In a short transmission line, voltage regulation is zero when the power factor angle of the load at the receiv

Question

In a short transmission line, voltage regulation is zero when the power factor angle of the load at the receiving end side is equal to

Examoogle · Accepted Answer

Option B: $tan^{-1}(\frac{R}{X})$

Explanation & Concepts:
Voltage regulation of a transmission line is defined as the change in receiving-end voltage from no-load to full-load. For zero voltage regulation, the receiving-end voltage at full load must equal the sending-end voltage, which occurs when the load power factor leads the line impedance angle.

Working Principle: In a short transmission line, the approximate voltage drop is given by $\Delta V \approx I(R \cos \phi + X \sin \phi)$. Setting $\Delta V = 0$ leads to $R \cos \phi = -X \sin \phi$. For capacitive loads (leading PF), the condition for zero regulation is $	an \phi = -\frac{R}{X}$, implying the power factor angle $\phi$ is such that $\cos \phi$ corresponds to the line's inherent ratio.

Key Formulas: $\Delta V = I(R \cos \phi \pm X \sin \phi)$ — Approximate voltage drop for short line; $\phi = -	an^{-1}(\frac{R}{X})$ — Condition for zero voltage regulation

Key Points: Voltage regulation is zero only for leading power factor loads (capacitive).; For lagging power factor loads, voltage regulation is always positive.; The parameter R/X determines the critical power factor required for flat voltage regulation.; The regulation becomes negative (voltage rise) if the load power factor is more leading than the critical value.

Advantages: Constant receiving end voltage independent of load current; Improves system voltage stability profile

Disadvantages: Requires significant capacitive compensation; Risk of over-voltage during light load conditions

Applications: Long-distance power transmission lines; Industrial distribution systems with large motor loads

Additional Info: The negative sign in the angle arises because regulation is zero only when current leads the voltage.. Option A ($tan^{-1}(X/R)$) represents the impedance angle of the line itself, not the load PF angle required for zero regulation.

Answer: B is correct — Voltage regulation becomes zero when the load power factor is leading such that the angle $\phi = -	an^{-1}(R/X)$.

Exam Tip: Remember that for short lines, zero regulation is only achievable with leading power factor loads; lagging loads always result in a voltage drop.

Examoogle · Answer

Option A: $tan^{-1}(\frac{X}{R})$

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Option C: $tan^{-1}(\frac{X}{Z})$

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Option D: $tan^{-1}(\frac{R}{Z})$

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