This simulator models an 87T transformer differential relay protecting a two-winding power transformer between HV and LV current-transformer boundaries. Separate ratio and phase compensation from percentage restraint, CT error and harmonic supervision, and see how through-current, internal faults, CT problems and inrush current each move the operate and restraint quantities.
• A real-time 3D differential zone — HV system, HV CT, protected transformer, LV CT, the 87T relay and isolation breakers — with camera home view, focus-selected-part, toggleable enclosure, auto-rotate, expand and tap-to-inspect components. • Eleven live controls: through current (0.2–8 pu), added internal-fault current (0–10 pu), LV CT ratio error (±30%), LV CT fundamental attenuation (0–80%), a reverse-LV-CT-polarity checkbox, a compensate-30°-vector-group-shift checkbox, percentage restraint slope (10–80%), minimum differential pickup (0.1–1 pu), a second-harmonic ratio fixture (0–40%), an enable-harmonic-blocking-at-15% checkbox, and an unrestrained high-set (4–15 pu). • Play/pause, single step, larger step, and 0.1×/1×/10×/60× playback speed. • Actions to apply a fault/inrush fixture, remove the added current, and reset & reclose. • An Operate/restraint analysis tab with two live charts, the underlying model equations, and snapshot measurements. • A Test & diagnose style Experiments tab with five guided experiments, an independent model-verification bench, and a timestamped event log with a copyable trial report. • A Learn & assess tab with guided lessons, a knowledge-check quiz and a written scope statement with a reference link.
The relay compares the HV current (already referred to a common per-unit base) against the LV current after removing the transformer's 30° vector-group phase shift. Operate current is the magnitude of the phasor difference between the two; restraint current is half the sum of their magnitudes. For an external (through) fault, properly compensated currents very nearly cancel, so operate current stays low relative to restraint — the relay stays secure.
For an internal fault, current is added inside the protected zone and does not balance at both CT boundaries, so operate current rises above the percentage-restraint boundary and the zone trips. CT ratio error, reversed polarity, or missing phase compensation can all push operate current up even without a real internal fault, which is why restraint slope, harmonic blocking and the unrestrained high-set element all exist as independent safeguards.
The operate boundary is max(minimum pickup, slope × restraint current) — a larger through current raises the boundary proportionally, so the relay tolerates a bounded amount of CT error on heavy through-fault current without misoperating. The second-harmonic ratio fixture is an independently imposed test value in this teaching model; when harmonic blocking is enabled, a ratio at or above 15% blocks the restrained low-set element, representing how energizing inrush current (rich in second harmonic) can be distinguished from a genuine internal fault.
The unrestrained high-set element bypasses harmonic blocking entirely once operate current reaches its own high threshold, on the reasoning that current that large is very unlikely to be inrush. This is a single referred phase-equivalent phasor model: CT saturation is a user-selected fundamental attenuation rather than a magnetic-transient simulation, there is no full three-phase compensation matrix or zero-sequence elimination, and none of it represents manufacturer-specific relay logic.
The relay compensates the LV current for the transformer's vector-group phase shift, then compares it against the HV current. Operate current is the magnitude of their phasor difference; restraint current is half the sum of their magnitudes. For a through fault, compensated currents nearly cancel and operate current stays below the percentage-restraint boundary. For an internal fault, current is added inside the protected zone, operate current rises above the boundary, and the zone trips.
The operate boundary is the larger of a minimum pickup and the restraint slope times restraint current. Because restraint current rises with heavy through current, the boundary rises too — this lets the relay tolerate a bounded amount of CT ratio error or saturation during external faults without a false differential trip, while still being sensitive to internal faults where operate current climbs independently.
Energizing inrush current is rich in second-harmonic content and can otherwise look like an internal fault to a differential relay. In this teaching model, the second-harmonic ratio is an independently imposed test fixture; when harmonic blocking is enabled, a ratio at or above 15% blocks the restrained low-set element from tripping, while an unrestrained high-set element still bypasses that block once operate current is large enough.
This is a single referred phase-equivalent phasor model. CT saturation is represented as a user-selected fundamental attenuation rather than a magnetic-transient simulation, the harmonic ratio is independently imposed rather than derived from a waveform, and there is no full three-phase compensation matrix, zero-sequence elimination, or manufacturer-specific relay logic.