Anaya Trans Tutorial Talk

Modelling and Controlof Wind Generation Systems

Dr Olimpo Anaya-Lara

TUTORIAL:Transmission and Integration of Wind Power Systems:

Issues and Solutions2nd International Conference on Integration of Renewable and

Distributed Energy ResourcesDecember 4-8, 2006, Napa, CA, USA

Dr Olimpo Anaya-Lara TUTORIAL: Control of Wind Generation Systems, 4 December 2006, Napa, CA, USA 2

Programme1. Introduction2. Wind turbine technologies3. Optimum power extraction from wind4. Dynamic model of the Doubly-Fed Induction Generator

(DFIG)5. Control of DFIG-based wind turbines

5.1. Provision of synchronising torque characteristic5.2. Short-term frequency control5.3. Provision of Power System Stabiliser (PSS)

6. Impact of wind farms on transient and dynamic stability7. PSS for a generic DFIG controller8. References


1. Introduction


Introduction Wind power is presently the most cost-effective renewable

technology and provides a continuously growing contribution toclimate change goals, energy diversity and security.

Integration of large amounts of wind power into electricity networksface however various strong challenges:

Technical characteristics of wind turbine technologies aredifferent from conventional power plants.

Wind intermittency Grid availability and reliability Grid Code compliance

Accurate modelling and control of wind turbine systems for powersystem studies are required to help solving these challenges


Wind turbine components

Combination of mechanicaland electrical systems

Mechanical:Aerodynamics and structural

dynamics

Electrical:Generator, power electronicconverters, control system,

protection equipmentSource: www.nordex-online.com


2. Wind turbine technologies


FSIG-based wind turbine

SCIG Soft-starter

Capacitorbank

NETWORK

Fixed-Speed Induction Generator (FSIG)-based wind turbines employ a squirrel-cageinduction generator directly connected to the network.

The slip (and hence the rotor speed) varies with the amount of power generated. In thisturbines the rotor speed variations are very small (1 or 2%).

The induction generator consumes reactive power and hence capacitor banks are used toprovide the reactive power consumption and to improve the power factor.

An anti-parallel thyristor soft-start unit is used to energise the generator once its operatingspeed is reached.

Power control is typically exercised through pitch control.


DFIG-based wind turbineWound-rotor

Induction generator

PWM converters

Network

Crowbarprotection

Doubly-Fed Induction Generator (DFIG)-based wind turbines employ a wound rotorinduction generator with slip rings to take current into or out of the rotor.

Variable-speed operation is obtained by injecting a controllable voltage into the rotor atslip frequency.

The rotor winding is fed through a variable frequency power converter. The powerconverter decouples the network electrical frequency from the rotor mechanical frequencyenabling the variable-speed operation of the wind turbine.

The generator and converters are protected by voltage limits and an over-currentcrowbar.


Wide-range SG wind turbine (SGWT)

GeneratorPower

converter Network

Gearbox

GeneratorSide

ConverterNetwork

SideConverter

This wind turbine uses a synchronous generator (it can either be an electrically excitedsynchronous generator or a permanent magnet machine.

The aerodynamic rotor and generator shafts may be coupled directly, or they can becouple through a gear box.

To enable variable-speed operation, the synchronous generator is connected to thenetwork through a variable frequency converter, which completely decouples thegenerator from the network.

The electrical frequency of the generator may vary as the wind speed changes, while thenetwork frequency remains unchanged.

The rating of the power converter in this wind turbine corresponds to the rated power ofthe generator plus losses.


3. Optimum power extractionfrom wind


Optimum power extraction from wind

Power in the airflow:

312airP AU=

Power extracted by the wind turbine rotor:

wt p airP C P= Where: : Air densityA : Area swept by the bladesU : Wind speedCp : Power coefficient

max 0.593pC = (Betz limit)

The turbine will never extractmore than 59% of the powerfrom the airflow

WIND


00.10.20.30.40.5

0 5 10 15 20Tip-speed ratio

C

p r RU =

r is the rotor speedand R is the radiusof the rotorPower coefficient/Tip speed ratio curve

Tip speed ratio :

Operating a wind turbine at variable rotational speed it is possibleto operate at maximum Cp over a wide range of wind speeds

To extract maximum power r should vary with the wind speedsuch as to maintain at its opt

Optimum power extraction from wind


G

e

n

e

r

a

t

o

r

p

o

w

e

r

Generator speed

Rated power

Maximum Powercurve (Popt)

Speed Limit

U = 12 m/s

U = 10 m/s

U = 8 m/s

U = 6 m/sU = 4 m/s

U = 2 m/s

Speed

Rated power

Cut-inspeed

Speedlimit

Shut-downspeed

Powerset-point

In practice the rotor torque (power) is used as set-point anda speed controller is designed to maintain the operation ofthe generator at the point of maximum power extraction

Wind turbine power curve


4. Dynamic model of the Doubly-FedInduction Generator (DFIG)


Typical DFIG wind turbine

CONTROL SYSTEM Networkoperator

Gearbox

Crowbar

DFIG

PWM Converters

Windmill

PowerNetworkC1 C2

Wound rotorinduction generator


DFIG power electronic converters

Back-to-back voltage source converters (VSCs)Converter C1 Converter C2

DC-linkMachine

Side (rotor)Grid side(Machine

stator)

Graetz bridge (two-level VSC) IGBT-based Pulse Width Modulated (Sinusoidal, Space Vector PWM) Typical switching frequencies above 2 kHz Trade-off between switching frequency (losses) and harmonics


DFIG power relationshipsA DFIG system can deliver power to the grid through thestator and rotor, while the rotor can also absorb power. Thisis dependent upon the rotational speed of the generator

P

r > s

Super synchronousoperation

P

r < s

Sub synchronousoperation

s rs

s

=


DFIG power relationshipsMechanical

Input ElectricalOutput

Power throughthe slip rings

Rotorlosses

Statorlosses

mP _air gapP

rP

sP

mP : Mechanical power delivered tothe generatorrP : Power delivered by the rotor_air gapP : Power at the generators air gapsP : Power delivered by the stator

_air gap sP P=_air gap m r s

s m r

P P P PP P P

= ==

s r rT T P =

r s sP Ts sP= =g s rP P P= +

s rs

s

=Slip


Dynamic model of the DFIG Derive voltage and

flux equations for thestator and rotor inthe abc domain.

Transform voltageand flux equations tothe dq referenceframe.

Model the inductiongenerator as avoltage behind atransient reactance.

r

as-

as

arbs-

bsbr

br-cs-

cr-cr

cs

br axisbs axis

cr axiscs axis

as axis

ar axisar-

Stator winding

Rotor winding

Air gap

Schematic diagram of aninduction generator


Stator and rotorcircuits of an induction generator

: Stator resistance: Rotor resistance: Stator leakage inductance: Rotor leakage inductance: Magnetising inductance

srsrm

RRLLL

ss s mrr r m

L L LL L L

= +

= +

, : Stator and rotorself-inductances

ss rrL L

rotation

rasi

bsi

csi

ari

bri

cri

asvbsv

csv

arvbrv

crv,r rR L,s sR LmL


DFIG 3rd order model(voltage behind transient reactance)

( )emr TTJdtd =1

Stator voltages: Rotor voltages:

Voltage components:

Rotor swing equation:

'

'ds s ds qs d

qs s qs ds q

v R i X i ev R i X i e = + +

= +

md qr

rr

Le L =m

q drrr

Le L = mrmr

s XXXXXX

+

+='ms XXX +=

r

mr

r

rro R

LLRLT +== ( )

s

qsqdsde

ieieT +

=

Transient reactance's:

Open circuit time constant:

( )

( )

'

'

1

1

d md qs s q s qr

s o rrq m

q ds s d s drs o rr

de Le X X i s e vdt T Lde Le X X i s e vdt T L

= + = + +


Vector diagram of DFIG operating conditions

r$

d

q

sv

si

sjX i

rvi r

ri

e

( )[ ]1 ms s s rs o rr

Ld j X X j s jdt T L = + e e i e v

In steady state

r dr qrv jv= +v

0d dt =e

m rrr

Ls Le v

r sv e

e : internal voltage vectorvs: terminal voltage vectorBr : rotor flux vectorvr : rotor voltage vector


5. Control of DFIG-basedwind turbines


Decoupled active and reactive power control

The dq transformation allows the two rotorinjection voltages vqr and vdr to be regulatedseparately

Power control Voltage control

qrv

drv


DFIG current-mode control

+ - + +77

P

I

qrv_qr refi qrv

qri

s mm s

L LL v

+

spTeT

r

+-

+ +77

P

I

drv_dr refi drv

dri

7+ +

1s mL

vcK7+ -

s refv

sv

Voltage control loop:

Torque control loop:

Compensationterm

Compensationterm

Source: Ref [4]


DFIG rotor flux magnitude and angle control

ControllerA

angrefXCompensator

AuxLoop 3

3auxu2auxu

1auxu

Power SystemStabiliser

capabilities

AuxLoop 2

AuxLoop 1

Provision ofSynchronising Power

characteristic

NetworkFrequency

support

Speed(slip)

sVsrefV -+

ePerefP -+

AVRCompensator

magrefXrV Rotor

voltage

Flux and Magnitude Angle Controller (FMAC)Source: Ref [3]


Synchronous Generatorand DFIG vector diagrams

Round rotor synchronous generator Doubly fed induction generator

fd =rotor field flux vectorfd fdE =

Efd = dc field voltagetE =terminal voltage vectorgE =generator internal voltage

(voltage behind synchronousreactance)

sI =stator current vectorr = rotor angleXS = synchronous reactance

r =rotor flux vectorsV =terminal voltage vectorigE =generator internal voltage

vector (voltage behindtransient reactance)

isI =stator current vectorrV =rotor voltage vector

ig = generator load angleir = rotor voltage angleX = transient reactance

r

d

q

igE

sV

isI

isjXI

ig

ig

rVir

d

q

ssjXI

r

gE

tE

sI fd

Source: Ref [3]


FMAC basic scheme

-

rv

Polartodq

Transf.

ir

drv

qrv

7++-sV

refsV 7

-7++

-7 ippp

kk s+

impm

kk s+ ( )mg s

iapa

kk s+ ( )ag s

ivpv

kk s+ ( )vg s

AVR compensator

refe

FMAC Controller

E

ref

Controller AeP

erefP

Power-speed function formax. power extraction

11 fsT+

Filter

Source: Ref [3]

( ) 1 0.024 1 0.0351 0.004 1 0.05vs sg s s s

+ +=

+ +( ) ( ) 1 0.41 2m a

sg s g s s+

= = +


Auxiliary loop 1:Synchronising power characteristic

-

magrV

Polartodq

Transf.

angrV

rdV

rqV

7++-sV

refsV 7

+ + -7+7+

-7

_ig sync

_ig Tippp

kk s+

impm

kk s+ ( )mg s

iapa

kk s+ ( )ag s

slip

Auxiliary loop to provide power-angle characteristic

ivpv

kk s+ ( )vg s

AVR compensator

DfigrefE

Dfig

FMAC basic scheme

DfigE

Dfigref

Controller AeP

erefP

Power-speedfunction formax. Powerextraction

11 fsT+

Filter

slip

WashoutfilterIntegrator

12

11

sTsT

++

PhaseCompensator

2 ss 1

sTsT+

Source: Ref [3]


Auxiliary loop 2:Power System Stabiliser

-

m a grV

P o l a rt o

d qT r a n s f .

a n grV

r dV

r qV

7++-

sV

r e fsV 7

+ + -7+7+

-7

_i g Ti pp p

kk s+

i mp m

kk s+ ( )mg s

i ap a

kk s+ ( )ag s

A u x i l i a r y l o o p t o p r o v i d e P o w e r S y s t e m S t a b i l i s e r

i vp v

kk s+ ( )vg s

A V R c o m p e n s a t o r

D f i g r e fE

D f i g

F M A C b a s i c s c h e m e

D f i gE

D f i g r e f

C o n t r o l l e r AeP

e r e fP

P o w e r - s p e e df u n c t i o n f o r

m a x . P o w e re x t r a c t i o n

11 fs T+

F i l t e r

s l i p

2a u xus l i p

W a s h - o u t C o m p e n s a t o r

1s T

s T+ ( )2ag s

L i m i t e r

S o u r c e : R e f [ 3 ]

( )2

21 0 . 0 42 0 0 1 0 . 2a

sg s s+

= +


Auxiliary loop 3:Short-term frequency regulation

-

magrV

Polartodq

Transf.

angrV

rdV

rqV

7++-sV

refsV 7

+ + -7+7+

-7

2ig

1igippp

kk s+

impm

kk s+ ( )mg s

iapa

kk s+ ( )ag s

slipAuxiliary loop tofacilitate short-term frequency

support

ivpv

kk s+ ( )vg s

AVR compensator

DfigrefE

Dfig

FMAC basic scheme

DfigE

Dfigref

Controller A

eP

erefP

Power-speedfunction formax. Powerextraction

11 fsT+

Filter

Networkfrequency

2ig

1sT

sT+sf ( )1ag s ( )2ag s

- 7+

( )3ag s1sT

sT+

Shaping function

trefslip

tslip

r

Source: Ref [3]

( )1500

1 5ag s s

=+

( )23 4 . 5

1 5asg s s

+=

+

( )30 . 8 1 . 2

1 3asg s s

+=

+


6. Impact of wind farms on transientand dynamic stability


Generic network model

SynchronousGenerator

DFIGWind Farm

orsynchronous

generator

MainSystem

LoadZF

Fault 1

Generator 1 Generator 2

Source: Ref [3]


Conventional synchronous plant operation

Generator 1 (G1): Synchronous generatorGenerator 2 (G2): Synchronous generator

FAULT 1 applied at t=0.2 s. Clearance time 150 ms.

(a) Synchronousgenerator (G1)

(b) Synchronousgenerator (G2)

G1 G2

G3

Source: Ref [3]


DFIG with synchronising power characteristic

Generator 1 (G1): Synchronous generatorGenerator 2 (G2): DFIG with FMAC basic control



(b) DFIGwind farm (G2)

G1 G2

G3

Source: Ref [3]



scheme plus auxiliary loop 1.G1 G2

G3



(b) DFIGwind farm (G2)

DFIG with synchronising power characteristic

Source: Ref [3]


DFIG with PSS capability


scheme plus auxiliary loop 2G1 G2

G3


(a) Synchronousgenerator (G1) (b) DFIGwind farm (G2)

Source: Ref [3]


DFIG contribution to frequency regulation

Loss of generation applied at t=0.5 s.

(a) Main System (G3) (b) Synchronousgenerator (G2)

Generator 1 (G1): Synchronous generatorGenerator 2 (G2): Synchronous generator

G1 G2

G3

Source: Ref [3]


DFIG contribution to frequency regulation


scheme plus auxiliary loop 3G1 G2

G3

Loss of generation applied at t=0.5 s.

(a) Main System (G3) (b) DFIGwind farm (G2)

Source: Ref [3]


Influence ofwind generation on dynamic stability

installed capacity of generator G2 (MVA)Capacitor factor 2 maximum capacity of G2 MVA (2400 MVA)f =

2242402,5202,8001/10

7508002,5202,8001/3

1,5001,6002,5202,8002/3

2,2402,4002,5202,8001

G2Rating(MW)

G2Rating(MVA)

G1Rating(MW)

G1Rating(MVA)

G2f2

Operating situationsFixed power P1 of G1

G1(SouthernScotland)

G2(NorthernScotland)

Main System(England-Wales)

Load L1

Bus1 Bus2

Bus3

Bus4X1 X2

X3

Load

Eigenvalue analysis

Source: Ref [2]


Generator 2: Synchronous generator

Variation of dominant eigenvalue loci with generation capacityAVR Control AVR + PSS Control


Source: Ref [2]


Generator 2: Wind generation

Variation of dominant eigenvalue loci with generation capacity

FSIG-wind farm DFIG wind farm withcurrent-mode control


Source: Ref [2]


Generator 2: DFIG wind farm with FMAC control

Variation of dominant eigenvalue loci with generation capacityFMAC basic FMAC basic + PSS control



PSS for a generic DFIG controller

GenericDFIG

Control

srefV

erefP

drV

qrV Rectan.to polartransf. rangV

Polar torectan.transf.

drV

qrV

rmagV

PSSslip

+ +

PSSu

Source: Ref [5]


DFIG Power System Stabiliser

GenericDFIG

Control

srefV

e r e fP

d rV

q rV R e c t a n .

t o p o l a rt r a n s f . r a n gV

P o l a r t or e c t a n .

t r a n s f .

d rV

q rV

r m a gV

+ +

P S Sus l i p

W a s h o u t C o m p e n s a t o r

51 5

ss+

213 0 0 1 0 . 2 s +

L i m i t e r0 . 8

0 . 8

S o u r c e : R e f [ 5 ]


Control performance (transient stability)Generator 1 (G1): Synchronous generatorGenerator 2 (G2): DFIG

Fault applied at t=0.2 s with a clearance time of 150ms. (Full line:DFIG with PSS; dotted line: DFIG without PSS)

DFIG in super synchronousOperation (slip = -0.2)

DFIG in sub synchronousOperation (slip = 0.2)

G1 G2

G3

Source: Ref [5]


Control performance (dynamic stability)Generator 1 (G1): Synchronous generatorGenerator 2 (G2): DFIG

Operating situations

G1 G2

G3

675-1828570.2

2,3033751,928-0.2

TotalpowerOutput MW

ConverterpowerMW

DFIG Statorpower MW

Slip

Influence of PSS loop on thedominant eigenvalue for subsynchronous (s=0.2) and supersynchronous operation (s=-0.2).(With PSS ; without PSS C)

Source: Ref [5]


Reference for further reading1. P. Kundur: "Power systems stability and control," McGraw-Hill, 1994.2. O. Anaya-Lara, F. M. Hughes, N. Jenkins, and G. Strbac, Influence of wind farms on

power system dynamic and transient stability, Wind Engineering, Vol. 30, No. 2, pp.107-127, March 2006.

3. F. M. Hughes, O. Anaya-Lara, N. Jenkins, and G. Strbac, Control of DFIG-based windgeneration for power network support, IEEE Transactions on Power Systems, Vol. 20,No. 4, pp. 1958-1966, November 2005.

4. O. Anaya-Lara, F. M. Hughes, N. Jenkins, and G. Strbac, Rotor flux magnitude andangle control strategy for doubly fed induction generators, Wind Energy, Vol. 9. No. 5,pp. 479-495, June 2006.

5. O. Anaya-Lara, F. M. Hughes, N. Jenkins, and G. Strbac, Power system stabiliser for ageneric DFIG-based wind farm controller, paper accepted for publication at the IEEAC/DC Conference, March, 2006

Modelling and Controlof Wind Generation Systems

Dr Olimpo Anaya-Lara

TUTORIAL:Transmission and Integration of Wind Power Systems:

Issues and Solutions2nd International Conference on Integration of Renewable and

Distributed Energy ResourcesDecember 4-8, 2006, Napa, CA, US

Anaya Trans Tutorial Talk

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