Modeling and Dynamic Analysis of a STATCOM for System Damping Enhancement

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1 oeling an Dynamic Analyi of a ACO for ytem Damping Enhancement aou Jabbari () Ghazanfar hahgholian () ehi ahavian () Ehan Attarpour () Ali Leilaeyoun () () Department of Electrical Engineering, Najafaba ranch, lamic Aza Univerity, fahan, ran () Department of Electrical Engineering, Naein ranch, lamic Aza Univerity, fahan, ran hahgholian@iaun.ac.ir Abtract- A tatic ynchronou compenator (ACO) control i preente to enhance the amping of the power ytem. he aim of thi paper i ynamic moeling an analyi of ACO for a ingle-machine infinite-bu () power ytem. Alo the applicability of PD type control in ynamic performance enhancement with eigenvalue analyi i tuie an hown to be feaible. he moel i then ue to invetigate the amping improvement of a an the reult obtaine are ytematically ecribe.. NRODUCON Power ytem are non linear ytem with a wie range of operating conition an time varying configuration an parameter. Large interconnecte power network are for increaingly heavier loa epecially if new line cannot be built becaue of the lack of right of way. Continuou avance in power electronic technologie have mae the application of FAC evice very popular in power ytem. Generally, the main objective of FAC are to increae the ueable tranmiion capacity of line an control power flow over eignate tranmiion route. Dynamic application of FAC controller inclue tranient tability improvement, ocillation amping an voltage tability enhancement [, ]. A goo number of paper are available on moeling, imulation, operation an control funamental of the FAC evice [3-8]. imulation of FAC controller i mainly one in the following two way: (a) etaile calculation in 3 phae ytem an (b) teay tate an tability analye [9]. he theoretical analyi an experimental verification of voltage regulation tability problem of ACO were preente in [0]. he author propoe phae compenation metho to achieve larger phae margin of the control loop to enhance the tability of ACO voltage regulating loop. An approach for comprehenively aeing the financial benefit to the network of three mot wiely ue FAC bae evice for voltage ag mitigation FAC preente in []. A ACO-bae var generator for meium power application, utilizing one-cycle control i propoe in [], which the witching freuency of the evice i contant. he eign of a pace vector pule with moulate two-leg fourwitch ACO to provie atifactory performance in performing variou reactive power flow control function uring teay-tate an tranient operation of power ytem in [3] preente. Damping the ocillation i not only important in increaing the tranmiion capability but alo for tabilization of power ytem conition after critical fault. One of the metho of amping of power ytem ocillation i control of the tranmiion line reactance. Reactance control can be achieve by erie or hunt compenation. here are variou hunt-connecte FAC evice. he ACO i hunt connecte reactive compenation euipment. A ACO i one of the funamental FAC evice that can be ue for voltage regulation an ynamic voltage control, becaue of it attractive teay tate performance an operating characteritic [4, 5]. n thi paper control of power ytem with ACO i invetigate. A linear mall-ignal ynamic moel of the wa erive uing tate-pace. A newly linearize block iagram which repreent the ynamic of power ytem i ecribe. imulation reult how the effect of the AC- O on the amping of the power ytem ocillation.. ALL GNAL ODEL n thi ection we will tuy the mall ignal performance of a ingle machine connecte to a large ytem through tranmiion line. he tuie ytem, hown in Figure, i a ingle-machine infinite-bu () power ytem euippe with the ACO at the bu bar of tranmiion line, where repreent the euivalent reactance between the machine bu an the intermeiate bu, an repreent the euivalent reactance between bu an the infinite bu. A ACO operate a a hunt connecte tatic var compenator whoe capacitive or inuctive output current can be controlle inepenent of the ac ytem voltage. Fig.. ACO intalle in power ytem with hunt loa he baic principle of operation of a ACO i the generation of a controllable ac voltage ource (U C ) behin a //$ EEE 087

2 tranformer leakage reactance ( ) by a voltage ource converter connecte to a c capacitor (C DC ). he relationhip hown in Figure are ue to tranform variable from xy reference frame to the. he rotor angle δ i the angle by which internal voltage (E ) lea the x-axi. δ i the angle of ACO bu voltage an δ i the angle of generator terminal voltage. he V- characteritic of a ACO i limite only by the maximum voltage an current rating a epicte in Figure 3. nuctive current generate by ACO i coniere poitive. hi controller can be operate over it full output current range even at very low voltage. oeling of ACO a a controllable reactive current ource with time elay i how in Figure 4. he following euation can be erive from voltage euation: U inδ tgδ = () U co δ + U [ U ] in δ tgδ = () [ U ] co δ U where U, U an U are voltage magnitue at i infinite bu, ACO bu an generator terminal, repectively. he voltage magnitue at bu can be written a: + U co( δ δ ) + U coδ U = (3) where = + i total reactance of line. he voltage of bu can be written a: U = λ ( λ ) + ( λ ) U + λ U + λ ( λ )U U coδ where λ i ue to how the fraction of line length at which the ACO i place. From the phaor iagram, the angle between the U an -axi i θ an can be written a: tgθ = E + + ( + + ( )(U + in δ + )(U L co δ + inθ ) coθ ) (4) (5) he an component of ACO bu voltage can be written a: Fig.. wo frame reference for phaor uantitie U + = [U inδ + inθ ] (6) + + U = [U co δ + coθ ] + E + + (7) he generator output power in preence of ACO can be expree in term of the δ, δ, U an U, a: Q E P U U U = in( δ + in( δ δ ) E ) U (U U ) U = coδ co( δ δ ) (8) (9) Fig. 3. he V- characteritic of ACO Fig. 4. ACO moel he output power ha been ecompoe into two component. he econ term how the effect of ACO an change with. Note that the coefficient of the econ term often i numerically poitive becaue δ for a normal ytem i greater than δ. Amplitue an angle of ACO voltage in term of generator terminal voltage angle how in Figure 5. he euation of the ytem are nonlinear an have to be linearize for mall ignal analyi. he following i a ummary of the ytem linear euation a a et of firt orer ifferential euation, with time t in econ, rotor angle δ in electrical raian, J i the inertia contant in econ an all other uantitie in per unit [6]. 088

3 Δ P = K Δδ + K Δ (3) E ED D E Δ = K Δδ + K Δ (4) UD Δ U = K Δδ + K Δ (5) Δδ D U Δ θ = K Δδ + K Δ (6) = ( K ) Δδ K Δ (7) D ΔQ = (U + K ) Δ + K Δδ (8) A o U he omain form of PD controller tranfer function i a follow: o UD KV GU ( ) = KVP + + KVD (9) KW GW ( ) = KWP + + KWD (0) o Fig. 5. ACO voltage in term of generator terminal voltage angle δ = ωo δ t (0) ω = t J ( P PE KD ω ) () t = ( K A U ) () + A where ω i relative pee, K D i the amping contant,, K A, A an U are the output current, gain, time contant an controller output of the ACO, P i the input mechanical power, repectively.. CONROL DEGN AND DYNAC ANALY An open loop ynamic analyi ha been mae uing the linear mall ignal moel. hi analyi, bae on tranfer function an oe plot, i imilar to the analyi for O (ingle input-ingle output) ytem. Proportional integral (P) an proportional integral erivative (PD) controller are wiely utilize in inutrial control ytem. he PD controller i ue to improve the ynamic repone a well a reuce or eliminate the teay tate error. he amping of the ytem i improve by ecreaing (increaing) the output power of the machine when it pee eviation i negative (poitive). Figure 6 how the block iagram repreentation of the mall ignal performance of the ytem moel with PD controller in the pee, G W (), an the voltage, G U (), loop. Contant K ED an K E are erive from the electric torue expreion, K D an K from the terminal current of generator, K UD an K U from the ACO bu voltage magnitue, K D an K from the ACO bu voltage angle. he bai for the block iagram an the expreion for the aociate contant are evelope below: Fig. 6. Function cheme for the ACO control V. ULAON REUL he nominal parameter of the ytem an the operating conition ue for the ample problem invetigate are given in able. All ata are given in per unit of value on the 0 VA, 4KV bae, except that J an time contant are in econ while freuency i in hertz. he hunt loa i repreente by the contant amittance. ALE DAA OF YE Component Parameter Value GENERAOR RANON LNE ACO J 7 K D 0 f K A A 0.0 O At very light loaing the ytem generate reactive power that mut be aborbe, while at heavy loaing the ytem conumer a large amount of reactive power that mut be replace. hree operating conition for the time repone 089

4 tuie are a hown in able. able ummarize the value of the enitivity contant uner the ytem conition. he teay tate operating point of the moel power ytem a a function loa conition i hown in able V. ALE OPERANG CONDON Loaing P EO Q EO U O Nominal Light Heavy ALE ENVY CONAN OF ODEL POWER YE Loaing Normal Heavy Light Contant K E Fig. 8. wing curve of the generator for variou value of K WP K ED K U K UD ALE V EADY AE OPERANG PON OF ODEL POWER YE teay LOADNG tate Normal Heavy Light U o U o U O o o θ o δ he root-locu plot for the change of K WP in the ytem with proportional controller in pee loop i hown in Figure 7. Figure 8 an 9 how the wing curve of the generator an the ACO output current for variou value of controller proportional gain. We can ee that without ACO, generator ha unampe ocillation. Alo, it i oberve that by increaing the value of K WP the ytem amping improve. Fig. 7. Locu of the root of the change proportional gain of controller in pee loop Fig. 9. he ACO output current for variou value of K WP he effect of gain on ytem amping with controller in pee loop for normal loaing ummarize in able V an V. ALE V HE EFFEC OF K W ON YE PERFORANCE WH K WP=00 an K WD=0 K W Eigenvalue ±j ±j ±j0.5 Damping ratio Natural freuency ALE V HE EFFEC OF K WD ON YE PERFORANCE WH K WP=00 AND K W=0 K WD 0 00 Eigenvalue ±j ±j3.83 Damping ratio Natural freuency Figure 0 an how the phae portrait (the loa angle an rotor pee) an ACO bu voltage variation with control only in the pee loop. he repone with no control, proportional-integral (P) an proportional-erivative (PD) controller are hown by curve a, b an c, repectively, which K WP =00, K WD =0 an K W =0. herefore, an increae in the gain K WD ecreae both the natural freuency (ω n ) an the amping ratio (η) of ytem 090

5 ocillation moe. Converely, increaing the gain K W poorly increae the ω n an poorly ecreae the η of the ytem ocillation moe. he effect of gain on ytem amping with controller in voltage loop for normal loaing ummarize in able V an V. herefore, the voltage loop provie very little amping. ALE. HE EFFEC OF K WD ON YE PERFORANCE WH K WP=00 AND K VP=00 Damping Natural K WD Eigenvalue ratio freuency ±j ±j ±j Figure an 3 how the variation of the loa angle an rotor pee for the variou loa conition with control in both pee an voltage loop. he repone with normal, heavy an light loa are hown by curve a, b an c, repectively, which K WP =00, K WD =0 an K VP =0. Fig. 0. he phae portrait of with ACO with control only in the pee loop Fig.. he ACO bu voltage variation with control both in the pee loop an voltage loop Fig.. he ACO bu voltage variation with control only in the pee loop ALE V. HE EFFEC OF K V ON YE PERFORANCE WH K VP=00 AND K VD=0 Damping Natural K V Eigenvalue ratio freuency ±j ±j ±j ALE V. HE EFFEC OF K VD ON YE PERFORANCE WH K VP=00 AND K V=0 Damping Natural K VD Eigenvalue ratio freuency ±j ±j he effect of erivative gain on ytem amping with proportional controller in voltage loop for normal loaing ummarize in able. Fig. 3. he phae portrait of with ACO with control both in the pee loop an voltage loop he gain matrix of controller i etermine by pole placement in orer to obtain the eire ytem propertie. he tracking control law i obtaine with a pole placement techniue. We etermine the PD gain via the pole placement metho. he gain of controller for eferent amping ratio in normal loaing ummarize in ale. he reult imulation i hown in Figure 4, 5 an 6. We can ee that percent overhoot i reuce with an increae in the real pole itance of imaginary axi, an the pee of repone i increae with an increae in the complex pole itance of real axi. 09

6 ALE. HE EFFEC OF K WD ON YE PERFORANCE WH K WP=00 AND K W=0 Cae Pole K WP K WD K VP A -350, -±j , -±j c -50, -3±j , -±j controller in the pee loop ha effective control over the electrical an electromechanical tranient. ACKNOWLEDGEN hi work ha been extracte from the reearch project entitle Analyi an imulation of the effect of the tatic ynchronou compenator on amping ingle-machine power ytem ocillation in lamic Aza Univerity Najafaba ranch, Efahan, ran. REFERENCE Fig. 4. wing curve of the generator for variou value of K WP Fig. 5. he ACO bu voltage variation with control only in the pee loop (able ) Fig. 6. he phae portrait of with ACO with control only in the pee loop (able ) V. CONCLUON hi paper invetigate the control ability of ACO, one in the pee loop an the other in the voltage loop, to increae power ytem tability by amping power ocillation. he variou imulation reult on a ingle area ytem uner change of parameter valiate the propoe approach. A [] G. hahgholian, E. Haghjoo, A. eifi,. Haanzaeh, "he improvement DACO to enhance the uality of power uing fuzzy-neural controller", Jour. of ran. on Elec. ech. (JE), Vol., No.5, pp.3-8, Winter 00. (in Perian) [].R. anaei, A.R. Kami, "mprovement of ynamical tability uing interline power flow controller", Av. in Elec. an Com. Eng. (AECE), Vol.0, No., pp.4-49, 00. [3] G. hahgholian, P. hafaghi,. oalem,. ahavian, Analyi an eign of a linear uaratic regulator control for tatic ynchronou compenator, EEE/CCEE, pp.65-69, Dec [4] Y. L. Huang, A.Q. W.. hattacharya,. G. an, "mall ignal moel bae control trategy for balancing iniviual DC capacitor voltage in cacae multilevel inverter bae ACO", EEE ran. on nu. Elec., Vol.56, No.6, pp.59-69, June 009. [5] D. urali,. Rajaram, ranient energy analyi for ACO an C application, nter. Jour. of Elec. an Pow. Eng., No.3, pp.9-97, 009. [6] R. Kuiava, R.A. Ramo, N.G. reta, "Control eign of a ACO with Energy torage ytem an power uality improvement", EEE/C, pp.-6, Feb [7] A.A. Gharaveii, A. Hakimi,..R. Rafiei, "Power ytem tability enhancement via ACO upplementary control bae on fuzzy energy function", EEE/PC, pp.-6, June/July 009. [8] G. hahgholian,. Ehtehariha, H. ahavi-naab,.r. Youefi, A novel approach in automatic control bae on the genetic algorithm in ACO for improvement power ytem tranient tability, EEE/C, pp.4-9, 008. [9] D.Povh, oeling of FAC in power ytem tuie, EEE/ PEW, Vol., pp , 004. [0] L. Chun, J. Qirong,. Jianxin, "nvetigation of voltage regulation tability of tatic ynchronou compenator in power ytem", EEE/PEW, Vol.4, pp , Jan [] J.V. ilanovic, Y. Zhang, "Global minimization of financial loe ue to voltage ag with FAC bae evice", EEE ran. on Pow. Deli., Vol.5, No., pp , Jan. 00. [] K. Chatterjee, D.V. Ghoke, A. Chanra, K. Al-Haa, "imple controller for ACO-bae var generator", Pow. Elec. E, No., Vol., pp.9-0, ar [3] ao-ung a, "pace vector moel an control of a two-leg fourwitch ACO", nter. Rev. of Elec. Engi. (REE), Vol.5. No.3, June 00. [4] V. pita, A. Alexanrovitz, E. Zeheb, "Deign of a robut tate feeback controller for a ACO uing a zero et concept", EEE ran. on Pow. Del., Vol.5, No., pp , Jan. 00. [5]. ankar,. Ramarey, Digital imulation of cloe loop controlle PFC uing PPCE, nter. Jou. of Elec. an Pow. Engi., Vol., pp.99-03, 008. [6] G. hahgholian, P. hafaghi,. oalem,. ahavian, Damping power ytem ocillation in ingle-machine infinite-bu power ytem uing a ACO, EEE/CCEE, pp.30-34, Dec