For a short line if the receiving end voltage is equal to sending end voltage under loaded condition

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Option D: Receiving end power factor is leading

Explanation & Concepts:
For a short transmission line, the sending end voltage $V_s$ is related to the receiving end voltage $V_r$ by the approximate relation $V_s \approx V_r + I(R \cos \phi_r \pm X \sin \phi_r)$. For $V_s = V_r$, the term $(R \cos \phi_r \pm X \sin \phi_r)$ must be zero. This condition is only physically possible when the receiving end power factor is leading, which provides a capacitive effect that offsets the voltage drop caused by the line resistance and inductive reactance.

Working Principle: In a short line, the voltage regulation depends on the load power factor. With a lagging load, there is always a voltage drop. When the load power factor is leading, the reactive power supplied by the capacitor helps in compensating for the inductive reactance drop, allowing the receiving end voltage to rise relative to the source, potentially making $V_r$ equal to or greater than $V_s$.

Key Formulas: $V_s \approx V_r + I(R \cos \phi_r + X \sin \phi_r)$ — Approximate sending end voltage for a short transmission line; $	ext{Voltage Regulation} = \frac{V_s - V_r}{V_r} 	imes 100$ — Percentage change in voltage

Key Points: Voltage regulation is positive for lagging power factor loads.; Voltage regulation is zero when $V_s = V_r$.; Voltage regulation is negative for leading power factor loads (Ferranti-like effect).; Short lines are modeled using a series impedance $Z = R + jX$.

Advantages: Improved voltage profile at the receiving end.; Reduced transmission losses if operating near unity power factor.

Disadvantages: Requires reactive power compensation equipment.; Operating with leading power factor may stress insulation if voltage rises uncontrollably.

Applications: Industrial power systems with large motor loads.; Distribution systems requiring voltage regulation.

Additional Info: Option B (unity power factor) results in $V_s > V_r$ because of the resistive voltage drop ($I 	imes R$).. The condition $V_s = V_r$ is a specific case of zero voltage regulation.

Answer: D is correct — The receiving end voltage can only equal the sending end voltage in a short transmission line when the load power factor is leading, as this creates a negative voltage drop contribution.

Exam Tip: Always remember: Lagging loads cause voltage drop, while leading loads can cause voltage rise (or zero regulation) in transmission lines.

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Option A: Sending end power factor is unity

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Option B: Receiving end power factor is unity

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Option C: Sending end power factor is leading

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