TEXT 15. Sag and Tension of Conductor

The energized conductors of transmission and distribution lines must be placed to totally eliminate the possibility of injury to people. Overhead conductors, however, elongate with time, temperature, and tension, thereby changing their original positions after installation. Despite the effects of weather and loading on a line, the conductors must remain at safe distances from buildings, objects, and people or vehicles passing beneath the line at all times. To ensure this safety the position of the conductor between support points under all wind, ice, and temperature conditions must be known.

The future behavior of the conductor is determined through calculations commonly referred to as sag-tension calculations. These tension limits specify certain percentages of the conductor’s rated breaking strength that are not to be exceeded upon installation or during the life of the line. These conditions, along with the elastic and permanent elongation properties of the conductor, provide the basis for determinating the amount of resulting sag during installation and long-term operation of the line. Accurately determined initial sag limits are essential in the line design process. If the conductor is damaged or the initial sags are incorrect, the line clearances may be violated or the conductor may break during heavy ice or wind loadings.

A bare-stranded overhead conductor is normally held clear of objects, people, and other conductors by periodic attachment to insulators. The elevation differences between the supporting structures affect the shape of the conductor catenary. The catenary’s shape has a distinct effect on the sag and tension of the conductor, and therefore, must be determined using well-defined mathematical equations.

The shape of a catenary is a function of the conductor weight per unit length, w, the horizontal component of tension, H, span length, S, and the maximum sag of the conductor, D.

       Note that x is positive in either direction from the low point of the catenary. The expression to the right is an approximate parabolic equation based upon a MacLaurin expansion of the hyperbolic cosine. For a level span, the low point is in the centre, and the sag, D, is found by substituting x=S/2 in the preceding equations. The exact and approximate parabolic equations for sag become the following:

The ratio, H/w, is commonly referred to as the catenary constant. An increase in the catenary constant, having the units of length, causes the catenary curve to become shallower and the sag to decrease. Although it varies with conductor temperature, ice and wind loading, and time, the catenary constant typically has a value in the range of several thousand feet for most transmission-line catenaries. The approximate or parabolic expression is sufficiently accurate as long as the sag is less than 5% of the span length.

       When a conductor is covered with ice and/or is exposed to wind, the effective conductor weight per unit length increases. During occasions of heavy ice and/or wind load, the conductor catenary tension increases dramatically along with the loads on angle and dead end structures. Both the conductor and its supports can fail unless these high-tension conditions are considered in the line design. Note that the conductor length depends solely on span and sag. It is not directly dependent on conductor tension, weight, or temperature. The conductor slack is the conductor length minus the span length.

       In calculating sag and tension for extensible conductors, it is useful to add a step to the preceding calculation of sag and tension for elevated temperature. This added step allows a separation of thermal elongation and elastic elongation effects, and involves the calculation of a zero tension length, ZTL, at the conductor temperature of interest. This ZTL is the conductor length attained if the conductor is taken down from its supports and laid on the ground with no tension. By reducing the initial tension in the conductor to zero, the elastic elongation is also reduced to zero, shortening the conductor. It is possible, then, for the zero tension length to be less than span length.

       Sag-tension calculations are normally done numerically and allow the user to enter many different loading and conductor temperature conditions. Both initial and final conditions are calculated and multiple tension constraints can be specified. The complex stress-strain behavior of conductors can be modeled numerically, including both temperature, and elastic and plastic effects. For conductors consisting of two material, an initial and final curve for each included.

1. Read and translate the text.

2. Read the text again and find the reasons of

1). importance of accurate sag limits determining.

2). the conductor catenary tension increase.

3). sag-tension calculations done numerically.

3. Match the words from the text their corresponding definitions.

4. Find synonyms.

5. Put the following words in the correct order to form a sentence.

1). of ice/ conductors/ on overhead/ The formation/ has/ on line/ the influence/ design.

2). transmission/ Overhead/ uniform/ length/ their/ in weight/ are/ conductors/ along.

3). external/ used for/ lines/ insulation/This article/ discusses/ transmission.

4). mostly/ insulation/ has/ internal/ Equipment.

6. Make an oral summary of the text.