Normally, the horizontal and vertical spacing between the phase conductors on a transmission line is decided by the minimum clearances required between the conductors and the supporting towers. In practice, for insulator strings installed on suspension towers and the jumper loops used on the tension towers, two different swing angles with corresponding conductor-tower clearances are normally specified. Additionally, phase conductor spacing is also affected by the following factors:

• The bigger the angle of incline (with the horizontal plane) of the top-tie structural member of the bottom crossarm, the bigger the vertical distance has to be between any two crossarms to maintain the specified conductor-tower clearance. This results in an increase in vertical spacing of phase conductors.

• The bigger the angle of incline (with the horizontal plane) of the outer (nearest) structural member of the tower hamper, the farther away the conductor has to be placed from the tower to maintain the specified conductor-tower clearance. This results in an increase in horizontal spacing of phase conductors.

• To avoid exact verticality among phase conductors and thereby reducing the probability of clashing under galloping phenomenon, the middle crossarm is usually kept somewhat longer than the other two (top and bottom) crossarms. This also results in an increase in the horizontal spacing of phase conductors.

These considerations determine the normal conductor spacing on transmission line towers. However, for circuits in a hilly terrain where long spans are encountered, an allowance also has to be made for conductor galloping/ice accretion, while fixing the minimum values of horizontal and vertical conductor spacing.

Transmission Line Design Practice

Transmission line specifications adopted by utilities include empirical formulas that are developed using the operational experience for the location. As a result, regional and national variations exist. These formulas relate the conductor spacing to the maximum conductor sag; for example, the greater the conductor sag, the larger the conductor spacing.

While the greater sags used on longer spans require some increase in conductor spacing, the topology, that is, a combination of steep inclines with long spans, is an important aspect that generally necessitates a substantial increase in conductor spacing, especially vertical spacing. Topology is often not given due consideration.

Figure 1 illustrates the effect of a steep incline (large difference in levels of supports) on the conductor catenary in a transmission line span in a simplified manner. Fig. 1(a) shows span AB of a transmission line on level ground (rolling terrain) where AA' and BB' are the supporting towers (of the same height) at the same level on either side of the span. Position O is the null (or lowest) point of the conductor catenary, and OO' is the maximum conductor sag that is equal when measured from the conductor attachment point at either support. With level ground and equal tower heights, the minimum conductor-to-ground clearance generally also will be at the null point, as shown by OG.

In Fig. 1(b), the right-hand support BB' is located on the foot of an inclined span A'B' that has the same horizontal span-length (L) as span AB in Fig. 1(a). However, the support A₁A₁' at the other end of the span is now located at a considerably higher level due to the steep incline in the ground profile. The curve A₁'O₁B' shows a new shape of the conductor catenary, O₁ being the new null point of the catenary. It has been assumed that the minimum ground clearance, O₁G₁, will still be at the null point. Although, depending on the profile of the incline, it could also be elsewhere along the conductor catenary. As seen in Fig. 1(b), the maximum sag of the conductor catenary (i.e., the vertical distance between the null point and the conductor-attachment point at the support) is now different for the two supports. Its height, O₁'O₁, is much more than the higher support (tower A₁A₁').

Comparing Figs. 1(a) and 1(b), if one of the supports is placed at a higher level because of an incline in a span of the same horizontal length, then:

• The null point of the conductor catenary moves away from the higher support and toward the lower support. The quantum of such a movement depends on the difference in the levels of the two supports.

• The maximum value of sag (from the higher support to the null point) is considerably bigger as compared to the maximum sag with both the supports at the same level.

As the empirical formulas determine the minimum spacing requirement for conductor galloping/ice dropping considerations (relating the spacing with the maximum conductor sag), the increase in the maximum sag due to the steep incline thus necessitates conductor spacings that are considerably higher than those used in normal overhead line design. Unless the conductor spacings are decided at the design stage, with due consideration for the possible values of “span length-support level difference” combinations along the complete route of the transmission line, the line may encounter serious outage/conductor damage problems during its operation.

Application by Indian Power Utilities

The importance of this aspect is illustrated by following an example for a 400-kV transmission line in India. The empirical formulas commonly used in India for minimum requirements of conductor spacing from conductor galloping/ice dropping considerations are as follows:

Minimum horizontal spacing, C_h = 0.62 (v f+l_k) + V/150 meters (1)

Minimum vertical spacing, C_v = 0.75 (v f+l_k) + V/150 meters (2)

where, C_h = Horizontal spacing of conductors at the tower, m.

C_v = Vertical spacing of conductors at the tower, m.

f = Conductor sag at maximum temperature of 75°C and no wind, m.

l_k = Swinging length of suspension insulator string, m.

V = Voltage of the transmission line, m.

Figure 2 shows a barrel-type suspension tower for a typical Indian 400-kV double-circuit line where A, B and C indicate the conductor attachment points on the tower crossarms for the two circuits (1 and 2), each phase comprising bundle conductors. The horizontal and vertical conductor spacing also have been identified as C_h and C_v.

The dimensional characteristics of the typical Indian 400-kV line are:

• Normal span length: 400 m (1312 ft).

• Conductor: Twin ‘MOOSE’ ACSR bundle (in horizontal formation) with 0.45 m (1.5 ft) intra-group spacing.

• Swinging length of insulator string, l_k: 3.85 m (12.63 ft).

• “Swing angle/Electrical clearance” combinations: (a) Swing angle = 22° with minimum clearance = 3.05 m (10 ft).

(b) Swing angle = 44° with minimum clearance = 1.86 m (6.1 ft).

The normal horizontal and vertical conductor spacing adopted for these lines in plane areas, having in general a level rolling terrain, are C_h = 12.6 m (41.3 ft) and Cv = 7.4 m (24.3 ft).

Figure 3 shows the conductor spacings as obtained from the empirical formulas (1,2) for the typical Indian 400-kV line for different combinations in the practical range of span lengths — from 500 to 2000 m (1640 to 6562 ft) — and support level difference — from 0 to 100 m (328 ft). Fig. 3(a) shows the vertical spacing, and Fig. 3(b) shows the horizontal spacing. The normal values of these clearances adopted on Indian 400-kV lines are also shown in these figures.

A close examination of Fig. 3 reveals the following:

• To allow for conductor galloping/ice dropping, the required values of the vertical and horizontal conductor spacing increase sharply with the increase in span length.

• An increase in support level difference (steepness of incline) necessitates a further substantial increase in these spacings, especially in the lower range of span lengths.

• The normal value of 7.4 m (24.3 ft) vertical conductor-spacing for typical Indian 400-kV lines only satisfies the conductor galloping/ice dropping requirements for a span length of less than 700 m (2297 ft), having a support level difference of less than 50 m (164 ft). This vertical spacing is increased by up to 100% for spans in excess of 1750 m (5741 ft).

• The horizontal conductor spacing of 12.6 m (41.3 ft) normally provided for typical Indian 400-kV lines adequately meets the requirement of conductor galloping/ice dropping with the exception of span lengths in excess of 2000 m (6562 ft) span that have a difference in support level greater than 75 m (246 ft).

Summary

This example of Indian 400-kV transmission line design practice provides confirmation that where the line is routed through hilly terrain areas with steep inclines, the horizontal and vertical spacing of phase conductors needs to be properly determined at the design stage for the line route topology. Failure to do so would inevitably result in serious operational problems with frequent line trip-outs and severe conductor/tower damage.

Dr. V.N. Rikh was awarded a BE degree in 1953, ME degree in 1977 and Ph.D. degree in engineering and technology in 1986. Following a 36-year career with the U.P. State Electricity Board, one of India's largest public sector power undertakings, in which Rikh reached the position as chairman, he retired but continued to work as an advisor to many government/public power utilities, including Power Grid Corporation of India. With 48 years experience in power transmission and distribution systems, Rikh currently works as a consulting engineer with a number of consultancy groups in India. He has published more than 100 technical papers and presented numerous papers at national and international conferences (including CIGR…, IEEE, IEE and IE). In addition to a number of honors and awards in India, he represented India as an expert on CIGR… Study Committee 36.

vnrikh@yahoo.com