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Research on Nonlinear Coordinated Control of Generator Excitation System Xihuai Wang, Tianfu Zheng, Jianmei Xiao Department of Electrical Engineering and Automation, Shanghai Maritime University, Shanghai 200135, China (E-mail:[email protected]) Abstract—A new design method of non-linear control system is provided in this passage. Exact Feedback Linearization theory of differential geometry is applied to the design of non-linear excitation control law for the single-machine infinite system, and non-linear excitation control law of generator is obtained, the design method provided in this message is very simple, Matlab/Simulink remains that excitation controller based on non-linear theory is very effective for the improvement of system stability and the stability of generator terminal voltage compared with the LOEC and traditional PID controller. Keywords—generator, excitation control, non-linear coordinated control, differential geometry 200135 Matlab/Simulink LOEC PID 1 [1] [2] PID PSS(Power System Stabilizer) LOEC(Linear Optimal Excitation Control) 04FA02 T0602 [3] [4] . LOEC [5] [6-9] [10] 1-4244-0332-4/06/$20.00 ©2006 IEEE 7537 Proceedings of the 6th World Congress on Intelligent Control and Automation, June 21 - 23, 2006, Dalian, China

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Page 1: [IEEE 2006 6th World Congress on Intelligent Control and Automation - Dalian, China ()] 2006 6th World Congress on Intelligent Control and Automation - Research on Nonlinear Coordinated

Research on Nonlinear Coordinated Control of Generator Excitation System

Xihuai Wang, Tianfu Zheng, Jianmei Xiao

Department of Electrical Engineering and Automation, Shanghai Maritime University, Shanghai 200135, China (E-mail:[email protected])

Abstract—A new design method of non-linear control system is provided in this passage. Exact Feedback Linearization theory of differential geometry is applied to the design of non-linear excitation control law for the single-machine infinite system, and non-linear excitation control law of generator is obtained, the design method provided in this message is very simple, Matlab/Simulink remains that excitation controller based on non-linear theory is very effective for the improvement of system stability and the stability of generator terminal voltage compared with the LOEC and traditional PID controller.

Keywords—generator, excitation control, non-linear coordinated control, differential geometry

200135

Matlab/Simulink

LOEC PID

1

[1]

[2]

PIDPSS(Power System Stabilizer)

LOEC(Linear Optimal Excitation Control)

04FA02T0602

[3]

[4].LOEC

[5] [6-9]

[10]

1-4244-0332-4/06/$20.00 ©2006 IEEE7537

Proceedings of the 6th World Congress on Intelligent Controland Automation, June 21 - 23, 2006, Dalian, China

Page 2: [IEEE 2006 6th World Congress on Intelligent Control and Automation - Dalian, China ()] 2006 6th World Congress on Intelligent Control and Automation - Research on Nonlinear Coordinated

[11-13]

)( δΔ

tVΔ

2[14]

⎩⎨⎧

=+=

)()()(

xhyuxgxfx

1

1 1,0 Xx = 0x V

vxxu )()( βα += )(xz Φ=vxxgxxgxfx )()()()()( βα ++= Φ z

⎩⎨⎧

=+=

CzyBvAzz

2

2 ,0 Xx ∈ 0x V

r 11 20,,0)( −≤≤∈∀= rkVxxhLL k

fg

2 VxxhLL rfg ∈∀≠− ,0)(1 3

1 0x r.

(1) nr = [15]

0)(

0)(

)()()(

1

2

2

==

===

xhLL

xhLL

xhLLxhLLxhL

nfg

nfg

fgfgg

4

⎪⎪⎩

⎪⎪⎨

==

====

−− )(

)()(

11

12

1

xhLyy

xhLyyxhyy

nfnn

f 5

1

uxhLLxhLy

yyyy

nfg

nfn )()( 1

32

21

−+=

==

6

0)(1 ≠− xhLL nfg

)]([)]([ 11 xhLvxhLLu nf

nfg −= −− 7

Tnyyyz ][ 21= 6 7

BvAzz +=

⎥⎥⎥⎥⎥⎥

⎢⎢⎢⎢⎢⎢

=

01

00000

00100010

A⎥⎥⎥⎥

⎢⎢⎢⎢

=

10

0

B

31

1

1mPΔ =0

2

fd

sd

dd

dq

dq

em

UT

UX

XXT

ET

E

DPPH

00

00

0

0

1cos11

)]([

+′

′−+′′

−=′

−−−=

−=

δ

ωωω

ωω

ωωδ

8

δ ω 0ωH qE′ q

D dd XX ′ d

0dT

LTdd XXXX ++′=′ ∑ fU mP

eP

δδ 2sin2

sin2

∑∑∑ ′−′

+′′

=qd

qds

d

sqe XX

XXUX

UEP 9

qX q LTqq XXXX ++=∑ sU

qd XX =′ eP

qqd

sqe IE

XUE

P ′=′

′=

δsin (10)

uXgXfX )()( += (11)

1 2 3G TX LX ∞

7538

Page 3: [IEEE 2006 6th World Congress on Intelligent Control and Automation - Dalian, China ()] 2006 6th World Congress on Intelligent Control and Automation - Research on Nonlinear Coordinated

TqEwX ],,[ ′= δ

⎥⎥⎥⎥⎥⎥⎥

⎢⎢⎢⎢⎢⎢⎢

′′−

+′′

′′

−−−

=

δ

δωωωωωω

cos11

sin)()(

0

00

0

0

sd

dd

dq

d

d

sqm

UX

XXT

ET

XUE

HHDP

HXf

T

dTXg ]100[)(

0

=

01 )( δδ −=== Xhyz (12)

,0)()()(0 =∂

∂= XgXXhXhLL gg

,0)( =xhLL fg 0sin)( 02 ≠′

−=∑

δω

d

s

dofg X

UHT

xhLL (13)

)(xh 3

5 2ωωω Δ=−=== 012 )(xhLzz f (14)

3

eem PH

PPH

z Δ−=−= 003 )(

ωω (15)

)(XZ φ=)(Xφ

⎥⎥⎥⎥⎥⎥

⎢⎢⎢⎢⎢⎢

′−

′′

=∂

∂=

∑∑

δωδω

φφ

sin0cos

010001

)(

00

d

s

d

sq

XHU

XHUE

XXJ

(16)

0cos ≠δ 090±≠δ φJ )(XZ φ=

8

⎪⎩

⎪⎨⎧

===

13

32

21

Vzzzzz

17

173322111 zkzkzkV −−−= 18

321 ,, kkk

7

),()]([)( 312 xhLxhLLx ffg−−=α

,)]([)( 12 −= xhLLx fgβ

,sincos)( 0 qqd EETx +′−=

δδδα

δωβ

sin)(

0

0

s

dd

UxHT

x ∑′−= (19)

qE qE

δcos)1( sd

d

d

dqq U

xx

xx

EE∑

′−+

′′= (20)

7

)(sin

sincos

0321

0

0

01

es

dd

qqdf

PHw

kwkkU

xHT

EETU

Δ+Δ−Δ−′

−+′−=

∑ δδω

δδδ

21

321 ,, kkk Riccati

21

tV

ttt VVVz Δ=−= 04 22

tV 0tV

2VVt =Δ tt VkV Δ=2 23

17 18 22 23 Azz = 24

⎥⎥⎥⎥

⎢⎢⎢⎢

−−−=

tkkkk

A

000001000010

321

Lyapunov

PzzzV T=)( 25P )(zV

QzzzPAPAzzV TTT −=+= )()( 26

][ PAPAQ T +−=

tkkkk ,,, 321 0>Q

[3]

δΔ−Δ=ΔV

Ve

Vt R

SP

RV 1 27

7539

Page 4: [IEEE 2006 6th World Congress on Intelligent Control and Automation - Dalian, China ()] 2006 6th World Congress on Intelligent Control and Automation - Research on Nonlinear Coordinated

δδV

Ve

VV

Ve

Vt R

SP

RRS

PR

V −Δ=Δ−Δ=Δ 11 28

9

δδ

δδδ

2*2cos2

cossin

2

∑∑

∑∑

′−′

+′

′+

′′

qd

qdS

d

Sq

d

Sqe

XXXXU

XUE

XUE

P 29

8 27 28 29

20

00

002

sin

sincos

sin2cos)(

sincos

VU

TXR

TETX

XXU

TU

SXU

XXX

TTE

U

S

ddV

dqdq

qdS

dS

VdS

d

ddd

d

qf

δ

δδδ

δδδ

δδ

δ

′+

′−−′

′+

′′−

−′′

=

30

qd XX =′

20

0

002

sinsincos

sincos

VU

TXRTE

TU

SXU

XXX

TTE

U

S

ddVdq

dS

VdS

d

ddd

d

qf

δδδδ

δδ

δ

′+′−

′+

′′−

−′′

=31

)(sin

sincos

0321

0

0

01

es

dd

qqdf

PH

kkkU

xHT

EETU

Δ+Δ−Δ−′

−+′−=

∑ ωωδ

δω

δδδ

(32)

ttS

ddVdq

dS

VdS

d

ddd

d

qf

VkU

TXRTE

TU

SXU

XXX

TTE

U

Δ′

+′−

′+

′′−

−′′

=

δδδδ

δδ

δ

sinsincos

sincos

00

002

(33)

21 fff UUU +=

4.

Matlab/Simulink 1LOEC PID

11

,55.6,.0.1,.15.0,922.12 0 sTupUupDsH ds ====,.8258.0 upxd = upxd .1045.0=′

2upxupx lT .0266.0,.0292.0 ==

3

upVupUupV

upEsradrad

tft

q

.0253.1,.838.1,.0253.1

.9361.0,/16.314,7439.0

000

000

===

=′== ωδ

12 3

(LOEC) PID

1 0.5s 50%0.2s eP ω

tV δ 2(a) (b) (c)

(d) 2

(a)

b

(c)

7540

Page 5: [IEEE 2006 6th World Congress on Intelligent Control and Automation - Dalian, China ()] 2006 6th World Congress on Intelligent Control and Automation - Research on Nonlinear Coordinated

(d)2

2 st 5.0= 5%δ tV 3(a) (b)

(a)

(b)3

5.

LOEC PID

[1] O.P.Malik, Amalgamation of adaptive control and AI

techniques:applications to generator excitation control,”Annual

Reviews in Control,28,pp.97-106,2004 [2] , , . . :

,1991. [3] , , . .

,1982 [4] , . . ,1992

[5] Lu Q,Sun Y and Mei S.Nonlinear control systems and power system dynamics.Boston:Academic Publishers,

2001 [6] , , .

. ,22(1) 91-96,2002. [7] , , .

. ,20(12) 52-56,2002. [8] Tielong Shen,Shengwei Mei,Qiang Lu etc. Adaptive nonlinear

excitation control with 2L disturbance attenuation for power

sustems, Automatica,39,pp.81-89,2003.

[9] , , .. ,32(5):32-35,2004.

[10] , .. ,30-32,2005.

[11] L.Cong,Y.Wang,D.J.Hill, Transient stability and voltage

regulation enhancement via coordinated control of generator excitation and SVC, ELECTRICAL POWER & ENERGY

SYSTEMS,27,pp.121-130,2005. [12] , , . FACTS

. ,23(9),6-10,2003.

[13] Ashfaque A.Hashmani,Youyi Wang,T.T.Lie, Enhancement of

power system transient stability using a nonlinear coordinated excitation and TCPS controller, ELECTRICAL POWER &

ENERGY SYSTEMS,24,pp.201-214,2002. [14] , , . .

,2001.

[15] , , . .,2003.

7541