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📘 Corona – Numerical Problems (GATE Level)

These problems focus on critical disruptive voltage and corona loss calculations.

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🔹 Problem 1 – Critical Disruptive Voltage

Given: r = 1.2 cm D = 120 cm m0 = 0.9 δ = 1 Formula: Vd = 21.1 m0 δ r ln(D/r) Step 1: ln(D/r) = ln(120/1.2) = ln(100) ≈ 4.6 Step 2: Vd = 21.1 × 0.9 × 1 × 1.2 × 4.6 = 21.1 × 4.968 ≈ 104.8 kV per phase

Critical disruptive voltage ≈ 105 kV

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🔹 Problem 2 – Effect of Altitude

Given: δ = 0.8 (high altitude) All other values same as Problem 1. Since: Vd ∝ δ New Vd: = 0.8 × 105

Vd ≈ 84 kV

Conclusion: Higher altitude → lower air density → lower corona voltage.

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🔹 Problem 3 – Effect of Conductor Radius

Original radius = 1 cm New radius = 2 cm Since: Vd ∝ r ln(D/r) Increasing radius increases Vd. Therefore: Larger conductor → less corona. Very common conceptual GATE question.

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🔹 Problem 4 – Corona Loss Concept

Given: Operating voltage = 120 kV Critical voltage = 100 kV Corona occurs only when: V > Vd Since 120 > 100,

Corona will occur.

If voltage < Vd → No corona.

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🔹 Problem 5 – Comparative Question

Two lines: Line A: r = 1 cm Line B: r = 2 cm Which has more corona loss? Since larger radius increases Vd,

Line A will have more corona loss.

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🔹 Problem 6 – Multiple Choice Type

Corona is reduced by: A) Increasing conductor spacing B) Increasing conductor radius C) Increasing air pressure D) All of the above

Answer: D

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🎯 GATE Important Observations

• Corona increases with voltage
• Corona decreases with conductor radius
• High altitude increases corona
• Bad weather increases corona

Corona = High Voltage Surface Ionization Phenomenon