Power System Stility Enhncement By Bsed Power Oscilltion Dmping r. Sntosh Kumr ripthi Associte Professor, Deprtment of Electricl Engineering, B.N. College of Engineering & echnology, Lucnow, Uttr Prdesh, Indi --------------------------------------------------------------------***--------------------------------------------------------------------- Astrct - his pper presents design nd nlysis of sed power oscilltion dmping. he Phillips- Heffron model of the Single chine Infinite Bus power system instlled with hs een used. he systemtic pproch for designing sed power oscilltion dmping hs een developed. he plces the Eigen vlue corresponding to mode of oscilltion t desired loction so tht the system hs desired degree of stility. he performnce of sed hs een exmined with different system conditions, under different line lodings of SIB power system. he effectiveness of proposed is verified y time domin simultion results in A-LAB environment. Key Words: FACS, Phillips Heffron model, nd SIB.. INRODUCION ody s power system is complex networ, sometimes mde of thousnds of uses nd hundreds of genertors. Aville power genertion usully does not situted ner growing of lod center. In order to meet the growing power demnd, utilities hve n interest in etter utiliztion of ville power system cpcities, existing genertion nd existing power trnsmission networ, insted of uilding new trnsmission lines nd expnding susttions. On the other hnd, power flows in some of the trnsmission lines re overloded, which hs s n overll effect of deteriorting voltge profiles nd decresing system stility nd security. In ddition, existing trditionl trnsmission fcilities, in most cses, re not designed to hndle the control requirements of complex nd highly interconnected power systems. his overll sitution requires the review of trditionl trnsmission methods nd prctices, nd the cretion of new concepts, which would llow the use of existing genertion nd trnsmission lines up to their full cpilities without reduction in system stility nd security. In the pst, power systems could not e controlled fst enough to hndle dynmic system condition. his prolem ws solved y over-design; trnsmission systems were designed with generous stility mrgins to recover from nticipted operting contingencies cused y fults, line nd genertor outges, nd equipment filures. Series cpcitor, shunt cpcitor, nd phse shifter re different pproches to increse the power system trnsmission lines lod ility. In pst dys, ll these devices re controlled nd switched mechniclly nd were, therefore, reltive slow. hey re very useful in stedy stte opertion of power systems ut from dynmicl point of view, their time response is too slow to effectively dmp trnsient oscilltions. If mechniclly controlled systems were mde to respond fster, power system security would e significntly improved, llowing the full utiliztion of system cpility while mintining dequte levels of stility. his concept nd dvnces in the field of power electronics led to new pproch introduced y the Electric Power Reserch Institute (EPRI) in the lte 9. Clled Flexile AC rnsmission Systems or simply FACS, it ws n nswer to cll for more efficient use of lredy existing resources in present power systems while mintining nd even improving power system security. In order to clerly determine the gols of this thesis, the concept of stility must e defined. A definition given in [] is s follows: Power system stility my e rodly defined s tht property of power system tht enles it to remin in stte of operting equilirium under norml operting conditions nd to regin n cceptle stte of equilirium fter eing sujected to disturnce. From this generl definition, two ctegories of stility re derived: smll-signl nd trnsient stility. Smll-signl stility is the ility of the system to return to norml operting stte following smll disturnce. Investigtions involving this stility concept usully involve the nlysis of the linerized stte spce equtions tht define the power system dynmics. rnsient stility is the ility of the system to return to norml operting stte following severe disturnce, such s single or multi-phse shortcircuit or genertor loss. Under these conditions, the linerized power system model does not usully pply nd the nonliner equtions must e used directly for the nlysis, nd must e solved y direct methods or y itertive step-y-step procedures [].Since the development of interconnection of lrge electric power systems, there hve een spontneous system oscilltions t very low frequencies in order of.-.hz. Once strted, the oscilltion would continue for while nd then dispper, or continue to grow, cusing system seprtion []. In order to dmp these power system oscilltions nd increse system oscilltions stility, the instlltion of Power System Stilizer (PSS) is oth economicl nd effective. PSSs hve een used for mny yers to dd dmping to electromechnicl oscilltions. o dte, most mjor electric 7, IRJE Impct Fctor vlue:. ISO 9: Certified Journl Pge 7
power system plnts in mny countries re equipped with PSS [].However, PSSs suffer drwc of eing lile to cuse gret vritions in the voltge profile nd they my even result in leding power fctor opertion nd losing system stility under severe disturnces. In ddition, in deregulted environment, plcement my e prolemticl due to genertor ownership recently ppered FACS (Flexile AC rnsmission System)-sed stilizer offer n lterntive wy in dmping power system oscilltion. Although, the dmping duty of FACS s often is not their primry function, the cpility of FACS sed stilizers to increse power system oscilltion dmping chrcteristics hs een recognized []. cn improve power oscilltion dmping effectively. he dmping cpility of is required to e investigted thoroughly for proper on line pplictions in chnging operting conditions. Different pproches sed on modern control theory hve een pplied to sed design. Wng [:7] hve presented modified linerized Phillips-Heffron model of power system instlled with nd ddressed sic issues pertining to design of sed power oscilltion dmping long with selection of input prmeters of to e modulted in order to chieve desired dmping..k. o hve presented fuzzy dmping of through genetic lgorithm []. L.Y. Dong hve proposed PI sed pproch for the dynmic control of with new control strtegy, the ctive nd rective power flow control ws chieved ensuring dmping of system oscilltions [9]. Z. Hung et. l. hve tested two dmping schemes for, one is voltge modultion in voltge control of shunt element nd other is power modultion in constnt power control of series element, cscde led-lg trnsfer function hs een used for the supplementry control []. mplitude modultion rtio of series VSC-B nd δ represents phse ngle of series VSC-B []. While considering DC lin, phse of trnsformer E nd the corresponding rm of VSC-E, expression for voltge is: Agin DC lin is considered, phse of trnsformer B nd the corresponding rm of VSC-B then voltge expression is Figure : in SIB power system. () he expression for voltge of phse nd c for VSC-E nd VSC-B re similr ut hve phse shift of π nd π, respectively. By pplying Pr s trnsformtion on the threephse dynmic differentil equtions of the nd ignoring the resistnce nd trnsients of the trnsformers, the dynmic model of the is [].. POWER SYSE INSALLED WIH Figure.shows single mchine infinite us power system instlled with unified power flow. Power system which comprises synchronous genertor connected to n infinite us through trnsmission line nd stepping up trnsformer. he genertor is ssumed to hve Automtic Voltge Regultor (AVR) controlling its terminl voltge. he single-mchine infinite-us (SIB) system used in this study is for etter understnding of trnsient stility since the purpose for the use of is to improve trnsient stility of the system. he is plced etween us nd us on the trnsmission line s shown in Figure. he is designed to control the power (rel nd rective) through line s well s the voltge t us using PW power. An sed on pulse width modultion (PW) technique is eing considered, it consist of two solid stte synchronous voltge source converters, shunt connected VSC E nd series connected VSC B, coupled through common dc lin cpcitor C dc nd n excittion trnsformer E nd oosting trnsformer B. he dc lin provides pth to exchnge ctive power etween the converters. Here, m e, m nd δ e, δ re the four input control prmeter of the. Here, m e is mplitude modultion rtio of shunt VSC-E, δ e is phse ngle of shunt VSC-E, m is () On neglecting the converter hrmonics, the following equtions cn e written relting the voltge t AC side terminl of shunt nd series connected converters VSC-E nd VSC-B to the cpcitor voltge V dc on the common dc-lin. () () he instntneous power t the AC nd DC terminls of shunt nd series connected converters VSC-E nd VSC-B re equl, if converters re ssumed to e lossless. Hence power lnce eqution is: () 7, IRJE Impct Fctor vlue:. ISO 9: Certified Journl Pge
(7) Since the net current to cpcitor is zero, the DC circuit cn e descried s: () E fd = K Efd + ( V V ) to t Using eqution () to (), the following results: Linerizing the dc lin cpcitor voltge eqution of From figure we following expressions cn e written s: (9) () Following finl linerized stte spce model of single mchine infinite us system with is otined s: ΔX =AΔX+BΔ U On solving the ove equtions nd following re the d- nd q-component of current I E nd I B. X E E q V fd dc u m m e e Where, Δ me, Δ δe,δ m, Δ δ re the lineriztions s of the input control signls of the Where A d K 7 D d K d pd qd d K 9 vd pe B qe d K ve ce pde qde K cde d vde p q c d K d pd qd d K vd cd Linerizing the following Dynmic Equtions of Genertor he linerized dynmic model of ove stte model shown y following figure., where only one input control signl is demonstrted, with the u eing m e or m or δ e or δ. It cn e seen tht the configurtion of the Phillip-Heffron model is exctly sme s tht instlled with SVC, CSC nd CPS presented in []. 7, IRJE Impct Fctor vlue:. ISO 9: Certified Journl Pge 9
- w m,δ should e within their limit nd the voltge of the DC lin cpcitor V dc should e ept constnt.. DESIGN OF CONROLLER he Linerized stte spce model of SIB power system is otined y phillips-heffron model s expressed y: pu - Ex(s) - qu qd vu vd p () Where A nd B re the mtrices of the system nd input respectively. X is the system stte vector, nd U is the input stte-vector. he mtrices A nd B re constnt under the ssumption of system linerity. If we use stte feedc, tht is, if we set U= -KX where K is the chosen gin mtrix, the eqution ecomes: V dc () cu - 7 And the prolem is to llocte ny set of eigenvlues to closed loop mtrix (A-BK) y choosing the gin mtrix K. Here in this thesis the gin mtrix K is chosen y ALAB tool. he syntx is given elow: Figure: Phillips-Heffron model of power system instlled with.. CONROLLER he dynmic chrcteristics of system cn e influenced y loction of eigenvlues, for good system response in terms of overshootsundershoot nd settling time, prticulr loction for system eigenvlues is desired depending upon the operting conditions of the system. he dmping power nd the synchronizing power re relted respectively, to rel prt nd imginry prt of eigenvlue tht correspond to incrementl chnge in the devition of the rotor speed nd devition of rotor ngle[], this Eigenvlue is nown s electromechnicl mode. Power oscilltion dmping cn e improved if rel prt of eigenvlue ssocited with mode of oscilltion cn e shifted to left-side in complex s-plne s desired. his thesis present such tht the closed loop designed system will hve desired degree of stility [, nd ]. For the power system representtion in stte spce form, closed loop gin mtrix A-BK otined y choosing the gin mtrix K through stte feedc control lw U = KX will hve ll its eigenvlue lies in left side of complex-plne. It is n esy ts to design power oscilltion dmping. ing use of proposed design pproch, sed power oscilltion dmping is designed to dmping of low frequency power oscilltions. his hs een ttempted on smple system. he expecttion from sed is to provide instntneous solution to power oscilltion dmping, the settling time s otined from response of system is expected to e s smll s possile. For minimizing settling time rel prt of eigenvlue corresponding to mode of oscilltion re required to e shifted more nd more on LHS of complex plne, this will require control effort. here is hrdwre limit of ny designed, for the cse of, in view of this, the control input prmeters m e,δ e nd 7, IRJE Impct Fctor vlue:. ISO 9: Certified Journl Pge () Where, vector p of desired self-conjugte closed-loop pole loctions, plce computes gin mtrix K such tht the stte feedc plces the closed-loop poles t the loctions p. In other words, the eigenvlues of (A-BK) mtch the entries of p (up to the ordering). K=plce(A,B,p)computes feedc gin mtrix K tht chieves the desired closed-loop pole loctions p, ssuming ll the inputs of the plnt re control inputs.. ANALYSIS OF CONROLLER AND SIULAION RESULS he effectiveness of proposed for dmping locl mode oscilltions hs een demonstrted with SIB system. he linerized stte spce model for SIB instlled with is given ove. Using pole-plcement design technique for SIB hs een designed. Also, to hve improved dmping nd hence the smll settling time of response, it is desired to shift the rel prt of eigenvlue corresponding to mode of oscilltion to LHS in complex s-plne. o chieve this, it is desired to plce eigenvlue corresponding to mode of oscilltion t loction on LHS of complex plne. he chnge in operting conditions of power system is common phenomenon, e.g., line loding vries over wide rnge of line my chnge, sometimes. For good design of dmping, esides the mximum effectiveness of the, the roustness of dmping to the vritions of power system operting conditions is n eqully importnt fctor to e ten under considertion. Hence, it is desirle for tht it must e le to respond for chnges in operting point long with stisfctory performnce. herefore, it is extremely importnt to investigte the effect of lod vritions on the performnce of the designed. In view of this, the
gnitude (pu) performnce of t following operting conditions re studied (i) percent decrese in line loding (ii) percent increse in line loding. For performing such investigtions, the eigenvlue nlysis with simultion results t ech loding condition hs een done. he effect of vrition in modultion index, nd converter ngle of oth converters re lso considered on the performnce of designed proposed. For performing such investigtion gin the eigenvlue nlysis with simultion results in vrition in modultion index nd converter ngle of oth converters hve een done. Eigen- vlues nlysis under we power system nd vrious line lodings le: Eigen vlues with for strong SIB system. Lod System % Decrese (. pu) -9.7 -.7 +.77i -.7 -.77i (.) -.7 Norml (. pu) -9.7 -.+.i -.-.i (.7) -.7 % Increse (. pu) -9.9 -.+7.i -. -7.i (.) -.7 le: Eigen vlues with for we SIB system. Lod % Decrese (. pu) Norml (. pu) % Increse (. pu) Only -. -. -. +.i -..i (.) -. -.9 -. -. +.i -..i (.) -.7 -. -.7 -. +.7i -..7i (.) -. System Only -9.7 -.+.9i -. -.9i (.77) -. -. -. -. +.i -. -.i (.9) -. -. -. -. +.i -..i (.7) -. -9.7 -. +.i -. -.i (.) -.79 -.9 -. -. +.9i -..9i (.) -. -.9 -. -. +.9i -..9i (.7) -. -9.9 -. + 7.i -. - 7.i (.) -.7 -. -.7 -. +.i -..i (.9) -.7 -. -.7 -. +.i -..i (.7) -.7 Eigen- vlues nlysis under strong power system nd vrious line lodings. he olded row of this tle represents the electromechnicl mode eigenvlue nd its dmping rtio. It cn e oserved from the tle tht with proposed gretly improve the system stility. -. -. -. +.i -..i (.7) -. -.9 -. -.9 +.i -.9.i (.) -.7 -. -.7 -. +.7i -..7i (.7) -. Simultion results under different system conditions nd vrious loding conditions. It cn e redily seen tht the proposed performs etter in terms of reduction of overshoot nd settling time thn system without nd with system with only. his is consistent with the eigenvlues nlysis results. Simultion results with vrition in system- stte, rotor ngle (δ) of genertor is only considered. he system responses re simulted using -file progrm of ALAB. Figures to show the comined system response without, with nd with t. pu,. pu nd. pu line loding with. power fctor of weer (dmping coefficient D=) nd stronger (dmping coefficient D=) SIB power system. It cn e oserved from these figures tht the with coordinted cn gretly improve the dmping of the system nd its stility under different line loding nd system condition s mention ove. - ime (sec) 7, IRJE Impct Fctor vlue:. ISO 9: Certified Journl Pge
gnitude (pu) gnitude (pu) gnitude (pu) gnitude (pu) gnitude (pu) gnitude (pu) gnitude (pu) gnitude (pu) gnitude (pu) gnitude (pu) - - - ime (sec) - - - - ime (sec) Figure. Vrition in delt with, without nd with of strong (D=) system t line lodings. pu,.. pu.nd. pu. - - - - ime (sec) - - - - ime (sec) - - - - ime (sec) le: Eigen vlues with vrition in phse ngle nd modultion index of oth converters. Converters phse nd modultion index System with only System with VSC-E δe=. VSC-B δ=. VSC-E me=. VSC-B m=. -. +.77i -..77i (.9) -.99+.9i -.99 -.9i (.9) --. +.77i -..77i (.7) -.97+.9i -.97 -.9i (.77) VSC-E δe=.7 VSC-B δ=.7 VSC-E me=.7 VSC-B m=.7 -.9 +.i -.9.i (.) -. +.9i -..9i (.) -.7 +.i -.7.i (.) -. +.9i -..9i (.7) VSC-E δe=.9 VSC-B δ=.9 VSC-E me=.9 VSC-B m=.9 -.7 +.7i -.7.7i (.) -. +.i -..i (.) -. +.7i -..7i (.9) -. +.i -.i (.79) he comprtive study from this tle shows tht vrition in converters phse ngle is more effective thn vrition in mplitude modultion index of oth converters; hence performnce of proposed is more effective. - - Figure. Vrition in rotor ngle without, with nd with of we (D=)system t line lodings. pu,.. pu.nd. pu. - - - ime (sec) - - - ime (sec) Eigen- vlues nd simultion results with vrition in converters input he vrition in converters ngle of is nother eqully importnt fctor for the study of performnce using eigenvlue nlysis. Under this section converters phse ngle t. pu,.7 pu nd.9 pu re ten respectively for the eigenvlue nlysis nd study the performnce of.le shows the comined study of eigenvlues of oth vritions in modultion index nd converters ngle of. From this tle it cn e oserve tht t lower vlue of per unit the vrition in converters phse ngle is more effective thn vrition in modultion index, nd higher vlue of per unit the vrition in modultion index of oth the converters is more effective. he olded row of this tle represents the electromechnicl mode eigenvlue nd its dmping rtio. - - - - ime (sec) Figur. Vrition in rotor ngle with, without nd with for oth converters phse ngle.,.7,.9 pu. - - - - ime (sec) - - - - ime (sec) 7, IRJE Impct Fctor vlue:. ISO 9: Certified Journl Pge
gnitude (pu) Figure. Vrition in delt of SIB system with,without with for modultion index of oth converters.,.7,. pu.. CONCLUSION Frequency oscilltions nd hence improving power system dynmic stility hve een verified through eigen- vlue nlysis nd simultion results with different system conditions nd under different line loding nd without ny line loding. Agin effectiveness of proposed in dmping low frequency E mode of oscilltions nd hence improving the power system stility lso hve een verified through eigenvlue nlysis nd simultion results with the vrition in modulting index of nd phse ngle of oth converters. 7. APPENDIX = J VA; X d = pu X d =.pu d =. sec; X q =. pu δ =.9 rdin; E q =. pu K = pu X =. X BV =. pu - - - - ime (sec) X e =. pu X te =. pu V =. pu pf=.; f = Hz. =. sec V dc =.; C dc =. F. [] nchur G. nd Wtson W., 97. Experience with supplementry dmping signls for genertor sttic excittion systems. IEEE rns. PAS, Vol. 9, pp. 99-. [] Chow J. H, nd Gsc J. S., 99. Concepts for design of FACS s to dmp power swings. IEEE rn on Power System, Vol., No., pp. 9-9. [] Wng H. F., 999. Dmping function of unified power flow. IEE Proceedings Genertion rnsmission nd Distriution, (), pp. 7. [7] Wng H. F., 999. Appliction of modeling into multi-mchine power systems. IEE Proceedings Genertion rnsmission nd Distriution, (),pp.. [] o.k., Ni Y. nd Wu F.F.,. Design of fuzzy dmping of through genetic lgorithm. Power Engineering Society Summer eeting, IEEE, Vol:, pp. 9 9. [9] Crow.L., Dong L.Y.nd Zhng L.,. A new control strtegy for the Unified Power Flow. Power Engineering Society Winter eeting, IEEE, Vol.:, pp 7-. [] Chen S., Hung Z., Ni Y., Shen C.. Wu F.F. nd Zhng B., (), Appliction of unified power flow in interconnected power systems modeling, interfce, control strtegy, nd cse study. IEEE rnsctions on Power Systems, Vol., No., pp 7-. [] Pndey R.K. nd Singh N.K.,. Anlysis of unified power flow in dmping power systemoscilltions. Proceeding of th Ntionl Power System Conference, vol II, pp. 9. [] Kundur P., 99. Power System Stility nd Control. New Yor, cgrw Hill. [] Di H.. nd cinnis B. C., Shieh L. S., 9. Liner qudrtic regultors with eigenvlue plcement in verticl strip.ieee rns. on Automtic Control, Vol. AC-, pp., -. [] unro Neil nd Ptel R. V., ultivrile system theory nd Design. Int. Series on System nd Control, Vol., Pergmon Press, NewYor.. REFERENCES [] Yu Y. N., 9. Electric Power System Dynmics, Acdemic Press. [] Anderson P.. nd Foud A., 99. Power System Control nd Stility. IEEE Press. [] Pi P. W nd Suer P.W. 99. Power System Dynmics nd Stility. Prentice Hll. 7, IRJE Impct Fctor vlue:. ISO 9: Certified Journl Pge