Question

9-6. The single-phase transmission line is operating with the receiving side of the line open-circuited. The sending end voltage is 8 kV at 50 Hz. How much charging current is flowing in the line?

Answer 1

It is given that a single-phase, transmission line consists of two aluminum conductors.

The length of conductor is 50 km.

Diameter of the conductor,

Spacing between two conductors,

This transmission line is a short line as the length is less than 80 km.

In order to calculate the charging current an appropriate model of the line has to be chosen, which includes the capacitance of the line also. For this reason the transmission line model of a medium length transmission line is chosen for this short line.

Figure 1

Write the equations for sending end voltage and current of medium length transmission line.

Calculate the charging current by open-circuiting the output of the transmission line. When the output is open circuited, the entire sending end current will be used to charge the capacitance.

As the output is open circuited,

And

Therefore, the charging current,

Write the formula for Inductance per meter of a single phase two wire transmission line.

where,

Substitute the known values in the inductance formula.

Calculate the total inductance of this transmission line for a length of will be

Calculate the inductive reactance of transmission line.

Write the formula for DC resistance per meter of the conductor.

where,

is the resistivity of the material in ohm-meters

is the cross-sectional area of the conductor in square meters

is the radius of the conductor in meter.

Here,

Resistivity of aluminum at

Substitute the known values, and calculate the DC resistance.

Calculate the total DC resistance of transmission line for a length of 50 km.

Calculate the AC resistance with the assumption that, at 50 Hz, ac resistance of the line is greater than its dc resistance.

Calculate the total series impedance of this line.

Write the formula for capacitance of a single phase two wire transmission line.

where,

is the permittivity of free space

Substitute the known values in the capacitance formula.

Calculate the capacitance per kilometer.

Calculate the shunt admittance of this transmission line.

Calculate the total shunt admittance.

The sending end voltage,

Calculate the charging current by substituting the known values.

Thus, the charging current flowing in the transmission line is: .