Optimal location for the allocation of reactive power sources in Transmission Network expansion and Reactive Power Planning

Transcription

1 Optmal locaton for the allocaton of reactve power sources n Transmsson Network expanson and Reactve ower lannng op D. Dhole and M. D. Khardenvs Abstract Transmsson network expanson plannng (TNE s a challengng ssue especally n new restructured electrcty markets envronment. TNE can be ncorporated wth reactve power plannng. In ths paper a meta-heurstc technque for solvng the TNER problems n regulated power systems usng the AC model s presented. The problem s solved by genetc algorthm. For each topology proposed by genetc algorthm an ndcator s employed to dentfy the weak buses for new reactve power sources allocaton usng performance ndex method. The contngency analyss s used to predct whch contngency make system volatons and rank the contngences accordng to ther relatve severty. Wth the allocaton of reactve power sources at the load buses, the crcut capacty ncreases and the cost of nstallaton could be decreased. In ths paper, locaton for the reactve power sources are dentfed by the performance ndex method whch s necessary before solvng the reactve power plannng usng genetc algorthm. The method s tested on a standard IEEE test system. Index Terms Contngency analyss, performance ndex, reactve power plannng, reactve power sources, Transmsson network expanson plannng, weak buses. I. INTRODUCTION As the electrcty consumpton grows rapdly, new transmsson lnes are necessary to provde alternatve paths for power transfer from power plants to load centers enablng contnuous supply. Owng to the large-scale nature of a transmsson system and ts complextes, TNE has always been a complex non-convex optmzaton problem. TNE s usually dvded nto the followng long term (up to 0 years, medum-term (up to 10 years and ort-term (up to 5 years [1]. enerally n TNE, a steady-state analyss s usually performed usng smplfed models, such as a lnearzed power flow model [], DC model or transportaton model [3]. Recently an accurate AC network modelng has been proposed [4]. Transportaton model, hybrd model, lnear dsunctve models and DC models have been used to acheve the prmary topology n the frst stage [5]. In a subsequent stage, the expanded network wll be checked for the other operatonal constrants. A DC model TNE problem can be solved both by. D. Dhole s pursung M. Tech (ES n ovt. College of Engneerng, Amravat, MS. rof. M. D. Khardenvs s Assstant rofessor at the Department of Electrcal Engneerng, ovt. College Of Engneerng, Amravat, MS classcal optmzaton methods and meta-heurstc technques such as smulated annealng [6], genetc algorthm [7], tabu search [8] and a greedy randomzed adaptve search procedure [9]. It ould be noted that the use of a DC model n TNE has followng dsadvantages- The dffculty of takng nto account the power losses n the ntal phase of plannng It s frequently necessary to renforce an expanson plan obtaned va a DC model satsfyng operatonal SC condtons In ort-term plannng, the steady state studes use an AC model n order to accurately assess the real power losses and to facltate relablty as well as securty. Developng a TNE model consderng operatng condtons seems to be desred for better power system utlzaton. In ths regard, reactve power sources are desred for- Increasng power transfer Improvng power factor Reducng real power losses Mantanng voltage profle n a permssble range. Thus, TNE and reactve power plannng (R are crucal ssues especally n modern power systems [10]. The obectve of the smultaneously transmsson expanson and reactve power plannng s to determne where, how many and when new devces such as transmsson lnes and reactve power sources must be added to an exstng network n order to make ts performance for a predefned horzon of plannng at mnmum total cost [11]. II. MATHEMATICAL MODEL FOR TNER The mathematcal model for the TNER problem s a mxed-nteger nonlnear programmng problem that dentfes the optmal soluton between producton cost, transmsson nvestments and load curtalment cost. The optmal power flow calculaton determnes how generators and transmsson network ould be operated to satsfy the operatonal constrants of the network. The obectve functon of the TNER s the summaton of the costs of new lnes and VAR sources nvestment, real power generaton as well as load curtalment cost. The obectve functon s- Mnmze T=I++L (1 595

2 Where, I = Investment Cost that s summaton of lne nvestment and Var sources nvestment cost = c T n f ( q, u ( Where, c crcut cost n added lnes q MVAR sze of VAR sources u bnary vector that ndcates whether to nstall reactve power sources at load buses or not f (q,u cost functon of reactve power (VAR sources = Real power generaton cost n = ( c (3 1 L = Cost of load curtalment real power generatons of generator on bus α, β, c constant coeffcent of power generaton n no. Of generators (from eq. 3 Subect to ( V,, n 0 (4 D C ( V,, n q 0 (5 D C (6 (7 q q q (8 V V V (9 S from S (10 S to S (11 0 n n (1 0 (13 c D 0 (14 D D V S from S to S C C V c D exstng real power generaton exstng reactve power generaton real power demand reactve power demand voltage magntude apparent power flow (MVA lmt, from sde apparent power flow (MVA lmt, to sde apparent power flow (MVA real load curtalment reactve load curtalment Maxmum real power generaton lmt Maxmum reactve power generaton lmt Maxmum voltage magntudes Mnmum real power generaton lmt V Mnmum reactve power generaton lmt Mnmum voltage magntudes f ( q, u ( c0 k c1 kqk uk (15 k l k l Represents load buses Ω l Set of all load buses c 0k Installaton cost for a VAR source at bus k c 1k q k u k unt cost for a VAR source at bus k MVAR sze of VAR source nstalled at bus k Bnary varable that ndcated whether to nstall reactve power source at bus k or not Eqn. (4 and (5 are real and reactve power balance equaton resp., eqn. (6 and (7 are real and reactve power generaton lmt resp., eqn. (8 s var source nstallaton lmt, eqn. (9 gves bus voltage lmt, eqn. (10 and (11 are apparent power flow lmt of lnes from sde and to sde resp., eqn. (1 s capacty constrants of newly added crcuts. The elements of vectors (V,θ,n and (V,θ,n are determned by followng equatons- ( V,, n V V [ ( ncos B ( nsn ] (16 N B ( V,, n V V [ ( nsn B ( ncos ] (17 N B Where,, NB represents buses and NB s the set of all busses, represents the crcut between buses and and s the dfference n phase angle between buses and. The elements of the bus admttance matrx ( and B are: ( n ( n g ( n l ( n 0 0 B( n ( nb nb B B( n b [ n( b l Here, 0 0 n g 0 0 g ng b n ( b ( b 0 0 ] (18 (19 g, b, b are the conductance susceptance and unt susceptance of the transmsson lne or transformer (f s a transformer b = 0, resp. and b s the unt susceptance at bus, whle the proposed model does not consder the phase fters. Elements ( of vectors S from and S to of eqn. (10 and (11 are gven by the followng relatonp- S frem frem from ( ( (0 596

3 S from from V g VV ( g cos b sn (1 V ( b b VV ( g sn b cos ( to to to ( ( (3 to to V g VV ( g cos b sn (4 V ( b b VV ( g sn b cos (5 The mathematcal model can be solved by optmzaton method n the transmsson network expanson and reactve power plannng to mnmze the cost of producton and nvestment of the new transmsson lnes and reactve power sources [1]. contngences. Also artfcal neural networks approaches based on I have been proposed for contngency selecton. In ths paper contngences are ranked usng a I based method. The rankng method used n ths paper s a fast and accurate method to rank the contngences accordng to ther severty on the power system. The rankng technque utlzes a wde system scalar I to quantfy the severty of each contngency wth actually calculatng the post contngency lne flows and bus voltages usng full AC load flow analyss. Contngences are ranked n the order of ther performance ndex values and processed startng wth the most severe contngency at the top of the lst proceedng down the rankng to the less severe ones. Outages are then ranked on the bass of ther correspondng performance ndces. In ths paper the contngences are ranked on the bass of lne loadng. III. CONTINENCY ANALYSIS Contngency analyss s one of the most mportant task encountered by the plannng and operaton engneers of bulk power system. Its purpose s to analyze the power system n order to dentfy the overloads and problems that can occur due to a contngency. Contngency analyss s abnormal condton n electrcal network. It puts a whole system or a part of the system under stress. It occurs due to sudden openng of a transmsson lnes, generator trppng, sudden change n generaton, sudden change n load value. Steady-state power system nsecurty such as transmsson lnes beng overloaded causes transmsson elements cascade outages whch may lead to complete blackout. The contngency analyss s used to predct whch contngences make system volatons and rank the contngences accordng to ther relatve severty. Contngency analyss s useful both n the network desgn stages and for network expanson works to detect network weaknesses. The weaknesses can be strengthened by transmsson capacty ncrease and ths can be done by allocatng the reactve power sources on the partcular weak bus whch s to be strengthened. The AC load flow analyss used to perform contngency analyss can be termed AC contngency analyss routne. A. Contngency Rankng In practce, electrc power engneers use ther udgment and past experence for selectng and nvestgatng severe contngences. In some nstants, ths approach may not dentfy all the crtcal contngences especally n large systems. Therefore, the development of a contngency rankng algorthm whch rank contngences based upon ther relatve severty s desrable. The contngences can be ranked based upon ther effects on lne loadng or bus voltages. A varety of algorthm are developed whch can be classfed nto two groups. One s performance ndex based method whch utlzes a wde system scalar performance ndex to quantfy the severty of each case by calculatng ther I values and rankng them accordngly [1]. The other s the screenng method whch s based on approxmate power flow solutons to elmnate those non-crtcal contngences. Wth the advancement of artfcal ntellgence, expert systems and fuzzy theory are proposed to estmate the severty of varous B. Determnaton of Weak Buses- Real ower Flow erformance Index Method Real power flow performance ndex correspondng to lne real power flow volatons. It s formulated by followng equaton and gves measure of lne MW overloads. NL wm L I ( n L lm n NL w m m1 lm n real power flow rated capacty exponent no. of lnes real non-negatve weghtng coeffcent whch may be used to reflect the mportance of lnes I wll be small when all the lnes are wthn ther lmts and reach a hgh value when there are overloads. Thus, I provdes a good measure of severty of the lne overloads for gven state of the power system. In ths paper, value of exponent has been taken as n= to avod maskng effect and w m =1, see [14]. IV. RESULT OF CONTINENCY RANKIN USIN I METHOD In order to fnd optmal locaton of reactve power sources, 6-bus garver system s smulated. The arver system has 6 buses and 15 branch canddates, the total demand s 760 MW, 15 Mvar. 6-bus garver system s own n Fg.1. MATLAB software has been used for smulaton. 597

4 Fg.1: 6-bus garver system AC power flow s performed by usng Newton Raphson Method n MATLAB. For the calculaton of I, real power flow L after removal of lnes one-by-one s taken from the MATLAB. Contngency analyss s performed on selected buses are dentfed and are ranked n order of ther severty. Table 1 ows the maxmum loadng parameters for each removal of lne one-by-one. The data s taken from [15]. Fg. 4: real power flow after removal of lne 1-5 Fg.5: real power flow after removal of lne -3 Fg.: real power flow removal of lne 1- Fg.6: real power flow after removal of lne -4 Fg.: real power flow after removal of lne 1-4 Fg.7: real power flow after removal of lne

5 Table : Contngency rankng for 6-bus garver system Rankng of Lne From To Maxmum severe lne no. bus bus loadng parameter Fg.8: Calculaton of I after removal of lne 1-, 1-4, 1-5 From Table t s cleared that lne number 1 connected between buses 1 to s most severe lne among all lnes. So we can select bus for allocaton of reactve power sources as bus 1 s generator bus and bus s load bus. Next, lne 4 connected between buses and 3 s severe but we cannot select ths because bus 3 s generator bus and bus s already selected. Smlarly, we select buses 4 and 5 for the allocaton of reactve power sources. In ths paper, optmal locaton for the allocaton of reactve power sources on the load buses s presented. Further, for the purpose of reactve power plannng, capacty of the Var sources are consdered. The bus data and branch data used n ths paper are gven n appendx. V. CONCLUSION Fg.9: Calculaton of I after removal of lne -3, -4, 3-5 Real power flow for the calculaton of I s taken from MATLAB and own n Fgs. from to 7. Calculaton of I s own n Fg. 8 and Fg.9. Table 1: Shows maxmum loadng parameter for each removal of lnes one-by-one Sr. no. Removal of lne From bus To bus Maxmum loadng parameter In ths paper, the severty of the weak bus has been found usng performance ndex method. The proposed algorthm has been appled to 6-bus garver system. For 6-bus system, lne no.1 connected between bus 1 and bus s most severe lne. Table ows the contngency rankng and buses on whch reactve power sources can be allotted. Result of erformance ndex method gves load buses, 4 and 5 for the allotment of reactve power sources and the result s compared wth result own n lterature [13]. Ths dentfcaton wll help n further transmsson network expanson and reactve power plannng. Bus Data: Bu s Type D, MW D, Mvar VI. AENDIX max, MW mn, MW max, Mvar 1 Vθ V mn, Mvar Here, 6 lnes are selected for on-lne rankng. Ths contngency rankng s based on the lne outage n system. Lne outage whch resulted n voltage nstablty s ranked the hghest value. Table ows the contngency rankng whch gves the severty on the system V

6 Branch Data: Bus from Bu s to r, pu x, pu b, pu S max, pu C, US$ n 0 n m ax [8] Edson Luz da Slva, Jorge Maurco Areza Ortz, erson Couto de Olverra and Slvo Bnato, "Transmsson network expanson plannng under a tabu search approach," IEEE Transactons on power systems, Vol.16, No.1, pp.6-68, Feb.001. [9] Slvo Bnato, erson Couto de Olvera and Joao Lzardo de Arauo, "A greedy randomzed adaptve search procedure for transmsson expanson plannng," IEEE Transacton on power systems, Vol. 16, No., pp.47-53, MAY-001. [10] Wenuan Zhang, Fangxng L and Leon M. Tolbert, "Revew of reactve power plannng: Obectves, constrants and algorthms, " IEEE Transactons on power systems, Vol., No. 4, pp , Nov [11] M. Rahman and M. radnead, "Integrated Ac transmsson network expanson and reactve power plannng" IIST, Transacton of electrcal engneerng, Vol. 35, No.E, pp , Dec-011. [1] Amn Mahoudabad, Masoud Radnead, Mad Zenaddn- Maymand, "A new model for transmsson network expanson and reactve power plannng n a deregulated envronment," Scentfc research publed onlne. Vol. 4, pp , Feb-01. Avalble: [13] Naman Krna Sharma, Sudhr. hulambrkar, Man raapat and Ankta Sharma, "Contngency rankng and analyss usng power system analyss toolbox (SAT," IISTE, Vol. 4, No. 6, pp [14] Madhura ad, rach Shnde and rof. S. U. Kulkarn, "Optmal locaton of TCSC by senstvty methods," Internatonal Journal of Computatonal Engneerng Reasearch (ceronlne.com, Vol., pp , Oct.-01. [15] M. J. Rder, A. V. arca and R. Romero, " ower system transmsson network expanson plannng usng AC model," IET eneraton, Transmsson and Dstrbuton, Vol. 1, pp , Aprl VII. REFERNCES [1] A. Mahmoudabad, M. Radnead, M. Mohammadan, M. Zenaddn Maymand, M. Rahman, H. khorasan, "An applcaton of CHA to concurrent ort-term transmsson expanson and reactve power plannng, " paper accepted for presentaton at the 011 IEEE Trondhem owertech. [] Len L. arver, "Transmsson network estmaton usng lnear programng, "IEEE transacton on power apparatus and system, Vol. pas-89, no.7, Sep/Oct [3] R. Romero, A. Montcell, A. arca and S. Haffner, "Test systems and mathematcal models for transmsson network expanson plannng," IEE roc-eneraton, Transmsson and Dstrbuton, Vol. 149, No.1, pp.7-36, January-00. [4] M. Rahman, M. Radnead, E. M. Carreno and R. Romero, "Effcent method for AC transmsson network expanson plannng," Electrc power system research, Vol. 80, pp , Feb-010. [5] erardo Latorre, Ruben Daro Cruz, Jorge Maurco Areza and Andres Vllegas, "Classfcaton of publcaton and models on transmsson expanson plannng," IEEE Transactons on power systems, Vol.18, pp , May 003. VIII. BIORAHIES op D. Dhole receved the B.E degree n Electrcal Engneerng from the overnment College of Engneerng, Chandrapur (M.S., Inda n 011. resently, e s an M Tech (ES student at ovt. College of Engneerng, Amravat (M.S., Inda. Mana D. Khardenvs receved the B.E. degree n Electrcal Engneerng from the Nagpur Unversty, Nagpur (M.S., Inda, n 1993, the M.E. (ES degree from the Amravat Unversty, Amravat, Inda, n 000. After her post graduaton, e worked n rrgaton department for 6 years. She has 11 year experence of teachng n overnment College of Engneerng, Amravat. resently, e s workng as Assstant rofessor n Electrcal Engneerng at ovt. College of Engneerng, Amravat (M.S., Inda. Her area of research nterest s transmsson network expanson plannng, hgh voltage transmsson. [6] R. A. allego, A. B. Alves, A. Montcell and R. Romero, " arallel smulated annealng appled to long term transmsson network expanson plannng," IEEE Transacton on power system, Vol. 1, No.1, pp , Feb [7] Kwang Y. Lee, Xaoma Ba and Young-Moon ark, "Optmzaton method for reactve power plannng by usng a modfed smple genetc algorthm," IEEE Transacton on power system, Vol.10, No.4, pp , Nov