Phase Academy Interactive Power Systems Lab

Differential Protection Simulator

Educational 87T · 87B

Differential Protection Simulator

Build intuition for how differential relays compare current entering and leaving a protected zone — internal vs external faults, CT mismatch, restraint slope, and inrush blocking.

87 · Differential Conceptual · Educational Simplified single-slope model Not relay setting software
System Normal — No Trip
I Entering (raw)
500
Amps
I Leaving
500
Amps
I Differential
0.0
Amps
Restraint Qty
500
Amps
Trip Decision
No Trip
Inrush Blocking
Inactive
🛡 Relay Margin & Current Balance
Margin to Trip
100%
I Entering (raw)500 A
500
I Leaving (relay-effective)500 A
500
I Differential0.0 A · trip at 125 A
0
Live Insight: Everything looks balanced. Current entering the zone equals current leaving — exactly what differential protection expects under normal load.
「∿」 Current Waveforms
Conceptual waveforms: entering (dark navy) and leaving (light blue, relay-effective) currents
📈 Operating Point Chart
📋 Event Log
Recent events and trip decisions (elapsed time since page load)
🔍 Protection Zone Visualization
The dashed boundary defines the protection zone. The relay compares current entering vs leaving this zone using relay-effective (CT-mismatch-applied) values. Bus mode shows actual multi-feeder summation.
What to notice: Differential protection is suspicious when current goes missing inside the zone. If the same current that enters also leaves, the relay stays calm.
📈 Operate vs. Restraint Characteristic
The relay trips when the operate quantity rises above the restraint characteristic line. Points above = trip.
⚖ Current Balance Breakdown (relay-effective)
Entering Current
500 A
Leaving Current
500 A
Differential (|In − Out|)
0.0 A
Restraint ((In + Out)/2)
500 A
How to read this: When the dark-navy and light-blue bars are equal, differential is zero. The bigger the gap between them, the more suspicious the relay gets.
🧪 Scenario Lab
Load a preset scenario, study its behavior, then tweak controls to explore edge cases. Each scenario tells a story.
Select a scenario above to load its parameters and see how differential protection responds.
📑 Scenario Analysis
Choose a scenario to see a detailed breakdown of why the relay does (or doesn't) trip.
🎯 Scenario Operating Point
⚡ Transformer Differential Concept
Transformers change voltage and current by their turns ratio. The relay compares compensated equivalent currents on each side — not raw amps.
Key concept: The relay doesn't compare raw primary vs secondary amps. It compares compensated secondary values — accounting for turns ratio and CT ratios. This simulator does not model phase-angle (vector group) compensation.

Why Differential Protection Matters

Differential protection is one of the fastest and most selective protection schemes in power systems. It protects a specific zone — a transformer, bus, generator, or cable — by applying a simple but powerful principle:

Current entering the zone should equal current leaving the zone. If it doesn't, something inside the zone is consuming (or diverting) that current — likely a fault.

This makes it fundamentally different from overcurrent protection, which just looks at magnitude. Differential protection cares about balance.

How Differential Logic Works

The relay calculates two quantities from the CT measurements on each side of the zone:

Operate quantity (Idiff) = |Iin − Iout| — the "missing" current.

Restraint quantity (Irestraint) = (Iin + Iout) / 2 — the through-current level.

The relay trips when: Idiff > max(Threshold, Slope × Irestraint)

Think of it like airport security: the restraint slope is how much leeway you give. During heavy traffic, you expect a little more "noise" in the measurements, so you raise the bar for tripping.

Real 87 elements evaluate this logic per phase on compensated quantities; this simulator uses a single magnitude pair to keep the concept front and center.

Internal vs External Faults

Internal fault: A fault inside the zone. In this simplified one-source model, current flows in but most of it is diverted to the fault, so outgoing current drops sharply. In real multi-terminal zones, current can flow into the fault from multiple terminals, and the differential is the sum of all terminal contributions.

External fault: The fault is outside the zone. Current flows through to reach the fault. Both sides increase together. Result: Idiff stays low → relay restrains.

External faults are dramatic, but not always this relay's problem. The relay protecting the faulted zone will handle it.

Inrush & Harmonic Blocking

Energizing a transformer draws large magnetizing inrush current on one side only — it looks exactly like an internal fault. Inrush is rich in 2nd harmonic, so this simulator uses simplified 2nd-harmonic blocking: when harmonic content meets the block threshold, the trip is blocked. Some real relays instead add harmonic content to the restraint quantity (harmonic-restrained implementations) rather than hard-blocking — both approaches exist in practice, with different security/dependability trade-offs.

Not modeled here (87U): Real transformer schemes also include an unrestrained high-set differential element (87U) that trips on very large differential current regardless of harmonic blocking — so a genuine fault during energization is still cleared. This simulator's toggles make inrush and faults mutually exclusive, which sidesteps exactly the scenario 87U exists for.

Common Mistakes

Mistake #1: Assuming external faults can't cause differential current. They can — if CTs saturate unevenly, false differential current appears. That's why the restraint slope exists.
Mistake #2: Forgetting about inrush. Energizing a transformer creates huge magnetizing current on one side only. Without 2nd-harmonic blocking (or an equivalent restraint), the relay would trip every energization.
Mistake #3: Ignoring CT sizing. Mismatched CTs produce standing differential current that eats into your margin to trip.

What to Notice in the Simulator

  • Normal load: Differential stays at zero (or near zero with CT mismatch).
  • Internal fault: Differential jumps — current enters but doesn't leave (simplified one-source model).
  • External fault: Both currents increase equally — differential stays low. In bus mode the through-fault is concentrated in one feeder, which is why uneven CT saturation matters.
  • CT mismatch: Creates standing differential that increases with load.
  • Inrush: Large differential with no real fault — 2nd-harmonic blocking can block the trip.
  • Borderline: Operating point near the trip line — small changes swing the decision. At exactly Idiff = threshold the relay does not trip: the criterion is a strict "greater than".

Test Your Knowledge

For education only · Verify against codes
This is a conceptual teaching tool designed to build intuition about differential protection principles. It is not relay setting software and should not be used for protection coordination, relay configuration, or any real-world application. Harmonic blocking is shown in a simplified form and does not model manufacturer-specific relay logic; unrestrained high-set (87U) and 5th-harmonic/over-excitation elements are not modeled. Phase-angle (vector group) compensation is not modeled. Always consult qualified protection engineers and manufacturer documentation for actual relay settings.