Power Systems : Fundamentals of Power System & Power Transmission

By Aman Agrawal|Updated : July 4th, 2022

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Transmission lines are the most essential part of power transmission systems. Transmission of bulk power can be accomplished either by alternating current (ac) or direct current (dc), using overhead lines, or underground cables. A transmission line is characterized by four parameters:

  1. Series branch resistance
  2. Series branch inductance
  3. Shunt branch capacitance
  4. Shunt branch conductance

The performance of the transmission line depends on these parameters.

The shunt capacitance increases with an increase in the magnitude of the operating voltage. The series resistance and the shunt conductance are the least important parameters as their effect on the transmission capacity is relatively very less. However, the series resistance completely determines the real power transmission  loss and hence, its presence must be considered. The shunt conductance accounts for the resistive leakage current. The leakage current mainly flows along the insulator strings and ionized pathways in the air, and changes with change in the weather, atmospheric humidity, pollution, and salt content. The effect of the shunt conductance under normal operating conditions is usually neglected.

1.1.  Conductors Used in Transmission Lines:

Although copper has a much higher conductivity, aluminum conductors are normally used for overhead transmission lines. An aluminum conductor is lighter, cheaper, and has a larger diameter than a copper conductor of the same resistance. Larger diameter results in a lower voltage gradient at the surface of the conductor and reduces undesirable effects like corona. Moreover, the supply of aluminum is abundant while that of copper is limited.

Stranded conductors provide flexibility when suspended from tower cross arms by insulator strings. Stranded conductors are assembled by winding wires of small diameters in layers, with alternate layers wound in the opposite direction to prevent unwinding and to coincide the radius of outer layer with the inner radius of the next layer. Electrically, each strand in the conductor provides a parallel path for the flow of current. Thus, using this process flexible conductors are built with larger cross-sectional area.

The advantage of having conductors with large diameters is that the electrical stress is reduced, thereby minimizing the occurrence of the corona effect on the line.

Aluminum-conductor steel-reinforced (ACSR):

Aluminum conductor steel reinforced (ACSR) cables consists of stranded steel wires having greater mechanical strength which are surrounded by current-carrying layers of aluminum strands and are most commonly used in overhead transmission lines.

Figure below shows the cross section of an ACSR cable with central core of seven steel strands and 24 aluminum strands in the two outer layers.


Resistance offered by Transmission Line:

Resistance causes power loss in a transmission line. Direct-current resistance Rdc, is obtained from the formula


where ‘ρ’ is the resistivity of the conductor material in Ω-m

‘l’ is the length of the conductor in m

‘A’ is the cross-sectional area of the conductor in m2

Effect of Non-uniform Distribution of Current:

Distribution of direct current across the cross section of a conductor is uniform. When an alternating current flows through a conductor, distribution of current across its cross section becomes non-uniform. The non-uniform distribution of alternating current in a conductor is due to skin effect.

The factors which govern the skin effect are as follows:

  1. Higher the frequency, more will be the skin effect.
  2. Larger the diameter of conductor, higher will be the skin effect.
  3. Skin effect occurs more in solid conductors than in stranded conductors.
  4. Distance between conductors.
  5. Resistivity of the material.
  6. Permeability of the material.

Proximity effect: Consider a transmission line having two conductor’s ‘A’ and ‘B’ of equal cross-sectional area. Line conductor’s ‘A’ and ‘B’ are divided into three equal sections named 1, 2, 3 and 1’, 2’, 3’ respectively.



When current flows through Conductor ‘A’, the flux generated around it links with Conductor ‘B’. Since the flux linking another conductor progressively increases while moving forward, hence inductance also increases accordingly. Thus, the density of the current flowing through the conductor is highest at nearby position and least at farther point of another conductor, resulting in uneven distribution of the current in the conductor cross section. Hence, proximity effect becomes more predominant as the distance between the conductors is reduced. Like the skin effect, the following factors which govern the proximity effect are as follows:

  1. Higher the frequency, more will be the proximity effect.
  2. Larger the diameter of conductor, higher will be the proximity effect.
  3. Distance between conductors.
  4. Resistivity of the material.
  5. Permeability of the material.

In overhead transmission lines, with normal spacing, the proximity effect is assumed to be negligible. However, in underground cables, where the distance between the conductors is small, proximity effect is taken into consideration.

Both the skin effect and proximity effect leads to the non-uniform current distribution in a conductor which results in an increase in the effective conductor resistance. At frequency of 50 Hz or 60 Hz, the ac resistance, Rac is approximately 2% higher than the dc resistance, Rdc.

Line Conductance:

For overhead lines, the real power loss is due to leakage current in the insulator and due to corona. The leakage current varies depending on the environmental conditions such as dirt, salt, and other contaminants, and the meteorological conditions such as temperature and humidity around the conductor.

When surface potential gradient of the conductor exceeds the dielectric strength of the surrounding air, ionization of the air space around the conductor takes place and this phenomenon is known as corona. Corona produces power loss, known as corona loss, owing to weather conditions and conductor surface irregularities. The effect of shunt conductance under normal operating conditions is usually neglected because it is negligible.


The transmission line parameters are resistance, inductance, and capacitance are referred as lumped parameters but uniformly distributed along the length of the line. However, the use of lumped parameters gives good accuracy for short lines of lengths less than 80 km and medium lines of lengths roughly between 80 km and 240 km.

For short length lines, the value of shunt capacitance is very small, and it can be neglected without loss of accuracy. For short lines, only the series resistance and series inductance of the total length of the line are considered.

A medium length lines can be represented by the series resistance and series inductance of the total length of the line as lumped parameters and half the total capacitance of the line lumped at each end of the line.

A Long length lines can be represented by the series resistance, series inductance as well as shunt capacitance as well as shunt conductance.

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