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A short line with R/X ratio 1, the zero regulation is obtained when the power factor of the load is
0.5
Unity
Zero leading
0.707 leading
0.5
Quick Summary: Zero voltage regulation in a short transmission line occurs when the receiving end voltage magnitude is equal to the sending end voltage magnitude. For a line with impedance $Z = R + jX$, this condition is met when the load power factor angle $\phi$ satisfies the relation $\tan(\phi) = -\frac{X}{R}$.
Zero voltage regulation in a short transmission line occurs when the receiving end voltage magnitude is equal to the sending end voltage magnitude. For a line with impedance Z=R+jX, this condition is met when the load power factor angle ╧Х satisfies the relation tan(╧Х)=тИТRXтАЛ.
%VR=VrтАЛI(Rcos╧Х+Xsin╧Х)тАЛ├Ч100 тАФ Percentage Voltage Regulation
tan(╧Х)=тИТXRтАЛ тАФ Condition for Zero Regulation
The voltage regulation of a short line is given by %VR=VrтАЛI(Rcos╧Х+Xsin╧Х)тАЛ├Ч100. For zero regulation, the numerator Rcos╧Х+Xsin╧Х must be zero, which implies Xsin╧Х=тИТRcos╧Х, or tan(╧Х)=тИТXRтАЛ. Given R/X=1, we have tan(╧Х)=тИТ1, leading to ╧Х=тИТ45┬░. The power factor is cos(тИТ45┬░)=0.707 leading.
Zero regulation implies the receiving end voltage is independent of the load current magnitude.
A leading power factor is essential to compensate for the voltage drop across the series inductive reactance.
For R/X=1, the power factor angle required is exactly тИТ45┬░.
Provides constant voltage profile regardless of load magnitude
Improves system efficiency by reducing reactive power flow
Requires capacitive compensation which can be costly
Potential for overvoltage during light load conditions
Distribution systems
Industrial power factor correction units
For lagging power factors, the voltage drop is additive, resulting in positive regulation.
Option B (Unity) only results in zero regulation if the line is purely reactive (R=0).
D is correct тАФ For a line with R/X=1, zero regulation is achieved at a leading power factor of 0.707 because the leading current creates a voltage rise that exactly offsets the resistive and reactive voltage drops.
Always remember that for any transmission line, zero regulation requires a leading power factor to cancel the inductive voltage drop, unless the line resistance is negative (which is physically impossible).