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TRANSFORMER PROTECTION • VIRTUAL EXPERIMENT

Numerical Percentage Biased Differential Relay

To test the numerical percentage biased differential relay for transformer protection

1. Transformer & Relay Settings
2. Test Current Injection
3. Transformer Differential Protection Scheme
Transformer Differential Protection — 87T HV SYSTEM CT CT-HV POWER TRANSFORMER T1 HV winding LV winding CT CT-LV LV SYSTEM NUMERICAL RELAY 87T I₁ I₂ PROTECTED ZONE Internal fault
Fig. 1 — Transformer differential protection and CT circuits
4. Experimental Procedure
  1. Set the transformer and relay parameters.
  2. Select a test condition.
  3. Adjust the CT secondary currents and phase angle.
  4. Observe Id, Ir and the operating threshold.
  5. Verify the position of the operating point.
  6. Record the experimental result.
5. Numerical Relay Status
Differential current Id 0.000 A
Restraining current Ir 0.000 A
Operating threshold 0.000 A
Trip time —
✓ RELAY STABLE — NO TRIP
6. Percentage-Biased Differential Characteristic
Fig. 2 — Operating characteristic: Id versus Ir
7. Differential Current Phasor Diagram
Fig. 3 — CT secondary current phasors
8. Live Calculation
I d = | I 1 + I 2 |
I r = | I1 | + | I2 | 2
I op = I pickup + S I r
Quantity Value
I₁ 0.000 A
I₂ 0.000 A
Angle 0°
Id 0.000 A
Ir 0.000 A
Bias slope 30%
Pickup 0.200 A
Iop 0.000 A
Relay decision STABLE
9. Experimental Observation Table
No. Condition I₁ I₂ θ Id Ir Iop Result
10. Engineering Interpretation
  • For normal load, CT secondary currents are ideally balanced and the differential current is small.
  • For an external fault, large through current produces substantial restraining current, improving relay stability.
  • For an internal fault, current imbalance produces differential current and the relay operates.
  • CT ratio errors and saturation can introduce spill current and may affect stability.
Important: This is an educational numerical model. Actual transformer differential relays may include vector-group compensation, zero-sequence compensation, multi-slope characteristics, harmonic restraint and manufacturer-specific algorithms.