Simulation of Tie Lines in Interconnected Power Systems Akhilesh A. Nimje 1, Rajendra M. Bhome 2, Chinmoy Kumar Panigrahi 3
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1 nernionl Journl of pplicion or nnovion in Engineering & Mngemen (JEM) We Sie: Emil: SSN 9-8 Specil ssue for Nionl Conference On Recen dvnces in Technology nd Mngemen for negred Growh (RTMG ) Simulion of Tie Lines in nerconneced Power Sysems khilesh. Nimje Rjendr M. home Chinmoy Kumr Pnigrhi ssocie Professor Deprmen of Elecricl Engineering Guru Nnk nsiue of Engineering & Technology nimjekhilesh9@gmil.com Hed Deprmen of Elecricl Engineering Guru Nnk nsiue of Engineering & Technology rnshome@gmil.com Den UG & Reserch KT Universiy huneswr pnigrhichinmoy@yhoo.co.in STRCT Modern dy rdiion is o inerconnec sysems opered y differen power compnies hrough ie lines nd his increses he reliiliy of elecric energy supply. is herefore imporn o inroduce he conceps for modeling inerconneced neworks for ddiion or removl of he ie lines for coningency nlysis. This pper vlides he modeling of he power neworks inerconneced hrough he ie line. piecewise mehod of inerconnecion hs een presened. The mehod is sed on he sic ssumpion h ech nework is simuled y liner model for is nlysis y he individul opering uhoriy. Keywords: simulion incidence mrix snd lone ie lines ec.. NTRODUCTON Mos if no ll of he world s elecric power supply sysems re widely inerconneced involving he connecions inside uiliies own erriories which exend o iner-uiliy inerconnecions nd hen o iner-regionl nd inernionl connecions. This is done for economic resons o reduce he cos of elecriciy nd o improve reliiliy of power supply []. The purpose of he rnsmission nework is o pool power plns nd lod ceners in order o minimize he ol power generion cpciy nd fuel cos. These inerconnecions enle king dvnge of diversiy of lods vililiy of sources nd fuel price in order o supply elecriciy o he lods minimum cos wih required reliiliy. n generl if he power delivery sysem ws mde up of rdil lines from he individul locl generors wihou eing pr of grid sysem mny more generion resources would e needed o serve he lod wih he sme reliiliy nd he cos of elecriciy would e much higher. Less rnsmission cpiliy mens more generion resources would e required regrdless of wheher he sysem is mde up of lrge or smll power plns. n fc smll disriued generion ecome more economiclly vile if here is ckone of rnsmission grid []. One cn-no e relly sure ou wh is opimum lnce is eween generion nd rnsmission unless he sysem plnners use dvnced mehods of nlysis which inegre rnsmission plnning ino n inegred sed rnsmission/ generion plnning scenrio. Simulion Mehod Figure shows four us power sysem inerconneced hrough wo ie lines of impednces & wih noher hree us power nework. oh he power sysems re independen excep for he inerconnecions nd re erhed herey providing common reference poin. niilly i is ssumed h oh he sysems opere in snd lone mode nd use he us of heir own neworks for nlyzing heir sysems. These resuls cn e ler modified y ech sysem o ke dvnge of he inerconnecions. eween wo neworks. my e noed h uses nd of he sysem re conneced o uses nd of sysem. The curren injecions nd volge ech us shown in figure re ssumed known nd represen he neworks in he snd-lone mode. Mhemiclly he relionship eween he us volges nd injeced currens wih he ie lines open my e wrien s [-]: Orgnized y: GN Ngpur ndi
2 nernionl Journl of pplicion or nnovion in Engineering & Mngemen (JEM) We Sie: Emil: SSN 9-8 Specil ssue for Nionl Conference On Recen dvnces in Technology nd Mngemen for negred Growh (RTMG ) us us () -y y y -y -y -y -y -y -y Power Sysem Figure.Two Power Sysem Neworks Conneced Through Tie Lines where us is he x us impednce mrix of sysem. Similrly us is he x us impednce mrix of sysem. The sk is o deermine he new injeced us currens nd he resuling chnged us volges in he wo power sysems when hey re inerconneced vi wo ie lines. ssume h he impednces of he wo ie lines conneced eween uses - nd - re nd respecively while he currens flowing hrough hem re nd respecively. ssume ll he chnged volges re represened y nd in sysem nd y nd in Power Sysem power sysem due o he injeced currens nd. The effec of he ie line currens cn e simuled y ering he inerconneced nework shown in figure ino wo pieces he ie lines nd using equion. ii pi ij pj ji qi jj qj pp ip pq iq qp jp qq jq () Orgnized y: GN Ngpur ndi
3 nernionl Journl of pplicion or nnovion in Engineering & Mngemen (JEM) We Sie: Emil: SSN 9-8 Specil ssue for Nionl Conference On Recen dvnces in Technology nd Mngemen for negred Growh (RTMG ) Figure shows he wo equivlen power sysems long wih he injeced currens. - - Power Sysem Power Sysem Figure. Equivlen sysem neworks long wih he injeced currens nd The impednce mrix cn e compued y susiuing i = j = p = nd q = in equion. Thus () For he individul sysem he us volges nd re unknown. Similrly for he sysem he us volges nd re lso known. y using following equion he ie line currens re compued. i p j q () () From he ove equion he Thevenin s equivlen circuis for he power sysem nd cn e perceived direcly. Figure shows he Thevenin s equivlen circuis for he wo power sysems. The phs rced y he ie line currens nd hrough he reference us is lso shown. The ie line o us incidence mrix is given y []: Orgnized y: GN Ngpur ndi
4 nernionl Journl of pplicion or nnovion in Engineering & Mngemen (JEM) We Sie: Emil: SSN 9-8 Specil ssue for Nionl Conference On Recen dvnces in Technology nd Mngemen for negred Growh (RTMG ) my e oserved h mrix shows he incidence of ie lines on he uses of sysem nd = = Figure. Thevenin s equivlen circuis of he inerconneced sysems showing he phs of he ie line currens nd hrough he reference us ssume h due o injeced ie line currens nd he chnged us volges in sysem re designed y nd re similrly he new us volges in sysem re represened y. y using : us Or The new us volges re compued s follows: us us us () (8) nd lernively he piece-wise mehod my lso e pplied o oin he new sysem volges s follows: us (9) us () Orgnized y: GN Ngpur ndi
5 nernionl Journl of pplicion or nnovion in Engineering & Mngemen (JEM) We Sie: Emil: SSN 9-8 Specil ssue for Nionl Conference On Recen dvnces in Technology nd Mngemen for negred Growh (RTMG ) n compuing he new us volges when he wo neworks re inerconneced hrough ie lines he mjor sk is he formion of loop impednce mrix. The compuion of he inverse of he loop impednce mrix however is simple since is order is dependen on he numer of ie lines nd is smll. Formion of Loop mpednce Mrix Mhemiclly he loop impednce mrix my e formed y using he piecewise mehod nd using he following equion. Equion shows h he loop impednce mrix is mde of he ie-line impednces nd he respecive su-mrices from he us impednce mrices mrices of ineres would e ii pi ij pj from ji us qi us nd jj qj nd ip pp us. Hence for he inerconneced nework shown in figure he su iq pq The rnch o us incidence mrix showing he incidence of he ie lines on he oundry uses of sysem is given y from jp qp jq us qq () Similrly from sysem The loop incidence mrix herefore is compued s. Orgnized y: GN Ngpur ndi
6 nernionl Journl of pplicion or nnovion in Engineering & Mngemen (JEM) We Sie: Emil: SSN 9-8 Specil ssue for Nionl Conference On Recen dvnces in Technology nd Mngemen for negred Growh (RTMG ) n generlized form he su mrices removed from he originl us nd us sysem impednce mrices my e expressed s: i j k i j k ii ji ki ij jj kj ik jk kk Tken ou from us mrix of sysem p q r s pp qp rp sp pq qq rq sq pr qr rr sr ps qs rs ss Tken ou from us mrix of sysem n he wo su-mrices i j nd k re he oundry uses of sysem nd p q r nd s re he oundry uses of sysem. The wo sysems re inerconneced vi ie lines he oundry uses [8 9]. nverse of he ove sumrices leds o he us dmince mrices. These us dmince mrices symolize he sysem nd conneced vi ie lines he oundry uses. These equivlen dmince su mrixes re clled wrd equivlens. Conclusion The digonl elemens of he loop impednce mrix re he sum of he impednces in he loop or he ph rversed y he ie line currens sring from he reference us of he sysem o he reference us of he sysem. The off digonl elemens of re represened y hose impednces hrough which ie line currens re flowing nd re he cuse for producing new sysem volges when he sysems re inerconneced. Reference: [] H. H. Hpp The ner-re Mrix: Tie Flow Model for Power Pools EEE Trnscions PS 9 No. pp [] T. K. Ngsrkr M. S. Sukhij Power Sysem nlysis Oxford Universiy Press New Delhi. [] H. H. Hpp N. E. Nour nerconnecion Modelling of Power Sysems EEE Power Summer Meeing nheim Clif. July 9. [] L. K. Kirchmyer Economic Operions of Power Sysems John Wiley 99. [] Glenn W. Sgg nd hmed H El-id Compuer Mehods in Power Sysem nlysis nernionl Ediion Mc- Grw Hill ook Compny Singpore 988. [] Willim D. Sevenson Jr. Elemens of Power Sysem nlysis Fourh Ediion Mc-Grw Hill nernionl Ediion Singpore 98. [] J. Ngrh D. P. Kohri Modern Power Sysem nlysis Tenh Ediion T Mc-Grw Hill Pulishing Compny Limied New Delhi 99. [8] khilesh Nimje Modeling of Power Pools in Muli-re Nework The nsiuion of Engineers (ndi) Oriss Se Cenre Mrch 8. [9] khilesh Nimje Sik Misr Coningency nlysis of he Power Nework The nsiuion of Engineers (ndi) Oriss Se Cenre Sepemer 8. Orgnized y: GN Ngpur ndi
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