3.1) and (3.2) are

D _x¼ADxþ BDu; (3.3)

Dy ¼ CDxþ DDu: (3.4)

In Eqs. (3.3) and (3.4), Dx is the state vector of dimension n, Dy is the output vector of dimen-

sion m, Du is the input vector of dimension r, A is the state or plant matrix of size n� n, B is

the control or input matrix of size n� r, C is the output matrix of size m� n, and D is the

(feedforward) state or plant matrix of size n� n.15,17,27

Equations (3.3) and (3.4) can be Laplace transformed. Thus, the state equations in the fre-

quency domains are obtained as

sDxðsÞ � Dxð0Þ ¼ ADxðsÞ þ BDuðsÞ; (3.5)

DyðsÞ ¼ CDxðsÞ þ DDuðsÞ: (3.6)

Rearranging Eq. (3.5), a solution to the state equations can be obtained

ðsI� AÞDxðsÞ ¼ Dxð0Þ þ BDuðsÞ; (3.7)

where I is an identity matrix.17,28,29

1. Eigenvalues and participation factor

a. Eigenvalues

The eigenvalues of a matrix A are given by the values of the scalar parameter k. The

eigenvalues are obtained from the characteristic equation of matrix A. The characteristic equa-

tion is given bydetðA� kIÞ ¼ 0: (3.8)

The eigenvalues of the matrix A provide important information about the response of the sys-

tem to small disturbance. The eigenvalues provide information about any oscillatory modes that

exist in the system.17,29,30

The eigenvalues of the state matrix A consist of a real component (r) and an imaginary

component (x) and are given by

k ¼ r6jx: (3.9)

The modes of oscillation of a power system are determined by the eigenvalues, which can also

determine its stability. For instance, real eigenvalues correspond to a non-oscillatory mode. A

negative real eigenvalue represents a decaying mode whilst a positive eigenvalue represents

aperiodic instability. Complex conjugate eigenvalues correspond to an oscillatory mode.17

b. Participation factor

The participation matrix provides a measure of the influence of each dynamic state on a

given mode. The participation matrix P is given by

Pi ¼

p1i

p2i

..

.

pni

26664

37775 ¼

/1iwi1

/2iwi2

..

.

/niwin

26664

37775: (3.10)



In normalised form, the participation factor is defined as

Pni ¼j/ni k winjPni¼1 j/ni k winj

; (3.11)

where n is the number of state variables, Pni is the participation factor of the nth state variable

into mode i, /in is the ith element of the nth right-eigenvector, win is the nth element of the ithleft-eigenvector.17,31,32

B. Small-signal analysis

1. Simplified large power system model

Figure 10 shows a fully rated converter wind turbine connected to a large power system.

The machine is a 5th order squirrel-cage induction generator. The system of equations that

describe the induction generator model is given in Table I. The drive train is modelled as a sin-

gle mass.

The large network is represented by the lumped inertia (2H) of the whole network. The

term KS Dd, called the synchronising power, acts like a restoring force of the spring-mass

system. It acts to accelerate or decelerate the rotating inertia back to the synchronous operat-

ing point. The term KD Dx, called the damping power, opposes changes in the rotor speed.

These two components act on each other and influence the dominant eigenvalues of the

power system. Stronger transmission systems with lower values of reactance have a larger

value of KS. Large KS provides more synchronising power to the generators of the

system.17,26,29,30

2. Parameters used in small-signal analysis

Table II shows the parameters used in determining the eigenvalues. The generator active

power is set at rated value of 1 pu and the slip is �0.01. The ratio proportional to the inte-

gral gain of the generator side controller was set at 250. The ratio of the proportional to the

integral gain in the grid side controller for angle and the grid side voltage controls were set

to 10.

FIG. 10. Fully rated converter wind turbine connected to a large power system.



a. Eigenvalues

Table III shows the eigenvalues of the grid connected fully rated converter wind turbines

with a 5th order induction generator model. It can be seen that all real parts of the eigenvalues

have negative values. This means that the system is small-signal stable. Also, Table III shows

that there are three oscillating modes. These oscillating modes are associated with the generator

dynamics, of x¼ 66 rad=s and rotor mode of x¼ 2.59 rad=s, and with the dynamics of the

large power system of x¼ 6.7 rad=s. It is observed that the stator mode is highly damped with

a damping ratio of 1. The rotor mode has low damping ratio of 0.02. The mode of oscillation

associated with the large power system has damping ratio of 0.12 which is considered good

damping value of the system.17,31

The number of modes of oscillation is due to the oscillating mode of the large power sys-

tem dynamics and the oscillation modes of the induction generator. The oscillating mode of the

large network dynamics is 6.7 rad=s. The number of modes of oscillation will reduce when the

order of induction machine is reduced. For the 3rd order machine model, the stator transient

dynamics is neglected. For the 1st order machine models, both the stator and rotor transient

dynamics are neglected, thus the 66 rad=s and the 2.59 rad=s frequency components disappear.

b. Participation factors

Table IV shows the participation factors of different state variables on the eigenvalue of

the FCWT with damping controller and using the 5th generator order model. The participation

matrix for the entire system was also obtained using the 3rd and 1st order models of the induc-

tion generator. It was found that when 3rd order model was used, the eigenvalues k1 and k2 are

not present, and when 1st order model was used, eigenvalues k1, k2, k3, and k4 are not present.

It is seen that the oscillating modes k1 and k2 are primarily associated with the stator flux

state variables with participation factor of 100% (Dwqs and Dwds). The oscillating modes k3 and

k4 are associated with the rotor flux state variables with participation factor of 100% (Dwqr and

Dwdr). The non-oscillating mode k5 is associated with the rotor speed of the induction genera-

tor. Oscillating modes k11 and k12 are associated with the large network dynamics (Ddn and

Dxn). The non-oscillating modes are associated with the generator and the grid side controller

state variables, the DC-link, and the power oscillation damping controller.

TABLE II. Parameters used in the small-signal analysis.

Generator active power Slip

kgepd

kgeid

¼kge

pq

kgeiq

kgrph

kgrih

kgrpVgr

kgriVgr

1 pu �0.01 250 10 10

TABLE III. Eigenvalues (5th order machine model).

Dynamics k r 6 j x f (Hz) f (damping ratio)

Generator 1,2 �4.2� 103 6 j66 10 1

3,4 �0.048 6 j2.59 0.4 0.02

5 �0.2852 0 1

Generator-side controller 6 �0.14 0 1

7 �0.10 0 1

DC-link 8 �4.2 0 1

Grid side controller 9 �0.1475 0 1

10 �0.0067 0 1

Large network 11,12 �0.8 6 j 6.7 1.0 0.12

PDC 13 �0.5196 0 1

14 �0.1 0 1



Table V in the Appendix provides the parameters used in the model.

C. Influence of the transmission line reactance on the network’s dominant eigenvalues

The transmission line impedance (reactance as the line resistance is neglected) is one of the

measures of grid strength. The high line impedance corresponds to an electrically weak AC

system. A weak AC system has undesirable effects such as voltage variations. The usual cause of

abnormally high impedance is the loss of one line of two or more parallel transmission lines. Line

compensation may be used to reduce the effective value of the transmission line reactance.

The influence of the transmission line reactance on the network’s dominant eigenvalues

was investigated. The fully rated converter wind farm (FCWF) is operating at 2100 MVA. The

total equivalent reactance from the FCWF was increased from 0.2 pu to 0.8 pu.17,33,34

In the grid connected FCWF, the short-circuit ratio (SCR) can be used for measuring the

strength of the AC grid with respect to the FCWF. The short-circuit ratio is defined as

SCR ¼ short circuit MVA of AC system

Rating of wind farm: (3.12)

The short circuit MVA is given by

SC MVA ¼E2

ac

Ztl

; (3.13)

where Eac is the ac voltage and Ztl (Ztl ¼ Xtl, when the resistance is neglected) is the imped-

ance of the AC transmission line. SCR, indicating the strength of the system from the system

impedance point of view, is defined as the AC system admittance expressed in per unit

power.17,29,30,34

Using the FCWF rating as the base MVA, a transmission line reactance of Xtl ¼ 0:2 pu cor-

responds to a high SCR of 5. A transmission reactance of Xtl ¼ 0:8 pu corresponds to a low

SCR of 1.25.17 Figure 11 shows the displacements of the dominant eigenvalues of the network

when the equivalent transmission line reactance is increased from 0.2 pu to 0.8 pu. It shows

that the eigenvalues moved towards the imaginary axis of the complex plane. Starting at a

TABLE IV. Participation of state variables on the eigenvalues (only dominant ones) obtained from the 5th order machine

model.

Dynamics

State

variable

Participation factors

on the eigenvalues (%) Comments

Generator D �wqs k1 ¼ 49:9; k2 ¼ 49:9 Oscillating modes k1 and k2 are associated with the

stator transient dynamics of the generator.D �wds k1 ¼ 49:9; k2 ¼ 49:9

D �wqr k3 ¼ 49:9; k4 ¼ 49:3 Oscillating modes k3 and k4 are associated with the

rotor transient dynamics of the generator.D �wdr k3 ¼ 49:9; k4 ¼ 49:3

D �xr k5 ¼ 99:9 Non-oscillating mode k5 is mainly associated with

the machine’s rotor speed.

Generator side

controller

Dx1 k6 ¼ 49:4; k7 ¼ 50:3 Non-oscillating modes k6 and k7 are with the gener-

ator side controller state variables.Dx2 k6 ¼ 51:1; k7 ¼ 48:8

DC-link D�vdc k8 ¼ 80:2 Non-oscillating mode k8 is associated with the DC-

link state variable �vdc.

Grid side controller Dx3 k9 ¼ 95:1 Non-oscillating modes k9 and k10 are associated

with the grid side controller state variables.Dx4 k10 ¼ 100:0

Large network Ddn k11 ¼ 47:3; k12 ¼ 47:3 Oscillating modes k11 and k12 are associated with

the large network dynamics.D �xn k11 ¼ 41:4; k12 ¼ 41:4

PDC Dx5 k13 ¼ 69:3 Non-oscillating modes k13 and k14 are associated

with the damping controller (compensator and

wash-out terms).k8 ¼ 14:7

Dx6 k14 ¼ 99:0



transmission line reactance of 0.2 pu, the eigenvalue is located at about �0.8535 of the real

axis. When the line reactance was increased to 0.8, the eigenvalues moved to about �0.851 of

the real axis.

The displacements of the eigenvalues when the transmission line reactance was increased

were not significant. It means that the strength of transmission system does not participate sig-

nificantly in the dynamic behaviour of the generator. Although the frequency and the damping

ratio changed, the generator dynamics remain decoupled from the grid.17,31

IV. CONCLUSIONS

The performance of a FCWT connected to a large power system was examined for small

perturbation using small signal analysis (both eigenvalue analysis and participation factors).

Detailed understanding of the interactions of the state variables of the FCWT model was pro-

vided by small-signal analysis. It also allows quantification of how much a state variable influ-

ences a particular mode. Transient studies were undertaken to complement the results of small-

signal stability analysis.

Eigenvalue analysis was conducted to determine the influence of the transmission line re-

actance on the networks dominant eigenvalues. It was shown that the strength of the transmis-

sion system does not affect significantly the FCWF dynamics. Although the frequency and the

damping ratio changed, the generator dynamics remain decoupled from the grid.

APPENDIX: PARAMETERS USED IN SIMULATIONS

FIG. 11. Influence of the equivalent transmission line reactance on the network’s dominant eigenvalues.

TABLE V. Parameters of FCWT connected to a large power system.

Induction generator parameters (squirrel cage): base of S¼ 2000 kVA, 2 MW, 690 V, 50 Hz, 4 poles, Rs ¼ 0:0049 pu,

Rr ¼ 0:0055 pu, Ls ¼ 0:0924 pu, Lr ¼ 0:0996 pu, Lm ¼ 3:9591 pu

Total wind turbine inertia constant, Hwt¼ 4.8 s

DC-link capacitance¼ 80 mF

Large power system parameters: (base S¼ 2000 kVA) Hn¼ 3.5 s, KD¼ 12, KS¼ 1, Xtl ¼ 0:2 pu, Xgr ¼ 0:02 pu



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http://www.enercon.de/www/en/windblatt.nsf/vwAnzeige/66BD14BABA22BCA2C12573A7003FA82E//WB-0407-en.pdf

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http://www.eirgrid.com/EirgridPortal/DesktopDefault.aspx?tabid=Grid%20Code&hx0026;TreeLinkModID=1451&hx0026;TreeLinkItemID=18


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http://dx.doi.org/10.1049/iet-rpg:20070128

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rse043113 final published

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