Model Reference Adaptive Control of FACTS

Transcription

1 6th NAIONAL POWER SYSEMS CONFERENCE, 5th-7th DECEMBER, 4 Model Reference Adptive Control of FACS Dipendr Ri, Rmkrishn Gokrju, nd Sherif Fried Deprtment of Electricl & Computer Engineering University of Ssktchewn, Ssktoon, SK S7N 5A9, Cnd Abstrct In this pper, n dptive pole-shift control technique for FACS devices is presented Adptive pole shifting techniques hve been successfully implemented in power system stbilizer pplictions in the pst One of the essentil prts of rel-time dptive control implementtion is the system identifiction using suitble recursive identifiction lgorithm he prcticl implementtion of such recursive technique for the system identifiction suffers from inbility to identify correct prmeters during lrge disturbnces such s three-phse fults In order to overcome this problem, d-hoc solutions: moving verge prmeter boundries, trcking constrined coefficient updte nd rndom wlk technique hve been suggested in litertures his work presents the use of robust RLS technique to del with lrge disturbnces he effectiveness of the proposed method hs been demonstrted in liner discrete system nd single-mchine infinite bus system to dmp power oscilltions using the dptive CSC control P Index erms FACS, CSC, power swing dmping I INRODUCION OWER systems re complex dynmic systems nd re subjected to unpredictble disturbnces such s injection or rejection of lods, chnges in operting points of mchines, nd system fults he presence of Flexible AC rnsmission System (FACS) devices further introduces nonlinerity in the system he trditionl phse led-lg controllers in power system re tuned for certin operting condition, which my not perform s desired t nother operting condition Adptive control techniques re desirble under such circumstnces he dptive controller dpts to new operting condition in rel-time nd yields optimum response over wide operting regions [-3] An dptive control lgorithm works on rel-time identified plnt model he model estimtor should be ble to trck chnges in power system rpidly nd smoothly for uniform control ction Recursive lest squre estimtion (RLS) method is one of the most populr system identifiction routine becuse of its simplicity nd numericl stbility [4] However, generl RLS lgorithm hs divergent behvior due to round-off errors [5] Furthermore, the noise model is very unrelistic in prcticl situtions nd in most of the pplictions; it results in erroneous prmeter estimtes for the RLS [6] Power system disturbnces re in generl lrge disturbnces such s chnge in lod nd system fults he prmeters identified in such conditions using norml RLS lgorithm cn hve rpid devitions [4, 7, 8] nd this cn cuse undesirble control output o rectify such problems, d-hoc solutions hve been proposed in the literture In [7] the uthors proposed the use of dynmic limit to the prmeters he use of trcking constrined coefficient in recursive updting formul of the identified prmeters is proposed in [4] nd the use of rndom-wlk term in updting the covrince mtrix for short durtion following the lrge disturbnces hs been proposed in [8] In this pper, uthors propose the use of robust recursive lest squre technique (RRLS) for the system identifiction he RRLS is stble nd yields smooth vrition in the prmeters even for lrge disturbnce scenrios [5] he pper is orgnized s follows Section II gives brief description of the model reference dptive control technique Section III describes the hyristor Controlled Series Cpcitor (CSC) control methodology he electromgnetic trnsient simultion results re presented in Section IV Finlly, in section V, conclusions re presented II MODEL REFERENCE ADAPIVE CONROL he bsic concept of model reference dptive control is shown in Fig he response of the nonliner power system including FACS devices is modeled by known model he coefficients of the model of the plnt re estimted in reltime using recursive lgorithm he estimted prmeters re used to design the controller to meet the specific requirement Once the optimized controller prmeters re chieved, the controller genertes pproprite control signl In this control rchitecture, the feedbck control loop is clled inner-loop while model djustment loop is referred to s outer-loop he inner loop is reltively fster compred to the outer loop [9] In this work, the dynmics of power system is pproximted by discrete ARMA model [-3]: A(z - ) y( = z -n d B(z - ) u( + C(z - ) e( () where, y(, u( nd e( re system output, system input nd noise terms respectively A(z - ), B(z - ) nd C(z - ) re the polynomils expressed in terms of the bckwrd shift opertor z - nd re defined s: A(z - ) = + z - + z n z -n B(z - ) = + b z - + b z b nb z -n b C(z - ) = + c z - + c z c nc z -n c n, n b nd n c re the order of the polynomils A(z - ), B(z - ), nd

2 FACS 6th NAIONAL POWER SYSEMS CONFERENCE, 5th-7th DECEMBER, 4 C(z - ) respectively he vrible n d represents the dely term Algorithm specifictions Reference, r Model Reference Adptive Control Controller design Controller Controller prmeters Model prmeters Control signl, u Fig Model reference dptive control schemtic A System identifiction Model Estimtion Power System System output, y he system prmeter estimtion is criticl step for designing proper dptive control of the system It is desirble to hve smooth identified prmeter vrition for lrge burst disturbnces, which re typicl type of disturbnces for power systems o cope with such lrge disturbnces, robust recursive lest squre pproch is implemented in this work his lgorithm is robust for cses tht rise due to numericl trunctions nd lrge disturbnces Eqution () is expressed s: y( ( W( t ) e( () where W ( t ) = [ n b b b nb c c c nc ] is the system prmeter vector, ( = [ y(t ) y(t ) y(t n ) u(t n d ) u(t n d ) u(t n d n b ) e(t-) e(t-n c )] is the smpled input/output dt vector nd e( is the error term hen the robust recursive lest squre lgorithm given in Eq (3) cn be utilized to identify the prmeter vector W( [5]: ( y r ( ( W( t ) t ) t ) t ) t ) ( ( t ) ( t ) ( t ) W ( I W ( t ) ( ( where, y r ( is the reference plnt output, ( is the prediction error nd is the covrince mtrix he initil conditions re )=ci, nd W()= he tuning prmeters re c > nd he initil vlue of c should stisfy the conditions c/ < nd ) ) Furthermore, selection of should stisfy the condition ( < /, where is smll positive number nd ( = /n B Pole-shift control concept A pole-shift feedbck controller hs the trnsfer function given s: (3) where, u( G( z ) y( F( z ) F(z - ) = + f z - + f z f nf z -n f G(z - ) = g + g z - + g z g ng z -n g nd n f = n b, n g = n he closed loop system configurtion of Eq () nd (4) is shown in Fig u ref u( Fig Closed-loop system configurtion B(z - ) A(z - ) G(z - ) F(z - ) From Eq () nd (4), chrcteristics eqution of the closed loop control is: y( (4) (z - ) = A(z - ) F(z - ) + B(z - ) G(z - ) (5) In pole-shift control, the chrcteristics eqution of Eq (5) tkes the form of A(z - ) with the pole shifted by fctor of he new chrcteristics eqution cn be obtined by replcing z - in A(z - ) by z - s follows: A(z - ) = A(z - ) F(z - )+ B(z - ) G(z - ) (6) Rerrnging the Eq (6) in mtrix form: or, n n n n b b b n b b b b n b b n b b b b3 b n b f f f n f g g g n g ( ) ( ) n n ( ) M w() = L() (7) he prmeters i nd b i re obtined from identifier he Eq (7) cn be solved for f i nd g i for known vlue of Once the vlues of f i nd g i re obtined, the control signl cn be computed using Eq (4) For fixed vlueof, control becomes specil cse of the pole-ssignment control he vlue of cn be selected to stisfy some optimized performnce indices One such performnce index is the minimiztion of the one time-step hed prediction error ie min J ( t, t ) E[ yˆ( t ) y ( t )] r (8) t where, ŷ(t+) is predicted output nd y r (t+) is the reference vlue he predicted output ŷ(t+) cn be clculted s:

3 6th NAIONAL POWER SYSEMS CONFERENCE, 5th-7th DECEMBER, 43 ˆ t y( t ) X ( b u( t, ) (9) where, X( = [ u(t-) u(t-n f ) y( y(t-) y(t-n g )], nd = [ b b 3 b nb n ] Minimiztion of the objective function defined in Eq (8) yields the optiml vlue of t he vlue of t should be kept in the rnge of [-/ t < t </ t ] to stisfy the stbility constrints, where t represents the lrgest bsolute vlue of the roots of chrcteristics eqution (z - ) [, 3] Furthermore, the control signl lso should lie within the control constrint: u min u(t, t ) u mx where u min nd u mx re minimum nd mximum control signl boundries III CSC CONROL he schemtic of CSC is shown in Fig 3 he primry purpose of the CSC is to provide series compenstion nd to boost the power trnsfer through the trnsmission line he power swing dmping is chieved by implementing supplementry controller he supplementry controller modultes the CSC impednce to chieve the power swing dmping he CSC impednce is mesured in terms of boost fctor kb, which is the rtio of the pprent rectnce of the CSC seen from the line to the physicl rectnce of the CSC cpcitor bnk Positive vlue of boost fctor is ssumed for cpcitive impednce nd negtive vlue for inductive impednce In this study, only the cpcitive operting region (positive boost fctor) is considered swing dmping controller he output of pole-shift controller is fed bck to CSC control s supplementry control signl kb he devition in line power flow through the trnsmission line from the stedy stte vlue is considered s plnt output nd fed to the pole-shift controller s well s identifier he performnce evlution of the proposed controller is crried out by compring with the simplex-optimized conventionl led-lg supplementry controller he block digrm of the conventionl supplementry controller is shown in Fig 5 It consists of wshout filter, two led lg phse compenstion blocks nd gin compenstion block he time constnts nd gin of the controller is optimized using simplex lgorithm he multiple time-domin simultion bsed simplex optimiztion technique introduced in [], which exploits the dvntge of multiple run enbled electromgnetic trnsient computer simultion tool to optimize the non-liner controller prmeters A simplex is geometric object formed by N+ points in the N-dimensionl spce he optimiztion lgorithm strts with the computtion of the objective function t ech of the vertices of the strting simplex in ech simultion run he vertex which hs highest objective functionl vlue is discrded nd new vertex is chosen for next run, which is the reflection of the discrded vertex through the centroid of the remining vertices he process continues until the chnge in objective functionl vlue is within the pre-defined tolernce level More detils on the lgorithm could be found in [] MAX L CSC r s F c s P s w +s +s w +s +s 3 +s 4 K p kb i C CSC R MIN Fig 5 Block digrm of the conventionl led-lg supplementry controller i L Fig 3 CSC schemtic i C + - v C he opertion of the CSC is controlled using controller shown in Fig 4 kb ref is the CSC boost level set point nd kb is the supplementry control signl for power swing dmping he proportionl-integrl type controller is used to control stedy stte CSC impednce t desired level he is the thyristor firing ngle nd the is the initil firing ngle kb ref kb kb Fig 4 CSC control err K p + s c he pole-shift controller is used s supplementry power he objective function for tuning the conventionl led-lg supplementry controller is given in Eq () he symbols c nd s represents fult clering time nd simultion end time, respectively Similrly, P L is the line power flow nd P L is the stedy stte pre-fult power flow he optimized prmeters re given in the Appendix A F obj s PL P L ( 4, K p ) dt () PL c IV POWER SYSEM CONFIGURAION USED FOR HE SUDY o demonstrte the vlidity of the proposed scheme, single mchine infinite bus with CSC compensted trnsmission line s shown in Fig 6, is considered s test system For the time domin simultion studies, the synchronous genertor is represented in the d-q- reference frme he trnsmission line is modeled s trnsposed noncoupled prmeters using series impednce representtion he infinite bus is represented simply s constnt mplitude

4 b - prmters - prmters System output 6th NAIONAL POWER SYSEMS CONFERENCE, 5th-7th DECEMBER, 44 sinusoidl voltge t synchronous frequency Circuit-brekers re represented s idel switches which cn open t current zero crossings he dynmics of the governor system of the turbine-genertor set re neglected nd the input mechnicl torque is ssumed to remin constnt corresponding to the stedy-stte operting conditions he dynmics of the turbine-genertor excittion system re included in the simultion model G A R L X L X CSC Fig 6 Schemtic digrm of the test system B R sys X sys P L, Q L he trnsmission line impednce is 58 pu on 5kV, 894MVA (mchine rting) bse he CSC is used to compenste portion of the trnsmission line he CSC compenstion level is defined s X CSC /X L nd is ssumed to be 3% For the dynmic simultion studies, the vrition of CSC boost fctor from to 3 pu is llowed he system operting condition corresponds to 76 + j pu power on mchine rting bse delivered to the infinite bus t o pu bus voltge he detils of the system prmeters re given in the Appendix B V SIMULAION SUDIES he proposed method is tested for known liner discrete system s well s power system including CSC (non-liner continuous time system) Vrious time-domin electromgnetic simultion studies re crried out to vlidte the performnce nd results re presented in following subsections A Liner discrete system exmple A liner third order discrete system: y( 95 y(t ) + 9 y(t ) y(t 3) = 5 u(t ) + u(t ) + 5 u(t 3) + e( () is considered for testing the proposed estimtion nd control method he error term e( ccounts for % white noise dded to the system he open loop poles of the plnt re t - 85 nd 9 ± j 9 he system coefficients re identified using the robust recursive lest squre lgorithm presented in Eq (3) he control signl is clculted using Eq (7) in ech smpling period such tht the cost function given in Eq (8) is minimized he system response to the squre wve reference wveform of mgnitude ± is plotted in Fig 7 long with identified system coefficients he controlled plnt is ble to trck the reference signl effectively Furthermore, the RRLS identifiction lgorithm is ble to identify correct coefficients he identified coefficient vritions re smooth even t lrge step chnge of reference wveform from - to + or + to - indicting the robustness of the pproch for lrge disturbnces - y ref ( y( () Reference (solid-gry) nd output (dotted) signls ctul identified (b) Denomintor coefficients ctul identified ime, seconds (c) Numertor coefficients Fig 7 Liner discrete time system response to step chnges in reference signl he open nd closed loop poles/zeros of the system re plotted in Fig 8 he open loop poles nd zeros re plotted in gry nd closed loop poles nd zeros re plotted in blck color wo of the open loop poles re outside the unit circle indicting n unstble plnt he pole-shift controller stbilizes the system by moving unstble poles inside the unit circle t the sme time minimizing the next time-step output prediction error he optiml pole-shift fctor is plotted in Fig 8 (b) he stedy stte optiml pole-shift fctor opt is 446 B A nonliner continuous system exmple CSC compensted power system he effectiveness of the proposed method for power swing dmping is demonstrted on single mchine infinite bus consisting of CSC compensted trnsmission line he plnt dynmics is pproximted by third order ARMA model he third order model is sufficient to represent plnt dynmics hving one oscillting component nd one decying component [] he disturbnce is ssumed to be three-phse to ground solid fult pplied t sec on bus A for 3 cycles b 3 b 3 b

5 b prmeters prmeters Pole-shift fctor ( ) P L, pu Imginry Prt Rel Prt () Pole-zero plot for open-loop (gry) nd closed-loop system (blck) ime, seconds (b) Pole-shift fctor Fig 8 Adptive optiml pole-shifting process for the discrete system opt estimted (blck) devition in power flowing from stedy stte in the trnsmission line he estimtion closely mtches to the originl signl Fig 9 (b) shows the identified plnt prmeters he coefficient vritions before nd fter the disturbnce is very smooth s expected he power oscilltion dmping of the proposed method is demonstrted in Fig Fig () shows the comprison between pole-shift supplementry controller, conventionl phse led-lg supplementry controller, nd without ny supplementry controller he conventionl led-lg supplementry controller is optimized using multiple timedomin simultion bsed simplex lgorithm It is evident tht the proposed method dmps-out the power oscilltion quickly compred to the trditionl led lg supplementry controller Furthermore, Fig (b) shows the pole-shift fctor nd Fig (c) shows the CSC boost fctor Pole-shift Led-lg No supplementry controller ime, seconds () Line power flow oscilltions 3 P L( P L( kb 6th NAIONAL POWER SYSEMS CONFERENCE, 5th-7th DECEMBER, P ime, seconds () Actul (gry) nd estimted (blck) devition in power flow ime, seconds 8 (b) Pole-shift fctor ( b ime, seconds (c) CSC boost fctor (kb) Fig Power swing dmping using RRLS bsed pole-shift supplementry control ime, seconds (b) Identified system prmeters Fig 9 Plnt prmeter estimtion using robust recursive lest squre (RRLS) method he response of the proposed RRLS estimtion lgorithm is presented in Fig 9 Fig 9 () shows the ctul (gry) nd b b VI CONCLUSION he pper proposed the use of the robust recursive lest squre identifiction technique (RRLS) s mens to mitigte the lrge vrition in identified coefficients during lrge disturbnces in the power systems he effectiveness of the proposed lgorithm in identifying the system prmeters in presence of lrge disturbnce is demonstrted through detiled time-domin electromgnetic simultions he lgorithm ws effective in identifying liner discrete system s well s nonliner power system prmeters Furthermore, the identified system prmeters were utilized in the dptive

6 6th NAIONAL POWER SYSEMS CONFERENCE, 5th-7th DECEMBER, 46 pole-shift supplementry controller of CSC for power swing dmping he results showed tht the pole-shift control is very effective in dmping power swing oscilltions A CSC prmeters APPENDIX he CSC prmeters nd trditionl led-lg supplementry controller time constnts nd gin re given in ble I ABLE I CSC DESIGN PARAMEERS CSC compenstion 3% of X L kb ref 75 C CSC 9494 µf L CSC 9 mh r s 5 k c s 5 µf PI controller K P =, C = 5 sec Simplex optimized ledlg supplementry w=3sec, = 3 =, = controller 4 = 34633, K P = A Mchine nd system prmeters Genertor dt: IEEE first benchmrk model genertor dt [], 894 MVA, 6 kv, r =, x l = 3, x d = 79, x q = 7, x d = 69, x q = 8, x d = 35, x q = 8, d = 43 s, d = 3 s, q = 85 s, q = 5 s, H = 6 rnsformers dt: 894 MVA, 6/5kV, x t = 4 pu Line dt: R L = 7 pu, X L = 58 pu, R SYS = X SYS = 69 pu Exciter dt: IEEE ype-a Sttic Exciter [], R =, C =, B =, A =, K A = 5, V RMAX =, V RMIN = - Stem Governer dt: GE mechnicl-hydrulic control [], Droop, R = 4 pu Speed rely lg time constnt = sec Gte servo time constnt 3= 5 sec Stem urbine Dt (pu): IEEE type therml turbine [], K =, K 3 = 5, K 5=, K 7 = K = 5, K 4= 5, K 6=, K 8= Stem chest time constnt 4 = 4 sec Reheter time constnt 5= 45 sec Reheter/cross-over time constnt 6= 7 sec REFERENCES [] A Ghosh, G Ledwich, O P Mlik, nd G S Hope, Power system stbilizer bsed on dptive control techniques, IEEE rnsctions on Power Apprtus nd Systems, no 8, pp , 984 [] O P Mlik, G P Chen, G S Hope, Y H Qin, nd G Y Xu, Adptive self-optimising pole shifting control lgorithm, IEE Proceedings D Control heory nd Applictions, vol 39, no 5, pp , 99 [3] G Rmkrishn nd O P Mlik, Rdil bsis function identifier nd pole-shifting controller for power system stbilizer ppliction, IEEE rnsction on Energy Conversion, vol 9, no 4, pp , Dec 4 [4] G P Chen nd O P Mlik, rcking constrined dptive power system stbiliser, IEE Proceedings-Genertion, rnsmission nd Distribution, vol 4, no, pp 49 56, 995 [5] fred hrris, Lecture notes on introduction to digitl signl processing for next genertion digitl receivers nd trnsmitters, Ssktoon, Cnd, [6] I D Lndu, R Lozno, nd M M Sd, Adptive Control Springer, 998 [7] Q H Wu nd B W Hogg, Robust self-tuning regultor for synchronous genertor, IEE Proceedings D Control heory nd Applictions, vol 35, no 6, pp , 988 [8] A Domhidi, B Chudhuri, P Korb, R Mjumder, nd C Green, Self-tuning flexible c trnsmission system controllers for power oscilltion dmping: cse study in rel time, IE Genertion, rnsmission & Distribution, vol 3, no, pp 79 89, 9 [9] K J Åström nd B Wittenmrk, Adptive Control Addison-Wesley Publishing, 989 [] IEEE Subsynchronous Resonnce sk Force, First benchmrk model for computer simultion of subsynchronous resonnce, IEEE rnsctions on Power Apprtus nd Systems, vol 96, no 5, pp , 977 [] IEEE recommended prctice for excittion system models for power system stbility studies, 99, IEEE Std [] Working Group on Prime Mover nd Energy Supply Models for System Dynmic Performnce Studies, Hydrulic turbine nd turbine control models for system dynmic studies, IEEE rnsctions on Power Systems, vol 7, no, pp 67 79, 99