A viable alternative to ADJUST SPEED over a wide range at MINIMAL COST

HE AIM OF WIND TURBINE SYS-

TEMS DEVELOPMENT is to contin-

uously increase output power. A few

years ago, the rated output power of

production-type units reached 200 kW. By 1999,

the average output power of new installations

climbed to 600 kW. The largest series production

units today are specified to deliver 1.5-MW output

power (Table 1). It is anticipated that in the near fu-

ture, power rating of wind turbines will increase fur-

ther, especially in offshore applications. For

example, the prototype of a Nordex N80 with a rated

power of 2.5 MW was installed in March 2000 near

Aachen.

Many low-power wind turbines built to-date were

constructed according to the “Danish concept” (Fig. 1),

in which wind energy is transformed into electrical en-

ergy using a simple squirrel-cage induction machine

directly connected to a three-phase power grid. The ro-

tor of the wind turbine is coupled to the generator shaft

with a fixed-ratio gearbox. Some induction generators

use pole-adjustable winding configurations to enable

operation at different synchronous speeds. However, at26

1077-2618/02/$17.00©2002 IEEE

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B Y S . M Ü L L E R ,

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& R I K W .

D E D O N C K E R

C

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FE

NR

ON

WIN

DG

MB

H

any given operating point, this Danishturbine basically has to operate at con-stant speed.

The construction and performance offixed-speed wind turbines very much de-pends on the characteristics of mechani-cal subcircuits, e.g., pitch control timeconstants, main breaker maximumswitching rate, etc. The response time ofsome of these mechanical circuits may bein the range of tens of milliseconds. As aresult, each time a gust of wind hits theturbine, a fast and strong variation ofelectrical output power can be observed.These load variations not only require astiff power grid to enable stable opera-tion, but also require a sturdy mechanicaldesign to absorb high mechanicalstresses. This strategy leads to expensivemechanical construction, especially athigh-rated power.

Adjustable Speed GeneratorsModern high-power wind turbines are ca-pable of adjustable speed operation. Keyadvantages of adjustable speed generators(ASGs) compared to fixed-speed genera-tors (FSGs) are:

� They are cost effective and providesimple pitch control; the control-ling speed of the generator (fre-quency) allows the pitch controltime constants to become longer,reducing pitch control complexityand peak power requirements. Atlower wind speed, the pitch angle isusually fixed. Pitch angle control isperformed only to limit maximumoutput power at high wind speed.

� They reduce mechanical stresses; gusts of wind canbe absorbed, i.e., energy is stored in the mechanicalinertia of the turbine, creating an “elasticity” that re-duces torque pulsations.

� They dynamically compensate for torque and powerpulsations caused by back pressure of the tower. Thisback pressure causes noticeable torque pulsations at arate equal to the turbine rotor speed times the num-ber of rotor wings.

� They improve power quality; torque pulsations canbe reduced due to the elasticity of the wind turbinesystem. This eliminates electrical power variations,i.e., less flicker.

� They improve system efficiency; turbine speed is ad-justed as a function of wind speed to maximize outputpower. Operation at the maximum power point can berealized over a wide power range. Fig. 2 illustratestypical output power-speed curves as a function of tur-bine speed and wind speed. As a result, energy effi-ciency improvement up to 10% is possible (Fig. 3).

� They reduce acoustic noise, because low-speed opera-tion is possible at low power conditions. 27

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TABLE 1. WIND POWER STATIONS CURRENTLY IN OPERATION WITHRATED POWER ABOVE 1.0 MW [1]

Manufacturer/Type

NominalPowerin (kW)

RotorControl

SpeedControl

RotorDiameter(m)

DeWind D6 1,250 Pitch Variable 64

AN BONUS 2,000 CombiStall Const 76

Nordex N80 2,500 Pitch Variable 80

Enron EW1.5s 1,500 Pitch Variable 70

Enercon E-66 1,800 Pitch Variable 70

Enron EW3.6 3,600 Pitch Variable 100

Pro&Pro MD70 1,500 Pitch Variable 70

Vestas V80 2,000 Pitch Variable 80

Pmech

PGen

ASG

Compensation

Grid

Fixed speed “Danish” concept.

1

Ele

ctric

al P

ower

P/P

N

1.2

1.0

0.8

0.6

0.4

0.2

00 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

Turbine Speed n/nN

Wind Speed

Pel

Electrical output power as a function of turbine speed. Pa-

rameter curves are plotted for different wind speeds. Maxi-

mum power point tracking (red curve) can be realized with

a speed variable system.

2

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In addition, most ASG-based wind turbines can offer is-land-operation capability. Island operation is difficult torealize with the Danish concept.

Direct-in-Line ASG SystemOne possible implementation scheme of ASGs is shown inFig. 4. A synchronous generator is used to produce vari-able-frequency ac power. A power converter connected inseries with the ASG transforms this variable-frequency acpower into fixed-frequency ac power. Although these di-rect-in-line systems have been built up to 1.5 MW, severaldisadvantages are apparent:

� The power converter, which has to be rated at 1 p.u.total system power, is expensive.

� Inverter output filters and EMI filters are rated for 1p.u. output power, making filter design difficult andcostly.

� Converter efficiency plays an important factor in to-tal system efficiency over the entire operating range.

Doubly Fed Induction Generator ASG SystemRecent developments seek to avoid most disadvantages ofdirect-in-line converter based ASGs. Fig. 5 shows an alter-native ASG concept that consists of a doubly fed inductiongenerator (DFIG) with a four-quadrant ac-to-ac converterbased on insulated gate bipolar transistors (IGBTs) con-nected to the rotor windings. Compared to direct-in-linesystems, this DFIG offers the following advantages:

� Reduced inverter cost, because inverter rating is typ-ically 25% of total system power, while the speedrange of the ASG is ±33% around the synchronusspeed (Fig. 6).

� Reduced cost of the inverter filters and EMI filters,becuase filters are rated for 0.25 p.u. total systempower, and inverter harmonics represent a smallerfraction of total system harmonics.

� Improved system efficiency; Table 2 shows the sys-tem losses for different windmill concepts. The lossesare shown separately for the generator and for theIGBT inverters. Approximately 2-3% efficiency im-provement can be obtained.

� Power-factor control can be implemented at lowercost, because the DFIG system (four-quadrant con-

verter and induction machine) ba-sically operates similar to asynchronous generator. The con-verter has to provide only excita-tion energy.

In addition, compared to silicon-con-trolled rectifier (SCR) based Kramerdrives [3], the DFIG with a four-quadrantconverter in the rotor circuit enables de-coupled control of active and reactivepower of the generator.

Dynamic Modelof a Doubly Fed InductionGeneratorTo develop decoupled control of activeand reactive power, a DFIG dynamicmodel is needed. The construction of aDFIG is similar to a wound rotor induc-tion machine (IM) and comprises athree-phase stator winding and athree-phase rotor winding. The latter isfed via slip rings. The voltage and torqueequations of the DFIG in a stationary ref-erence frame are:

{ }v r idt

jSj S Sj

Sj= ⋅ + =∂ψ

1 2 3, ,

(1)

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100%Power

Profit:Speed

Variation

Profit: Pitch Control

Reference: Stall,Constant Speed

Wind Speed

Efficiency gains due to adjustable speed wind turbines.

3

PGen

Filter

Grid

=

3~ =

3~

Pmech

Gear Box

SG

Direct-in-line wind turbine system.

4

Converter

Grid

PGen

s*PGens*PGen

3~

3~==

Filter

DFM

Doubly fed induction generator wind turbine system.

5

{ }′ = ′ ⋅ ′ + =v r idt

jRj R Rj

Rj∂ψ1 2 3, ,

(2)

Tp

id

del j

j

j

= ⋅ ⋅=∑

2 1

3 ψϑ

.

(3)

In these equations, all quantities are referred to thestator, i.e., transformed rotor quantities (superscript ′) areused. Transforming these equations from three-phase totwo-phase components and subsequently rotating all vari-ables into a synchronous reference frame (dq) according to

v

v v

vd = ⋅

⋅ + ⋅ − ⋅

+ ⋅ + ⋅

2

3

2

3

2

3

1 2

3

cos cos

cos

ϑ ϑ π

ϑ π

(4)

v

v v

vd = ⋅

− ⋅ − ⋅ − ⋅

− ⋅ + ⋅

2

3

2

3

2

3

1 2

3

sin sin

sin

ϑ ϑ π

ϑ π

(5)

yields

v v j vd q= + ⋅(6)

v r idt

jS S SS

S S= ⋅ + + ⋅ ⋅

∂ψω ψ

(7)

′ = ′ ⋅ ′ +′

+ ⋅ ⋅ ′v r idt

jR R RR

R R

∂ψω ψ

(8)

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S

is

isvs

vs

vb

vb

Xs

jXs si

Synchronous Machine-TypeEquivalent Circuit

i ′R

Maximum output power as a function of slip s (left) or

speed ratio n/n0 (right).

6

is is

is

jXs sσI

Xsσ X′Rσ′

XM

vm

vs

vs

IM

vMiMv R

s

Induction Machine-TypeEquivalent Circuit

i ′Ri ′R

′

Equivalent circuit and vector diagram of the (synchronous)

DFIG.

7

P/Pr

PS

PG

PGC

1

0.5

0.25

0.75

-0.25

PR

Slip–0.3–0.2–0.10.10.20.3

P/Pr

PS

PG

PGC

1

0.5

0.25

0.75

-0.25

PR

n/n01.31.21.10.90.80.7

Induction machine type equivalent circuit and vector diagram of the DFIG.

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ψS S S m RL i L i= ⋅ + ⋅ ′

(9)

ψR m S R RL i L i= ⋅ + ⋅ ′

(10)

{ }T p iel S S= − ⋅ ⋅ ⋅3

2Im

*ψ ,

(11)

with ω ω ωR S= − mech , the rotor slip frequency.The synchronous reference frame can be linked to the

stator or rotor flux of the machine. However, a referenceframe linked to the stator voltage space vector v S is a conve-nient alternative because the DFIG operates as a generatormaintaining or being fed with constant stator voltage [4].Hence, stator voltage and stator current are either given (lineoperation) or controlled (island operation) variables.

Two interpretations of the DFIG dynamic equations arepossible, depending on the state variables selected in the

model. A synchronous machine model is obtained when se-lecting the flux linked to the rotor currents [or back-elec-tromotive force (EMF) voltage] as a state variable.Selecting the air-gap flux (or magnetizing current) as astate variable invariably leads to an induction machine typemodel. This can be demonstrated easily for steady state.Both models give valuable insights on how the DFIGworks and can be controlled.

In steady-state and neglecting-stator resistance, thestator voltage (7) reduces to

V j L I VS S S S b= ⋅ ⋅ +ω(12)

V j L Ib S m R= ⋅ ⋅ ′ω .(13)

In (13), voltage vector V b represents the back-EMFvoltage induced in the stator by rotor current IR ′. This ro-tor current can be considered as the field current of the(synchronous) DFIG. The associated DFIG steady-stateequivalent circuit and vector diagram are shown in Fig. 7.

By selecting the magnetizing current as a state variable,the next steady-state equivalent circuit and vector diagramcan be found (Fig. 8).

In this induction machine-type equivalent circuit, a slips can be introduced, according to

s S

S

R

S

= − =ω ωω

ωω

mech .

(14)

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Decoupling Rotation

Rotation

Rotation

PWM

Control ofGrid SideConverter

PWM

+

+

-

-

QG Set

PG Set

VRdq VR

φ φVS r–

IRdq

VDC

IGCIR

PositionEncoder

φ φVS r–

+

-

φVS

φr

Calculationof Angle of

Voltage VectorISdq

Calculation ofActive and

Reactive Power

PG

QG

IS

VS

IN

Filter

Vector controller block diagram for DFIG.

9

TABLE 2. COMPARISON OF LOSSESOF DIFFERENT TURBINE SYSTEMS

Generator Inverter

DanishConcept

Cannot be constructed economi-cally, due to mechanical reasons.

Direct Line ca. 3.5 % ca. 3 %

DFIG ca. 3.5% ca. 0.75%

Neglecting rotor resistance and rotorleakage inductance, one can derive thatthe rotor voltage amplitude equals

V s a VR S≈ ∗ ∗SR ,

(15)

with a SR , the voltage-transformationratio between stator and rotor. This ra-tio is selected such that the voltage rat-ing of the four-quadrant convertermatches the stator voltage at maximumspeed to avoid transformers in the rotor circuit.

The active power delivered to the rotor by thefour-quadrant converter and the mechanical power deliv-ered to the shaft of the generator can be calculated accord-ing to the well-known IM equations

P s PR S= ∗(16)

( )P s PSmech = − ∗1 .

(17)

Both (14) and (15) clearly describe thepower flow in the DFIG for over-syn-chronous and under-synchronous opera-tion. Above synchronous speed, thefour-quadrant converter operates as agenerator of active power deliveringpower to the grid parallel to the DFIG.Below synchronous speed, thefour-quadrant converter circulates (by-passes) active power from the grid intothe rotor circuit. Fig. 6 illustrates theserelationships.

DFIG Vector ControlTo guarantee stable operation and enable independent con-trol of active and reactive power of the DFIG, amodel-based feed-forward controller is developed usingthe dynamic model equations mentioned above. A blockdiagram is shown in Fig. 9. Fundamentally, the proposedcontroller is a vector controller, because the synchronousreference frame in which the machine equations are de-scribed is linked to the stator voltage space vector v s andnot to the stator or rotor flux vector, as is common infield-oriented controllers for drives.

31

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IG [A

]

1000

1000

500

20 40 60 80 100

Grid Current

Time [ms]

Time [ms]

Time [ms]

IG1 [A]IG2 [A]IG3 [A]

IR [A

]

800

800

400

600

600

300

400

400

200

200

200

100

0

0

0

–200

–200

–100

–400

–200

–600

–300

–800

–400

–1000

–500

Rotor Current

IR1 [A]IR2 [A]IR3 [A]

0

0

100

100

200

200

300

300

400

400

500

500

Active Power

PG [kW]

PG

[kW

]

PG,Set [kW]

DFIG ac line current (top), rotor current (middle), output ac-

tive power command and instantaneous active power

(bottom).

10

Act

ive

Pow

er in

P.U

.A

ctiv

e P

ower

in P

.U.

2

2

1.8

1.8

1.5

1.5

1.2

1.2

1

1

0.8

0.8

0.5

0.5

0.2

0.2

0

0

–0.2

–0.2

0.1

0.1

0.2

0.2

0.3

0.3

0.4

0.4

0.5

0.5

0.6

0.6

0.7

0.7

0.8

0.8

0.9

0.9

1

1

0,7 NSyn0,8 NSyn0,9 NSyn1,0 NSyn1,1 NSyn1,2 NSyn1,3 NSyn

0,7 NSyn0,8 NSyn0,9 NSyn1,0 NSyn1,1 NSyn1,2 NSyn1,3 NSyn

Time [s]

Time [s]

(a)

(b)

Transient active power step response of DFIG. (a) Response

without decoupling at different speeds. (b) Response with

decoupling.

11

IT IS ANTICIPATEDTHAT THE POWER

RATING OFWIND TURBINESWILL INCREASE.

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All measured quantities, i.e., stator and rotor currenti S and i R , are transformed into the synchronous refer-ence frame. A decoupling circuit calculates from the de-sired active and reactive power signals the rotor voltagecommand v Rd and v Rq . A reverse vector rotation com-putes magnitude and phase of the rotor voltage com-mand in a stationary reference frame. Furthermore, themeasured rotor current signals are used for rotor currentregulation to minimize the effects of parameter detun-ing and inverter gain errors.

Simulation ResultsDetailed system simulations were performed to evaluatethe performance of the vector-controlled doubly fed gener-ator. Fig. 10 illustrates the DFIG line current, rotor cur-rent, and output active power. Notice the low THDcontent in the line current of the DFIG system.

To analyze system response and tune feedback parame-ters, an active power step response is simulated. Fig. 11(a)shows the response when the decoupling network is inac-tive, i.e., the machine is controlled using the basicsteady-state voltage model based on slip control. Note thatsystem performance depends on speed due to the couplingbetween d and q variables. Fig. 11(b) shows system re-sponse when decoupling is performed according to the dy-

32

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–80

–80

–80

–80

–60

–60

–60

–60

–40

–40

–40

–40

–20

–20

–20

–20

0

0

0

0

20

20

20

20

40

40

40

40

60

60

60

60

80

80

80

80

100

100

100

100

–20

–20

0

0

20

20

40

40

Frequency [Hz] (Field Coord.)

Frequency [Hz] (Field Coord.)

Frequency [Hz] (Field Coord.)

Frequency [Hz] (Field Coord.)

–360

–360

–270

–270

–180

–180

–90

–90

0

0

90

90

Mag

nitu

de [d

B]

Mag

nitu

de [d

B]

Ang

le [°

]A

ngle

[°]

_______ 0,7 NSyn_______ 0,8 NSyn_______ 0,9 NSyn_______ 1,0 NSyn_______ 1,1 NSyn_______ 1,2 NSyn_______ 1,3 NSyn

_______ 0,7 NSyn_______ 0,8 NSyn_______ 0,9 NSyn_______ 1,0 NSyn_______ 1,1 NSyn_______ 1,2 NSyn_______ 1,3 NSyn

(a)

(b)

Bode diagram of the rotor voltage to stator current IS/VR ad-

mittance. (a) Admittance IS/VR Bode plots without decoup-

ling. (b) Admittance IS/VR Bode plots with decoupling.

12

0

510

15

20

0 100 200 300 400 500 600t /s

Wind Speed m/s

1650170017501800185019001950

0 100 200 300 400 500 600t /s

Rotor Speed rpm

–4–202468

1012

0 100 200 300 400 500 600t /s

Pitch Angle °

020406080

100120

0 100 200 300 400 500 600t /s

Torque Set Value %

0

500

1000

1500

2000

0 100 200 300 400 500 600t /s

Output Power kW

(a)

(b)

(c)

(d)

(e)

Recorded waveforms on a 1.5 MW DFIG system. (a) Wind

speed. (b) DFIG rotor speed. (c) Pitch angle of turbine

blades. (d) DFIG controller output power command. (e)

DFIG measured output power.

13

namic model of the DFIG. The system’s response is quickand speed invariant.

The same performance improvement can be noticed inthe frequency domain. Small signal Bode plots for theI VS R ∗ transfer function (admittance) are shown in Fig.12 [(a) for slip control and (b) for decoupled operation].

The 3-dB bandwidth reaches ±20 Hz when decoupledcontrol is turned on. Note that a positive frequency indi-cates a rotation of the superimposed small signal space vec-tors in the direction of the fundamental component, i.e., ata frequency above 50 Hz. A negative frequency indicates asmall signal analysis with a frequency below 50 Hz. Onecan notice that the slip controlled DFIG has a strong de-pendency on speed.

Experimental ResultsMeasurements were made on a wind turbine system hav-ing a doubly fed Concycle generator produced by SEG,Germany. The rated power is 1.5 MW, and the ratedspeed is nr=1,800 rpm. Typical results are illustrated inFig. 13. The top trace shows variation of wind speed as afunction of time (elapsed time 0-600 s). Fig. 13(b) showsgenerator speed.

The main turbine controller aims at controlling speedusing pitch control [Fig. 13(c)]. Up to the time instantt=350 s, the pitch control is not very active because maxi-mum power is not reached. Hence, the main controllerseeks to maximize output power according to the maxi-mum efficiency curve shown in Fig. 4. Beyond 350 s, onecan see wind speed going up to approximately 15 m/s. Fig.13(d) shows that the wind turbine controller now limitsthe torque command at 100%. The actual output powerdelivered to the grid is shown in Fig. 13(e) and matches thecommand value perfectly.

Notice that in this constant, maximum power mode,the pitch controller sets the blades to keep speed withinbounds. At the time instance t=450 s, the elasticity of thevariable-speed DFIG wind turbine system is demon-strated. For a short while, wind speed rapidly reaches 17m/s. The pitch controller is not capable of following thisfast gust of wind. Hence, the speed of the turbine blades isallowed to increase storing energy into the turbine’s iner-tia. During this transient, output power remains practi-cally constant, avoiding power surges into the power grid.

SummaryThis article shows that adjustable speed generators for windturbines are necessary when output power becomes higherthan 1 MW. The doubly fed induction generator systempresented in this article offers many advantages to reduce

cost and has the potential to be built economically at powerlevels above 1.5 MW, e.g., for off-shore applications.

A dynamic model of the DFIG was derived to develop avector controller to decouple dynamically active and reac-tive power control. Simulations show excellent response ofthe DFIG independent of speed. Measurements obtainedfrom 1.5 MW units currently in operation confirm the the-oretical results.

AcknowledgmentThe authors would like to thank Tacke Windenergie,Salzbergen, Germany, for the measurements shown in Fig.13.

References[1] Windenergie (2001) [Online]. Available: http://www.

wind-energie.de/informationen/informationen.htm

[2] Q.N. Ph, Praxis der feldorientierten Drehstromantriebs-regelung. Ex-

pert Verlag, 1993.

[3] R.W. De Doncker, “AC-AC power converters,” in Wiley Encyclope-

dia of Electrical and Electronics Engineering, J. Webster, Ed. New

York: Wiley, 1999, vol. 1, pp. 13-25.

[4] T. Jahns and R.W. De Doncker, “Control of generators,” in The Con-

trol Handbook, W. Levins, Ed. Boca Raton, FL: CRC, 1996.

[5] D. Arsudis, “Doppeltgespeister Drehstromgenerator mit

Spannungszwischenkres-Umrichter im Rotorkreis für

Windkraftanlagen,” Ph.D. dissertat ion, Fakultät für

Maschinenbau und Elektrotechnik Technische Universität

Braunschweig, Germany, 1989.

[6] H. Späth, Steuerverfahren für Drehstrommaschinen: Theoretische

Grundlagen. Berlin, Germany: Springer-Verlag, 1983.

[7] H. Stemmler and A. Omlin, “Converter controlled fixed-frequency

variable-speed motor/generator,” presented at the IPEC ‘95, Japan.

[8] E. Bogalecka, “Dynamics of the power control of double fed induc-

tion generator connected to the soft grid,” in Proc. IEEE Int. Symp.

Ind. Electron., Budapest, 1993, pp. 509-513.

[9] H.K.. Lauw, C.H. Weigand, and D.A. Marckx, “Variable-speed

wind system design: Final Report,” U.S. Dept. of Energy, Washing-

ton, DC, Rep. DOE/BP/99893-TI, 1993.

S. Müller (s.mueller@newage-avkseg.com) and M. Deicke arewith SEG GmbH & Co. in Kempen Germany. Rik W. DeDoncker is with the Institute for Power Electronics and Electri-cal Drives in Aachen Germany. Deicke is a Member of theIEEE, and De Doncker is a Senior Member of the IEEE. Thisarticle first appeared in its original format at the 2000IEEE/IAS Annual Meeting.

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EE

.OR

G/

IAS