Positive-sequence V1/I1
The operating phasor is positive-sequence current and the polarizing phasor is positive-sequence voltage. Pickup also requires the maximum phase current to reach the configured threshold.
Quantity selection
67P and 67N use different measurement domains.
Residual 3V0/3I0
The operating phasor is residual current and the polarizing phasor is residual voltage. Explicit decoded neutral/residual channels are preferred over calculated phase-sum fallback.
Directional equation
The selected region is derived from operating angle and MTA.
operatingAngle = normalize(angle(Iop) - angle(Vpol))
torque = cos(operatingAngle - characteristicAngle)
forwardRegion = torque > 0
selected = forwardRegion when sense = Forward
not forwardRegion when sense = ReverseA directional decision becomes unavailable when the polarizing-voltage magnitude is below the configured minimum. Current pickup, selected direction, elapsed delay, SMV pickup permission, and SMV trip permission remain separate conditions.
Operate chain
A directional trip requires more than positive torque.
01Complete trusted phasor set
02Current above pickup
03Polarizing voltage available
04Selected direction true
05Pickup permission granted
06Configured delay elapsed
07Trip permission granted
Deterministic evidence
Forward operate is paired with reverse restraint.
| Scenario | Input relationship | Expected behavior | Automated anchor |
|---|---|---|---|
DIR-001 | 67P current aligned with configured forward characteristic | Directional pickup, delay, virtual trip | DirectionalPhase67_TripsForwardAndRestrainsReverse |
DIR-002 | 67P reverse-region current | No pickup and no trip | Same paired test method |
DIR-003 | Balanced phase sum with independent residual channels | 67N uses explicit 3I0/3V0 and operates | DirectionalEarth67N_PrefersIndependentResidualChannelOverBalancedPhaseSum |
Evidence output
Direction is preserved as review context.
The directional decision records polarizing availability, selected direction, operating angle, torque, operating magnitude, polarizing magnitude, and a readable reason string. The protection operation record also preserves operated element, phase or earth attribution, timestamps, quantity, settings identity, and trust state.
Engineering value: reviewers can see why the element considered a case forward or reverse rather than receiving only a binary trip indication.
Current boundary
This is a transparent beta implementation, not a complete vendor relay characteristic.
Not currently implemented
- Memory polarization
- Negative-sequence polarization for 67N
- Phase-specific cross polarization
- Load encroachment or power-swing supervision
- Directional comparison schemes
- Type-tested relay characteristic tolerances
Future validation track
- Angle sweep across forward/reverse boundaries
- Minimum-voltage supervision sweep
- Residual-channel provenance cases
- Noise and unbalance sensitivity
- Off-nominal frequency effects
- Hardware-in-the-loop timing comparison