⚡ 87 Differential Protection
Interactive Learning Module for Relay Technicians
Operating Characteristic — Dual-Slope k₁/k₂
Slope 1
Slope 2
Breakpoint
Op. point
One-Line Diagram — Zone of Protection
📚 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
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.