GATE EE 2023 Set 1 — Question 33
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Power Systems → Transmission Line Performance → ABCD Constants
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Question
A 50 Hz, 275 kV line of length 400 km has the following parameters:
Resistance, ;
Inductance, ;
Capacitance, ;
The line is represented by the nominal- model. With the magnitudes of the sending end and the receiving end voltages of the line (denoted by and , respectively) maintained at 275 kV, the phase angle difference () between and required for maximum possible active power to be delivered to the receiving end, in degree is _____________ (Round off to 2 decimal places).
Resistance, ;
Inductance, ;
Capacitance, ;
The line is represented by the nominal- model. With the magnitudes of the sending end and the receiving end voltages of the line (denoted by and , respectively) maintained at 275 kV, the phase angle difference () between and required for maximum possible active power to be delivered to the receiving end, in degree is _____________ (Round off to 2 decimal places).
Correct answer
83 to 84
Solution
In a transmission line represented by the nominal- model, the active power delivered to the receiving end is given by , where is the transfer impedance parameter. Maximum active power is delivered when the phase angle difference (or ) is equal to the angle of the parameter, i.e., . For the nominal- model, .
Total resistance .
Total inductance .
Angular frequency .
Total reactance .
The transfer impedance is .
The angle .
Therefore, the required phase angle difference for maximum power delivery is .
Total resistance .
Total inductance .
Angular frequency .
Total reactance .
The transfer impedance is .
The angle .
Therefore, the required phase angle difference for maximum power delivery is .
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