DATNANOE LTng dung thiet bi FACTs trong he thdng dien HTD nham nang cao dugc dn dinh he thdng da dugc chimg minh rat nhieu trong cic ly thuyet ve dn djnh cung nhu trong thyc tien.. Muc d
Trang 1L)NG DUNG G R A M i A N DIEU KHIEN TIM VI TKJ DAT TOI UU CUA SVC
NHAM DAP T A T NHANH DAO D Q N G H $ T H O N G
OPTIMAL PLACEMENT OF SVC USING CONTROLLABILITY GRAMIAN
TO DAMP OSCILLATIONS
Le Cao Qiiyen
Cong ty CP tuvdn \
Nguyen Hong Anh ilimg dien 4 Tnr&ng Dai hgc Quy Nha
Tran Quoc Tuan
Grenoble INP Phdp
TOM TAT
Thiit bi bit tinh (SVC) dung cho vi^c ning cao chit lux?ng diin dp vd d$p tit nhanh cdc dao d^ng trong hi thing diin Oil v&i hi thing diin dan giin, thiet bj bu ngang cdng suit phin khing dS chimg td hiiu qui khi d$t t$i vj tri giu'a du&ng ddy vi vj tri niy du^ xem la vj tri tii uv Tuy nhiin vdi
hi thong diin phirc t^p viic tim m0t vi tri tii wu cua SVC li rat phuc t$p Ngodi ra trong hi thing diin, hiiu qud cua SVC trong viic d$p tit nhanh chdng cic dao ddng hi thing phu thu0c rit nhiiu vdo w tri dit cua no Bdi bdo ndy trinh biy vS mdt ning lux?ng t&i h^n di/a trin Gramian diiu khien trong bdi toin tim vj tri dit tii uv cho SVC di dip tdt cdc dao d^ng hi thing Hiiu qud cua phuxyng phdp di xuit duoc kiim chirng trin hi thong diin New England 39 nut bdng phin mem PSS/E vi Matlab
ABSTRACT
Static Var Compensations (SVC) controller is used to improve voltage and damp oscillations in power system It has been proved that the centre 01- midpoint of a transmission line is the optimal location for shunt FACTS devices or reactive power support and the proof is based on the simpHTied line model However, it is dif^cult to find optimal placement of SVC on large-scale power system In addition the effectiveness of SVC controller, particularly to damp oscillations depends on its location very much in the power system This paper presents an energetic approach based on controllability Gramian for optimal placement of SVC to damp the oscillations The effectiveness of the proposed method has been tested on New England 39-bus system by using PSS/E and Matlab software
I DATNANOE
LTng dung thiet bi FACTs trong he thdng
dien (HTD) nham nang cao dugc dn dinh he
thdng da dugc chimg minh rat nhieu trong cic
ly thuyet ve dn djnh cung nhu trong thyc tien
Tuy nhien mot HTD Ion neu dau tu lap dat
FACTs o nhieu vi tri khic nhau chua chac da
nang cao khi nang duy tri dn djnh he thong ma
cd the gay ra phan irng ngugc do su tac dpng
qua lai ciia cac thiet bi nay Ben canh dd chi phi
de dau tu dan trai li rat tdn kem va khong thuc
te Do dd viec xac djnh vi tri (dugc gpi la vj tri
tdi uu) trong Iudi dien dk lip dSt FACTs, mk
a vj tri nay thik bj FACTs se the hien het
chuc nang ciia nd li dang dugc quan tam
SVC dugc ung dung rpng rai trong he
thdng truyen tai vdi nhi^u muc dich khac nhau
Muc dich CO ban nhat thudng dugc sii dung d6
dieu khien dien ap tai diam ySu nhit trong he
thdng, ngoai ra cic thiet bj SVC ciing dugc sii dung de lam giim cac dao dpng cdng suit, cai thien dp dn djnh qua dp \a giam ton hao he thdng nhd tdi uu dieu khien cong suit phan khang Tuy nhien hieu qua trong viec dieu khien SVC phu thupc \ao vj tri ciia SVC
Cac bai loin chpn lira vi tri toi uu ciia SVC da dugc nghien curu trong thdi gian dai [2-4], [6] Cic nghien cuu tim vi tri dat thiet FACTs trudc day thudng diing phuong phap phan tich iri rieng (eigen value) de tim thanh phan tham gia cua cac thanh cai, may phat tac dpng nhieu nhit den gia trj tri rieng gan zero Phuong phip phan tich nay gap nhieu khd khan
do ma Iran tr?ng thai doi vdi HTD Idn cd kich
cd rll ldn, ben canh do sd lugng thanh phin anh hudng den gia in trj rieng gan zero lai rat nhieu
va viec lim mpt thanh phan anh hudng nhit la khdng kha thi Mpt so phuong phip cai tien khic nhu phuong phap "chi so dieu khien modal" (modal controllability index) [9],
Trang 2phuong phap "he sd du" (residue factor
method) [10] cho ket qua vj Iri chpn lua tdi uu
hau nhu chinh xic hem, tuy nhien vdi nhiJtig
HTD ldn vdi nhieu miy phat va cd cau true
dieu khien phirc tap thi cac phuong phap nii) Igi
khdng tin cay lam
Bai bao niy trinh bay mpt phuong phap
moi ve Gramian dieu khien trong viec tim diem
bil toi uu ciia SVC Diem bii tdi uu 6 phuong
phip nay dua tren vj tri ma he thdng dua gii tri
nang lugng dieu khien den gii tri cue daị Hieu
qua ciia phuong phap de xuat se dugc kiem
chimg Iren mo hinh HTD New England 39 niil
thdng qua bai loan khao sat on djnh qua do tren
mien thdi gian vdi mpt so trudng hgp linh loan
IỊ GRAMIAN DIEU KHIEN
2.1 Khai nifm Gramian [5]
Xem xet mpt he Ihong dugc mieu ta bdi
cac ma tran trang thai:
xit) = Ạx{t) + B.u(t)
CJ day X la vecto cua cac bien trang thai,
u va y la cac vecto cua cac bien trang thai dieu
khien va do ludng
Gia su he phuong trinh (1) cd trat tu cac
bifin trang thai x dugc xic dinh nhu sau:
X=[A5i,A5i, A5n, Affigi, At0g2, AC0gn, z]
A5n va AcOgn bieu diln gdc va toe do rolo ciia
may phit thu n tuong ung,
A la ma tran trang thai, B la ma tran diiu khien
vi C la ma Iran dau rạ
Chiing ta gia su ring he phuong trinh (1)
cd tinh diSu khien va quan sat
Cac ham di6u khi6n, quan sat qua dp ciia
he thdng tuydn tinh vdi thdi gian Hen tuc dugc
xic dinh nhu sau:
L,{X.T)= min 1 J||w(T)f ^ T , x ( - r ) - 0
i„(x,r) = ]• j|[y(T)f dz.xm = x,u^o
(2)
LỊX,T) = -X'W,''iT)X
2 (3)
L„lX.T)=~X'W„iT)X
Oday:
W, {T)= ^ e"BB' é''dt,
T
W„{T) = ^ế'C'Ce"dl
la cac Gramian dieu khi6n va quan sat qua dp theo thai gian Wc{T) va Wn(T) co gia tn duong xac djnh tai thai diem t=T theo phucmg trinh vi phan Lyapunov :
-iy^.(.l)+AlV^.il)+W^.(,l)Á =-BB',tV,-iO) = 0 „ -W„{t) + ÁIV„l,t) + W„(l)jl = -C'C,IV„m=0
Ngu he thong trong he phucmg trinh (4)
la on dinh tiem can xung quanh mpt gia tri, thi
ham dieu khien L^vk ham quan sat L(,duac
xac dinh va cho boi;
1 r
(5)
i , - min - f ||I/(T)||- rfT,4-oo) = 0
La=^]\\y{^)fdT,x{0) = X,u^Q
6 day:
T-*c^:\\mW^{T) = Wcy^
Vim W^iT)^ Wo
Gia tri Wc va Wo la ket qua tinh loan tir phuong trinh Lyapunov va la gii Iri dircmg duy nhat:
AW^ + W , A ' ' + B B ^ - O
ÁW„+WoA + C'C = 0 (6)
Cac ham dieu khien, quan sat qua dp
dugc cho bai:
Tir cic he phuong trinh (I) va (2) cd the thiy ring de cue tieu hda nang lugng dau vao di6u khien chiing ta can cue lieu hda (Wc)'' hay tuong duong voi cue dai hda Wc Cac tin hieu
do ludng cd the su dung nhu la mot tieu chuan
Trang 3trong tinh toin nang lugng va dua vao trong
viec linh loan cue dgi hda Wc
2.2 Phuong ph^p Gramian trong h&\ todn
tim diem bii to! u'u
Su dyng phuong phap Gramian quan sit
\a dieu khien cho mgc dich tim vj iri lip dat toi
uu cac thiet bj dieu khien dS dugc dua ra trong
rat nhieu bao cio khoa hpc [11-12] Tuy nhien
khdng mpt tac gii nio dua ra ihu^t loan ve diem
dai Idi uu cua cac thiet bi dieu khien ddi vdi h?
thong dien Trong phan na\ s5 thiet Igp inpt
thugt loan tim diem d^t tdi uu ciia mpt thiet bj
dieu khien thdng qua viec lim ra mpt nang
lugng tdi han tir cic Gramian dieu khien irong
he thdng
Cic gii trj nang lugng Gramian dieu
khien dugc tinh toin thong qua khao sit he
thdng vdi nhieu kjch ban vgn hanh khic nhau
Cic kjch bin (n-1) la nhiing kich bin thucmg
gap trong he ihong, do vay s6 dugc xem xet
Hinh 1 trinh bay md hinh ham truyen
dieu khien SVC trong dd tin hieu dien ip thanh
cii dugc dua vao so sanh vdi mpt tin hieu dien
ip dat, de tao ta mot gii tri cdng suat phan
khing mong muon
VTCf VOTMSG I V , |
Hinh I Srxdd khdi ciia SVC- "CSTATT' trong
thu vi^n phdn mem PSS/E
Theo [7], giai ihual xac dinh diem dit tdi
uu ciia SVC nhu sau:
1 Cng vdi mpt vi tri dat SVC tren thanh cai
thu i (i=l-^n va khong phai thanh cai lien quan
den miy phat) Tinh toan xac lap he thong theo
cac kjch ban cho trudc thiij (j=I^m), Xac djnh
cac thanh phan ma tr^n Aij, B,j, C,, img vdi lirng
kjch ban theo timg vj tri dat SVC Cac trudng
hgp mat on djnh bj loai trir bing viec ki6m tra
cac dieu kien dn dinh tir ma Iran dac tinh A,j
2 Xac djnh nang lugng Gramian dieu khiln
Wcij theo phuong trinh;
A,iWc„ + Wc„AVBijB'ii=0 (7)
3 Chpn Ivta vi tri tdi uu theo lieu chi
\mxW'^') = I.^a (8)
Vi tri loi uu ciia SVC dugc lira chpn dua tren vj tri cho yia trj tong nSng lugng dieu khiin
li ldn nhat
III TIM DiftM BU TOI I I f UA SVC CHO HTD NEW ENGLAND 39 NUT H? thong dien "New England" gdm 39 niil trong dd cd 10 may phat Ket qua phan bi cdng suat dugc trinh biy Irong hinh 2
Chucmg trinh PSS/L dugc su dung trong bai loan phan tich on djnh dao dpng be cung nhu phan tich on dinh qua dp tren mien thoi gian Cac ma tran trang thii A,B,C dugc linh toan thdng qua module Lsysan tu chucmg trinh PSS/E Cic gia trj nSng lugng Gramian dieu khien dugc tinh loan bing phan mem Matlab
Cac truang hgp tinh toin dugc cho d bing 1, trong dd nang lugng Gramian dieu
khien img vdi timg v j tri d%i SVC thdng qua cac
trudng hgp tinh toin dugc cho d bing 2
Bdng I Cdc tnr&ng hop tinh loan
Thir tu Trudng hgp dudng day cit ra |
I
1 Khdng cat dudng da\ ;
2 Dudng day 4-14 •
3 Dudng d:\\ 17-18 ^
4 Dudng day 25-26
5 DudTigd;i> 16-17 _6 Dudng di\ 23-24 Thyrc hien tinh loan nang lugng Wc cho cac trudng hgp SVC dat lan lugt d cic niit tren he thdng Cic ket qua ghi nhan cho thay SVC d cac nut 83, B4, B5, B6, B7, B8, B9 co gia tri ning lugng rat thap, \i vay trong tinh loan se chi xem xet SVC dat d mit B5 nhu li mpt nut dai dien cho tat ci cic niit cd gia tri nang lupng thap nay
Trang 4• • | - 39l_^+18
Hinh 2 Ket qud phu ho lOnj suat
Bdng 2 Ket qud tinh todn nang luang toe ' 'le
thong ung v&i moi vi tri ddt SVC
SVC
tai
ntit
B5
B13
B14
B I 5
B16
B17
B18
B21
B24
B26
B27
B28
Nang lirtjfng he thong ttroTig irng v ^
viiriaatsvc.cWcxio")
TH
I
0.00
6.67
5.39
5.03
7.21
6.07
6.22
7.06
5.93
7 94
5.78
6.96
TH
2
0.00
6.09
4.99
5.04
7.19
5.55
5.71
6.48
5.97
7.18
5.71
6.49
TH
3
0.00
6.56
5.47
6.31
7.99
6.71
2.82
7.95
7.21
7.11
6.36
9.94
TH
4
0.00
6.01
5.38
5.13
7.24
5 59
4 77
7.14
6.02
5.11
5.90
6.74
TH
5 0.00 6.40
5.68 5.52
7.44
5.76 5.06 7.86 6.82 6.78 2.47 2.79
TH
6
0.00 6.44 5.06 6,40
7.34
6.32 5.33 7.05 6.58 6,95 6,15 6,75
Tiing nang lirffng cac
TH
0,000 38.17 31.97 33,43
44.41
36,00 29,91 43,54 38,54 41,07 32,37 39.67
,l(Tp
6 bang 2 cho thiy SVC dat tai nut s6 16
'•4t qua tdng nang lugng qua cac trudng
(' ;!i loan la cao nhat Ke den \k nut 21,
• 1 nut 5 Tuy nhien xet nang lugng ung
ciia HTD New England 39 niit
vdi mdi truong hgp tinh toin thi cd su thay the cho nhau, vi du d trudng hpp 2 (TH2) cat dudng day 4-14 gia tri nang lugng dat dugc neu
S C dat d nut 21 la thap hon so vdi SVC dat d niit 26 nhung doi vol trudng hep 5 (cat dudng day 27-26) hoac trudng hpp 6 (cat dudng day 14-15) thi lai ngugc lai vi vay vdi cac vi tri nay khong dugc gpi la vj tri lap dat tdi uu vi khong the bao triim het cac trudng hgp tinh toan tren
he Ihong Doi vai SVC dat d nut 16 da phan gia
tn nang lugng linh loan dupe deu Ion han so vdi cac trudng hgp khac vi vay vi tri dat SVC tai nut 16 la vi tri tdi uu Nham de kiem chimg ket qua vi tri diem dat SVC d nut 16 la tdi uu, bai bao tien hanh tinh toan khao sat dn dinh qua
dp trong mien thdi gian vdi cac trudng hgp cat sir cd 3 pha nhu bang 3 Trong do SVC se xem xet dat d mpt so vj tri khac nhau
Bdng 3 Cdc iru&ng hap tinh todn su co
TT Su CO gin nut Dudng day cat tai
t=0,35sec
1 Nut 3
2 Nut 17
3 Nut 18
Dudng day 3-4 Dudng day 16-17 Dudng day 17-18 Til hinh 3 den 5 mo phdng trudng -Jigj: loai trir sir cd ba pha dudng day 3-4 va 16-17
Trang 5Hinh 3 Dao dgng gdc rolo may phdt G8-trir&ng
h(/p cdt str CO ba pha du&ng ddy 3-4 Xet 3 fru&ng
h(rp SVC dd' 'gi mi' 5 16 vd 27
Hinh 4 Dao dgng gdc roto may phdt G6-truan[ h(rp cdt •itr cd ha pha dxr&ng ddy 3-4 Xet 3 truong h^p S^C dgt tai nut 5.l6va2l |
Hinh 5 Dao dgng gdc roto may phdt G7-Truang
hop cdt sir CO ba pha dir&ng ddy 16-17 Xet 3
tru&ng hap SVC dgt tgi nut 13, 16 vd 27
Hinh 6 Dao dgng gdc roto md\ phdt G4-trudn\ hgtp cdt sued ba pha dirang ddy 17-18 Xet 3 truang hap 5KC dgt tgi mil 16 21 vd 27
Hinh 7 Dao dgng goc roto may phdt GS-trir&ng
hap cdt su c6 ba pha duang ddy 17-18 Xet 3
tru&ng hap SVC ddt tgi mil 16 28 vd 27
Hinh S Dao dgng gdc roto may phdt G6-tru&n hap cdt su CO ba pha du&ng ddy 17- IS Xet 3 trudng hop SVC dgt tgi nut 16 28 vd 27
Trang 6Ket qua cho thay dao ddng goc roto cic
may phat vdi trudng hpp SVC dat tai niit 16 tai
nhanh Gia tri thdi gian dao dpng goc di ve xac
lap trong khoang lOsec den 14sec, trong khi d6
khi SVC dat tai niit 13, 27 hoac 5 gdc rolo cua
cac may phat van tiep tuc dao dong, Cic vj tri
cd gia tri nang lugng tdi han cang nho dao dpng
gdc roto hau nhu cang lau
Mpt vi du khic xem xet vdi 3 trudng hgp
SVC dat lai cic mit 16, 21 va 27 Trong bang 2
ket qua gii trj nang lugng tdi han tinh loan tSng
din theo vj tri SVC dat tai niit 27 d^n 21 va 16
Khao sat su co 3 pha tren dudng day 17-18 theo
trudng hgp tinh loan sd 3 d bing 3, diem su cd
gan thanh cai 18 va su cd dugc loai trir bang 2
may cat d 2 dau dudng day tai thai diem
0.35sec
Ket qua d cac hinh 6, 7, 8 cho thay SVC
tai nut 27 CO dao dpng gdc roto giam rit cham,
cac trudng hgp SVC lai 16 va 21 cho kha nang
dap tat dao dpng la nhu nhau (trudng hgp cat
dudng day 17-18 cho gii tri nang lugng d 2 vi
tri dat SVC d niit 16 va niit 21 la ngang nhau)
Vdi cac ket qui tinh toin dugc cho thay
ro rang vdi cac SVC dat tai nhiing niil cd tdng
nang lugng tinh toin ldn thi cho kha nang nang
cao on djnh tdt hon so vdi cac vj tri cd tdng
nang lugng tinh toan nhd
So sanh vdi vi tri dat toi uu cua SVC tai
niit 27 dugc de trinh tir phucmg phip "modal
controllability index" [9] thi thay thdi gian de
dap tat dao dgng gdc may phat cua phuong
phip nay keo dai hon va cd bien dp ldn hon
Nhu vay cd the thay phuong phip de xuat tir bai
bio cho ket qua tdt hon
TAI LIEU THAM KHAO
1 Gronquist J F., Sethares W A., Alvarado F L., LasseterR H (1995), Power oscillation damping control strategies for FACTS devices using locally measurable quantities, IEEE Trans, on Pov^er Systems, 10(3)
2 Haque M.H (2002), Optimal location of shunt FACTS devices in long transmission lines" lEE Proceedings on Generation Transmission and Distribution, 147(4), pp 218-222
3 Larsen E V., Sanchez-Gasca J J., Chow J H (1995), Concept for Design of FACTS Controllers
to Damp Power Swings, IEEE transaction on Power Systems, 10(20)
4 Leleu S., Abou-Kandil H., Bonnassieux Y (2001), Piezoelectric actuators and sensors location for active control of flexible structures, IEEE Transactions on Instrumentation and Measurement, 50(6)
IV KET LUAN Phuong phip phan tich nSng lugng tdi hgn Gramian img dung vao khao sit trong mo hinh New England 39 nut, nhim tim diem dat l6i uu ciia thiet bj SVC Vi tri toi uu ciia SVC dugc lira chpn dua tren vi tri co tong nSng lugng Gramian dieu khien la Idn nhat Vai phuong phap de xuat cho thay vi tri tim dupe deu thda man cac yeu cau de ra li dam bao dap lai (damping) nhanh cic dao dpng h? thong sau khi cat sir cd qua cac khao sal dn djnh qua dp trong mien thai gian
\ PHVLVC Cac thong so mo hinh may phat diing cho phan lich dn djnh dugc cho ben dudi: Cac may phat la loai " GENROE" cd thong so:
Xd=] 8, Xq=l 7, X|=0.2, X'd=0.3, X'q-0.55, X"d=0.25, X"q=0.25, RA=0.0025, T'do=8.0 T'dq=0 4, T"dO=0 03, T"qO=0 05, H=6.5S(1 0) = 0.0377, S(l.2)-0.1821, X1=0.2 Kich tir la loai "EXSTl" cd thdng s6:
T R = 0 0 1 , Tc=l, TB=1, T A = 0 0 1 , KA=200, VRMAX
=6.4 , VRM[N=-6, KC=0, KF=0, TF=1
SVC la loai "CSTATT" cd thong sd : T|=0.65, T2=0, T}=0.2, T j = 0 , K=10,
Droop =0.02, VMAX=1.2, VMIN= - 1 , ICMAX =1-0, IcMIN =1.0 V,,„,m=0.2
Eumii=l-2 XT=0.1, Acc=0.5
Trang 7T.>l- CHl KHOA Hpr & CONG NGHf CAC TUUONG DAI lipCK? THUAT * S6 86 J
5 Moore B.C (1981), Principal component analysis in linear systems: < irollabiliQ', Observability, and Model reduction, IEEE Transaction on Automatic and Control,21- pp 17-32,
6 Mithulananthan N., Canizares C A., J Reeve Rogers G J (2003), Comparison of PSS, SVC, and STATCOM Controllers for Damping Power System Oscillations, IEEE Trans on Power System, vol 18
7 Nguyen D T., Georges D., Tuan T.Q (2008), An Energy Approach lo Optimal Selection §
Controllers/Sensors in Power System, International Journal of Emerging Electric Power Systems, (8)
8 Power technologies (2002), PSS/E29: Program Operation Manual, Power lechnologies INC* USA
9 Singh S.N., Kumar B.K., Srivastava S.C (2007), Placement of FACTS controllers using modal controllability indices to damp out power system oscillations, lET Generation Transmission Distribution 1(2), pp 209-217
10 Sadikovic, Korba P., Anderson G (2005), Application of FACTS Devices for damping Power system Oscillations, Power Tech, IEEE Russia
11 Wicks M A Decario R A (1998), An Energy Approach lo Controllability, Proceedings of the 27th Conference on Decision and Control, Texas
Dja chi lien he Le Cao Quyen - Tel.: (058) 2220.405, email: lecaoquyen@gmail.com
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