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THESIS FOR THE DEGREE OF LICENTIATE OF ENGINEERING

Modeling of Wind Turbines

for Power System Studies

TOMAS PETRU

Department of Electric Power Engineering

CHALMERS UNIVERSITY OF TECHNOLOGYGoteborg, Sweden 2001



Modeling of Wind Turbines for Power System StudiesTOMAS PETRU

c TOMAS PETRU, 2001.

Technical report no 391L

Department of Electric Power Engineering

Chalmers University of Technology

SE-412 96 Goteborg

Sweden

Telephone + 46 (0)31-772 1660

Fax + 46 (0)31-772 1633

E-mail: [email protected]

Chalmers Bibliotek, ReproserviceGoteborg, Sweden 2001



Modeling of Wind Turbines for Power System Studies

TOMAS PETRUDepartment of Electric Power EngineeringChalmers University of Technology

Abstract

When wind turbines are installed into the electric grid, the power quality is affected.Today, strict installation recommendations often prevail due to a lack of knowledge

on this subject. Consequently, it is important to predict the impact of wind turbineson the electric grid before the turbines are installed.

The thesis describes relevant power quality issues, discusses different configurationsof wind turbines with respect to power quality and draw requirements regarding windturbine modeling. A model of a stall-regulated, fixed-speed wind turbine system isintroduced and its power quality impact on the electric grid is evaluated. The modelis verified with field measurements.

Key words: wind turbine, power quality, flicker, modeling, prediction, measure-

ments, verification



Acknowledgements

This thesis is the result of the project ”Modeling of Wind Turbines for Power SystemStudies” supported by Sydkraft AB. The financial support is gratefully acknowl-edged.

Thanks also to the National Board of Energy Administration (Energimyndigheten)for financing measurement campaigns and equipment.

I would like to express my deep gratitude to Dr. Torbjon Thiringer for his supervi-

sion, valuable discussions and never-ending encouragement, patience and support.The job behind this thesis could hardly have be done without the help I have ob-tained from him and I am not thinking just about the work. Many thanks.

Thanks to Ingemar Carlen from the Department of Thermo and Fluid Dynamics atChalmers University of Technology for his valuable help. An electrical engineer isusually not familiar with aerodynamics. A few discussions saved a lot of time andprovided me with confidence.

Lars Barth at GEAB and Goran Olsson at Vattenfall AB on the island of Gotland

have helped a lot with serving and maintaining the measurement systems. I appre-ciate their willingness, the measured data are a very important and valuable part of my thesis.

Thanks are also due to Professor Essam Hamdi and Dr. Ola Carlson for proof-reading the draft manuscript.

Finally, many thanks to all my colleagues and the staff at the Department of ElectricPower Engineering - the working atmosphere is very important for me and I havebeen provided with a good one.



Contents

1 Introduction 1

1.1 Utilization of wind turbines . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Modeling wind turbines . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.4 Aim of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.5 Relation to previous research . . . . . . . . . . . . . . . . . . . . . . . 3

1.6 Thesis layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Power Quality 5

2.1 Wind power and power quality . . . . . . . . . . . . . . . . . . . . . 52.2 Power Quality problems . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2.1 Steady state voltage impact . . . . . . . . . . . . . . . . . . . 7

2.2.2 Dynamic voltage variations . . . . . . . . . . . . . . . . . . . 8

2.2.3 Harmonic distortion . . . . . . . . . . . . . . . . . . . . . . . 9

2.2.4 Voltage transients . . . . . . . . . . . . . . . . . . . . . . . . . 9

3 Wind Turbine Systems 11

3.1 Basic overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.2 Blade aerodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.3 Aerodynamic power control . . . . . . . . . . . . . . . . . . . . . . . 13

3.3.1 Stall control . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.3.2 Active Stall control . . . . . . . . . . . . . . . . . . . . . . . . 15

3.3.3 Pitch control . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.4 Fixed-speed system . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.5 Variable-speed system . . . . . . . . . . . . . . . . . . . . . . . . . . 17

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3.5.1 An induction machine and rotor resistance control . . . . . . . 18

3.5.2 An induction machine with rotor converter . . . . . . . . . . . 18

3.5.3 Induction machine with squirrel cage rotor . . . . . . . . . . . 19

3.5.4 Systems with a synchronous machine . . . . . . . . . . . . . . 19

3.6 Comparison of power quality impact . . . . . . . . . . . . . . . . . . 20

3.7 Wind turbine model in grid simulation program . . . . . . . . . . . . 20

4 Measurements 23

4.1 Measurement set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

4.2 Bockstigen-Valar data acquisition . . . . . . . . . . . . . . . . . . . . 24

4.3 Alsvik data acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . 25

5 Wind turbine modeling 27

5.1 Structure of the system . . . . . . . . . . . . . . . . . . . . . . . . . . 27

5.2 Wind simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

5.2.1 Single point wind simulation . . . . . . . . . . . . . . . . . . . 28

5.2.2 Wind field simulation . . . . . . . . . . . . . . . . . . . . . . . 29

5.3 Aerodynamic conversion . . . . . . . . . . . . . . . . . . . . . . . . . 30

5.4 Drive-train model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

5.5 Generator model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

5.6 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

5.6.1 Comparison in frequency range, I . . . . . . . . . . . . . . . . 34

5.6.2 Comparison in frequency range, II . . . . . . . . . . . . . . . . 35

5.6.3 Comparison of Pst impact . . . . . . . . . . . . . . . . . . . . 37

5.6.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

5.7 A simplified model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

5.7.1 Spatial filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

5.7.2 Rotational sampling filter . . . . . . . . . . . . . . . . . . . . 40

5.7.3 Induction lag filter . . . . . . . . . . . . . . . . . . . . . . . . 41

5.7.4 Parameter determination . . . . . . . . . . . . . . . . . . . . . 41

5.8 Simplified model - results . . . . . . . . . . . . . . . . . . . . . . . . . 42

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6 Conclusions and future work 47

6.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

6.2 Results evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

6.2.1 Advanced model . . . . . . . . . . . . . . . . . . . . . . . . . 47

6.2.2 Simplified model . . . . . . . . . . . . . . . . . . . . . . . . . 48

6.3 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

A Technical Data 49

A.1 Wind turbine data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

A.2 Drive train data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

A.3 Generator data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

B List of publications 51

iii



Abbreviations

ASR active stall-regulated systemFSS fixed-speed system

HSF spatial filter transfer functionHRSF rotational sampling filter transfer functionPCC point if common conectionPEC power electronic converterPR pitch-regulated systemRSF rotational sampling filterSF spatial filterSR stall-regulated systemVSS variable-speed system

Terms

α [deg] angle of attackϕ [rad] angle between voltage and current vecorsϑ [deg] angle between free wind speed and tangential speed of a blade

segmentωG [rads−1] angular speed of a generatorωT [rads−1] angular speed of a turbine (high speed shaft)Ω [rads−1] angular speed of a turbine (low speed shaft)

ϑG [rad] angle of a generator shaftϑT [rad] angle of a turbine shaft (high speed shaft)σ [−] dampingγ [−] decay factor over the disc

a [−] constantB [kg m2 s−1] absorption of a shaftd [m] turbine diameterD [N ] drag forcef [Hz] frequencyFE [N ] edge forceFF [N ] flap forcefTla [Nm] amplitude of the advanced shaft torque frequency componentfTls [Nm] amplitude of the simplified shaft torque frequency componentI [A] currentIp [A] current, active power corresponding componentIq [A] current, reactive power corresponding componentis [A] stator current vectorir [A] rotor current vector referred to the stator sideJG [kg m2] generator moment of inertiaJT [kg m2] turbine moment of inertia

k [kg m2 s−2] stiffness of a shaftL [N ] lift force

iv



Lm [H ] magnetizing inductanceLsλ [H ] stator leakage inductanceLrλ [H ] rotor leakage inductance referred to the stator sideP [W ] active power

Pst [−] short time flicker severity indexPlt [−] long time flicker severity indexpp [−] number of pole pairsQ [VAr] reactive powerR [m] turbine radiusRg [Ω] grid resistanceRs [Ω] stator winding resistanceRr [Ω] rotor winding resistance referred to the stator sideTG [Nm] torque on a generator shaftTT [Nm] torque on a turbine shaftTHD [

−] total harmonic distortion

UN [V ] nominal grid voltageUPCC [V ] voltage at the point of common conectionus [V ] stator voltage vector∆URg

[V ] voltage drop over the grid resistance∆UXg

[V ] voltage drop over the grid reactanceV1 [−] RMS value of a fundamental vaweVk [−] RMS value of a kth harmonics vaweW [m/s] wind speed acting on a bladeWS [m/s] free wind speedXg [Ω] grid reactance

Z0 [−] roughness of the surface

v



Chapter 1

Introduction

1.1 Utilization of wind turbines

Mankind has used the wind as a source of energy for several thousands of years. Itwas one of the most utilized sources of energy together with hydro power during theseventeenth and eighteenth centuries [1]. By the end of the 19th century the firstexperiments were carried out on the use of windmills for generating electricity. Theinternational oil crisis of 1972 initiated the utilization of renewable resources on alarge scale, wind power among others.

Today, wind power is a fully established branch on the electricity market and it is

treated accordingly. The energy gain is not the only criteria to be considered wheninstalling new wind turbines; cost efficiency, the impact on the environment and theimpact on the electric grid are some of the important issues of significant interestwhen making decisions about new wind turbine installations.

Electricity is traded like any other commodity on the market and there are, therefore,standards which describe its quality. In the case of electric power they are commonlyknown as the Power Quality standards. Any device connected to the electric gridmust fulfill these standards and this is a particularly interesting and important issueto be considered in the case of wind power installations, since the stochastic natureof wind and standardized parameters of electricity are joined together there. Amathematical model of a wind turbine capable of predicting its interaction with thegrid is, thus, an important topic.

1.2 Modeling wind turbines

Various models of wind turbines have been developed. They have different purposesand, therefore, treat different features of the wind turbine system and they span, infact, all the aspects relevant to such a device.

The purpose of aerodynamic simulations is to verify and optimize blade design,according to prescribed criteria. Examples of such criteria might be maximization

1



of useful forces, minimization of unwanted loads, adjustment of blade characteristicfor a chosen nominal wind speed, etc . . . . Mechanical engineers are mostly concernedwith the safe and economical dimensioning of the whole wind turbine system, and aproper mechanical model of the wind turbine will make their task simpler. General

purpose models concerned with the electrical properties of wind turbines are widelyused. There are also economical models, which evaluate the cost effectiveness of manufacturing and installing wind turbines. Models predicting weather conditions,and consequently, the corresponding power production from large wind farms, areimportant when planning the control of a power system with high penetration bywind power. The prediction of power output is also important on a liberalizedelectricity market since it is this factor which influences the price of electricity.Finally, there are models developed with the aim of evaluating the impact of windturbines on the environment (a determination of noise generated by the operationof the wind turbine is one example).

The model developed and evaluated in this thesis is concerned with predicting thepower quality impact on the electrical network. Such a model makes it possible foran electric grid owner to make a decision about a new wind turbine installation inadvance and in such a way as to prevent possible power quality problems. Moreover,a simulation of the interaction between an electric grid and a wind turbine can assessthe suitability of some wind turbine types when solving a power quality problemalready present in the grid. An important part of the thesis is the verification of thedeveloped model against field measurements of a full-scale wind turbine.

1.3 Literature review

The problem of the interaction between wind turbines and the electric grid has beentreated by many authors. The reasons for predicting the power output from a windturbine are various: the impact on the grid, the design of the wind turbine controllerand stating the power quality standards are some typical examples.

Papers by Estanquiero [2], Bossanyi [3] and Jenkins [4] deal with predicting thepower quality impact on the connected grid. Wind turbine models of different com-plexity were incorporated into a grid simulation program and conclusions regarding

the requirements on the model complexity were drawn. These models incorporatedthe aerodynamic part of different complexities. The driving torque on the generatorshaft was either calculated using a professional software package or, on the contrary,significantly simplified to a very rough approximation of reality.

Leithead has presented in [5], [6] and [7] a detailed description of the wind turbinemechanical parts. The structural dynamics of the whole drive train was thoroughlydescribed and analyzed. The aerodynamic interaction between free wind and theturbine itself was incorporated into an overall model in the form of various filtersapplied to the free wind data.

Rodriguez [8] has also adopted the filter approach, mentioned above, and developeda model to be used, partly, in wind turbine control design and, partly, in powerquality impact prediction.

2



The work presented by Thiringer [9] has described a detailed analysis of inductionmachine dynamics. The induction machine models of different orders were presentedand compared with laboratory measurements. The same author has presented in [10]and [11] measurements and analysis of the power quality impact by stall-regulated,

fixed-speed wind turbines.

Sørensen [13] and Larsson [14] have presented measurements of wind turbines’ elec-trical performance. An analysis of the measured quantities was presented and con-clusions regarding the power quality requirements for wind turbine installations weredrawn.

1.4 Aim of the thesis

The aim of the presented thesis is to measure and evaluate the power quality impactof wind turbines on the grid. Furthermore, the dynamic voltage quality impact is tobe predicted when this issue is of interest. For this purpose, a wind turbine modelof a fixed-speed, stall-regulated system has been developed. An important aspect of the thesis is to verify the model with measurements.

1.5 Relation to previous research

Measurements on wind turbines and the related power quality impact evaluationhave been reported, as well as various models which describe electric aspects of wind turbines. Comparisons of measured and predicted impact of wind turbines onthe power quality of the electric grid are, however, rarely shown.

The challenge here is to integrate knowledge from available models reported in theliterature. Aerodynamic, mechanical and electric parts have been joined in oneintegral model. It should be noted, however, that the purpose of the model developedhere is to predict power quality impact on the grid. The model has, consequently,been simplified when acceptable to the model purpose.

The method of representing the driving torque calculation presented in [3] has notbeen adopted here. The use of a professional software package specifically designedfor aerodynamic studies of higher complexity is not a suitable option for use in gridsimulation programs with a large number of wind turbine models to be integratedinto an electric grid model. The reason for such a decision is usually the highcomputational demand of such a professional software package. The very simplifiedtorque on the generator shaft as presented in [4], on the other hand, might be a goodoption when analyzing basic properties of the modeled system but is of secondaryimportance when predicting the power quality impact of a wind turbine.

The implementation of the extensive mechanical parts presented in [5] and [6] has notbeen implemented here. The careful study and deep understanding of the presentedsubject would require far too much time and it has been replaced, therefore, by a

3



simpler variant of the drive train description. This fact has, however, been kept inmind by the author and can be considered in future model development.

An important objective of the thesis is the verification of the presented model withsite measurements. Such a comparison has not been reported in the literature and

is, therefore, of significant importance.

1.6 Thesis layout

Chapter 2 summarizes the power quality aspects that are of particular interestwhen analyzing wind turbine impact on the electric grid.

Chapter 3 gives a basic overview of wind turbine systems that are commonly usedtoday. An overview of aerodynamic control strategies and electric configurations is

attached together with a summary of their impact on power quality. Suggestionsregarding the needs when predicting power quality impact of different wind turbinesystems are also presented.

Chapter 4 presents the data acquisition set-up. Two measurement sites are intro-duced and some results are presented.

Chapter 5 describes the model developed in the thesis and simulated results. Com-parisons with measurements are presented and some partial conclusions are drawn.

Chapter 6 summarizes results of the thesis and presents suggestions for future

work.

4



Chapter 2

Power Quality

2.1 Wind power and power quality

The Power Quality area is very broad and it has many branches that deal withdifferent problems and issues. Any device to be connected to the electric grid has tofulfill standardized power quality requirements. This is to ensure that the electricgrid is protected from unacceptable disturbances. The connected device, therefore,is connected to the grid with electric quantities within guaranteed limits. Someexamples of the problems dealt within power quality standards are static voltagelevel, voltage fluctuations, voltage transients, voltage harmonic distortion, voltage

unbalance and power supply interruptions.

Some of the power quality terms are of particular interest when confronting windpower applications. The wind power stations are likely to violate some of the powerquality limits when they are improperly chosen for specific grid conditions. Theselimits have been widely discussed in literature, some examples are given in [13]and [14]. A summary of these power quality problems is included in the followingsections. An overview of common wind turbine systems used today is also given,together with a discussion of their characteristic power quality impact.

2.2 Power Quality problems

A wind turbine is designed to supply active power to the grid. A reactive powerexchange between the wind turbine and the grid depends on the type of the windturbine; it can be consumed, produced or no reactive power can be exchanged withthe grid. As a consequence of this fact, the voltage at the point of common connec-tion, UPCC, is influenced. This is demonstrated in Figure 2.1 and Figure 2.2 and isdescribed in Equation 2.1.

U PCC = Rg

p

U n+ X g

q

U n+ U n (2.1)

5



Figure 2.1: Connection of a wind turbine to the grid

Figure 2.2: Vector diagram

6



Where:

UN nominal voltage of the gridUPCC voltage at the point of common connection (PCC)P,p active power produced

Q, q reactive power consumedRg grid resistanceXg grid reactance∆URg

voltage drop over the grid resistance∆UXg

voltage drop over the grid reactanceI generator currentIp generator current, active power corresponding componentIq generator current, reactive power corresponding componentϕ angle between voltage and current vectors

Higher active power production, i.e. a higher Ip, is followed by an increase in thevoltage drop over the grid resistance, ∆URg

, and a consequent increase in the voltageUPCC. More consumed reactive power, i.e. higher Iq, causes, on the contrary, anincrease in the voltage drop over the grid reactance and a corresponding decrease inthe voltage UPCC.

A power quality evaluation of a wind turbine is addressed for two different opera-tional modes. First, it is investigated under normal operation during which aspects,such as the steady state voltage impact, dynamic voltage variations and the har-monic distortion on the grid are of interest. Second, the impact on the grid when aturbine is being connected, i.e. during the start up of the turbine, is analyzed. Volt-

age dips and their consequences are of interest here. Voltage transients originatingin the switching of a capacitor bank are another power quality problem of interestwhen analyzing the start up of a turbine.

2.2.1 Steady state voltage impact

The steady state voltage level at the PCC is a power quality problem which iscommon to most of the wind turbine systems. It is, by its nature, the problempotentially related to any source or load of electric power. Since the distribution

(transmission) lines will always have an impedance, there must be a voltage drop(increase) in it in order to make it possible for power to be transmitted. Since thevoltage in the system must be kept within stated limits, the voltage drop in the gridimpedance must not exceed the stated value.

In the case of a conventional power station, the natural way of avoiding such aproblem is to design the transmission lines according to specific requirements. Thisis, however, rarely the case with a small wind turbine installation. Building newtransmission lines or reinforcing present ones in such a case is almost never done,it would be far too expensive compared with the total gain from the installation.

An installation of large wind parks, today typically located offshore, with a numberof turbines is, of course, a completely different situation. In such a case, adjustingtransmission capacity is not a major cost in the overall scope of such a project.

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Keeping the voltage at PCC below given limits without any need for grid reinforce-ment is, as discussed above, a typical problem in the installation of one or few windturbines. In Sweden, this limit is stated to be up to +2.5% of the nominal gridvoltage [15]. As is seen in Equation 2.1, this can be done with a suitable control of

the reactive power. The controllability of reactive power, with respect to the typeof the wind turbine system, is discussed in the following sections.

2.2.2 Dynamic voltage variations

Dynamic voltage variations at the PCC and in its neighborhood are another powerquality issue of interest. Dynamic voltage variations are, as previously stated, aconsequence of the power flow via the grid impedance. This consequence is now,

however, studied for a shorter time interval. While the steady state voltage varia-tions are evaluated on a time base of minutes to hours, dynamic voltage fluctuationsare evaluated in the order of seconds to a fraction of a second.

A consequence of such dynamic voltage fluctuations is, for example, flickering of an incandescent light bulb. Humans are especially sensitive to variations with afrequency of around 9 Hz. In such a case, voltage variations with an amplitude of about 0.25 % of the nominal voltage can be annoying. Dynamic voltage fluctuationsare commonly called flicker. Flicker definition and evaluation is described in [16].The standardized quantities defined to represent flicker are the short time flickerseverity index - Pst and the long time flicker severity index - Plt. Flicker is evaluatedas demonstrated in Figure 2.3.

Figure 2.3: Flicker evaluation

The first part, the lamp-eye-brain chain model, is a mathematical way to emulate

the behavior of the mentioned incandescent light bulb and, consequently, its percep-tion by human eye and brain. The result of this model is called the instantaneousflicker level, IFL, and this is the quantity to be statistically evaluated. The statisticevaluation results are the Pst and Plt indexes.

Pst=1 means that the majority of humans will be annoyed by the flickering light.The relation between the frequency of the voltage variations and their amplitudefor Pst=1 is presented in Figure 2.4. The curve shown is obtained for sinusoidaldisturbances. There is also a curve corresponding to rectangular disturbances.

Dynamic voltage variations caused by wind turbines can be reduced either by usinga variable speed system instead of a fixed speed system or by a suitable control of the reactive power. More on this is in the following sections.

8



10−1

100

101

102

10−1

10

0

101

f [Hz]

d U

[ % ]

Figure 2.4: Flicker curve

2.2.3 Harmonic distortion

Voltages and currents in the electric grid are ideally pure sinusoidal functions. How-ever, when non-linear loads or power electronic devices, for example, are used, theydraw currents that are periodic but not purely sinusoidal and, as a consequence,the voltages also lose their purely sinusoidal shape. A periodic waveform can bedecomposed into a sum of harmonic functions with the frequency of the fundamen-tal periodic waveform and its integer multiples. A quantity describing the level of distortion in voltage and current waveforms is defined as the voltage total harmonicdistortion, THDU, and the current total harmonic distortion, THD I, respectively.

The definition of the THD according to [17] is:

THD =

nk=2 V

2k

V 1(2.2)

Where:

V1 RMS value of the fundamental componentVk RMS value of kth harmonics

n number of evaluated harmonics

When considering wind turbines with respect to harmonic distortion, only systemswith integrated PECs are of interest since a system without PECs is very unlikelyto cause any major problem of this sort.

2.2.4 Voltage transients

Connecting an induction machine and/or a capacitor bank is followed by a high

current. In the past, this has been a significant problem when turbines were directlyconnected to a low voltage grid. Today, turbines are typically connected via atransformer to a grid with a higher voltage and the impact on the grid during the

9



start up of the turbine is less problematic. The voltage transients are still, of course,subjected to the standardized limits.

10



Chapter 3

Wind Turbine Systems

3.1 Basic overview

There are several wind turbine systems used today. Different configurations of thesystems mean, among the other aspects, that these systems also have different im-pacts on the electric grid, i.e. on its power quality. A discussion of different systemsis attached in Publication 1. Further discussion regarding various topologies of con-necting wind turbines to the electric grid and related control possibilities is presentedin Publication 3.

3.2 Blade aerodynamics

There are different aerodynamic power control strategies used today. To understandthe principal differences between these strategies it is suitable to study an overviewof blade aerodynamics as this gives an insight into aerodynamic control principles.

With reference to Figure 3.1, two main forces act on a blade. The lift force, L, isorthogonal to the wind speed acting on the blade, W, and it is the force characteristic

of an airfoil. The drag force, D, on the other hand, has the same direction as thewind speed acting on the blade and it is the force characteristic of any body placedin an air flow. All of these forces are quadratic functions of wind speed and theirsize is strongly influenced by the airfoil shape and by the angle of attack, α, theangle under which the blade experiences the wind, W.

Where:

WS free wind speedW wind speed acting on the bladeL lift force

D drag forceα angle of attack

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Figure 3.1: A wind turbine blade

Once the shape of the airfoil is given, wind speed and the angle of attack decide thesize of the two mentioned forces. Figure 3.2 shows the lift and drag coefficients C L

and CD, respectively, as functions of the angle of attack for a chosen blade profile.

0 10 20 30 40 500

0.5

1

1.5

angle of attack [deg]

l i f t a n d

d r a g

c o e f i c i e n t s

CL

CD

Figure 3.2: Lift and drag coefficients as functions of the angle of attack.

The air flow around the blade is, for the presented blade profile, fairly laminar upto the angle of attack at about 10 deg. The drag force coefficient is very low in thisregion. When the angle of attack reaches the value of about 15 deg the air flowon the trailing edge of the blade becomes more turbulent and the value of the liftcoefficient decreases as a consequence of this effect, which is called stalling. Thedrag force coefficient now starts to increase.

The lift and the drag forces transformed into another coordinate system introduce

the edge force, FE, and the flap force, FF. The edge force creates the shaft torquewhile the flap force introduces the thrust on the turbine. The edge and the flapforces are presented in Figure 3.3 for low and high angles of attack. Their relations

12



to the lift and the drag forces are described in Equations 3.1 and 3.2, respectively.

Figure 3.3: Forces on a blade

F E = L cos(ϑ)−D sin(ϑ) (3.1)

F F = L sin(ϑ) + D cos(ϑ) (3.2)

Where:

FE edge forceFF flap forceϑ angle between free wind speed and tangential speed of a blade

segment

3.3 Aerodynamic power control

The force developed on a blade is a function of: free wind speed, turbine rotationalspeed and the blade pitch angle. These three quantities determine the angle of attack. Based on this fact, different control strategies can be introduced. It is,however, worth presenting first Figure 3.4 and Figure 3.5 which show the output

power from and thrust force on the turbine, respectively, as functions of free windspeed for different blade pitch angles. The turbine rotational speed has been keptconstant in this case. The results in Figure 3.4 and Figure 3.5 have been obtainedusing an NACA-63200 wind profile.

3.3.1 Stall control

When the pitch angle of the blade is constant, i.e. the blade is firmly attached tothe hub, only the stall effect, introduced in the previous section, controls the power.

Such a configuration reaches rated power only around nominal wind speed, as shownin Figure 3.4. The thrust force increases, however, with wind speed, as is illustratedin Figure 3.5.

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5 10 15 20 250

100

200

300

WS [m/s]

P [ W ]

0

1

2

3

4

10 15 20 25 30 35

nominal power

Figure 3.4: Power as a function of wind speed for different pitch angles

5 10 15 20 25−10

0

10

20

30

40

WS [m/s]

T h r u s t [ k N ]

0 − 4 10 15 20 25

30 35

Figure 3.5: Thrust as a function of wind speed for different pitch angles

14



The main advantage, here, is the fixed connection of the blades to the hub. This con-nection is a robust and less expensive option compared with the options introducedin the following sections.

A predestined power output for the whole operational wind speed range is, however,one drawback. The turbine does not produce rated power even when enough poweris available in the wind. Such a situation can occur for several reasons. The mostapparent one is operation at a wind speed higher than the nominal one. Anotherexample is a case in which the aerodynamic performance of the blades decreases dueto dirt on their surfaces. Finally, changes in air density, caused by variations in airpressure or in temperature, influence the power available in the wind, too, but theturbine cannot respond to these changes.

3.3.2 Active Stall control

In order to always produce rated power whenever it is available in the wind, activestall control can be employed. Another often used name for this aerodynamic controlprinciple is combi-stall control. Turbine blades are, in such a case, slightly pitchedduring high wind speed periods in order to obtain the desired nominal power. InFigure 3.4 a pitch angle between 0 - 4 deg represents the corresponding controlrange. The thrust is almost independent of these small changes in the pitch angle,as shown in Figure 3.5.

Active stall control enables better exploitation of the wind turbine system during

high wind speed periods. Moreover, the slope of the power curve for these high windspeed periods is such that a variation in wind speed will introduce a rather modestvariation in output power. Another advantage of the pitching method is that itmakes emergency stopping and starting of the wind turbine easier.

One drawback, however, is the need for a flexible connection of blades to the hub.

3.3.3 Pitch control

This control strategy is, in principle, the same as active stall-control; turbine bladesare pitched in order to obtain the desired power output. The objective in this caseis to keep a fairly laminar air flow around the blades for the whole wind speedoperational range and, in this way, minimize unwanted thrust loads on the system.The pitch angle now varies within a wider range, in Figure 3.4 this range is roughlybetween 0 - 35 deg.

The advantage is, again, better exploitation of the wind turbine system duringhigh wind speed periods. Another advantage is also a decrease in thrust on theturbine, for the presented data this is about one third of the thrust force acting on a

stall-regulated turbine close to maximum wind speed. Pitch control also facilitatesstarting and emergency stopping of the turbine in the same way as active stall-control.

15



One drawback, of course, is the need for a pitching mechanism. Another drawback isthe slope of the power curve at high wind speeds. As can be observed in Figure 3.4,even a small variation in wind speed introduces a large variation in output power.The pitching mechanism is not fast enough to avoid these power fluctuations [14].

3.4 Fixed-speed system

A fixed-speed wind turbine system is a simpler way of connecting wind power ontothe electric grid. Today, such a system uses an induction machine almost exclusivelyfor converting the mechanic power extracted from wind into electric power. Theinduction machine’s operational characteristics, together with its rather low priceand robustness, are the main reasons for this.

The stall and the pitch aerodynamic control strategies presented in the precedingsections have been used in combination with a fixed-speed system. A summary of advantages and drawbacks of these systems is presented below. A layout showing ageneral configuration of a fixed-speed system is shown in Figure 3.6.

Figure 3.6: Fixed-speed wind turbine - principal layout

With reference to Figure 3.6, apart from the turbine and the induction machine, afixed-speed system incorporates a gearbox. This is because the rotational speed of the turbine is always lower than the generator speed. An economically feasible mul-tipole induction machine design applicable to wind power applications has not beenfound so far, [30]. Another common part is the capacitor bank typically designed

to compensate for the induction generator no-load reactive power consumption. Fi-nally, a soft starter is a standard part of the system. It is used only during the startup of the turbine and it lowers the current when the turbine is being connected tothe grid. A wind turbine without a soft starter would draw a very high currentduring start up and the corresponding voltage drop in the grid would exceed thestated limits. Moreover, the gearbox would suffer from transient torques.

All fixed-speed systems have some common power quality problems. These arethe influence on static voltage level and on dynamic voltage variations and voltagetransients related to the connection of the turbine, such as magnetization of thegenerator and the connection of the capacitor bank [12].

The static voltage level problem is caused by the fact that the basic configurationof a fixed-speed system does not offer the potential to control reactive power con-

16



sumption. The impact on the static voltage level is, therefore, predestined and it issimply a function of the produced power, [19].

The impact on dynamic voltage variations depends on the aerodynamic control usedas does the voltage transient when the system is being connected to the grid. Finally,harmonic pollution to the grid is negligible since no power electronic converters areemployed.

A stall-regulated turbine in combination with a fixed-speed system has been verypopular due to its relatively low price, simplicity and robustness. The main advan-tages are: the mediocre impact on dynamic voltage fluctuations which has not beena major problem in most of the present installations. The voltage transient due tothe start up of the turbine is minimized by using a soft starter, however, the voltagetransient is not removed completely.

The use of active stall-control has recently become rather popular. It is likely to takeover the position established by the purely stall-regulated turbine, mainly for unitswith a high rated output power roughly over 1 MW. This configuration, basically,maintains all the power quality characteristics of the stall-regulated system. Theimprovement lies in better utilization of the overall system, due to the use of activestall-control. The flexible coupling of the blades to the hub also facilitates emer-gency stopping and start up and, therefore, extends the advantages. One drawback,however, is a higher price for the pitching mechanism and related controller.

Pitch-control in combination with a fixed-speed system has also been used. Themajor drawback with such a configuration is the higher impact on dynamic voltage

variations. This is because of the power curve slope discussed in subsection 3.3.3.The system, however, offers many advantages and it is used mainly in combinationwith the variable-speed systems that are discussed below. The main advantages of pitch-control are that it facilitates start up and emergency stopping and lowers themechanical loads on the whole wind turbine system. Power controllability has beenalready mentioned.

3.5 Variable-speed system

Since wind speed varies, the mechanical power on the generator shaft cannot bekept constant when the rotor speed is fixed. Furthermore, effects like tower shadow,an uneven distribution of wind speed over the rotor disc and mechanical oscillationsin the drive train contribute to variations in mechanical power. If, in principle, thegenerator runs at a fairly constant speed, as is the case for an induction machine,the major part of the mechanical power fluctuations will be transmitted into fluc-tuations in the electric output power. A variable-speed system, on the contrary,keeps the generator torque fairly constant and, consequently, it is the turbine speedthat changes. Variations in incoming power are absorbed by rotor speed changes.

The result is fairly constant electric power, i.e. without any significant variations.The variable-speed system must, on the other hand, incorporate a generator con-trol system that can operate with variable speed. To fulfill such a requirement,

17



power electronic equipment must be used. The types of generators used today areinduction and synchronous machines.

An aerodynamic power control principle almost exclusively used used in combination

with the variable-speed systems today is pitch control. The main advantage of sucha system is the decrease in load on the turbine drive-train. Since loads are decreased,the whole drive-train can be designed accordingly and the cost for the drive trainand mechanical suspension devices are, thus, also decreased.

3.5.1 An induction machine and rotor resistance control

A generator configuration used for limited variable-speed operation of a wind tur-

bine is an induction machine with variable rotor resistance. The stator winding isdirectly connected to the grid and the rotor circuit of the generator is equipped withpower electronic switches and resistors, all placed on the rotor. This configurationallows for control of rotor resistance and, consequently, provides variable-speed op-eration. One advantage of this scheme is the removal of the conventional slip ringsand brushes arrangement; the semiconductor switches being controlled via signalstransmitted from the stationary controller.

3.5.2 An induction machine with rotor converter

Another system used today employs an induction machine with a wound rotor. Therotor winding is connected to a PEC via slip rings and brushes. The stator windingof the generator is connected directly to the grid and the speed of the generatoris controlled by the PEC connected to the rotor. The PEC does not need to bedesigned for the generator rated power and its rating depends, principally, on thedesired speed range. Today, 30 % of the rated power is typically used in sizingup the PEC. Additionally, this configuration allows for control of reactive power.Figure 3.7 presents a sketch of this configuration.

Figure 3.7: Variable-speed system, induction machine with wound rotor

18



3.5.3 Induction machine with squirrel cage rotor

An induction machine with a squirrel cage rotor connected to the grid via a PECis also an alternative for variable speed operation of an induction machine. In this

case, the PEC must be designed for the full rated power of the system. The rangeof the variable-speed operation is, in principle, from zero to anything that the windturbine can handle. Reactive power controllability is a natural property of thissystem. Figure 3.8 presents a sketch of such a configuration.

Figure 3.8: Variable-speed system, induction machine with squirrel cage rotor

3.5.4 Systems with a synchronous machine

A synchronous machine connected to the grid via a PEC is the last possible config-uration discussed here for a variable-speed system. The PEC converts the variable-frequency generator voltage into the grid frequency. A synchronous generator di-rectly connected to the grid cannot be used due to the fact that sufficient dampingcannot be obtained. However, using a PEC controlled synchronous machine servesto damp mechanical oscillations. Reactive power controllability is a natural prop-erty of this system. A principal configuration of a variable-speed system with asynchronous machine is presented in Figure 3.9.

Figure 3.9: Variable-speed system with synchronous machine

The use of a synchronous machine offers the potential to make a good multi-poledesign [28], and thus avoid the use of a gear box. This is an important objective

since the gear box is a component that has tendency to break. Use of a permanentmagnet synchronous machine is becoming more common and this machine bringsfurther simplifications to the system, [28].

19



3.6 Comparison of power quality impact

Having reviewed the basic principles of the most common wind turbine systems usedtoday, their power quality impact on the electric grid will now be considered. An

overview of the power quality impact of different systems is summarized in Table3.1.

Table 3.1: Comparison of power quality impactU Pst THD Start up

SR-FSS uncontrolled mediocre - highASR-FSS uncontrolled mediocre - mediocrePR-FSS uncontrolled high - mediocreVSS-I uncontrolled mediocre - mediocreVSS-II controlled low mediocre / high low

To make Table 3.1 more readable the following abbreviations were used:

U steady state voltage impactPst dynamic voltage variations impact (flicker)THD harmonic distortion to the gridStart up voltage disturbances during the start upSR stall-regulated turbineASR active stall-regulated turbine

PR pitch-regulated turbineFSS fixed-speed systemVSS-I variable-speed system with the induction machine and

the rotor resistance controlVSS-II other variable-speed systems

Analyzing the content of table 3.1 enables identification of modeling requirementsfor a given wind turbine system.

3.7 Wind turbine model in grid simulation pro-

gram

When the steady state voltage level is of interest, the wind turbine outputs, activeand reactive power, can be described as functions of mean wind speed. In thegrid simulation program, they can simply be represented as sources of active andreactive power. Active power is given by the static power curve of the wind turbine,the relation between mean wind speed and the produced active power, while theamount of reactive power exchanged with the grid is decided according to the controlobjectives of the specific turbine.

For fixed-speed systems, as well as for a variable-speed system with an inductionmachine and rotor resistance control, the reactive power is a function of the active

20



power according to the P-Q relation of the generator used. No-load reactive powerconsumption is typically compensated for with a capacitor bank. For the othervariable-speed turbines, reactive power is independent of active power and can beput to an arbitrary value, often zero.

Dynamic voltage variations of such a magnitude that the Pst level on the grid couldbe substantially affected mainly originate in fixed-speed systems. A reasonablycorrect prediction of dynamic behavior up to a frequency of about 10 - 20 Hz is of interest.

A model of a stall-regulated, fixed-speed system is described in Chapter 5. A modelof an active stall-regulated turbine can be obtained by slightly modifying a stall-regulated model, since the characteristics of these two systems, with respect todynamic voltage variations, are fairly similar. A model of a pitch-regulated, fixed-speed wind turbine is more complicated. Since a pitch-regulated, fixed-speed system

gives rise to major problems with dynamic voltage variations, apart from largemechanical stresses, it is no longer installed to the electric grid and other systemsare used instead. A model of such a system is, thus, of little practical value.

Since variable-speed systems have, in most cases, a low impact on dynamic voltagevariations, generally far below the stated limits, dynamic voltage variations predic-tion models of these systems seem to be of little practical interest. Moreover, thebehavior of these systems is mainly dependent on the control algorithms used. Thesevary depending on the turbine manufacturer and are usually kept confidential.

High harmonic distortion is a problem that can occur when variable-speed systemsare used. However, with a properly designed harmonic filter, this problem can beavoided. Other parts of the wind turbine are of little practical interest here.

21



22



the sample and hold function, and finally to transform the signals from the analogto digital domain. The computer controls the adjustment of the data acquisitioncard, its filtering and sampling frequency, and stores the acquired data. A modem isnot necessary but it is a very valuable part of the system. The possibility for remote

checking and controlling the system is an important function in data acquisition atremote sites.

4.2 Bockstigen-Valar data acquisition

A project concerned with evaluating the power quality of a wind farm connected toa weak grid was conducted at the first Swedish off-shore wind farm situated close

to the south-west coast of the island of Gotland in the Baltic sea. There, five semi-variable, stall-regulated wind turbines, each rated at 500 kW, are connected to thegrid with a short circuit ratio, the ratio between the short circuit capacity of thegrid and the rated power of the wind power installation, of about 7.5. Figure 4.2presents the wind farm configuration.

Figure 4.2: Bockstigen-Valar wind farm

The wind turbines operate at variable-speed during low wind speed periods whenthe output power per turbine is up to about 100 kW. When there is a higher windspeed the turbines run at a fixed-speed. The PECs are used, in such a case, tominimize the power quality impact on the grid. A description of control objectives,performed data acquisition and main results together with conclusions can be foundin Publication 2, Publication 3 and Publication 4.

A general conclusion is that the Bockstigen wind park utilizes the existing linecapacity to the maximum without violating the stated power quality limits.

24



4.3 Alsvik data acquisition

A wind farm consisting of four 180 kW stall-regulated, fixed-speed turbines locatedon the island of Gotland was chosen for the collection of data to verify the stall-

regulated, fixed-speed system model. Figure 4.3 presents the Alsvik wind farmlayout, where the term d designates rotor diameter.

Figure 4.3: Alsvik wind farm

The location on the coast offers the potential for comparing the impact of differentwind conditions, less disturbed sea winds and more disturbed land winds, on the

outputs from the turbines. Moreover, the geometry of the wind farm, the placementof the turbines and the distances between them, further extends the range of possiblecase studies since different wake operations can be evaluated.

Each turbine is equipped with an induction generator and a capacitor bank. Allturbines share one common 400 V/10 kV transformer. Figure 4.4 presents theelectrical connection layout.

The data acquisition system has collected grid voltages and currents from turbinesWT2, WT3 and WT4; turbine WT1 broke down before the start of the test program.Wind direction and three wind speed signals, at the hub level and at the upper and

lower margin of the rotor swept area, were collected too. The sampling rate usedduring the data acquisition was an important option and had to be chosen withrespect to the purpose of the measurements.

25



Figure 4.4: Alsvik - grid connection

The main objective here was to evaluate the impact of wind turbines on dynamicvoltage variations. Frequency components up to 20 Hz are of interest when evaluat-ing Pst values. According to [26] frequency components up to 400 Hz are of interestwhen the dynamic voltage variations are to be evaluated. This would require a sam-pling frequency of about 1200 Hz. Since the storing capacity of the DAQ system isnot unlimited, an acceptable lower frequency had to be chosen.

Based on the results obtained during the Bockstigen-Valar data acquisition, Pub-lication 2, and on a comparison with a calibrated measurement system Siemensoscillostore P 513, a sampling rate of 256Hz was chosen. Figure 4.5 presents thecomparison of data acquired with the oscillostore and the data collected with the

data acquisition system and, consequently, evaluated according to the standards[16]. As can be seen, the results obtained from the data acquisition system followthe values given by the oscillostore very well.

0 50 100 1500

0.1

0.2

0.3

0.4

time [min]

P s t [ − ]

Figure 4.5: Pst comparison : solid line - data acquisition system, dashed line withdots - oscillostore

26



Chapter 5

Wind turbine modeling

Based on the discussion in the preceding sections the decision was made to de-velop a model of a stall-regulated, fixed-speed wind turbine system. The followingsections describe individual building blocks of the modeled system and simultane-ously present the results obtained for a specific wind turbine. Where appropriate,comparisons of measurements and simulations are shown.

5.1 Structure of the system

The model of the overall wind turbine system integrates several building blocks.Figure 5.1 shows a diagram representing the basic structure of the model.

Figure 5.1: A wind turbine model structure

As is seen, there is no controller or visible feedback loops in the presented systemstructure. The stall-regulated, fixed-speed system is self-controlled, i.e. its opera-tional characteristics keep the system running within operational limits without theneed for an external controller. The logic that controls starting up and shuttingdown of the turbine, as well as the protection devices, have no influence on thecontinuous operation of the system and they are, thus, not incorporated into themodel.

In the following sections, the individual model components are described.

5.2 Wind simulation

Continuous changes in wind speed are the main reason for power fluctuations inturbine output. The power in the wind is a cubic function of the wind speed and it

27



is important, therefore, to create a correct wind model if realistic results are to beobtained.

Wind is usually described by its frequency spectra. For instance, the Kaimal spectralmodel [20] used in this thesis is an example.

Mean wind speed and turbulence intensity are the quantities of interest when an-alyzing wind from the viewpoint of the power quality impact of a wind turbine onan electric grid. The turbulence intensity is defined as a standard deviation of thewind, WS, over its mean value as follows:

TI =std(WS)

mean(WS)(5.1)

The wind becomes turbulent when it passes obstacles in its way. Different terrain

profiles contain different kinds of obstacles and the quantity representing this prop-erty is a roughness of the surface, Z0. Some surface examples are the sea, low grassor forest. There is an empirical relationship between the roughness of the surfaceand turbulence intensity. This relationship can be found, for example, in the bookby Freris [18]. The roughness of the surface is an important parameter when windwith given turbulence intensity is to be simulated.

Figure 5.2 presents an example of frequency spectra of two measured wind profiles.

10−2

100

10−4

10−2

100

102

f [Hz]

W S [ m / s ]

Figure 5.2: Wind spectra, black trace - TI = 5 % , gray trace - TI = 20 %

Both wind profiles were obtained at the Alsvik measuring site with a mean windspeed, in both cases, of 10 m/s. The black trace represents wind with a turbulenceintensity of about 5 % (sea wind), while the gray trace represents wind with aturbulence intensity of about 20 % (land wind).

5.2.1 Single point wind simulation

A method for simulating wind speed at a single point has been presented by Persson[21]. A time series of wind with a given mean speed value and a turbulence intensitycan be created. The turbulence intensity is controlled by a choice of the surface

28



roughness and the height of the single point above the surface. An arbitrary samplingfrequency of the time series can also be chosen.

This approach [21] to simulate wind can be used for developing simple models.In this thesis, this model is designated as the simplified model. An example of acomparison of a frequency spectra of measured (black) and simulated (gray) windseries is shown in Figure 5.3.

10−2

100

10−4

10−2

100

102

f [Hz]

W S [ m / s ]

Figure 5.3: Wind spectra comparison - single point wind simulation, black - mea-sured, gray - simulated

The mean wind speed is 10 m/s and the turbulence intensity here is about 5%. Asis seen, the agreement between measurement and simulation is very good.

5.2.2 Wind field simulation

When a more detailed model of a wind turbine is to be developed, a simulationof the wind at one point is not sufficient. This is because the wind speed overthe whole rotor swept area is not constant; different blades and even different bladesegments are exposed to slightly different wind speeds. Winkelaar [22] have proposeda method that creates a time series of wind over a specified area, in the case of awind turbine this is the discretized rotor swept area. In this thesis, a model based

on the simulation of a wind field is designated as the advanced model. Longitudinal,lateral and vertical wind speed time series are created. Figure 5.4 shows an exampleof the rotor swept area discretization.

Figure 5.4: Wind field discretization

29



When simulating wind over the whole rotor swept area, a time series of wind foreach node of the discretization is produced. Knowing the number of blades andthe rotational speed of the turbine, a true time series of the wind acting on eachindividual blade segment can be determined. Details of this approach are described

in Publication 5. An example of a comparison of a frequency spectra of wind at afixed point and a frequency spectra of wind acting on a blade segment is presentedin Figure 5.5.

10−2

10−1

100

10−4

10−2

100

f [Hz]

W S [ m / s ]

Figure 5.5: Wind spectra comparison - wind field simulation, gray - wind speed ata fixed point, black - wind speed acting on a blade segment

Inspecting the frequency spectra of wind speed acting on an outer blade segment of any chosen blade reveals an important feature. In the frequency band corresponding

to the rotational speed of the rotor and its integer multiples, wind speed frequencycomponents are amplified. The data in Figure 5.5 correspond to a turbine rotationalspeed of 42 rpm which gives a frequency of 0.7 Hz. The frequency band amplifica-tion around this frequency is apparent. Multiples of this frequency band result inamplification across the whole upper frequency range.

The origin of the amplifications mentioned above is the uneven nature of windspeed distribution across the rotor swept area. Wind speed at a single point in therotor swept area is regularly experienced by the blade. Since wind speed at such apoint slightly changes during one rotor revolution, it gives rise to the amplificationof the discussed frequency band instead of amplifying only one distinct frequencycomponent. This phenomenon applies to all points in the rotor swept area. Finally,the resulting wind speed acting on a blade is not a sinusoidal function and thereforeeven multiples of the basic frequency band can be observed.

5.3 Aerodynamic conversion

Knowing the longitudinal component of the wind speed acting on a blade segment,the speed of the blade segment, itself, and the blade pitch angle, the angle of at-

tack 1 can be calculated. Edge and flap forces are than calculated according to the1see page 11

30



momentum theory published in the work of Eggleston and Stoddard [23] and inthe work of Freris [18]. Blade profile aerodynamic data are, of course, a necessaryrequirement. When the edge forces on all blade segments are known, the torque oneach blade and the total shaft torque can be determined.

Lateral and Vertical wind speed components are also incorporated into determiningthe forces acting on the blades. It was observed, however, that there is no significantimpact on the power quality prediction capability of the overall wind turbine modeland, thus, a decision was taken to omit these two wind speed components in thepresented model.

The mentioned aerodynamic conversion approach does not, however, describe dy-namic features of aerodynamic conversion, such as dynamic hysteresis [27]. A dy-namic representation of aerodynamic conversion is not within the scope of this thesis.

Provided that the blade pitch angle and the rotor speed are fixed, the torque on ablade segment will be a function of wind speed. Instead of using the momentumtheory, an interpolation can be used to calculate torque from wind speed. Bothapproaches have been used and no detectable difference between obtained resultshas been found for wind speeds within the operational range of the wind turbine,i.e. 4 to 25 m/s. The momentum theory is not valid for wind speeds outside thisoperational range but these wind speeds are not of interest for the wind turbinemodel presented here.

Figures 5.6 and 5.7 show spectra of calculated torque on one blade and total shaft

torque, respectively.

10−2

10−1

100

101

100

101

102

103

f [Hz]

T [ N m ]

Figure 5.6: Spectra of a blade torque

The same phenomenon as the one discussed in section 5.2.2 is apparent here. Thefrequency spectra of blade torque exhibits the aforementioned frequency band am-

plifications. When a three-bladed turbine is used, the observed band amplificationsshift to new frequencies, which are three times the values of the original frequencies(Figure 5.7).

31



10−2

10−1

100

101

100

101

102

103

f [Hz]

T [ N

m ]

Figure 5.7: Spectra of a shaft torque

5.4 Drive-train model

A drive-train model represents the mechanical behavior of the turbine. In a verysimplified form, the model consists of turbine and generator inertia and the shaftconnecting them, as shown in Figure 5.8. The model is fully described in Equation5.2 and Equation 5.3.

Figure 5.8: Drive-train model

k∆ϑ + B∆ω = J GdωGdt

+ T G (5.2)

T T = J T dωT dt

+ k∆ϑ + B∆ω (5.3)

∆ω = ωT −

ωG

∆ϑ = ϑT − ϑG

Where:

TT, TG torque on the turbine and on the generator shaft, respectivelyωT, ωG angular speed of the turbine and of the generator shaft, respectivelyϑT, ϑG angle of the turbine and of the generator shaft, respectivelyJT, JG moment of inertia of the turbine and of the generator, respectivelyk stiffness of the shaftB damping of the shaft

Gearbox inertia is integrated into turbine inertia while gearbox softness is added toshaft stiffness. All parameters and quantities are referred to the high speed end of

32



the gearbox. This model represents the dominant drive-train frequency of the drive-train only. Models with a higher level of complexity can be found in the literature,the papers presented by Leithead [5],[6],[7] are some examples.

5.5 Generator model

A model of a generator is the last part of the overall wind turbine model. Inductionmachine models of varying complexity have been used here. A standard fifth ordermodel expressed in the d-q coordinate system presented by Kovacs [24] has beenused here as a reference.

us = Rsis + ddt

[Lsis + Lmir] (5.4)

0 = Rrir +d

dt[Lmis + Lrir] (5.5)

T G = pp · Im[(Lsis∗

+ Lmir∗)is] (5.6)

Ls = Lm + Lsλ

Lr = Lm + Lrλ

Where:

us stator voltageis stator currentir rotor currentTG developed generator torqueRs stator winding resistanceRr rotor winding resistance referred to the stator sideLm generator magnetizing inductanceLsλ stator leakage inductanceLrλ rotor leakage inductance referred to the stator sidepp number of pole pairs

Neglecting stator transients reduces the model to a third order as presented byRodriguez [25]. It has been shown in [29], however, that the third order model doesnot provide results accurate enough for dynamic voltage variation evaluation.

5.6 Simulation results

The model described in the thesis has been used to simulate the Alsvik wind turbine.

A technical description of the turbine is given in Appendix A. The details of theimplementation can be found in Publication 5. Some key results and the mainconclusions are presented below.

33



5.6.1 Comparison in frequency range, I

Figures 5.9 and 5.10 show a comparison of measured and simulated active andreactive power spectra, respectively. In these results, mean wind speed is about 10

m/s and turbulence intensity is about 10 %.

10−2

10−1

100

10110

0

102

104

f [Hz]

P [ W ]

Figure 5.9: Comparison of measured and simulated active power spectra, gray -measured, black - simulated

10−2

10−1

100

101

100

102

104

f [Hz]

Q [ V

A r ]

Figure 5.10: Comparison of measured and simulated reactive power spectra, gray -measured, black - simulated

It can be seen that the simulated results approximately follow the measured results.There are, however, some discrepancies observed in both active and reactive powerspectra comparisons. Starting with the lower frequencies, a discrepancy can beobserved in the frequency range of about 0.7 Hz. The simulated results have higheramplitudes compared with the measured ones. It has been found here that a smallerror in estimating drive-train parameters (e.g. the turbine moment of inertia orthe stiffness of the shaft) results in a significant error in the computation. Moreaccurate parameters of the drive-train and a more advanced drive-train model areof particular importance here if this disagreement is to be avoided or reduced.

Another difference can be found in the frequency band at about 1.1 Hz. Here, themeasured results have a higher amplitude. These frequency components originate

34



in the wind turbine tower oscillations as described by Thiringer [11]. To simulatethis phenomena, a tower model has to be developed.

Periodic power pulsations observed by Thiringer in [11] are completely missing inthe simulated results of Figures 5.9 and 5.10. These have not been simulated inthe presented model. Aspects like tower shadow, mass unbalance of blades, smalldifferences in the aerodynamic performance of the blades or gearbox characteristicsaffect these periodic power pulsations.

Finally, the discrepancy in the frequency band at about 1.5 Hz and generally acrossall the upper frequency components in the presented spectra are lower in the simu-lated results. A reason for this discrepancy is discussed below.

5.6.2 Comparison in frequency range, II

The latter discrepancy in the preceding section was subjected to further investiga-tions. Based on the work by Thiringer [9] the behavior of the induction machinewas studied. It has been found that the distorted torque on the generator shaft isnot the only source of the disturbances. The applied voltage on the generator alsoinfluences its output and this influence cannot be omitted.

The power quality of the Alsvik wind turbine site (the quality of voltage, in partic-ular) has been treated in Publication 6. Figure 5.11 presents an example of voltagespectra of the Alsvik site.

10−2

10−1

100

101

10−4

10−2

100

f [Hz]

U [ V

]

Figure 5.11: Voltage spectra at the Alsvik site

It is apparent that the voltage contains disturbances. A generator exposed to suchdisturbances produces active and reactive powers with a corresponding frequencycontent. Figure 5.12 and Figure 5.13 show a comparison of measured and simulatedactive and reactive power spectra, respectively, when the measured voltage is appliedto the generator model.

It is seen that the agreement between the measured and simulated results has beensignificantly improved. The improvement is especially apparent in the comparisonof reactive power spectra.

35



10−2

10−1

100

101

100

102

104

f [Hz]

P [ W ]

Figure 5.12: Comparison of measured and simulated active power, gray - measured,black - simulated

10−2

10−1

100

101

100

102

104

f [Hz]

Q [ V

A r ]

Figure 5.13: Comparison of measured and simulated reactive power, gray - mea-sured, black - simulated

36



5.6.3 Comparison of Pst impact

The model presented in this thesis has been developed to predict the Pst impact of astall-regulated, fixed-speed wind turbine on a grid. The main results are presentedhere for both simulation with applied constant voltage and simulation with appliedmeasured voltage from the Alsvik site.

Figure 5.14 presents a comparison of measurements and simulations as a functionof mean wind speed. The grid at Alsvik has a short circuit power of about 40 timesrated wind turbine power and the grid angle is 70 deg.

8 10 12 14 16 180

0.02

0.04

0.06

Wind speed [m/s]

P s t

[ − ]

Figure 5.14: Pst on 70 deg grid, * - measured, o - simulation with applied measured

voltage, square - simulation with applied constant voltage

Figure 5.14 illustrates the impact of the measured voltage on the results. Thesimulations with applied measured voltage agree very well with the measurements,while the simulations with applied constant voltage provide much lower values.

There is an important objective, however, that must be mentioned. The grid angle of 70 deg used above fits well the Alsvik generator parameters used in the simulations.A voltage disturbance originating in the active power flow through the grid resistanceis counteracted, to a large extend, by a voltage disturbance originating in the reactive

power flow through the grid reactance. This agreement between grid and machineparameters helps to obtain the presented good results.

Figure 5.15 presents the Pst impact on a grid with a 30 deg grid angle. It can beseen that the agreement between the measured and simulated results is not as goodas the one presented in Figure 5.14. Another important observation is that on sucha resistive grid the Pst values are much higher. The use of measured voltage is of secondary importance in such a case.

It is observed, however, that a significant part of the presented disagreement orig-

inates in the omission of periodic power pulsations. When these are removed fromthe measurements, the discrepancy between measurements and simulations becomessmaller, as is seen in Figure 5.16.

37



8 10 12 14 16 180

0.05

0.1

0.15

0.2

0.25

Wind speed [m/s]

P s t

[ − ]

Figure 5.15: Pst on 30 deg grid - I, * - measured, o - simulation with applied measuredvoltage, square - simulation with applied constant voltage

8 10 12 14 16 180

0.05

0.1

0.15

0.2

0.25

Wind speed [m/s]

P s t

[ − ]

Figure 5.16: Pst on 30 deg grid - II, * - measured, o - simulation with appliedmeasured voltage, square - simulation with applied constant voltage, x - measuredwith removed periodic power pulsations

38



5.6.4 Conclusions

The presented results demonstrate the model’s capability of predicting the powerquality impact of a stall-regulated, fixed-speed wind turbine on a grid. The ac-

tive and reactive power spectra comparisons, however, present some disagreementsbetween measurements and simulations.

For the presented wind turbine, the frequency components up to a frequency of about0.5 Hz originate mainly in the wind and the predicted results agree very well withmeasured results. The middle frequency components, within a range of 0.5 Hz to3 Hz, mainly originate in drive-train dynamics and in the aerodynamic conversionon the turbine blades. Finally, the upper part of the frequency spectra, aboveapproximately 4 Hz, is mainly influenced by generator dynamics and its response togrid voltage disturbances.

When the Pst impact on the grid is used as an instrument for model assessment,the impact should be evaluated on grids with different grid angles. A grid with aslightly dominant reactance is likely to yield a good comparison of measurementsand simulations, in the presented case the discrepancy is below 5 %. A grid witha dominating resistance gives, on the other hand, a higher discrepancy up to about25 %. It should be noted, however, that it is more difficult to compare the resultsof Pst on the resistive grid .

5.7 A simplified model

The wind generation part of the presented model plays a significant role. This is,however, the most time consuming part of the overall model of the wind turbine.Since the model is to be integrated into a grid simulation program, the computingrequirements have to be reduced to an absolute minimum.

One option is to store a pre-calculated torque time series corresponding to differentwind conditions and different wind turbine systems for later use. Another possibilityis to use an approach presented by Leithead [7], in which the wind is simulated at

one point only. For instance, the approach presented in Section 5.2.1 can be used,and consequently, modified with various aerodynamic filters. A resulting filteredwind can then be used in the same way as in the advanced model. An overview of aerodynamic filters is presented below.

5.7.1 Spatial filter

The first filter is referred to as a spatial filter, SF, and it serves to damp the higher

frequency components present in wind. This gives an adequate representation of therotor blades’ filtering properties. The transfer function of the spatial filter describedby Leithead [7] is:

39



H SF (s) =

√2 + bs

(√

2 + bs√a)(1 + b√

as)

(5.7)

b = γ R

WS

Where:

H SF spatial filter transfer functionγ the decay factor over the disc (γ = 1.3)R turbine radiusWS average wind speed at the hub heighta a=0.55

Some possible ways of simplifying this filter were investigated. The theoretical

work has shown that it is sufficient to use a first order transfer function withoutsignificantly affecting the characteristics of the spatial filter. The simplified transferfunction of the spatial filter is:

H SF (s) =1

sb + 1=

1s

2πf cut+ 1

(5.8)

The cut-off frequency of the spatial filter, f cut, is a critical parameter with a crucialinfluence on the model results. A way of obtaining the cut-off frequency is presentedin Section 5.7.4.

5.7.2 Rotational sampling filter

The second filter represents the rotational sampling of the wind caused by the rotorblades as they sweep the rotor disc, and is, therefore, called a rotational samplingfilter, RSF. This phenomenon was discussed in Section 5.2.2. Thus, this filter is onlyeffective within a limited frequency range. In other frequency regions, this filter hasa gain of near unity. The concept of the rotational sampling filter presented byRodriguez [8] has been adopted and simplified to:

H RSF (s) =1Ω2 (s + Ω)2

1(Ω2+(σΩ)2)

[s + (σΩ + jΩ)][s + (σΩ− jΩ)](5.9)

Where:

H RSF rotational sampling filter transfer functionΩ angular turbine speedσ damping factor

The damping factor of the rotational sampling filter, σ, is, again, a critical parameterwith a crucial influence on the model results. A procedure which determines thevalue of the damping factor is presented in Section 5.7.4.

40



5.7.3 Induction lag filter

There is one more aerodynamic filter mentioned in the literature [7], [8]. This isthe induction lag filter that represents the dynamic effect of an adjustment of the

wake in response to a change in wind speed. This filter has a unity gain in the lowfrequency region, but amplifies the whole higher frequency region of the wind speedsignal. This filter has, however, not been used in the presented simplified model.The reason is that the high frequency components of the power output of the windturbine are caused, to a very large extent, by grid voltage variations, as presentedin Section 5.6.2. Thus, the effect of the induction lag filter has a minor effect onperformance.

5.7.4 Parameter determination

The cut-off frequency of the spatial filter and the damping factor of the rotationalsampling filter, discussed above, are the key parameters to be determined here.Figure 5.17 presents the two mentioned filters together with their summation.

10−2

10−1

100

101

10−2

10−1

100

101

f [Hz]

g a i n

[ − ]

SF

RSF

SF+RSF

Figure 5.17: Aerodynamic filters

In order to determine the two filter parameters, a comparison has been made of results obtained from the advanced and the simplified approaches. The cut-off fre-quency of the spatial filter and the damping factor of the rotational sampling filterwere varied in order to find a minimum value of the error function 5.10.

error =2.5

f =0.5

[(logfTla(f )

fTls(f ))2

1

weight(f )] (5.10)

Where:

f frequencyfTla(f) amplitude of the advanced shaft torque frequency component

fTls(f) amplitude of the simplified shaft torque frequency componentweight(f) weighting coefficient for the frequency f

41



The frequency spectra of the shaft torque obtained from the advanced simulation,discussed in Section 5.2.2, and the frequency spectra of the shaft torque, obtainedfrom the simplified approach with aerodynamic filters, have been compared. Thedifferences in the results obtained by the two models were weighted by a correspond-

ing value from the flicker curve (Section 2.2.2) and consequently summed up overthe frequency range 0.5 to 2.5 Hz. In this frequency region, the two filters modifythe wind speed most in the case of the wind turbine used here. As was shown earlierin this thesis, (Section 5.6.2), the higher frequency components, above 2.5 Hz, aremainly influenced by the electric grid and, therefore, the disturbances from shafttorque are of secondary importance. The rotor blades have little influence on resultsin the low frequency region (below 0.5 Hz) and the filters, consequently, should notaffect these frequencies.

An example of this optimization process is shown in Figure 5.18.

0.2 0.3 0.4 0.5 0.60

500

1000

1500

f cut−off

[Hz]

e r r o r [ − ]

Figure 5.18: Filter parameters adjustment

Each point in Figure 5.18 represents a simulation with a specific cut-off frequencyand a specific damping. As is apparent, several results give an error with a valuevery close to the minimum error. The optimization process (see the error functionEquation 5.10), however, does not provide distinct values of the cut-off frequencyand the damping.

Using the optimization process described above, the values of the spatial filter cut-off frequency and of the rotational sampling filter damping were determined for

different wind speeds and turbulence intensities. They are presented in Figures 5.19and 5.20, respectively. The solid line represents 5 % turbulence intensity , the dashedline represents a turbulence intensity of 10 % and the dash-dotted line represents aturbulence intensity of 15 %.

5.8 Simplified model - results

A comparison of the results obtained from the advanced and simplified simulations

are presented below. The wind turbine model was simulated at a constant voltageand with the measured voltage applied to the generator. The comparison is madein the frequency domain and, consequently, the Pst values are also compared.

42



10 15 200.3

0.35

0.4

0.45

0.5

wind speed [m/s]

fc

u t − o f f

[ H z ]

Figure 5.19: Cut-off frequency as a function of wind speed, solid line - TI=5 % ,dashed line - TI=10 % , dash-dotted line - TI=15 %

10 15 200.1

0.12

0.14

0.16

0.18

0.2

wind speed [m/s]

d

a m p i n g [ − ]

Figure 5.20: Damping as a function of wind speed, solid line - TI=5 % , dashed line- TI=10 % , dash-dotted line - TI=15 %

43



Figures 5.21 and 5.22 present a comparison of the active and the reactive powers inthe frequency domain when constant voltage is applied to the generator model.

10−2

10−1

100

101

100

105

f [Hz]

P [ W ]

Figure 5.21: Active power spectra comparison - I, gray - the advanced model, black- the simplified model

10−2

10−1

100

101

10

0

105

f [Hz]

Q [ V

A r ]

Figure 5.22: Reactive power spectra comparison - I, gray - the advanced model,black - the simplified model

It has been observed that the simplified model results agree very well with theadvanced model results, up to a frequency of about 2.5 Hz. This is the frequencyrange where the spatial filter and the rotational sampling filter are tuned. Figures

5.23 and 5.24 present a comparison of the active and the reactive powers in thefrequency domain when the measured voltage is applied to the generator instead.

The influence of the measured voltage has now been clearly demonstrated. Whilethe reactive power comparison presents very good agreement, the active power com-parison shows a discrepancy in the frequency region between 2.5 to 5 Hz. Here, thesimplified model does not produce the same results as the advanced one.

The Pst impact as a function of wind speed is compared for the two grids used inSection 5.6.3. Figure 5.25 presents a comparison on the grid with a grid angle of 70deg while Figure 5.26 presents a comparison on the grid with a 30 deg grid angle.

These results confirm the conclusion of Section 5.6.4. The grid with a grid angleof 70 deg is less sensitive to model accuracy. The grid with a grid angle of 30 deg

44



10−2

10−1

100

101

100

105

f [Hz]

P [ W ]

Figure 5.23: Active power spectra comparison - II, gray - the advanced model, black- the simplified model

10−2

10−1

100

101

100

105

f [Hz]

Q [ V

A r ]

Figure 5.24: Reactive power spectra comparison - II, gray - the advanced model,black - the simplified model

8 10 12 14 16 180

0.02

0.04

0.06

Wind speed [m/s]

P s t

[ − ]

Figure 5.25: Pst on a 70 deg grid, * - the advanced model, o - the simplified model

45



8 10 12 14 16 180

0.05

0.1

0.15

0.2

Wind speed [m/s]

P s t

[ − ]

Figure 5.26: Pst on a 30 deg grid, * - the advanced model, o - the simplified model

shows the consequence of the discrepancy in Figure 5.23, i.e. the Pst values obtained

using the simplified model are somewhat higher.

46



Chapter 6

Conclusions and future work

6.1 Summary

A model of a stall-regulated, fixed-speed wind turbine system capable of predictingdynamic voltage variations in the connected electric grid has been presented andevaluated in this thesis. Reasons for modeling such a wind turbine system havebeen discussed.

Individual model building blocks have been introduced. Two different approachesfor simulating wind have been described. These approaches differ in computational

requirements, a more advanced approach is not suitable for time effective modelingof the system, but it is used as a tool to adjust the other, less time-consuming ap-proach. The other building blocks of the wind turbine model, the parts representingaerodynamic conversion, drive-train mechanics and the generator , are common toboth approaches.

6.2 Results evaluation

A comparison of the simulated results with field measurements has been shown. Thecomparison has been done in two steps. First, the frequency spectra of the acquiredand simulated results; namely the active and reactive powers, have been presented.Second, the results have been used to calculate dynamic voltage variations and,subsequently, the resulting Pst values were compared.

6.2.1 Advanced model

The differences between measured and simulated Pst values vary depending on the

character of the grid used for evaluation. While a grid with a grid angle of 70 degshows very good agreement with an error up to about 5 %, a more resistive gridwith a grid angle of 30 deg reveals the model’s imperfections (error up to 25 %).

47



It has been found that generator shaft torque disturbances are not the only sourceof the uneven power production of the turbine. Also, the quality of the grid voltagehas a significant impact on the model outcome. This is directly related to the gridangle. It has been shown, here, that use of constant voltage on a resistive grid (grid

angle of 30 deg) does not have a significant effect on accuracy. On the other hand, itis essential to use the actual measured voltage on the grid with a 70 deg grid angle.

6.2.2 Simplified model

The simplified model results have been compared with the advanced model results.Similar conclusions to the ones made above have been drawn. The results of thesimplified model are very similar to those of the advanced model for a grid with thegrid angle of 70 deg. The grid with the grid angle of 30 deg reveals, however, thatthe two presented models produce slightly different results.

6.3 Future work

Based on the knowledge gained during the model development and during the mea-suring and data evaluation, the author suggests the following for future work:

Extending the model to accommodate the effect of grid disturbances and/or faultswould increase its applicability and practical value. A further development of theelectric part of the model and, especially, its interaction with the connected electricgrid is, therefore, recommended.

A model implementation in a grid simulation program is another suggestion forfuture work. Models of other wind turbine systems based on the discussion inSection 3.7 are also recommended for future study.

An improvement of model accuracy might be an option for future work. The inclu-sion of aspect, such as the tower shadow effect, three dimensional wind simulation,dynamic description of aerodynamic conversion or an improvement of the drive trainmodel are issues of interest.

Finally, the sensitivity of the prediction performance of the model to the accuracyof system parameters is seen as a valuable study for the future. Wind turbineparameters with an acceptable accuracy are not always available and, thus, a rela-tion between the accuracy of system parameters and the accuracy of results is animportant issue to be studied.

48



Appendix A

Technical Data

A.1 Wind turbine data

location Alsvik wind farmIsland of Gotland, Sweden

rated power 180 kW

hub height 30 mrotor diameter 23.2 mnumber of blades 3rotor speed 42 r/minblade profile NACA-63200gearbox ratio 23.75

A.2 Drive train data

(all data referred to the high speed shaft)

turbine inertia JT 102.8 kg m2

generator inertia JG 4.5 kg m2

stiffness of the shaft k 2700Nm/radabsorption of the shaft B −

49



A.3 Generator data

nominal voltage Un 400 V number of pole-pairs p 3

stator resistance Rs 0.0092 Ωrotor resistance Rr 0.0061 Ω(referred to the stator)stator leakage inductance Lsλ 186 µH rotor leakage inductance Lrλ 427 µH (referred to the stator)magnetizing inductance Lm 6.7 mH

50



Appendix B

List of publications

Publication 1

Wind power stations - the impact on the electric grid, basic configurations and anexample of utilisation, Tomas Petru, The conference on Electric Power EngineeringELEN2000, Prague, Czech Republic, 25.-26.9.2000

Publication 2

Power quality impact of a sea-located hybrid wind park, T. Thiringer, T. Petru,C. Liljegren, accepted to the IEEE Transactions on Energy Conversion, 2001

Publication 3

Integration of wind parks - example from Bockstigen, T. Petru, T. Thiringer, NordicWind Power Conference NWPC’2000, Trondheim, Norway, 13.-14.3. 2000

Publication 4

Active flicker reduction from a sea-based 2.5 MW wind park connected to a weakgrid, T. Petru, T. Thiringer, 2000 IEEE Nordic Workshop on Power and IndustrialElectronics NORpie/2000, Aalborg, Denmark, 13.-16.6.2000

Publication 5

Measurement and modeling of power quality impact of a stall-regulated wind tur-

bine, T. Petru, T. Thiringer, the Electromotion journal, accepted for publication inJune 2001

Publication 6

Flicker contribution from wind turbine installations, T. Thiringer, T. Petru, S. Lund-berg, submitted to IEEE transactions on Energy conversion

51



52



Bibliography

[1] David A. Spera: Wind Turbine Technology, ASME PRESS (1994)

[2] A.I.Estanquiero, J.M. Ferreira de Jesus, J. Gil Saraiva, A wind park grid in-teraction model for power quality assessment, European Union Wind Energy

Conference, Goteborg, Sweden (1996)

[3] E.A. Bossanyi, P. Gardner, L. Craig, Z. Saad-Saoud, N. Jenkins, J. Miller,Design Tool for prediction of flicker, European Wind Energy Conference, DublinCastle, Ireland (1997)

[4] N. Jenkins, Z. Saad-Saoud, A simplified model for large wind turbines, Euro-pean Union Wind Energy Conference, Goteborg, Sweden (1996)

[5] W.E. Leithead, M.C.M. Rogers, Drive-train Characteristics of Constant SpeedHAWT’s: Part I - Representation by Simple Dynamics Models, Wind Engi-neering Vol. 20 No. 3 (1996)

[6] W.E. Leithead, M.C.M. Rogers, Drive-train Characteristics of Constant SpeedHAWT’s: Part II - Simple Characterisation of Dynamics, Wind EngineeringVol. 20 No. 3 (1996)

[7] J. Wilkie, W.E. Leithead, C. Anderson, Modelling of Wind turbines by SimpleModels, Wind Engineering Vol. 13 No. 4 (1990)

[8] Rodriguez-Amenedo J.L., Rodriguez Garcia F., Burgos J.C., Experimental Rig

to emulate Wind Turbines, International Conference on Electric Machines,Istanbul-Turkey, September - 1998

[9] T. Thiringer, Measurements and Modelling of Low-Frequency Disturbances inInduction Machines, Ph.D. thesis, Chalmers University of Technology 1996,ISBN 91-7197-384-2

[10] T. Thiringer, Power Quality Measurements Performed on a Low-Voltage GridEquipped with Two Wind Turbines, IEEE Transactions on Energy Conversion,September 1996

[11] T. Thiringer, J.-A. Dahlberg, Periodic Power Pulsations from a Three-bladedWind Turbine, IEEE Power Engineering Summer Meeting, 12-16 July, 1998

53



[12] A. Larsson, T. Thiringer, Measurements on and Modelling of Capacitor-Connecting Transients on a Low-voltage Grid equipped with Two Wind Tur-bines, International Conference on Power System Transients (IPST’95), Lisbon,Portugal, September 3-7, 1995, proceedings p. 184-188

[13] A. Larsson, P. Sørensen, F. Santjer, Grid Impact of Variable-Speed Wind Tur-bines, European Wind Energy Conference (EWEC ’99), Nice, France, 1-5 Mars,Proceedngs, p.786-789

[14] A. Larsson, The Power Quality of Wind Turbines, Ph.D. thesis, Chalmers Uni-versity of Technology 2000, ISBN 91-7197-970-0

[15] Anslutning av Mindre Produktionsanlaggningar till elnatet (AMP), Sverigeselleverantorer (1999), (in Swedish)

[16] International Electrotechnical Commission, IEC 61000-4-15, Flickermeter -

Functional and design specifications (11/1997)

[17] International Electrotechnical Commission, IEC standard, Publication 61000-4-7, Electromagnetic Compatibility, General Guide on Harmonics and Inter-harmonics Measurements and Instrumentation (1991)

[18] L.L. Freris, Wind Energy Conversion Systems, Prentice Hall International (UK)Ltd, 1990

[19] S. Lundberg, Electrical limiting factors for wind energy installations, Diplomathesis, Chalmers University of Technology 2000, ISSN 1401-6184

[20] Stochastic turbulence models, IEC(E) 61400-1/FDIS

[21] Erik Persson, One-dimensional wind simulation, Studies in statistical quality,control and reliability 1996:2, ISBN 992-273382-x

[22] Winkelaar D., Fast three dimensional wind simulation and the prediction of stochastic blade loads, 10th ASME Wind Energy Symposium, ASME 1991

[23] Eggleston D. M., Stoddard F.S., Wind Turbine Engineering Design, ISBN 0-442-22195-9

[24] Kovacs P.K., Transient phenomena in electrical machines, Elsevier, Budapest,1984

[25] Francis Dennis Rodriguez, A refined method of neglecting stator transients ininduction loads, Ph.D. thesis, Purdue University 1986

[26] International Electrotechnical Commission, IEC 61400-21, Wind Turbine Gen-erator Systems

[27] Stig-Øye A.F.M., Unsteady wake effects caused by pitch angle changes, ReportTech. Univ. of Denmark, 1986

[28] Anders Grauers, Design of Direct-driven Permanent-magnet Generators forWind Turbines, Ph.D. thesis, Chalmers University of Technology 1996, ISBN91-7197-373-7

54



[29] Vladislav Akhmatov, Hans Knudsen, Arne Hejde Nielsen, Jørgen Kaas Peder-sen, Niels Kjølstad Poulsen, Modelling and transient stability of large windfarms, 2nd International Workshop on Transmission Networks for OffshoreWind Farms, 2001, Royal Institute of Technology, Stockholm, Sweden

[30] Petri Lampola, Directly driven alternating current generators for wind powerapplications, ISBN 951-222826-2

55



Publication 1

Wind power stations - the impact on the electric grid, basic

configurations and an example of utilisation

Tomas Petru, The conference on Electric Power Engineering ELEN2000, Prague,Czech Republic, 25.-26.9.2000



Publication 2

Power quality impact of a sea-located hybrid wind park

T. Thiringer, T. Petru, C. Liljegren, accepted to the IEEE Transactions on EnergyConversion, 2001



Publication 3

Integration of wind parks - example from Bockstigen

T. Petru, T. Thiringer, Nordic Wind Power Conference NWPC’2000, Trondheim,Norway, 13.-14.3. 2000



Publication 4

Active flicker reduction from a sea-based 2.5 MW wind park

connected to a weak grid

T. Petru, T. Thiringer, 2000 IEEE Nordic Workshop on Power and Industrial Elec-tronics NORpie/2000, Aalborg, Denmark, 13.-16.6.2000



Publication 5

Measurement and modeling of power quality impact of a

stall-regulated wind turbine

T. Petru, T. Thiringer, the Electromotion journal, accepted for publication in June2001



Publication 6

Flicker contribution from wind turbine installations

T. Thiringer, T. Petru, S. Lundberg, submitted to IEEE transactions on Energyconversion

Pet Ru Tomas Lic

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