📘 Transformer Differential Protection – Numerical Problems (Step-by-Step)
These problems help understand CT ratio selection, differential current calculation, percentage bias, and inrush restraint concepts.
🔹 Problem 1: Basic Differential Current
A 20 MVA, 132/33 kV transformer is protected by differential relay. CT ratio on HV side = 200/1 CT ratio on LV side = 800/1 During internal fault: HV side current = 150 A LV side current = 600 A Check whether relay operates.
Step 1: Convert to Secondary Currents
HV secondary current = 150 / 200 = 0.75 A LV secondary current = 600 / 800 = 0.75 A
Since currents are equal → No differential current.
Relay does NOT operate (External fault condition).
🔹 Problem 2: Internal Fault Case
Same transformer, but during internal fault: HV side current = 150 A LV side current = 300 A
Step 1: Convert to Secondary
HV secondary = 150 / 200 = 0.75 A LV secondary = 300 / 800 = 0.375 A
Step 2: Calculate Differential Current
I_diff = |0.75 − 0.375| = 0.375 A
If pickup setting = 0.2 ASince 0.375 > 0.2 → Relay Operates
🔹 Problem 3: Percentage Differential Protection
CT secondary currents: I₁ = 1.2 A I₂ = 1.0 A Slope setting = 30% Check operation.
Step 1: Calculate Differential Current
I_diff = |1.2 − 1.0| = 0.2 A
Step 2: Calculate Average Current
I_avg = (1.2 + 1.0)/2 = 1.1 A
Step 3: Calculate Bias Current
Bias setting = 0.3 × 1.1 = 0.33 A
Since 0.2 < 0.33 → Relay does NOT operate
🔹 Problem 4: Inrush Current Detection
Transformer energized and relay measures 5 A secondary current. Second harmonic component = 25% of fundamental. Harmonic restraint setting = 15%. Will relay operate?
Since 25% > 15% → Inrush condition detected → Relay restrained.
🎯 Important Concepts
- Differential protection detects internal faults only
- CT ratio must match transformer ratio
- Percentage bias avoids false tripping
- Harmonic restraint prevents inrush tripping
Transformer Differential = Fast & Selective Internal Fault Protection
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