ECE 3600 Lumped-Parameter Transmission Line Models b

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Corey Hodges
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1 Lumpd-Paramtr Transmission Lin Modls b Lon-th Lins: ovr 40 (50 mils) (ovr 00 mi in som tts) Nd: Units lin th:, d stik to th sam unit th for all paramtrs mils ma also b usd Rsistan pr unit th: r Units ndutan pr unit th: l H H OR ndutiv ratan pr unit th: Capaitan pr unit th: OR Capaitan admittan pr unit th: Condutan to round: Common assumption: 0 simns ind: Units r ur impdan: = Propaation onstant: = ( r )( ) f our alulator dosn't hav hprboli tri funtions ris impdan Z sris = Z sinh( ) = Z OR hunt admittan: hunt impdan: = = tanh tanh = = ( ) ( ) or f our alulator an't handl ompl ponnts ( a b j ) = a b j = a /b (in radians) Modl: Z sris V Z shunt Transmission Lin nots p6

2 Mdium-th Lins: (50 to 50 mils) (00-00 mi in som tts) Nd: Units lin th:, d stik to th sam unit th for all paramtrs mils ma also b usd Rsistan pr unit th: r Units ndutan pr unit th: l H H OR ndutiv ratan pr unit th: Capaitan pr unit th: OR Capaitan admittan pr unit th: Condutan to round: Common assumption: 0 ind: ur mpdan: = Onl ndd if load is in trms of L Units ris Rsistan: R lin = r ris impdan Z sris = ( r ) hunt admittan: OR hunt impdan: = = or V Z sris Z shunt OR: r V hort-th Lins: lss than 80 (50 mi) (lss than 00 mi in som tts) V am as abov but without th apaitors r Transmission Lin nots p7

3 Transmission Lin Eampls E A 500 kv transmission lin is 500 lon and has th lin paramtrs shown blow Us th lon-th modl to find V and if th lin is loadd to 900 MVA and LL is 490 kv Assum th phas anl of is 0 o and assum load pf = 500 LL 490 kv LL r Assum: MVA φ Not: Ths ar tpial valus for a 500 kv transmission lin b Lon-th lin modl: ur mpdan: r = j Propaation onstant: ( r )( ) = j ris impdan: Z sris sinh( ) Z sris = j hunt admittan: Y shunt tanh (Not usd in m solution) = j hunt impdan: tanh = j olv iruit: = φ 0604 A (Not ompl in this as baus pf = othrwis inlud a phas anl alulatd from th pf or load othr information) Z sris = 890 kv V L Zshunt R L Z shunt Zshunt Zshunt = j A L Zshunt L = j A V V R L Z sris V = j V V = 909 kv ar V = 4874 d Zshunt V Zshunt = j A V = 5068 kv Zshunt L = j A = 096 A ar = d Transmission Lin nots p8

4 Transmission Lin nots p9 E A 45 kv transmission lin is 0 lon and has th lin paramtrs shown blow ind V and if th lin is loadd to 09 L with pf = 95% lain LL is 50 kv pf LL 50 kv LL r Mdium-th lin modl: ur mpdan: Assum: Assum th phas anl of is 0 o if is ivn Not: Ths ar tpial valus for a 45 kv transmission lin = 885 ris impdan: Z sris ( r ) Z sris = j Y hunt admittan: Y shunt shunt j = 49698j µ Not usd in m solution hunt impdan: Z = shunt 0 0 j iur out L: L 09 L L = 90 MVA Atual: φ ( 09 L loadin) olv iruit: φ j R aos( pf ) = i A (Nativ phas anl baus th pf is lain) Z sris = kv L V Z shunt Zshunt Zshunt Zshunt = 465j A L Zshunt L = j A V V R L Z sris V = j V V = kv ar V = 78 d Zshunt V Zshunt = j A Lin volta: V = 5566 kv Zshunt L = j A = 88 A ar = 06 d Transmission Lin nots p9

5 E A 0 kv transmission lin has th followin th and lin paramtrs 50 r Transmission Lin nots p Mdium-th lin modl: ris impdan: Z sris ( r ) Z sris = 9 +75j Y hunt admittan: Y shunt shunt j = 0j m hunt impdan: a) Th load is 50 with a powr fator of 087, ladin ind th lin urrnt, Lin = j k Z R sris 0 kv V ( 9 75 j ) Z L 50 in shunt 5 pf 087 V = 79 kv jk 0 m Z j L aos( pf ) Assum th phas anl of V is 0 o Zshunt if V is ivn = 75 6j = 50 / 954 o Z Z sris Lin Z = j = 97 / -504 o b) ind th load lin volta Lin Z sris = j kv V Z Lin = j A = 609A / 504 o V Lin Z sris = j kv = 466kV / -8 o Rivin lin volta = = 59 kv Noti that is bir than V, this an happn whn th rivin-nd powr fator is ladin ) What is th "powr anl" (δ)? δ = ar = 804 d d) How muh powr is dlivrd to th load? P L = V R pf = 44 MW Powr stimat for th sam and V sin( 8 d) V, but nltin th lin rsistan: ~ = 40 MW Z sris ) Eprss this loadin in trms of L ur mpdan: = 56 = 44 L load Transmission Lin nots p0

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

2/12/2013. Overview. 12-Power Transmission Text: Conservation of Complex Power. Introduction. Power Transmission-Short Line //03 Ovrviw -owr Transmission Txt: 4.6-4.0 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