Optimal Placement of TCSC Based on A Sensitivity Approach for Congestion Management

Transcription

1 fteenth atonal Power Systems Conference (PSC), IIT Bombay, December 2008 Optmal Placement of Based on A Senstvty Approach for Congeston Management Srnvasa Rao Pud, S.C. Srvastava, Senor Member, IEEE Abstract One of the maor operatng challenges n the electrcty markets s to manage transmsson system congeston to ensure ts secure operaton. Ths paper has manly addressed the ssue of congeston management utlzng Thyrstor Controlled Seres Compensator (). Proper locaton of a ACTS controller s key to mze ts benefts. Ths paper presents a senstvty factor based approach for the optmal placement of the to mze the congeston cost. The senstvty of the congested lne flow wth respect to flow n other lnes has been used for the placement of the. The effectveness of the proposed method has been demonstrated on IEEE 30- system and a 75- Indan system. I. ITRODUCTIO In a compettve electrcty market, congeston occurs when the transmsson network s unable to accommodate all the desred transactons due to volaton of system operatng lmts. The open power market utlzes the transmsson system ntensvely, whch n turn leads to frequent congeston. The economc theory suggests that the most logcal way to charge for electrcty usage s through Locatonal Margnal Prce (LMP)/spot prce. When congeston begns to take place under heavy demand, prce volatlty and market mbalances may occur and the consumers, n such regons, have to bear the prce spke. In such a case, the customers suffer and the very purpose of the restructurng and ntroducng competton s defeated. Hence, congeston management s an mportant ssue to be addressed n the restructured market. Ths s generally handled by the system operator (SO), who s nether buyer nor seller of the electrcal energy. The restructured electrcty markets, worldwde, have popularly used the Poolco model [2]. The Poolco model, n general, utlzes spot prcng of electrcty [1] and an assocated bd based dspatch to match generators supply wth customers demand. Under the spot prcng scheme, the tarffs charged by GECOs and pad by the customers are the nodal prces or the ncremental prces. These are the by-product of securty constraned optmal power flow. By usng OP, wth stff constrants enforced on transmsson lne one can ensure secure transfer of power to the customers wthout any curtalments. The mpact of forcng lne flow to reman wthn ts lmtng value, under congeston by the OP, s reflected n Srnmvasa Rao Pud (emal: srnu_p19@yahoo.co.n) and S. C. Srvastava, (emal: scs@tk.ac.n) are wth the Department of Electrcal Engneerng, Indan Insttute of Technology, Kanpur , Inda. the prces and the Locatonal Margnal Prce (LMP) ncreases. The dfference n the LMP across an nterface gves a measure of degree of congeston across the lnk. Hgher s the dfference n the LMP, the more the lnk s congested. To reduce ths dfference n the LMP, leadng to reducton n the congeston, lexble AC Transmsson Systems (ACTS) controllers can be used. However, due to ther hgh cost, the optmal locaton, approprate sze and settng of the ACTS controllers s mportant. Implementaton of these devces can change the prces at certan es, drectly affectng some generators and loads [10]. There are several methods for fndng the optmal locatons of the ACTS controllers n vertcally ntegrated systems as well as unbundled power systems [4 8]. In [4], a loss senstvty approach has been proposed for placement of seres capactors, phase shfters and statc VAR compensators. Other works have ncorporated ACTS controllers n optmal power flow formulaton [6, 7] wth dfferent obectve functons. Raaraman et al. [5] have used contnuaton power flow method for obtanng the sze and locatons of seres compensators to ncrease the loadablty lmt of the system. After placement of the seres compensaton n each lne, the loadablty wth a unform loadng factor at each s computed wth the help of the contnuaton power flow technque. In large power systems, where load change s not unform, t s dffcult to decde the optmal locaton of seres compensaton. In [8, 9], the optmal locatons of ACTS devces are obtaned by solvng the economc dspatch problem ncludng the cost of these devces makng the assumpton that all lnes, ntally, have these devces. In the presence of blateral/multlateral contracts, t s dffcult to use ths method. In ref. [12], optmal placement of for reducng congeston cost, has been presented by usng a performance ndex, whch ncorporates two factors. One s the senstvty matrx of the wth respect to the congested lne and the other s the shadow prce correspondng to the congested lne. In ref. [15], authors proposed LMP dfference and congeston rent contrbuton methods for optmal locaton of to reduce the congeston cost. The proposed methodologes are based on LMPs that are by-products of OP formulaton. But, ths method selects the lne whch s more congested as the best locaton of, causng t to operate n nductve mode and nvolves tme ntensve procedure. Ths paper presents a new method for optmal locaton of seres ACTS Controllers for congeston management n the 558

2 fteenth atonal Power Systems Conference (PSC), IIT Bombay, December 2008 deregulated electrcty markets. The proposed method s a modfcaton of the congeston rent contrbuton method [15], whch makes use of economc sgnal gven by the LMP for decdng the congeston n a lne. Thyrstor Controlled Seres Compensator (), a seres ACTS controller, has been consdered n ths work for congeston management. A senstvty based method has been suggested for optmal locaton of the. An OP formulaton has been used for decdng ts optmal settng and studyng ts mpact on the congeston cost. A pool type of market s consdered n ths paper. The rest of the paper s organzed as follows. Secton II presents the formulaton of the OP ncorporatng and the soluton approach. The proposed placement methodology for n deregulated market s descrbed n Secton III. umercal results along wth some observatons and dscussons are presented n Secton IV. The maor contrbutons and conclusons of the paper are summarzed n Secton V. nally, appendx for congeston rent contrbuton method [15] has been gven n secton VI. sn cos sn cos 2 P V G VV G cos B (1) 2 Q V B VV G sn B (2) 2 P V G VV G cos B (3) 2 Q V B VV G sn B (4) where, xr cxcx G r x r x xc (5) B V 2 2 xcr x xcx r x r x xc S 2 2 Z =r +x S V (6) II. MODELIG AD OPTIMAL PLACEMET O Although ACTS controllers are utlzed n the system to perform ther prmary task of stablty control, they also mprove the steady state performance of the system. The present work has only consdered ther mpact on the congeston management, formulated as a steady state problem. A statc Power Inecton Model (PIM) [11, 13] of the has been used. The necton model represents the as a devce that nects certan amount of actve and reactve power n a node. V B sh Z =r +x -x c g. 1: Statc model of lne wth V B sh g.1 shows a model of transmsson lne wth connected between es and. The transmsson lne s represented by ts lumped -equvalent parameters, connected between the two es. Durng steady state, the can be consdered as a statc reactance x c. The controllable reactance x c s drectly used as the control varable n the power flow equatons. The correspondng power necton model of, ncorporated n the transmsson lne, s shown n g. 2. The real (P ) and reactve (Q ) power nectons, due to at es and are gven by the followng equatons S =P +Q S =P +Q g. 2: Statc power necton model of where, V, V and, are voltage and angle at es and, respectvely. G and B are the conductance and susceptance of the lne-. In the present study, the above model s ncorporated n the OP. The mum compensaton by s assumed to be lmted to 60% of the reactance of the un-compensated lne, n whch the s placed. A. OP ormulaton: Optmal Power low (OP) has been used n ths work under pool based electrcty markets to calculate generaton dspatch and load schedules, to obtan nodal prces or LMPs and to manage congeston n the systems. It s based on the bds submtted by the generators and loads (f the demand has prce elastcty) and the network data. The generally accepted obectve s to mze the socal welfare (or to mze the generaton cost, f loads are nelastc). In ths work, t s assumed that the loads are nelastc to the prce varatons. Therefore, the socal welfare functon becomes the total cost of supplyng electrcty. However, the formulaton can be easly extended to nclude demand bds to mze the socal welfare. The problem s stated mathematcally as G Mn CPG (7) 1 subect to Power balance equaton: P, V P P 0, for any node G D Q, V Q Q 0, for any node G D If s located n lne between es and, the power 559

3 fteenth atonal Power Systems Conference (PSC), IIT Bombay, December 2008 balance equatons at nodes and are gven by P, V P P P 0, for node G D G D G D Q, V Q Q Q 0, for node P, V P P P 0, for node Q, V QG QD Q 0, for node Apparent lne flow lmt: S, V S Power generaton lmt: P P P G G G G G G Q Q Q Bus voltage and angle lmts: reactance lmt: V V V c c c x x x Where, G s the number of generators, C (P G ) s the bd curve of th generator, P G and P G are the mum and the mum actve power generaton lmts of a generator at, Q G and Q G are the mum and the mum reactve power generaton lmts of generatng unt at, V and V are the mum and the mum voltage lmts at, S s the apparent power flow n transmsson lne connected between nodes and, and S s ts mum lmt. P G and Q G are the actve and reactve power generatons at node, P D and Q D are the actve and reactve power loads at node, P and Q are the net actve and reactve power nectons at node, x c and x c are the mum and mum lmts of the reactance and s the number of nodes n the system. B. Soluton Technque The augmented obectve functon of the above OP problem augmentng all the constrants s expressed as L C P P P P P G G P G D 1 1 L Q Q QG QD Q L S S 1 1 G G G PG PG PG PG PG PG QG QG QG G V V V x (8) c c c x c c Q Q G G QG V V V x x c x x where, P and Q are the Lagrange multplers assocated wth the equalty constrants (power balance equatons) and m,,, n,,,,, are the L P G PG Q G Q G V V x c Lagrange multplers assocated wth the nequalty constrants (lne flow lmt, generator real and reactve power lmts, xc voltage lmts and reactance lmts, respectvely). The soluton of the OP gves the values of these multplers along wth the dspatch result. Optmal toolbox of the MATLAB has been used for the soluton of the OP problem ncorporatng the n the MATLAB envronment. Each multpler n (8) has economc sgnfcance. The mportant one s the Lagrange multpler P assocated wth the real power balance equatons. It s the real power spot prce or nodal prce or LMP and can be used for prcng energy n electrcty markets [14]. LMP s generally composed of three components, a margnal energy component (same for all es), a margnal loss component and a congeston component. In ths, the congeston component arses because of lne flow constrants and the voltage constrants. When these are nactve, LMP conssts of margnal energy component and the margnal loss component only. Thus, one can get congeston component from the LMP by runnng the OP, wth and wthout congeston constrants, and take the dfference of the LMP n both the cases. The dervaton of the nodal spot prces, applyng the frst order optmalty condton to the augmented functon shown n (8), s derved n [3]. or a case of real power spot prce at, consderng all constrants n the OP, the decomposton of the nodal spot prce nto three components s as follows. L PL P e L P (9) P e L, C, 1 (10) The decomposton of nodal spot prce obtaned from OP wthout congeston constrants nto two components s as follows. wo e L, (11) where, e s the margnal energy component at the reference (same for all es), L, s the margnal loss component and C, s the congeston component. The dfference of the above two equatons wll gve the congeston component of the LMP at. wo C, (12) If the necton (or extracton) at a partcular ncreases the flows across the congested nterface, the spot prce at that ncreases. After fndng congeston component of LMP usng the above method, there may be small loss component that wll exst snce power flows wll change wth and wthout congeston constrants. Ths mpact has been neglected n ths work. Smlarly, for, the spot prce (LMP) can be wrtten smlar to the equatons (10), (11) and (12), as e L, C, (13) (14) wo e L, (15) wo C, Takng the dfference of the spot prce between two es and, one gets 560

4 fteenth atonal Power Systems Conference (PSC), IIT Bombay, December 2008 (16) Equaton (16) shows that the nodal prce dfference between any two es depend on the congeston throughout the network. The prce dfferental, by defnton, gves the congeston rent (.e. merchandse surplus). The surplus arses because generators are compensated by LMP at the respectve generator es (whch are generally low) and loads are charged by LMP at the respectve load es (whch are generally hgh). The congeston rent of ndvdual lne secton and the total congeston cost are calculated as gven n appendx n secton VI. III. SESITIVITY ACTOR BASED METHOD The proposed method fnds out the senstvty of flow n the most congested lne wth respect to flow n the other lnes and places the n a lne, whch causes mum reducton n the power flow of the most congested lne. The most congested lne has hghest congeston rent. The proposed senstvty factor method s explaned below. Consder that the most congested lne s between es and. Let P be the base case real power flow through that lne. Consder another lne between es m and n havng real power flow P mn and P nm from m to n and n to m, respectvely. Let P new be the new lne flow between es and. If the flow n lne-mn,.e. P mn s changed by a small amount, the changes n the lne flows can be wrtten as, P Pnew P. The proposed senstvty ndex s defned as the rato of P to the base case real power flow transmtted n the most congested lne.e. P for a small change n flow n lne-mn. sens, mn changencongested lne flow P (17) orgnal flowncongested lne P The senstvty factor can be found by utlzng the senstvty propertes of Jacoban matrx obtaned from ewton-raphson load flow at a base case operatng pont. The changes n P mn have been smulated by consderng two fcttous generators at end es of the lne, havng outputs P mn and P nm. or the senstvty analyss, the value of P mn s taken as 5% of the actual flow of the lne consdered. Once voltage and angle msmatch vectors are calculated for all the es, t s trval to obtan lne flows. After gettng the new power flows, the dfference n power flows n the congested lne.e. P and hence, the senstvty factor can be computed. The lnes, whch have the most negatve senstvty factor value, can be selected for the optmal placement of the. Calculaton procedure of the proposed method s summarzed n the followng steps: Step 1: Run the base case OP to calculate the LMP at all the es and the power flow across all the lne sectons. Step 2: Calculate congeston rent of ndvdual lnes usng LMP values and power flows calculated n step 1. Select the most congested lne, whch has hghest value of the congeston rent gven by eq. (21). Step 3: nd the senstvty factors for the most congested lne wth respect to all other lnes usng eq. (17). Select a lne-mn, whch has mum negatve value of the senstvty factor for the placement. Step 4: Run the OP, wth n the lne-mn and calculate the congeston rent of the most congested lne and the total congeston cost. If the optmal locaton s between two generator es the next best locaton wll be selected. Step 5: Sometmes placement of ACTS causes congeston n some other lnes. In such cases, go to the next lne n descendng order of the senstvty value. Ths method consders the operaton n capactve as well as nductve mode and separaton of congeston component of LMPs. It drectly dentfes the lne, where has to be optmally placed unlke prorty lst n the congeston rent contrbuton method [15]. IV. CASE STUDY The proposed methodology for the optmal placement of the for congeston management has been mplemented on IEEE 30- test system and 75- Indan system. A. IEEE 30 system: IEEE 30- system has 41 lne sectons. In Table 1, the result of OP.e. LMP values, wth and wthout congeston constrants, are shown. Congeston component of LMP are also shown n Table 1. rom the base case OP, wthout any congeston constrants, power flow through lne 11 s MVA, whch s above ts mum ratng (137 MVA). These are also reflected n the LMP dfference and congeston cost of that lne. The congeston cost s $/hr, whch s very hgh as compared to other lnes. Congeston cost of each lne n the system s shown n Table 3, wth and wthout. Table 1: LMP values and congeston component of LMP wth n lne- 12 and wthout any Bus o LMP wth out constrants ( wo ) LMP wth constrants ( ) Wthout wth Congeston component of LMP Wthout Wth

5 fteenth atonal Power Systems Conference (PSC), IIT Bombay, December 2008 Utlzng the proposed senstvty based method, the senstvty of ths lne wth respect to all other lnes are obtaned. Some of the lnes wth most negatve senstve values, n descendng order of ther magntude are gven n Table 2. rom ths table, t s observed that the lne 12 has the mum negatve senstve value. Hence, the lne 12 s the best locaton for a placement. When s placed n the lne 12, congeston cost of the lne 11 gets reduced to $/hr and the congeston cost of total system also reduces from $/hr to $/hr. Table 2: Senstvty of lne-11 power flow wth respect to other lnes Lne o: rom To Senstvty values normalzed to lne Table 3: LMP dfference and congeston rent of each lne wth n lne-12 and wthout any Lne o: Dfference n LMP of end es Congeston rent = ( *P ) rom () To () ($/hr) Wthout Wth Wthout Wth B. 75 Indan system: Indan 75- system has 98 lne sectons. In Table 4, the result of OP.e. LMP values, wth and wthout congeston constrants, are shown. Congeston component of LMP are also shown n Table 4. rom the base case OP, wthout any congeston constrants, power flow through lne 91 s MVA, whch s above ts mum ratng (300 MVA). These are also reflected n the LMP dfference and congeston cost of that lne. The congeston cost s IR/hr, whch s very hgh as compared to other lnes. Congeston cost of each lne n the system s shown n Table 6 wth and wthout. Table 4: LMP values and congeston component of LMP wth n lne-92 and wthout any Bus o: LMP wth constrants ( ) Congeston component of LMP LMP wth out constrants ( wo ) (IR/MWh) (IR/MWh) Wthout Wth (IR/MWh) Wthout Wth Some of the lnes wth most negatve senstve values, n descendng order of ther magntude are gven n Table 5. rom ths table, t s observed that the lne 92 has the mum negatve senstve value. Hence, the lne 92 s the best locaton for a placement. When s placed n the lne 92, congeston cost of the lne 91 gets reduced to IR/hr and the congeston cost of the total system also reduces from IR/hr to IR/hr. Table 5: Senstvty of lne-91 power flow wth respect to other lnes Lne o: rom To Senstvty values normalzed to lne Lne o: Table 6: LMP dfference and congeston rent of each lne wth n lne-92 and wthout any rom To Dfference n LMP **Congeston rent = of end es ( *P ) () () (IR/MWh) (IR/MWh) Wthout Wth Wthout Wth **all values are multple of 10 5 V. COCLUSIOS In ths paper, a senstvty factor based method has been proposed for optmal locaton of to manage congeston n the electrcty markets. rom the results obtaned on the IEEE 30 and 75 Indan systems, the followng man conclusons can be drawn. Optmal placement of causes reducton n the congeston cost of the most congested lne and reduces the LMP values. 562

6 fteenth atonal Power Systems Conference (PSC), IIT Bombay, December 2008 The proposed method of senstvty based optmal placement of performs better than the congeston rent based method [15]. The congeston rent based method nvolves addtonal smulaton to check the mpact of placement of n each of the lnes, n the prorty table, on the congeston cost. Invarably t selects the most congested lne tself for the placement, whch wll operate n nductve compensaton mode. On the other hand the proposed method drectly dentfes a lne, havng hghest mpact on the flow n congested lne, for the placement. VI. APPEDIX A. Congeston rent contrbuton method [15]: Accordng to ths method, the decomposton of the nodal spot prce at nto three components s as follows. (18) e L, C, Smlarly, for, the spot prce can be wrtten as (19) e L, C, Takng the spot prce dfference between two es and, one gets L, L, C, C, (20) The congeston rent of the ndvdual lne s calculated as CC P (21) The total congeston cost s calculated as TCC L 1 P (22) The congeston rent contrbuton of the ndvdual lne s defned as CC CCC (23) TCC nally, n ths method a prorty lst s formed wth hgh prorty lnes havng larger magntude of the CCC. The number of lnes to be consdered for prorty lst depends on the sze of the system. or each lne n the prorty lst, OP can be run wth placed n that lne and the total congeston rent can be computed. The best locaton of the s the one where by placng, mum congeston cost s acheved. [6] G. Huang and S.-C. Hseh, ast textured algorthms for optmal delvery problems n deregulated envronments, IEEE Trans. on Power Systems 13 (2), 1998, pp [7] J.A. Momoh and J.Z. Zhu, A new approach to optmal power flow wth phase shfter, n Proceedngs of IEEE Internatonal Conference on Systems, Man, and Cybernetcs, vol. 5, 1998, pp [8] T.T. Le and W. Deng, Optmal lexble AC transmsson systems (ACTS) devces allocaton, Electr. Power Energy Syst. 19 (2), 1999, pp [9] E.J. de Olvera and J.W.M. Lma, Allocaton of ACTS devces n a Compettve Envronment, Proc. of the 13th PSCC, 1999, pp [10] S.C. Srvastava and R.K. Verma, Impact of ACTS devces on Transmsson Prcng n a De-regulated Electrcty Market, Proceedng of Internatonal Conference on Electrc Utlty Deregulaton and Restructurng and Power Technologes 2000 (DRPT 2000), Cty Unversty, London, Aprl 2000, pp [11] C. Lehmkoster, Securty Constraned Optmal Power low for an Economcal Operaton of ACTS devces n Lberalzed Energy Market, IEEE Trans. on Power Delvery, vol.17, o. 2, Aprl 2002, pp [12] Kwang-Ho Lee, "Optmal Stng of for Reducng Congeston Cost by usng Shadow Prces," Electrc Power and Energy Systems, vol. 24, Oct. 2002, pp [13] Y. Xa,Y.H. Song and Y.Z. Sun, Power flow control approach to Power Systems wth Embedded ACTS devces, IEEE Trans. on Power Systems, vol. 17, o. 4, ovember 2002, pp [14].L. Alvarado, Controllng Power Systems wth Prce Sgnals, Decson Support Syst., vol. 40, 2005, pp [15]. Acharya and. Mthulananthan, Locatng Seres ACTS devces for Congeston Management n Deregulated Electrcty Markets, Electrc Power Systems Research, vol. 77, 2007, pp VIII. BIOGRAPHIES Srnvasa Rao Pud receved hs B.E. degree from SRKR Engneerng College Bhmavaram, Inda, and M.Tech degree from Indan Insttute of Technology Kanpur, Inda, both n Electrcal Engneerng, n 2006 and 2008, respectvely. Hs research nterests nclude ACTS controllers and power system restructurng. S. C. Srvastava receved hs PhD n Electrcal Engneerng from Indan Insttute of Technology Delh, Inda. He s presently workng as Professor n the Department of Electrcal Engneerng at the Indan Insttute of Technology Kanpur, Inda. Hs research nterests nclude energy management system, power system optmzaton, securty analyss, voltage stablty and power system restructurng. He s a fellow of the Indan atonal Academy of Engneerng (IAE), Insttuton of Engneers (Inda) & IETE (Inda) and senor member of the IEEE. VII. REERECES [1].C. Schweppe, M.C. Caramans, R.D. Tabors and R.E. Bohn, Spot Prcng of Electrcty, orwell, MA, Kluwer, [2] W.W. Hogan, Contract etworks for Electrc Power Transmsson, Journal of Regulatory Economcs, vol. 4, Sept. 1992, pp [3] M. Hsu, An Introducton to the Prcng of Electrc Power Transmsson, Utltes Polcy, vol. 6, o. 3, Sept. 1997, pp [4] P. Preedavcht and S.C. Srvastava, Optmal reactve power dspatch consderng ACTS devces, Electrc Power Systems Research. 46 (3), 1998, pp [5] R. Raaraman,. Alvarado, A. Manac, R. Camfeld and S. Jalal, Deteraton of locaton and amount of seres compensaton to ncrease power transfer capablty, IEEE Trans. on Power Systems 13(2), 1998, pp