Why Line Capacitance is Neglected in Short Transmission Lines?

The transmission lines whose length ranges up to 80 km are referred to as short transmission lines. Transmission lines are categorized on the basis of line length and not on the operating voltage.


In the case of short transmission lines due to shorter line lengths, the source connecting the load through lines can see only the impedance of the load and not the characteristic impedance of the line. This is because, the voltage and current wave which travels with the speed of light i.e., 3 x 108 m/sec in overhead transmission lines takes very little time to reach the receiving end in short transmission lines.

Why Line Capacitance is Neglected in Short Transmission Lines?

In a short transmission line, load impedance dominates the circuit behavior, with little consequence of characteristic impedance of the line on the circuit's behavior. This results in a very low value of shunt capacitance between the lines and the earth which is negligible.


The source connecting the load via a short transmission line is shown in the figure below.

Why Capacitance is Neglected in Short Transmission Lines?

Where,
  • Vs = Sending end voltage
  • Is = Sending end current
  • R = Resistance of short transmission line
  • Xl = Reactance of the line
  • Vr = Receiving end voltage
  • Ir = Receiving end current
  • l = length of the transmission line.

In the case of long and medium transmission lines due to long line lengths, the source connecting the load through them can see the characteristic impedance of the line rather than the impedance of the load. The time taken by the voltage and current waves to reach the receiving end in long and medium transmission lines is at t = 833 ┬Ásec and t = 53.4 ┬Ásec respectively.


Therefore, the characteristic impedance of the line dominates the load impedance in circuits behavior. So, the capacitance effect is taken into consideration during the analysis of medium and long transmission lines. Hence, for a short transmission line, the shunt capacitance effect is neglected.


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