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ElectricalPower System

The sending end voltage of a feeder with reactance 0.2 pu is 1.2 pu. If the reactive power supplied at the receiving end of the feeder is 0.3 pu, the approximate drop of volts in the feeder is

0.2 pu

0.06 pu

0.05 pu

0.072 pu

Correct Answer

⚙️ TE • Technical Concept & PrincipleElectricalPower System

Option C

0.05 pu

Quick Summary:

The voltage drop $\Delta V$ in a short transmission line is approximated by the expression $\Delta V \approx IX \sin \phi + IR \cos \phi$ . Given that the feeder is purely inductive ( $R \approx 0$ ), the formula simplifies to $\Delta V \approx I X \sin \phi = QX / V$ , where $Q$ is the reactive power.

⚙️TETechnical SolutionConcept & Principle

💡 Explanation

🔢 Key Formulas

$\Delta V \approx \frac{QX}{V}$ — Approximate voltage drop for inductive line

$Q = VI \sin \phi$ — Reactive power definition

⚙️ Working Principle

In a short transmission line where the resistance $R$ is negligible compared to reactance $X$ , the voltage drop is primarily influenced by the reactive power flow. Since $Q = VI \sin \phi$ , substituting $I \sin \phi = Q/V$ into the approximation $\Delta V \approx IX \sin \phi$ gives $\Delta V \approx \frac{QX}{V}$ . For small voltage variations, $V$ is approximately the nominal or sending end voltage.

📌 Key Points

▸
Voltage drop in power systems is heavily dependent on reactive power (Q) when line resistance is low.
▸
The calculation uses the approximation $\Delta V = \frac{0.3 \times 0.2}{1.2} = 0.05$ pu.
▸
This formula is valid for short lines where the phase angle between sending and receiving end voltage is small.

✅ Advantages

▸
Simplifies power system analysis significantly.
▸
Provides quick estimation for load flow studies.

❌ Disadvantages / Limitations

▸
Inaccurate for lines with high resistance-to-reactance ratio.
▸
Assumes constant voltage magnitude which may not hold during heavy loading.

🛠️ Applications / Uses

▸
Voltage profile regulation studies.
▸
Quick estimation in grid stability assessments.

📄 Additional Information

▸
Calculation: $0.3 \times 0.2 = 0.06$ ; $0.06 / 1.2 = 0.05$ .
▸
Option A (0.2) is the reactance value itself; Option B (0.06) is the product of Q and X; Option D (0.072) is a result of calculation errors.

📊 Diagram / Illustration

✅

C is correct — The approximate voltage drop is calculated using the formula $\Delta V \approx \frac{QX}{V} = \frac{0.3 \times 0.2}{1.2} = 0.05$ pu.

Core Concepts Used

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Power System Voltage Drop Reactive Power Flow Short Transmission Line Model

💡 EXAM TIP

Always verify if the line is inductive or resistive; most transmission lines are treated as inductive, simplifying the drop to primarily depend on reactive power.

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