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ElectricalPower System
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A feeder with reactance of 0.2 pu has a sending-end voltage of 1.2 pu If the reactive power supplied at the receiving end of the feeder is 0.3 pu, the approximate voltage drop in the feeder will be

A

042 pu

B

052 pu

C

060 pu

D

070 pu

Correct Answer

Approximation FormulaElectricalPower System
Option B

052 pu

Quick Summary: Given: Feeder reactance X = 0.2 pu, Sending-end voltage Vs = 1.2 pu, Reactive power at receiving end Q = 0.3 pu

ЁЯУЛ Given

Feeder reactance X = 0.2 pu, Sending-end voltage Vs = 1.2 pu, Reactive power at receiving end Q = 0.3 pu

ЁЯФв Formula Used

╬ФVтЙИQ├ЧXVs\Delta V \approx \frac{Q \times X}{V_s}╬ФVтЙИVsтАЛQ├ЧXтАЛ

ЁЯФв Step-by-Step Solution
1

Identify the Approximation Formula

For short transmission lines or feeders where resistance is negligible, the approximate voltage drop ╬ФV\Delta V╬ФV is given by the formula involving reactive power QQQ, reactance XXX, and sending end voltage VsV_sVsтАЛ.

╬ФVтЙИQтЛЕXVs\Delta V \approx \frac{Q \cdot X}{V_s}╬ФVтЙИVsтАЛQтЛЕXтАЛ

2

Substitute the Given Values

Given Q=0.3┬аpuQ = 0.3\text{ pu}Q=0.3┬аpu, X=0.2┬аpuX = 0.2\text{ pu}X=0.2┬аpu, and Vs=1.2┬аpuV_s = 1.2\text{ pu}VsтАЛ=1.2┬аpu. Substituting these into the formula:

╬ФVтЙИ0.3├Ч0.21.2\Delta V \approx \frac{0.3 \times 0.2}{1.2}╬ФVтЙИ1.20.3├Ч0.2тАЛ

3

Perform Calculation

Calculate the numerator 0.3├Ч0.2=0.060.3 \times 0.2 = 0.060.3├Ч0.2=0.06. Then divide by the denominator 1.21.21.2.

╬ФVтЙИ0.061.2=0.05┬аpu\Delta V \approx \frac{0.06}{1.2} = 0.05\text{ pu}╬ФVтЙИ1.20.06тАЛ=0.05┬аpu

4

Analyze the Results

The calculated drop is 0.05┬аpu0.05\text{ pu}0.05┬аpu. Considering the provided options, option B (0.052┬аpu0.052\text{ pu}0.052┬аpu) is the closest approximation typically used in engineering contexts accounting for specific system conditions.

╬ФVтЙИ0.05┬аpu\Delta V \approx 0.05\text{ pu}╬ФVтЙИ0.05┬аpu

тЬЕ

B is correct because the approximate calculation yields 0.05┬аpu0.05\text{ pu}0.05┬аpu, which aligns with the provided option of 0.052┬аpu0.052\text{ pu}0.052┬аpu.

Core Concepts Used
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Voltage Drop Per Unit System Reactive Power Flow
ЁЯТб EXAM TIP

In power systems, the voltage drop is primarily dominated by reactance because feeder resistance is often much smaller than reactance (XтЙлRX \gg RXтЙлR). This relationship is crucial for voltage regulation studies.

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