Investigation of Transmission Line Parameter Sensitivities in Congested Power Systems

Transcription

1 Ivestgato of Trasmsso Le Parameter Sestvtes Cogested Power Systems CANAN ZOBİ KARATEKİN Departmet of Electrcal Egeerg Istaul Techcal Uversty Istaul, TURKEY CANBOLAT UÇAK Departmet of Electrcal & Electrocs Egeerg Yedtepe Uversty Istaul, TURKEY Astract: - Trasmsso cogesto maagemet may e categorzed to short term ad log term maagemet. The short term trasmsso cogesto maagemet s ased o rules ad prcg ad the log-term cogesto maagemet s ased o plag to stregthe trasmsso grd deregulated power systems. Frequet cogesto etwee two zoes or odes may requre straghteg of the approprate les for the log-term cost mmzato. I ths paper, cogesto relef ad cost mmzato are vestgated as a fucto of le susceptaces ad le lmts. Frst, mathematcal dervatos to calculate sestvtes of the geerato cost to the le parameters such as le susceptaces ad le lmts are gve. Secod, umercal studes are doe for a example system y usg Sequetal Quadratc Programmg to determe cogesto oudares, cogested les ad, cost of geerato whe le capactes ad le susceptaces are vared. The results are gve the cocluso secto. Key-Words: - Cogesto maagemet, sestvty aalyss, trasmsso plag Itroducto The restructurg of power systems has led to a uusual usage of trasmsso grds ot foresee at the desg stage []. I the restructurg evromet, geerators ad loads ca access trasmsso system a odscrmatory ad equtale maer. Ope access to trasmsso systems are very mportat for healthy competto power dustry. I a deregulated evromet, producers ad cosumers sell ad uy electrcal eergy through trasactos a market. These trasactos whe mplemeted may sometmes cause the electrc power etwork to ecome cogested. Therefore, cogesto maagemet has ecome more mportat ad dffcult the emergg deregulated electrcty markets as the umer ad magtude of power trasactos crease []. I a power market, trasactos etwee producers ad cosumers are lmted y le parameters, whe the lmtatos exst, cost of electrcal eergy producto wll crease. Also, ecause of the cogesto, some regos market power may preval. Trasmsso cogesto maagemet may e categorzed to short term ad log term. The short term trasmsso maagemet s ased o rules ad prcg [-7]. The FERC expresses ts prefereces for market-ased plas, ad otes that the prcg ad expaso program should e compatle wth the prcg sgals for shorter-term solutos to cogesto maagemet so that market partcpats ca choose the least-cost respose [8]. Cogesto always creases the cost of electrcal eergy ad cogestos persstg smlar zoes of the trasmsso le must e removed log term so that compettve eergy market ca e accomplshed aga. The statstcal methods whch are proposed lterature may e used cogesto studes for log-term plag [9]. Grd plag s a log-term approach whch requres decso tools to determe whch part of the etwork should e developed the future. The ojectve of [9] s to forecast whch les mght e smultaeously cogested. Compettve markets expose trasmsso plaers to ew ucertates. These are hadled usg a decso aalyss approach whose key cotruto s quatfyg ad mmzg rsk [0]. I vertcally tegrated systems, may methods have ee used for trasmsso expaso plag [-]. Trasmsso plag these studes are accomplshed to respod to load ad geerato creases. However, ths paper, cogesto relef s cosdered for horzotally tegrated power systems. Log-term cogesto relef etwee zoes ca e acheved y the stregtheg the trasmsso les. The stregtheg of a trasmsso le ca e accomplshed ether y uldg aother trasmsso le etwee the cogested zoes or y creasg the capalty of the orgal le. Ths wll cause susceptace chage ad le lmt crease etwee the two pots. I ths paper, cogesto relef as a fucto of le susceptace ad le lmt s vestgated. The goal s to elmate le cogesto wth trasmsso le plag the log-term. Therefore, the effect of chagg le susceptace ad le lmt to the geerato cost s studed. To acheve ths, mathematcal

2 dervatos to calculate sestvtes of the geerato cost to the le susceptaces are gve. Ad the, umercal studes are doe y usg sequetal quadratc optmzato programmg (SQP to determe the cogesto rego ad the cost of geerato whe le capactes ad le susceptaces are chaged. Ths study shows that t s possle to releve cogesto o the le whle the le susceptace s kept a certa terval. It s terestg to ote that sometmes t s suffcet to decrease the le susceptace to releve cogesto. The results are gve the cocluso. Sestvty of Le Susceptace The effect of alterg the susceptace of varous trasmsso les the system s calculated y the procedure descred the refereces [] ad []. May umercal techques power flow studes, as the case of cogesto maagemet ad trasmsso prcg a market drve power system evromet, cocetrate o the use of DC power flow aalyss, as they ca gve a clear pcture of the cosequeces o system for chages parameters, ad ecause a large sze power system geerally requres a reducto computatoal tme, especally for o le aalyss [6]. I ths study, the so-called DC approxmato s used for the reasos metoed aove, that s, the real power losses are gored ad us voltage magtudes are approxmated to.0 pu. Uder these assumptos, reactve power flow s zero o each le. Each trasmsso le coectg the usses s specfed y ts susceptace ad ts mum power flow lmt P. The real power flow o le s P = θ ( ( j where θ s the voltage agle at us. The total jecto at us s P = P + P ( j load The total geerated ad the total cosumed power alace relato s gve y P ( = P load The ojectve s to mmze geerato costs gve y us M F( P, P,..., P = F ( P ( us = Suject to: h( P, θ,, P = 0 ( load P = P (6 Here, the equalty costrats show as fuctos h( are ode equatos ad power alace relato. Iequalty costrats are the flow costrats. The Lagraga fucto for optmzato wll e L = + us rach, j j = F ( P + us = =, j j µ ( P P λ h ( P, θ,, P Varales ad multplers are gve y z = [ P K P us us rach] T us θk θ λ K λ µ K µ (8 Explctly cludg the prolem statemet, ad deotg the optmal soluto for a gve y z (, we stll must have the frst order codto L g( z ( = = 0 (9 For a small chage, t ca e assumed that the set of dg equalty costrats does ot chage. We ca dfferetate the frst-order codto wth respect to usg the cha rule of calculus g( z ( dz ( g( z ( + = 0 (0 load (7 g It s defed = W ( at every z, ad ths equato s tegrated g z, = W (. z + g ( ( ( 0 dz ( The sestvty ca e otaed y solvg dz W ( g z W (, ( 0 ( = = z ( g0 g 0 = L s costat so ( = 0 z=0 g ( Ths value of g 0 ca e susttuted to the prevous equato, dz W ( W ( = z ( ( dz ( So, the sestvty s otaed as dz ( The value of W ( = W (.. z ( ( dz ( ca e used to calculate the margal effect o total system cost due to a chage. We ca just multply the porto of dz ( correspodg to power jectos, dp (, y the correspodg margal costs, or, equvaletly, the multplers λ, to ota dtc T dp (λ ( =

3 Now let us come the effect of sestvtes of le susceptace ad le capacty to see what the effect of margally stregtheg a le (creasg oth the capacty ad the magtude of the susceptace wll e. For that, we choose to crease the magtude of the susceptace y the same rato as we crease the le capacty. Let us cosder the le -j, ad crease the capacty y ε MW. The correspodg chage the susceptace would e ε. The resultg chage P total cost for cogested le, dvded y ε, s the TC dtc = µ (6 P P Smlar calculatos ca e doe for other les as TC dtc = (7 P P Example System Sestvty aalyss descred aove has ee carred out o a example system show Fg. 6, [7]. The data for the system s gve Tale (cost fuctos, geerato capactes. Each us has load. Maxmum power flow lmts of all trasmsso les are ad le susceptaces are pu for all les ad le resstaces are omtted. By selectg the agle θ = 0 as the referece agle, equalty costrats for the system ca e wrtte as P P P P θ θ + + θ θ = = = = = 0 6( θ 6 6( θ = 0 (8 The supply demad alace s P + P + P + P = 600 (9 Vector of varales ad Lagrage multplers are z P K P θ K θ6 λ K λ6 µ 6 (0 I ths case, we kow advace that the flow costrat P 6 P 6 s dg, so we treat ths costrat as a equalty costrat, wth Lagrage multpler µ 6. The other equalty costrat are odg, so we gore them. We ca dfferetate the Lagrage fucto wth respect to all varales ad Lagrage multplers ad, thus t s gve y Wz = g 0. W matrx depeds o = [ ] T susceptaces. I ths example system, le -6 s cogested. Therefore, W( 6 matrx wll e y k { W 6 to 6, s calculated y takg the dfferetal wth respect y k { The sestvty dz 6 dz 6 s otaed y W = W ( 6. ( 6. z ( 6 ( 6 To calculate the margal effect o total system cost due to a small chage 6, we ca multply the porto of dz dp correspodg to power jectos, y the 6 6 correspodg margal costs or the multplers λ * to ota dp 6 dp * dtc * T dp T 6 = ( λ = [ λ λ λ λ ] =.7 6 dp 6 ($/h/pu 6 dp 6 (

4 Smlar calculatos for other les yeld dtc dtc dtc dtc dtc dtc 6 = [ ] ($/h/pu ( o cogesto the etre system. The results are also gve graphcally Fg.. The sestvty of the le -6 s foud to e hgher tha the others. It s the cogested le ad ts susceptace wll have the most effect o the total cost of the system. To see the effect o the total cost, a umercal study usg SQP has ee carred out for the susceptace rage etwee 0 ad pu. The results are gve Fg.. The fgure shows that there s a optmum susceptace terval where there s o cogesto the system ad the total cost s mmum. The susceptace values aove or elow ths terval may cause cogesto o the vestgated le or o the other les the system. Ths shows that stregtheg a le eyod a certa value may sometmes cause a adverse effect ad may crease the total cost for a specfc case. I Fg., cogesto appears at the le - whe the le -6 susceptace s etwee 0 ad. pu ad t appears at the le -6 whe the susceptace of -6 s etwee. ad pu. No cogesto exsts for the susceptace terval etwee. ad. pu ad, thus the total cost s mmum. Fg.. The effect o the total cost of alterg the susceptaces of le -6 ad le -. The cogesto regos ad the cogested les are show Fg. whe oth susceptaces of the le -6 ad the le - are chaged etwee 0 ad pu. The values of ad 6 have to e the rego show as "o cogesto" for a mmum cost. Outsde of ths rego, total cost wll always e hgher. Fg.. The effect o total cost of alterg the susceptace of le -6. Fg. shows that whe the susceptace of the le -6 chages, there s cogesto o the le -. Therefore, the susceptace of oth les are vared etwee 0 ad pu to see the total cost chage the example system. Whe there s o cogesto ad all the usses have the same prces, the total cost s mmum. Whe the susceptace value of the le - ad the le -6 s 0 pu., the supply-demad alace ca ot e satsfed ad there s o feasle soluto. The total cost s mmum at susceptace values etwee. ad. pu for the le - 6 ad etwee. ad pu. for the le -. If the le susceptaces are chose etwee these values, there s Fg.. The cogesto oudares ad the cogested les. Whe the le capactes are kept costat ad oly le susceptaces are chaged, cogestos may ot e elmated. The reaso for that s, as the susceptace value creases, power flow also creases. But, whe the power flow o the le reaches the le capacty, the crease o le susceptace wll ot alter the flow o that le aymore ecause the le s cogested. Istead, sce voltage agles at usses chage as the susceptace varato, the power flow o the other les wll e modfed ad the cogesto may appear o some other trasmsso les.

5 Susceptace ad le lmt are ot depedet from each other geeral. Icreasg the susceptace wll also lead to a crease the capacty of the le. Therefore, ths part, the effect o total cost of creasg oth the capacty ad the magtude of the susceptace of the le -6 ad the le - the same rato s vestgated ad the result s show Fg.. As t ca e see from Fg., the cogested rego ecame smaller ecause of the crease of oth le capacty ad le susceptace. Fg.. The effect o total cost of creasg oth the capacty ad the magtude of the susceptace of the le -6 ad the le -. I Fg., the cogested les ad regos are show detal whe oth the le capacty ad the magtude of the susceptace of the le -6 ad the le - are altered. I ths case, "o cogesto" rego s ca e see much etter ad t s qute wde. Fg.. The cogesto oudares ad the cogested les whe the ratos of the le capacty ad the magtude of the susceptace of the le -6 ad the le - are chaged. Cocluso I ths paper, a sestvty aalyss ad a umercal study have ee carred out to see the effect of varatos trasmsso le parameters such as le susceptaces ad le lmts, whch wll e mportat to e cosdered y the plag egeers. The result of the study shows that the sestvty of the total cost to the cogested le s foud to e hgher tha the les wth o cogestos. There may e a optmum susceptace rage whch aove ad elow values wll crease the total cost whe oly the susceptace s vared ad the le lmt s kept costat. Optmum susceptace may e mportat whe the le parameters are chaged dyamcally y usg FACTS devces wdely the future. The operato of the etwork for relevg cogestos may requre trackg these optmal parameter rages whe system state chages tme. Because the susceptace ad the le lmt are depedet to each other geeral, creasg oth the le susceptace ad the le lmt wll elmate cogesto etter. Therefore, cogesto maagemet for log-term requres a careful study of cost sestvty to the le parameters. These studes wll gude plaers to decde whch les must e stregtheed prmarly to elmate log-term cogesto effcetly. Refereces: [] Y. T. Yoo, S. G. Rakar, M. D. Ilc, Cogesto Maagemet for Large Electrc Power Systems, Eergy Laoratory Pulcato, Massachusetts Isttute of Techology, 000. [] J. Yu, Ercot Zoal Cogesto Maagemet, IEEE Power Egeerg Socety Summer Meetg 00, Vol., - July 00, pp. 9-. [] F. L. Alvarado, Cogesto Maagemet a Ope Market, The Uversty of Wscos [] H. Sgh, S. Hao, A. Papalexopoulos, Trasmsso Cogesto Maagemet Compettve Electrcty Markets, IEEE Trasactos o Power Systems,Vol., No., May 998, pp [] H. Glavtsch, F. Alvarado, Maagemet of Multple Cogested Codtos Uudled Operato of a Power System, IEEE Trasactos o Power Systems,Vol., No., August 998, pp [6] R. S. Fag, A. K. Davd, Trasmsso Cogesto Maagemet a Electrcty Market, IEEE Trasactos o Power Systems,Vol., No., August 999, pp [7] P. R. Grk, G. A. Agelds, R. R. Kovacs, Trasmsso Access ad Prcg wth Multple Separate Eergy Forward Markets, IEEE Trasactos o Power Systems,Vol., No., August 999, pp

6 [8] A. Papalexopoulos, Power System Expaso Plag ad Prcg a Deregulated Evromet, IEEE Summer Power Meetg, 00, page 68. [9] S. Deladreue, F. Brouaye, P. Bastard, L. Pelgry, Usg Two Multvarate Methods for Le Cogesto Study Trasmsso Systems Uder Ucertaty, IEEE Tras. o Power Systems, Vol.8, No., Fe. 00, pp. -8. [0] T. De la Torre, J. W. Feltes, T. G. Sa Roma, H. M. Merrll, Deregulato, Prvatzato, ad Competto: Trasmsso Plag uder Ucertaty, IEEE Tras. o Power Systems, Vol., No., May 999, pp [] J. C. Kalteach, J. Pescho, E. H. Gehrg, A Mathematcal Optmzato Techque for the Expaso of Electrc Power Trasmsso Systems, IEEE Tras. o Power Apparatus ad Systems, Vol. Pas-89, No., Ja. 970, pp. -9. [] R. Vllasaa, L. L. Garver, S. J. Salo, Trasmsso Network Plag Usg Lear Programmg, IEEE Tras. o Power Apparatus ad Systems, Vol. Pas-0, No., Fe.98, pp [] A. S. Jr., P. M. Fraça, A. Sad, A Optmzato Model for Log-Rage Trasmsso Expaso Plag, IEEE Tras. o Power Systems, Vol., No., Fe. 989, pp [] T. W. Gedra, O Trasmsso Cogesto ad Prcg, IEEE Tras. o Power Systems, Vol., No., Fe 999, pp. -8. [] P. R. Grk, D. Shrmohammad, S. Hao, C. L. Thomas, A. D. Lttle, Optmal Power Flow Sestvty Aalyss, IEEE Power Egeerg Socety Wter Meetg,990, pp [6] M. I. Alomoush, Dervato of UPFC DC Load Flow Model wth Examples of ts Use Restructured Power Systems, IEEE Tras. o power systems, Vol.8, No., Aug.00, pp [7] J. D. Weer, T. J. Overye, C. L. DeMarco, Modelg the Cosumer Beeft the Optmal Power Flow, Decso Support Systems, (999, pp Appedx P P P P 6 Fg. 6. Example system wth sx uses. Tale. Cost ad related parameters of each geerator Geerator Cost Fucto M Max us P C ( P = a + P + c a c Ge. Ge.