INFLUENCE OF TCSC FACTS DEVICE ON STEADY STATE VOLTAGE STABILITY

Transcription

1 INFLUENCE OF TCSC FACTS DEVICE ON STEADY STATE VOLTAGE STABILITY GABER EL-SAADY, 2 MOHAMED A. A. WAHAB, 3 MOHAMED M. HAMADA, 4 M. F. BASHEER Electrcal Engneerng Department Aut Unverty, Aut, Egypt 2, 3&4 Electrcal Engneerng Department Mna Unverty, Mna, Egypt E-mal: gaber@yahoo.com ma_abdelwahab@hotmal.com, mohamed_m-hamad-a@yahoo.co.u, mfarou3@yahoo.com Abtract The nfluence of ere Flexble AC Tranmon Sytem (FACTS) devce namely, Thyrtor-Controlled Sere Capactor (TCSC) on the teady tate voltage tablty the man obectve of th paper. The Lne tablty Index LSI under excepted lne outage contngence ued to dentfy the crtcal lne whch condered a the bet locaton for TCSC. A modal analy ued to defne the weaet bu of the tuded ytem. The FACTS devce mplemented and ncluded nto the Newton-Raphon power flow algorthm, and the control functon formulated to acheve the voltage tablty enhancement goal. The analy preformed on tandard IEEE 3 bu ytem. The propoed cheme are teted under dfferent loadng condton and dfferent nonlnear voltage dependent load. The mulaton reult demontrate the feablty and effectvene of the devce and the propoed algorthm. Keyword-voltage tablty; TCSC; FACTS; voltage dependent load I. INTRODUCTION The utlte nteret about the voltage ntablty and voltage collape problem ncreae due to tructural change n the electrcal ector, uch a thoe caued by prvatzaton and deregulaton, modfcaton of the networ topology, a well a ever ncreang n load demand brought by economc and envronmental preure that led the power ytem to operate near t tablty lmt. Several blacout are reported n many countre relate to voltage tablty problem []. A an example, there are x blacout durng x wee affectng mllon of people n US, Sweden, UK, and Denmar [2]. Generally, voltage collape the proce by whch the equence of event accompanyng voltage ntablty lead to a low unacceptable voltage profle n a gnfcant part of the power ytem. Voltage collape may be a poble outcome of voltage ntablty, whch defned a the attempt of load dynamc to retore power conumpton beyond the capablty of the combned tranmon and generaton ytem [3]. A large number of reearcher have been tuded the voltage tablty problem. Ther attenton ha reulted wth a numerou number of paper, boo, and report beng publhed. Mot of thee are reported n the extenve bblography [4]. The voltage ntablty may be clafed nto tranent and teady tate, the latet the man concern n th paper. Steady tate voltage tablty or Small-dturbance voltage tablty refer to the ytem ablty to mantan teady voltage when ubected to mall perturbaton uch a ncremental change n ytem load [5]. Many of meaure ued to prevent voltage ntablty [6] uch a, () Placement of ere and hunt capactor, () Generaton rechedulng, () Intallaton of ynchronou condener, (v) Under- Voltage load heddng, (v) Blocng of Tap-Changer under revere operaton, (v) Placement of FACTS controller. The lat method condered n th tudy. FACTS a termnology that embrace a wde range of power electronc controller. Thee devce ue no delay and hgh current power electronc devce avalable today for afe and accurate repone. They are able to control the parameter uch a voltage magntude and ther angle, lne mpedance, actve and reactve power flow [7]. There are many type of FACTS uch a, Superconductng magnetc energy torage (SMES), Statc Var Compenator (SVC), Statc Synchronou Compenator (STATCOM), Statc Synchronou Sere Compenator (SSSC), Thyrtor Controlled Sere Capactor (TCSC), Interlne Power Flow Controller (IPFC), and Unfed Power Flow controller (UPFC). TCSC condered n th paper to enhance teady tate voltage tablty by ncorporate the devce nto the Newton-Raphon proce under dfferent type of voltage dependent load. The ret of th paper tructured a follow. In ecton II, the concept of the teady tate voltage tablty model ntroduced. The tructure and operaton prncple of TCSC preented n ecton III. In ecton IV, the detaled tatc voltage tablty model of TCSC decrbed. The mathematcal model of the voltage dependent load explaned n ecton V. In ecton VI the propoed methodology for the bet placement of TCSC condered. The reult obtaned for the tet ytem gven and dcued n Secton VII. Fnally, Secton VIII contan the concluon. Internatonal Journal of Power Sytem Operaton and Energy Management ISSN (PRINT): , Volume-, Iue-4, 22 36

2 II. STEADY STATE VOLTAGE STABILITY The teady tate (tatc) analy method manly depend on the teady tate model, uch a power flow model or a lnearzed dynamc model decrbed by the teady tate operaton. Thee method [8-] can be dvded nto:. Load flow feablty method, whch depend on the extence of an acceptable voltage profle acro the networ. Th approach concerned wth the maxmum power tranfer capablty of the networ or the extence of a olved load flow cae. There are many crtera propoed under th approach. Some of thee crtera are the followng: - The reactve power capablty (Q-V curve). - Maxmum power tranfer lmt (P-V curve). -Voltage tablty proxmty ndex (VSI) or the load flow feablty ndex (LFF ndex). 2. Steady tate tablty method, whch tet the extence of a table equlbrum operatng pont of the power ytem. Some of the crtera propoed under th approach are: - Egenvalue of lnearzed dynamc equaton. - Sngular value of Jacoban matrx (SVJ). - Sentvty matrce. The maxmum power tranfer lmt (P-V curve) method ued here a a meaure for voltage tablty. The procedure ued to tudy the nfluence of TCSC on the tatc voltage tablty begn wth the power flow a the frt tep. The power flow model ued to tudy teady tate voltage tablty nce the power flow equaton yeld adequate reult, a ngularte n related power flow Jacoban can be aocated wth actual ngular bfurcaton of the correpondng dynamcal ytem []. The Newton-Raphon power flow equaton repreented by: Wherever Tme pecfed, Tme Roman or Tme New Roman may be ued. If nether avalable on your word proceor, pleae ue the font cloet n appearance to Tme. Avod ung btmapped font f poble. True-Type or Open Type font are preferred. Pleae embed ymbol font, a well, for math, etc. Wherever Tme pecfed, Tme Roman or Tme New Roman may be ued. If nether avalable on your word proceor, pleae ue the font cloet n appearance to Tme. Avod ung btmapped font f poble. True-Type or Open Type font are preferred. Pleae embed ymbol font, a well, for math, etc. III. STRUCTURE AND OPERATION PRINCIPLES OF TCSC Thyrtor controlled ere compenator (TCSC) one of the mot popular FACTS controller, whch allow rapd and contnuou modulaton of the tranmon lne mpedance [2]. TCSC vary the electrcal length of the compenated tranmon lne whch enable t to be ued to provde fat actve power flow regulaton [7]. It alo, provde powerful mean of controllng and ncreang power tranfer level of a ytem by varyng the apparent mpedance of a pecfc tranmon lne [3]. The bac tructure of TCSC a thyrtor controlled reactor (TCR) connected n parallel wth a capactor a hown n Fg. \ Bu Capactor Reactor Thyrtor Tranmon lne Tranformer Bu P J J2 J Q J J V V 2 22 The power flow model for voltage tablty analy repreented by: () P ( x, ) F ( x, ) Q ( x, ) (2) Fgure. Schematc dagram of TCSC between bu and bu. The mpedance charactertc curve of a TCSC devce hown n Fg. 2, that drawn between effectve reactance of TCSC and frng angle α [4,5]. Z αclm to 8 Capactve Regon where F(x,λ) power flow equaton and λ Loadng Factor (LF) or ytem load change that drve the ytem to collape n the followng way: P Q P D, P, D, Q D, Q, D, (3) where P D, and Q D, repreent the ntal actve and reactve load at bu and contant λ P and λ Q repectvely repreent the actve and reactve load ncreae drecton of bu. 9 to αllm Inductve Regon Reonance Regon αllm αclm Fgure 2. Impedance charactertc curve of a TCSC. Impedance charactertc of TCSC how, both capactve and nductve regon are poble through varyng frng angle (α) a follow: 9 < α < α Llm Inductve regon α Internatonal Journal of Power Sytem Operaton and Energy Management ISSN (PRINT): , Volume-, Iue-4, 22 37

3 α Llm < α < α Clm Capactve regon α Clm < α < 8 Reonance regon Whle The maxmum and mnmum value of frng angle hould be elected n uch a way a to avod the TCSC operatng n hgh mpedance regon (at reonance) whch reult n hgh voltage drop acro the TCSC. Th lmtaton can be ued a a contrant durng load flow analy [7]. IV. MODELING OF TCSC CONTROLLER FOR STATIC VOLTAGE STABILITY For tatc applcaton, FACTS devce can be modeled by power necton model (PIM) [6]. The necton model decrbe FACTS a devce that nect a certan amount of actve and reactve power to a node, o that a FACTS devce repreented a PQ element. The advantage of the PIM are that t doe not detroy the ymmetrcal tructure of the admttance matrx and allow effcent and convenent ntegraton of FACTS devce nto extng power ytem analytcal tool [7]. Fg. 3 how a model of tranmon lne wth a TCSC connected between bue and m. Durng a teady tate, the TCSC can be condered a a reactance X TCSC. The controllable reactance X TCSC drectly ued a the control varable n the power flow equaton. X Bu TCSC Y Bu m I I m F * X V V m S V ( I ) V (6) R X R ( X X ) F * X V V m S m V m ( I ) V m (7) R X R ( X X ) The real and reactve power necton due to the ere capactor of TCSC at bue and m are gven by (8) to () [9]: P V G V V [ G co B n ] (8) F 2 F F F m Q V B V V [ G n B co ] (9) F 2 F F F m P V G V V [ G co B n ] () F 2 F F F m m mm m Q V B V V [ G n B co ] () F 2 F F F m m mm m Where, G F X R X 2X R X R ( X X ) * * V Fgure 3. Modelng of tranmon lne wth TCSC. The current through the lne after nertng TCSC obtaned by: I ( V V ) / [ R ( X X )] (4) m The ere capactor ntally repreented a a current dependent voltage ource, whch later tranformed nto a current ource I n parallel wth the lne [8] where, The correpondng power necton model of the TCSC ncorporated wthn the tranmon lne F F hown n Fg. 4 The nected power S and S m are defned by : Fgure 4. TCSC necton model. Vm Internatonal Journal of Power Sytem Operaton and Energy Management ISSN (PRINT): , Volume-, Iue-4, B F 2 2 X R X X X R X R ( X X ) G G G F F F mm B B B F F F mm To mplement voltage control functon model of TCSC n Newton-Raphon algorthm, there are two I X I / ( R X ) model (5) of TCSC. In the frt one, X Tcc condered a the tate varable, Where the ere reactance I Bu V S Y S m Bu m S P Q F F F S P Q F F F m m m V m I m aduted automatcally, wthn lmt, to atfy a pecfed amount of actve power flow through t. In the econd model TCSC frng angle choen to be the tate varable n the Newton Raphon power flow oluton. Where TCSC reactance frng-angle charactertc, gven n the form of a nonlnear relaton. The frt model ued n th tudy. To mprove the tatc voltage tablty, The bu voltage control mode ued, So the bu voltage control contrant of bu gven by p VC V V (2)

4 p Where V the bu voltage control reference After nert TCSC between bu and bu m, The power flow relatonhp changed to be a : P P P P P P P h h h h h h h V V V X h m h m F F F F F P P P P P P P V V V X h m h m P h F F F F F h P P P P P P P P m m m m m m m V V V X P h m h m m Q Q Q Q Q Q Q m Q h h h h h h h h V V V V X h Q h m h m V F F F F F Q Q Q Q Q Q Q Q m V m V V V X... h m h m... VC F F F F F Q Q Q Q Q Q Q X Tcc m m m m m m m V V V X h m h m VC VC VC VC VC VC VC V V V X h m h m (3) Where, h :2,3,,n Equaton (3) a modfcaton of (), whch repreent Newton-Raphon power flow equaton wth TCSC. V. MATHEMATICAL MODELS OF VOLTAGE DEPENDENT LOADS A tatc model expree the actve and reactve power at any ntant n tme a functon of the bu voltage magntude and frequency at the ame ntant. Statc load model ued both for eentally tatc load component (e.g., retve and lghtng load), and a an approxmaton for dynamc load component [2]. The exponental functon of voltage can be expreed n term of nomnal operatng pont degned by the ubcrpt " ". Contant current model: When α and β equal, the tatc model power vare drectly wth voltage varaton. Contant mpedance model: When α and β equal 2, the tatc load model power vare drectly wth the quare of voltage magntude. Contant power model: When α and β equal zero the tatc model power contant n pte of voltage magntude varaton. It alo called a contant MVA model. VI. BEST PLACEMENT METHODOLOGY FOR TCSC FACTS DEVICE To determne the bet locaton of TCSC devce, the propoed methodology begn wth dentfyng the crtcal lne ung LSI durng lne outage contngency. Then, modal analy utlzed to defne the weaet bu, to form the voltage control functon, Thee procedure are done a follow: A. Identfyng Crtcal Lne Ung LSI and Lne Outage Contngency Analy When a lne outage occur the Jacoban matrx need to be modfed to reflect the outage effect [2]. To mae uch modfcaton a nomnal crcut of an outage lne - preented n Fg. 5. The two power necton and whch repreent the effect of the outage [22]. The outage effect mulated by mang the two power necton and equal to the power flow on the outage lne wth oppote gn. Therefore, 2 2 ( ) c c c C S S S P Q Y V V Y e V V Y e (5) 2 2 ( ) c c c C S S S P Q Y V V Y e V V Y e (6) P V V Y V Y (7) 2 c S co( ) S co Q V V Y n( ) V Y n Y V (8) 2 2 c S S C Bu Z R X Bu PL P V QL Q V V (4) V S c Y c Y c Fgure 5. Lne outage power necton model for lne - S c where, P L, Q L are load actve and reactve power, P,Q are actve and reactve power conumpton at rated voltage V, α the actve power exponent, β the reactve power exponent, V the bu voltage, and V the rated voltage There are three type of tatc load modelng dependng on the value of α and β a follow: P V V Y V Y (9) 2 c S co( ) S co Q V V Y n( ) V Y n Y V (2) 2 2 c S S C Internatonal Journal of Power Sytem Operaton and Energy Management ISSN (PRINT): , Volume-, Iue-4, 22 39

5 where Y Z Y e Ung (7) to (2) the Jacoban matrx form n () modfed to reflect the effect of the actve and reactve power necton at bue and. Totally 6 element need to be modfed, and they are combned together to form the matrx J P P P P V V P P P P V V J Q Q Q Q V V Q Q Q Q V V The element of J (whch are lted n [22]) hould be added to ther correpondng poton n the orgnal. Th proce repreented n matrx form a follow: v. By comparng the two lt the common lne are extracted, and the lne outage wth hghet ran dentfed a the bet TCSC locaton. B. Defnng the Weaet Bu of the Networ After defnng the proper lne to locate TCSC, modal analy ued to elect and aure the weaet bu requred to form the voltage control functon. Modal or egenvalue analy method can predct voltage collape n complex power ytem networ. It nvolve manly the computng of the mallet egenvalue and aocated egenvector of the reduced Jacoban matrx obtaned from the load flow oluton. the partcpaton factor can be ued effectvely to fnd out the weaet node or bue n the ytem [24]. In order to concentrate on the reactve demand and to mnmze computatonal effort by reducng the Jacoban matrx n Newton-Raphon power flow equaton repreented by (), P putted to be zero o And J J V (25) 2 t J ' J M JM (22) Q J J V (26) 2 22 Where M ha the followng form: From (25) and (26) N M (23) N Where nx2 zero matrx, N a pare matrx n the form N=[e e ], and e, e are pare column vector wth only one unty element at poton and repectvely. The lne tablty ndex LSI ued n th paper n contngency ranng [23]. LSI can be defned by: LSI R P X Q (24).25V 2 Where R, X are the retance and reactance between endng and recevng bue. P, Q are the reactve and actve power at recevng bu. V voltage at endng bu. The computatonal procedure are a follow:. Bae load flow computaton done, and LSI value are computed.. The value of LSI are raned and the hghet value are recorded n lt.. All lne outage contngence are mulated by removng each lne at a tme. v. Run load flow program under elected lne outage and reevaluate LSI value for all lne n each cae. v. The hghet LSI value from every lne outage are elected and regtered n Lt 2 Q J V [ J J J J ] V (27) R Where J R the reduced Jacoban matrx of the ytem. The egenvalue and egenvector of the reduced order Jacoban matrx J R are ued for the voltage tablty charactertc analy. To detect voltage ntablty, mode of the egenvalue matrx J R dentfed. The magntude of the egenvalue provde a relatve meaure of proxmty to ntablty. Egenvalue analy of J R wll be a follow: J R Where Φ = rght egenvector matrx of J R Γ = left egenvector matrx of J R Λ =dagonal egenvalue matrx of J R And Φ Γ= Equaton (28) may be wrtten a: J R (29) From (29) and (27) V Q or Q V Internatonal Journal of Power Sytem Operaton and Energy Management ISSN (PRINT): , Volume-, Iue-4, 22 4

6 m Where K a cale factor to normalze vector Q o that 2 2 Influence of TCSC FACTS Devce on Steady State Voltage Stablty Where the egenvalue, the column rght a PV bue and other bue a PQ bue. For all egenvector and the row left egenvector of matrx. cae, the convergence tolerance e -2 ytem bae MVA p.u. and Each th egenvalue λ and correpondng rght and left egenvector defne the th mode of the ytem. The th modal reactve power varaton defned a: A explaned n the prevou ecton LSI under lne outage analy, and modal analy are ued to dentfy the bet locaton of the TCSC, and the weaet bu requred to form the voltage control Q K functon, (3) then the TCSC devce ncorporated to the the tuded ytem. K (32) Wth Φ the th element of Φ The correpondng th modal voltage varaton : V m Q m (33) Equaton (33) ndcate that f all the egenvalue are potve, J R potve defnte and the V-Q entvte are alo potve, and the ytem voltage table [25]. The ytem condered voltage untable f at leat one of the egenvalue negatve. A zero egenvalue of J R mean that the ytem cloe to voltage ntablty. Furthermore, mall egenvalue of J R determne the proxmty of the ytem to beng voltage untable. So, Once the mnmum egenvalue and the correpondng left and rght egenvector have been calculated, the partcpaton factor can be ued to dentfy the weaet node or bu n the ytem. The procedure may be ummarzed a follow: Obtan the load flow for the bae cae of the ytem and get the Jacoban matrx J and the reduced Jacoban J R Compute the egenvalue to dentfy how the ytem cloe to ntablty and fnd the mnmum egenvalue λ mn of J R. Calculate the rght and left egenvector of J R and compute the partcpaton factor P for (λ mn ). The hghet P ndcate the mot partcpated th bu to th mode (whch the cloet mode to ntablty) n the ytem. Generate the Q-V curve to the th bu. By ung Q-V curve, t poble to now what the maxmum reactve power that can be acheved or added to the weaet bu before reachng mnmum voltage lmt or voltage ntablty. VII. SIMULATION RESULTS Voltage tablty enhancement ung the propoed TCSC FACTS devce done through the mulaton of IEEE 3- bu tet ytem (hown n Fg. 6). Studed ytem data obtaned from [26]. All the reult are produced by program developed n MATLAB oftware pacage. The ytem cont of 6 machne, 3 bu, and 4 lne. Bu condered a lac bu, whle 5 node Internatonal Journal of Power Sytem Operaton and Energy Management ISSN (PRINT): , Volume-, Iue-4, 22 4 ytem. The effect of the ytem wthout and wth TCSC tuded under dfferent loadng condton and dfferent load type to nvetgate the ablty of the FACTS devce to enhance tatc voltage tablty of 28 Fgure 6. The IEEE 3-bu power ytem. A. Bet Locaton for TCSC Placement To defne the approprate placement of TCSC, frtly the bae load flow tudy carred out, the LSI computed and raned, and the mot ten evere lne accordng to LSI value are recorded n Table I. Then the lne outage are mulated and the LSI are computed for each lne outage cae and the hghet LSI value for each cae extracted, and the mot erou outage contngency are dentfed and lted n Table II. The outage of L38 and L39 gve non convergence reult "NC" and LSI greater than one whch mean that thee lne cae the ytem untable. From the two table, t appeared that L38, L39, and L2 are the common lne between the crtcal lne lt n the bae cae and n the lne outage contngency cae. And the lne L38 (the lne connectng bue 27-3) the mot crtcal lne whch have the hghet LSI value. furthermore nvetgatng the LSI value of Table II ndcate that the lne L38 telf ha the hghet LSI value under mot of the lne contngence So, the lne L38 choen to place TCSC devce. TABLE I. 8 7 G4 G3 G G THE HIGHEST RANKED LINES ACCORDING TO LSI Lne No From -To LSI Ran 38 L L L L L L L L L L G G

7 TABLE II. LSI FOR THE STUDIED POWER SYSTEM UNDER DIFFERENT LINES OUTAGE Lne Lne Outage No L L8 L3 L6 L2 L27 L3 L32 L38 L39 L NC NC L NC NC L NC NC L NC NC L NC NC L6 NC NC L7 NC NC L NC NC L NC NC L NC NC L. NC NC L NC NC L NC NC L NC NC L NC NC L NC NC L NC NC L NC NC L NC NC L NC NC L NC NC L NC NC L NC NC L NC NC L NC NC L NC NC L NC NC L28.28 NC NC L29.35 NC NC L NC NC L NC NC L NC NC L33 NC NC L NC NC L35 NC NC L36 NC NC L NC NC L NC L NC ---- L4 NC NC L4 NC NC The hghet LSI value durng lne outage The crtcal lne outage that cae a non converge tate B. Identfcaton of The Weaet Bu To defne the weaet bu, the modal analy method appled to the uggeted tet ytem (a n ecton VI.B). The voltage profle of the bue preented n Fg. 7. Voltage, [p.u.]..7.6 Fgure 7. The IEEE 3-bu power ytem.5 Then, the mnmum egenvalue Bu Number of the reduced Jacoban matrx are calculated and regtered n Table III TABLE III. THE EIGENVALUES FOR THE PQ BUSES Bu No Egenvalue Bu No Egenvalue After that, the weaet load bue, whch are ubected to voltage collape, are dentfed by computng the partcpatng factor. The reult are hown n Fg. 8 Internatonal Journal of Power Sytem Operaton and Energy Management ISSN (PRINT): , Volume-, Iue-4, 22 42

8 Partcpaton Factor Bu No. Fgure 8. Partcpaton factor for PQ bue Fg. 7 how the voltage profle of all bue of the IEEE 3 bu ytem a obtaned form the load flow. It can be een that all the bu voltage are wthn the acceptable level (±5%) except bu number 3, whch about 44 p.u. The total number of egenvalue of the reduced Jacoban matrx J R 24, a there are 24 PQ bue. Thee egenvalue are hown n Table III. All the egenvalue are potve whch mean that the ytem voltage table. It can be notced that the mnmum egenvalue that equal to.53 the mot crtcal mode. The partcpatng factor for th mode ha been calculated and the reult are hown n Fg. 8. The reult how that, the bue 3, 29 and 26 have the larget partcpaton factor. The hghet partcpaton factor value at bu 3 llutrate the remarable role of th bu n the voltage collape. The Q-V curve are depcted n Fg. 9 for the weaet bue of the crtcal mode a expected by the modal analy method. The curve verfe the reult obtaned prevouly by modal analy method. It can be een that bue 3, and 26 are the crtcal bue compared the bu 29 but wth eepng n mnd the partcpaton factor bu 3 wll be the mot crtcal one. where any more ncreae n the reactve power demand n that bu wll caue a voltage collape. Therefore Bu 3 elected to form the voltage control functon. C. Smulaton Reult Wth Effect of TCSC Ung Lnear Load To nvetgate the effect of the TCSC devce ung lnear load (P-contant load), PV curve of the crtcal bue 3, 29, and 26 wthout and wth TCSC (TCSC at lne 27-3) are hown n Fg. to Fg. 2. Fg. ndcate that the devce ucceed to fx the voltage of the mot crtcal bu 3 to the obectve value ( p.u.), depte the ncreang of the loadng factor to.4. Alo, Fg. and Fg. 2 how an mprovement n the voltage profle n bue 29 and 26. So, all the reult are hown that the voltage profle are enhanced and conequently the voltage tablty margn of the tuded ytem are mproved due to ung TCSC. V mag at bu 3, pu Loadng Factor at bu 3 Fgure. P-V curve of bu 3 wthout and wth TCSC V mag at bu 29, pu Q-V Curve for Bue 26,29,3 Bu 3 Bu 29 Bu 26 Fgure Loadng Factor at bu 3 P-V curve of bu 29 wthout and wth TCSC. B u V o lta g e, [p.u.] Reactve Power, [p.u.] Fgure 9. Q-V Curve for crtcal bue V mag at bu 26, pu Loadng Factor at bu 3 Fgure 2. P-V curve of bu 26 wthout and wth TCSC Internatonal Journal of Power Sytem Operaton and Energy Management ISSN (PRINT): , Volume-, Iue-4, 22 43

9 D. Smulaton Reult wth Effect of TCSC ung Voltage Dependent Load To explore the effect of the TCSC devce on the propoed ytem under dfferent nonlnear voltage dependent load, PV curve of the bue 26, 29, and 3 wthout and wth TCSC are plotted n Fg. 3 to Fg. 2. Fgure are zoomed when requred to explan the cae. Alo, the loadng factor are changed accordng to cae tablty. Fgure 3 to 5 mulate the change n voltage magntude of the three bue n the tuded ytem wthout TCSC under contant current (CI), contant mpedance (CZ), and contant power (CP) load. Thee fgure ndcate that the voltage magntude are decreaed to underable level that lead to voltage collape. V mag of bu 3,pu CZ Load CI Load CP Load Fgure 3. P-V curve of bu 3 for dfferent load type V mag of bu 29,pu CZ Load 5 CI Load CP Load Fgure 4. P-V curve of bu 29 for dfferent load type V mag of bu 26,pu CZ Load CI Load CP Load Fgure 5. P-V curve of bu 26 for dfferent load type In fgure 6 to 8 a comparon between the ytem wth TCSC and wthout TCSC ung contant current load are depcted. Alo, In fgure 9 to 2 the ame proce done, ung contant mpedance load type (contant power cae are tuded a lnear load). In fgure 2, 8 and 2 the TCSC ha a mall effect on bu 26 th becaue of bu 26 not connected drectly to bu 3 that connected to TCSC th mean that the redtrbuton of reactve power by the devce ha not a large effect of th bu. In general TCSC how a good performance and enhance the voltage tablty margn of the ytem. V mag of bu 3,pu Fgure 6. V mag o f bu 29,pu. P-V curve of bu 3 for contant current load Fgure 7. P-V curve of bu 29 for contant current load V mag of bu 26,pu. Fgure P-V curve of bu 26 for contant current load Internatonal Journal of Power Sytem Operaton and Energy Management ISSN (PRINT): , Volume-, Iue-4, 22 44

10 REFERENCES Fgure 9. P-V curve of bu 3 for contant mpedance load V mag of bu 29,pu Fgure 2. P-V curve of bu 3 for contant mpedance load [] W. Bale: Cambrdge Worng Paper n Economc CWPE 47, 24[onlne] Avalable: bttream/8-/386//ep34.pdf. [2] Y.V. Maarov, V.I. Rehetov, A. Stroev, and I. Voropa, Blacout preventon n the Unted State, Europe, and Rua, Proceedng of the IEEE, vol. 93, no., Nov. 25, pp [3] T.V Cutem, Voltage tablty of electrc power ytem, Sprnger, 998. [4] Aarapu V., Lee B., Bblography on voltage tablty, IEEE Tran. Power Syt., vol. 3, no., Feb. 998, pp [5] IEEE/CIGRE Jont Ta Force on Stablty Term and Defnton, Defnton and clafcaton of power ytem tablty, IEEE Tran. Power Syt., vol. 9, no. 2, May 24, pp [6] S. Gupta, R.K Trpath, and R.D. Shula, Voltage tablty mprovement n power ytem ung fact controller: Stateof-the-art revew, Proceedng of Internatonal Conference on Power, Control and Embedded Sytem (ICPCES), Allahabad, Inda, Nov. 2, pp. -8. [7] S. Sreeth, Sha P Smon, and M P Selvan, Power flow analy ncorporatng frng angle model baed TCSC, Proceedng of 5th Internatonal Conference on Indutral and Informaton Sytem (ICIIS 2), Inda 2, Jul 29 - Aug, pp [8] C. W. Taylor, "Power ytem voltage tablty." New Yor: Mcgraw-Hll, 994. V mag of bu 26,pu [9] V. A. Venov, V. A. Stroev, V. I. Idelchc, and V. I. Traov, "Etmaton of electrc power ytem teady-tate tablty n load flow calculaton," IEEE Tranacton on Power Apparatu and Sytem, vol. PAS-94, May/June 975, pp [] J. C. Chow, R. Fchl, and H. Yan, On the evaluaton of voltage collape crtera IEEE Tran. Power Syt., vol. 5, no.2, May 99, pp [] A. Sode-Yome, N. Mthulananthan, K.Y. Lee, " A Comprehenve comparon of FACTS devce for enhancng tatc voltage tablty," IEEE Power Engneerng Socety General Meetng, 27, Florda, USA, June 27, pp. -8. Fgure 2. P-V curve of bu 3 for contant mpedance load VIII. CONCLUSION In th paper the nfluence of TCSC on teady tate voltage tablty wa nvetgated. Detaled teady tate model of FACTS devce wa preented focung on the ncluon of the devce nto the power flow analy proce. A novel technque for electng bet placement of the devce and to form the voltage control functon were propoed. The tuded ytem wa teted under dfferent loadng condton and dfferent lnear and nonlnear load type. The devce proved ther ablty to enhance voltage tablty margn. [2] T. Datta, P. Nagendra, and S. Halder nee Dey, An Integrated model of modern power ytem n the preence of TCSC and STATCOM controller to ae global voltage tablty, Jont Internatonal Conference on Power Electronc, Drve and Energy Sytem (PEDES), New Delh, Inda, Dec. 2, pp. -6. [3] Bndehwar Sngh, Utlte of dfferental algebrac equaton (DAE) model of SVC and TCSC for operaton, control, plannng & protecton of power ytem envronment, Internatonal Journal of Revew n Computng, vol. 7, Sep. 2, pp [4] Anwar S. Sddqu, Rahm Jan, Mad Jaml and Gupta C. P., Congeton management n hgh voltage tranmon lne ung thyrter controlled ere capactor (TCSC), Internatonal Journal of Power Sytem Operaton and Energy Management ISSN (PRINT): , Volume-, Iue-4, 22 45

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