Class notes on electrical power transmission and distribution (for students, 6th semester)

Introduction to notes

The transmission line performance is based on its electrical parameters such as resistance, inductance and capacitance. As we know the transmission lines are used for delivering electrical power from one end to other end or one node to other node.

The path of power flow i.e. the transmission line can be represented as an electrical circuit having its parameters connected in a particular pattern. Since the transmission line consists of conductors carrying power, we need to calculate the resistance, inductance and capacitance of these conductors.

Resistance of transmission line

The resistance of the conductor (transmissmn line) can be determined by:

R = ρ × l / A

Where:

• ρ is the resistivity of the wire in Ω-m,
• i is the length m meters and
• A is the cross sectional area mm²

When alternating current flows trough a conductor, the current density is not uniform over the entire cross section but is somewhat higher at the surface.

Moreover in a stranded conductor, the length of each strand is more that the length of the composite conductor thus increasing the value of the resistance from that calculated.

Inductance of transmission line

In order to determine the inductance of transmission line, we shall first drive expression for the inductance of a solid conductor and it will be extended to a single phase transmission line. Then we shall derive expression for inductance of a group of conductors and then extend it to three-phase transmission line.

Inductance of solid conductor

The inductance of solid conductor can be determined by calculating the flux linkage due to current flowing and using.

L = λ / I

Where: L  is the inductance in Henry, λ is the flux linkage in Weber-turns and I is the phasor current in Ampere.

Inductance of solid conductor due to internal flux

Let us consider solid conductor of radius r [cm] and the current flowing I [A] as shown in figure above.

As we know Ampere’s law states that the magnetomotive forces mmf in ampere-turns around a closed path is equal to the net current in amperes enclosed in the path.