87 Differential Protection Learning Module

⚡ 87 Differential Protection

Interactive Learning Module for Relay Technicians

Current & Relay Settings
I₁ Primary 5.0 A
I₂ Secondary -5.0 A
Relay Settings
Slope 1 k₁ 25%
Slope 2 k₂ 50%
Breakpoint IBP 6.0 A
Min. Pickup Imin 0.3 A
Operating Characteristic — Dual-Slope k₁/k₂
Slope 1
Slope 2
Breakpoint
Op. point
One-Line Diagram — Zone of Protection
ZONE OF PROTECTION XFMR Bus A Bus B CT1 600:5 ⚠ SAT CT2 600:5 ⚠ SAT 87 DIFF NORMAL ⚡ FAULT EXT FAULT I₁ = 5.0 A I₂ = 5.0 A
✓ RELAY STABLE
IOP
0.00
A
IRT
5.00
A
Threshold
1.55
S1
Decision
RESTRAIN
Normal Load: Equal currents entering and leaving. IOP ≈ 0. Relay stable.
📚 Theory Reference
Operating quantities:
  IOP = |I₁ + I₂|  (vector sum — operate current)
  IRT = (|I₁| + |I₂|) / 2  (restraint current)

Dual-slope trip condition:
  IRT ≤ IBP :  IOP > k₁×IRT + Imin
  IRT > IBP :  IOP > k₁×IBP + k₂×(IRT−IBP) + Imin

✓ Normal Operation

Current in = current out. CTs cancel — IOP ≈ 0. Point in Slope 1 restrain region.

⚠ Internal Fault

Current from both sides INTO zone — same CT polarity → high IOP → crosses slope → TRIP.

→ External Fault

High through current lifts IRT into Slope 2. IOP ≈ 0 — Slope 2 provides security.

📉 CT Saturation

Saturated CT under-reports → false IOP. Steep Slope 2 threshold prevents misoperation.