A three phase, 50 Hz transmission line operates at 220 kV. The line has 400 Ω surge impedance. Find

Question

A three phase, 50 Hz transmission line operates at 220 kV. The line has 400 Ω surge impedance. Find the surge impedance loading

Examoogle · Accepted Answer

121 MVA

Explanation: Given: Three-phase voltage V_L = 220 kV, Surge impedance Z_c = 400 Ω, Frequency f = 50 Hz

Formula Used: $$SIL = \frac{V_L^2}{Z_c}$$

Steps: Identify the formula for Surge Impedance Loading: The Surge Impedance Loading (SIL) of a transmission line is defined by the square of the line voltage divided by its surge impedance.. Substitute given values: Given $V_L = 220 	ext{ kV} = 220 	imes 10^3 	ext{ V}$ and $Z_c = 400 	ext{ } \Omega$.. Calculate the result: Squaring the voltage gives $48400 	imes 10^6$. Dividing by $400$ results in $121 	imes 10^6 	ext{ VA}$.

Answer: C is correct because the calculated surge impedance loading for the given parameters is 121 MVA.

Exam Tip: SIL is independent of the line length and frequency, and it represents the load at which the line absorbs as much reactive power as it generates.

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