a non-linear control algorithm for improving performance of wind generator using doubly-fed...

A NON-LINEAR CONTROL ALGORITHM FOR

IMPROVING PERFORMANCE OF WIND GENERATOR

USING DOUBLY-FED INDUCTION GENERATOR

INSTITUTE OF ELECTRICAL POWER ENGINEERING

Chair Electric Drives and Basics of Electrical Power Engineering

M.Sc. Phung, Ngoc Lan

Athens, Feb/Mar.2006

A non-linear control algorithm for improving performance of wind generator using doubly-fed induction generator

Introduction

Conventional control of doubly fed induction machine (DFIM) in wind generator

Based on the continuous or discreet model of DFIM

Decoupling in active- and reactive power (P&Q) control

A voltage dip – what happened ?

A new control scheme !

Decoupling of P&Q is guaranted

Better performance in dynamical operation mode

Non-linear control of DFIM with Exact-Linearization

Current model of DFIM is able to be exactly linearized !

A new current controller is with only P-Type controllers

The complete control structure is simple.

Decoupling is guaranteed - „Direct-Decoupling“


Contents

1. DFIM – Model and its characters.

2. Conventional control of DFIM in wind generator

3. „Exact-Linearization“ – Concept and implementation with DFIM

4. Control structure with „Direct-Decoupling“

5. Conclusion and prospects


Control system of DFIM in wind generator

PM Powermodule; S Switch; L Inductor

Microcontroller

3~

3~

PM

3~

S

DFIM

n

PM

Transformer

L Udc

UsUn

Ir Is


Demonstration of voltage-, flux- and current vector in d-q coordinator

u ss sj

0,sd sq s

u , 0sd s squ u

u i

u i

ss ss s s

rr rr r r

dR j

dtd

R jdt

s sq

si

d q

si

si

sdi sqi

s

u s

sdu


' '

' '

'' '

''

1 1 1 1 1 1 1( ) ( )

1 1 1 1 1 1 1( ) ( )

1 1 1

1 1

rdrd r rq sd sq rd sd

r s s r m

rqr rd rq sq sd rq sq

r s s r m

sdrd sd s sq sd

s s m

sqrq s sd sq

s s

dii i u u

dt T T T L L

dii i u u

dt T T T L L

di u

dt T T L

di

dt T T' 1

sqm

uL

Electrical model of DFIM in d-q coordinator

2

1 m

s r

L

L L s

ss

LT

R r

rr

LT

R


u ,T

s sd squ u

1

2

BB

Br

rr

ur

21A

1Br

11A

i rird

dt

22A

12A

's

'sd

dt

u s1Bs

2Bs

Electrical model of DFIM in state-space

xAx B u B us s r r

d

dt

' ' 'x i , , , ,T T

r s rd rq sd sqi i

11 12

21 22

A AA

A A

u ,T

r rd rqu u

1

2

BB

Bs

ss

- Rotor angular speed: Input variable of the model

- Model of DFIM in state-space shows a bilinear system

r

11

1 1 1( )

A1 1 1

( )

rr s

rr s

T T

T T


Contents



3. „Exact-Linearization“ – Concept and implemetation with DFIM




' :ss

m

magnetizing currentL

Control variables of the active- and reactive power

232 ( i )

3

2

ssd sd sM

s

sd sd

s

p u i Rm

u ip

2 2 2cos

isd sd

s sd sq

i i

i i

' 0ssd sd rd

m

Li i

L

' 'ssq sq rq s

m

Li i const

L

The active power P and reactive power Q will be separately controlled through ird and irq

d

q

u s

'

s

ir

sqi

sdi

rqi

rdi

is

'

sq

sdu


A control structure of DFIM in wind generator

From DC link

Udc

kt

lt

mtDFIM

Griduvw

rau

rbuj re

rdu

rqu

Current Controller

*rdi

*rqi-

-

DNW

*Gm

Gm

*

IE

LAuNd su

N

rdi

rqi

FPT

rdi

rqi

sdi

sqi

N

n

Gm

r

'sq

r

Torque&Power factorController

-

-

- DNW: Decoupling NetWork- PWM: Pulse Width Modulation- LA: Line voltage Angle acquisition- GC: Generator side Converter

GC

PWM

- FPT: Flux, Power factor and Torque Calculation- dq: line voltage oriented reference frame- αβ: stator fixed reference frame- ab: rotor fixed reference frame

sdi

sqi

, ,rk l mi

, ,su vwi

Nuvu

Nvwu

j re

3

2

rai

rbi

3

2

si si

Nje

sdqi'sq


Contents



3. „Exact-Linearization“ – Concept and

implementation with DFIM




Why do we apply „Exact-Linearization“ ?

• The nonlinear characters of DFIM

• Exact linearization guarantees not only the linearity between inputs and outputs but also the decoupling between each pair of input and output variable in the new model ---> ‚noninteracting‘

• Performance of system in dynamical operation mode should be improved

• With the success of exact-linearization, different methods to design controllers for the new linear model could be applied.


„Exact-Linearization“ – the concept (1)

• Given a nonlinear MIMO-System with m inputs and m outputs

xf (x) H(x)u

y g(x)

d

dt

1

u ;

m

u

u

1

x ;

n

x

x

1

y

m

y

y

1 x

f x

xn

f

f

1 x

g x

xm

g

g

1 2H(x) h (x) h (x) h (x)m

• then it is able to transfer the system in another state-space, where the linearity between the inputs and outputs is guaranted.

Matrix L is invertible

1 1

1

1

1 11 1

1 1

(x) (x)

L x

(x) (x)

m

m m

m

r rh f h f

r rh f m h f m

L L g L L g

L L g L L g

• when the following conditions are satisfied:

Sum of elements of vector of relative degree

1 2r mr r r n :n

:jr

Number of state variables

Relative degree j-th


„Exact-Linearization“ – the concept (2)

• With a coordinator transformation

1

1

11 1

1 111

1

1

x x

x x

z m x

xx

xx m

m

rr f

mmn

rmf mr

m g

m L gz

gz m

L gm

• And with a state feedback controller

1u a(x) L (x)w

• The new linear system will be

zAz Bw

y Cz

d

dt

• A coordinator transformation

• Requirements of knowing the feedback of state variables

• The linearity between inputs and outputs is effective in the whole new state-space

Notice

xu

x

zAz Bw

y Cz

d

dt

Linear system

yw

Nonlinear system

1a(x) L (x)w xf (x) H(x)u

d

dt g(x)


' '

' '

1 1 1 1 1 1 1( ) ( )

1 1 1 1 1 1 1( ) ( )


r s s r m

rqr rd rq sq sd rq sq

r s s r m

rr

dii i u u

dt T T T L L

dii i u u

dt T T T L L

d

dt

„Exact-Linearization“ – Implementation with DFIM

Considering three equations of DFIM

1 1

r s

aT T

1b

1

r

cL

1

m

dL

1

s

eT

with

11 2

2 2 1 2 1 3

3

1

2

3

1 0' ' 0 1

0 00 1' '


rqr rd rq sd sq rq sq

rr

xax xdi

ai i e b cu du x ax u u x udtdi xi ai b e cu dudt

yd

dt y

y

1

2

3

1 0 0

0 1 0

0 0 1

x

x

x

, then


„Exact-Linearization“ – Implementation with DFIM (1)

The model in state-space will be in form of

x f (x) H(x)u

y g(x)

with

1 1 1 1 1 1

2 2 2 2 2 2

3 3 3 3 3

1 2

2 1

3

(x)

x ; y ; g(x) (x) ; f (x)

(x) 0

h (x) 1 0

H(x) h (x) 0 1 ;

h (x) 0 0 1

rd

rq

r

x i y x g x ax

x i y x g x ax

x y x g x

x

x

1

2

3

' '

u ' 'sd sq rd sd

sd sq rq sq

r

u e b cu du

u b e cu du

u

By having

Sum of elements of vector of relative degree:

1 2 3r 1 1 1 3r r r

:jr Relative degree j-th

Matrix L is invertible

2 2

-11 1

1 0 1 0

L x 0 1 L x 0 1

0 0 1 0 0 1

x x

x x

Exact-linearization of the considering system can be implemented with the state feedback controller:

1 21

2 1

1 0

u a(x) L (x)w 0 1 w

0 0 10

ax x

ax x


„Exact-Linearization“ – Implementation with DFIM (2)

In the new state-space, system will be:

In detail:

1

2

3

0 0 0 1 0 0 wz 0 0 0 z 0 1 0 w

, y w0 0 0 0 0 1

wy z

dt

or dt

dt

zAz Bw

y Cz

d

dt

• The linearity between inputs and outputs.

• Decoupling between each channel – defined as ‚direct-decoupling‘

• The transfer function of the new system consists of only Integration elements

• The coordinator transformation have only algebraic operations

Notice

1 rdx i

2 rqx i

a

a

r

+

+-

+

++

d

d

e

e

b

b

1/ c

1/ c

sdu

squ

'sd

'sq

1u

2u

++

-+

--

++

rdu

rqu

1w

2w


Contents



3. „Exact-Linearization“ – Concept and implementation with DFIM




v

1 rdx i

2 rqx i

a

a

r

+

+-

+

++

d

d

e

e

b

b

1/ c

1/ c

sdu

squ

'sd

'sq

1u

2u

++

-+

--

++

rdu

rqu

1w

2w

Structure of the new linear model

Coordinate

Transformation

(State feedback

Controller)

Doubly fed

induction machine

Grid

-

3w r

1w 2w

s

sdqu 'sdq

rdu

rqu

Windm

Gm

r

rdqi


Control system of DFIM in wind generator with direct-decoupling

From DC link

Udc

kt

ltmt

DFIM

Griduvw

CoordinateTransformation

rau

rbuj re J

rdu

rqu1w

2w

d-q axis Controller

*rdi

*rqi-

-

DNW

*Gm

*j

IE

LAuNd su

NJ

rdi

rqi

FPT

rdi

rqi

sdi

sqi

Nj

n

3w

rw

j

Gm

rJ'sqy

rJ' , ,sq sduy w

Torque&Power factorController

-

-

- DNW: Decoupling NetWork- PWM: Pulse Width Modulation- LA: Line voltage Angle acquisition- GC: Generator side Converter

GC

PWM

- FPT: Flux, Power factor and Torque Calculation- dq: line voltage oriented reference frame- αβ: fixed reference frame on stator- ab: fixed reference frame on rotor

sdi

sqi

, ,rk l mi

, ,su vwi

Nuvwu

j re J3

2

rai

rbi

3

2

si asi Nje J

, 'sdq sqi y

Switch

d

d

e

e

b

b

1/ c

1/ c

sdu

squ

w

'sdy

'sqy

1u++

-+

--

+

rdu

rdu2u


Circuit diagram with Plecs

Tm

ASM

Vdc

2VC

V

vab

vbc

ua ub uc

Convert

V

ugrid_uvw 4VuVvVw

voltage dip3

Rec Pulse

4

Inv Pulse

5

is_uvw5

A

A

A

us_uvw 6

V

vab

vbc

ua ub uc

Convert1

V

Synch

6

mL

7

R Charge

2

A

A

A

It_uvw 3

Start

1

A

A

ir_klm1

Am

parameter

7


Performance of linearized model and current controller

w

w

w

1

2

3

dt

dt

dt

é ùê úê úê ú= ê úê úê úê úë û

òòò

y

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-500

0

500

1000

1500

2000

2500

3000

3500

Time [s]

Ird

I

rq

w

1

w

2

ird

irqw1

w2

Performance of w1, y1 (ird) and w2, y2 (irq)

ird

irq

w1

w2

1

2

3

w

y w

w

dt

dt

dt

Performance of current controller

1.1 1.15 1.2 1.25 1.3 1.35 1.4-60

-50

-40

-30

-20

-10

0

10

20

30

40

Time [s]

Roto

r cur

rent

[A]

ird

irq

irq*

ird*

ird* & ird

irq* & irq

1/sPird*,irq*

ird,irq


Simulation: Grid voltage and electrical torque

3.2 3.4 3.6 3.8 4 4.2 4.4-3000

-2500

-2000

-1500

-1000

-500

0

500

1000

Time [s]

Sta

tor

volta

ge

[V] -

Ele

ctric

al T

orq

ue

[Nm

]

Grid voltage~50%

~75%

100%

Torque – Linear ControlTorque – Nonlinear Control


Simulation: Active and reactive power

3.2 3.4 3.6 3.8 4 4.2 4.4-1

0

1

2

3

4

5

6x 10

5

Time [s]

Act

ive

[W] a

nd

re

act

ive

po

we

r [V

AR

]

P – Linear Control

P – Nonlinear Control

Q – Linear Control

Q – Nonlinear Control


Simulation: Rotor current

3.2 3.4 3.6 3.8 4 4.2 4.4-400

-200

0

200

400

600

800

Time [s]

Ro

tor

curr

en

t [A

]

ird – Linear Control

ird – Nonlinear Control

irq – Linear Control

irq – Nonlinear Control


Conclusion and perspectives

• Control system of DFIM with exact-linearization: practical and easy to implement.

• The simulation with Matlab/Simulink/Plesc shows good results, the

complete control system is being verified on experiment rig

• Performance of system is improved with the static ‚direct-decoupling ‘ current controller

• Advanced methods can be used in design process of controllers


Thank you for your attention !

a non-linear control algorithm for improving performance of wind generator using doubly-fed...

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