12 Wind Turbine Generator Modeling and Simulation Where Rotational Speed is the Controlled Variable

7/22/2019 12 Wind Turbine Generator Modeling and Simulation Where Rotational Speed is the Controlled Variable

1/8

IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 40, NO. 1, JANUARY/FEBRUARY 2004 3

Wind Turbine Generator Modeling and SimulationWhere Rotational Speed is the Controlled Variable

Lucian Mihet-Popa, Frede Blaabjerg, Fellow, IEEE, and Ion Boldea, Fellow, IEEE

AbstractTo optimize the power produced in a wind turbine,the speed of the turbine should vary with the wind speed. A simplecontrol method is proposed that will allow an induction machineto run a turbine at its maximum power coefficient. Various typesof power control strategies have been suggested for application invariable speed wind turbines. The usual strategy is to control thepower or the torque acting on the wind turbine shafts. This paperpresents an alternative control strategy, where the rotational speedis the controlled variable. The paper describes a model, which isbeing developed to simulate theinteraction between a wind turbineand the power system. The model is intended to simulate the be-havior of the wind turbine using induction generators both duringtransient grid fault events and during normal operation. Sample

simulation results for two induction generators (2/0.5 MW) vali-date the fundamental issues.

Index TermsAerodynamic model, drive train, induction gen-erator, soft starter.

I. INTRODUCTION

ONE OF THE simplest methods of running a wind gener-

ation system is to use an induction generator connected

directly to the power grid, because induction generators are the

most cost-effective and robust machines for energy conversion.

However, induction generators require reactive power for mag-

netization, particularly during startup, which can cause voltage

collapse after a fault on the grid. To overcome such stabilityproblems, the use of power electronics in wind turbines can be

a useful option. [4], [5], [9], [12]

The installation of wind turbines in power systems has devel-

oped rapidly in the last 20 years and the national and interna-

tional growth rates and policies indicate that this development

will continue. During 1999, 3920 MW of wind turbine capacity

was installed in the world, making up a total accumulated in-

stallation of 13 932 MW of wind power at the end of 1999 [1].

The system model proposed in this paper is devel-

oped in the dedicated power system simulation tools

MATLAB-SIMULINK and DIgSILENT, which give ac-

cess to an extensive library of grid components, but require

implementation of the relevant wind turbine model. The model

Paper ICPSD-TE 02070, presented at the 2002 OPTIM, Brasov, Romania,May 1618, and approved for publication in the IEEE TRANSACTIONS ONINDUSTRY APPLICATIONS by the Energy Systems Committee of the IEEEIndustry Applications Society. Manuscript submitted for review November 29,2002 and released for publication September 26, 2003.

L. Mihet-Popa and I. Boldea are with the University Politehnica ofTimisoara, RO-1900 Timisoara, Romania (e-mail: [email protected];[email protected]).

F. Blaabjerg is with Aalborg University, DK-9220 Aalborg East, Denmark(e-mail: [email protected]).

Digital Object Identifier 10.1109/TIA.2003.821810

Fig. 1. Simplified scheme of wind turbine model.

also includes wind speed fluctuations and control of a soft

starter, enabling simulation of the power quality characteristics

of the wind turbine. Finally, the model can be used to study

alternative control strategies for wind turbine and additional

equipment such as compensation units and storage systems.

II. WINDTURBINEMODELING

The purpose of the model is to simulate the dynamical be-

havior and the electrical properties of a wind turbine. The mod-

eling of the wind turbine should create a model as simple as

possible from a mechanical point of view, but capable of pro-

viding a good description of the electrical characteristics of awind turbine.

The wind turbine is characterized by the nondimensional

curves of the power coefficient as a function of both tip

speed ratio and the blade pitch angle . The tip speed

ratio is the ratio of linear speed at the tip of blades to the speed

of the wind.

In order to simulate the wind turbine as part of a distribu-

tion system, models have been developed and implemented in

MATLAB-SIMULINK and DIgSILENT for each element.

The wind turbine model consists of different component

models: wind model, aerodynamic model, transmission model,

and of the electrical components such as induction generator,

soft starter, capacitor bank, and transformer model [2].As shown in Fig. 1, the wind model generates an equiva-

lent wind speed , which, together with the blade pitch angle

and rotor speed , are input to the aerodynamic block.

The output of the aerodynamic model is the aerodynamic torque

, which is the input for the transmission system together

with the generator speed . The transmission system has

as output the mechanical torque on the high-speed shaft,

which is used as an input to the generator model. Finally, the

blade angle control block models the active control loop, based

on the measured power and the set point.

0093-9994/04$20.00 2004 IEEE


2/8

4 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 40, NO. 1, JANUARY/FEBRUARY 2004

Fig. 2. Wind fluctuation (m/s) as a function of time (s).

Fig. 3. Block diagram of the wind turbine.

A. Wind Model

The wind models describe the fluctuations in the wind speed,

which influence the power quality and control characteristics of

the wind farm. Thus, the wind speed model simulates the wind

speed fluctuations that influence the fluctuations in the power

of the wind turbines. The wind acting on the rotor plane of a

wind turbine is very complex and includes both deterministic

effects (mean wind, tower shadow) and stochastic variations due

to turbulence. [2]

Fig. 2 shows a simulation result of a wind speed as a function

of time, based on a lookup table, at an average of a wind speed

m/s.

B. Aerodynamic Model

A wind turbine is essentially a machine that converts the ki-

netic energy of the moving air (wind) first into mechanical en-

ergy at the turbine shaft and then into electrical energy [3].

Fig. 3 describes the conversion of wind power into

mechanical and thereafter into electrical power .

The interaction of the turbine with the wind is complex but

a reasonably simple representation is possible by modeling the

aerodynamic torque or the aerodynamic power as described

below.

The force of thewind creates aerodynamic lift and drag forces

on the rotor blades, which in turn produce the torque on the wind

turbine rotor [3].

The aerodynamic torque is given by

(1)

where is the aerodynamic power developed on the main

shaft of a wind turbine with radius at a wind speed and

air density . It is expressed by

(2)

The air density is dependent on the temperature and on the

pressure of the air.

The dimensionlesspower coefficient represents

the rotor efficiency of the turbine. It is taken from a lookup table,

which contains the specific aerodynamic characteristics for the

turbine.

This coefficient depends on the tip speed ratioand on the blade angle ; denotes the rotor

speed. For a constant-speed turbine, the power coefficient de-

creases when the wind speed increases ( small). This fact

is used in the passive stall control wind turbine.

The efficiency coefficient changes with different nega-

tive values of the pitch angle ( , , , ) but the best

efficiency is obtained for .

The aerodynamic model is based on curves for the given

rotor blades.

C. Transmission System Model

To describe the impact of the dynamic behavior of the windturbine, a simple model is considered, where the tower bending

mode and the flap-bending mode of the wind turbine are ne-

glected. It is assumed that all the torsion movements are con-

centrated in the low-speed shaft, as . Emphasis is placed on

the parts of the dynamic structure of the wind turbine, which

contribute to the interaction with the grid, i.e., which influence

the power. Therefore, only the drive train is considered in the

first place because the other parts of the wind turbine structure

have less influence on power.

The drive train model is illustrated in Fig. 4. The input to

the model is the aerodynamic torque. This is converted into the

torque on the low-speed shaft , which is further scaled down

through the gearbox to the torque on the high-speed shaft .The generator inertia is implemented as part of the generator

model, not as a part of the transmission system. The output of

the model is the torque on the high-speed shaft .

The rotor is modeled by inertia , low-speed shaft only

by a stiffness (the torsion damping is neglected), while the

high-speed shaft is assumed to be stiff. Thus, the transmission

is described by the following equations:

(3)

(4)


3/8

MIHET-POPA et al.: WIND TURBINE GENERATOR MODELING AND SIMULATION 5

Fig. 4. Drive train model in the wind turbine.

It is also assumed that the losses in the gearbox are zero, thus,

the gear transmits ideally from the low speed to high speed. The

output of the model is

(5)

where is the ratio of the gear box.

D. Induction Generator Model

The generator model is a combined mechanical and electro-

magnetic model. The mechanical model includes the inertia of

the generator rotor in the generator model.

The generator wind turbine is of the squirrel-cage induction

type. Based on the existing generator data, a preliminary study

has been made in MATLAB using the power system block-set

built in the induction machine model and a custom model,

simulating different dynamic behavior as seen in Fig. 5.

The equations used to build up the Matlab-Simulink induc-

tion machine model are

(6)

(7)

(8)

where the stator and the rotor fluxes have the following expres-

sion:

(9)

(10)

The parameters in these equations are as follows:, stator resistance and rotor resistance, respectively;

, stator and rotor leakage inductance;

magnetizing inductance;

speed of the reference system;

pole pairs of the machine

, stator and rotor current phasors

(Note:all the rotor quantities are reduced to the stator.)

Later, the induction generator was defined using the DIgSI-

LENT 12.0.116 built-in improved induction (asynchronous)

machine model [7]. The reasons why the built-in DIgSILENT

model (squirrel cage with current displacement) has been used

are as follows.

Fig. 5. Simulated torque, speed, and stator current transients versus timeduring generator startup. Turbine torque steps up at , fromfull-load torque: 13.050 N 1 m to pull-out torque: 38.000 N1 m.

Fig. 6. Induction machine model built up in DiGSILENT Power Factory [7].

1) Different cage rotors can be considered with rotor current

displacement.

2) The machine can be defined based on its measured

torqueslip curve, short-circuit test, and nameplate

values.

3) Electrical parameter variations can also be considered;

An eventual implementation of a new model in DIgSI-

LENT can be done by some controlled voltage sources and pa-

rameter variation cannot be considered, as there is no measured

data for that.

The built-in DIgSILENT model is presented in Fig. 6.

E. Soft-Starter Model

In order to reduce the transient current during connection of

generator to the 0.96-kV grid, a soft starter is used. When the

generator speed increases above the synchronous speed, the soft

starter is connected, and using firing angle control the generator

is connected over the grid.

In DIgSILENT, the soft starter is a stand-alone element.

The commutation devices are two thyristors connected in

antiparallel for each phase. A complete control in details of

the soft starter using the firing angle as input is possible just

in electromagnetic transient (EMT) simulation mode, where

every thyristor switching is modeled in detail, while the rms

simulation uses a simplified model (as a controlled voltage


4/8


source). The relationship between the firing angle and the

resulting amplification of the soft starter is highly nonlinear

and depends additionally on the power factor of the connected

element. In the case of a resistive load can vary between

0 (full on) and 90 (full off). While in the case of a purely

inductive load varies between 90 (full on) and 180 (full

off) . For any power factor in between, it will be somewhere

between these limits [8].

III. CONTROLBLOCK(TURBINECONTROLUNIT)

Wind turbines are designed to produce as much electrical

energy as possible. Wind turbines are therefore generally de-

signed so that they yield maximum outputat wind speedsaround

1215 m/s [3].

In case of stronger winds it is necessary to waste part of the

excess energy of the wind in order to avoid damaging the wind

turbine. All wind turbines are therefore designed with some sort

of power control such as pitch control or stall control.

Passive stall control relies on inherent machine characteristics

in the way that the aerodynamic power is limited when the windspeed increases.

Active stall constant speed combines the advantages of pas-

sive stall, namely simplicity due to the absence of a pitch mech-

anism, with the advantages of pitch control, namely, controlla-

bility. Thus, it provides additional control capabilities beyond

passive stall, required for offshore and large utility develop-

ments, while it makes it possible to avoid additional technical

complexity of pitch control turbines. [2], [3]

The control strategy used in the present paper involves the

combined interaction between wind model, pitch control, and

the aerodynamics of the wind turbine. The blade angle control

block models the active stall control of the wind turbine, based

on the measured power and the set point, where rotational speedis the controlled variable.

IV. SIMULATIONRESULTS

Simulation results on wind turbines with 2- and 0.5-MW in-

duction generators are presented. The scheme also presents a

case of load-flow simulation, when the wind turbine works at

nominal conditions and full power factor compensation is used.

In order to limit the starting current transients during the 2-MW

generator connections to the grid, a soft-starter startup is used.

The generators areconnected when thegenerator speed is higher

than the synchronous speed.

To simulate thewind turbine, models have been developed for

each element and implemented in the dedicated power systemsimulation tool DIgSILENT [7], which provides the ability to

simulate load flow, rms fluctuations, and transient events in the

same software environment. The DIgSILENT simulation tool,

therefore, has a dedicated model forinduction generators, which

takes into account the current displacements in the rotor, the

torqueslip, and short-circuit test curves. Also models of syn-chronous machines, transformers, bus bars, grid models, static

converters etc are provided.

Fig. 7 contains the grid representations from 50kVdouble-bus-bar systems down to the wind turbine. The wind

turbine contains the tower cable making the connection to the

0.96-kV/10-kV transformer and the 10-kV cable at the bottom

Fig. 7. Electrical diagram of 2.0/0.5-MW generators.

of the tower. The 10-kV cables are modeled using the existing

DIgSILENT model toolbox.

The power factor compensation units are represented by a

capacitor bank on this scheme and a static var system (SVS)

unit. The switching of capacitors is done as a function of average

value of measured reactive power. The generators are full-load

compensated.

The wind model describes the fluctuations in the wind speed

, which influences the power quality, and which gen-

erates a hub wind speed described in [10].

The simulations shown in Fig. 8 illustrate the effect of the

rotational sampling. This hub wind speed is used as input to the

rotor wind model to produce an equivalent wind speed ,

which accounts for therotationalsamplingon each of theblades.

The aerodynamic torque accelerates the

wind turbine rotor, with the generator disconnected from the

grid, until the rotor speed is close to its

nominal value. Then the generator is connected to the grid as

seen in Fig. 9. The basic idea is to control the rotational speedusing only measurement of the power (or torque), as it is de-

picted in Fig. 1 and by (1) and (2) as well.

Results for two induction generators (0.5 and 2 MW) are pre-

sented in Figs. 10 and 11. These figures contain traces of rotor

speed, current magnitude, and total active and reactive power

for startup of the wind turbine with directly connected induc-

tion generators at 1505 r/min (1.007 p.u.).

The starting current of the 0.5-MW machine is three times

higher than the rated current, while the starting current of the

large induction machine (2 MW) is eight times higher than its

rated value. It is clear that for the 2-MW machine it is imperative

to reduce the startup current.


5/8


Fig. 8. Rotor wind and hub wind model.

Fig. 9. Transmission model during startup. Aerodynamic torque (torque_rot), mechanical torque (torque_mec), generator speed (omega_gen), and rotor speed(omega_rot) of wind turbine system.

As can also be seen in Figs. 10 and 11, the induction

generators have a peak consumption of reactive power right

after connection to the grid. The reactive power is required to

magnetize the generators. The steady-state voltage is dependent

on the reactive power consumption of induction generator (IG).

Therefore, it is important to supply the IG with a reactive


6/8


Fig. 10. Startup with directly connected and operation of 0.5-MW induction generator. Speed, reactive power, current, and active power of the generator.

Fig. 11. Startup with directly connected and operation of 2-MW induction generator. Speed, reactive power, current, and active power of the generator.


7/8


Fig. 12. Startup with soft starter and operation of 2-MW induction generator. Speed, reactive power, current, and active power of the generator.

Fig. 13. Reactive power compensation with capacitors connected in steps and the soft starter bypassed controller (SS_controller: K ).


8/8


power compensation unit to provide the reactive power balance

and to improve the voltage stability.

In Fig. 12 the connection of the 2-MW generator to the grid

is realized by a soft starter. The soft starter limits the current and

torque transients and implicitly reduces the reactive power peak

value. When the induction machine of 2 MW was connected to

the grid through the soft starter, the starting current was reduced

to 1.1 times of rated current, while the reactive power peak be-came 13.5 times smaller than when the machine was directly

connected to the grid.

When the soft starter is bypassed and, thus, the 2-MW in-

duction generator is connected, the power-factor compensation

is performed by the capacitor bank (Fig. 13). It is also seen in

Fig. 13 how the capacitor banks are connected in steps after the

2-MW generator is connected to the grid. The capacitors can be

switched on and off individually as a function of average value

of reactive power during a certain period of time.

Very recently [11], the use of external resistances in series

with the induction machine has been proposed, instead of using

the conventional soft starter, to reduce the grid connection

transients of a constant-speed wind turbine. As the resistor

setup is cheaper and its reliability is greater, this alternative

method seems very practical. However, the flexibility brought

by the soft-starter capacity to perform the duty of an automatic

power switch with corresponding protection means should also

be considered.

V. CONCLUSION

A wind turbine model has been built to simulate the influence

on the transient stability of power systems. The model of the

wind turbine includes the wind fluctuation model, which will

also make the model useful to simulate the power quality and to

study control strategies of a wind turbine. The control scheme

has been developed for turbine control including soft-starterstartup and power-factor compensation.

The constant-speed wind turbine has to be operated at the op-

timum tip speed ratio, which givesthe maximum power transfer.

The comparative results between MATLAB-Simulink and

DIgSILENT show a good similarity during generator startup

and steady-state performance.

The computer simulations prove to be a valuable tool in pre-

dicting the system behavior.

The above-presented model can be a useful tool for the wind

power industry to study the behavior and influence of big wind

turbines on power distribution networks.

REFERENCES[1] International wind energy developmentWorld market update 1999,

BTM Consults Aps., Ringkobing, Denmark, 2000.[2] A. D.Anca D. Hansen, P.Poul Sorensen, L.L. Janosi, and J. Bech,Wind

farm modeling for power quality, in Proc. IEEE IECON01, vol. 3,2001, pp. 19591964.

[3] (2003) Guided Tour on Wind Energy. Danish Wind Turbine Manufac-turers Assoc.. [Online] Available: www.windpower.org

[4] E. Muljadi and C. P. Butterfield,Pitch controlled variable-speed windturbine generator,inConf. Rec. IEEE-IAS Annu. Meeting, vol. 1, 1999,pp. 323330.

[5] S. A. Papathanassious and M. P. Papadopoulus,Dynamic behavior ofvariable speed wind turbines under stochastic wind,IEEE Trans. En-ergy Conversion, vol. 14, pp. 16171623, Dec. 1999.

[6] A. Miller, E. Muljadi, and D. S. Zinger,A variable speed wind turbinecontrol, IEEE Trans. Energy Conversion, vol. 12, pp. 181186, June1997.

[7] DiGSILENT Power Factory user manuals, presented at the DiGSI-LENT GmbH Training, Aalborg Univ., Aalborg, Denmark, Aug. 1618,2000.

[8] G. Seguier, Power Electronic Converters-AC/DC Conversion. NewYork: McGraw-Hill, 1986.

[9] L. H. Hansen, P. Sorensen, and U. S. Paulsen,Variable speed wind tur-bine using full conversion, in Proc. of NORpie 2000, Aalborg, Den-mark, 2000, pp. 115119.

[10] P. A. C. Rosas, P. Sorensen, and H. Bindner,Fast wind modeling ofwind turbines,presented at theSpecial Topic ConferenceWind Power

for the 21st Century, Kassel, Germany, Sept. 2000.[11] T. Thiringer,Grid-friendly connecting of constant-speed wind turbines

using external resistors, IEEE Trans. Energy Conversion, vol. 17, pp.537542, Dec. 2002.

[12] F. Blaabjerg and Z. Chen,Power electronics as an enabling technologyfor renewable energy integration,J. Power Electron., vol. 3, no. 2, pp.8189, Apr. 2003.

Lucian Mihet-Popa received the B.S. and M.S.degrees in electrical engineering in 1999 and2000, respectively, from the University Politehnicaof Timisoara, Timisoara, Romania, where he iscurrently working toward the Ph.D. degree in the De-partment of Electric Drives and Power Electronics.

He was a Guest Researcher at Aalborg University,Aalborg East, Denmark, in 2000 and 2002. Hisresearch interests include control and modeling ofinduction machines and detection and diagnosis offaults, in particular, for wind turbine applications.

Frede Blaabjerg (M88SM97F03) received theM.S.and Ph.D.degreesin electricalengineeringfromAalborg University, Aalborg East, Denmark, in 1987and 1995, respectively.

He is currently a full Professor at Aalborg Univer-sity. He has visited universities in Italy and Australiaand has authored or coauthored more than 300published papers and coauthored the bookControl in

Power Electronics(New York, Academic, 2002). Hisresearch areas are in power electronics, static powerconverters, ac drives, switched reluctance drives,

modeling, characterization of power semiconductor devices and simulation,wind turbines, and green power inverters.

Dr. Blaabjerg is a member of the European Power Electronics and Drives As-sociation and the IEEE Industry Applications Society. He is an Associate Ed-itor of the IEEE TRANS.ONINDUSTRYAPPLICATIONS, IEEE TRANSACTIONS ONPOWERELECTRONICS,Journal of Power Electronics, and of the Danish journal

Elteknik. He became a member of the Danish Academy of Technical Sciencein 2001. In 2002, he became a member of the Board of the Danish ResearchCouncils. He has received four IEEE Prize Paper Awards.

Ion Boldea (M77SM81F96) received the M.S.

and Ph.D. degrees in electrical engineering from theUniversity Politehnica of Timisoara, Timisoara, Ro-mania, in 1967 and 1973, respectively.

He is currently a full Professor at the UniversityPolitehnica of Timisoara. He has visited universitiesin the U.S. and the U.K. repeatedly and has publishedextensively on linear and rotary electric machines,drives and power electronics. His latest books (withS.A. Nasar) are Electric Drives (Boca Raton, FL:CRC Press, 1998) and Induction Machine Handbook

(Boca Raton, FL: CRC Press, 2001). He is an Associate Editor ofElectricPower Components and Systems and Director of the Internet-only Journal of

Electric Engineering (www.jee.ro).Prof. Boldea is a member of the Industrial Drives and the Electric Machines

Committees of the IEEE Industry Applications Society (IAS) and wasCo-Chairman of the OPTIM International Conferences (IAS sponsored) in1996, 1998, 2000, and 2002.

12 Wind Turbine Generator Modeling and Simulation Where Rotational Speed is the Controlled Variable

Documents

Transcript of 12 Wind Turbine Generator Modeling and Simulation Where Rotational Speed is the Controlled Variable