Adaptive Stabilizing Control of Power System through Series Voltage Control of a Unified Power Flow Controller

Transcription

1 Adptive Stilizing Control of Power System through Series Voltge Control of Unified Power Flow Controller AHMA Rhim SA Al-Biyt Deprtment of Electricl Engineering King Fhd University of Petroleum & Minerls Dhhrn, Sudi Ari E-mil: Keywords: Power system stility, UPFC, dmping control, dptive control, pole-shifting control Astrct The unified power flow controller (UPFC) is FACTS device, which is used to control the` power flow on trnsmission line The dynmic nd trnsient ehvior of power system cn e improved y controlling the voltge mgnitude nd phse ngle of the converter voltges in the UPFC Self-tuning dptive control of the voltge mgnitude of the series converter for power system stility is presented in this rticle The control is derived through pole-shifting technique employing the predicted plnt model The controller hs een tested for rnges of operting conditions nd for vrious disturnces From numer of simultion studies on simple power system it ws oserved tht the dptive lgorithm converges very quickly nd lso provides roust dmping profiles INTRODUCTION The unified power flow controller (UPFC) is normlly locted on trnsmission network requiring rective support The usul form of UPFC consists of two voltge source converters, which re connected through common DC link cpcitor The first voltge source converter known s sttic synchronous compenstor (STATCOM) injects n lmost sinusoidl current of vrile mgnitude t the point of connection The second voltge source converter known s sttic synchronous series compenstor (SSSC) injects sinusoidl voltge of vrile mgnitude in series with the trnsmission line The rel power exchnge etween the converters is ffected through the common DC link cpcitor UPFC cn e used for power flow control, loop flow control, lod shring mong prllel corridors, providing voltge support, enhncement of trnsient stility, mitigtion of system oscilltions, etc [,] The stility nd dmping control spect of n UPFC hs een investigted y numer of reserchers [3-7] The dditionl dmping control circuits cn e instlled in norml power flow controllers Most of the control studies in power systems re sed on linerized models of the nonliner power system dynmics The methods include exct lineriztion, liner qudrtic regultor theory, direct feedck lineriztion, etc Stilizers sed on conventionl liner control theory with fixed prmeters cn e very well tuned to n operting condition nd provide excellent dmping under tht condition, ut they cnnot provide effective control over wide operting rnge for systems tht re nonliner, time vrying nd suject to uncertinty It is desirle to develop controller which hs the ility to djust its own prmeters, finding the system structure or model on-line ccording to the environment in which it works to yield stisfctory control performnce Appliction of dptive control theory to excittion control prolems is well documented in the literture [8, 9] Adptive control of SVC systems hs lso een reported in the literture [, ] UPFC is reltively new power electronics sed device, nd its control studies hve generlly een limited in this regrd This rticle considers stilizing control design procedure of the voltge mgnitude of the series converter of the UPFC The design is crried out through vrile pole shifting method employing the identified plnt model prmeters which re tuned dptively POWER SYSTEM MODEL WITH UPFC Fig shows single mchine system connected to lrge power system us through trnsmission line instlled with UPFC The UPFC is composed of n excittion trnsformer (ET), oosting trnsformer (BT), two threephse GTO sed voltge source converters (VSC), nd DC link cpcitor [, 3] m nd α refer to mplitude modultion index nd phse ngle of the control signl of the two voltge source converters (E nd B), respectively which cn e djusted through their own control loops Representing the synchronous genertor-exciter system through 4 differentil equtions, including the series nd prllel trnsformer line dynmics, nd one differentil eqution to represent the DC link, the composite model of synchronous genertor UPEC system cn e expressed through the 9 th order dynmic reltionship, x = f [ x, u] () Here, the stte vector x =[I Ed I Eq I Ld I Lq V c δ ω e q E fd ] T nd u=[m E α E m B α B ] T The first 4 sttes re the d-q SCSC 6 5 ISBN:

2 components of the shunt nd series (line) currents respectively; V c is the DC cpcitor voltge, nd the lst 4 re those for the genertor-exciter system The control vector comprises of the mgnitude nd phse ngles of the converter voltges B(z - ) = + z - + z z z -4 + (4) The vector of prmeters θ(t)= [, ] T re clculted recursively on-line through the recursive lest squre [8] technique using, θ(t+) = θ(t) +K(t) [y(t) θ T (t)ψ(t)] (5) The mesurement vector, modifying gin vector, nd the covrince mtrix, respectively re, Figure A single mchine infinite us system with UPFC SELF-TUNING ADAPTIVE REGULATOR Self tuning control employs feedck controller loop in which the controller prmeters re modified depending on the error etween the rel plnt output nd estimted outputs, s shown in Fig The control for the plnt is designed using liner plnt model, prmeters of which re estimted nd updted recursively u PLANT CONTROLLER PARAMETER IDENTIFIER PLANT MODEL Figure Block digrm of self-tuning controller The plnt model is ssumed to e of the form, A(z - )y(t)=b(z - )u(t)+e(t) () where, y(t),u(t) nd e(t) re system output, input nd the white noise, respectively; z - is the dely opertor The polynomil A nd B re defined s, A(z - ) = + z - + z z z -4 + (3) y ψ(t)= [-y(t-) y(t-)y(t-n ) u(t-) u(t-)u(t-n )] T Pt () ψ () t Kt () = (6) λ() t + ψ T () t P() t ψ() t T P(t + ) = [P(t) K (t)p(t) ψ (t)] λ(t) λ(t) is the forgetting fctor; n nd n denote the order of the polynomils A nd B, respectively The identified prmeters in (5) cn e considered s the weighted sum of the previously identified prmeters nd those derived from the present signls For systems with constnt prmeters λ = produces convergence of the lgorithm while for systems with time-vrying prmeter vrile forgetting fctor given y [], λ (t)=trce[p(t) K(t) ψ T (t)p(t)]/trce(p ) (7) is required to mintin the trce of the error covrince mtrix constnt In the ove, P is the initil error covrince mtrix nd P(t) is the mtrix t the itertion efore discounted y λ Using the forgetting fctor, the error covrince mtrix is updted t ech smpling instnt y, P(t)=P(t-)/ λ (t) (8) THE CONTROL STRATEGY Using the prmeters otined from the rel time prmeter identifiction method, self-tuning controller sed on pole ssignment is computed on-line nd fed to the plnt Under the pole shifting control strtegy, the poles of the closed loop system re shifted rdilly towrds the centre of the unit circle in the z-domin y fctor α, which is less thn one The procedure for deriving the pole shifting lgorithm [3] is given elow Assume tht the feedck loop hs the form, ut () Gz ( ) yt () F( z ) where, = (9) F(z - ) = + f z - + f z - + f 3 z -3 + f 4 z f nf z -nf ISBN: SCSC 6

3 G(z - ) = g + g z - + f z - + f 3 z -3 + f 4 z f ng z -ng n f = n -, n g = n - From () nd (9) the chrcteristic polynomil cn e derived s, T(z - )= A(z - )F(z - ) + B(z - )G(z - ) () The pole-shifting lgorithm mkes T(z - ) tke the form of A(z - ) ut the pole loctions re shifted y fctor α, ie A(z - )F(z - ) + B(z - )G(z - ) = A(α z - ) () Expnding oth sides of () nd compring the coefficients give, n n n n n The ove is written in the form, f ( α ) ( α ) fnf = g n ( n ) α n g n g MZ(α )=L(α) () If prmeters [{ i }, { i }] re identified t every smpling period nd pole-shift fctor α is known, the control prmeters Z=[{f i },{g i }}] solved from () when sustituted in (9) will give, u(t, α) = X T (t)z = X T (t)m - L(α) (3) In the ove, X(t)=[-u(t-) -u(t-)u(t-n f ) -y(t) y(t-) y(t- )y(t-n g )] The controller ojective is to force the system output y(t) to follow the reference output y r (t) The ojective function cn then e expressed s, J = min[ yt () yr ()] t (4) α In the ove, y(t)= u(t) + X T β; β=[- - 3 ] If the vrition of J with respect to α cn e mde smller thn predetermined error ound ε, it cn e shown tht minimum will occur when, J ε α = α (5) J ε + α where, ε is smll numer chosen to void the singulrity This cn then e expressed s, α = ε In the ove, ε ff [ ] + ff 3 + f J u u = ; = ; 3 = f f f u α α (6) The prtil derivtives re evluted from (3) nd (4), nd updtes of the control is otined considering first few significnt terms of the Tylor series expnsion of utα (, )The lgorithm cn e strted y selecting n initil vlue of α nd updting it t every smple through the reltionship, α (t)= α(t-)+ α (7) The control function is limited y the upper nd lower limits nd the pole shift fctor should e such tht it should e ounded y the reciprocl of the lrgest vlue of chrcteristic root of A (z - ) The ltter requirement is stisfied y constrining the mgnitude of α to unity PERFORMANCE OF THE CONTROLLER The input nd output of the plnt were considered to e the series converter voltge mgnitude of the UPFC nd the genertor speed vrition, respectively In order to excite the plnt for the identifiction nd control process, sequence of torque step disturnces to the genertor shft re simulted The digonl elements of the initil covrince mtrix P is ssumed e x 5, the initil pole shift fctor nd the forgetting fctor were used The strting vlues of ll the prmeters were considered to e in ll the simultions for consistency The model order to e estimted ws ssumed to e 3 Fig3 shows the genertor speed devition with no control when excited y the sequence of torque steps of +5%, -5%, +5% nd -5% The nominl loding is 85 pu t 9pf lgging The genertor terminl voltge t this lod is 7 pu nd the us voltge is pu The response of the system with the online control strtegy nd convergence of the prmeters is shown in Figs 4-8 Fig4 shows the vrition of the genertor speed with the pole-shift control pplied to the identified process It is pprent tht the electromechnicl trnsients re dmped SCSC 6 53 ISBN:

4 very well y the dptive controller The plnt prmeters re unknown t the strt of the estimtion process which gives the poorer response in the erly prt of the trnsients Fig 5 shows the vrition of the pole shift fctor s the estimtion procedure progresses The convergence of the {} nd {} prmeters in the in the dptive lgorithm re shown in Figs 6 nd 7, respectively The estimtion lgorithm converges to the desired vlues rpidly The convergence of the lgorithm is independent of the initil choice of the pole shift fctor α The vrition of the control function is depicted in Fig8; it cn e oserved tht very good dmping cn e provided with minimum control effort Figure 5 Online dpttion of the pole shift fctor Figure 3 Genertor speed vrition with no control Figure 6 Online dpttion of the prmeters in the model function Figure 4 Genertor speed devition with the online dptive stilizing control Figure 7 Online dpttion of the prmeters ISBN: SCSC 6

5 Fig shows the vritions of the genertor terminl voltge for three loding conditions () pu, () nd (c) 85 pu It cn e seen tht tht the control strtegy restores the voltge very quickly from totl collpse These simultions were crried out with the converged plnt model nd pole-shift fctor s otined in the nominl loding considered in Figs 3- In rel pplictions, the models s well s the controls will e tuned on-line nd is, hence, expected to provide etter performnce All these simultion results indicte good dynmic ehvior of the power system with the dptive UPFC controller Figure 8 The control signl using the pole-shift method TESTING THE ADAPTIVE CONTROLLER A numer of cse studies were performed with the dpted system prmeters nd the pole shift prmeters rrived t in the previous section For 5% input torque pulse on the genertor, the rotor ngle vritions recorded for 5 operting conditions re shown in Fig9 These re for genertor outputs of ) pu, ) pu, c) 85pu, d)78 pu, nd e)6pu It cn e oserved tht the dmping properties re very good for the whole rnge of opertion considered Fig shows the trnsient ngle vritions of the genertor with the proposed dptive control strtegy for severe three-phse fult of s durtion for the lodings considered in Fig9 It is to e noted tht without control the system is under dmped, in generl, nd unstle in some cses Fig shows the response without control (p) nd with control (q) for the three phse fult condition t pu loding Figure Genertor rotor ngle following three-phse fult for the lodings s in Fig 9 Figure 9 Genertor rotor ngle vritions following 5% torque pulse for 5 loding conditions Figure Comprison of response without control (p) nd the proposed dptive control (q) following three-phse fult t pu loding SCSC 6 55 ISBN:

6 Figure Terminl voltge vrition of genertor following three-phse fult for different loding conditions CONCLUSIONS An dptive control technique hs een used to enhnce the dynmic performnce of power system instlled with unified power flow controller The control employed is the mgnitude of the series converter voltge The proposed stilizing technique identifies the plnt model on-line nd genertes control to stilize the closed-loop system employing pole shift technique The lgorithm hs een shown to converge to estimted prmeter model rpidly The on-line controller hs demonstrted to provide very good dmping to the system trnsients The roustness of the control strtegy ws tested y considering the converged vlues otined from the test phse It ws oserved tht the control provided roust performnce over wide rnge of power system opertion ACKNOWLEDGEMENT The uthors wish to cknowledge the fcilities provided y the King Fhd University of Petroleum nd Minerls towrds this reserch This work is funded y KFUPM under Project FT-5-9 REFERENCES [] Nvi-Niki, A, nd Irvni, MR, Stedy Stte nd Dynmic Models of Unified Power Flow Controller (UPFC) for Power System Studies, IEEE Trns on Power Systems, 996, (4), pp [] Dong, LY, Zhng, L, nd Crow, ML, A New Control Strtegy for Unified Power Flow Controller, IEEE PES Winter Meeting,, Vol, pp [3] Seo, J, Moon, S, Prk, J nd Choe, J, Design of Roust UPFC Controller for Enhncing the Smll Signl Stility in the Multi-mchine Power Systems, IEEE Power Engineering Society Winter Meeting,, Vol 3, pp97- [4] Wng, HF, Dmping Function of Unified Power Flow Controller, IEE Proc-Gener Trnsm Distri, 999, 46(), pp8-87 [5] Tmey, N nd Kothri, ML, Dmping of Power System Oscilltions with Unified Power Flow Controller (UPFC), IEE Proc-Gener Trnsm Distri, 3, 5(), pp9-4 [6] Wu, X, Qu, Z, nd Mohptr, RN, Stility Constrined Opertion of UPFC Devices, IEEE Trnsmission& Distriution Conference & Exposition,, Vol, pp3-36 [7] Wng, HF, Applictions of Modeling UPFC into Multi-mchine Power Systems, IEE Proc-Gener Trnsm Distri, 999, 46(3), pp36-3 [8]WMHussein nd OPMlik, Study of System Performnce with Duplicte Adptive Power System Stilizer, Electric Power Components nd Systems, 3, 3, [9] A Soos nd OPMlik, An H Optiml Adptive Power System Stilizer, IEEE Trns on Energy Conversion,, 7(), [] JR Smith, DA Pierre, DARuderg, I Sdhigi, APJohnson nd JFHuer, An Enhnced LQ Adptive VAr Unit Controller for Power System Dmping, IEEE Trns on Power Systems, 989, 4(), []PKDsh, PCPnd, AMShrf nd EFHill, Adptive Controller for Sttic Rective Power Compenstion in Power Systems, Proc IEE, 987, 34(3), [] RLozno-Lel nd C Goodwin-Grhm, A Glolly Covergent Adptive Pole-plcement Algorithm with Persistency of Excittion Requirements, IEEE Trns on Automtic Control, 985, AC 3(8), [3] OPMlik, GPChen, GS Hope, QHQin nd GYXu, Adptive Self-optimizing Pole Shifting Control Algorithm, IEE Proc-D, 99, 39(5), ISBN: SCSC 6