ENERGETIS AND ELETRIAL ENGINEERING P. D. Lezhnuk, Dc. Sc. (Eng.), Prof.; M. M. heremsn, and. Sc. (Eng.), Prof.; V. V. herkashna, and. Sc. (Eng.), Ass. Prof. UNIFIATION OF OVERHEAD LINES IN THE ONDITIONS OF THE MARKET OF TWO-PARTY AGREEMENTS AND BALANING ELETRI ENERGY MARKET The paper consders one of he rends n he developmen of elecrc ransmsson overhead lnes n he condons of he marke of wo-pary agreemens and balancng elecrc energy marke: opmzaon of he paramerc seres of wre cross-secons. Keywords: elecrc ransmsson overhead lnes, wre cross-secons, crera mehod. Inroducon Developmen of compeve relaons n he elecrc power ndusry of Ukrane s conneced wh mplemenaon of he model of wo-pary agreemen marke and balancng elecrc energy marke (TABM), whch expands he possbles of he elecrc energy supplers, users and producers. TABM marke model consss of he segmens ha provde realzaon of compeve relaons beween s parcpans. TABM condons requre new scenfc undersandng, frs of all, for creaon of a new scenfc plaform for he developmen of elecrc neworks (EN) [1, ]. Elaboraon of he mehods for searchng opmal soluons ha would subsanae a raonal srucure and form paramerc seres of he elecrc nework equpmen s a perspecve change n hs drecon. Problem saemen The foundaon of he raonal srucure of overhead lnes (OL) s sandardzaon and unfcaon level of he paramerc seres of wre cross-secons ha reflecs he possbly of usng sandard desgn soluons, sandard manufacurng processes, sandard equpmen for OL manufacure and repar. OL desgn and consrucon pracce leads o he expanded applcaon of unform (sandardzed) OL componens. Unfcaon effcency s manfesed mos srongly n he sysem approach o he organzaon of OL desgn and consrucon. Evdenly, such approach ensures: - a shorened me for OL developmen and consrucon hrough he use of a lmed number of poles, foundaons, wre brands, nsulaons and fngs; - qualave relably conrol durng her manufacure; - reducon of personnel errors durng OL consrucon and operaon; - reducon of he servce sock of OL separae componens; - lowerng of OL consrucon cos due o compeon beween separae OL manufacurers [3]. Thus, n order o elaborae recommendaons on he creaon of scenfc plaform for OL developmen, s necessary o fnd he possbles o reduce separae sandard szes of OL componens and, prmarly, of OL poles and wres. The ask of reducng sandard szes of poles has been, o a ceran degree, solved and OL wre cross-secons have been normalzed accordng o he Elecrcal nsallaon rules of Ukrane [4]. However, here s no feasbly sudy on he choce of wre cross-secons, whch would be relevan n TABM condons. The paper ams a consderng one of he rends of OL developmen n TABM condons - opmzaon of he paramerc seres of wre cross-secons, formulaon of an opmaly creron for paramerc seres of wre cross-secons and proposng recommendaons on OL unfcaon. Науков прац ВНТУ, 013, 4 1
Analyss of he publcaons ENERGETIS AND ELETRIAL ENGINEERING As he analyss of nformaon sources has shown, opmzaon of he elecrc nework equpmen on he prncples of unfcaon, ncludng ha of paramerc seres of wres cross-secons, s of curren mporance for he world elecrc power engneerng. Frs works n hs drecon were carred ou n he eghes of he las cenury [5]. A presen sage he sraegy of he elecrc power engneerng developmen s based on unfcaon prncples. The complex power engneerng modernzaon program of Russa for he perod ll 030 s based on he prncples of unfcaon and sandardzaon, ncludng unfcaon of equpmen, echnologcal soluons and confguraon [3]. Ths approach has been mplemened n a number of far-abroad counres. I s based on reducng he number of manufacured wre brands. As a basc secon for dfferen volage classes, a sngle cross secon s used, whch, akng no accoun he scale growh facor, sasfy he cross-secon nomenclaure n erms of bandwdh. E.g., n Grea Bran for he lnes wh he volage of 13 75 400 KW wres wh cross-secon АС 175 mm, АС 400 mm are used. In Germany for he lnes of 110 0 400 KW one brand of seel-alumnum wre wh АС 560/50 mm cross-secon s used (for OL 0 400 KW wh wo wres per phase). In Ialy only hree wre cross-secons are recommended for wde applcaon: for OL 13 380 KW 18/1 mm, 65/43 mm, 50/66 mm. In zech Republc n neworks 110 KW and more hree wre brands are used: АС 40 mm, АС 450 mm, АС 670 mm. In France for he consrucon of OL wh he volage of 5 400 KW sandard wre cross-secon 570 mm s used 1 6. Basc research maerals Whle searchng for opmal soluons, whch subsanae a raonal srucure and form paramerc seres of elecrc equpmen, he work was performed and recommendaons were elaboraed on unfcaon of he wre cross-secon scale. I s based on he saemen ha OL has economc power nervals only f he resrcon, ensurng dsngushably of he separae varans accordng o he economc creron, s sasfed. ondons for he exsence of economc nervals are gven by: r r 1 1, K K 1 1, K K K K 1 1 r 1 r, (1) r r where r - acve ressance of he -h wre; K - nvesmens n he -h lne. rera (1) reflec only echncal sde and se he necessary condons for he exsence of economc power nervals. Snce OL s an objec of a echncal-economc characer, ceran resrcons reflecng economc relaons of he unfed objec are o be sasfed. Sasfyng he condons of dsngushably of wo elecrc ransmsson varans wh wres of dfferen crosssecons s consdered o be one of such requremens. Thus, f we assume he exsence of an economc nerval of he h cross-secon, he condon of equal economc effcency s o be observed: 1 1 1 1, () where dscoun coss of OL; - a permssble value ha defnes he zone of equal economc effcency. ondon () s no only he necessary, bu also a suffcen one for he h wre. Is non-fulflmen conradcs he condon of he exsence of an economc power nerval n erms of equal economc effcency for he h cross-secon (see he fgure 1). Науков прац ВНТУ, 013, 4
ENERGETIS AND ELETRIAL ENGINEERING (+1) / -1 +1 (-1) / Р / (-1) Р (+1) / Р Fg. 1. Economc power nervals for he wres of F, F +1, F -1 cross-secons I s known ha n he analyss of echncal-economc OL ndcaors n TABM condons one of he man crera of echncal-economc relaons s mnmal dscoun cos [5]: ( х) mn, х Х. There does no exs a generally acceped concepon n he pracce of consrucon and mplemenaon of echncal-economc models. In each specfc case consrucon of a compuaonal model and he mehod of s soluon are closely nerrelaed. Moreover, n solvng he general opmaly problem s necessary o ake no accoun he characer of nal nformaon, relably of whch s somemes raher low. Ths leads o he uncerany of nal nformaon [5 7]. Proceedng from he saed above, compuaonal model of he dscoun coss n 1 km of OL could be presened as 1 β) 1 ( Е р)( а вf) ( I ρ F, (3) where 1 nvesmen componen of he echncal-economc model of OL (nvesmens); echncal componen of he echncal-economc model of OL (operaon coss); Е bank rae, %; р facor of allowances for deprecaon, repar and manenance of he lne; а consan componen of he cos of 1km OL ha depends on he ype of poles, OL desgn soluon, volage class, currency uns, (c.u.)/km; F wre cross-secon, mm ; І maxmal curren n he lne, А; ρ ressvy of he conducor maeral, Оm mm / km; τ he me of maxmal losses, h/ year; β un cos of elecrc energy losses, c.u./ (KW h). Invesmens n TABM condons nclude he cos of land n OL cos as well as loan paymens, deprecaon and ake no accoun nflaon. For dfferen volage classes 1, n a general form, could be presened as 1 Е Тs nom 100 Еnom 100 1 1 100 100 where Е nom a nomnal bank rae, %; α nflaon rae; Т s normave servce lfe, year; К cos of 1 km OL of he h volage class akng no accoun he cos of land, c. u./km [7]. Takng he above-menoned no accoun, a pon Р 1 he values of dscoun coss n OL made of wre wh he h cross-secon concde wh hose n OL made of wre wh he ( 1) crosssecon (see he fgure 1) and he followng expressons wll be vald: Науков прац ВНТУ, 013, 4 3 1 1 К (4)
1 1 The rao of expressons (5) s gven by: 1 1 We use expresson (6) n relaon (): or р р K 1r K r 1 л л K 1 1 ENERGETIS AND ELETRIAL ENGINEERING Науков прац ВНТУ, 013, 4 4 K r r r K r r r 1 1 1 K r 1 1 r Kr 1 r 1 r K r r r 1 K r K r r r 1 1 1 1 K r K r r r 1 1 1. (5) dem. (6) K r K r r r 1 1 1 (1 ). (8) K r K r r r 1 1 The obaned creron reflecs no only he echncal, bu also he economc bass for he consrucon of unfed OL. The above consderaons could be used for elaboraon of he resrcon mehods based on he exsng unfcaon. I should be noed ha observng he crera resuls n obanng he mos correc soluon. The condon for dsngushably of he wo OL varans, deermned by he boundares of equal economc effcency, depends, o a ceran exen, on he scale of wre cross-secons wh whch hose lnes are made. On he oher hand, f he resrcons on equal effcency condons are no aken no accoun, wo varans formed by neghborng wre cross-secons wll be equally effcen snce he scale growh facor n hs case s nadequaely low. Feasbly of such a soluon depends on he mehod used, mahemacal apparaus as well as on he characer and accuracy of he objec descrpon. In he condons of he absence of full nal nformaon for he analyss of elecrc nework objecs s necessary o use generalzaon mehods based on he heory of smlary, mahemacal programmng and smulaon. One of such mehods s a crera mehod wh he elaboraed algorhms ha enable quanave descrpon of opmal echncal and economc relaons of he objec n boh cases: avalably and unavalably of full nal nformaon. The gven mehod was used as a research ool ha makes possble o subsanae paramerc seres of wre cross-secons. Besdes, a mahemacal model of OL, applcable n TABM condons, was used. I s dsngushed manly by he dfference n analycal relaon beween he nvesmens n OL and wre cross-secon. Formulaon of he problem s suffcenly accurae, physcal meanng of he objec beng preserved [5]. Thus, mahemacal model of he dscoun coss n OL can be presened as: Тs А 11 А 1 1 1 1 К110 ( I ρ F 1 β) Еnom 100 where А. 100 Wh a ceran error, (9) could be presened as a sngle general model: (7) ; (9) 0,5 1 А1 F А F. (10) The crera mehod for analyzng he generalzed echncal-economc model (10) has shown ha
a he pon of mnmum ENERGETIS AND ELETRIAL ENGINEERING 1 A 1 A 0, (11) 1 where π 1 and π smlary crera, π 1 =4/5, π =1/5, ha can be obaned from he sysemac procedures of he crera mehod. The values of he parameers of funcon (10), expeden n erms of economc effcency, are deermned from he condon F A 1 0 A 1 0,8. (1) Le us perform he followng ransformaons: nroducon of a generalzed consan А =А /р and wrng (11) n a relave form provded ha basc value of he generalzed consans concdes wh he real value of hese consans А,.e. А 1 = А = 1 Then 1 ( А1 ) ( А P ) (13) or Smlarly, for (1) 0,4 P. (14) A P A 1 0,8 F (15) or From (14) and (16) could be wren F P 1,6. (16) Науков прац ВНТУ, 013, 4 5 4 F. (17) In a general case formaon of he permssble soluon exsence regon depends on he nal nformaon error δ, he accuracy of whch wll be deermned by he value of ε. The resuls of such esmaon are as follows: δ, % ±1 ± ±3 ±4 ±5 ±6 ±7 ±8 ±9 ±10 F 1.14 1.8 1.45 1.56 1.66 1.77 1.89.05.0.60. Thus, he error of operaonal characerscs plays an essenal role n he scale growh facor subsanaon. From pracce s known ha he accuracy of engneerng calculaons s a leas 10%. Therefore, he mos approprae scale growh facor of wre secons n hs case should no be less han.5. The eases way o ge hs growh facor s o elmnae nermedae sandard values of he wre cross-secon scale. As EN form a complex dynamc sysem, he ssue of unfcaon of such neworks should, o a ceran exen, solve he problems of reconsrucon. The ssue of OL unfcaon has a sgnfcan nfluence on reconsrucon me ha ncludes he me for replacng he wres of a ceran crosssecons wh bgger ones n order o ncrease OL bandwdh and o mprove he elecrc energy qualy [5, 6]. Le us show ha reconsrucon me s conneced wh he wre cross-secon scale used for nework consrucon. The law of power varaon s known n a relave form:
where q s an average value of he load ncremen. Usng expressons (16) and (18), we can wre 0 ENERGETIS AND ELETRIAL ENGINEERING Р Р (1 q), (18) Р( 1 q) F Науков прац ВНТУ, 013, 4 6 0,65. (19) The obaned expresson shows he rae of he wre cross-secon change for a gven characer of he load. I should be noed ha f he wre cross-secon value F б, n he year when OL was consruced and pu no operaon s aken as a basc one and cross-secon of he wre a he perod of OL reconsrucon s aken as he followng cross-secon, he rao F F (0) F wll represen he cross-secon scale growh facor. Le us assume ha we have wo dfferen cross-secon scales characerzed by facors б F and 1 The load growh rae we assume o be equal boh n he frs and n he second case. Then, n accordance wh (0) and Relaons (1) and () could be wren n he form of F. 1 0,65 Р( 1 q) F (1) 0,65 Р( 1 q) F. () ln F n F 1 1 dem. (3) In hs expresson me defnes he nerval from he begnnng of operaon lfe o he frs reconsrucon. The obaned expresson does no depend on he load growh rae and s deermned only by he chosen scale of wre cross-secons. Besdes, from () and (3) we can deermne he reconsrucon me ha depends on OL bandwdh and gven load growh rae q. We assume ha P 0 1as s relaed o he begnnng of OL operaon. Then 0 ln F 0,65. (4) ln(1 q) As a resul of calculaon of he reconsrucon erms for wre cross-secon scales wh he facor F =, an average value of me rao was deermned o be equal o. Thus, as a bass for OL unfcaon, s necessary o use a sandardzed cross-secon scale ha makes possble o mnmze he number of reconsrucons. The obaned characerscs of OL cross-secon scale unfcaon gve scenfc subsanaon for he bass of unfcaon procedure. In hs case from several OL opons we should choose he one ha wll sasfy he condon of economc feasbly of he seleced objec wh regard o relably, mananably, addonal nvesmens n he reconsrucon, ec. The ask wll be smplfed f he analyss of varous opons s performed purposefully. For hs s necessary o choose a bass. E. g., OL cross-secon from he unfed scale, whch s he mos common among he exsng OL, could be used as a basc one.
ENERGETIS AND ELETRIAL ENGINEERING The ask of formng he unfcaon bass s confned o he nvesgaon of OL wre cross secons dependng on clmac and load condons. A number of desgn nsuons conduced research n order o oban relave frequences of OL loads on he bass of sascal processng. The obaned resuls have shown ha he growh facor of he wre cross-secon scale, ha s close o, s he mos accepable one [5]. Ths nformaon aken as a bass, wre cross-secon values for dfferen volage classes were obaned. Le us llusrae he above by he example of he cross-secon scale formaon for OL 110 KW. I s known ha wde-scale elecrfcaon was carred ou n he 70s of he las cenury and he selecon crera were somewha dfferen. Ths facor was aken no consderaon when basc varan for he research was formed. The cross-secon scale s bul assumng ha К n and a sngle cross-secon s used for a gven volage class. The able presens possble opmal soluons for hs saemen of he problem akng no accoun redsrbuon of OL lenghs. Varans of dsrbuon of OL lenghs for OL cross-secons of 70mm, 10mm, 40mm and dscoun coss n accordance wh he varans Table of he research Dsrbuon of OL lenghs n accordance wh cross-secons, %,% varan 70 mm 10 mm 40 mm 1 (basc) 38 35 7 100 38 1 41 99,5 3 38 0 6 99,9 4 4 0 76 99,6 5 9 0 91 99,9 6 0 0 100 100 7 4 49 7 98,1 8 9 64 7 97,0 9 0 73 7 96,6 10 4 35 41 97,6 11 9 9 6 97, 1 0 4 76 98,0 13 0 9 91 99,8 14 0 38 6 96,8 15 0 58 4 96,1 16 9 49 4 96,5 17 4 14 6 98,3 18 9 14 77 98,5 From he able s evden ha all he opons are equally effcen. A he same me, varan 6 s he opmal one n erms of reconsrucon, ncreasng of OL bandwdh, reducon of elecrc energy losses and mprovemen of OL relably [4]. onclusons The paper consders one of OL developmen rends n TABM condons: opmzaon of paramerc seres of wre cross-secons. An opmaly creron of he paramerc seres of wre cross-secons s elaboraed and recommendaons on OL unfcaon are proposed. Ths wll make possble o mnmze he number of reconsrucons, o ncrease OL bandwdh, o reduce elecrc energy losses and o mprove relably of EN. REFERENES 1. Закон України про засади функцонування ринку електричної енергї України [Електронний ресурс // Режим доступу : ]hp://zakon4.rada.gov.ua/laws/show/663-18.. Кириленко О. В. Балансуючий ринок електроенергї його математична модель / О. В. Кириленко, І. В. Блнов, Є. В Парус // Технчна електродинамка. 011.. С. 36 43. 3. Энергетическая стратегия России на период до 030 г. [Электронный ресурс] // Режим доступа: hp://mnenergo.gov.ru/aboumnen/energosraegy/. Науков прац ВНТУ, 013, 4 7
ENERGETIS AND ELETRIAL ENGINEERING 4. Правила устройства электроустановок. // Х.: Изд-во «Форт», 009. 704 с. 5. Будзко И. А. Унификация воздушных линий электропередечи / И. А. Будзко, Ю. Н. Астахов, Н. М. Черемисин // Электричество. 198.. С. 1 11. 6. Файбисович Д. Л. Предложения по унификации сечений проводов воздушных линий напряжением 110 750 кв / Д. Л. Файбисович // Энергетик. 003. 3. С. 1. 7. Выбор приоритетного направления в проектировании воздушных линий электропередачи в условиях рыночных отношений / Н. М. Черемисин, В. В. Черкашина // Сборник трудов VI Всероссийской научнотехнической конференции с международным участием Энергетика: управление, качество и эффективность использования энергоресурсов. Россия. Благовещенск: АГУ 011. Т.1. С. 105 110. Lezhnuk Pero Dc. Sc. (Eng.), Professor, Head of he har of Elecrc Saons and Sysems. Vnnysa Naonal Techncal Unversy. heremsn Mykola and. Sc.(Eng.), Professor, har of Energy Supply of Agrculure. Kharkv Naonal Techncal Unversy of Agrculure. herkashna Veronka and. Sc. (Eng.), Asss. Professor, har of Elecrc Energy Transmsson, cherk34@rambler.ru. Naonal Techncal Unversy «Kharkv Polyechnc Insue». Науков прац ВНТУ, 013, 4 8