Electrical Power Systems

Analysis of Sag and Tension 403
When the ice coated conductor is acted upon by a light drift wind particularly where the ground
slopes at right angles to the transmission line vibration is initiated because wind travels up the
slope and appears to get underneath the conductor. The stranding of conductors significantly
contributes to these vibrations. These vibrations may cause flashover between conductors. It is
difficult to prevent these vibrations but horizontal configuration of transmission line can be
used to reduce the impact of galloping or dancing of conductors.
EXERCISE
15.1 Conductor diameter of an overhead transmission line is 1.95 cm and span between towers is
244 m. If the allowable tension is 3629 kg. ind (a) sag in still air condition without ice covering
(b) vertical sag when there is an ice covering of 0.96 cm radial thickness and a horizontal wind
pressure of 38.94 kg/m 2 of projected area. Weight of ice is 909.27 kg/m 3 (c) The line is carried by
insulator strings 1.45 m long. What should be the height of lowest cross–arm to give a minimum
ground clearance of 8 m under bad weather conditions? Weight of conductor is 0.847 kg/m.
Ans: (a) 1.74 m; (b) 3.37 m; (c) 12.82 m
15.2 An overhead transmission line is supported at a river crossing from two towers whose heights are
33.6 m and 29 m above water level. The allowable tension is 3404.69 kg and weight of conductor
is 0.849 kg/m. Determine (a) clearance between the lowest point on the conductor and water level
(b) horizontal distance of this point from the lower support. Given that span L = 336 m.
Ans: (a) 27.405 m; (b) 113.11 m
15.3 Determine the erection sag and tension of a transmission line at 65ºC in still air. The line has a
span of 300 m. ACSR conductor has the following data: Area = 240 mm 2 ; overall diameter =
20 mm; weight = 1.0 kg/m; ultimate strength = 8000 kg; coefficient of linear expansion = 18.44 ×
10 –5 /ºC; modulus of elasticity = 9320 kg/mm2 . Also assume radial thickness of ice is 1.0 cm and a
wind pressure 40 kg/m 2 of projected area and a temperature of –5ºC as the worst condition.
Weight of the ice is 910 kg/m 3 and factor of safety = 2.0. Ans: 20.76 m; 541.9 kg.
15.4 The weight of conductor of a overhead transmission line is 0.407 kg/m. The ultimate strength is
407.74 kg and factor of safety is 2.0. Span length is 160 m. Determine (a) sag, (b) total length of
the line between supports. Ans: (a) 6.38 m; (b) 160.73 m.
15.5 An overhead transmission line conductor weighs 0.35 kg/m. Ultimate strength is 800 kg and
factor of safety is 2.0. Span length is 160 m. One support is at a height 70 m from the ground.
Determine the minimum clearance from the ground and the lowest point of the catenary from the
supports if the second support is at a height (a) 40 m (b) 65 m from the ground.
Ans: (a) 40 m; (b) 64.14 m.
15.6 A overhead transmission line has a span of 275 m between level supports. The conductor has a
radius of 0.9765 cm and weighs 0.844 kg/m and has an ultimate breaking strength of 11925 kg.
Conductor has a radial covering of ice 0.953 cm thick and is subjected to a horizontal wind
pressure of 40 kg/m 2 of the ice covered projected area. actor of safety is 3.0. Weight of the ice is
913.5 kg/m3 . Determine (a) sag and (b) vertical sag Ans: (a) 5.36 m (b) 3.9 m.
15.7 An overhead transmission line over a hill side is supported by two 30 m high towers with a
gradient 1 in 20. The horizontal distance between the towers is 300 m. Weight of the conductor
is 1.492 kg/m and ultimate breaking strength is 4400 kg. The lowest conductor is fixed 6 m below
the top of each tower and factor of safety is 2.0. Determine (a) the clearance of the lowest point of
the conductor from the ground, and (b) the minimum ground clearance.
Ans: (a) 18.3 m; (b) 16.46 m.
15.8 A transmission line on a mountain side is supported between two points separated by a horizontal
distance of 400 m and at the heights of 900 m and 1150 m above sea level, respectively. Conductor