Sliding Mode Control of Wind Energy Generation Systems Using PMSG and Input-Output Linearization

Sliding Mode Control of Wind Energy Generation Systems Using PMSG and Input-Output Linearization

Xiangjun Li, Wei Xu, Xinghuo Yu and Yong Feng RMIT University, Australia

Platform Technologies Research Institute 2

Outline

Background.

Introduction to PMSG.

Input-output linearization.

SMC design.

Simulation studies.


Background

We need the energy supply to be sustainable!!!


Background

Fig. 1. The future smart grid (http://energyinformative.org/what-is-the-smart-grid/)


Background

Fig. 2. The installed capacity of wind generation.


Background

Several factors have made wind power generation cost competitive:

The improvement of aerodynamic efficiency of wind turbine;

The potential market and government incentives;

New control schemes for the variable-speed wind turbine which allow the optimization of wind turbine performance.


Background

Constant speed system. Require sturdy mechanical design; Require stiff power grid.

Variable speed wind energy generation. Is able to optimize wind energy absorption; Smooth power output.


PMSG

Fig. 3. The rationale and structure of PMSG.

Magnetic induction of

electric current

Force on current

carrying lines


PMSG

Fig. 4. Mechanical configurations.


PMSG

Fig. 5. Application of PMSG in wind energy generation.


PMSG

Permanent magnetic synchronous generator is a type of generator in which the excitation field is generated by permanent magnet;

The mechanical frequency matches the required electrical frequency.

PMSG requires less parts than other generators such as induction generator. Thus, it is more mechanically reliable.

PMSG is widely used in wind energy generation and hydro electricity generation.


PMSG

By field orientation control (FOC), it can operate the optimal working point and minimize the losses in generator and power electronic circuit;

The use of a multi pole synchronous generator (large diameter synchronous ring generator) can give direct drive function without a gearbox;

Higher efficiency for no additional power supply for the magnet field excitation;

Higher reliability due to the absence of mechanical components such as slip rings, lighter and therefore higher power to weight ratio.


PMSG

The control schemes depend on the accurate generator parameter, which vary with temperature and frequency;

The permanent may increase the price of machine and meet with demagnetization phenomenon;

The power factor of machine cannot be adjusted easily.


PMSG

Fig. 6. The electrical configuration of the PMSG.


Problem Description

m

opt

windP

mdV

mqV mdV

mqi

mqV

mdi

mdU mqU DCV

ndV

nqi

nqV

ndi

ndU nqU

_grid dV

_grid qV

Fig. 7. Signal flow chart of the system.


This page is only for you to keep in mind about the relationships of those signals

mdV

mqV

mmCwindP

mdV

mqVmqU

mdU

mdi

mqi

The arrow means “determined by”

eC


Problem Description

31( , )

2 w pP AV c

2 0.1710.022 5.6

2pc e

2.237 m

mec

V

2.237

11.48opt

V p opt mecp

Wind power intensity

Mechanical power of wind turbine

Performance coefficient

Tip speed ratio

Optimal angular frequency


Problem Description

md s md sd md e sq mqv R i L i L i

'e m e

JC C

p

/m mecC P

PMSG model

mq s mq sq mq e sd md e pv R i L i L i

Electrical:

Mechanical:

( )e sq sq md mq mq pC p L L i i i


Problem Description

3 / 2 / 2 4 / 3

3 / 2 / 2 4 / 3

md md mDC pwm md

mq mq mDC pwm mq

v U V R i

v U V R i

'

'

' 0

DC mDC mDC mDC mDC mDC

DC nDC nDC nDC nDC nDC

mDC nDC DC DC

V R i L i V

V R i L i V

i i C V

PWM converter algebraic model

DC link algebraic model

The grid side model is the symmetrical.


Problem Description

( ) ( )

( )

x f x g x u

y h x

T

md mq nd nqu U U U U

T

md mq m DC nd nqx i i V i i

mdi

mqi

ndi

nqi

mDCV Voltage of the capacitor Angular velocity of the rotator

Machine side current in d-q axis Grid side current in d-q axis


Problem Description

2

( )0

m md m mq mq md

m mq m md md m p mq

sq sd md mq mq p m

nd nq pccd

nd nd

R i L i L

R i L i L

p L L i i i J pC Jf x

Ri Li v L

Ri Li L

0 0 0

0 0 0

0 0 0 0( )

0 0 0

0 0 0

DC md

DC mq

md DC mq DC nd DC nq DC

DC

DC

V L

V L

g xi C i C i C i C

V L

V L

1 2 3 4( ) ( ) ( )( () )T

m md nq

T

DC

h x h x h x h xh x

i i V

,


PMSG

Parameter Description Value

Rated generator power 2MW

Rated generator voltage 4kV

Number of pole pairs 11

Moment of inertia 2.525*106kgm2

PM flux 166.8Wb

Stator d-axis inductance 0.367H

Stator q-axis inductance 0.250H

Stator resistance 0.08

Filter inductance 33mH

Filter resistance 0.078

Inductance between grid side conv. And grid 0.0295H

Resistance between grid side conv. And grid 0.086

DC link capacitance 100

mP

mV

PJp

sdL

sqL

sR

fnL

fnR

LRDCC F


Input-Output Linearization

1

2, 1( ) ( , )m f h gu fL x L L h x u

2, 2( ) ( , )md f h gui L x L h x u

3, 3( ) ( , )nq f h gui L x L h x u

4, 4( ) ( , )nq f h guV L x L h x u

1( ) ( )Nu E x T x1m v

2mdi v

3nqi v

4nqV v


Uncertainty Analysis

0

0

( ) ( ) ( )

( ) ( ) ( )

f x f x f x

g x g x g x

0 0

( ) ( )

( ) ( ) ( ) ( )

i f i gu i

f i g u i f i gu i

h L h x L h x u

L h x L h x u L h x L h x

0

0 0

1 2 3 4

1 ( ) / ( )

( ) ( ) ( ) / ( )

( , , , )

i gu i g u i i

f i f i gu i g u i

i i i

h L h x L h x v

L h x L h x L h x L h x

v v v v v

1 2 3 4( , , , ) ( ) ( 2,3,4)Ti iv v v v M x V i

1 2 3 4

TV v v v v 4( )iM x i is independent of iv


Uncertainty Analysis

0

0

( ) ( ) ( )

( ) ( ) ( )

f x f x f x

g x g x g x

0 0 0 0

0 0 0

0

0

0 0

0

21 1 1 1

1 1 1

21 1 1

21 1 1

21 1 1 1

1

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( )

(

f g u f f f

gu f f f g u f

f gu f f gu

g u gu f gu gu

f f f f f

gu f

h L h x L L h x L L h x

L L h x L L h x L L h x

L h x L L h x L L h x

L L h x L L h x L h x

v L L h x L L h x L h x

L L h x

0

0

0

1 1

1 1

21 1

) ( ) ( )

( ) ( )

( ) ( )

g u f gu f

f gu f gu

g u gu gu

L L h x L L h x

L L h x L L h x

L L h x L h x

1 1 1 1 2 3 4 1 1 1 2 3 4( , , , ) ( , , , )h v v v v v v v v v 1 1 2 3 4 1( , , , ) ( )Tv v v v M x V

1 1 2 3 4( , , , ) ( )Tv v v v V Q x V 41( )M x 4 4( )Q x


SMC Design

1 2 3 4( , , , )i i i ih v v v v v

0

0

( ) ( ) ( )

( ) ( ) ( )

f x f x f x

g x g x g x

1 1 1 1 2 3 4 1 1 1 2 3 4( , , , ) ( , , , )h v v v v v v v v v

sgn( ( )) 2,3,4i i iv U h x i

1 2

2 1 2( , )

z z

z H z z bv

1 1sgn Mv U z z


SMC Design

Theorem 1. System (1) can be stabilized by the control laws 1( ) ( )u E x N x

where

0

0

0

0

21 1 1

2 2

3 3

4 4

sgn( ( ) ) ( )

sgn( ( )) ( )( )

sgn( ( )) ( )

sgn( ( )) ( )

M f

f

f

f

U h x h L h x

U h x L h xN x

U h x L h x

U h x L h x

if

1

2,3,41 0

i i

i i

iU M

1 1 2 1 31,

2

2 2 1 3

2 2

2 2 1 3 2 2 1 3

1 1

, ,

1 , 1 4 0

1 1 4 1 1 4

2 2

iji j

Q a M a a

a a a a

a a a a a a a aU

a a

ijQ ij Q 1a 2a 3awhere is the th item of matrix , , , and are positive

constants.


By choosing the uniform control gain for all subsystems , the coupling between them through uncertainty items can be decoupled.

After the decoupling, the stability of the overall system can be achieved by stabilizing each subsystem.

Here we only carry out the simulation study of the subsystem , which is the angular speed of the rotator. The units of the variables are unified. The angular speed and the angular acceleration are two states depicted in Figure 8 and Figure 9.

Simulation Studies:Sub-system 1( )mh

ih

1h


Simulation Studies:Sub-system

Fig. 8. State trajectory of the closed-loop system.

1( )mh


Simulation Studies:Sub-system

Fig. 9. System response of the closed-loop system.

1( )mh


Conclusion

The structure of the wind energy generation system using PMSG has been introduced.

The system, which is described by mathematical model in state space, has been formulated and linearized by the input-output linearization technique.

Uncertainties are included in the modeling and linearization.

SMC controls have been designed to stabilize the system.

Simulation studies are conducted to verify the results.


Thanks for your attention!

Questions please.

Sliding Mode Control of Wind Energy Generation Systems Using PMSG and Input-Output Linearization

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