Transmission Line Parameters - What are they?

Generally, the electrical power is generated far away from the load centres. In order to transmit this generated power to the load centres transmission lines are used. The transmission line consists of conductors having a uniform cross-section throughout the line. These conductors are supported on towers and are spaced at a distance from each other. The air between the conductors acts as the insulating medium.

But when the electrical power is transmitted through the transmission lines, the receiving end wave of voltage and current is not similar to the sending end. This is due to the presents of electrical parameters or constants know as transmission line parameters.

Transmission Line Parameters or Constants :

The transmission lines are the electrical circuits having parameters or constants like resistance, inductance, capacitance and shunt conductance, which are distributed along the entire length of the line as shown below.

Resistance and inductance are the series parameters whereas capacitance and shunt conductance are the shunt parameters. Let us see briefly about various transmission line parameters.

Resistance :

The presence of resistance is due to the fact that every electric conductor offers some opposition to the flow of electric current through it. The resistance is the major cause of the power losses in the transmission line.

In general, the presence of resistance in the transmission line is due to the fact that every electric conductor offers some opposition to the flow of electric current through it. The resistance of the line is given by,

R = ρl/A

• ρ = Resistivity of the material
• l = Length of the conductor
• A = Area of the cross-section of the conductor.

So, the resistance increases with the length of the line and decreases with an increase in diameter (since the area of cross-section, a diameter) and it is independent of the distance between conductors.

The presence of resistance in the transmission line causes power loss (I²R loss) in the transmission line. The value of resistance of an overhead line conductor can be calculated based upon the following factors,

• Skin Effect - The alternating current flowing through the conductors is non-uniformly distributed throughout its length. This is because the outer strands of the conductor carry more current than the inner strands. This non-uniform distribution of current causes an increase in resistance of the conductor to the flow of alternating current.
• Spiralling of Conductors - The spiralling of conductors plays a vital role in transmission lines. The conductors of transmission lines do not have any spiralling at the centre. However, there are spiralled around the centre conductor, which increases the resistivity of the conductors to an extent of about 2% for the first layer, 4% for the second layer and so on. In case, if we have three-strand spiralled conductors then the resistivity is increased to about 1%. The spiralling of conductors is shown in the figure below.
  
• Temperature Rise of the Conductor - The effect of temperature on resistance is linearly proportional for pure metals, i.e., if the temperature rises then resistance also increases. If we know the values of final temperature t_f and material resistance R_i at initial temperature t_i and its temperature coefficient α_i, then the resistance R_f at final temperature can be expressed as,
  R_f = R_i[1 + α_i(t_f - t_i)]
  Whereas, for different temperature values the temperature coefficient α can be found out by using the following formula.
  α_f = α_i/[1 + α_i(t_f - t_i)]
  Similarly, the resistivity ρ of metal also changes with temperature. The relationship between ρ_i and ρ_f can be written as,
  ρ_f = ρ_i[1 + α_i(t_f - t_i)]
  The variation of resistance with temperature is shown below.
  

Inductance :

When alternating current flows in the transmission lines, the conductors produce alternating magnetic flux. Due to this, there will be a change in the number of flux linkages with the conductor and hence causes to induce an emf according to Faraday’s Law. This induced emf is nothing but inductance to be present in the line.

The inductance of a conductor is the ratio of total magnetic flux linkages to the current flowing through it or flux linkages per ampere.

L = ψ/I

The inductance of the line increases with the length of the line and also the distance between conductors and decreases with an increase in the diameter of the conductor. This inductance is distributed along the length of the line and limits the power transfer capability of the line.

Capacitance :

We know that capacitance is formed by two conducting plates separated by an insulating medium. In the same manner, there exists a capacitance between two conductors of a transmission line or between a conductor and earth. Here, the air present between acts as an insulating medium thus forming capacitance.

The capacitance of the line causes a charging current to flow or charging of conductors and affects voltage regulation, efficiency and power factor of the line. It constitutes the shunt parameter of the transmission line and is distributed along the length of the line. It is expressed as the ratio of charge to the potential difference or charge per potential difference.

C = q/V farad

The capacitance of the line increases with the length of the line and decreases with an increase in distance between conductors. Factors that govern the capacitance of the transmission line are,

• Length of the line
• Distance between conductors
• Presence of earth
• Electric field intensity.

Shunt Conductance :

Shunt conductance is a shunt parameter of transmission line parameters. It is the flow of leakage current between conductors or between a conductor and earth at the insulators of the transmission line. This flow of leakage current depends upon the condition of the air between transmission lines. Generally, the value of shunt conductance on account of leakage current is very small and can be neglected.

Hence the transmission line parameters (resistance, inductance and capacitance) affect the performance of the transmission line. Thus it is necessary to consider all these parameters while designing and determining the performance of a transmission line.