The change in real power P produces little effect on receiving end voltage because

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Examoogle · Accepted Answer

The voltage drop associated with this change is in quadrature with reference voltage

Explanation: In power transmission lines, the receiving end voltage is primarily governed by the flow of reactive power ($Q$), whereas real power ($P$) transfer is governed by the power angle ($\delta$). Because the transmission line reactance ($X$) is significantly greater than its resistance ($R$), the voltage drop produced by real power flow is essentially in quadrature with the receiving end voltage, resulting in a negligible effect on its magnitude.

Working Principle: Consider the voltage drop $\Delta V \approx \frac{RP + XQ}{V_r}$. For typical transmission lines, $X \gg R$. Real power change $\Delta P$ contributes to a drop in-phase with the current but in quadrature with the reference voltage, causing a phase shift rather than a magnitude change. Conversely, changes in reactive power $\Delta Q$ directly impact the voltage drop magnitude because $X\Delta Q$ is aligned with the reference voltage component.

Key Formulas: $\Delta V \approx \frac{R P + X Q}{V_r}$ — Approximate voltage drop formula; $P = \frac{V_s V_r}{X} \sin \delta$ — Power transfer equation

Key Points: Transmission lines are primarily inductive ($X \gg R$); Real power ($P$) affects the phase angle difference between sending and receiving ends; Reactive power ($Q$) is the primary control variable for voltage magnitude; Voltage drop due to real power is nearly orthogonal to the reference voltage vector

Advantages: Decoupled control of voltage and frequency; Efficient reactive power compensation via capacitor banks

Applications: Load flow studies; Voltage stability analysis in power grids

Additional Info: In highly resistive circuits (e.g., low voltage distribution), the assumption $X \gg R$ fails, and $P$ will significantly affect voltage.. Option B is correct because the inductive reactance $X$ creates a 90-degree phase shift between current and voltage, causing real power-related voltage drops to align in quadrature with the reference.

Answer: B is correct — The voltage drop associated with active power flow is primarily reactive due to high line inductance, placing it in quadrature with the receiving end voltage.

Exam Tip: Always remember the decoupling principle: $P - \delta$ (Real power controls angle) and $Q - V$ (Reactive power controls magnitude) for transmission systems.

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