2/12/2013. Overview. 12-Power Transmission Text: Conservation of Complex Power. Introduction. Power Transmission-Short Line

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1 //03 Ovrviw -owr Transmission Txt: ECEGR 45 owr ystms Consrvation of Complx owr hort in owr Transmission owr Transmission isualization Radial in Mdium and ong in owr Transmission oltag Collaps urg Impdanc oading r. Hnry oui r. Hnry oui Introduction W want to dtrmin th complx powr (or, ) flowing out of gnrators and through transmission lins Most utility-scal powr plants fatur synchronous gnrators controlld by xcitr, which influncs d (powr angl) controlld by prim movr, which influncs Consrvation of Complx owr Complx powr (and, ) ar consrvd ingl lin xampl + = in ystm xampl A AB in Complx powr consumd by ara B: AB + G + G + G3 G G B G3 r. Hnry oui 3 r. Hnry oui 4 owr Transmission owr Transmission-hort in c n a b oad oad n a c b I j j j I I pr-phas rprsntation Gn. short lin Gn. modl j j j by symmtry r. Hnry oui 5 r. Hnry oui 6

2 //03 owr Transmission-hort in Magnituds of and ar controlld by xcitrs of th gnrators and ar fairly constant can b incrasd by incrasing th mchanical powr of Gn. and/or by dcrasing th mchanical powr of Gn. (rcall powr angl in ECEGR 450) j j j j j j Incrasing th rciving nd voltag ( ) incrass th complx powr flowing from gnrator ( ) Tru Fals I I r. Hnry oui 7 r. Hnry oui 8 Incrasing th rciving nd voltag ( ) incrass th complx powr flowing from gnrator ( ) Tru Fals j j j I I whr C owr Transmission isualization j C j B j j j C B j j indpndnt of C B j j j j r. Hnry oui 9 r. Hnry oui 0 owr Transmission-hort in owr Transmission-hort in If is varid, and swp out circls in complx plan radius= snding-nd C snding-nd circl C B rciving-nd circl j C j B - cntrd at C radius= B cntrd at C radius= B C rciving-nd r. Hnry oui r. Hnry oui

3 //03 owr Transmission-hort in owr Transmission-hort in Obsrvations circls do not intrsct if voltag magnituds ar not qual as incrass from 0, activ powr snt and rcivd incrass thr is a maximum amount of ral powr snt 80 and rcivd - osslss lin (R = 0) 0 = - circls li on -axis Most transmission lins hav small rsistanc compard to inductanc r. Hnry oui 3 r. Hnry oui 4 owr Transmission-hort in Assum losslss lin (R = 0) sin sin cos cos ractanc of th lin maximum powr transfr: W will driv ths xprssions latr owr Transmission-hort in Undr normal oprating conditions: Approximating sin cos in radians Rsults in sin is snsitiv to 0 is snsitiv to voltag magnitud r. Hnry oui 5 r. Hnry oui 6 osslss lin owr consumd by th load is = (0 + j0) MA Assum C is slctd to mak = 00,000 = Find th corrsponding ractiv powr injctd by th capacitor, C = j500 C load MW losslss lin assumption sin 0 MW 6 0 x 0 sin 0 MW cos C cos 30 x 0.68 MAR.68 MAR r. Hnry oui 7 r. Hnry oui 8 3

4 //03 Ractiv powr compnsation is rmovd = 00,000 Can th load of 0 MW b supplid? What is for this oprating point? = j500 load C B j C 0.00 j B 00 j 0.00 (0M,0) 00 rciving nd circl r. Hnry oui 9 r. Hnry oui 0 Radial in By ythagoran thorm: x0 00 x 0.00 x 00 x x ,700 (vry low compard to ) th capacitor bank gratly improvd th voltag at bus can b calculatd as 45 dgrs (0M,0) osslss radial lin W want to find th and rlationship t f = - i I j I cos f cos I cosf jsinf j I sinf j sinf f tanf =j I r. Hnry oui r. Hnry oui sin cos sin cos cos Radial in prvious rsult using cos sin cos cos Radial in substituting for th cosin trm using tanf 0 arranging for th quadratic quation 4 r. Hnry oui 3 r. Hnry oui 4 4

5 //03 Radial in oltag Collaps solutions to quad. qn 4 F = 0.97 lagging F =.0 F = 0.97 lading Two solutions! Two rciving-nd voltags that supply. owr systm is opratd at th highr voltag solution. Is thr a limit to th powr that can b dlivrd? voltag collaps points r. Hnry oui 5 r. Hnry oui 6 oltag Collaps oltag collaps is charactrizd by a prcipitous dclin in voltag at th rciving nd bus as mor powr is dmandd owr systms should b dsignd and opratd to avoid this condition oltag collaps is a function of svral paramtrs, including: snding and rciving nd voltag magnituds powr factor angl of th load lin impdanc A dc xampl can b usd xplain th mchanism of collaps R =.5 W + + R = 5 W = powr to loads r. Hnry oui 7 r. Hnry oui 8 owr Transmission-Mdium and ong ins W now must account for complx powr through th shunts owr Transmission-Mdium and ong ins Rcall from short lins (snding nd) j j j Now includ th snding nd shunt j j j ong in r. Hnry oui 9 r. Hnry oui 30 5

6 () (AR) //03 owr Transmission-Mdium and ong ins owr Transmission-Mdium and ong ins Rciving nd short lin j j j Now includ th shunts j j j Not that for long lins, us and For mdium lins, us and Influnc of and is usually limitd How dos this affct th snding and rciving nd circls? r. Hnry oui 3 r. Hnry oui 3 urg Impdanc oading (I) urg Impdanc oading (I) A losslss lin trminatd in its charactristic impdanc ( c ) is said to b urg Impdanc oadd (I) Undr ths conditions: = I = I Th transmittd powr is I = / c For losslss lins, c is ral < C < 0 Transmission lin absorbs ractiv powr (inductiv) = C = 0 > C >0 Transmission lin supplis ractiv powr (capacitiv) x (Ohms) y = j z = j0.789 c = 383 W ngth = 000 km - = 38kv r. Hnry oui 33 r. Hnry oui 34 urg Impdanc oading (I) < C > nding nd voltag highr than rciving = C = > C < nding nd voltag lss than rciving! Frranti ffct.5 x dcrasing load (Ohms) What tim of day do you xpct th voltag at th nd of long transmission lins to b th highst? r. Hnry oui 35 r. Hnry oui 36 6

7 //03 urg Impdanc oading I_Movi.mat ( = C ) I_Movi_.mat ( = 0.5 C ) I_Movi_3.mat ( = 00 C ) urg Impdanc oading (I) xampl 4., 4.3 for mor dtails r. Hnry oui 37 r. Hnry oui 38 tability imits tability imits Incrasing incrass th powr flow across th lin For losslss lins, maximum powr transmission occurs whn = 90 o sin - It is dsird to limit for stability rasons Considr a losslss long transmission lin Transmittd powr is j With losslss assumptions tanh tanh c sinh jcsin jc Ral powr transmittd: R R j r. Hnry oui 39 r. Hnry oui 40 tability imits ia Eulr s Idntity and assuming voltag magnitud at ach nd of th lin ar qual: sin j R R c sin From th I dfinition: sin I sin imiting, limits maximum powr transfrrd For a fixd, as lngth incrass, maximum powr transfr dcrass For vry long lins with x = p/, I cannot b xcd / I stability limit st at = 45 o imits lin lngth (mi) typical thrmal limit r. Hnry oui 4 r. Hnry oui 4 7

8 //03 ummary (hort in) ummary (hort osslss in) j j j j j j sin cos I I I I pr-phas rprsntation pr-phas rprsntation r. Hnry oui 43 r. Hnry oui 44 ummary (hort in) iscussd powr circls for powr transmission analysis j j j j j osslss lins: sin j cos ummary (Mdium in) * j j j * j j j (if a short lin modl is usd) r. Hnry oui 45 r. Hnry oui 46 ummary (ong in) j j j j j j ummary iscussd radial lins two oprating points: on is stabl, on unstabl voltag collaps: limits th amount of powr that can b supplid to a load tability limits tnd to limit powr transfr for long lins r. Hnry oui 47 r. Hnry oui 48 8