ARTICLE IN PRESS

Renewable Energy 32 (2007) 1301–1316

0960-1481/$ -

doi:10.1016/j

�CorrespoE-mail a

pablole@ing

marcia.marti

www.elsevier.com/locate/renene

Validation of fixed speed wind turbine dynamicmodels with measured data

M. Martinsa, A. Perdanaa, P. Ledesmab,�, E. Agneholma, O. Carlsona

aDepartment of Electric Power Engineering, Chalmers University of Technology, S-412 96 Goteborg, SwedenbDepartamento de Ingenierıa Electrica, Universidad Carlos III de Madrid, Butarque 15, 28911 Leganes, Spain

Received 8 March 2006; accepted 6 June 2006

Available online 8 August 2006

Abstract

Power system dynamics studies involving fixed-speed wind turbines normally use a wind turbine

model consisting of two lumped masses, an elastic coupling and a induction generator model which

neglects stator transients. However, validations of this model with measured data are rarely reported

in the literature. This paper validates the model using a recorded case obtained in a fixed speed, stall

regulated 180 kW wind turbine through a voltage dip. The work analyses the performance of the

reduced order induction generator model which neglects stator transients, compared to the detailed

induction generator model. It also includes a study of the convenience of representing mechanical

damping in the drive train, and an evaluation of the single mass mechanical model.

r 2006 Elsevier Ltd. All rights reserved.

Keywords: Wind energy; Dynamic modelling; Fixed speed wind turbine; Induction generator; Transient stability

1. Introduction

Wind energy installed in the world has increased largely over the last decade, growingfrom 2500MW in 1992 to 48,000MW in 2005 [1]. This means a growth rate of nearly 30%per year. Although not uniformly, almost three quarters of this power has been installed inEurope. Penetration levels are specially high in Denmark (20%), Germany (5%) and Spain(5%). More specifically, some regions already meet a great amount of the demanded power

see front matter r 2006 Elsevier Ltd. All rights reserved.

.renene.2006.06.007

nding author. Tel.: +3491 62 45 991; fax: +34 91 62 49 430.

ddresses: marcia.martins@chalmers.se (M. Martins), abram.perdana@chalmers.se (A. Perdana),

.uc3m.es (P. Ledesma), evert.agneholm@gothiapower.com (E. Agneholm),

ns@chalmers.se (O. Carlson).

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from wind energy: Navarra in Spain already meets 50% and Schleswig–Holstein, inGermany 30%. According to European Commission targets wind energy will continue togrow in Europe and will reach 69,900MW in 2010 [2].Wind energy conversion systems are very different in nature from conventional

generators, and therefore dynamic studies must be addressed in order to integrate windpower into the power system [3]. At a local scale the contribution of wind farms to the faultcurrents must be studied in order to design a proper protection scheme, while at a system-wide scale, power system dynamics and transient stability must be analysed. Besides,several system operators have published grid code specifications for the connection of windfarms, and as a result, dynamic studies have to be performed in order to know whether thewindmills fulfil these requirements and to implement the appropriate measures ifnecessary.A large percentage of the installed wind turbines are fixed speed, stall-regulated turbines

with induction generators. This technology is simpler than the variable speed one andprecedes it in time. As a result several fixed-speed wind turbine models have already beendeveloped and used to perform dynamic studies. However, validations of these modelswith field measurements are rarely reported in the bibliography [5].Most of the fixed speed wind turbine models for transient stability simulations use an

induction generator model which neglects stator transients [5–10], although there is no fullagreement on this point [11]. Regarding the drive train model, several models ranging fromone to four lumped masses [6] have been used depending on the purpose of the study,although one-mass [7,8] or two-mass [5,9–11] models are the most commonly used.The study presented in this paper uses measured data to validate most common fixed

speed wind turbine models found in the bibliography. The data used for the validationwere obtained accidentally when a voltage dip reached a windmill whose voltage andcurrent was monitored. The aim of the validation is to increase the confidence of theelectric utilities and system operators in the fixed speed wind turbine models, in order toperform the necessary studies to integrate wind energy into the power system.The paper is structured in five parts which include, respectively, a brief description of the

dynamic models to be validated, the procedure followed during the validation, adescription of the measured data, the software tools used in the study and the validation ofthe models.

2. Wind turbine models

2.1. Mechanical models

Two different mechanical models for the drive train have been considered: a two-massmodel and a single mass model. Fig. 1 represents the two-mass model, where one lumpedmass accounts for the low-speed shaft (which includes hub and blades) and the other oneaccounts for the high-speed shaft (which includes the rotor of the generator). In the singlemass model, one lumped mass accounts for all the rotating parts of the windmill. Only theequations of the two-mass model are given here:

dytg

dt¼ og � ot, (1)

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Hg

τem

Ht

D

K

τwind

Fig. 1. Mechanical model.

M. Martins et al. / Renewable Energy 32 (2007) 1301–1316 1303

dot

dt¼

1

2Ht

ðtwind þ Kytg þDðog � otÞÞ, (2)

dog

dt¼

1

2Hg

ð�tem � Kytg �Dðog � otÞÞ, (3)

where ytg is the angle between the turbine rotor and the generator rotor, ot, og, Ht and Hg

are the turbine and generator rotor speed and inertia constant, respectively, K and D arethe drive train stiffness and damping constants, twind is the torque provided by the windand tem is the electromagnetic torque. All parameters are in per unit.

2.2. Induction generator models

Two main induction generator models are used when performing power system dynamicstudies:

�

1

var

A detailed model which includes electromagnetic transients both in the stator and therotor circuits, containing four electromagnetic state variables.

� A simplified model which neglects stator transients, containing two electromagnetic

state variables.1

The following is a brief description of both models.

2.2.1. Model including stator transients

The asynchronous machine equations, expressed in a reference frame rotating atsynchronous speed and taking positive currents going out from the machine, are [7,13]:

lds ¼ X sids þ X midr, (4)

lqs ¼ X siqs þ X miqr, (5)

vds ¼ �Rsids þ oslqs �dlds

dt, (6)

vqs ¼ �Rsiqs � oslds �dlqs

dt, (7)

This model is sometimes referred in the literature as the third order model, accounting for the two electric state

iables and the generator speed. Hence, the detailed model is referred as the fifth order model.

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ldr ¼ X ridr þ X mids, (8)

lqr ¼ X riqr þ X miqs, (9)

0 ¼ �Rridr þ soslqr �dldr

dt, (10)

0 ¼ �Rriqr � sosldr �dlqr

dt, (11)

tem ¼ lqridr � ldriqr, (12)

where the subindexes (s, r) stand for the rotor and stator quantities, respectively, and thesubindexes (d, q) stand for the components aligned with the d- and q- axis in a synchronousrotating reference frame. Variable l represents the flux linkage, u the voltage and i thecurrent. Variables os and og are the synchronous and generator rotor speed, respectively,while s is the slip defined as s ¼ ðos � ogÞ=os. The electric parameters of the machine, Rs,X s, X m, Rr and X r, stand for the stator resistance and reactance, mutual reactance androtor resistance and reactance, respectively. All variables are in per unit.

2.2.2. Model neglecting stator transients

Neglecting stator flux linkage transients is common when performing stabilitysimulations [13]. It is done by neglecting terms dlds=dt and dlqs=dt in Eqs. (6) and (7),which is equivalent to assuming infinitely fast electromagnetic transients in the statorwindings.Rearranging Eqs. (4)–(12) in a convenient way leads to the well-known simplified model

[12,13], which represents the machine connected to the grid as a voltage source v0d þ jv0qbehind a transient impedance Rs þ jX 0s as shown in Fig. 2. The rate of change of thevoltage source and the electromagnetic torque are governed by the following equations:

dv0ddt¼ �

1

T 00½v0d � ðX s � X 0sÞiqs� þ jsobasev0q, (13)

dv0q

dt¼ �

1

T 00½v0q þ ðX s � X 0sÞids� � jsobasev0d , (14)

tem ¼ v0d ids þ v0qiqs, (15)

where s is the slip, T 00 ¼ X r=Rr and X 0s ¼ X s � X 2m=X r.

vd +jvq vds +jvqs

RsXs ids + jiqs

’ ’ ’ ’

’

Fig. 2. Induction generator model neglecting stator transients.

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This model is suitable for integration with conventional transient stability softwareprograms, where grid electric variables are represented as phasors and hence preserve onlythe fundamental frequency component.

3. Validation procedure

Model validation has been performed using a sample of data obtained on a 180 kW stall-regulated fixed-speed wind turbine over a period of 4 s. The relevant parameters of thewind turbine are shown in Appendix A. The recorded data are the instantaneous voltageand current at the machine terminals, with a sampling frequency of 256Hz. As an example,Fig. 3 shows the recorded voltage at each phase over a 40ms time frame.

A dynamic model validation procedure, outlined in Fig. 4, has been developed takinginto account the available data. Positive-sequence line-to-ground voltage and currentphasors have been obtained from the recorded data using the following transformation [4]

vkx

vky

" #¼ T

vka

vkb

vkc

264

375 (16)

where vka , vk

b , vkc are the kth recorded voltage data and vk

x, vky are the rectangular coordinates

of the kth instance of the voltage phasor. The transformation matrix T is calculated as

T ¼1ffiffiffi2p

cosðykÞ cosðyk

� 2p3Þ cosðyk

þ 2p3Þ

� sinðykÞ � sinðyk

� 2p3Þ � sinðyk

þ 2p3Þ

" #,

yk¼ otk þ f0,

1 1.01 1.02 1.03 1.04-400

-300

-200

-100

0

100

200

300

400

500

Time (s)

Vol

tage

(V

)

Phase a

Phase b

Phase c

Fig. 3. Extract from voltage measurements.

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currentsampling

vx,y

grid

simulation

windmill

voltagesampling

transf.3 => 2 3 => 2

va,b,c

P, Qsimulated

ix,y

transf.

ia,b,c

P, Qmeasured

compensating capacitors neutral

model validation

Fig. 4. General procedure for the validation of the models.

M. Martins et al. / Renewable Energy 32 (2007) 1301–13161306

where tk is the time at which the kth measurement sample was obtained, o is the gridfrequency and the angle f0 has been chosen so that the initial voltage angle is zero. Thesame transformation is applied to the current replacing v by i in Eq. (16).

Voltage and current phasors are easily obtained expressing vkx þ jvk

y and ikx þ jik

y in polar

coordinates. Wind turbine active and reactive output power have been obtained as

Sk ¼ 3ðvkx þ jvk

yÞðikx � jik

yÞ, (17)

Pk ¼ realðSkÞ, (18)

Qk ¼ imagðSkÞ, (19)

where Sk, Pk and Qk are the apparent, active and reactive power at time tk.

4. Recorded case

Figs. 5 and 6 show the measured voltage module and angle over the recorded period,while Figs. 7 and 8 show the active and reactive power. It can be seen in Fig. 7 that thewind turbine is working at a low-power operating point (at approximately 0.05 pu), whichcorresponds to a low wind speed. The consumption of reactive power is relatively high(approximately 0.33 pu) despite the reactive power compensation.Two different transients may be observed in Figs. 5 to 8:

(1)

At time 0.5 s the terminal voltage drops approximately 5%, followed by a slowrecovery and a slight angle oscillation. Active power suffers oscillations of around

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0 1 2 3 40.34

0.35

0.36

0.37

0.38

0.39

0.4

Time (s)

Lin

e-to

-lin

e vo

ltage

mod

ule

(kV

)

Fig. 5. Voltage phasor module.

0 1 2 3 4-50

-40

-30

-20

-10

0

10

Time (s)

Vol

tage

ang

le (

degr

ees)

Fig. 6. Voltage phasor angle.

M. Martins et al. / Renewable Energy 32 (2007) 1301–1316 1307

10 kW in amplitude. Reactive power absorption decreases as a result of the voltagedecay, and increases slightly after the transient in order to recover rotor flux linkage.

(2)

At time 1.6 s there is a sharp voltage decay of about 10%, followed by voltage andangle oscillations. There are also high active power oscillations of more than 50 kW in

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0 1 2 3 4-100

-50

0

50

100

150

Time (s)

Act

ive

pow

er (

kW)

Fig. 7. Measured wind turbine active power.

0 1 2 3 4-100

-50

0

50

100

Time (s)

Rea

ctiv

e po

wer

(kV

A)

Fig. 8. Measured wind turbine reactive power.

M. Martins et al. / Renewable Energy 32 (2007) 1301–13161308

amplitude, while the behaviour of the reactive power after the disturbance shows asimilar profile to voltage oscillations. The frequency at the end of the measured data isapproximately 0.05Hz lower than at the beginning, as can be seen measuring the rampat the right of Fig. 6.

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Since the second transient produces higher active and reactive power oscilla-tions than the first one, it provides a better pattern to perform the validation ofthe models. Hence, in order to provide clearer graphics and to make the discussionof the results easier, only second transient (from 1.5 to 4 s) is analysed in the follow-ing sections.

5. Software tools

Two different transient stability simulation programs have been used to simulate therecorded case:

(1)

PSS/E, by Siemens PTI. As there was no wind turbine model in the standard librarywhen the study was performed, a user-defined model for the turbine and the inductiongenerator was developed and implemented.

(2)

Power Factory, by DIgSILENT. This program allows performing simulations bothneglecting and regarding stator transients, hence facilitating the comparison betweenthe two induction generator models. The fixed speed wind turbine model provided inthe standard library has been used.

Since most models provided by these programs are black boxes with no access to thesource code, the coincidence of the simulations when using the wind turbine model in bothprograms has reinforced the confidence in the results.

6. Simulations and validation of the models

This section shows the results obtained using the different models, together withdiscussions about the results and the accuracy of the models to simulate the relevantphenomena. The following models are analysed:

�

Two-mass without damping mechanical model, together with regarding statortransients generator model. � Two-mass without damping mechanical model, together with neglecting stator

transients generator model.

� Two-mass with damping mechanical model, together with neglecting stator transients

generator model.

� One-mass mechanical model, together with neglecting stator transients generator

model.

6.1. Two-mass without damping mechanical model, regarding stator transients generator

model

The detailed induction generator model described in Section 2.2.1, together with thetwo-mass mechanical model described in Section 2.1 have been used. No mechanicaldamping has been modelled ðD ¼ 0Þ.

Fig. 9 compares the active power production from the measurements with the activepower obtained from the simulation, while Fig. 10 compares the reactive power output.

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1.5 2 2.5 3-150

-100

-50

0

50

100

150

Act

ive

Pow

er (

kW)

Time (seconds)

MeasuredSimulated

Fig. 9. Active power using two-mass without damping mechanical model, together with regarding stator

transients generator model.

M. Martins et al. / Renewable Energy 32 (2007) 1301–13161310

It can be observed that:

�

Power oscillations in simulations and measurements have a similar frequency. � Power oscillations in the simulation are poorly damped compared with

the measurements, which is normal taking into account that no damping wasmodelled.

6.2. Two-mass without damping mechanical model, neglecting stator transients generator

model

The same case has been simulated using the reduced order induction generator modelwhich neglects the stator transients described in Section 2.2.2. Fig. 11 shows the windturbine active power, while Fig. 12 shows the reactive power. It can be seen, comparingthese figures with Figs. 9 and 10, that electro-mechanical oscillations are accuratelyrepresented by the reduced order generator model, although fast electromagnetic transientsare not retained.These results are in accordance with the results reported by other authors [5,6,8,10,15]

and reinforces the opinion that the induction generator reduced order model accuratelyrepresents wind turbine electromechanical transients for transient stability studies.Fig. 13 shows the turbine and generator rotor speed obtained in the simulation.

Generator rotor speed is largely affected by the perturbation, while turbine speed remainsalmost constant. This is due to the fact that turbine inertia is much larger than generatorrotor inertia [14]. It can be seen, comparing Figs. 11 and 13, that active power oscillationsand rotor oscillations have a similar shape. This observation will be taken up again whendiscussing the one-mass model in Section 6.4.

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1.5 2 2.5 3-150

-100

-50

0

50

100

150

Rea

ctiv

e Po

wer

(kV

Ar)

Time (seconds)

MeasuredSimulated

Fig. 10. Reactive power using two-mass without damping mechanical model, together with regarding stator

transients generator model.

1.5 2 2.5 3-150

-100

-50

0

50

100

150

Act

ive

Pow

er (

kW)

Time (seconds)

MeasuredSimulated

Fig. 11. Active power using two-mass without damping mechanical model, together with neglecting stator

transients generator model.

M. Martins et al. / Renewable Energy 32 (2007) 1301–1316 1311

6.3. Two-mass with damping mechanical model, neglecting stator transients generator model

Poorly damped active power oscillations obtained in Fig. 11 suggest the convenience ofincluding a mechanical damping in the model. A damping constant D ¼ 3 pu. produces the

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1.5 2 2.5 3-150

-100

-50

0

50

100

150

Rea

ctiv

e Po

wer

(kV

Ar)

Time (seconds)

MeasuredSimulated

Fig. 12. Reactive power using two-mass without damping mechanical model, together with neglecting stator

transients generator model.

1.5 2 2.5 3103

103.5

104

104.5

105

105.5

106

106.5

107

Spee

d (r

ad/s

ec)

Time (seconds)

Gen. speedTurbine speed

Fig. 13. Simulated generator and turbine rotor speed, using two-mass without damping mechanical model

together with neglecting stator transients generator model.

M. Martins et al. / Renewable Energy 32 (2007) 1301–13161312

results shown in Figs. 14 and 15. It can be seen that agreement between the measurementsand the simulation after the first oscillation improves notably.However it must be noted that neglecting mechanical damping provides less but more

conservative results, and that the mechanical damping of the drive train of a wind turbineis often not known and difficult to estimate.

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1.5 2 2.5 3-150

-100

-50

0

50

100

150

Act

ive

Pow

er (

kW)

Time (seconds)

MeasuredSimulated

Fig. 14. Active power using two-mass with damping mechanical model, together with neglecting stator transients

generator model.

M. Martins et al. / Renewable Energy 32 (2007) 1301–1316 1313

6.4. One-mass mechanical model, neglecting stator transients generator model

Simulations using the one-mass mechanical model, in which the turbine, the gear boxand generator rotor are lumped into a single rotating mass, provide bad results and do notreproduce power oscillations. Fig. 16 shows the rotor speed simulated using the one-massmodel. It can be seen, comparing Figs. 13 and 16, that the one-mass model cannotrepresent accurately rotor oscillations, which has a major effect on power oscillations, andhence could conceal an unstable situation [16].

7. Conclusions

The following conclusions may be obtained from the study:

�

There is a good agreement between the measured power oscillations and the simulatedones when using both induction generator models, neglecting and including statortransients. Hence, the simplified model which neglects stator transients is accurateenough to represent the studied case. � A two-mass mechanical model is necessary to accurately represent the electromecha-

nical oscillations, and provides a good agreement between the measurements and thesimulations. A one-mass model does not represent the case accurately enough.

� Introduction of mechanical damping has a significant effect and is necessary to achieve

a good agreement between the measurements and the simulations, while neglect-ing mechanical damping provides higher oscillations and hence more conservativeresults.

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1.5 2 2.5 3-150

-100

-50

0

50

100

150

Rea

ctiv

e Po

wer

(kV

Ar)

Time (seconds)

MeasuredSimulated

Fig. 15. Reactive power using two-mass with damping mechanical model, together with neglecting stator

transients generator model.

1.5 2 2.5 3103

103.5

104

104.5

105

105.5

106

106.5

107

Spee

d (r

ad/s

ec)

Time (seconds)

Gen. speedTurbine speed

Fig. 16. Simulated generator and turbine rotor speed using one-mass model.

M. Martins et al. / Renewable Energy 32 (2007) 1301–13161314

�

As there are no major technological differences between fixed-speed stall-regulated windturbines of different sizes, the results might be extrapolated to larger wind turbines.However, the study is limited to the available data, and further validation of the modelwith other wind turbines, other operating points closer to the rated power, and different

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disturbances would be desirable. Furthermore, it would be convenient to performshortcircuit tests on isolated windmills in order to obtain a wide range of samples.

Acknowledgements

Financial support from the Swedish National Energy Administration, Nordic EnergyResearch, Svenska Kraftnat and Vattenfall is greatly appreciated. The authors would liketo thank Torbjorn Thiringer for providing the field measurements and for his valuablecomments on the study.

Appendix A. Parameters

Tables A.1–A.4 show the relevant parameters of the study.

Table A.1

Turbine parameters

Parameter Value Units

Rated power 180 kW

Rated voltage 400 V

Hub height 30 m

Rotor diameter 23.2 m

Rotor rated speed 42 r.p.m.

Gearbox ratio 23.75

Table A.2

Drive train parameters

Parameter Value Units

Rated power 210 kVA

Turbine inertia constant Ht 2.6 s

Generator inertia constant Hg 0.22 s

Stiffness constant K 141.0 p.u.

Damping factor (when applied) D 3.0 p.u.

Table A.3

Generator parameters

Parameter Value Units

Rated power 210 kVA

Rated voltage 415 V

Stator resistance Rs 0.0121 p.u.

Stator leakage inductance X s 0.0742 p.u.

Mutual inductance X m 2.7626 p.u.

Rotor resistance Rr 0.0080 p.u.

Rotor leakage inductance X r 0.1761 p.u.

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Table A.4

Capacitor bank parameters

Parameter Value Units

Rated power 210 kVA

Grid rated voltage 400 V

Capacitor bank susceptance B 0.11 p.u.

M. Martins et al. / Renewable Energy 32 (2007) 1301–13161316

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