[ieee 2006 6th world congress on intelligent control and automation - dalian, china ()] 2006 6th...
TRANSCRIPT
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
[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
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
δδV
Ve
VV
Ve
Vt R
SP
RRS
PR
V −Δ=Δ−Δ=Δ 11 28
9
δδ
δδδ
2*2cos2
cossin
2
∑∑
∑∑
′−′
+′
′+
′′
=Δ
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
(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