TAP CHi KHOA HQC & C6NG NGHp CA( TKH6"NG OAI IIQC KV THU^T * s6 86-2012 L)NG DUNG GRAMiAN 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 \ ilimg dien Nguyen Hong Anh 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$p tit nhanh cdc dao d^ng hi thing diin Oil v&i hi thing diin dan giin, thiet bj bu ngang cdng suit phin khing dS chimg td hiiu qui d$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 hi thing diin, hiiu qud cua SVC 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 bd 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 i 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 pow system In addition the effectiveness of SVC controller, particularly to damp oscillations depends on 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 th 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 he thdng dien (HTD) nham nang cao dugc dn dinh he thdng da dugc chimg minh rat nhieu cic ly thuyet ve dn djnh cung nhu thyc tien Tuy nhien mot HTD Ion neu dau tu lap dat FACTs o nhieu vi tri khic chua chac da nang cao nang tri dn djnh he thong ma cd the gay phan irng ngugc su tac dpng qua lai ciia cac thiet bi 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) Iudi dien dk lip dSt FACTs, mk a vj tri thik bj FACTs se the hien het chuc nang ciia nd li dang dugc quan tam SVC dugc ung dung rpng rai he thdng truyen tai vdi nhi^u muc dich khac Muc dich CO ban nhat thudng dugc sii dung d6 dieu khien dien ap tai diam ySu nhit he thdng, ngoai 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 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 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 phan tham gia cua cac cai, may phat tac dpng nhieu nhit den gia trj tri rieng gan zero Phuong phip phan tich gap nhieu khd khan ma Iran tr?ng thai doi vdi HTD Idn cd kich cd rll ldn, ben canh sd lugng phin anh hudng den gia in trj rieng gan zero lai rat nhieu va viec lim mpt 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], TAP CHi KHOA HQC & CONG NGH$ CAC TRU6"NG D^I HQC KV THU^T * SO 86 - 2012 phuong phap "he sd du" (residue factor method) [10] cho ket qua vj Iri chpn lua tdi uu hau nhu chinh xic hem, 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 viec tim diem bil toi uu ciia SVC Diem bii tdi uu phuong phip dua tren vj tri ma he thdng dua gii tri nang lugng dieu khien den gii tri cue dai 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 tren mien thdi gian vdi mpt so trudng hgp linh loan LI.X,T) = -X'W,''iT)X (3) L„lX.T)=~X'W„iT)X Oday: W, {T)= ^ e"BB' e'''dt, T W„{T) = ^e^''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 : II GRAMIAN DIEU KHIEN 2.1 Khai nifm Gramian [5] -iy^.(.l)+AlV^.il)+W^.(,l)A' =-BB',tV,-iO) = Xem xet mpt he Ihong dugc mieu ta bdi cac ma tran trang thai: -W„{t) + A'IV„l,t) + W„(l)jl = -C'C,IV„m=0 xit) = A.x{t) + B.u(t) y = C.x(t) (1) CJ day X la vecto cua cac bien trang thai, u va y la cac vecto cua cac bien trang thai dieu khien va ludng Gia su he phuong trinh (1) cd trat tu cac bifin trang thai x dugc xic dinh nhu sau: Ngu he thong 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; i, - fr ||I/(T)||- - rfT,4-oo) = (5) La=^]\\y{^)fdT,x{0) = X,u^Q X=[A5i,A5i, A5n, Affigi, At0g2, AC0gn, z] A5n va AcOgn bieu diln gdc va toe 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 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)= 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 nhat: AW^ + W , A ' ' + B B ^ - O A'W„+WoA + C'C = J||w(T)f ^ T , x ( - r ) - (2) i„(x,r) = ]• j|[y(T)f dz.xm = x,u^o Cac ham dieu khien, quan sat qua dp dugc cho bai: (6) 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 ludng cd the su dung nhu la mot tieu chuan „ TAP CHi KHOA HQC & C N G NGHf CAC TRUING BA'HQC KYTHU^T * Sd 86-2012 tinh toin nang lugng va dua vao viec linh loan cue dgi hda Wc A,iWc„ + Wc„AVBijB'ii=0 2.2 Phuong ph^p Gramian h&\ todn tim diem bii to! u'u \mxW'^') = I.^a 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 rat nhieu bao cio khoa hpc [11-12] Tuy nhien khdng mpt tac gii nio dua 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 mpt nang lugng tdi han tir cic Gramian dieu khien irong he thdng III TIM DiftM BU TOI I I f UA SVC CHO HTD NEW ENGLAND 39 NUT H? thong dien "New England" gdm 39 niil dd cd 10 may phat Ket qua phan bi cdng suat dugc trinh biy Irong hinh Chucmg trinh PSS/L dugc su dung 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 Hinh trinh bay md hinh ham truyen dieu khien SVC dd tin hieu dien ip 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 VOTMSG (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 Cic gii trj nang lugng Gramian dieu khien dugc tinh toin thong qua khao sit he thdng vdi nhieu kjch ban vgn hanh khic Cic kjch bin (n-1) la nhiing kich bin thucmg gap he ihong, vay s6 dugc xem xet VTCf (7) Chpn Ivta vi tri tdi uu theo lieu chi Cac truang hgp tinh toin dugc cho d bing 1, 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 I V,| Bdng I Cdc tnr&ng hop tinh loan Thir tu Trudng hgp dudng day cit cm) | I Hinh I Srxdd khdi ciia SVC- "CSTATT' thu vi^n phdn mem PSS/E Theo [7], giai ihual xac dinh diem dit tdi uu ciia SVC nhu sau: Cng vdi mpt vi tri dat SVC tren cai thu i (i=l-^n va khong phai 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 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 Khdng cat dudng da\ ; Dudng day 4-14 • ^ Dudng d:\\ 17-18 Dudng day 25-26 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 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 Xac djnh nang lugng Gramian dieu khiln Wcij theo phuong trinh; 32 T^P CHI KHOA HQC & CONG NGHf CAC TRUONG DAI HQC KY THU^T * SO 86 - 2012 ••|- 39l_^+18 Hinh Ket qud phu ho lOnj suat ciia HTD New England 39 niit Bdng Ket qud tinh todn nang luang toe ' 'le thong ung v&i moi vi tri ddt SVC TH I TH TH TH TH TH Tiing nang lirffng cac TH Nang lirtjfng he thong ttroTig irng v ^ SVC tai ntit viiriaatsvc.cWcxio") B5 0.00 0.00 0.00 0.00 0.00 0.00 0,000 B13 6.67 6.09 6.56 6.01 6.40 6.44 38.17 B14 5.39 4.99 5.47 5.38 5.68 5.06 31.97 BI5 5.03 5.04 6.31 5.13 5.52 6,40 33,43 B16 7.21 7.19 7.99 7.24 7.44 7.34 44.41 B17 6.07 5.55 6.71 59 5.76 6.32 36,00 B18 6.22 5.71 2.82 77 5.06 5.33 29,91 B21 7.06 6.48 7.95 7.14 7.86 7.05 43,54 B24 5.93 5.97 7.21 6.02 6.82 6.58 38,54 94 7.18 7.11 5.11 6.78 6,95 41,07 B27 5.78 5.71 6.36 5.90 2.47 6,15 32,37 B28 6.96 6.49 9.94 6.74 2.79 6,75 39.67 B26 bang cho thiy SVC dat tai nut s6 16 '•4t qua tdng nang lugng qua cac trudng (' ,l(Tp ;!i loan la cao nhat Ke den \k nut 21, • nut Tuy nhien xet nang lugng ung vdi mdi truong hgp tinh toin thi cd su thay the cho nhau, vi du d trudng hpp (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 (cat dudng day 27-26) hoac trudng hpp (cat dudng day 14-15) thi lai ngugc lai vi vay vdi cac vi tri 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 mien thdi gian vdi cac trudng hgp cat sir cd pha nhu bang Trong SVC se xem xet dat d mpt so vj tri khac Bdng Cdc iru&ng hap tinh todn su co TT Su CO gin nut Dudng day cat tai t=0,35sec Nut Dudng day 3-4 Nut 17 Dudng day 16-17 Nut 18 Dudng day 17-18 Til hinh den mo phdng trudng -Jigj: loai trir sir cd ba pha dudng day 3-4 va 16-17 TAP CHi KHOA HQC & C N G N G H $ CAC TRUING DAI HQC KY THUAT * S6 86 Hinh Dao dgng gdc rolo may phdt G8-trir&ng Hinh Dao dgng gdc roto may phdt G6-truan[ h(rp cdt •itr cd pha dxr&ng ddy 3-4 Xet h(/p cdt str CO ba pha du&ng ddy 3-4 Xet fru&ng truong h^p S^C dgt tai nut 5.l6va2l | h(rp SVC dd' 'gi mi' 16 vd 27 Hinh Dao dgng gdc roto may phdt G7-Truang hop cdt sir CO ba pha dir&ng ddy 16-17 Xet tru&ng hap SVC dgt tgi nut 13, 16 vd 27 Hinh Dao dgng gdc roto md\ phdt G4-trudn\ hgtp cdt sued ba pha dirang ddy 17-18 Xet truang hap 5KC dgt tgi mil 16 21 vd 27 Hinh Dao dgng goc roto may phdt GS-trir&ng hap cdt su c6 ba pha duang ddy 17-18 Xet 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 trudng hop SVC dgt tgi nut 16 28 vd 27 34 TAP CHI KHOA HQC & CONG NGH$ CAC TRU'CfNG DAI HQC KY THUAT * S 86 - 2012 IV KET LUAN Ket 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 khoang lOsec den 14sec, d6 SVC dat tai niit 13, 27 hoac 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 Phuong phip phan tich nSng lugng tdi hgn Gramian img dung vao khao sit 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 li dam bao dap lai (damping) nhanh cic dao dpng h? thong sau cat sir cd qua cac khao sal dn djnh qua dp mien thai gian Mpt vi du khic xem xet vdi trudng hgp SVC dat lai cic mit 16, 21 va 27 Trong bang 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 pha tren dudng day 17-18 theo trudng hgp tinh loan sd d bing 3, diem su cd gan cai 18 va su cd dugc loai trir bang may cat d dau dudng day tai thai diem 0.35sec \ 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: Ket qua d cac hinh 6, 7, 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 (trudng hgp cat dudng day 17-18 cho gii tri nang lugng d vi tri dat SVC d niit 16 va niit 21 la ngang nhau) 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: 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 TR=0.01, Tc=l, TB=1, TA=0.01, 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, Tj=0, K=10, 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 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 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 TAI LIEU THAM KHAO 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) 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 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) 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) 35 T.>l- CHl KHOA Hpr & CONG NGHf CAC TUUONG DAI lipCK? THUAT * S6 86 J 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, 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 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) Power technologies (2002), PSS/E29: Program Operation Manual, Power lechnologies INC* USA 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 Cdng Ty Cd Phan Tu Van Xay Dung Dien 11 Hoang Hoa Tham - TP Nha Trang - Tinh Khanh Hda ... 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 (trudng hgp cat dudng day 17-18 cho gii tri nang lugng d vi tri dat SVC. .. SVC dat tai niit 16 tai nhanh Gia tri thdi gian dao dpng goc di ve xac lap khoang lOsec den 14sec, d6 SVC dat tai niit 13, 27 hoac gdc rolo cua cac may phat van tiep tuc dao dong, Cic vj tri cd... nut 5.l6va2l | h(rp SVC dd'' ''gi mi'' 16 vd 27 Hinh Dao dgng gdc roto may phdt G7-Truang hop cdt sir CO ba pha dir&ng ddy 16-17 Xet tru&ng hap SVC dgt tgi nut 13, 16 vd 27 Hinh Dao dgng gdc roto