ElectricalPower System

In overhead line with surge impedance of 400 Ω is connected to a transformer by a short length of cable of surge impedance of 100 Ω. If a rectangular wave of 40 kV travels along the line towards the cable than the voltage of the wave traveling from the junction of overhead line through the cable toward the transformer will be

16 kV

24 kV

32 kV

36 kV

Correct Answer

⚙️ TE • Technical Concept & PrincipleElectricalPower System

Option A

16 kV

Quick Summary:

When a traveling wave encounters a change in surge impedance (junction), a portion of the wave is transmitted and a portion is reflected. The voltage of the transmitted wave ( $V_t$ ) is determined by the refraction coefficient of the junction between the overhead line and the cable.

⚙️TETechnical SolutionConcept & Principle

💡 Explanation

🔢 Key Formulas

$V_t = \frac{2Z_2}{Z_1 + Z_2} \times V_i$ — Transmitted voltage at junction

$V_r = \frac{Z_2 - Z_1}{Z_2 + Z_1} \times V_i$ — Reflected voltage at junction

⚙️ Working Principle

The refraction coefficient ( $\alpha$ ) at the junction is calculated as $\alpha = \frac{2Z_2}{Z_1 + Z_2}$ , where $Z_1 = 400 \ \Omega$ (overhead line) and $Z_2 = 100 \ \Omega$ (cable). The transmitted voltage is $V_t = \alpha \times V_{incident}$ . Substituting the values gives $V_t = (\frac{2 \times 100}{400 + 100}) \times 40 \text{ kV} = (\frac{200}{500}) \times 40 \text{ kV} = 0.4 \times 40 \text{ kV} = 16 \text{ kV}$ .

📌 Key Points

▸
Surge impedance discontinuity causes wave reflection and refraction.
▸
Transmission of voltage waves is governed by the refraction coefficient.
▸
Since $Z_2 < Z_1$ , the transmitted voltage wave magnitude is lower than the incident wave magnitude.
▸
The sum of reflected voltage and incident voltage equals the transmitted voltage at the junction.

✅ Advantages

▸
Predictable behavior for insulation coordination.
▸
Allows calculation of stress on equipment connected to transmission lines.

❌ Disadvantages / Limitations

▸
Reflected waves can cause voltage doubling if the cable end is open.
▸
Complex analysis required for multiple junctions.

🛠️ Applications / Uses

▸
Protection of transformers using lightning arresters.
▸
Insulation coordination in power grids.

📄 Additional Information

▸
Here $Z_1 = 400 \ \Omega$ and $Z_2 = 100 \ \Omega$ .
▸
Option B (24 kV) would result if one erroneously calculated the reflection instead of transmission, or used incorrect impedance values.

📊 Diagram / Illustration

✅

A is correct — The transmitted voltage is calculated using the refraction coefficient, resulting in 16 kV.

Core Concepts Used

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Surge Impedance Traveling Wave Theory Reflection and Refraction Coefficients

💡 EXAM TIP

Remember that if $Z_2 < Z_1$ , the transmitted voltage is always less than the incident voltage; if $Z_2 > Z_1$ , the transmitted voltage is greater than the incident voltage.

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