Swing angle

Design of Transmission Lines in India : a Review of MultipleSwing Angle-clearance CombinationsDr V N Rikh, Fellow

Proper live metal clearances have to be maintained under various swing angles of the suspension insulatorstrings/jumper loops on a tower, in order to ensure a reliable performance of the transmission lines. The requiredswing angle-clearance combinations for lines of different voltages are determined on the basis of a pre-specifiedcriterion of flashover probability. These combinations decide horizontal and vertical spacing of the powerconductors and thereby determine the tower configuration, weight and cost. Presently three to five swing angle-clearance combinations are commonly specified for Indian transmission lines of each voltage. On the other hand,in many countries generally only two or three combinations are specified. Based on detailed analysis this paperattempts to prove that if even two judiciously selected swing angle-clearance combinations are used, they wouldadequately determine optimum tower configuration and the remaining extra combinations presently specified couldbe dispensed with, without jeopardizing the reliability of the lines.

Keywords : Transmission line; Line insulation; Swing angle; Line metal clearances

NOTATIONS

C0 , C15 , C10, etc : location of critical live metal part of thephase power conductor with swing anglesof 0°, 15°, 30° etc

L0 , L15 , L30, etc : live-metal clearances specified for swingangles of 0°, 15°, 30° etc, cm

c : minimum clearance between the live metalparts phase power conductor and the nearest(carthed) part of the tower structure or live-metal clearance, cm

h : half width of the tower hamper at the criticalpoint (where the clearance arc from theswung, live metal parts touches it), cm

l : swinging length of the suspension stringduly adjusted for any longitudinal (to thestring axis) projection of the guard ring/bandle spacer, cm

lo : length of hanger of the suspensionstring, cm

r : transverse (to the string axis) projection, ifany, of the critical point of the guardring/bundle spacer, cm

α : angle at which the uppermost (nearest to theconductor) structural member of the under-neath cross-arm is inclined to horizontalplane, degrees

α′ : angle at which the nearest structural mem-ber of the tower hamper is inclined to thevertical plane, degrees

θ : angle of swing of the suspension insulatorstring or of the jumper loop of tension insu-lator string, degrees

Φ : tan − 1 [r ⁄ √ (r2 + l2)]

INTRODUCTION

One of the most important criteria for ensuring a reliable perform-ance of transmission lines under all weather conditions, is toensure that proper live metal (conductor to nearest earthed partsof the tower structure) clearances are maintained under variousangles (depending on wind speeds) of swing of the suspensioninsulator strings for a suspension tower (or the jumper loops fora tension tower). The required live-metal clearances for differentangles of swing of suspension insulator strings (or jumper loopsfor tension towers) are determined on the basis of a pre-specifiedcriterion of flashover probability. When the suspension strings,supporting the power conductors, hang vertically under ‘no-wind’ conditions, the live-metal clearance is maintained at a valuethat ensures a probability of flashover across the air-gap within apre-specified value of, say, less than 2%. As the string/conductorattachment point, swings toward the tower body under the influ-ence of the wind, the critical value of flashover voltage gradientacross the gap correspondingly increases due to faster de-ioniza-tion of the air. This results in a reduced requirement of live-metalclearances under higher wind velocities (and consequently biggerswing angles of the string/conductor attachment points) to ensurethe same level of pre-specified flashover probability across theair- gap.

The swing angle-clearance combinations presently adopted forIndian transmission lines are based on the aforesaid logic.Usually three to five swing angle-clearance combinations arespecified for transmission lines of each voltage on the basis ofdetailed analysis of prevailing weather conditions and flashovercharacteristics of air-gaps. The values of these swing angle-clearance combinations commonly specified in India1, are shownin Table 1.

These combinations have yielded a reasonably satisfactory per-formance of the transmission lines in this country over severaldecades.

The 66kV, 132kV and 220kV transmission lines in India (singlecircuit as well as double circuit) commonly use self-supportingbarrel type towers. However, while 400kV double circuit Indian

Dr V N Rikh resides at 188-A, Saket, Meerut 250 003.

This paper was received on September 26, 2003. Written discussion on this paperwill be received until July 31, 2004.

Vol 85, May 2004 21

lines also use barrel type towers, the 400kV single circuit linescommonly use corset (or Wasp-waisted) type of towers.

A study of swing angle-clearance combinations adopted in othercountries reveals that, in many countries, generally only two andsometimes a maximum of three, combinations are specified fordesigning tower configuration. This paper therefore attempts toanalyze the impact of each of the combinations (shown in Table1) on the tower configuration for Indian transmission lines, anddetermine whether all these combinations play a critical role indetermining tower configuration/s or some of these (combina-tions) could be dispensed with, without jeopardizing reliability ofthe transmission lines.

PARAMETERS AFFECTING TOWERCONFIGURATION

The swing angle-clearance combinations, along with the follow-ing two important design parameters help determine the horizon-tal, as well as the vertical, spacing of the power conductors and,in turn, help decide the configuration, dimensions and thereforethe weight/cost of the towers;

�� The slope α and α′ (to the vertical plane) of the outermost(nearest to the conductor) structural member of the towerhamper, and

�� The slope α (to the horizontal plane) of the uppermost(nearest to the conductor) structural member of theunderneath cross-arm.

The values of α and α′ are determined in the process of economicoptimization of tower configuration.

For any given values of α′,

�� An increase in (inward) swing-angle, θ, of the insulator string(or, jumper loop, for a tension tower) requires acorresponding increase in the horizontal spacing of the phaseconductor/s maintain the specified live-metal clearance,Similarly, any increase in the live-metal clearance, c, requiresa corresponding increase in the horizontal spacing.

�� The requirement of vertical spacing of the phase conductors, however, decreases with any increase in (inward)swing-angle, θ, of the insulator string (or, jumper loop, for atension tower), though an increase in the live-metal clearancec, still requires a corresponding increase in the verticalspacing.

On the other hand, with a given value of swing angle-clearancecombination;

�� An increase in the outward (towards the conductor, eg, inthe Barrel type towers)) slope α′ of the tower hamper,increases the horizontal spacing while an increased inward(away from the conductor, eg, in a corset type tower) slopeα′ of the tower hamper reduces the horizontal spacing of theconductors, and

�� An increase in the upward (towards the conductor) slope αof the uppermost member of underneath cross-arm results inan increased vertical spacing of the conductors. As perprevalent design practice, a downward slope of theunderneath cross-arm member is not adopted.

The effect of the slopes (towards the phase conductor/s) of thetower hamper as well as that of the nearest member of underneathcross arm, on the horizontal and vertical conductor spacings, isillustrated for a Barrel type tower in Figure 1.

In case of a corset type tower, the slope of Tower Hamper is awayfrom the (outer) phase conductor/s and its effect on the horizontalconductor can be visualized from a typical Figure 2. As the corsettype tower is used for single circuit lines (usually of 400kV), thereis no vertical formation of the conductors.

IMPACT OF SWING ANGLE-CLEARANCECOMBINATIONS ON THE TOWER CONFIGURATION

As explained above, for any given values of α and α′, eachswing angle-clearance combination will require certain mini-mum values of horizontal and vertical spacings of the power

Table 1 Swing angle-clearance combinations adopted for Indian transmission lines

Swing Angle, degree Live Metal Clearance, mm

66 kVLines

132 kVLines

220 kVLines

400 kVLines

0 915 1530 2130 3050

15 915 1530 2130 —

22 — — — 3050

30 760 1370 1830 —

44 — — — 1860

45 610 1220 1675 —

Figure 1 Effect of tower hamper and X-arm slopes on conductor spacings for barrel type tower

22 IE(I) Journal-ID

conductors. If the horizontal and vertical spacing requirementsfor each of the three (or four) swing angle-clearance combinationsspecified for the lines of a particular voltage (eg, 66kV) as aboveare determined, it can be seen that only one of the combinations(generally, with higher swing angle) will be critical for the re-quirement of (maximum) horizontal spacing while some othercombination (generally with lower seing angle) will be critical forthe vertical spacing, for the given values of α and α′. Thus, forthe selected values of α and α′, only two combinations wouldnormally be critical for fixing tower configuration while theremaining combinations, will require spacings which are less thanthe critical values and thus play no part in deciding the towerconfiguration.

The commonly used, practical value of α is between 0° and +15°while the value of α′ may range between +5° and +20° for Barreltype towers and between 0° and −20° for corset type tower. If thecritically of all the swing angle-clearance combinations (specifiedfor a particular line voltage) could be examined over the aforesaidpractical range of α and α′, it will reveal whether all the specifiedcombination do play a determining role for tower configurationor one/two of them, are not critical and could be dispensed with.

Considering a typical case of suspension tower, it can be shownthat the horizontal and vertical spacings of the phase conductorsare given by :

Ch = 2 [(√l2 + r2) sin (θ ± Φ) + cos (θ ± Φ) tan α′

+

l0 tan α′ + c sec α′ + h] (1)

Cv = (√l2 + r2) cos (θ ± Φ + sin (θ ± Φ tan α +

c sec α + l0 (2)Using these expressions, the requirement of horizontal spacingsfor each specified swing angle (with corresponding live metalclearance) for the aforesaid range of α′, are shown in the follow-ing figures :

�� Figure 3(a) - 66kV lines (barrel type towers)

�� Figure 3(b) - 132kV lines (barrel type towers)

�� Figure 3(c) - 220 kV lines (barrel type towers)

�� Figure 3(d) - 400 kV double circuit lines with barrel typetowers

�� Figure 3(e) - 400 kV single circuit lines with corset typetowers

Figure 2 Effect of slope of tower hamper on conductor spacing, Ch, for corset type tower Figure 3(a) Variation of horizontal spacing, Ch, with the slope of Tower

Hamper (66 kV lines)

Figure 3(b) Variation of horizontal spacing, Ch, with the slope of Tower Hamper (132 kV lines)

Figure 3(c) Variation of horizontal spacing, Ch, with the slope of Tower Hamper (220 kV lines)

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Similarly, the requirement of vertical spacings for each specifiedswing angle of α, are shown in the following Figures (there beingno vertical spacing for a corset type tower):

�� Figure 4(a) - 66kV lines (barrel type towers)

�� Figure 4(b) - 132 kV lines (barrel type towers)

�� Figure 4(c) - 220 kV lines (barrel type towers)

�� Figure 4(d) - 400 kV double circuit lines with barrel typetowers

The aforesaid analysis is based on the values of relevant dimen-sions as shown in Table 2.

Table 2 Typical values of relevant dimensions

Item Typical Value for Line Voltage

66 kV 132 kV 220 kV 400 kV

Swing length of suspensionstring, l, cm

97 163 234 385

Transverse projection of guardring, r, cm

10 12 15 20

Hanger length of suspensionstring, l0, cm

5 5 10 35

Critical half-width of towerhamper, h, cm

50 75 85 100

Figure 3(d) Variation of horizontal spacing, Ch, with the slope of Tower Hamper (400 kv line — barrel type tower)

Figure 3(e) Variation of horizontal spacing, Ch, with the slope of Tower Hamper (400 kV line — corset type tower)

Figure 4(a) Variation of vertical spacing, Cv, with the slope of underneath X-arm for (66 kV lines)

Figure 4(b) Variation of vertical spacing, Cv, with the slope of underneath X-arm for (132 kV lines)

Figure 4(c) Variation of vertical spacing, Cv, with the slope of underneath X-arm for (220 kV lines)

Figure 4(d) Variation of vertical spacing, Cv, with the slope of underneath X-arm for (400 kV lines — barrel type tower)

24 IE(I) Journal-ID

CRITICALITY OF SPECIFIED SWINGANGLE-CLEARANCE COMBINATIONS

A close examination of the Figures 3 and 4 reveals the followingfacts in respect of swing angle-clearance combinations (denotedonly by corresponding Swing angles in the following paragraphs)specified for the Indian transmission lines of different voltages:

66kV lines [Figures 3(a) and 4(a)]:

�� For deciding horizontal spacing, the swing angle of 45° iscritical for the entire range of α′ except for α′ in a small rangeof 18° to 20° where a 30° swing angle requires only amarginally (less than 1%) higher value of horizontal spacing.

�� For deciding vertical spacing, the swing angle of 15° iscritical for the entire range of α expect for α in a small rangeof 5° to 7° where 15° swing angle requires a marginally (lessthat 3%) higher value of horizontal spacing.

132 kV lines [Figures 3(b) and 4(b)]:

�� For deciding horizontal spacing, the swing angle of 45° iscritical for the entire range of α′.

�� For deciding vertical spacing, the swing angle of 15° iscritical for the entire range of α expect for α in a small rangeof 5° to 7° where 0° swing angle requires a marginally (lessthan 2%) higher value of horizontal spacing.

220 kV lines [Figures 3(c) and 4(c)]:


�� For deciding vertical spacing, the swing angle of 15° iscritical for the entire range of α expect for α in a small rangeof 5° to 7° where 0° swing angle requires a marginally (lessthan 1.5%) higher value of horizontal spacing.

400 kV double circuit lines on barrel type of tower [Figures 3(d)and 4(d)]:


�� For deciding vertical spacing, the swing angle of 0° is criticalfor most of the range of α expect for α′ in a small range of16° to 20° where 22° swing angle requires a marginally (lessthan 1.5%) higher value of horizontal spacing.

400 kV single circuit lines on corset type tower [Figure 3(e)]

�� For deciding horizontal spacing, the swing angle of 44° iscritical for the entire range of α′ except for α′ in a small rangeof 0° to − 3° where a 22° swing angle requires only amarginally (less than 0.5%) higher value of horizontalspacing.

OBSERVATIONS

On the basis of criticality of specified swing angle-clearancecombinations on Indian transmission lines as explained above andacknowledging that a marginal reduction of less that 3% in thespacings will not materially/practically affect the performance ofthe transmission lines, it can be noted that the following swing

angle-clearance combinations could adequately determine theoptimum tower configurations, as the other specified combina-tions do not play any role in affecting tower configuration :

66 kV lines on barrel type towers:

�� Swing angle = 45°, Live metal clearance = 610 mm


132 kV lines on barrel type towers :

�� Swing angle - 45°, Live metal clearance = 1220 mm


220 kV lines on barrel type towers:



400 kV DC lines on barrel type towers:



400 kV SC lines on corset type towers :


CONCLUSIONS

On the basis of aforesaid analysis, it can be seen that a maximumof two swing angle-clearance combinations, if judiciouslyselected, could completely and adequately determine optimumtower configuration for a pre-specified level of performance(flashover probability) of the transmission lines and the remain-ing (one or two) presently specified combinations could be dis-pensed with, without jeopardizing the reliability of the lines.

The analysis presented in this paper is based on the configurationof a suspension tower. However, it can be shown that similarresults would be obtained for tension towers also.

This analysis is also based on the presumptions that :

�� Live metal clearances presently specified with differentswing angle (for different voltage lines) are properlyco-coordinated for the pre-specified level of flashoverprobability.

�� 66 kV SC/DC lines, 132 kV SC/DC lines, 220 kV SC/DClines and 400 kV DC lines use standard barrel type towersand 400 kV SC lines use corset type towers.

�� The values of α′ and α are within the practical range assumedin the analysis.

REFERENCES1. ‘Transmission Line Manual.’ (Book) Publication No 268, Central Board ofIrrigation and Power, New Delhi.

2. S S Murthy and A R Santhakumar. ‘Transmission Line Structures.’ (Book)McGraw-Hill Book Company, Singapore 1990.

3. V N Rikh. ‘Economic Stranding and Size of ACSR for H V Power Lines.’Journal of The Institution of Engineers (India), part EL-3, vol 53, February 1973,pp 127-134.

4. IS802 (Part 1/Sec 1) : 199, Indian Standard on ‘Use of Structural Steel inOverhead Transmission Line Towers-Code of Practice.’ Bureau of Indian Stand-ards, New Delhi.

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Education

Swing angle