Receiving end voltage for long transmission line under no load condition is

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Option B: More than sending end voltage

Explanation & Concepts:
In a long transmission line, the receiving end voltage ($V_R$) under no-load conditions is higher than the sending end voltage ($V_S$) due to the Ferranti effect. This phenomenon is caused by the line's significant distributed shunt capacitance drawing a charging current, which flows through the line inductance and causes a voltage rise.

Working Principle: Transmission lines possess distributed shunt capacitance along their length. Under no-load conditions, the charging current $I_C = j\omega C V$ flows through the series line inductance ($L$). As this current flows from the sending end to the open receiving end, it creates a voltage drop across the line inductance that is approximately 90° leading the voltage, resulting in a phasor addition that makes the receiving end voltage higher than the sending end.

Key Formulas: $V_R = V_S / \cos(\beta l)$ — relation for receiving end voltage where $\beta$ is phase constant and $l$ is length; $I_{charging} = j\omega C V_{line}$ — fundamental charging current leading voltage by 90°

Key Points: Ferranti effect is prominent in long transmission lines (>200 km).; It is negligible in short and medium lines due to lower shunt capacitance.; The voltage rise depends on the square of the line length.; Shunt reactors are used at the receiving end to compensate for this effect.

Advantages: Useful for voltage regulation studies; Indicates capacitive nature of long lines

Disadvantages: Causes insulation stress on equipment; Requires reactive power compensation to avoid overvoltage

Applications: EHV/UHV Transmission systems; Long-distance power grids

Additional Info: The phenomenon is named after Sebastian Ziani de Ferranti.. Option A is incorrect as it describes the typical loaded condition where voltage drops due to impedance.. Option C is only true for an ideal, zero-length line or specific compensated conditions.

Answer: B is correct — Due to the Ferranti effect, the distributed shunt capacitance of long lines causes the receiving end voltage to exceed the sending end voltage at no-load.

Exam Tip: Always remember that for short lines, $V_R V_S$ because the capacitive effect dominates the inductive effect.

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Option A: Less than sending end voltage

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Option C: Equal to sending end voltage

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Option D: Any of above

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