Improve Static Voltage Stability Edge with Optimal Placement of UPFC and PST

Transcription

1 Internatonal Research Journal of Appled and Basc Scences 014 Avalable onlne at ISSN X / ol, 8 (11: Scence Explorer ublcatons Improve Statc oltage Stablty Edge wth Optmal lacement of UFC and ST Seyed Ehsan Lary Seyed Zadeh 1, Afshn Lashkar Ara 1. Department of Electrcal Engneerng, Dezful Branch, Islamc Azad Unversty, Dezful, Iran. Department of Electrcal Engneerng, Dezful Branch, Islamc Azad Unversty, Dezful, Iran Correspondng Author emal: ehsan_lar@yahoo.com ABSTRACT: The man goal of ths paper s fndng optmal place of unfed power flow controller (UFC and phase shfter (ST n the power systems. In other words, the man concentraton s on connectng FACTS and OF tools opnon usng ST and UFC power necton model to fnd the best place of settng these elements n power networks. The obectve functon of mzng statc voltage stablty edge (system loadablty factor s dscussed n ths paper. Smulaton results are offered on IEEE 118_ bus standard network and they suggest that proposed algorthm ncludes the better resoluton and there s a more lttle tme than the other placement methods. Key words: OF, UFC, ST, optmal placement, power necton model. INTRODUCTION In recent year, voltage collapse problem has been a basc and mportant problem to explot electrc power systems[1]. Recent fndngs report a power system dsablty to keep voltage constantly, n all dsrupted buses. oltage collapse pontngs are known as system loadablty edge s known as power level that system collapses before t. Many ways are mplemented to dentfy voltage stablty on statc analyss technques based on power flow ways[]. A smple way to fnd a system loadablty mum lmt s usng a common power flow and gradual ncreasng load near power flow dvergence. A power flow Jacoban matrx n power mum causes to dverge power flow, because of unqueness. Therefore, contnous power flow (CF approach s used to over come ths problem[3]. Some contnous power flow problems are, unconsderng explotaton lmtatons and also takng a long tme algorthm. So, optmal power flow s used to overcome these problems. Optmal power flow s unlnear programmng and dentfyng power system control parameters as f t optmzes a obectve functon and physcal and effcent restrctons mposed by equpment lmtatons and also, t meets system securty lmtatons. OF s a man nstrument to optmze and desgn power flow progressvely, and t was frstly propounded n 196 and t took a long tme to mplement as a effcent and successful algorthm that s useful every day. In[4,5], the procedures offered to resolve OF n dfferent resources are dscused. ON the other hand, developng consume n power systems confront power transton lmtaton problem. And power flow controllers, such as controllng generators, regulatng voltage and condenser banks are not enough to solve ths problem. Today, controllng FACTS controllers based on power electroncs tools[6], can control power flow wth advantage of stablzng buses voltage level n acceptable lmtaton, ncreasng securty of system and explotng near capacty lmts, constantly. Thus, a need of an nstrument s presented to desgn power systems wth FACTS tools. Taranto n [7], for example, has suggested a method to solve optmal power flow problem ncludng FACTS tools based on lnear programs. Ths procedure can consder seres compensatory and phase shfter, but t can't consder lnes lmtatons. In resource[8] s used lnear programmng based on securty lmtatons to solve OF and determne FACTS controllers parameters. Chung and L n[9] have presented a genetc algorthm method to fnd FACTS tools parameters. In sources[10,11], connectng FACTS and OF tools algorthm has been used based on Newton's approach, source[1] studes statc voltage stablty lmtaton, usng HSO and SO algorthm methods. In source[13] s dscussed, ncreasng statc voltage stablty edge usng some FACTS elements. THE man purpose of ths paper s, provdng a method to fnd and select the best place of settng ST and UFC elements based on ncreasng statc voltage stablty lmtaton. In ths paper, optmzaton software named wth Generalzed Algebrac Modelng System has been used to solve OF problem and ths algorthm s tested on IEEE 118_ bus network.

2 Upfc Inecton Model A UFC can be represented n the steady-state by two voltage sources representng basc components of output voltage waveforms of the two converters and mpedances beng leakage reactances of the two couplng transformers. Fgure 1 depct a two voltage-source model of UFC[14]. oltage of bus s taken as 0 ' reference vector, 0 and se The voltage sources, se and sh,are controllable n both ther magntudes and phase angles. se could be defned as: se r e (1 0 r r and o The value of r and are defned wthn specfed lmts gven by Equaton (1 The steady-state UFC mathematcal model s developed by replacng voltage source I parallel wth the transmsson lne, where b 1/ X I se se se se se b ( se se by a current source Fgure 1. Two voltage-source model of UFC The current source Fgure. I se can be modeled by necton powers at the two auxlary buses and as shown n * s se * s ( se Fgure. Replacement of seres voltage source by a current source. S ( I (3 S I (4 The nected powers S s and S s can be smplfed accordng to the followng operatons, by substtutng Equaton (1 and ( nto Equaton (3. * S ( b r e (5 s se By usng the Euler Identty, ( e cos sn Equaton (5 takes the form: ( 90 * s se S ( e b r (6 s se S b r[cos( 90 sn( 90] (7 By usng trgonometrc denttes, Equaton (7 reduces to: Ss rbse sn rb se cos (8 Equaton (6 can be decomposed nto ts real and magnary components, Ss s s, where 199

3 s rbse sn (9 s rbse cos (10 Smlar modfcatons can be appled to Equaton (4; the fnal equaton takes the form: S b r sn( s se b r cos( se (11 Equaton (11 can also be decomposed nto ts real and magnary parts, S s s s, where b r sn( (1 s se b r cos( (13 s se Based on Equatons (9, (10, (1, and (13, the power necton model of the seres connected voltage source can be seen as two dependent power nectons at auxlary buses and, as shown n Fgure 3[15,16]. Fgure 3. Equvalent power nectons of seres branch. The apparent power suppled by the seres converter s calculated as. * ' * S seres se I re (14 X se. Actve and reactve power suppled by the seres converter can be calculated from Equaton (14: seres se * S re (( re / X (15 ( ( seres se S r e (( r e e e / X (16 ( seres se se se S b r b r e b e (17 S b r b r (cos sn seres se se b (cos( sn( se (18 The fnal form of Equaton (19 can be wrtten as: S seres = seres + seres, where: seres se se rb sn( rb sn (19 seres se cos( se cos se rb rb r b (0 The reactve power delvered or absorbed by converter 1 s not consdered n ths model, but ts effect 1993

4 can be modeled as a separate controllable shunt reactve source. In ths case the man functon of reactve power s to mantan the voltage level at bus I wthn acceptable lmts. In vew of the above explanatons, shunt can be assumed to be 0. Consequently, steady-state UFC mathematcal model s constructed from the seres connected voltage source model wth the addton of a power necton equvalent to shunt + 0 to bus I, as depcted n Fgure 4. shunt 0 Fgure 4. Equvalent power necton of shunt branch. Fnally, steady-state UFC mathematcal model can be constructed by combnng the seres and shunt power nectons at both bus I and bus as shown n Fgure 5., UFC, UFC, UFC, UFC Fgure 5. Steady-state UFC mathematcal model. The elements of the equvalent power nectons n Fgure 5 are, upfc se se, 0.0rb sn 1.0rb sn( (1, upfc rbse sn( ( upfc se, rb cos (3, upfc rbse cos( (4 st Inecton Model phase shfter sngle lnear model s shown, consderng reactances of dspersng transformers, n fgure (6. In ths fgure, seres substrate of phase shfter s modeled as a voltage source and the value s stated as follow[17]: k e (5 B E S Et B X Bt X R I S X E I E I B Fgure6. phase shfter sngle lnear model arallel substrate of phase shfter s modeled by Z and X and a voltage R source that t s recevng bus voltage. Usng fgure(6 and changng, lnear crptc voltage sources to parallel flow source wth 1994

5 these lnes, ST power necton model s obtaned, based on fgure(7. and reactve powers to th bus respectvely, and th bus respectvely., ST and ST, and, ST are necton actve ST, are necton actve and reactve powers to (6, ST bsek sn(,, (7 ST ST (8 (9, ST bse k bsek cos( bsek cos(, ST bsek cos( Fgure7. ST power necton model roblem Formulaton Set up FACTS elements have adventages such as preventng over load, reduce losses and decrease cost of generator, ncrease a system loadablty and etc n power systems. It's possble that each of these characterstcs are selected as a obectve functon wth FACTS element for OF problem. In ths paper, a system loadablty factor s selected as a goal to assess a statc voltage stablty edge. A. Obectve functon To obtan a system loadablty mum(statc voltage stablty lmt, a system loadablty factor ( s used as a obectve functon of problem[18]. F (30 B. Condtons and lmtaton of problem roblem condtons are parallelsm and unequal functons that t's necessary to be suppled n optmal response searchng process. arallelsm restrctons arallelsm restrctons are smlar to parallelsm equatons of actve and reactve powers used n normal power flow of same power floes wthout FACTS tools. These condtons are those equatons of power flow wth Newton's Raphson's, Gous saydel's method that are stated as follow: G G G G D D D D cos( (31 1,..., N B sn ( 1,..., N B cos( 1,..., N B sn ( 1,..., N B (3 (33 (

6 D ( 1 D ( 1 D 1 G ( 1 k D G 1 G (35 (36 (37 : The number of system buses, and and and : roductve actve and reactve powers n th bus. G G G G D and D : Demanded actve and reactve powers n th bus. and and and : voltage magntude and voltage phase angle of th bus. and and and : voltage magntude and voltage phase angle of th bus. In above equatons, varables wth superscrpt (^ are related to a system crtcal pont. As mentoned before, we have used power necton model of these elements to add FACTS elements wth OF problem. FACTS elements nect actve and reactve power to each of lnear frst and fnal buses connected to t. Thus, relatons of (31, (3, (33, (34 change, consderng these necton powers to power system, as follow: G G G G FACTS FACTS FACTS FACTS D D D D cos( 1,..., N B sn( 1,..., N B cos( 1,..., N B sn( 1,..., N B (38 (39 Unequal restrctons Unequal restrctons used to mplement proposed algorthm nclude these cases: 0 (4 mn G mn G mn G mn G mn mn S (43 G G G G (44 G G (45 (46 G G (47 (48 S (49 Equaton(49 s related to lnes transferable power. ST and UFC elements lmtaton: ermssble lmt relevant to element controllable parameter s as follow: UFC varables lmtaton: 0 r 1, ST varable lmt: (40 (

7 Implementng roposed Approach In ths secton, proposed approach s mplemented on IEE 118_ bus network. IEEE network s used to show effect of ST and UFC to mprove statc voltage stablty edge, here. Optmzng the obectve functon accomplshs n two stages, n frst stage, the obectve functon s optmzed wthout set up FACTS element and percent of ncreasng system loadablty (statc voltage stablty lmt s obtaned, and n the next stage, the effect of set up ST and UFC elements on statc voltage stablty edge s reveald. In ths paper, two softwares GAMS and MATLAB are used to fnd placement of FACTS elements. GAMS software acts as a medator that receves the data of network after preparng by MATLAB software, and t consders to solve OF problem. Flow chart of proposed approach s shown n fgure(8. start Input system data M 1 es Is there transformer n lne? N0 Add FACTS necton model nto power flow equaton Calculate the new bus matrx and send to GAMS Send and save data to MATLAB M M+1 M<=Nl es N0 Fnd best locaton of FACTS by MATLAB results end Fgure8. Flow chart of the proposed algorthm IEEE 118_ bus network Ths network has 118 buses, 186 lnes and 54 generators. In ths network mum load power s, 44 megawatts and mum producton s, megawatts, that t's selected to show ablty and velocty of proposed algorthm for OF n larg networks. As shown n table1, the value of ncreasng permssble load for 118_ bus network wthout employng FACTS elements s and mum loadablty s between buses 76, 77 nstead of set up ST n all lnes, and also between buses 77, 80 nstead of set up UFC n all lnes. 1997

8 FACTS ARAMETERS σ º =. r= γ º= Table 1. Results of eee 118- bus system locaton Load ablty (bus-bus CONCLUTIONS Wthout FACTS Wth ST Wth UFC So far, the most approachs are presented to fnd placement of FACTS tools, are lmted to small systems, and t needs long tme to calculate. In ths paper s used two softwares GAMS and MATLAB for placement. Results suggest preference UFC n mzng system load ablty than ST. REFRENCES Abdel salam HA, Aly GEM, Abdel karm M, Shebl KM.004. "Optmal locaton of the Unfed ower System Contrller n electrcal power system," IEEE roceedngs on larg Engneerng Systems Conference on ower Engneerng, pp Aghae J, shayanfar H, Amady N.008. Incorporatng ower System securty nto market-clearng of day-ahead ont energy and reserve auctons,europan Transacton On Electrcal ower, etep-99. Ambrz H, Acha E, Fuerte E.000. "Advanced SC Model for Newton Raphson load flow and Newton optmal power flow studes," IEEE Transactons On ower System. ol. 15, No. 1, pp Amady N, elayat MH.009. "Evaluaton of the mum loadablty pont of power systems consderng the effect of statc load models",energy converson and Management, ol. 50, pp Chung T S, L.001. "A hybrd GA approach for OF wth consderaton of FACTS Devces," IEEE ower Engneerng Rev, ol., pp Fuerte-Esquvel CR, Acha E "A Newton-type algorthm for the control of power flow n electrcal power networks," IEEE, Transactons On ower System. ol. 1, No. 4, pp Ge S, Chalmg TS "Optmal Actve ower Flow Incorporatng FACTS Devce wth power flow control constrants," Electrcal ower Energy System. ol. 0, No. 5, pp Hngoran NG "power electroncs n electrcal utltes: Role of power electroncs n future power system", roc IEEE, ol. 4, pp Kundur.009.ower system stablty and control",mc Graw-Hll Inc. Momoh J, El-Hawary M, Adapa R "A revew of selected optmal power flow," lterature to 1993 art I: nonlnear and quadratc programmng approachs, IEEE Transactons On ower System, ol. 14, No. 1, pp Momoh J, El-Hawary M, Adapa R "A revew of selected optmal power flow," lterature to 1993 art II: Newton, lnear programmng and nteror pont methods, IEEE Transactons On ower System, ol. 4, No. 1, pp Mor H, Sek K.007. "Contnuaton Newton-GMRES ower Flow wth Lnear and Nonlnear redctors",ieee, pp Noroozyan M, Angqust L, Ghandhar M, Andersson G "Use of UFC for optmal power flow control", IEEE, Transactons On ower System Delvery. ol. 1, No. 4, pp Ongakul W, Behasaprta.00. "Optmal ower Flow wth FACTS devces by hybrd TS/SA approach," Electrcal ower and Energy Systems, pp adhy N, Abdel moamen MA.004. "ower flow control and solutons wth multple and mult-type FACTS Devces'" Electrcal ower & Engneerng System. ower Systems Test Case, The Unversty of WashngtonArchve, [Accessed 15/7/008]. Saravanan M, Mary Raa Slochana, S, enkatesh, rnce Stephen Abraham J.007. Applcaton of partcle swarm optmzaton technque for optmal locaton of FACTS devces consderng cost of nstallaton and system loadablty, Electrc ower Systems Research, ol. 77, No. 3-4, pp Taranto GN, nto LMG, erera MF.199. "Representaton of FACTS Devces n ower System Economc Dspatch," IEEE, Transactons On ower System. ol. 7, No., pp ural AM, Tumay M.007. "Mathematcal modelng and Analyss of a Unfed power flow controller: A comparson of two approaches n power flow studes and effects of UFC locaton," Electrcal ower and Energy Systems, ol. 9, pp