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ElectricalPower System

Surge voltage of 1000 kV is applied to an overhead transmission line with its receiving and open. If the surge impedance of the line is 500 Ω, then total surge power in the line is

2000 MW

500 MW

2 MW

0.5 MW

Correct Answer

⚙️ TE • Technical Concept & PrincipleElectricalPower System

Option A

2000 MW

Quick Summary:

The surge power in a transmission line is determined by the relationship between the surge voltage ( $V$ ) and the surge impedance ( $Z_s$ ). The power delivered by a traveling wave is given by the product of voltage and current, where current is defined as $I = \frac{V}{Z_s}$ .

⚙️TETechnical SolutionConcept & Principle

💡 Explanation

🔢 Key Formulas

$P = \frac{V^2}{Z_s}$ — Surge power calculation formula

$I = \frac{V}{Z_s}$ — Surge current relationship

⚙️ Working Principle

When a surge voltage wave propagates along a transmission line, it carries energy in the electromagnetic field. The instantaneous power associated with this wave is $P = V \times I$ . Substituting the characteristic impedance relation $I = \frac{V}{Z_s}$ , we obtain $P = \frac{V^2}{Z_s}$ . Given $V = 1000 \text{ kV}$ and $Z_s = 500 \text{ } \Omega$ , the power is $P = \frac{(1000 \times 10^3)^2}{500} = 2 \times 10^9 \text{ W} = 2000 \text{ MW}$ .

📌 Key Points

▸
Surge impedance $Z_s = \sqrt{\frac{L}{C}}$ is independent of line length.
▸
The power calculated here represents the instantaneous surge power, not steady-state power.
▸
The receiving end being open affects voltage reflection but does not change the power calculation at the moment of surge arrival.

✅ Advantages

▸
Simple calculation using characteristic line constants
▸
Helps in selecting insulation levels for equipment

❌ Disadvantages / Limitations

▸
Calculated value is transient and exists for a very short duration
▸
Does not account for line losses or corona effects

🛠️ Applications / Uses

▸
Insulation coordination studies
▸
Lightning arrester placement design

📄 Additional Information

▸
Surge impedance for overhead lines typically ranges between 400-600 $\Omega$ .
▸
Option B (500 MW) is a common distractor resulting from omitting the squaring of the voltage term.

📊 Diagram / Illustration

✅

A is correct — The surge power is calculated using the formula $P = \frac{V^2}{Z_s}$ , which yields $2000 \text{ MW}$ for $V = 1000 \text{ kV}$ and $Z_s = 500 \text{ } \Omega$ .

Core Concepts Used

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Surge Impedance Traveling Wave Theory Transient Power

💡 EXAM TIP

Remember that surge impedance is purely resistive in a lossless line approximation, so surge power is purely active power.

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