The per unit regulation of a short transmission line having a per-unit resistance voltage drop Vr and a per-un

Question

The per unit regulation of a short transmission line having a per-unit resistance voltage drop Vr and a per-unit reactance voltage drop of Vx at rated current and power factor cos Θ, is given by

Examoogle · Accepted Answer

Option C: $V_r \cos 	heta + V_x \sin 	heta$

Explanation & Concepts:
Voltage regulation of a short transmission line is defined as the change in voltage at the receiving end when the load is removed, expressed as a percentage of receiving end voltage. For a short line, the regulation is approximately given by $V_r \cos 	heta + V_x \sin 	heta$, where $V_r$ and $V_x$ are the per-unit resistance and reactance drops.

Working Principle: In a short transmission line, the series impedance $Z = R + jX$ is significant while shunt capacitance is neglected. The phasor diagram of such a line shows that for a load current $I$ at lagging power factor $\cos 	heta$, the voltage drop component along the reference voltage phasor is $I(R \cos 	heta + X \sin 	heta)$. When normalized by the base/rated voltage, this yields the per-unit regulation formula.

Key Formulas: $	ext{Regulation} \approx V_r \cos 	heta + V_x \sin 	heta$ — Approximation for lagging power factor; $	ext{Regulation} \approx V_r \cos 	heta - V_x \sin 	heta$ — Approximation for leading power factor

Key Points: The formula assumes the receiving end voltage is the reference phasor.; This approximation is valid for short transmission lines where shunt capacitance is negligible.; The regulation depends heavily on the load power factor angle $	heta$.

Advantages: Simplifies calculation of terminal voltage variations.; Provides quick insights into line performance without complex matrix operations.

Disadvantages: Not suitable for long transmission lines where distributed parameters are critical.; Becomes inaccurate if the power factor is very low.

Applications: Distribution network voltage drop analysis.; Short distance power transmission planning.

Additional Info: For unity power factor, $\sin 	heta = 0$, so regulation is simply $V_r$.. Option A and B are incorrect as they do not account for the decomposition of voltage drop based on the phase angle $	heta$.

Answer: C is correct — The per-unit voltage regulation of a short transmission line is accurately represented by the projection of the voltage drop onto the receiving end voltage phasor, resulting in $V_r \cos 	heta + V_x \sin 	heta$.

Exam Tip: Remember that for leading power factor loads, the sign of the reactance drop term changes to minus ($- V_x \sin 	heta$), which can lead to negative voltage regulation (voltage rise).

Examoogle · Answer

Option A: $(V_r + V_x) \cos 	heta$

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Option B: $(V_r + V_x) \sin 	heta$

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Option D: $V_r \sin 	heta + V_x \cos 	heta$

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