Available Transfer Capability Calculation with Transfer based Static Security -Constrained Optimal Power Flow

Transcription

1 Proceedgs of the 5th WSEAS Iteratoal Coferece o Applcatos of Electrcal Egeerg, Prague, Czech Republc, March 12-14, 26 (pp3-35) Avalable Trasfer Capablty Calculato wth Trasfer based Statc Securty -Costraed Optmal Power Flow M. GANDCHI*, M. TARAFDAR HAQUE, A. YAZDANPANAH Islamc Azad Uversty, Ahar Brach* Departemet of Power Egeerg, Uversty of Tabrz Faculty of Electrcal ad Computer Egeerg, Tabrz IRAN Abstract -I power market evromet, avalable trasfer capablty (ATC) s a mportat dex, dcatg the amout of the further usable trasmsso capacty for commercal tradg. ATC calculato s o-trval whe statc securty costrats are cluded. I ths paper, a ovel formulato of the ATC problem has bee adopted based o Trasfer based Statc Securty-Costraed Optmal Power Flow (TSSCOPF) soluto to corporate the effects of voltage lmts as well as the tradtoal le flow (thermal loadg) effects. Ths method, calculates ATC problem wth statc securty costrats to a base case master problem ad a seres of sub problems relevat to varous cotgeces. The mathematc model s formulated ad a mproved soluto algorthm s preseted. Computer testg results o the IEEE 3-bus system show clearly the effectveess of the proposed method ad soluto algorthm. KEYWORDS: power market, avalable trasfer capablty (ATC), Power System, Statc Stablty, Optmal Power Flow. 1 Itroducto I recet years, electrc power systems are experecg a epochal revoluto due to a creasgly compettve market. Nowadays, more tha before, securty problems such as overloads, uacceptable traset voltage dps ad system stablty ca occur. I ths ew busess evromet t s more ad more mportat for the system operator to kow how addtoal power ca be safely trasferred across the system. I may power systems, the maxmum power trasfer across crtcal corrdors or terfaces s lmted by stablty cosderatos [1]. If the trasfer level creases too much, stablty may occur for certa dsturbaces. A good kowledge of these stablty costrats s very mportat to operate the system close to ts stablty lmts avodg vulerable states [2]. These aspects have motvated the developmet of methodologes to evaluate exstg power trasfer capabltes ad trasmsso margs wth cosder of the physcal ad operatoal lmtatos of the trasmsso system, such as crcut ratgs ad bus voltage levels. Also, as power systems become more heavly loaded, voltage collapse pheomea are more lkely to occur, especally systems wth log-dstace les [3]. Therefore, there s a eed for a OPF-based algorthm, whch troduces a form of statc stablty costrats, to computg ATC. Ths paper presets a ew method for computato of ATC that uses the OPF techque solved by evolutoary programmg algorthm, whch ca hadle o-smooth fuel cost fucto of geeratg uts. The techque troduces a form of stablty costrat of voltage magtude ad power flow varatos wth respect to the crease of real power trasfer. The trasfer capablty of the system s aalyzed uder two dfferet sets of trasfer, whch are area-to-area ATC ad pot-topot ATC. Area to-area ATC s the addtoal amout of power that s trasferred from the seller area to the buyer area. O the other had, pot-topot ATC s the addtoal amout of power that s trasferred from the seller bus to the buyer bus. ATC s also aalyzed ad quatfed by cosderg the effect of cotgeces, such as le outages. Cosderg outages of all les for a large-scale tercoected power system s mpractcal ad, therefore, cotgecy rakg s used to select the crtcal les that may adversely affect the ATC durg outages. The accuracy ad effectveess of the ATC method usg the Trasfer based Securty- Costraed Optmal Power Flow (TSSCOPF) techque s verfed o the IEEE 3-bus test system.

2 Proceedgs of the 5th WSEAS Iteratoal Coferece o Applcatos of Electrcal Egeerg, Prague, Czech Republc, March 12-14, 26 (pp3-35) 2. TTC Formulato ad Comparso of Methods 2.1 Curretly Used TTC Determato Methods The popularly used methods to calculate TTC ca be categorzed to the followg three types: 1) Cotuato power flow (CPF) methods[4]; 2) Repeated power flow (RPF) methods; 3) Trasfer based securty costraed optmal power flow (OPF) methods[5]. Both OPF ad RPF eable trasfers by creasg the complex load wth uform power factor at every load bus the sk area ad creasg the jected real power at geerator buses the source area cremetal steps utl lmts are curred. The mathematcal formulato of TTC usg OPF ad RPF ca be expressed as follows: Maxmze λ Subject to P P U U G cosδ B sδ = (1) Q G G D Q D j= 1 j= 1 U U j j ( ) ( G s B cosδ ) = δ (2) U U m U (3) max S S max (4) Where λ : scalar parameter represetg the crease bus load or geerato. λ = correspods to o trasfer (base case) ad λ = λmax correspods to the maxmal trasfer; P G, Q G :real ad reactve power geerato at bus ; P D, Q D :real ad reactve load demad at bus : bus umber of the system; U, U j :voltage magtude at bus, j ; G B :real ad magary part of the 'th elemet of bus admttace matrx; δ : voltage agle dfferece betwee bus ad bus j ; U, U m : lower ad upper lmts of voltage max magtude at bus ; S : apparet power flow le ; S max : thermal lmt of le. I the above power flow equatos (1) ad (2), P G (geerator real output source area), P D (real load sk area), adq D (reactve load sk area) are chaged the followg way [2]: PG = PG ( 1+ λkg ) (5) PD = PD ( 1+ λkd ) (6) QD = QD ( 1+ λkd ) (7) Where: P G : orgal real power geerato at bus whch s source area; P D, Q D : orgal real ad reactve load demad at bus whch s sk area; k G, k D : costats used to specfy the chage rate geerato ad load as λ vares. TTC level each case (ormal or cotgecy case) s calculated as follows: TTC = P λ P D ( max ) D (8) Sk Sk Where P D ( λ max ) sum of load at sk area Sk whe λ = λmax ; sum of load at sk area whe λ =. P D Sk The RPF repeatedly solves covetoal power flow equatos at a successo of pots alog the specfed trasfer drectos whle CPF solves a set of augmeted power flow equatos to obta the soluto curve passg through the ose pot wthout ecouterg the umercal dffculty of ll codtog. There are detaled descrptos about CPF [6], [7], ad [8]. The advatage of CPF s that t wll ot ecouter the umercal dffculty of ll codtog so that t ca get complete ad curve to calculate voltage stablty margs whle ts dsadvatage s that the mplemetato of CPF volves parameterzato, predctor, corrector ad step-sze cotrol, whch are complcated. OPF possesses several advatages. Compared to ay RPF method OPF ca provde ad curves for voltage stablty study. Adjustmet method of cotrol varables OPF s relatvely easer. Compared to CPF The mplemetato method s much easer ad tme to covergece s reduced. 2.2 Proposed TTC Determato Method To overcome the defcecy of the cotuato power flow (CPF) ad repeated power flow (RPF) methods, a Trasfer-Based Statc Securty- Costraed Optmal Power Flow (TSSCOPF) s proposed ths paper. It assumes that oly all

3 Proceedgs of the 5th WSEAS Iteratoal Coferece o Applcatos of Electrcal Egeerg, Prague, Czech Republc, March 12-14, 26 (pp3-35) OPF-optmzed parameters volvg the selected source ad sk area ca be dspatched, whch ca be satsfed decetralzed structure. The formulato of TSSCOPF s show the Appedx. TSSCOPF s a good method to use the future applcato sce OPF adjusts the real power output at the source area, the real ad reactve load at the sk area a fxed cremetal step whle TSSCOPF ca adjust those varables ay way. OPF s utlzed to determate TTC ths paper because t s perhaps the most sgfcat techque for obtag mmum cost geerato patters a power system wth exstg trasmsso ad operatoal costrats. I order to gve a complete descrpto of methods to determate TTC, TSSCOPF s preseted the Appedx ad ca be used for decetralzed applcato. 3. Geeral Procedure to Determe of TTC The geeral procedure to determe TTC (cosderg TRM) s as follows. 1) Select a case (ormal or ay cotgecy case from cotgecy lst). 2) Smulate load level by a ormal dstrbuto. 3) Establsh ad solve the base case power flow (o trasfer, λ =). If there s o lmt volato, go to Step 4). Otherwse, set TTC level for the selected case at that load level as zero. Retur to Step 2) to smulate aother load level. 4) Use RPF to make a step crease trasfer power ( λ creased by λ ). 5) Establsh ad solve the power flow problem. 6) Check the soluto to Step 5) whether ay lmt s volated. If o lmt s volated, go to Step 4). If there s ay volato, decrease the trasfer power by the mmum amout ecessary to elmate the volato ad the go to Step 7). The mmum amout s determed by decreasg by 1% of each tme ad the gog to Step 5) utl the volato s goe. 7) Compute the TTC level at the maxmal. Ths s the TTC level for the selected case at that load level. Retur to Step 2) to smulate aother load level utl a covergece crtero of the TTC level for the selected case s reached. The go to Step 8). 8) Retur to Step 1) to select the ext case. If all cases have bee selected, go to Step 9). 9) Compute the TTC for ths source/sk trasfer case. ATC s the mmal value of all the TTC levels. Whe TRM s ot cosdered, gore Step 2) ad after computg TTC level at Step 3) or Step 7), go to Step 8) drectly. 4. Case Studes ad Results 4.1. Test System The IEEE 3 bus Relablty Test System (RTS) s used ths paper to demostrate the proposed methods. The dagram of the RTS system s show Fg. 1. I order to study ATC, the RTS system s dvded to three areas, whch are show Table 1 ad Fg. 1. Te les betwee areas are lsted Table 2. I ths study, the respect voltage volato of each bus s assumed to be +.6p.u. The MVA power flow or the thermal ratgs of the le lmts are for both cotgecy ad base case codtos Test Results ad Dscusso Pror to the ATC calculato, cotgecy rakg s performed o the 6 les the system whch after cotgecy selecto, 3 les have bee detfed as crtcal les [9]. I ths study, these three crtcal les whch are coected from bus 4 to bus 12 ad from bus 9 to bus 1 ad from bus 1 to bus 2 are selected as the test case the determato of the area-to-area ad the pot-topot ATC. The ATC s the determed by referrg to the maxmum power trasfer that cause the lmtg levels of MVA power flow or voltage magtude, respectvely. The outage of crtcal le the trasfer capablty aalyss s cosdered because t wll gve a huge mpact to the ATC result. The shaded area Table 3 (3-1, 3-2, 3-3, 3-4, 3-5), shows ths crtcal te les. Usg the proposed ATC method, the results of the area-toarea ATC ad the pot-to-pot ATC are obtaed as show Tables 3 (3-1, 3-3, 3-4, 3-5) ad 4, respectvely. Results show Tables 3 ad 4 dcate that the lmtato occurs for all the cases of power trasfer are due to over voltage lmts. For stace, from the area-to-area ATC results show Table 3-1, by cosderg a outage te le 4-12 as a cotgecy, the ATC from areas 1 to 2 s MW ad t s lmted by the over voltage o bus 16. Smlarly, from the pot-to-pot ATC results show Table 4, by cosderg a out aged te le as a cotgecy, the ATC betwee buses 2 ad 23 s 53.19MWad t s lmted by over voltage o bus 11. The ATC results show Tables 3 ad 4 prove that the proposed ATC calculato method dcate the effects of

4 Proceedgs of the 5th WSEAS Iteratoal Coferece o Applcatos of Electrcal Egeerg, Prague, Czech Republc, March 12-14, 26 (pp3-35) voltage lmts as well as the cotgecy ad le outages effects o evaluatg ATC. I ths paper, ATC evaluated by cosderg of the crtcal le outages that adversely affect the trasfer capablty of a power trasmsso system. Fg. 1. IEEE 3 bus RTS system. 5. Cocluso Ths paper, proposes a ew approach for steadystate ATC calculato. Ths method take to accout system lmtatos such as bus voltage ad trasmsso curret lmts, for evaluatg area-toarea ad pot-to-pot ATC, usg the statc securty costraed optmal power flow method (SSCOPF). I the proposed ATC method, pror to ATC evaluato the crtcal le outages that adversely affect the trasfer capablty of a power trasmsso system are obtaed through the process of cotgecy rakg ad selecto. The effectveess of the proposed method s verfed by smulato studes o the IEEE 3-bus system. 6 Refereces [1] Avalable Trasfer Capablty Deftos ad Determato, North Amerca Electrc Relablty Coucl 1996, Avalable: ad Artfcal Neural Networks, IEEE Tras. Power Sys. 15 (1) 2. ftp://ftp.erc.com/pub/sys/all, updl/docs/archves/atcfal.pdf [2] W. L, M. Shaaba, Z. Ya, Y. N, ad Felx F. Wu. Avalable Trasfer Capablty Calculato wth Statc Securty Costrats, IEEE Tras. Power Sys , 23. [3] H. D. Chag, C. S. Wag, A. J. Flueck, Lookahead Voltage ad Load Marg Cotgecy Selecto Fuctos for Large-scale Power Systems, IEEE Tras. Power Sys [4] V. Ajjarapu ad C. Chrsty, The Cotuato Power Flow: A Tool for Steady State Voltage Stablty Aalyss, IEEE Tras. Power Sys., Vol. 7, pp , Feb [5] D. Ga,, R. J. Thomas, ad R. D. Zmmerma, Stablty-Costraed Optmal Power Flow IEEE Tras. o Power Sys., Vol. 15, No. 2, May 2. [6] G. C. Ejebe, J. G. Waght, M. Satos-Neto, ad W. F. Tey, Fast Clculato of Lear Aalable Tasfer Cpablty, IEEE Tras. Power Sys., Vol. 15, pp , Aug. 2. [7] G. C. Ejebe, J. Tog, J. G. Waght, J. G. Frame, X. Wag, ad W. F. Tey, Avalable Trasfer Capablty Calculatos, IEEE Tras. Power Sys., Vol. 13, pp , Nov [8] B. Stott ad J. L. Marho, Lear Programmg for Power System Network Securty Applcatos, IEEE Tras. Power Apparat. Sys., Vol. PAS-98, pp , May Jue [9] S. Greee, I. Dobso, ad F. L. Alvarado, Cotgecy Rakg for Voltage Collapse va Sestvtes from a Sgle Nose Curve, IEEE Tras. Power Sys., Vol. 14, pp , Feb Table 1: Three Areas RTS Area Bus Ge. Capacty (MW) Load(MW) Marg(MW) 1 1,2,3,4,5,6,7,8,9,11, ,13,14,15,16,17,18,19,2, ,21,22,24,25,26,27,29, Table 2: Te Les betwee Areas Area Te Les Area 1 to area 2 Le 2-4 Area 1 to area 3 Le 28-27,9-1,6-1 Area 2 to area 3 Le 1-2,23-24,1-17

5 Proceedgs of the 5th WSEAS Iteratoal Coferece o Applcatos of Electrcal Egeerg, Prague, Czech Republc, March 12-14, 26 (pp3-35) Table 3-1: TTC Levels ad ATC Values from Area 1 to Area 2 Normal Te Le 4-12 outage Table 3-2: TTC Levels ad ATC Values from Area 2 to Area 1 Normal Te Le 4-12 outage Table 3-3: TTC Levels ad ATC Values from Area 1 to Area 3 Normal Te Le outage Te Le 9-1 outage Te Le 6-1 outage Table 3-4: TTC Levels ad ATC Values from Area 3 to Area 1 Normal Te Le outage Te Le 9-1 outage Te Le 6-1 outage Table 3-5: TTC Levels ad ATC Values from Area 2 to Area 3 Normal Te Le 1-2 outage Te Le outage Te Le 1-17 outage Table 3-6: TTC Levels ad ATC Values from Area 3 to Area 2 Normal Te Le 1-2 outage Te Le outage Te Le 1-17 outage Table 4: Results of Pot-to-Pot ATC POINT OF TRANSFER SELLER BUS BUYERBUS LINE OUTAGES LIMITATION BUS ATC(MW)

6 Proceedgs of the 5th WSEAS Iteratoal Coferece o Applcatos of Electrcal Egeerg, Prague, Czech Republc, March 12-14, 26 (pp3-35) Appedx The mathematcal formulato of TSCOPF ca be represeted as follows: Maxmze f ( P ( ), ( ), ( )) G Source P Dj j Sk Q Dj j Sk = P PD D Sk Sk Subject to: ( δ δ ) (9) P P U U G cos B s = G D j j = 1 ( sδ cosδ ) (1) Q Q U U G B = G D j j = 1 G P P D PG Source P (11) D QD QD Sk D / D D / D (12) P P = Q Q (13) U U U (14) S m max S (15) max The real power output of geerators source area ad real/reactve load sk area ca be adjusted order to get maxmum trasfer capablty. Ad the complex load s adjusted wth costat power factor.