Control and simulation of doubly-fed induction generator Control and simulation of doubly-fed induction generator for variable-speed wind turbine systems based on an for variable-speed wind turbine systems based on an

integrated Finite Element approachintegrated Finite Element approach

Qiong-zhong Chen*, Michel DefournyQiong-zhong Chen*, Michel Defourny##, Olivier Brüls*, Olivier Brüls*

*Department of Aerospace and Mechanical Engineering (LTAS), University of Liège, Belgium

# SAMTECH Headquarters, Liège, Belgium

EWEA 2011, Brussels, Belgium

2

OutlineOutline

Background

Control of DFIG

Integrated simulation approach

Examples & validation

Conclusions

3

BackgroundBackground

Wind turbine concepts

Evolution of WT size:

Increased flexibility Increased coupling effects

(Data source: A. Perdala, dynamic models of wind turbines, PhD thesis, 2008)

WT types Gen. types

DFIG WTs DFIG

FSWTs SCIG

FCWTs PMSG, SCIG etc.

Other OSIG

Equipped gen. types

(Figure from EWEA factsheets)

4

BackgroundBackground

Computer-aided analysis for WT systems Software specialized in a certain field

Aerodynamics: AeroDyn etc. Structure: ADAMS/WT etc. Electrics: DIgSILENT etc.? Different systems on different simulation platforms?? No detailed coupling analysis

Integrated simulation packages: GH Bladed, Simpack Wind, HAWC2, FAST etc.

? Weak coupling (DLLs or co-simulation) ?? Numerical stability?

Need for integrated optimization tools (Bottasso, 2010)

5

BackgroundBackground

Samcef for Wind Turbine (S4WT) Nonlinear FE flexible multibody solver: SAMCEF/MECANO One single platform:

Aeroelastics, multibody, control, electrodynamics etc. Flexibility in blades, shafts, tower etc. Simulation approaches: Weak & strong coupling

An integrated model on S4WT(Courtesy: Samtech)

…

6

Highlights of the paperHighlights of the paper

Improved control strategies of DFIG WTs Grid-synchronization Power optimization

Strongly-coupled approach for mechatronic systems [B. & Golinval 2006]

Integrated structure-control-generator analysis on S4WT

Brüls, O. and Golinval, J. C. The generalized-α method in mechatronic applications. Zeitschrift für angewandte mathematik und mechanik (ZAMM) 86, 10 (2006), 748-758.

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Control of DFIGControl of DFIG

Working process of WT systems

Control of DFIG: soft grid connection power optimization

Gear box

Grid

AC/ DC

DC/ AC

SWs

SWg SWr

Transformer

DFIG

RSC GSC

Wind turbine

A schematic configuration of a DFIG wind turbine

E

A B

C

D

Power Optimization

Power Limitation

Win

d p

ow

er

Wind speed

0

Tu

rbin

e o

utp

ut

pow

er

Rotor speed

0 A

B

C

D, E Power Optimization

Power Limitation

8

Grid synchronization controlGrid synchronization control

Objective: Regulate stator voltage, frequency, phase angle

grid before connection

Method: Grid-voltage-oriented reference frame Vector control PI Controller designed based on internal model control

(IMC) method

+

_ Gr(s)

+ + qrVqr_refi qri

l r drs L i

+

DFIG

Cqr(s)

l r drs L i

_

FF term

+

_ Gr(s)

+ + drVdr_refi dri

l r qrs L i

_ DFIG

Cdr(s)

l r qrs L i

+

FF term

D,q-axis rotor current control loops

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Power controlPower control

Objective: Follow a pre-defined power-speed characteristics

profile speed regulation

Method Stator-flux-oriented reference frame

Vector control q-axis rotor current active power d-axis rotor current reactive power

IMC or pole placement method for design of controllers

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Power controlPower control

Power control scheme

Controllers: PI or IP regulators Design of controllers

PI : IMC method (current loop) IP : pole placement method (speed loop)

controller: CTω(s)

+

_

qr_refi

qri

qrvref

e_refT

dr_refi

dri

refQ drv

DFIG

controller: CiT(s)

controller: CiQ(s)

controller: Cvi_qr(s)

controller: Cvi_dr(s)

+

_

+

_

Decoupled speed and reactive power control of DFIG

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Design of controllersDesign of controllers

PI controller for q-axis rotor current i-v transfer function

PI controller on IMC

IMC parameter:

For electrical dynamics, the rise time is set to 10ms

1

( ) 1( )

( )qr

vi_qrqr

rs

I sG s

XV sR s

ω

1 1( ) ( ) rvi_qr qr

s

X RC s G s

s ω s

riseln 9 /= t

+

_ Cvi_qr(s) Gvi_qr(s)

¯ + qrVqr_refiqri

qrE

current control block

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Design of controllersDesign of controllers

IP controller for speed control Close-loop transfer function

Pole placement method

For over-damped systems:

For mechanical dynamics, the settling time is set to 1s, DFIG alone 2.5s, with WT system

+

_ Ki/s 1/(Js)

+ + e_refTref

Kp

+

_

mT

r

2

( )

( ) ( )ir

ref p i

K /Js=

s s + K /J s+ K /J

2

2p d nd

i nd

K = J

K = J

5.8nd sd= /t

Speed control block

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Integrated simulation approachIntegrated simulation approach

Strongly-coupled representation for mechatronic systems

Extended generalized-α solver Coupled 1st / 2nd order systems Second order accuracy Unconditional stability More details can be referred to [B. & Golinval 2006]

qMq Φ ( λ Φ) g(q,q, ) L y 0

Φ(q) 0

x f (q,q,q,λ, x, y, ) 0

y h(q,q,q,λ, x, y, ) 0

T ak p t

k

t

t

Mechanism

Control system

y ( , , , )q q q

Coupling in a mechatronic system

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Mechatronic Modelling on SAMCEFMechatronic Modelling on SAMCEF

Considerations for the Mechatronic modelling: Functional system decomposition Modularized, parameterized components

E.g. DFIG, PI, PID modules etc. Nodes are introduced for

Mechanical DOFs State variables Outputs

On a general-purpose use User-friendly Reusable

A uniform tangent matrix for Newton iteration

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Examples & validationExamples & validation

2MW DFIG parameters:

WT parameters:

Base voltage (line-to-line): Vbase= 690 V;Base power: Pbase= 2 MW;Grid frequency: fs= 50 Hz;Number of poles: np= 4;Stator resistance: Rs= 0.00488 p.u.;Rotor resistance : Rr= 0.00549 p.u.;Stator Leakage inductance: Lsl= 0.09241 p.u.;Rotor leakage inductance: Lrl= 0.09955 p.u.;Mutual inductance: Lm= 3.95279 p.u..

Inertia of the generator rotor: 100kg·m2

Blade length: 41m;Tower height: 75m;Gearbox ratio: 106Etc.

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Ex. 1:DFIG with defined input torqueEx. 1:DFIG with defined input torque

Simulation situation Synchronization process starts at 0.8

p.u. of the rotating speed

Reactive power reference: 0 p.u.

Speed (active power) control situation: Reference speed:

Input torque:

1 p.u., time 4sec

0.9 p.u., 4sec time 6sec

1.1 p.u., time 6sec

s

1 p.u., time 8.5sec

0.5time 5.25 p.u., 8.5sec time 9.5sec

0.5 p.u., time 9.5sec

mT

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ResultsResults

Grid synchronizationSynchronization starts

Synchronization finishes

A-phase grid voltage A-phase stator voltage

Grid synchronization process

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ResultsResults

Power controlSpeed response

Reactive power response

Rotor current response

iqr

idr

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Ex. 2: DFIG with WT structure modelEx. 2: DFIG with WT structure model

WT models on S4WT wind

8 m s, time 8sec

11 m s, time 8sec

/

/

Integration of DFIG with WT structure model on S4WT

Simulation situation: Initial WT speed:

1.1rad/s (0.74p.u.) Grid synchronization

starts at 0.8p.u. of generator speed

Reactive power reference: 0

Active power control according to wind speed:

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ResultsResults

Grid synchronizationSynchronization starts

Synchronization finishes

A-phase grid voltage A-phase stator voltage

Grid synchronization process

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ResultsResults

Power control

Active power

Reactive power

Schematic power-speed characteristics

Speed response

Power response

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ResultsResults

Influence of structural flexibility

With more rigid structure With more flexible structure

Generator torque

With more rigid structure With more flexible structure

Speed response

Blade Rigi. Flex.

Young’s module (Gpa) 100 30

Damping (N/m/s) 4.55e-2 4.55e-3

Shaft Rigi. Flex.

Bending stiffness (Nm/deg) 86.92 43.46

Bending damping (kg·m2/s) 0 0

Torsional stiffness (Nm/deg) 55.85 27.93

Torsional damping (kg·m2/s) 7858 785.8

Other applied elements: Flexible tower Simple gearbox, bedplate

elements etc.

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ConclusionsConclusions

Improved control strategies for DFIG Grid synchronization & power control Solution to the difficulty in the configuration of the

controllers’ coefficients

Integrated FE approach with strong coupling instead of weak coupling Unconditional stability, less intricacy Could be less efficient

Modular models of the generator/control systems for S4WT package (on a general purpose)

Integrated variable-speed DFIG WT system model analysis and validation

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In acknowledgement of DYNAWIND (grant number: 850533)

funded by Wallonia government, Belgium

Thank you for your Attention!