Power System Analysis

1. POWER SYSTEM
ANALYSIS

2. CHAPTER NO # 5
LINE CONSTANTS
Equivalent to
Ch-09 (Electrical Design of Over Head Lines)
In “Principles of Power System by V.K. Mehta and Rohit Mehta”

3. Overview
• As the overhead transmission line will consist of a group of wires running parallel to each other,
carried on supports which provide insulation between the various conductors and between each
conductor and earth
• The conductors will have a definite resistance depending upon their dimensions and the material
from which they are made and also, since the magnetic field produced by the current in one
conductor will link with the others, there will be an inductance associated with each wire
• Moreover, there will be a capacitance between the pairs of conductors and between each
conductor and earth. Finally, the insulation will not be perfect and will consequently carry a
leakage current to earth, this latter effect can be represented by assuming a leakage resistance to
be connected between the wire and earth
• In order that the line may be considered as part of a complete power system the values of the
above quantities must be known and so will calculate them in this chapter

4. Conductor Material & Construction
• The two most common materials in use are hard-drawn copper and aluminum.
• Aluminum has the advantage of high conductivity and low weight and is therefore suitable for
long spans, in spite of the fact that it also has a high coefficient of expansion and a low tensile
strength
• Either copper or aluminum may be used for short spans, but fro high voltage work where long
spans are involved aluminum conductors with a steel core added to provide strength are almost
universally used
• Copper equivalent area: it is convenient to refer to the area of an aluminum conductor in terms
of area of a copper conductor having the same conductor
• Stranded rather than solid conductors are usually used, each conductor being formed from a
number of separate strands
• In case of steel-cored aluminum conductors the central strand or (strands) is steel. The main
reason for the use of stranded conductor is to avoid vibration troubles which may lead to a solid
conductor breaking at the supports, they are also easier to handle and, for a given cross-
sectional area, they can be obtained in much grater lengths

5. Resistance
• When applying the above formula it may be necessary to take into account the fact that the
conductor may be stranded, thus increasing the resistance as compared with solid conductor
of equivalent cross-sectional area, the increase being of the order of 1 or 2%. A further
increase in resistance may be caused by ‘skin effect’
• SKIN EFFECT: When a conductor is carrying steady state current (d.c.) This current is uniformly
distributed over the whole section on the conductor. However, an alternating current flowing
through the conductor doesn’t distribute uniformly, rather than it has the tendency to
concentrate near the surface of the conductor. The tendency of alternating current near the
surface of a conductor is known as Skin Effect
• The ‘skin effect‘ increase with permeability and conductor cross-section and also with the
frequency. Because of its dependence on cross-section it is much smaller with stranded than
with solid conductors.

6. Inductance of a Single phase Overhead Line

9. Inductance of a three-phase Overhead Line

10. Now, for a three conductor system, the sum of
the instantaneous current at any instant is
zero and therefore the last term in the above
expression is zero , the physical significance of
this is that the total flux surrounding the three
conductor is zero

11. Equilateral Spacing

12. Equalisation of Reactance Drops by Transposition

16. Multiconductor Lines

17. Capacitance of a Single Phase Overhead Line

18. Capacitance of a Three-phase Line

19. Useful values of Inductance & Capacitance
• Basically we have taken two different values of spacing and conductor diameter and we have
came to the idea that no matter what is the value of the spacing and conductor diameter, the
inductor and capacitor values are same and also LC values came out to be the same
• 1st considered Low line voltage with large conductor, say 25mm diameter and spacing of
0.67m which is about minimum met within practice. Then d/r = 670/12.5 = 53.5 and log d/r
=3.98; this gives a value of L = 8.96 x 10^-4 henrys/km and C = 1.4 x 10^-8 farads/km.
• 2nd ;we take the case of a British Grid Line with a spacing of 4m and a conductor diameter of
20mm. The calculated values are L = 8.2 x 10-4 henrys/km and C = 1.5 x 10-8 farads/meter