GATE Electrical Engineering - Complete Master Library

 

📘 Symmetrical Fault Analysis (3-Phase Fault)

Three-phase fault is the most severe fault. All phases shorted together. Used for maximum fault current calculation.

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🔹 1️⃣ Why 3-Phase Fault is Important?

• Gives maximum short circuit current
• Used for circuit breaker rating
• Simplest fault to analyze

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🔹 2️⃣ Fault Current Formula

In per unit:

I_fault = V_prefault / Z_th

Usually: V_prefault = 1 pu Therefore:

I_fault = 1 / Z_th

Where: Z_th = Thevenin impedance seen from fault point

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🔹 3️⃣ Fault MVA

Fault MVA = (Base MVA) / Z_th

Very important formula.

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🔹 4️⃣ Example 1 – Simple Generator Fault

Generator: 100 MVA, X = 0.2 pu Fault at terminals. Z_th = 0.2 pu Fault current: = 1 / 0.2

I_fault = 5 pu

Fault MVA: = 100 / 0.2

Fault MVA = 500 MVA

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🔹 5️⃣ Example 2 – Generator + Transformer

Generator X = 0.2 pu Transformer X = 0.1 pu Total Z_th: = 0.2 + 0.1 = 0.3 pu Fault current: = 1 / 0.3

I_fault ≈ 3.33 pu

If base MVA = 100 MVA: Fault MVA: = 100 / 0.3 ≈ 333 MVA

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🔹 6️⃣ Convert Fault Current to Actual

Base current: I_base = S_base / (√3 V_base) Example: 100 MVA, 11 kV I_base = 100 × 10⁶ / (√3 × 11000) ≈ 5250 A If fault current = 5 pu: Actual fault current: = 5 × 5250

I_actual ≈ 26.25 kA

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🔹 7️⃣ Important Observations

• Lower reactance → higher fault current
• Fault current independent of load
• Used for breaker selection

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🎯 GATE Focus

• I_fault = 1/Z_th
• Fault MVA formula
• Add per unit reactances
• Convert to actual current carefully

Symmetrical Fault = Maximum Short Circuit Condition