Protection · Device 87T

Transformer Differential Protection (87T): Proving the Dual Slope, Inrush Restraint and REF on the Actual Relay

How an 87T scheme stays stable for load and inrush yet trips internal faults — bias, dual slope, 2nd/5th-harmonic restraint and REF — proven number by number on SEL-787, MiCOM, ABB and Siemens.

Published 2026-08-03 · EI Portal

Transformer differential protection (87T) has to do three hard things at once: stay perfectly stable for load and external through-faults, operate quickly for an internal fault, and refuse to be fooled by the large differential current of magnetising inrush. This article explains how each mechanism works — and then proves it, number by number, on four real relay families: MiCOM P632/P633/P634, ABB RET/REG (REX640), Siemens 7UT86 and the SEL-787. Same scheme, proven on the actual relay's own characteristic.

The core idea — and why it isn't that simple

Differential protection compares current in against current out. For a healthy transformer what goes in comes out, so the differential (operate) current is near zero; for an internal fault it isn't. Simple — except a transformer changes the current between its windings, so you cannot just subtract the raw CTs. Before any comparison the relay rotates one side by the vector-group clock (clock × 30°) and removes zero-sequence on earthed-star windings, so the phasors line up and cancel. Get the clock or the zero-sequence handling wrong and a healthy transformer shows spill current.

The default scenario throughout this article is a 90 MVA, 132/33 kV transformer, HV YN clock 0, LV delta clock 9, with HV CT 400/1 and LV CT 2000/1 — a typical two-winding grid transformer.

The percentage-bias characteristic — and the dual slope

Real CTs are not perfect, so even a healthy scheme has a little spill — more at high through-current, where CT saturation bites. The percentage-restraint (biased) characteristic raises the operate threshold as the restraint (through) current rises, so genuine internal differential current trips while external-fault spill stays restrained. A dual slope sharpens the trade-off: a gentle first slope for sensitivity near load, a steep second slope above a knee for security at high through-fault.

On an SEL-787 the operate current is IOP and the restraint current is IRT (the scalar sum of the winding magnitudes). The dual-slope threshold is:

threshold(IRT) = max( O87P , SLP1 · IRT )              for IRT ≤ IRS1
      threshold(IRT) = SLP1·IRS1 + SLP2·(IRT − IRS1)         for IRT > IRS1
      operate when IOP ≥ threshold(IRT)   (and not harmonic-blocked)
      

With the SEL-787-4 factory Group Settings the tool starts from O87P 0.3, SLP1 25%, SLP2 70%, IRS1 6, U87P 10, PCT2/PCT4 15%, PCT5 35%, HRSTR = Y, HBLK = N — the manual's own defaults, shown as tunable starting points, not prescribed values.

A worked SEL-787 dual-slope example

The sharpest way to see the dual slope is a sensitive internal fault and a heavy external fault, side by side.

Take an internal fault at IRT 4.38. Because 4.38 is below the knee IRS1 (6), the threshold is on the first slope: 0.25 × 4.382 ≈ 1.096. The operate current exceeds 1.096, so IOP ≥ threshold → OPERATE (trip).

Now take a heavy external through-fault at IRT 16.26. This is above the knee, so the steep second slope applies: 0.25 × 6 + 0.70 × (16.26 − 6) = 1.5 + 0.70 × 10.26 ≈ 8.68. The compensated currents still cancel — the differential is 0.000 — so the scheme is RESTRAINED, and even a real CT error spilling current would have to beat the raised 8.68 threshold.

That single pair of points is the whole argument for the dual slope: sensitive at IRT 4.38, secure at IRT 16.26.

Inrush and over-excitation: harmonic restraint

Energise a transformer and magnetising inrush can push several times rated current into the differential — but it is not a fault. The discriminator is harmonic content. Inrush is rich in 2nd harmonic (and 4th); internal faults are not. On the SEL-787 the HRSTR logic uses 2nd/4th-harmonic restraint with cross-phase blocking (HBLK), while a separate 5th-harmonic element blocks on transformer over-excitation.

In the proving library a 45% 2nd harmonic (above PCT2 15%) makes the harmonic restraint raise the operate threshold to 4.380 — the differential (1.348 pu) rides through below it on inrush. A 40% 5th harmonic (above PCT5 35%) trips the 5th-harmonic block and restrains on over-excitation. Both are flagged as warnings, not trips.

Restricted earth fault (REF): catching what the phase 87 misses

For an earth fault near the star point, phase differential can be insensitive — the phase currents barely change. A restricted earth fault element compares neutral and residual current to catch it. The proving library makes the point cleanly: the differential current is 0.102 pu, below the 0.300 pickup, so the phase differential does not operate — yet the zero-sequence directional REF operates on the neutral CT (operate 0.800 pu against a 0.100 threshold) and trips. The REF catches the internal earth fault the phase 87 misses.

Four relays, four vocabularies — all manual-backed

Each backend speaks its own manual's language:

• MiCOM P632/P633/P634 (GE/Schneider) — winding-native backend with autotransformer arrangement templates and an optional REF companion. Harmonic thresholds: 2nd 20%, 5th 35%.
• ABB RET/REG (REX640) — models TR2PTDF / TR3PTDF differential, LREFPNDF / HREFPDIF companion REF and CTSRCTF supervision. Harmonics 2nd 15%, 5th 35%; slope 0.2 without tap-changer, 0.455 with.
• Siemens 7UT86 — models the manual I-DIFF characteristic, I-DIFF Fast, the unrestrained differential, timed 2H/CWA/5H/add-on stabilisation memory, tap-changer current adaptation, and companion 87N restricted ground fault.
• SEL-787 — percentage-restraint 87R (IOP/IRT, dual-slope SLP1/SLP2/IRS1, O87P pickup), the unrestrained 87U, 2nd/4th-harmonic restraint (HRSTR) with cross-phase blocking (HBLK), independent 5th-harmonic over-excitation blocking, and the zero-sequence directional REF.

The SEL-787 proving library at a glance

Six engine-run, hand-checked scenarios on the factory settings:

The commissioning trap

The classic stability error is a reversed CT polarity or a CT ratio / correction mismatch. Either makes the currents add instead of cancel, so a scheme that looks fine at no-load trips on load. This is exactly the kind of thing best caught on paper, before energising.

Pick a relay — MiCOM P63x, ABB RET/REG, Siemens 7UT86 or SEL-787 — load a scenario, and watch the phasor compensation, the operating point on the dual slope, the harmonic block flags and the decision. It never invents a value you haven't entered.

Frequently asked questions

Is this the vendor's configuration software?

No. It is a vendor-faithful proving and interpretation workspace with manual-backed settings. It is not a relay configurator, it does not generate a settings file, and it does not replace the manufacturer's tools, a commissioning sign-off, or a protection study.

Where do the SEL-787 default settings come from?

They are the SEL-787-4 manual Group Settings factory defaults — O87P 0.3, SLP1 25%, SLP2 70%, IRS1 6, U87P 10, PCT2/PCT4 15%, PCT5 35%, HRSTR = Y, HBLK = N — shown as tunable starting points, not prescribed values.

How is the dual-slope threshold calculated?

threshold(IRT) = max(O87P, SLP1·IRT) for IRT ≤ IRS1, and SLP1·IRS1 + SLP2·(IRT − IRS1) for IRT > IRS1. The scheme operates when IOP ≥ threshold and is not harmonic-blocked. Worked: IRT 4.382 → 1.096 (trip); IRT 16.26 → 8.68 (restrained).

Why does the REF trip when the phase differential doesn't?

For a low-level internal earth fault near the star point the phase currents barely move — the operate current is 0.102 pu, below the O87P 0.300 pickup, so the phase 87 stays put. The zero-sequence directional REF on the neutral CT sees the residual and operates (0.800 pu against its 0.100 threshold), catching the fault the phase element misses.