How to Test a Transformer Differential Relay (87T)

Transformer differential protection is simple in principle and awkward in practice. The principle is a current balance: what goes into the transformer should come out of it. The awkwardness comes from everything that legitimately breaks that balance in a healthy transformer — the vector group, mismatched current transformer ratios, an on-load tap changer moving under load, magnetising inrush, and overexcitation. An 87T element spends most of its design effort not detecting faults but refusing to react to those five things.

That is why a plan which only measures pickup tells you very little. This article walks through a full 87T test sequence, what each step proves, and the injection mistakes that produce confident but wrong conclusions.

Key takeaways

• An 87T element compares a per-phase differential current against a restraint quantity derived from the through-currents; the restraint, not the pickup, is what makes it usable.
• Before injecting anything you need the vector group, both winding ratings, both CT ratios, the reference current basis and the tap-correction factor.
• Inject either the compensated quantities the relay expects or primary-equivalent currents with relay-side compensation enabled. Mixing the two is the classic way to “prove” a correct relay is wrong.
• Through-fault stability and harmonic blocking map onto real misoperation modes, and are most often missing from the record.
• Acceptance limits come from the manufacturer’s declared accuracy. IEC 60255-187-1 governs how differential performance is specified and verified; IEEE C37.91 gives the application context.

What the 87T element protects, and what it compares

The 87T element covers faults inside the differential zone: winding-to-earth and winding-to-winding faults, bushing and lead faults, and faults in the connections between the zone-boundary CTs. It is a unit protection, fast and without coordination delay, because its selectivity comes from the zone boundary rather than from time grading.

For each phase the relay forms two quantities. The differential (or operate) current is the vector sum of the compensated, ratio-matched currents from every winding of the zone. The restraint (or bias) current is a scalar measure of the through-current — depending on the manufacturer it may be the arithmetic mean of the winding current magnitudes, half their sum, or the largest of them. That definition changes where the operate points land on the plane you are about to sweep, so read it out of the relay manual before you compute anything.

The characteristic is normally a dual-slope line on a plane with restraint current on the horizontal axis and differential current on the vertical:

Idiff_required = Ipickup                                     for Ibias <= Iknee
Idiff_required = Ipickup + m2 * (Ibias - Iknee)              for Ibias >  Iknee

where the first region may itself be sloped by m1 rather than flat,
depending on the relay's setting model.

Some relays express slope 1 from the origin, some from the pickup level; some define the knee as a bias breakpoint, some as an intersection of two lines. Two relays with identical numeric settings can therefore have measurably different boundaries, so the characteristic you plot against must be the one the relay’s own documentation defines.

Why 87T is harder than line differential

A line differential scheme compares two ends of the same conductor. Ratio, phase and turns are the same at both ends, so a healthy line produces near-zero differential current. A transformer breaks every one of those assumptions.

Vector group phase shift. A transformer with a delta winding on one side and a star winding on the other displaces the line currents by a fixed angle, conventionally a multiple of 30 degrees and identified by the clock-hour figure in the vector group designation (IEC 60076-1 clock notation). A Dyn11 unit places the LV phasors at the 11 o’clock position relative to HV at 12, a 30 degree displacement. Sign conventions for which side leads differ between texts and between relay manuals, so treat the manual’s compensation table as authoritative rather than reasoning it out from memory. The relay resolves this either by rotating one winding’s phasors internally or by expecting the tester to supply already-rotated quantities.

CT ratio mismatch. The two windings carry different rated currents, and their CTs are chosen from standard ratios, so the secondary currents at rated load are not equal. The relay applies an amplitude matching factor per winding, usually derived from a reference current basis:

Iref(winding) = S_ref / (sqrt(3) * U_winding)

100 MVA, 132/33 kV:
  HV rated current = 100e6 / (1.732 * 132e3) = 437 A
  LV rated current = 100e6 / (1.732 * 33e3)  = 1750 A

With HV CT 600/1 and LV CT 2000/1:
  HV secondary at rating = 437 / 600  = 0.729 A
  LV secondary at rating = 1750 / 2000 = 0.875 A
  amplitude mismatch     = 0.875 / 0.729 = 1.20

A 20 percent standing imbalance is far above any sensible pickup. The relay’s matching factors remove it; your expected-value calculation has to reproduce them.

On-load tap changer range. Moving the tap changes the turns ratio, so a relay matched at nominal tap sees a real differential current at the extremes of the range — a plus or minus 10 percent range contributes up to roughly 10 percent false differential at full through-current if matching is set to mid-tap. Some relays read tap position and correct continuously; most do not, and the slope setting is expected to absorb it. Note which case you are in, because it changes what a “correct” slope looks like.

Magnetising inrush. Energising a transformer draws an asymmetric, heavily distorted magnetising current into one winding only, which is by definition differential current. It is rich in second harmonic, and relays block on the ratio of second-harmonic to fundamental in the differential current, either per phase or cross-blocked across phases.

Overexcitation. Sustained overvoltage drives the core into saturation and produces a magnetising current rich in odd harmonics, with fifth harmonic the usual discriminant. A fifth-harmonic block prevents tripping on that condition.

Zero-sequence current on the earthed winding. An earth fault outside the zone, or an earthed star winding fed from a delta, can circulate zero-sequence current that appears in the star-side line currents but has no counterpart on the delta side. Relays remove it — either implicitly, because the compensation matrix that applies the 30 degree rotation also cancels zero sequence, or explicitly through a zero-sequence subtraction setting on the winding with an earthed neutral. Check which mechanism is active: it changes the differential current you will measure for a single-phase injection.

Preparing to test

Assemble and record the following before the test set comes out of the case. A large share of the “relay is wrong” findings in commissioning reports are missing entries in this list.

Item	Why you need it
Vector group and clock figure	The compensation the relay applies or expects
Winding ratings (MVA, kV)	The reference current basis per winding
CT primary and secondary ratings	Amplitude matching factor and injection scaling
Reference current basis in the relay	Whether settings are per-unit of winding rating, CT rating or a fixed reference
Tap-correction method and factor	Whether tap error is corrected or absorbed by slope
Differential pickup	Minimum operate level at low restraint
Slope 1, knee/bias breakpoint, slope 2	The dual-slope boundary to verify
Unrestrained (high-set) level	Where restraint and harmonic blocking are bypassed
Second-harmonic threshold and mode	Per-phase or cross-blocked, and the asserting ratio
Fifth-harmonic block threshold	Overexcitation restraint level
Zero-sequence elimination setting	Changes single-phase injection results
CT connection and polarity drawing	Which test channel feeds which relay input

Published examples often put pickup around 0.2 to 0.3 of reference current, slope 1 in the 20 to 30 percent region, and the unrestrained element around eight to twelve times reference. Those are orientation figures only — each is a design decision for the specific unit and the site’s fault duty. Test against the setting file, never against a remembered typical value.

The test sequence

1. Minimum pickup

Inject into one winding only, at low current, and raise the current until the element operates. With single-side injection the restraint quantity is small, so this locates the flat (or low-slope) region of the characteristic. Repeat per phase — a wiring or compensation error often shows as one phase behaving differently. If the relay eliminates zero sequence on the winding being injected, single-phase injection is attenuated; use a two- or three-phase pattern instead and state which in the record.

Proves: the measuring element’s sensitivity and the per-phase input path.

2. Slope characteristic verification

This is the substance of the test. Choose several restraint values spread across the plane — a few below the knee, one close to it on each side, and several well into the slope 2 region. At each, search for the differential current at which the element just operates.

The mechanics: drive the two windings’ currents so that the restraint quantity holds at the target while the differential current is stepped or ramped. For a two-winding relay whose restraint is the mean of the winding magnitudes, that means adjusting both channels together rather than moving one. A bisection search converges quickly — bracket the operate point between a known no-operate and a known operate level, then halve the interval until the bracket is inside the resolution the plan commits to.

Plot measured operate points against the computed dual-slope line. The shape of the error matters more than any single point: a uniform offset suggests a matching-factor or reference-basis mismatch, a rotating error suggests a compensation mismatch, and a discontinuity near the knee usually means you and the relay disagree about how the knee is defined.

Proves: the restraint characteristic across its working range, including the knee transition.

3. Unrestrained high-set element

Inject a differential current above the high-set level at a restraint value where the restrained element would be blocked, and confirm operation — ideally with a shorter operate time than the restrained path. Then verify just below the level that the high-set does not pick up.

Proves: the fast path for heavy internal faults, and that it is not set so low as to defeat harmonic blocking during inrush.

4. Second-harmonic inrush blocking

Inject a differential current comfortably above pickup with a superimposed second-harmonic component, and vary the harmonic ratio. Find the ratio at which blocking asserts and, separately, the ratio at which it releases — the two differ if the relay has hysteresis, and the release point determines how quickly the element becomes available after energisation. Record both.

If the relay cross-blocks, repeat with harmonic content in one phase only and confirm the other phases are held as the setting describes. Cross-blocking is a security feature that can also delay tripping for a genuine fault during energisation, so its behaviour belongs in the record.

Proves: the inrush restraint that keeps the transformer connected during energisation.

5. Fifth-harmonic overexcitation blocking

The same procedure with a fifth-harmonic component. Some relays reduce or remove fifth-harmonic blocking above a defined level, so that a genuine fault during an overvoltage is not blocked indefinitely; if that setting exists, test its boundary too.

Proves: overexcitation restraint, and that it releases when it should.

6. Through-fault stability

Inject balanced, in-phase-correct current through the zone — into one winding and out of the other, at the compensated equivalent — at load level and then at through-fault level, and confirm the element does not operate. Sweep upward to the highest current the test set can deliver.

This is the test most often skipped and the one that maps most directly onto real misoperations. Its usual findings are reversed polarity on one CT circuit, a matching factor entered against the wrong winding, an interposing CT that has been rewired, or a shorting link left in.

Proves: security for load and external faults — the property that keeps the transformer in service.

7. Operate time at a representative point

Measure operate time at a point clearly inside the characteristic — say two to three times the required differential current at a mid-range restraint value — and record the timing reference used. One point is enough; the characteristic verification has already covered the boundary.

Proves: the element’s operating time under declared conditions, and the output path.

8. Where CT saturation enters

Everything above uses clean injected sinusoids at the relay terminals, so the current transformers are not in the loop at all. The misoperation mode where one side’s CT saturates during a through-fault and the relay sees a large false differential current cannot be produced by that kind of test; it needs CT dimensioning review and waveform playback. See CT saturation and relay testing, and IEEE C37.110 for CT application in relaying.

Injecting correctly

Three current channels drive winding 1; a second three drive winding 2. Which physical channel maps to which relay input comes from the CT connection drawing, not from channel numbering convention.

The decision to make explicitly is where compensation happens:

• Relay-side compensation. Leave the relay’s vector-group and matching settings active and inject primary-equivalent currents — the currents the CTs would actually deliver for the condition being simulated, with the real phase displacement between windings. The relay does the rotation and matching. This tests the compensation as configured, which is usually what commissioning needs.
• Test-side compensation. Compute the compensated, ratio-matched quantities yourself and inject those. This isolates the measuring element from the compensation logic, which helps when chasing a discrepancy, but it only tells you about the characteristic.

The classic error is doing half of each: injecting currents that are already phase-shifted into a relay that then applies its own 30 degree rotation. The result is a standing differential current on through-current injection and a slope characteristic that looks displaced and rotated. It is easy to write that up as “relay does not match settings” when the relay is behaving exactly as configured. If a through-fault stability test shows a large standing differential, suspect the injection scheme before the relay.

The second common error is a per-unit basis mismatch. If the relay expresses pickup in per-unit of a reference current derived from winding MVA and you compute expected values in per-unit of CT rating, the expected values are wrong by the matching factor — 1.20 in the example above — and every measured point sits consistently off the line.

Assessing the results

Record measured against expected for every point, with the deviation, and compare it against a tolerance declared before testing. That tolerance should come from the manufacturer’s stated accuracy under the reference conditions the manufacturer declares. Published differential pickup and slope accuracies are commonly framed in the low single-digit percent range, sometimes with an absolute floor for small values, but the figure in the relay’s technical data for the applicable setting range governs.

Two references sit behind this. IEC 60255-187-1 specifies how the functional and performance requirements of differential protection for motors, generators and transformers are to be stated, tested and documented — it defines what a manufacturer’s accuracy claim has to mean and how to verify it. IEEE C37.91 is an application guide for protecting power transformers: it holds the reasoning about fault types, CT behaviour and scheme selection, not test tolerances. IEEE C37.233 covers system-level protection testing, the layer above these element tests.

Resolve any out-of-tolerance point before writing the report. The order of suspicion that saves the most time: injection scheme, per-unit basis, setting file version, wiring, then the relay.

Records that stay useful

An 87T record that cannot be reconstructed three years later is of limited value in a misoperation review. As-found and as-left values both belong in it, with the setting file identifier and checksum if the relay provides one, the firmware version, the test set model and calibration date, the injection scheme used, the CT data for both windings, and the restraint definition assumed.

Where a formal maintenance regime applies, the evidence requirements are explicit — see the PRC-005 evidence checklist and NERC PRC-005-6. Versioned test templates make this far less painful than rebuilding the plan each time; XRIO templates covers carrying settings from the relay into the test plan without retyping them.

Rehearsing the plan before you lift a lead

Much of the cost of an 87T test is discovering, on site, that the plan was wrong: the wrong restraint definition, the wrong per-unit basis, test points that all land in one slope region, a harmonic search with too coarse a step. All of those are findable at a desk.

GridAPM ProtectionAI includes an 87T module that runs the slope sweep and the harmonic-block searches against a built-in simulator, so the whole sequence — compensation, matching factors, test-point spread, boundary searches, expected-versus-measured plots — can be exercised and corrected before it becomes field time. To be plain about the limits: published v1.3 is simulator-only, and the v1.4 source candidate’s bounded OMICRON path does not implement or physically qualify this 87T workflow. What it provides is a rehearsed, versioned plan and report structure, not a qualified injection. See ProtectionAI capabilities for what is built and what is not, and relay testing software for how this fits alongside the test-set vendors’ own tools.