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Virtual Laboratory: Numerical Overcurrent / Earth-Fault Relay

Testing of a typical numerical type overcurrent and earth-fault relay

Single-Line Protection Test Circuit

11 kV BUS SOURCE CB CT 400/5 A LOAD EARTH CT SECONDARY NUMERICAL RELAY 50 / 51 / 51N TRIP COMMAND FAULT POINT PRIMARY CURRENT CT measurement → numerical processing → pickup comparison → selected relay characteristic → trip decision
Power circuit CT measurement circuit Fault / trip Healthy state
Primary Current
80.0
A RMS
CT Secondary
1.000
A RMS
Current Multiple
1.00
× pickup
Operating Time
∞
seconds

Current, Pickup & Fault Level

Relay Characteristic Curves

Mathematical Model & Calculation

CT Secondary Current
I s = I p × I CT,sec I CT,pri
Multiple of Pickup
M = I s I pickup
DMT
t = TMS
IDMT / VIDMT / EIDMT
t = k × TMS M α − 1
Calculations will appear here.

Relay Decision & Characteristic Selection

Pickup Criterion
I s ≥ I pickup ⇒ Relay − Pickup
Trip Criterion
M > 1 ⇒ Trip
Waiting for test conditions...
Curve Type k α Behavior
DMT Definite — — Fixed time
IDMT Standard inverse 0.14 0.02 Moderate inverse
VIDMT Very inverse 13.5 1.00 Strong inverse
EIDMT Extremely inverse 80 2.00 Very strong inverse
Important: The curves shown here are an educational numerical-relay model based on commonly used IEC inverse-time equations. Actual commercial protection relays can include tolerances, filtering, definite-time stages, instantaneous stages, manufacturer-specific curves and additional protection logic.