Transmission line Constants
The transmission lines are basically Electrical Circuits having distributed constants. These constants are
b) Inductance and
These constants or parameters are uniformly distributed along the entire length of the line and their concentration at any point is not possible.
The performance (Voltage regulation and Efficiency) of a transmission line depends to a considerable extent on these constants.
Therefore, it is very important to study the various factors effecting these constants.
These constants are usually expressed as resistance or Inductance or capacitance per kilometre.
Every Electrical Conductor offers opposition to the flow of current and this opposition is called the resistance.
In a single phase or 2 – wire DC line the loop resistance is taken as double of resistance of eighter Conductor but in 3 – phase System the resistance per phase is the resistance of eighter Conductor.
The steady direct Current will distribute itself uniformly over the whole cross section of a Conductor but alternating Current does not Distribute uniformly but tends to concentrate near the surface of a Conductor. In fact in AC system no current flow through are core and the entire Current is concentrated at the surface regions.
This phenomenon is called the skin effect and it causes the resistance to increase slightly, particularly when the diameter of the Conductor is large.
At low frequency this effect is very small, in fact it is only of importance with high frequencies or with solid Conductors of Larger X-section.
The skin Effect is much smaller with stranded Conductors than with solid Conductors.
It can increases with the increase in X-section, permeability and Supply frequency.
Inductance of a Transmission line
Inductance of a single – phase overhead Transmission line is given by the Equation
[ 1 + 4 log e d/r ] × 10^-7 H/m
Where r is the radius of Conductor and d is the spacing between Conductors in cm ( d being very large in comperison to r ).
Inductance of each Conductor in an equilaterally spaced Conductor three phase Transmission line is given by the Equation
[ 0.5 + 2 log e d/r ] × 10^-7 H/m
The Proximity effect also results in
non – uniform Distribution of current in
x – section of a Conductor.
So, like skin Effect, proximity effect affects the current Distribution and results in an increase in the resistance of the Conductor the decrease of self – Reactance.
The phenomenon is more pronounced for large Conductors, high frequencies and closed proximity. The magnitude of the effect, at normal supply frequencies in the case of the side spacing of Conductors Required for overhead Transmission lines, is so small that it can be ignored.
In case of stranded Conductors, the proximity Effect is substantially eliminated.
Capacitance of a Transmission line
Capacitance of a single phase Transmission line is given by
π e /log e d/r F/m.
Capacitance of equilaterally spaced line is given by
2π e / log e d/r F/m.
Transposition of Conductors
As already mentioned the Inductance and capacitance of each phase will be different in case of Conductors of three – phase line being spaced irregularly.
The apparent resistance of the Conductors is also affected on account of Transfer of power between the phases, which occur due to mutual Inductance.
Thus all the three line Constants are affected by irregular spacing of the Conductors in a 3 – phase line.
The unbalancing effect on account of irregular spacing of Conductors can be avoided by Transposition of Conductors, as shown in fig. 1.
Fig. 1 Transposition of a 3 – phase line
In practice the Conductors should be so transposed that each of three possible arrangement of Conductors exists for one – third of the total length of line.
An unbalanced System, my be Conductors symmetrically placed, cannot be Represented by three simple Inductances, without making transportation.
The effect of unbalanced Current is neutralised in case of Conductors bring transposed regularly at intervals.
The transposition of Conductors also reduced the disturbance to the nearby communication Circuits.
In composite line, the line carrying telephone line Conductors below the power line Conductors, it is also necessary to transposed the telephone line Conductors in order to keep down the disturbances.