World Journal of Engineering and Technology, 15, 3, 89-96 Published Online Ocober 15 in SciRes. hp://www.scirp.org/journal/wje hp://dx.doi.org/1.436/wje.15.33c14 Calculaion of he Two High Volage Transmission Line Conducors Minimum Disance Wenjie Huang 1, Jinglin Zhu 1, Zhihang Du 1, Zheng Zhang 1 Shanghai Elecric Power Design Insiue co., LTD, Shanghai, China Economic and Technology Research Insiue of Shanghai Elecric Power Company, Shanghai, China Email: huangwj@sepd.com.cn, 445173@qq.com Received 9 Augus 15; acceped 15 Ocober 15; published Ocober 15 Absrac In he design of high volage ransmission lines ineviably needed o change he arrangemen of wires, and he disance beween he wires direcly affeced by changing he arrangemen of he wires. The disance beween he wires is difficul o judge by experiences. Therefore, i is urgenly o develop a way o accuraely calculaing he minimum disance beween he wires when changing he arrangemen beween he wo wires, and deermine he minimum disance can mee he requiremens of sandards and regulaions or no. Through he hinking, based on he balance equaion and he space curve wire calculus mehod, a more accurae mehod of calculaing he wo wires in a variey of condiions he minimum spacing was derivaed, and he sensiiviy of he minimum disance was analysized based on he mehod. Keywords Overhead Transmission Lines, Disance of Two Lines, Equaion of Wire Balance, Wire Sag 1. Inroducion When he high volage ransmission lines are designed, i is ineviably needed o inersec across, change he arrangemen modes of wires, and ec., for example, 5 kv line spans he kv line, ge-in ganry span of overhead lines, and ec. When he above siuaions happen, i is ineviably needed o check he minimum disance beween wo wires so as o deermine wheher i saisfies he requiremen of regulaion [1]. However, he difficulies of validaion lie in (1) he inersecion siuaion, which needed o be checked, is ofen very complex, and he wo wires o be checked face he siuaions such as differen ypes, differen safey coefficiens, and so on. () Boh he esablishmen and soluion of he space curve equaion are difficul, and relying on a simple arificial modeling calculaion canno obain he exac soluion. (3) The spacings of wires are differen due o he differen sags under differen working condiions, so i is difficul o judge he working condiion for he minimum spacing, and ec. There are much calculaing sudy achievemen concerning he phase spacing of wires in our counry. In he Reference [], he hree-dimensional CAD is used o esablish he hree-dimensional model of phase spacing of lead-in span wire, and a kind of mehod o calculae he phase spacing of wires by using he inerac- How o cie his paper: Huang, W.J., Zhu, J.L., Du, Z.H. and Zhang, Z. (15) Calculaion of he Two High Volage Transmission Line Conducors Minimum Disance. World Journal of Engineering and Technology, 3, 89-96. hp://dx.doi.org/1.436/wje.15.33c14
ive hree-dimensional CAD according o he heory of oblique parabola and hree-dimensional lef conversion calculaion is proposed. Reference [3] sudied he compuing mehod of minimum phase spacing of wires under considering he windage and wihou considering he windage, and analyzed he calculaion examples of relevan projecs. According o he above difficulies and he curren saus, space curve equaion [4]-[6] of wires was precisely esablished and he minimum disance beween wo wires was calculaed by using he inegral-differenial mehod of space curve and Malab ool in consideraion of he sag of wires under differen working condiions based on he equaion of wire balance. Simulaneously, he accuracy of he calculaion mehod was analyzed, and he sensiiviy of minimum disance beween wo wires wih he change of ower heigh difference, he change of safey coefficien, he change of span, and so on was sysemaically calculaed by aking he energy-saving wire (aluminum alloy core aluminum sranded conducor) as an example.. Calculaion Mehod of Spaial Minimum Disance beween Two Wires.1. Esablishmen of Space Curve Equaion of Wires The emphasis of calculaing he minimum disance beween wo wires in space is o esablish he calculaion model of space curve of wires. Firs of all, he hree-dimensional recangular coordinae sysem is esablished by aking he ower cener as he original poin, he exension direcion of beam as X axis, upward exension direcion of ower as Z axis, and he exension line direcion of wire as Y axis, as shown in Figure 1. Figure 1. Case diagram of modeling calculaion. The space curve equaion was esablished by aking wire 1 as an example. I is assumed ha hanging poins coordinaes in he T 1 and T ower of he wire are (x 1, y 1, z 1 ) and (x, y, z ), respecively, and hen he space curve parameer equaion of wire 1 beween he wo suspension poins is as follows [5]. x = x1 + ( x x1) y = y1 + ( y y1) z = z1 + ( z z1) where is he spaial locaion parameers. l The wire sag was also considered, and he sag formula of inclined parabola of wire was f = γ according o reference [4], hen he sag of any poin in he space wire 8σ cos β is 9
γ ( l x') x' f = σ cos β where f is he wire sag wih he uni m. γ is he comprehensive relaive load of wire wih he uni N/mm m. l is he horizonal disance of wire beween wo hanging poins wih a uni m. x ' is he disance from any poin of wire o suspension poin (x 1, y 1, z 1 ) wih a uni m. β is he angle of elevaion difference wih a uni. Then he calculaion mehod of he above various parameers can be deermined according o he model. l = ( x x1) + ( y y1) x' = ( x x1) + ( y y1) = ( x + ( x x ) x ) + ( y + ( y y ) y ) = l L= (( x x1) + ( y y1) + (z z1) cos β = l / L 1 1 1 1 1 1 The calculaed simplified formula of he above parameers are inroduced ino he sag formula, hen ( ) γ Ll f = σ.. Correcion of Spaial Wire Equaion in Consideraion of Windage There appears a cerain windage for he wire under he acion of breeze, and is angle of windage is ϑ= arcan γ4 / γ 1, hen sin ϑ= γ4 / γ and cos ϑ= γ1 / γ can be obained. Afer he windage of wire, he change of sag in Z axis is z = f cosϑ, and he change of sag on he horizonal plane is xy = f sinϑ. I is assumed ha he sraigh line linking wih he suspension poins of wire and he X axis in XY plane consiues an angle α, and hen α = arcan y x y y y y y x x x x 1 1 1 1 1, sinα = =, cosα = = x 1 ( x x1) + ( y y1) l ( x x1) + ( y y1) l Due o he windage direcion of wire along X axis unfixed, when he direcions of windage are differen, he variable quaniy in X and Y axis of he line beween wo hanging poins caused by wire sag are shown in Table 1 in consideraion of synchronous windage. Hence, when he wire has he windage along posiive direcion of X axis, he space equaion of wire can be expressed as: γ Ly ( y1)( ) x = x1 + ( x x1) + σ γ Lx ( x1)( ) y y1 ( y y1) = + σ γ Ll( ) z = z1 + ( z z1) σ While he wire has he windage along negaive direcion of X axis, he space equaion of wire can be obained Table 1. Variaion in X and Y axis caused by sag under differen direcions of windage. Direcion of windage Variable quaniy Windage along posiive direcion of X axis Windage along negaive direcion of X axis Change along X axis Change along Y axis /m X /m Y γ Ly y σ ( )( ) 1 ( )( ) 1 γ Lx x σ γ Ly y σ ( )( ) 1 γ Ly y σ ( )( ) 1 91
by exchanging he plus-minus sign of above sag correcion formula..3. Elecrical Disance beween Two Wires in Space The parameer equaion of space wire has been obained in consideraion of he sag and windage according o he above analysis. I is assumed ha he wo wires in space are line1 and line, respecively, he hanging poins coordinaes of line1 are A (x 1, y 1, z 1 ) and B (x, y, z ), respecively, and he hanging poins coordinaes of line are C (x 3, y 3, z 3 ) and D (x 4, y 4, z 4 ), respecively. Then he disance beween any poins in wo wires can be calculaed according o he disance formula beween wo poins in space. γ L( y4 y3)( ) d = [ x3 + ( x4 x3) + σ γ L1( y y1)( 1 1 ) x1 ( x x1) 1 ] σ γ L( x4 x3)( ) + [ y3 + ( y4 y3) σ γ L1( x x1)( 1 1 ) y1 ( y y1) 1 + ] σ γ Ll ( ) + [ z3 + ( z4 z3) σ γ Ll 11( 1 1 ) z1 ( z z1) 1 + ] σ Visibly, d is he binary quaric equaion, and he minimum of d needs o be resolved. According o he differenial mehod, le d / 1 =, d / =, and hen he binary cubic equaion se concerning he posiion funcion 1 and is obained. Subsequenly, he Malab plaform can be used o solve d, hus he minimum of d is obained. The binary cubic equaion has muliple ses of soluions, so he range of funcion values 1 [ y1, y], [ y3, y4] needs o be defined. Moreover, 1 and appear in pairs, d has a unique soluion afer he definiion of funcion values, and i can be quickly solved in Malab environmen. 3. Sensiiviy Analysis of Minimum of Spaial Two Wires When he arrangemen mode of high volage overhead lines changes, he elecrical spacing of wire mus be verified. Especially, i is commonly seen ha he ge-in ganry span wire is convered from he horizonal layou of ganry o he verical arrangemen form ouside of a saion. I is analyzed ha he sensibiliy of minimum disance beween wo wires wih he change of disance beween erminal ower and ganry, he change of heigh difference beween erminal ower and ganry, change of safey coefficien of relaxaion span, and so on by aking he ge-in ganry span of kv lines engineering and adoping he JL1/LHA1-465/1 (aluminum alloy core aluminium conducor). 3.1. Model Analysis The model of sensiiviy analysis is shown in Figure []. Where he ype of he wire is JL1/LHA1-465/1, and he parameers are shown in Table. 3.. Change Law of Minimum Disance beween Two Wires under Differen Spans 1) Change law of disance wih he span under differen working condiions According o he sipulaions of GB 5545-1, he minimum phase spacings in span under he acion of inerphase operaing overvolage a 5 kv and he volage grade below 5 kv are shown in Table 3. The regulaion only sipulaes he minimum disance of phase spacing of wire under operaing condiions, and he minimum phase spacing of wire is. m under kv. Bu he minimum disance beween wires does no necessarily happen under operaing condiions. Hence, i is necessary o compare he disance beween wires under high emperaure o ha under operaing condiions, as shown in Figure 3. 9
Figure. Model of sensiiviy analysis. Table. Parameers of energy-saving wire. Type of he wire Aluminum alloy core aluminium conducor Seel (Aluminium-coaed seel) 9.85 Secional area (mm ) Aluminum (Aluminium alloy) 463.88 Toal cross secion 673.73 Aluminium/seel (Aluminium-coaed seel) cross-secion raio. Diameer (mm) 33.75 Uni weigh (kg/km) 1864. Comprehensive elasic coefficien (MPa) 55 Comprehensive expansion coefficien (1/ C) 3 1 6 Calculaed ensile force (kn) 137. Tension-weigh raio (T/W) 7.49 Table 3. The minimum inerphase inervals in span under he acion of inerphase operaing overvolage. Nominal volage/kv 11 33 5 Inerphase inerval (in span)/m 1.. 3. 4.55 Figure 3. Comparison of disances beween wires under differen working condiions. 93
As shown in Figure 3, he minimum disance of wire under he operaing condiions is obviously greaer han he minimum disance under he high emperaure condiions. Moreover, when he minimum span is m, he minimum phase spacings under boh operaing condiions and high emperaure condiions can mee he requiremens of regulaion. Bu he minimum disance of wires under he operaing condiions canno represen oher condiions o sudy he minimum disance of wires. Therefore, i is likely o use he minimum disance of wire under high emperaure condiions o sudy he minimum disance of wires. ) Change law of disance wih span under he high emperaure In he calculaion model, he wo hanging poins coordinaes of wire 1 are (7,, 7) and (3.5, y, 14), respecively, as well as he hanging poins coordinaes of wire are (7.8,, 33.5) and (, y 4, 14), respecively. In addiion, he difference of hanging poins disance beween wire 1 and wire in he erminal ower is 6.5 m. Figure 4. Change law of minimum spacing beween wo wires under differen spans and differen safey coefficiens. I is clearly observed ha (1) Under he idenical safey coefficien, he disance beween wo wires in space increases wih he increase of he span. However, he ampliude of increase coninuously decreases as well as he disance ends o be smooh and seady. Taking k = 15 as an example, when he span is in - 3 m, he rae of change of he increase of he shores disance is abou 5.5%. When he span is in 11-1 m, he change rae is only.7%. Namely, he greaer he span is, he weaker he conrol of minimum disance beween wo wires in space by he wire ension is. () Wih he increase of safey coefficien, he change law of he shores disance beween wo wires in space wih he span becomes more and more obvious, as well as he rae of change is greaer. As k = 3.4, he change rae of span in - 1 m is 3.8%, while k = 15, he rae of change is 15.3% wih he same span. So when designing he change of he arrangemen mode for wires, i is quie necessary o check wheher he space disance beween wo wires mee he requiremens. (3) Under he idenical span and differen safey coefficiens, i is observed ha he wires relax and he sag of wires increases wih he increase of securiy coefficiens. These make he minimum disance beween wo wires coninuously reduce. (4) I is required in he regulaion ha he inerphase disance of kv wires is no less han m. Bu only considering he operaion saus in he engineering is no enough, i is sill considered o mee he requiremen of m for he phase spacing under he high emperaure, moreover, he phase spacing should be increased by % under he allowable condiions. In his case, he phase spacing should no be less han.4 m. When he wires are relaxing, he safey coefficien and he span should be simulaneously conrolled, for example, as k = 15, he span should no be less han 3 m, while k =, he span should no be less han 5 m. 3.3. Change Law of Minimum Disance wih he Span under Differen Heigh Differences When designing he ge-in/ou ganry span, i is ofen encounered ha he difference beween he nominal heigh of erminal ower and he heigh of ganry is greaer. Hence, he change of he minimum disance of wo wires in space wih differen heigh differences needs o be sudied. So when k = 15, he change of he minimum disance in space beween wo wires of ge-in ganry span needs o be iniially accouned by designing Δh = 13 m, m, 3 m, 4 m and ec. 94
Figure 5. Change law of minimum disance beween wo wires in space wih he span under differen heigh differences. As can be seen ha: (1) Wih he increase of he heigh difference beween he erminal ower and ganry, he minimum spacing beween wo wires are coninuously reducing, and he greaer he heigh difference is, he greaer he shorened ampliude is. Moreover, when Δh is in 13 m - m, m - 3 m, and 3 m - 4 m, he corresponding rae of change is.8%, 1.5%, and 1.94%, respecively, wih he span of 6 m. () Wihin he idenical span, he minimum disance beween wo wires are coninuously shorening wih he increase of he heigh difference. However, as he span becomes greaer, he shores disance beween wo wires ends o be consisen. Namely, he greaer he span is, he weaker he conrol of he shores disance beween he wo wires by heigh difference is. 4. Conclusions Based on he equaion of wire balance, space curve equaion of wires was precisely esablished and he minimum disance beween wo wires in space was calculaed by using he inegral-differenial mehod of space curve and Malab ool in consideraion of he sag of wires under differen working condiions. Simulaneously, he sensiiviy of minimum disance beween wo wires wih he change of ower heigh difference, he change of safey coefficien, he change of span, and so on was sysemaically calculaed by aking he energy-saving wire (aluminum alloy core aluminium conducor) as an example. Moreover, he conclusions are obained as follows. (1) Under he same safey coefficien, he disance beween wo wires in space increases wih he increase of span, bu he increase ampliude gradually decreases as well as he disance ends o be sable. Moreover, he greaer he span is, he weaker he conrol of he minimum disance beween he wo wires in space by he change of wire ension caused by he change of securiy coefficien of wire is. () Under he same span, he sag of he wire increases wih he increase of he safey coefficien, which makes he minimum disance beween he wo wires coninuously decrease. (3) Wih he increase of ower heigh difference beween boh sides, he minimum spacing beween wo wires gradually decreases, and he greaer he heigh difference is, he greaer he shorened ampliude is. (4) Wihin he same span, he minimum disance beween wo wires gradually shorens wih he increase of he heigh difference. Bu he greaer he span is, he weaker he conrol of he shores disance beween wo wires by he heigh difference is. References [1] GB 5545-1. Code for Design of 11kV - 75kV Overhead Transmission Line. [] Yang, X.M., Feng, N. and Wu, S.P. (1) Precise Calibraion for Phase Disance of Approach Span Based on Three- Dimensional Space Technology. Elecric Power Consrucion, 33, 46-48. [3] Bai, X.L., Ge, Q.L. and Yu, W.W. (1) Analysis of Leas Phase Disance of Overhead Transmission Line. Elecric Power Science and Engineering, 6, 37-43. 95
[4] Zhang, D.S. (3) Design Handbook for Elecric Power Transmission Line. China Power Press, Beijing. [5] Gong, Y.Q., Liang, N.C. and Gong, Y.G. (9) A Formula Mehod for Conducor Elecric Clearance of Overhead Transmission Line. Elecric Power Consrucion, 3, 4-7. [6] Rohlfs, A.F. and Schneider, H.M. (1983) Swiching Impulse Srengh of Compaced Transmission Line Fla and Dela Configuraions. IEEE Transacions on Power Apparaus and Sysems, 1, 8-831. 96