J. Electrical Systems 3-2 (2007): Regular paper

Transcription

1 R. K. Saket R. C. Bansal Col. Gurmt Sngh J. Electrcal Systems 3-2 (2007): Regular aer Relablty Evaluaton of Power System Conserng Voltage Stablty an Contnuaton Power Flow JES Journal of Electrcal Systems Ths artcle escrbes the methoology for evaluaton of the relablty of an comoste electrcal ower system conserng voltage stablty an contnuaton ower flow, whch takes nto account the eak loa an steay state stablty lmt. The voltage stablty s obtane for the robable outage of transmsson lnes an removal of generators along wth the combne state robabltes. The loss of loa robabltes (LOLP) nex s evaluate by mergng the caacty robablty wth loa moel. State sace s truncate by assumng the lmts on total numbers of outages of generators an transmsson lnes. A recton correcton technque has been use along wth one mensonal search metho to get otmze stablty lmt for each outage states. The algorthm has been mlemente on a sx-bus test system. Keywors: Contnuaton ower flow, loss of loa robablty, otmzaton, eak loa, voltage stablty lmt. NOMENCLATURE α : loa artcaton factor β : vector of tan θ, an θ beng ower factor angle at th bus γ : a vector of bus voltage angles η : recte value of contnuaton varable f : th lne real ower (MW) flow lmt f : lne real ower flow lmt k : vector of generaton artcaton NC : total number of reactve ower control varables lmt P : statc voltage stablty lmt P, P : lower an uer lmts of real ower generaton at th bus mn mn max Q, Q : lower an uer lmts of reactve ower generaton lmts at th bus max th U : reactve ower control varables U, U : lower an uer lmts of reactve ower control varables at th bus mn max Electrcal Eng. Deartment, Banaras Hnu Unversty, Varanas, UP, Ina, saketrk@yahoo.com. Electrcal & Electroncs Eng. Deartment, School of Engneerng an Physcs, The Unversty of the South Pacfc Suva, Fj, rcbansal@hotmal.com. Allahaba Agrcultural Deeme Unversty, Allahaba, UP, Ina. gurmtsngh3@reffmal.com. Coyrght JES 2007 on-lne : journal.esrgrous.org

2 J. Electrcal Systems 3-2 (2007): V, V : lower an uer lmts of bus voltage at th bus mn max V : a vector of bus voltage magntues t : loa arameter X k : contnuaton varable 1. INTRODUCTION In recent years relablty evaluaton of the combne generaton-transmsson (bulk ower system) has been a major concern n ower system lannng. Recent aers [1]-[4] resent an extensve bblograhcal survey for evaluaton of relablty of ower system. A comoste system can be ve n many oeratng states n terms of the caacty avalable to fulfll eman subject to the satsfacton of securty lmts (lne flows an voltage lmt). Hence, the evaluaton of a relablty nex for a comoste system s very much comutatonally emanng. Power system relablty s usually categorze nto the regons of aequacy an securty. System aequacy s efne as the ablty of the system to suly ts loa accountng lne flow constrants an accountng outages of generators an branches whereas system securty (ynamc) s efne as the ablty of the ower system to wthstan sturbances arsng from faults or unscheule removal of bulk ower suly equment. Ths means that aequacy assessment s the steay state ost outage analyss of the comoste ower system whle securty assessment (n relablty evaluaton asect) nvolves ynamc conton analyss. Ths aer focuses attenton on aequacy assessment. A lnear rogrammng moel accountng voltage an lne flow constrants for aequacy assessment of bulk ower system has been use n [5]. Perera et al. [6] eveloe a relablty evaluaton methoology for comoste system base on Monte-Carlo samlng wth a varance reucton scheme, whch ermts the ncororaton of lanner s exerence or analytcal moels as Regresson varables. Deng et al. [7] roose an effcent new aroach for ower system relablty evaluaton usng the ecomoston smulaton aroach. The nterconnecte systems n ths aroach have been moele by a robablstc flow network wth caactate areas. Each area s enote by a noe n the network. Source an loa are reresente by atonal noes. Bllnton et al. [8] eveloe a system state transton samlng metho for comoste system relablty evaluaton usng Monte Carlo smulaton technque. Meo et al. [9] resente the effects of voltage collase roblems n the relablty evaluaton of comoste system an escrbe an aroach to calculate voltage collase relate bulk relablty nces as well as ther mact on the aequacy relablty nces. The aequacy analyss of each selecte system state s carre out n two stes. A system state transton sequence s utlze to calculate frequency nex. Mtra et al. [10] ncororate c loa flow moel n the ecomoston-smulaton metho for evaluatng mult-area relablty evaluaton. State enumeraton aroach usng toologcal analyss has been use to evaluate bulk ower system relablty n [11]. System frequency, uraton an avalablty nces have been obtane usng toologcal enumeraton. The metho requres the use of ac or c loa flow to test the conton of contngency state. Sngh et al. [12] have use state sace runng for evaluaton of bulk ower system relablty by erformng Monte Carlo smulaton selectvely on those regons of the state sace where loss of loa states are more lkely to occur. Khan [13] use securty-base moel to evaluate relablty of a comoste ower system an resente an aroach to quantfy a ower network nto several oeratng states n terms of egree of aequacy an securty (statc) constrants. 49

3 R. K. Saket et al.: Relablty Evaluaton of Power System Conserng Voltage Stablty an Contnuaton Power Flow A methoology for relablty assessment at a restructure ower system usng relablty network equvalent technques has been resente n [14]. The man objectve of ower system restructurng an eregulaton s to ntrouce cometton n the ower nustry an to allow customers to select ther sulers base on rce an relablty. Ros et al. [15] resente a methoology to evaluate the relablty an to calculate nterruton costs at the loa bus level n the bulk ower system. The methoology s base on a non-sequental Monte-Carlo smulaton combne wth a lnear otmzaton moel n whch the loa at every bus s reresente by two comonents.e. a frm an non-frm orton. Execte values of not serve energy, not serve eman, an LOLP are comute for the whole system. Bllnton et al. [16] eveloe a system for unrelablty cost assessment of an electrc ower system usng relablty network equvalent aroaches. Unrelablty cost evaluaton of an entre ower system roves a set of nexes, whch can be use by a system lanner to balance the nvestments n fferent segments of the system n orer to rove accetable loa ont relablty. Nowaays voltage stablty s a serous roblem that ower utltes usually exlore n the lannng stage. It s essental that the caacty state of combne generaton an transmsson system must be evaluate base on statc voltage stablty lmt. It has become mortant because ths lmt n ower network s aroachng much earler than thermal or angle stablty constrane lmt ue to network lmtatons or reactve ower efcency. Meo et al. [9] resente an aroach to calculate voltage collase relate bulk relablty nces as well as ther mact on comoste ower system aequacy nces base on restorng system solvablty by loa sheng. A methoology has been resente n [17], whch nuces voltage stablty conseraton n aequacy assessment of bulk ower system. The voltage stablty ncator s calculate for all ossble system contngences. A bsectonal algorthm s then use to etermne the amount of loa, whch s requre to be she to allevate all voltage stablty volatons. In ths artcle, a methoology has been eveloe to evaluate robablty of falure base on eak loa for the comoste system accountng voltage stablty conseratons. Steay state voltage stablty lmt for ossble lne outages an generaton outages has been calculate along wth the combne generaton an transmsson state robabltes. Thus the caacty robablty may be merge wth sutable loa moel (eak loa/loa uraton curve) to evaluate the LOLP nex. State sace s truncate by assumng the lmts on total number of comonent (generaton an transmsson lne) falure. 2. STEADY STATE VOLTAGE STABILITY LIMIT USING PREDICTOR- CORRECTOR TECHNIQUE Prector-corrector technque overcomes the non-convergence of conventonal Newton- Rahson (N-R) metho of loa flow analyss near the voltage stablty lmt [18]. Ths technque uses an teratve rocess nvolvng rector an corrector stes. Usng a known ntal soluton an the tangent vector, a new soluton s recte for a secfe attern or loa ncreases. Usng these estmate soluton corrector ste converges to exact soluton ont. Contnuaton ower flow equatons are smlar to those of conventonal ower flow analyss excet that the ncrease n total loa s ae as a loa arameter t. The general form of equatons s gven as FV (, δ, t, k, β, α ) = 0 (1) 50

4 J. Electrcal Systems 3-2 (2007): Prector Ste It s assume that ntal loa flow soluton s avalable. For rectng the next ste soluton tangent vector s obtane by settng fferental of eqn. (1) equals to zero as follows δ Fδ Fv F t v = 0 t F F F where Fδ =, Fv =, Ft = δ v t The aearance of loa arameter t as one more equaton. To solve eqn. (2) one of the comonents of the tangent vector s set to +1 or 1. Ths also removes ll contonng of the equatons. Ths comonent s calle contnuaton arameter. Now eqn. (2) s wrtten as δ Fδ Fv Ft 0 v T e 0 0 = 1 ± k t Intally the loa arameter s chosen as contnuaton arameter an the corresonng comonent of tangent vector s set to +1. When the system s heavly stresse, then the contnuaton arameter s chosen to be the state varable beng the greatest rate of change near the gven soluton an sgn of ts sloe etermnes the sgn of the corresonng comonent of tangent vector. After solvng for tangent vector the recton for the next soluton s gven as 0 δ δ δ 0 v = v + σ v t 0 t t where { 0, v 0, t 0 } δ s the ntal soluton vector. Convergence of the corrector ste soluton manly eens on the ste sze σ, f convergence s not obtane n corrector ste that recte soluton shoul be obtane agan, usng eqn. (4), wth reuce value of ste sze σ an agan corrector ste s reeate wth new recte soluton. 2.2 Corrector Ste In corrector ste the contnuaton ower eqn. (1) s augmente by one more equaton that secfes the contnuaton arameter as follows: Fv (, δ,, tk, α, β) = 0 ( Xk η) Eqn. (5) s solve by N-R metho usng the ntal conton as gven by eqn. (5). The ntroucton of one atonal equaton secfyng X k moels the Jacoban on N-R metho, (2) (3) (4) (5) 51

5 R. K. Saket et al.: Relablty Evaluaton of Power System Conserng Voltage Stablty an Contnuaton Power Flow non-sngular even at collase ont. Thus, t s ossble to obtan steay state voltage stablty lmt. Intal loa flow soluton, varous oeratng lmts P lmt (0) ntal max. loablty Set teraton count: = 1 Start wth control varable: =1 Set teraton count: K=1 U = U + ΔU k k 1 Obtan statc voltage stablty lmt usng rector-corrector metho Is Yes lmt lmt (k) > (k 1)? K=K+1 U = U No k 1 P lmt (o) = P lmt (k 1) P=P+1 No Is P>NC Yes lmt P (I) = P lmt (O) Yes I=1+1 No P lmt (I) = P lmt (I 1) < t? C = P lmt (I) System caacty STOP Fgure 1: Flow chart for obtanng maxmum loaablty usng metho of local varaton (MLV) an rector-corrector metho. 52

6 J. Electrcal Systems 3-2 (2007): OPTIMIZATION OF STEADY STATE VOLTAGE STABILITY LIMIT For each generatng caacty state the objectve s to obtan the maxmum statc voltage stablty lmt accountng to real an reactve ower generaton lmts. The comlete formulaton can be wrtten as J P lmt = max{ } (6) Subject to followng constrants mn U U U max, = 1, NC (7) mn Q Q Q max, = 1, NC (8) mn P P P max, = 1, NC (9) V V V = NC (10) f mn max, 1, f (11) lmt The metho use n otmzng the objectve functon of eqn. (6) s a local varaton or rect search metho. In ths each teraton, one control varable s vare an va maxmum contnuaton ower flow algorthm maxmum of eqn. (6) s obtane. Ths s reeate for all control varables wthn lmts tll no change n objectve functon s observe. In each teraton t s also observe that the control s vare tll no volaton of the oeratng constrant takes lace. These constrants are reresente n relatons to equatons (7)-(11). The comutatonal stes are shown n the flowchart of Fg. 1. Startng ont of the algorthm s to comute ntal loa flow soluton an ntal maxmum loaablty lmt lmt [ P (0)] wthn secfe oeratng constrants. Inner teraton loo obtan maxmum loaablty lmt by varyng nvual control varables U, for = 1, NC n sequence. Such sequence s reeate by outer teraton loo. Ths outer loo s reeate tll there s no th change n statc voltage stablty lmt. Δ U enotes the change n control varables n th k teraton. It s worth mentonng at ths stage that for etermnng statc voltage stablty lmt, loa s ncrease n secfe recton at each bus tll there s no volaton n oeratng constrants. 4. EVALUATION OF PROBABILITY OF FAILURE FROM PEAK LOAD CONSIDERATION Dscrete robabltes for varous generatng states are obtane usng Markov moelng base on constant falure an rear rate. Then for each caacty states, usng the contnuaton ower flow (rector-corrector metho of Secton 2) the statc voltage stablty s obtane for base case an for fferent lne outage contons. For evaluatng such lmts total outage comonents are normally consere less than fve. Hence, for nvual lne outages an at the most ouble lne outages are consere. Outages of more number of transmsson lnes may not be sgnfcant as robablty of occurrence of such contons are small an may be neglecte. In the resent case statc securty lmts have been consere. Ths means that after the outage of the comonents synchronsm s mantane. Probabltes of lne outage states are agan evaluate usng Markov moelng as avalablty an unavalablty functons. Generaton an transmsson lne states are merge an corresonng to each combne states robabltes are calculate. States then 53

7 R. K. Saket et al.: Relablty Evaluaton of Power System Conserng Voltage Stablty an Contnuaton Power Flow can be arttone an robablty of success an falure,.e., avalablty an unavalablty of bulk ower systems are evaluate. The stes are shown n the flow chart of Fg. 2. Secfcally usng falure rate (λ ) an rear rate ( μ ), the avalablty ( A ) an unavalablty ( A ) of each generatng unt s calculate as μ A = ( λ + μ ) (12) A λ = ( λ + μ ) (13) State robabltes PX ( ) can be calculate as P( X ) A A = Π Π (14) k k n where k les n the sets of generaton avalable an n les n sets of alternator not avalable th n state. Hence, generaton caacty an caacty robabltes are obtane as X, C an PX ( ). Smlarly, the transmsson network state Y an assocate robabltes PY ( ) are obtane. Combne state sace s obtane by mergng the generaton an transmsson system as follows Z an = ( X, Y ) (15) k j PZ ( ) = ( PX ( ), PY ( )) (16) k j Caacty corresonng to each combne state s obtane by solvng the otmzaton roblem. Comoste system caacty an robabltes CZ ( ) an PZ ( ) an loa moels are merge to evaluate success an falure robablty. 5. RESULTS AND DISCUSSIONS The algorthm eveloe n the aer s base on IEEE sx-bus [Aenx A] test system. Bus No 1 an 2 are generator buses. It s assume that generator bus No 1 s connecte wth 4 generators havng real ower generaton caacty 0.5. u each. Reactve ower lmt of each generator s also assume 0.5 u. Smlarly generator Bus No 2 s connecte wth 4 generator havng 0.25 u real ower generaton caacty each. A reactve ower lmt of each generator s taken of equal caacty,.e., 0.25 u. Shunts are rove at loa Bus No. 4 an 5 of magntue 0.05 u each. The falure an rear rate of each generator has been assume to be 0.4/year an 9.6/year, resectvely. Smlarly, falure an rear rate of each transmsson lne has been assume to be 0.02/year an 0.25/year. Hence, avalablty an unavalablty of each generator are gven as 0.96 an Smlarly, avalablty an unavalablty of each transmsson lne are gven as an

8 J. Electrcal Systems 3-2 (2007): Inut Data: 1. Caacty of each unt 2. λan μ of each unt an transmsson lne 3. Loa moel Preare caacty outage robablty table, whch gves, (x), C an X for generaton system. Obtan states of transmsson network by conserng maxmum two lne outages, calculate Yj an Yj Obtan combne states Zk = (X, Yj) for comoste system an (Zk) For each state Z obtan maxmum loaablty Merge the loa moel wth comoste system state moel an evaluate s an PF STOP Fgure 2: Flow chart for evaluatng falure an success robablty of comoste ower system. Table I: Generaton caacty outage robablty table State x Caacty at State 1 (u) Caacty at State 2 (u) Total Caacty C (u) Probablty State (x ) State (x ) X 0 Y X 0 Y X 0 Y X 1 Y X 1 Y X 1 Y X 2 Y X 2 Y X 2 Y 2 The robablty of event when all lnes are workng s gven as. A 7 = The 6 robablty of event one lne faulty an all other workng s gven as AA = , where A stan for avalablty an A stan for unavalablty of that artcular transmsson lne/generator. The robablty of two lnes faulty an fve lnes workng s 2 5 gven as follows : AA = The robablty of workng all generators at 4 Staton 1 or staton 2 s A = The robablty of falng one generator at each of staton s gven as AA 1 3 = The robablty of two generators workng successfully conserng outage of two generators at ether staton s gven as follows: 2 2 AA =

9 R. K. Saket et al.: Relablty Evaluaton of Power System Conserng Voltage Stablty an Contnuaton Power Flow The outage of two generators at each bus has been consere for relablty evaluaton. Smlarly, outage of maxmum two transmsson lnes has been consere. The combne generatng caacty outage robablty table s gven n Table I where, X an Y are notatons for generator buses 1 an 2, resectvely. Subscrt ncates number of unavalablty of generator at that bus as gven below: 0 = all generators are avalable at secfe bus. 1 = one generators s unavalable at secfe bus. 2 = two generators are unavalable at secfe bus. For each caacty state of Table 1 contnuaton ower flow soluton was mae an overall comoste statc voltage stablty lmts were evaluate n base case conton, as well as sngle an ouble lne outage contons. For the safe lmts oeraton the actual workng lmt has been assume to be 80% of crtcal loang onts n each case. Table 2: Peak loaablty wth caacty an lne outage states of electrcal ower system L 0 L 1 L 3 L 5 L1L2 Z0 ( X0, Y 0) CX ( ) = PX ( ) = Z4 ( X1, Y 1) CX ( ) = PX ( ) = PX ( ) = Z8 ( X2, Y 2) CX ( ) = ,66 0,61 Success robablty of comoste system 0,56 0,51 0,46 0,48 0,68 0,88 1,08 1,28 1,48 1,68 1,88 2,08 Peak loa of comoste system Fgure 3: Peak loa v/s success robablty of nterconnecte comoste electrcal ower system base on voltage stablty unt 56

10 J. Electrcal Systems 3-2 (2007): Table 3: Comoste electrcal ower system caacty outage robablty Lne outage state No outage Generaton caacty outage state Peek loaablty of comoste state Probablty of comoste state P (x ) XY XY ,7 XY x ,4 XY x ,7 XY x ,7 XY x XY x XY XY x XY x XY x10-3 2,7 XY x10-6 5,2 XY x XY x XY x10-5 1,4 XY x XY x10-8 1,7 XY x10-9 4,5 XY x10-6 5,7 XY x10-3 4,5 XY x XY ,3 XY x10-7 1,6 XY x10-9 2,7 X 2 Y x10-9 2,4 X 2 Y x10-9 3,5 X 2 Y x10-9 2,5 X 2 Y x10-9 2,6 X 2 Y x10-9 1,3 X 1 Y x10-7 1,5 X 2 Y x10-9 The robablty of each transmsson network has also been evaluate an eak loaablty wth all ossble caacty an robablty states of comoste electrcal ower system are gven n Table 2. The combne states (transmsson an generaton) an corresonng caacty (reuce to 80%) were obtane. The system avalablty an unavalablty were calculate for fferent values of eak loas. The robablty an caacty for comoste system state was arrange n escenng orer of loaablty gven n Table 3. From Table 3 for fferent eak loa conseraton, success an falure robabltes obtane are gven 57

11 R. K. Saket et al.: Relablty Evaluaton of Power System Conserng Voltage Stablty an Contnuaton Power Flow n Table 4. The grahcal lots of success an falure robablty aganst eak loa are shown n the Fg. 3. The algorthm eveloe n ths aer has been mlemente on 6-bus test system [14]. From Fg. 3 t s observe that as the eak loa of the system ncreases, the success robablty of the system automatcally ecreases. Table 4: Peak loa an success/falure robablty Peak loa Success robablty (P s ) Falure robablty (P f ) CONCLUSIONS A methoology has been eveloe for calculatng the falure robablty of comoste generaton an transmsson system base on voltage stablty conseraton. Snce the ssue of reactve ower efcency has become a rme mortance for heavly stresse moern ower network. The conseraton of voltage stablty n relablty evaluaton wll gan more an more mortance. Falure robablty has been evaluate by mergng together (1) generaton, (2) transmsson an (3) loa moels n sequence. REFERENCES [1] IEEE Commttee Reort, Bblograhy on the Alcaton of Relablty Methos n Power System Relablty Evaluaton, IEEE Transactons on Power Systems, Vol. 3, N o. 4, Nov. 1988, [2] R.N. Allan, R. Bllnton, A.M. Breoth, an C.H. Grgg, Bblograhy on the Alcaton of Probablty Methos n Power System Relablty Evaluaton, IEEE Transactons on Power Systems, Vol. 9, N o. 1, Feb. 1994, [3] R.C. Bansal, T.S. Bhatt an D.P. Kothar, Dscusson of Bblograhy on the Alcaton of Probablty Methos n Power System Relablty Evaluaton, IEEE Transactons on Power Systems, Vol. 17, N o. 3, Aug. 2002,

12 J. Electrcal Systems 3-2 (2007): [4] R. Bllnton, M. F. Fruzabo an L. Bertng, Bblograhy on the Alcaton of Probablty Methos n Power System Relablty Evaluaton , IEEE Transactons on Power Systems, Vol. 16, N o. 4, Nov. 2001, [5] R. Bllnton an E. Khan, A Securty Base Aroach to Comoste Power System Relablty Evaluaton, IEEE Transactons on Power Systems, Vol. 7, N o. 1, Feb. 1992, [6] M.V.F. Perera an L.M.V.G. Pnto, A New Comutatonal Tool for Comoste Relablty Evaluaton, IEEE Transactons on Power Syst., Vol. 7, N o. 1, Feb. 1992, [7] Z. Deng an C. Sngh, A New Aroach to Relablty Evaluaton of Interconnecte Power Systems Inclung Planne Outages an Frequency Calculaton, IEEE Transactons on Power Systems, Vol. 7, N o. 2, May 1992, [8] R. Bllnton an W. L, A System State Transton Samlng Metho for Comoste System Relablty Evaluaton, IEEE Transactons on Power Systems, Vol. 8, No. 3, Aug. 1993, [9] A.C.G. Meo, J.C.O. Mello, an S. Granvlle, The Effects of Voltage Collase Problems n the Relablty Evaluaton of Comoste Systems, IEEE Transactons on Power Systems, Vol. 12, N o. 1, Feb. 1997, [10] J. Mtra an C. Sngh, Incororatng the D.C. Loa Flow Moel n the Decomoston- Smulaton Metho of Mult Area Relablty Evaluaton, IEEE Transactons on Power Systems, Vol. 11, N o. 3, Aug. 1996, [11] S. Jonnavthula an R. Bllnton, Toologcal Analyss n Bulk Power System Relablty Evaluaton, IEEE Transactons on Power Syst., Vol. 12, N o. 1, Feb. 1997, [12] C. Sngh an J. Mtra, Comoste System Relablty Evaluaton Usng State Sace Prunng, IEEE Transactons on Power Systems, Vol. 12, N o. 1, Feb. 1997, [13] M.E. Khan, Bulk loa onts relablty evaluaton usng a securty base moel, IEEE Transactons on Power Systems, Vol. 13, N o. 2, May 1998, [14] R. Bllnton an P. Wang, Deregulate Power System Plannng Usng a Relablty Network Equvalent Technque, Proc. IEE- Generaton Transmsson an Dstrbuton, Vol. 146, N o. 1, 1999, [15] S. M. Ros, P.V. Val, an D.L. Kguel, Bus Base Relablty Inces an Assocate Costs n the Bulk Power System, IEEE Trans. Power Systems, Vol. 13, N o. 3, Aug. 1998, [16] R. Bllnton an P. Wang, Dstrbuton System Relablty Cost/Worth Analyss Usng Analytcal an Sequental Smulaton Technques, IEEE Transactons on Power Systems, Vol. 13, N o. 4, Nov. 1998, [17] R. Blnton an S. Aboresha, Voltage Stablty Conseraton n Comoste Power System Relablty Evaluaton, IEEE Transactons on Power Syst., Vol. 13, N o. 2, May 1998, [18] V. Ajarau an C. Chrsty, The Contnuaton Power Flow: A Tool for Stuy Voltage Stablty Analyss, IEEE Transactons on Power Systems, Vol. 7, N o. 1, Feb. 1992, [19] L. D. Arya, P.R. Bjwe, an D.P. Kothar, Allevaton of Lne Overloas an Voltage Volatons by Correctve Rescheulng, Proc. IEE-Generaton Transmsson an Dstrbuton, Vol. 140 N o. 4, July 1993, Aenx: Sx-Bus System Data System ata No. of Bus No. of Shunt No. of Lnes No. of generators

13 R. K. Saket et al.: Relablty Evaluaton of Power System Conserng Voltage Stablty an Contnuaton Power Flow Lne ata Lne Bus No. No. From To Resstance n er unt (u) Reactance u B lne n u Ta Bus ata Bus Voltage V δ P G Q G P L Q L 1 (Slack) (PV) (PQ) (PQ) (PQ) (PQ) Shunt ata Bus Shunt Maxmum reactve generaton Bus Q lmt