The document discusses swing angle-clearance combinations specified for transmission lines in India. It analyzes how the combinations impact tower configuration and whether all specified combinations are necessary. The analysis shows that for most line voltages, only two judiciously selected swing angle-clearance combinations are sufficient to determine optimal tower configuration. The remaining extra combinations specified do not affect tower design and could be removed without compromising reliability. Using only two critical combinations could simplify transmission line design processes.

1. Design of Transmission Lines in India : a Review of Multiple
Swing Angle-clearance Combinations
Dr V N Rikh, Fellow
Proper live metal clearances have to be maintained under various swing angles of the suspension insulator
strings/jumper loops on a tower, in order to ensure a reliable performance of the transmission lines. The required
swing angle-clearance combinations for lines of different voltages are determined on the basis of a pre-specified
criterion of flashover probability. These combinations decide horizontal and vertical spacing of the power
conductors 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 paper
attempts to prove that if even two judiciously selected swing angle-clearance combinations are used, they would
adequately determine optimum tower configuration and the remaining extra combinations presently specified could
be dispensed with, without jeopardizing the reliability of the lines.
Keywords : Transmission line; Line insulation; Swing angle; Line metal clearances
NOTATIONS INTRODUCTION
C0 , C15 , C10, etc : location of critical live metal part of the One of the most important criteria for ensuring a reliable perform-
phase power conductor with swing angles ance of transmission lines under all weather conditions, is to
of 0°, 15°, 30° etc ensure that proper live metal (conductor to nearest earthed parts
L0 , L15 , L30, etc : live-metal clearances specified for swing of the tower structure) clearances are maintained under various
angles of 0°, 15°, 30° etc, cm angles (depending on wind speeds) of swing of the suspension
c : minimum clearance between the live metal insulator strings for a suspension tower (or the jumper loops for
parts phase power conductor and the nearest a tension tower). The required live-metal clearances for different
(carthed) part of the tower structure or live- angles of swing of suspension insulator strings (or jumper loops
metal clearance, cm for tension towers) are determined on the basis of a pre-specified
h : half width of the tower hamper at the critical criterion of flashover probability. When the suspension strings,
point (where the clearance arc from the supporting the power conductors, hang vertically under ‘no-
swung, live metal parts touches it), cm wind’ conditions, the live-metal clearance is maintained at a value
l : swinging length of the suspension string that ensures a probability of flashover across the air-gap within a
duly adjusted for any longitudinal (to the pre-specified value of, say, less than 2%. As the string/conductor
attachment point, swings toward the tower body under the influ-
string axis) projection of the guard ring/
ence of the wind, the critical value of flashover voltage gradient
bandle spacer, cm
across the gap correspondingly increases due to faster de-ioniza-
lo : length of hanger of the suspension tion of the air. This results in a reduced requirement of live-metal
string, cm clearances under higher wind velocities (and consequently bigger
r : transverse (to the string axis) projection, if swing angles of the string/conductor attachment points) to ensure
any, of the critical point of the guard the same level of pre-specified flashover probability across the
ring/bundle spacer, cm air- gap.
α : angle at which the uppermost (nearest to the
conductor) structural member of the under- The swing angle-clearance combinations presently adopted for
neath cross-arm is inclined to horizontal Indian transmission lines are based on the aforesaid logic.
plane, degrees Usually three to five swing angle-clearance combinations are
specified for transmission lines of each voltage on the basis of
α′ : angle at which the nearest structural mem- detailed analysis of prevailing weather conditions and flashover
ber of the tower hamper is inclined to the characteristics of air-gaps. The values of these swing angle-
vertical plane, degrees
clearance combinations commonly specified in India1, are shown
θ : angle of swing of the suspension insulator in Table 1.
string or of the jumper loop of tension insu-
lator string, degrees These combinations have yielded a reasonably satisfactory per-
Φ : tan − 1 [r ⁄ √ (r2 + l2)] formance of the transmission lines in this country over several
 decades.
Dr V N Rikh resides at 188-A, Saket, Meerut 250 003. The 66kV, 132kV and 220kV transmission lines in India (single
This paper was received on September 26, 2003. Written discussion on this paper circuit as well as double circuit) commonly use self-supporting
will be received until July 31, 2004.
barrel type towers. However, while 400kV double circuit Indian
Vol 85, May 2004 21

2. Table 1 Swing angle-clearance combinations adopted for Indian On the other hand, with a given value of swing angle-clearance
transmission lines combination;
Swing Angle, degree Live Metal Clearance, mm l An increase in the outward (towards the conductor, eg, in
66 kV 132 kV 220 kV 400 kV
the Barrel type towers)) slope α′ of the tower hamper,
Lines Lines Lines Lines increases the horizontal spacing while an increased inward
0 915 1530 2130 3050 (away from the conductor, eg, in a corset type tower) slope
15 915 1530 2130 — α′ of the tower hamper reduces the horizontal spacing of the
22 — — — 3050
conductors, and
30 760 1370 1830 — l An increase in the upward (towards the conductor) slope α
44 — — — 1860 of the uppermost member of underneath cross-arm results in
45 610 1220 1675 —
an increased vertical spacing of the conductors. As per
prevalent design practice, a downward slope of the
lines also use barrel type towers, the 400kV single circuit lines underneath cross-arm member is not adopted.
commonly use corset (or Wasp-waisted) type of towers. The effect of the slopes (towards the phase conductor/s) of the
A study of swing angle-clearance combinations adopted in other tower hamper as well as that of the nearest member of underneath
countries reveals that, in many countries, generally only two and cross arm, on the horizontal and vertical conductor spacings, is
sometimes a maximum of three, combinations are specified for illustrated for a Barrel type tower in Figure 1.
designing tower configuration. This paper therefore attempts to In case of a corset type tower, the slope of Tower Hamper is away
analyze the impact of each of the combinations (shown in Table from the (outer) phase conductor/s and its effect on the horizontal
1) on the tower configuration for Indian transmission lines, and conductor can be visualized from a typical Figure 2. As the corset
determine whether all these combinations play a critical role in type tower is used for single circuit lines (usually of 400kV), there
determining tower configuration/s or some of these (combina- is no vertical formation of the conductors.
tions) could be dispensed with, without jeopardizing reliability of
the transmission lines. IMPACT OF SWING ANGLE-CLEARANCE
COMBINATIONS ON THE TOWER CONFIGURATION
PARAMETERS AFFECTING TOWER
CONFIGURATION As explained above, for any given values of α and α′, each
swing angle-clearance combination will require certain mini-
The swing angle-clearance combinations, along with the follow- mum values of horizontal and vertical spacings of the power
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 therefore
the weight/cost of the towers;
l The slope α and α′ (to the vertical plane) of the outermost
(nearest to the conductor) structural member of the tower
hamper, and
l The slope α (to the horizontal plane) of the uppermost
(nearest to the conductor) structural member of the
underneath cross-arm.
The values of α and α′ are determined in the process of economic
optimization of tower configuration.
For any given values of α′,
l An increase in (inward) swing-angle, θ, of the insulator string
(or, jumper loop, for a tension tower) requires a
corresponding increase in the horizontal spacing of the phase
conductor/s maintain the specified live-metal clearance,
Similarly, any increase in the live-metal clearance, c, requires
a corresponding increase in the horizontal spacing.
l 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 a
tension tower), though an increase in the live-metal clearance
c, still requires a corresponding increase in the vertical Figure 1 Effect of tower hamper and X-arm slopes on conductor spacings
spacing. for barrel type tower
22 IE(I) Journal-ID

3. 
Cv = (√ 2 + r2) cos (θ ± Φ + sin (θ ± Φ tan α +


l  
c sec α + l0 (2)
Using these expressions, the requirement of horizontal spacings
for each specified swing angle (with corresponding live metal
clearance) for the aforesaid range of α′, are shown in the follow-
ing figures :
l Figure 3(a) - 66kV lines (barrel type towers)
l Figure 3(b) - 132kV lines (barrel type towers)
l Figure 3(c) - 220 kV lines (barrel type towers)
l Figure 3(d) - 400 kV double circuit lines with barrel type
towers
l Figure 3(e) - 400 kV single circuit lines with corset type
towers
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)
conductors. If the horizontal and vertical spacing requirements
for each of the three (or four) swing angle-clearance combinations
specified for the lines of a particular voltage (eg, 66kV) as above
are 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 other
combination (generally with lower seing angle) will be critical for
the vertical spacing, for the given values of α and α′. Thus, for
the selected values of α and α′, only two combinations would
normally be critical for fixing tower configuration while the
remaining combinations, will require spacings which are less than
the critical values and thus play no part in deciding the tower
configuration. Figure 3(b) Variation of horizontal spacing, Ch , with the slope of Tower
Hamper (132 kV lines)
The commonly used, practical value of α is between 0° and +15°
while the value of α′ may range between +5° and +20° for Barrel
type towers and between 0° and −20° for corset type tower. If the
critically of all the swing angle-clearance combinations (specified
for a particular line voltage) could be examined over the aforesaid
practical range of α and α′, it will reveal whether all the specified
combination do play a determining role for tower configuration
or one/two of them, are not critical and could be dispensed with.
Considering a typical case of suspension tower, it can be shown
that the horizontal and vertical spacings of the phase conductors
are given by :
 
Ch = 2 [(√ 2 + r2) sin (θ ± Φ) + cos (θ ± Φ) tan α′ +

l   Figure 3(c) Variation of horizontal spacing, Ch , with the slope of Tower
l0 tan α′ + c sec α′ + h] (1) Hamper (220 kV lines)
Vol 85, May 2004 23

4. Figure 3(d) Variation of horizontal spacing, Ch , with the slope of Tower
Figure 4(b) Variation of vertical spacing, Cv, with the slope of
Hamper (400 kv line — barrel type tower)
underneath X-arm for (132 kV lines)
Figure 3(e) Variation of horizontal spacing, Ch , with the slope of Tower
Hamper (400 kV line — corset type tower)
Figure 4(c) Variation of vertical spacing, Cv, with the slope of
Similarly, the requirement of vertical spacings for each specified underneath X-arm for (220 kV lines)
swing angle of α, are shown in the following Figures (there being
no vertical spacing for a corset type tower):
l Figure 4(a) - 66kV lines (barrel type towers)
l Figure 4(b) - 132 kV lines (barrel type towers)
l Figure 4(c) - 220 kV lines (barrel type towers)
l Figure 4(d) - 400 kV double circuit lines with barrel type
towers
The aforesaid analysis is based on the values of relevant dimen-
sions as shown in Table 2.
Figure 4(d) Variation of vertical spacing, Cv, with the slope of
underneath X-arm for (400 kV lines — barrel type tower)
Table 2 Typical values of relevant dimensions
Item Typical Value for Line Voltage
66 kV 132 kV 220 kV 400 kV
Swing length of suspension 97 163 234 385
string, l, cm
Transverse projection of guard 10 12 15 20
ring, r, cm
Hanger length of suspension 5 5 10 35
string, l0, cm
Figure 4(a) Variation of vertical spacing, Cv, with the slope of Critical half-width of tower 50 75 85 100
underneath X-arm for (66 kV lines) hamper, h, cm
24 IE(I) Journal-ID

5. CRITICALITY OF SPECIFIED SWING angle-clearance combinations could adequately determine the
ANGLE-CLEARANCE COMBINATIONS optimum tower configurations, as the other specified combina-
A close examination of the Figures 3 and 4 reveals the following tions do not play any role in affecting tower configuration :
facts in respect of swing angle-clearance combinations (denoted 66 kV lines on barrel type towers:
only by corresponding Swing angles in the following paragraphs) l Swing angle = 45°, Live metal clearance = 610 mm
specified for the Indian transmission lines of different voltages:
l Swing angle = 15°, Live metal clearance = 915 mm
66kV lines [Figures 3(a) and 4(a)]:
132 kV lines on barrel type towers :
l For deciding horizontal spacing, the swing angle of 45° is
critical for the entire range of α′ except for α′ in a small range l Swing angle - 45°, Live metal clearance = 1220 mm
of 18° to 20° where a 30° swing angle requires only a l Swing angle = 15°, Live metal clearance = 1530 mm
marginally (less than 1%) higher value of horizontal spacing. 220 kV lines on barrel type towers:
l For deciding vertical spacing, the swing angle of 15° is l Swing angle = 45°, Live metal clearance = 1675 mm
critical for the entire range of α expect for α in a small range
of 5° to 7° where 15° swing angle requires a marginally (less
l Swing angle = 15°, Live metal clearance = 2130 mm
that 3%) higher value of horizontal spacing. 400 kV DC lines on barrel type towers:
132 kV lines [Figures 3(b) and 4(b)]: l Swing angle = 22°, Live metal clearance = 3050 mm
l For deciding horizontal spacing, the swing angle of 45° is l Swing angle = 0°, Live metal clearance = 3050 mm
critical for the entire range of α′. 400 kV SC lines on corset type towers :
l For deciding vertical spacing, the swing angle of 15° is l Swing angle = 44°, Live metal clearance = 1840 mm
critical for the entire range of α expect for α in a small range
CONCLUSIONS
of 5° to 7° where 0° swing angle requires a marginally (less
than 2%) higher value of horizontal spacing. On the basis of aforesaid analysis, it can be seen that a maximum
of two swing angle-clearance combinations, if judiciously
220 kV lines [Figures 3(c) and 4(c)]:
selected, could completely and adequately determine optimum
l For deciding horizontal spacing, the swing angle of 45° is tower configuration for a pre-specified level of performance
critical for the entire range of α′. (flashover probability) of the transmission lines and the remain-
l For deciding vertical spacing, the swing angle of 15° is ing (one or two) presently specified combinations could be dis-
critical for the entire range of α expect for α in a small range pensed with, without jeopardizing the reliability of the lines.
of 5° to 7° where 0° swing angle requires a marginally (less The analysis presented in this paper is based on the configuration
than 1.5%) higher value of horizontal spacing. of a suspension tower. However, it can be shown that similar
400 kV double circuit lines on barrel type of tower [Figures 3(d) results would be obtained for tension towers also.
and 4(d)]: This analysis is also based on the presumptions that :
l For deciding horizontal spacing, the swing angle of 22° is l Live metal clearances presently specified with different
critical for the entire range of α′. swing angle (for different voltage lines) are properly
l For deciding vertical spacing, the swing angle of 0° is critical co-coordinated for the pre-specified level of flashover
probability.
for most of the range of α expect for α′ in a small range of
16° to 20° where 22° swing angle requires a marginally (less l 66 kV SC/DC lines, 132 kV SC/DC lines, 220 kV SC/DC
than 1.5%) higher value of horizontal spacing. lines and 400 kV DC lines use standard barrel type towers
and 400 kV SC lines use corset type towers.
400 kV single circuit lines on corset type tower [Figure 3(e)]
l For deciding horizontal spacing, the swing angle of 44° is
l The values of α′ and α are within the practical range assumed
critical for the entire range of α′ except for α′ in a small range in the analysis.
of 0° to − 3° where a 22° swing angle requires only a REFERENCES
marginally (less than 0.5%) higher value of horizontal 1. ‘Transmission Line Manual.’ (Book) Publication No 268, Central Board of
spacing. Irrigation and Power, New Delhi.
2. S S Murthy and A R Santhakumar. ‘Transmission Line Structures.’ (Book)
OBSERVATIONS McGraw-Hill Book Company, Singapore 1990.
On the basis of criticality of specified swing angle-clearance 3. V N Rikh. ‘Economic Stranding and Size of ACSR for H V Power Lines.’
combinations on Indian transmission lines as explained above and Journal of The Institution of Engineers (India), part EL-3, vol 53, February 1973,
pp 127-134.
acknowledging that a marginal reduction of less that 3% in the
4. IS802 (Part 1/Sec 1) : 199, Indian Standard on ‘Use of Structural Steel in
spacings will not materially/practically affect the performance of Overhead Transmission Line Towers-Code of Practice.’ Bureau of Indian Stand-
the transmission lines, it can be noted that the following swing ards, New Delhi.
Vol 85, May 2004 25