Question

Determine the equivalent circuit for the line in Problem 5.14 and compare it with the nominal circuit.

Short answer

(a) The value of characteristic impedanceis.

(b) The value ofis.

(c) The value ofparameters are,,and.

Step-by-step solution

Write the given data from the question.

Refer to the problem 5.14.

The length of given three phase line is.

The voltage of given three phase line is.

The frequency of given three phase line is.

The positive sequence series impedance of given three phase line is.

The positive sequence shunt impedance of given three phase line is.

Determine the formula of characteristic impedance,   and  parameters.

Write the formula of the value of characteristic impedance.

…… (1)

Here, is impedance and is length of line.

Write the formula of.

…… (2)

Here, is impedance, is admittance and is length.

Write the formula of line parameters of the equivalent circuit.

…… (3)

Here, is equivalent admittance and is equivalent impedance.

Write the formula of line parameters of the equivalent circuit.

…… (4)

Here, is equivalent impedance.

Write the formula of line parameters of the equivalent circuit.

…… (5)

Here, is equivalent admittance and is equivalent impedance.

Write the formula of line parameters of the equivalent circuit.

…… (6)

Here,is equivalent admittance andis equivalent impedance.

(a) Determine the characteristic impedance of three phase line.

Determine the expression of characteristics impedance.

Substitute for and for into equation (1).

Hence, the characteristics impedanceis .

(b) Determine the.

Determine the value of.

Substitutefor,forandforinto equation (2).

Solve further as

Hence, the value ofis.

(c) Determine the value of given line parameters.

Determine the expression of.

Solve further as

Determine the expression of.

Solve further as

Determine the value of equivalent impedance

Here, is characteristics impedance and is dimensionless quantity.

Substitute for and for into above equation.

Determine the value of characteristics admittance.

Here, is admittance and is length of line.

Substitute for and for into above equation.

Determine the value of equivalent admittance

Here, is characteristics admittance and is dimensionless quantity.

Substitute for and for into above equation.

Draw the circuit diagram of nominalcircuit.

Figure 1

Draw a circuit diagram of equivalentcircuit.

Figure 2

Differentiate the nominal circuit and equivalentcircuit parameters.

The value of resistanceisand value of equivalent resistanceis.

Hence, the value of resistanceissmaller than the nominal resistance.

The value of reactanceisand value of equivalent reactanceis

Hence, the value of equivalent reactanceissmaller than the reactance.

The value of Susceptanceisand value of admittanceis

Hence, the value of Susceptanceislarger than value of admittance.

The value of Shunt conductanceis.