📘 Advanced Transformer Differential Protection – Hard Numerical Problem
This problem includes CT compensation, vector group consideration, percentage bias calculation and relay stability verification.
🔹 Given Data
- Transformer: 40 MVA, 220/66 kV
- Vector group: Y-Δ
- CT ratio (HV side): 400/1
- CT ratio (LV side): 1200/1
- Percentage bias slope: 25%
- HV side current = 800 A
- LV side current = 2100 A
🔹 Step 1: Convert to Secondary Currents
HV secondary current = 800 / 400 = 2 A LV secondary current = 2100 / 1200 = 1.75 A
🔹 Step 2: Account for Vector Group
For Y-Δ transformer:
- CT on delta side connected in star
- CT on star side connected in delta
After compensation, compare magnitudes directly.
🔹 Step 3: Calculate Differential Current
I_diff = |2 − 1.75| = 0.25 A
🔹 Step 4: Calculate Average (Bias) Current
I_avg = (2 + 1.75)/2 = 1.875 A
🔹 Step 5: Calculate Operating Threshold
Operating limit = Slope × I_avg = 0.25 × 1.875 = 0.469 A
🔹 Step 6: Decision
Since I_diff (0.25 A) < 0.469 A Relay DOES NOT operate.
This is likely an external fault or CT mismatch case.
🔹 Internal Fault Scenario
Suppose LV current drops to 1200 A.LV secondary = 1200 / 1200 = 1 A I_diff = |2 − 1| = 1 A I_avg = (2 + 1)/2 = 1.5 A Operating limit = 0.25 × 1.5 = 0.375 A
Since 1 A > 0.375 A → Relay Operates.
🎯 Important Learning Points
- CT ratio must compensate transformer ratio
- Vector group affects CT connections
- Percentage bias improves stability
- Relay operates only when I_diff exceeds slope limit
Advanced Differential Protection = Stability + Sensitivity
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