I have presented so far sag and tension calculation based on the linear cable model which does not account for plastic elongation in the conductor. In this post, I will introduce the three types of conductor models being used to predict the sag as well as the tension in transmission lines.
To understand those models, we need to grasp the two types of elongation that a conductor may experience.
Classifications of Conductor Elongation
The first type is the elastic elongation wherein it is reversible. It is composed of:
1. Linear Thermal Elongation
It is a reversible linear elongation due to temperature changes.
Conductors used in power lines will expand or contract with changes in the temperature. The rate of expansion or contraction is dependent on the conductor materials and of the degree of temperature change. For composite conductor like ACSR, the coefficient of thermal expansion (COE) of aluminum strands is different from that of steel. At knee-point temperature, the steel core will carry all the tension while in the aluminum strands will be zero.
2. Linear Elastic Strain
It is a reversible linear elongation due to tension change.
The conductor materials will follow the Hooke’s law at some point, wherein changes in the tension would also change the total conductor length. This elastic elongation is “spring-like”. Ideally, when the tension is removed the conductor will return to its original length.
B. PLASTIC ELONGATION
The second type is the plastic elongation wherein it is irreversible. It is composed of:
3. Strand Settlement and deformation (initial plastic elongation)
It is the rapid irreversible plastic elongation under initial loading ( initial tension of 15-20% of RTS ) due to a combination of strand settlement deformation, and rapid (<1 hour) metallurgical creep of aluminum wires during the process of stringing and sagging.
4. Short-time high-tension plastic elongation (Design Loading Plastic Elongation) –
After the conductor has been sagged and clipped, ice and/or wind may raise the tension
It is the rapid irreversible plastic elongation which occurs as the result of high conductor tension due to wind and ice loads.
5. Long-time “metallurgical” creep elongation (Creep Plastic Elongation)
After conductor has been sagged and clipped, the aluminum layers will continue to elongate plastically even for moderate everyday tensions of 15%-25% of RTS. Over 10 years or more, the plastic elongation of aluminum layers due to such long-time creep elongation may exceed that associated with high short-time loads. This is especially true in geographical areas not subject to ice or hurricane force winds.
Although relatively slow, it is the irreversible plastic elongation which occurs due to persistent moderate tension over the life of a transmission line.
3 Types of Conductor Models
1. LINEAR ELASTIC (LE) MODEL
In LE model, the conductors are modeled as linear springs with a single modulus of elasticity and single coefficient of thermal expansion. For composite conductor like ACSR, the effective modulus of elasticity and COE must be calculated due to the aluminum strands and steel core. You may recall the formulas for this in this post.
LE model ignores (1)”settlement & strand deformation”, (2) “short-time high tension elongation” and (3) “long-time metallurgical creep elongation”. (Refer to the figure above.)
2. SIMPLIFIED PLASTIC ELONGATION (SPE) MODEL
Same as in LE model, SPE models the conductors as linear springs. However, the
SPE model ignores (1)”settlement & strand deformation”, but accounts for (3) “short-time high tension elongation” and (5) “long-time metallurgical creep elongation” by using a typical value of plastic conductor elongation.
3. EXPERIMENTAL PLASTIC ELONGATION (EPE) MODEL
Overhead conductors are modeled as non-linear springs that elongate elastically as a function of tension, plastically as a function of tension and time, and thermally as a function of temperature. The non-linear behavior of steel core and aluminum layers can be modeled separately for ACSR.
Plastic elongation is calculated based on laboratory tests of the stranded conductor. For composite conductors, the elongation of each component is calculated separately.
Plastic elongation of the conductor due to (1)” settlement and strand deformation”, (3) “short-time high tension loads”, and (5) “long-time metallurgical creep elongation” is calculated for an assumed series of loading events over the life of the line. For composite conductor at high temperature, the bi-linear thermal elongation and any aluminum compression effects are calculated as a function of assumed loading history.
EPE model include all five as factors to affecting the sag and tension in the line.
All three elongation models assume linear elastic elongation under tensile load and linear thermal elongation due to changes in conductor temperature. They differ in the manner in which plastic elongation is calculated.
References: CIGRE. Sag-Tension Calculation Methods for Overhead Lines. 2016.