60422610 rtdi sag and tension calculations for mountainous terrain

7/29/2019 60422610 RTDI Sag and Tension Calculations for Mountainous Terrain

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Sag and tension calculations formountainous terrainJ. Bradbury, Dip. Tech. (En g.), G.F. Kuska, C. Eng., M.I.E .E., and D.J. Tarr

Indexing terms: Cables an d overhead lines, Power transmissionAbstract: While normal sag and tension calculations based on the 'equivalent-span' concept are satisfactory,when applied to transmission lines located in a reasonably undulating terrain, the answers obtained by thismethod are inaccurate for mountainous terrain. An alternative method of calculation, which is based on theanalysis of the change of state equation for each span of a section in turn, is given. It is shown that whenusing this new approach the full effect of both the suspension and tension insulators can be included togetherwith the influence of the running-out blocks on the sag of the conductor.The paper also shows how this concept can be adapted to the function of line design and gives severalexamples of critical areas where existing m ethods may give unacceptable results.When stringing conductors in mountainous terrain, it is not always practical to measure the conductor sagusing conventional techniques and the paper gives three additional means which may be used, and discussesthe advantages and disadvantages of each.

a = coefficient of therm al expansion of complete conduc-tor, per deg C/3 = blow-out angle of cond uctor (Fig. 2b), degrees7 = angle to the vertical of the suspension or tension insu-lator sets, degreesAh = height difference betw een tower and cond uctor attach-ment p oints (Fig. 9), mAx = horiz ontal difference corresponding to Ah, m5 = angle betwee n chord line and the horizo ntal in the un-

A = cross-sectional area of cond uctor, mm 2a,b,c,d = constants depending on sag>>C catenary constant = H/W,mE = Young's modulus of complete condu ctor, kg/mm 2H = horizontal tension of conductor, kgH' = comp onent of tension in line with AG (Fig. 2d), kgh = height difference between attach me nt poin ts at adjacenttowers, mht = vertical distance from tower to instrum ent, mK = unstretched length of condu ctor in a span (i.e. lengthafter removing the tension at 0 C), mL = chord length between adjacent to wers (Fig. 1), m/ = length of tension or suspension insulator set, mS = stretched length of conductor in a span, mT = total (tangential) tension in conductor, kgV = vertical load at attachment po int due to conductor (up-lift load denoted by negative value), kgW = conductor weight per unit length, kg/mW h = conductor wind load per unit length (wind actingnormal to conductor), kg/mW r = resolved cond uctor weight per unit length in the plane(as shown in Fig. 2c), kg/mW v = W + weight of ice per unit length, kg/mW' = resolved conductor weight per unit length in the plane(as shown in Fig. 2b), kg/mX = horizontal span length, mXo = horizontal distance from attachment point to lowpoint datum (Fig. 1), mXp = horizontal distance from any point on the catenary tolow point datum (Fig. 1), mx = horizontal distance from attachment point to any

point on the catenary, mxt = horizontal distance from tower to instrumen t, my = sag from chord line at point x on the catenary, my0 = sag from attachment point at low point datum (Fig.yh = maximum value of y occurring at point X/2 (absence oftension insulators) (Fig. 1), myh' = maximum value of y not necessarily at point X/2 inpresence of tension insulators (Fig. 4), mZ = transverse horizontal load at attachment point due toconductor, kg

Paper 20S4C (P8), first received 2nd November 1981 and in revisedform 20th May 1982The authors are with Balfour Beatty Power Construction Limited, PowerTransmission Division, 7 Mayday R oad, Thorton Heath, Surrey CR47XA, England

resolved plane, degrees6 = conductor temperatu re, Ci// = angle between ch ord line and the horizo ntal in the re-solved plane (Fig. 2d), degreesto = weight of tension or suspension insulator set, kg = angle of the tangent at point F to the horizontal(Fig. 1), degreesSubscripts 1 and 2 d enote different values for the same vari-ables.1 IntroductionSince the advent of transmission lines, theories have been pro-gressively developed to define the sag and tension behaviour ofthe conductor. Initially these were oriented towards manualcalculations and , consequently, were based upon the parabolictheory (Boyse and Simpson [1]). With the introduction ofcomputers most theories are now based upon the accuratecatenary equ ations (Rieger [2 ]). In multi-span sections, it isusual to assume that the horizontal tensions will react tochanges in load and temperature as a single span referred to bythe well known term 'equivalent span'. The mathematicaltreatment to obtain the 'equivalent span' is based upon para-bolic theory, and there is no similar concept using full ca-tenary equations.While the methods give acceptable and practical results forthe majority of lines constructed'in normal, reasonably undu-lating terrain, e.g. in the UK, in mountainous areas thesetheories produce significant errors. Overhead-line engineers arealready aware of this problem, as illustrated by Winkelman [3],which develops the parabolic and catenary theories for appli-cation to inclined sections. Our recent experience, on applyingthis method to very mountainous terrain, highlighted the pres-ence of further inaccuracies which will result in the towers andconductors experiencing loads in excess of their limiting designvalues. In an attempt to overcome these problems, a theoryhas been developed which is the subject of this paper. Atthe development stage it became evident that the above in-accuracies were valid for both the single- and multi-spansections.This paper was originally presented to the 2nd inter-national conference on 'Progress in cables and overhead lines

IEEPROC , Vol. 129, Pt. C, No. 5, SEPTEMBER 1982 0143-7046/82/050213 + 08 $01.50/0 213

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for 220 kV and above ' [4] and has now been expanded to in-clude practical examples using the methods of calculationsdescribed.2 Theory2.1 Basic equationsBefore detailed considerations were given to the problem, itwas recognised that there are two theories, inelastic [2,3] andelastic (Hattingh [5]), applicable to the solution of a catenary.Considering the two theories, it became evident that the elastictreatment requires lengthy computation without producingworthwhile improvements in the accuracy of the result. It istherefore felt that the inelastic theory gives a tolerableaccuracy, and, for this reason, the inelastic catenary equationsare used. These, by reference to Fig. 1, are given below:

LTcatenary constant C = = c / c o s h ^ -

length of conductor between points A and DS = Csinh C

horizontal length Xo (D' A)Xo = - C s i n h " 1 h X2Csinh

alsoXo = Cs inh" 1 H

vertical component of tension at point AV = / / s i n h ^ -

total tension at point AT = ^

half-span sagyh = C | c o s h - 1 1 +

2 Csinh X2C~

(1 )(2 )

(3)

(4)

(5 )

(6 )

(7 )

(8 )

XoFig. 1 Inclined spanSign convention: Xo positive and Xp negative for the case shown, i.e. ifpoint F is to the left of D, Xp becomes positive21 4

angle to the horizontal of the tangent at point F= tan"1! s i n h l - ^ |} (9)

2.2 Change-of-state equationWhen considering a length of conductor suspended betweentwo towers, after it has been clamped in, it is assumed that theunstretched length K of the conductor at 0C is constant, i.e.it equals the length given by the catenary equation less theelastic and thermal changes.To utilise the above statement in the development of thechange-of-state equation, two simplifications have been maderelated to the unstretched length of the conductor and itstension. With respect to the former, an assumption was madethat, when calculating the elastic and thermal changes, the valueof K is equal to the chord length L. This assumption causes anerror of less than 0.01 % in the estimation of the unstre tche dlength. It is felt th at this accuracy is sufficient for practicalpurposes, but, if further accuracy is required, it can be improvedby adopting the second-term-approximation system given instep (d) of Section 3.1.

Regarding the tension, in calculating the elastic changes, themean total tension in the conductor length has been assumedto equal the horizontal tension.Referring to Fig. 1, the change-of-state equation becomes:

sinh h sinhC2

yi A (Y )EA (10)

where subscripts 1 and 2 denote two different conditions.It should be noted that this equation is only valid for still-air conditions. When the conductor is subjected to wind actingnormal to it, the vertical and transverse forces present mustbe resolved in the deflected plane of the conductor beforeapplying eqn. 10. The method for resolving these forces isgiven in Fig. 2 and explained below:

Step 1: Fig. 2a shows an inclined span under the influenceof a wind force. Consider the forces acting on the conductorelement, i.e. the wind force W h acting normal to the conductorand the vertical force W v due to the conductor and ice weight.Force Wv must be resolved along two axes normal to and par-allel with the chord line.Step 2: Fig. 2b shows a section through the element (Fig. 2a)along the X X axis. The forces acting are W h, Wv cos 5 and W vsin 5, the latter applied parallel with the chord line. The result-ant force W' acting at an angle j3 to th e vertical is obtaine d.Step 3: Fig. 2c shows the inclined span rotated about axisAB through angle /3. The forces in the deflected plane, W' andW v sin 5, are combined to give the resultant force W r acting atan angle i// to the normal to the chord line.Step 4: Fig. 2d shows the inclined span rotated about pointA, such that the chord line makes an angle \p to the line AG.This line represents the 'horizontal' plane in which the catenaryequations are valid. Under this condition, force W r is theonly force present and acts 'vertically', thus satisfying the re-quirements to solve the change-of-state equation (eqn. 10).To use eqns. 110 the parameters H and W should be replacedby H' and W r, respectively.Having solved eqn. 1 for the unknown H' 2 it should benoted that this is the 'horizontal' tension in the rotated plane(Fig. 2d~), and not the inline horizontal force at the tower. Toobtain the tension components H, V and Z at tower A (Fig. 2a),it is first necessary to calculate the Vertical' force in the rotated

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Q =W hc =W v s i n 8d = Wwcos6

Fig. 2 Resolution of forces under wind conditionsa Span subjected to a wind force normal to the conductor6 Deflection of element through section X Xc Span through section Y Yd Span in resolved plane

suspensioninsulator

Fig. 3 Forces on suspension insulatorsa Conductor on running-out blocksb Conductor clamped in

suspensioninsulator

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plane at point A (eqn. 6) and then reverse the above step-by-step procedure.2.3 Effect of suspension insulatorsTwo conditions must be considered, when the conductor is onrunning out blocks, and when it is clamped in.2.3.1 Conductor on running-out blocks: Consider Fig. 3a whichshows the conductor mounted immediately below the sus-pension insulator. Assuming the block to be frictionless, itfollows that:

T = \IH\ + v\ = \ltii + v\ (11)Taking moments about point Q, the following equation isderived:

7 = tan - l H 2 (12)Furthermore, as the block is free to rotate thus permittingconductor movement between spans, the unstretched lengthin individual spans is not constant. Obviously, the total un-stretched length in a section is constant.2.3.2 Conductor clamped in: Once the conductor is clampedin, the unstretched length in individual spans remains constant,because no conductor movement occurs at the clamp.Considering this condition, it is evident that although pre-vious theories assumed the suspension set to be always verticalthis assumption is incorrect, because the verticality dependsupon the geometry of the section and the temperature. Forthis reason Fig. 3b shows the suspension insulator at an angle7 to the vertical. Again by taking moments about Q, eqn. 12can be derived. It follows that the horizontal tensionsH x andH2 in the adjacent spans are different unless 7 equals zero.2.4 Effect of tension insulatorThe length and weight of a tension insulator cause errors in sagand tension, particularly in EHV downleads. However, withregard to tension, the reduction in span length X and the slightvariation in height difference h have only a marginal influence

Fig. 4 Span with tension insulator216

on the solution of eqn. 10 and are ignored. As far as the errorin sag is concerned , the effect can be significant.By reference to Fig. 4, the following equations apply:

alsotan3/ =

H7 V + co/2

V A / J 2 + Ax 2

AxAh (13)

(14)The horizontal tension H is known from the change-of-stateequation and the insulator weight co given. The vertical forceV is dependent on Xo and hence on Ah. The solution for Ahand Kcan be achieved by iterative technique.To provide the necessary sagging information during string-ing, the maximum sag y^ (which does not necessarily occurat X/2) must be calculated. In this respect, it should be notedthat eqn. 8 no longer applies; and a practical approach is givenbelow:(i) Calculate y for three different values of*(ii) Solve

y = ax2 + bx + c (15)(iii) Calculate JC for maximum sag, i.e. JC = b/2a(iv) Substitute x from (iii) into eqn. 15 thus obtaining ^

3 Application of theory by computer programmingFor the purpose of tower design, profiling and stringing, anoverhead line con tracto r requ ires data resulting from a largenumber of sag and tension calculations. These must, particu-larly in mountainous terrain, reflect the geometry of the line.Under conditions of excessive gradients the suspension insu-lator will swing longitudinally, with the result that the hori-zontal tensions in adjacent spans may not be equal. Conse-quently, the 'equivalent span' concept is not valid. The solutionto the problem lies in the evaluation of the elastic and thermaleffects in the conductor in each individual span, i.e. span-by-span analysis. Without the aid of a computer program it is notpractical to undertake these calculations. While the program-ming of the sag equations was straightforward, the tensionequations presented some difficulties. For multi-span sectionsthese were overcome by the method outlined below:3.1 Starting conditionsTo carry out the calculations two parameters of the line mustbe known at a given point in time, namely, the angle 7 of allsuspension insulators and a limit tension. Normally thesuspension insulators are assumed to be vertical at the expectedstringing temperature. The assumed tension values relate to alimit in the h orizontal or total compo nent, as required by thespecification. For calculating the left-hand side of eqn. 10 theprocedure is as follows:

(a) The vertical and transverse loads are estimated at eachtower position.(b) The total tension is estimated at the first tower.(c) The left-hand side of eqn. 10 is evaluated for the firstspan in the section, using the value of the chord lengthfor the unstretched length.(d ) Should further accuracy in the unstretched length berequired (see Section 2.2), the left-hand side of eqn. 10can be recalculated using the value for the unstretchedlength found under step (c) above. (This improves theaccuracy in calculating the unstretched length t o b etterthan 0.0001 %).(e) Steps (c) and (d ) are repeated for all spans in the section

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taking in to a ccoun t th e angle 7, if any, of the suspensioninsulator, using eqn.12 for calculation of the hori-zontal tension in succeeding spans.3.2 Condition whe n conductor is clamped inThis refers to the evaluation of the right-hand side of eqn. 10,i.e. for a condition other than the starting condition. Theprocedure adopted is as follows:(a ) Using the equivalent-span technique the horizontal,vertical and transverse tensions are estimated at each

tower.(b ) The total tension is estimated at the first tower.(c) The right-hand side of eqn . 10 is evaluated for each spanand angle 7 of the suspension insulator, changed toaccommodate any variation in the chord length. Beforeconsidering the next span the horizontal tension isaltered according to eqn 12.(d ) By reiteration of steps (b) and (c), convergence on theposition of the conductor attachment point at the lasttower is obtained.3.3 Condition when conductor is on running-out blocksThis refers to the conductor being free to move and the pro-cedure adopted is the same as under Section 3.2 with the ex-ception of step (c), which is as follows:(c) A summation of the values for the right-hand side ofeqn. 10 is made. When considering successive spans, the hori-zontal tension is changed according to eqn. 11.4 App lication of theory to practical l ine situationsConventional sag and tension methods are satisfactory for themajority of situations, and use of the method described above,cannot be normally justified in view of the additional data re-quired. Computer runs have shown that for normal level single-span sections there is no difference between conventionalmethods and the one now proposed; unlike multi-spans, whereeven with level span sections, there is a small difference ofapproximately 0.3 % between the theories. This is due to thefact that under wind condit ions , if conventional suspensioninsulators are used, the bottom of the suspension insulatorwill move in the transverse direction, causing an increase in thechord length between the fixing points. This effect is includedin the present theory, but ignored in conventional techniques.As conditions on the line change from a level span, the differ-ence between conventional methods and the one proposedgradually increases. Under extreme circumstances, limitedinvestigations have shown that conventional theories willunderestimate the maximum tension and sag by up to about20%; hence, it is apparent that in critical situations there is aneed for more accurate sag and tension techniques. It is there-fore necessary to have available a method of assessing thesecritical situations. As guidelines, the following empirical con-ditions have been developed , to determin e the sections in whichthe more rigorous treatment given in this paper should beconsidered:

(a) if the span gradient for any span within the section ex-ceeds 0.2 or if the average span gradient w ithin the sec-tion exceeds 0.15(b ) if the conventional sag and tension using the modifi-cations given by Winkelman [3] give an offset in excessof 0.5 m(c) for all sections contain ing spans in excess of 1 km, e.g.river crossings(d) if aircraft warning spheres are fitted(e) if for some reason one or more suspension sets are notdesigned to be vertical at the time of clamping.

Naturally, when considering a complete line, it is not ideal toIEEPROC , Vol. 129, Pt. C, No. 5, SEPTEMBER 1982

adopt more than one sag and tension method for its construc-tion. Hence, at an early stage, one method is selected and usedthrougho ut the line; even though , when the conventionalmethod is selected, isolated sections may be found whichslightly exceed th e limits given abo ve. With some line constru c-tions, where conventional techniques may be ideal, isolatedmountainous sections may be present where the method fromthis paper must be considered.5 Practical app lication to line designFollowing the development of the program, it has been foundincreasingly useful in connection with studies and calculationsrelevant to the following design activities:(a) the determination, for tower-design purpose, of all loadsimposed by the conductors and earthwires(b) the design and selection of profile-plotting templateswhich reflect the effect of gradients(c) the investigation of tower loads in cases where a combi-nation of long and short spans may result in unaccept-able out-of-balance longitudinal and vertical loads(d ) an accurate determination of sags and tensions in cir-cumstances where the route topography imposes asevere limitation on tower locations. This, in cases ofexcessive grad ients, can lead to critical ground -clearanceproblems(e) the production of sags and tension data for field use. Inmountainous terrain the output refers to two stringingconditions:(i) when the conductor in a section is located on run-ning-out blocks(ii) when the conductor in a section is clamped in(f) the evaluation of suspension-insulator longitudinal-swing and out-of-balance tension s. This may be re-quired when dealing with very long sections(g) use as a general-purpose design aid for the evaluationof sags and tensions leading to rapid solution of field

problemsIn order that a better understanding of this theory can be ob-tained, a number of examples are given below. These examplesrelate to a 'Zebra' conductor (54/7/3.18mm ACSR) strung totypical UK loading conditions. This Section, however, doesnot constitute a criticism of UK practice which employs aspecial technique, see below, for safely overcoming the inade-quacies of conventional sag and tension calculations, mentionedin this paper.In the UK external loads and factors of safety related totransmission lines are governed by the Statutory Instruments1970, number 1355. Clause 9.2 defines the minimum factorof safety for total (tangential) tensions of the conductors as

2.0. For the 'Zebra' conductor this corresponds to a tension of6722 kg. The conventional UK practice for sag and tension cal-culations for this conductor is to employ a maximum hori-zontal tension of 55 05 kg. The difference between these twofigures is more than sufficient to account for any increasesin tension due to the nature of the terrain in the UK.5.1 Variation of tensions with span gradientsIn most specifications, the maximum working tension (MWT)in the conductors refers to the maximum tension anywhere inthe conductor's length. This occurs at the highest point ofattachmen t of the conductor to the tower. Tension calculations(eqn. 10) are ruled by the horizontal tensions. Thus, the tensionused in eqn. 10 should be reduced as the span gradient isincreased, to ensure that the MWT is not exceeded. Fig. 5illustrates this reduction in horizontal tension against spangradient, to ensure that the tension on a 366 m span does notexceed 2651 kg under still-air conditions anywhere in the span

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length. This shows, considering a span having a difference inheight between th e cond uctor attachmen t poin ts of 100 mthat the tension in eqn. 10 should be reduced to 2454 kg, areduction of 7.4%. Even on level spans, this figure shows thespecified ten sion shou ld be reduced by 0.7% , a fact oftenignored when conventional sag and tension equations are used.

n2000.60. 5

- 0.4cI 0.3oin 0.2

0 .10

>. specified max imum>v tension\ \

: \\

\

- 150g E

100? cj |c si - oa, a" 50 ^

2000 2200 2400 2600hor izontal tension, kgFig. 5 Horizontal tension on a 366 m span to ensure conductor'stension should not exceed 26 51 kg5.2 Profile plottingThe problems mentioned in Section 5.1 cause further compli-cations during the profile plotting stage, because the templatesare based on horizontal tensions. It follows, therefore, thattemplate selection is a function of equivalent span length andspan gradient. This problem has been solved by introducing agraph, Fig. 6, from which template selection is made .

equivalent span,m-Fig. 6 Sketch of template selection graph

Fig. 6 is obtained by determining the number of templates,and tensions for each te mpla te, to be used during plotting. Theprogram is run to predict the horizontal tension, at maximumoperating temperature, from the specified limiting conditionsfor a number of spans and span gradients. From this data, Fig. 6can be drawn by plotting the lines corresponding to the hori-zontal tension chosen for the templates. The straight line givenin the Figure represents the level single-span condition, belowwhich the graph is indeterminate.In practice, this graph is used in the following manner:(a) The worst span in a section is visually selected, usuallyhaving the highest span gradientAny tem plate is offered to this span and the weightb) span at the highest tower read off the template(c) The weight span is checked against Fig. 6, and thecorrect template selected for use in final plotting5.3 Transverse loads on suspension earth wire peaksAs eqn. 12 shows, the suspension insulator is not normally

vertical and, hence, longitudinal loads of a magnitude H2 Hi are transmitted to the suspension towers. The magnitudeof this force is influenced by the length of the insulator stringor earthwire set. In the case of insulator sets, owing to theirlength, the transmitted force is normally very small. However,in recent years, there has been a tendency to reduce the lengthof the earthwire set which connects the earthwire to the tower.Fig. 7 shows that if this set is made too short, this may giverise to high longitudinal loads at the tower. This Figure wasconstructed assuming a level two-span section having 150and 500 m span length s. It was further assumed the set isvertical when under wind conditions, and the longitudinalout-of-balance forces shown are calculated at 75 C in still air.

&

o


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the effect of the weight of ice load and extra wind load on theadded masses, together with their weight, mu st also be includedin the tension calculations.To accommodate this additional tension caused by fittingspheres, while still maintaining the required factors of safety,the selected earthwire must be sufficiently strong. Failureto achieve this can result in a situation in which the sag of theearthwire dictates the main conductor sags, which can prove tobe an uneconomical solution.6 Sag measuring techniquesWhen stringing conductors in mountainous terrain it is notalways possible or desirable to use the conventional saggingtechn iqu e. To provide field staff with alternatives, four furthermethods have been developed. Each has its limitations, but theselection of the appropriate method will be dictated by sitecircumstances, and is made by the stringing engineer.6.1 Conventional methodThis is illustrated in Fig. 9a , where the gun sight and thesighting board are fixed to the towers at a distance yh> belowthe conductor attachment points. The field application isstraightforward, but limited to cases when yh' is less than thetower heights. Its accuracy will decease with small spans.6.2 Modified conventional methodBy reference to Fig. 9b , it is seen that this method applies toconditions when the gun sight and the sighting board cannotbe located on the tower. It requires care in accurate locationof the theodolite, and has the same limitations as in Section6.1.

6.3 Low-point methodWith this method (Fig. 9c), the instrument, e.g. theodoliteor dumpy level, is located at a distance y0 below the con-ductor attachment point. Obviously, its application is limitedto cases having a low-point d atum , and the accuracy achievedis dependent upon the variation of y0 with changes in tem-perature. If the variation is small the method may be unsuitable.6.4 Tangent methodFig. 9d illustrates the case where the location of the theodoliteis defined by limited access. In application, the stringing en-gineer, having fixed its location, is required to make use of thefollowing equations:

(16)(17)here d = C In (tan 0 + sec 0)

The difficulty in using this method lies in the reiterative calcu-lation for 0 and the accuracy with which it has to be measured.For reason of accuracy and site calculation this method is tobe avoided if possible.6.5 Tension methodWhen considering short span sections, an accurate saggingmethod can be achieved by the use of a load cell prior to con-ductor marking and the installation of tension insulator. Thistechnique lends itself to situations where compression dead-ends are made aloft.6.6 Stringing tablesIt is not possible to provide site staff with sufficient informa-tion in conventional sag-chart form to string conductors using

sightingboard

Fig. 9 Method of sag measurementa Conventionalb Modified conventionalc Low-point datumd TangentIEEPROC , Vol. 129, Pt. C, No. 5, SEPTEMBER 1982 21 9



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Table 1 : Typical stringing table obtained from computerTemperature

C

0.005.0010.0015.0020.0025.0030.0035.00

Horizontalloadkg

24002290218920962011193318621796

Totallow towernumberkg

24002290218920972012193418621796

tensionhigh towernumberkg

24222312221121182033195518831817

Halfspansagm

3.323.483.643.803.964.124.204.44

low tower numberXm

-31.95-25.86-20.26-15.13-10.43-6.11-2 .14

1.51

Ym

0.600.520.460.420.400.390.390.40

high towerXm

233.74227.65222.05216.92212.22207.90203.93200.28

numberYm

16.5016.4216.3616.3216.3016.2916.2916.30

all five methods given above. The program provides computer-printout tables, illustrated in Table 1, which has an addedadvantage over conventional sag-chart owing to ease of readingrather than interpolation of graphs.7 ConclusionsTo satisfy the statutory ground clearance requirements, and toensure that the specified factors of safety of the line are main-tained, an accurate method of span-to-span analysis has beendeveloped. This is of particular importance in mountainousterrain, where existing techniques may result in noticeableerrors.Normally, in reasonable terrain, consideration need not begiven to the out-of-balance loads due to the longitudinal swingof the suspension insulator. However, in long multi-span sec-tions with excessive gradients this effect can be significant andshould be examined.In mountainous terrain, where the conventional method ofsagging is either impossible or impracticable, then, alternativemethods must be available to the site organisation. During theconstruction of the 400 kV line through the formidable Zagrosmountains in Central Iran, it was necessary to apply the fullrange of meth ods, as detailed under Section 6, each being deter-mined by the relative conditions of each section encountered.

In many instances, where conditions were so severe that theuse of helicopters became the only means of access, the use ofthe tension method, where the tangential tension is measuredby a load cell, proved extremely effective.8 AcknowledgmentsThe authors acknowledge the help of their colleagues in thepreparation of this work, and wish to thank the GeneralManager of the Power Transmission Division, Balfour BeattyPower Construction Limited, and the Directors of BalfourBeatty Limited for permission to publish this paper.9 References1 BOYSE, CO ., and SIMPSON, N.G.: 'The problem of conductorsagging on overhead transmission lines', J. IEE, 1944, 91, Pt. II,pp . 219-2382 RIEGER, H.: 'Der Freileitungsbau' (Springer Verlag, 1960)3 WINKELMAN, P.F .: 'Sag-tension computations and field measure-ments of Bonneville Power Adm inistration', Trans. A mer. Inst. Elect.,Engrs., 1959, 78, Pt. Ill B pp. 1532-15474 BRADBURY, J., KUSKA, G.F., and TARR, D.J.: 'Sag and tensioncalculations in mountainous terrain'. IEE Conf. Publ. 176, 1979,pp . 1-55 HATTINGH, J.T.: 'A universal stress-sag chart (for line computa-tions)' (Blackie & Sons, 1936)

22 0 IEEPROC, Vol. 129, Pt. C, No. 5, SEPTEMBE R 1982

60422610 rtdi sag and tension calculations for mountainous terrain

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