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
Mdium-th Lins: 80-40 (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
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 009 06 Assum: 0 50 0 6 900 MVA φ Not: Ths ar tpial valus for a 500 kv transmission lin b Lon-th lin modl: ur mpdan: r = 505 04j Propaation onstant: ( r )( ) = 5797 0 5 +06 0 j ris impdan: Z sris sinh( ) Z sris = 508 + 577j hunt admittan: Y shunt tanh (Not usd in m solution) = 449 0 6 +5 0 j hunt impdan: tanh = 45 7894j 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 = 7 +885j A L Zshunt L = 06 0 + 885j A V V R L Z sris V = 8 0 5 +659 0 5 j V V = 909 kv ar V = 4874 d Zshunt V Zshunt = 48 +94j A V = 5068 kv Zshunt L = 88 +705786j A = 096 A ar = 40097 d Transmission Lin nots p8
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 095 0 LL 50 kv LL r 007 076 Mdium-th lin modl: ur mpdan: Assum: 0 458 0 6 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 = 84 +87j 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 ) = 877 868i A (Nativ phas anl baus th pf is lain) Z sris = 94449 kv L V Z shunt Zshunt Zshunt Zshunt = 465j A L Zshunt L = 8768 4050j A V V R L Z sris V = 0 5 +704 0 4 j V V = kv ar V = 78 d Zshunt V Zshunt = 508 +5564j A Lin volta: V = 5566 kv Zshunt L = 877 +54j A = 88 A ar = 06 d Transmission Lin nots p9
E A 0 kv transmission lin has th followin th and lin paramtrs 50 r 006 05 Transmission Lin nots p0 0 4 0 6 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 = 0467 56544j = 97 / -504 o b) ind th load lin volta Lin Z sris = 656 +45557j kv V Z Lin = 588459 +58096j A = 609A / 504 o V Lin Z sris = 95 45557j 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