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# Long Transmission Line Performance Step by step Solution with Explanation

A long transmission line delivers a load of 60 MVA at 124 kV, 50 Hz, at 0.8 power factor lagging. Resistance of the line is 25.3 Ω, reactance is 66.5 2 and admittance due to charging capacitance is 0.442×10-3 mho. Find (a) A, B, C, D constants (b) Sending end voltage, current and power factor (c) regulation (d) efficiency of the line.

# Long Transmission Line Performance Answers and Explanation

Solving Long Transmission Line Performance

• Frequency: 50 Hz

• Power Factor (receiving end): 0.8 lagging

(a) A, B, C, D constants (not applicable for long lines):

For long transmission lines, the nominal pi model is not recommended. The distributed parameter model is used for more accurate analysis. Therefore, A, B, C, and D constants are not applicable in this case.

Z = R + jX = 25.3 Ω + j66.5 Ω

1. Sending End Voltage (Vs): We can't directly calculate Vs due to the distributed nature of a long line. However, for approximate analysis, we can use an iterative method or specialized software.

(c) Voltage Regulation:

Voltage regulation refers to the change in voltage between sending and receiving ends. Due to line impedance, there will be a voltage drop from sending end to receiving end.

Line Losses = 3 * I^2 * R

= 3 * (240 A)^2 * 25.3 Ω ≈ 1.7 MW (approximate)

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