Transformer Differential Protection: Percentage Restraint Characteristic, CT Matching & Yd Vector Group Compensation, 2nd/5th Harmonic Blocking, and REF Coordination

Abstract

Transformer differential protection (ANSI 87T) is the primary fast protection for internal phase-to-phase and phase-to-ground faults in power transformers. Unlike a generator or busbar differential scheme — where the protected zone is electrically symmetric and the primary and secondary currents are nominally equal — a transformer differential scheme must contend with: (1) the transformer turns ratio (current magnitude difference), (2) the vector group phase shift (Yd1, Yd11, etc.), (3) the magnetizing inrush current that appears as a differential current but is not a fault, (4) different CT ratios and saturation characteristics on the HV and LV sides, and (5) the fact that the transformer's own impedance limits the differential current for internal faults near the neutral end of the winding. This article explains each of these challenges and the standard solutions: percentage restraint (biased differential) characteristic — the dual-slope operating curve that provides security against CT errors during through-faults while maintaining sensitivity for internal faults, CT ratio matching and Yd phase-angle compensation — how the numerical relay internally compensates for the transformer vector group, second and fifth harmonic blocking to discriminate inrush and overexcitation from internal faults, and coordination with restricted earth fault (REF, ANSI 64REF) protection to cover winding-ground faults near the neutral that the differential relay may not detect.

1. The Percentage Restraint Characteristic

1.1 Differential and Restraint Currents

The numerical differential relay computes two fundamental quantities from the sampled terminal currents:

Differential current (I_diff): The vector sum of all currents entering and leaving the protected zone.

I_diff = |I_HV + I_LV| (after ratio and phase-angle compensation — see Section 2)

For a healthy transformer (no internal fault) with matched CT ratios and correct compensation: I_diff ≈ 0 (or, in practice, a small "spill" current due to CT errors, the transformer's magnetizing current, and OLTC tap-position variation).

Restraint current (I_restraint): A function of the current magnitudes entering and leaving the protected zone. The most common definition:

I_restraint = (|I_HV| + |I_LV|) / 2 (average restraint)

Alternative: I_restraint = max(|I_HV|, |I_LV|) (maximum restraint — more conservative)

1.2 Dual-Slope Operating Characteristic

The relay trips when the differential current exceeds a threshold that increases with the severity of the through-current (to provide security against CT saturation during through-faults):

Region 1 — Minimum Pickup (No Restraint, I_restraint = 0): I_diff > I_diff_min → Trip unconditionally. I_diff_min is typically 0.2-0.3 × I_rated (20-30% of the transformer's rated current). This region provides sensitivity for low-current internal faults (turn-to-turn faults, high-resistance ground faults).

Region 2 — Slope 1 (Restrained Region): I_diff > I_diff_min + Slope1 × (I_restraint - I_restraint1)

Slope1 is typically 20-30%. This region provides the primary operating characteristic: for every increase in through-current, the differential pickup current increases proportionally. The slope accounts for CT errors that increase with current.

Physical basis for Slope1: CT ratio error (typically ±1-5% for Class 5P CTs), plus the transformer's OLTC tap-position range (±10% from the nominal tap means the ratio compensation applied by the relay is correct only at the nominal tap — at extreme tap positions, a differential "error" current of up to 10% of rated appears as a normal condition, not a fault).

Slope1 > (CT_error) + (Tap_changer_deviation) + (Relay_measurement_error)

For a typical installation: 5% (CT error) + 10% (OLTC range) + 2% (relay error) = 17%. Setting Slope1 = 25% provides a 8% security margin.

Region 3 — Slope 2 (High-Current Region): I_diff > I_diff_min + Slope1 × (I_break2 - I_restraint1) + Slope2 × (I_restraint - I_break2)

Slope2 is typically 50-80%. This region addresses CT saturation during severe external faults: at high through-current (>5-10 × I_rated), one of the CTs (typically the one with the higher burden — longer lead length or the CT closer to the fault source) may saturate, causing a false differential current. The steeper slope prevents false tripping.

Typical settings:

Parameter	Typical Setting	Physical Meaning
I_diff_min (pickup)	0.2-0.3 × I_rated	Minimum differential current for trip
Slope1	25-30%	Restrained region slope (CT error + OLTC range)
I_restraint1 (end of Slope1)	0.5-2.0 × I_rated	End of normal operating region
Slope2	60-80%	High-current region slope (CT saturation security)
I_break2	3-5 × I_rated	Transition point to Slope2 (CT saturation onset current)

2. CT Matching and Yd Vector Group Compensation

2.1 CT Ratio Matching

The transformer has a turns ratio that converts the primary rated current to the secondary rated current. The CT ratios on the HV and LV sides are typically selected to produce approximately equal secondary currents at the relay terminals:

HV CT ratio ≈ I_HV_rated / (1 A or 5 A) LV CT ratio ≈ I_LV_rated / (1 A or 5 A)

For a 50 MVA, 132/33 kV, YNd1 transformer:

• I_HV_rated = 50 × 10⁶ / (√3 × 132,000) = 218.7 A → HV CT ratio: 250/1 A
• I_LV_rated = 50 × 10⁶ / (√3 × 33,000) = 874.8 A → LV CT ratio: 1,000/1 A

CT secondary currents: HV = 218.7/250 = 0.875 A, LV = 874.8/1,000 = 0.875 A → Matched.

In a numerical relay, any residual mismatch (due to standard CT ratio availability) is compensated by the relay's tap setting or ratio correction factor.

2.2 Vector Group Compensation

The fundamental problem: A YNd1 transformer shifts the LV line current by +30° (or -30°, depending on the convention) relative to the HV line current, due to the delta-wye winding configuration. If the relay compares the HV and LV currents without compensating for this phase shift, it will see a "phase difference" equal to the vector group angle — even under perfectly balanced load — and will trip.

Solution — Internal compensation in the numerical relay:

The relay is programmed with the transformer vector group (e.g., YNd1, YNd11, Dyn11, YNyn0). The relay internally applies a phase-shift matrix to one set of CT inputs (typically the wye-side currents) to cancel the transformer's natural phase shift. The two common compensation matrices:

Y-side compensation (YNd1, YNyn0): The wye-side currents are processed through a zero-sequence removal matrix and a phase-angle shift:

For YNd1 (LV lags HV by 30°):

• The relay shifts the HV wye currents by 0° (no shift for the wye-connected HV)
• The relay shifts the LV delta currents by -30° (to align with the HV reference)

For Dyn11 (LV lags HV by 30°, same physical transformer as YNd1 but different winding designation):

• The LV star is the HV; the HV delta is the LV; the phase shift is applied to the side designated as the reference

Modern numerical relays (Siemens SIPROTEC 7UT, SEL-787, GE T60, ABB RET670) perform this compensation internally and transparently — the commissioning engineer need only program the correct vector group. The relay's metering display will then show the phase-aligned currents, and the differential current should read near zero under balanced load.

2.3 Zero-Sequence Current Filtering

For a transformer with a grounded-wye winding and a delta winding, a ground fault on the wye side produces zero-sequence current on the wye side but not on the delta side (the delta winding traps zero-sequence flux). If the differential relay does not filter the zero-sequence current from the wye-side measurement, the zero-sequence current appears as a differential current (since it is not seen on the delta side), causing a false trip.

Solution: The relay applies a zero-sequence elimination matrix to the wye-side currents:

I_A_comp = (2 × I_A - I_B - I_C) / 3 → Removes the zero-sequence component, leaving only positive- and negative-sequence components.

This filtering is standard for numerical relays and is automatically applied when the vector group is configured with a wye winding. For transformers with a delta tertiary winding, the zero-sequence current path through the tertiary must also be considered — some relays require the tertiary CT input to fully cancel the zero-sequence flux.

3. Harmonic Blocking/Restraint

3.1 Second Harmonic Blocking (Inrush Discrimination)

As covered in detail in the Magnetic Inrush Current article, the asymmetric inrush current waveform is rich in the second harmonic (100 Hz). The relay measures the second harmonic content relative to the fundamental:

I_2nd / I_fundamental > x% → Block differential trip (the event is inrush, not a fault)

Typical setting: x = 15% for standard CGO steel core transformers; x = 10% for low-loss core transformers (amorphous, domain-refined).

Cross-blocking vs. phase-segregated: Cross-blocking (second harmonic detected in ANY phase → block trip on ALL phases) is the standard. Phase-segregated blocking (block only the phase with inrush) provides faster tripping for a simultaneous fault on a non-inrush phase, at the cost of reduced security.

3.2 Fifth Harmonic Blocking (Overexcitation Discrimination)

Overexcitation (Volt/Hz >1.05-1.10 pu) — caused by the system voltage exceeding the transformer's rated voltage, or by frequency dropping while voltage remains constant — drives the core into saturation. The magnetizing current increases significantly, and, like inrush, it is rich in odd harmonics — particularly the fifth (250 Hz). The relay uses:

I_5th / I_fundamental > y% → Block differential trip (the event is overexcitation, not a fault)

Typical setting: y = 30-35% for standard CGO steel; y = 20-25% for Hi-B steel (which produces lower harmonic content during overexcitation).

Fifth harmonic blocking is simpler than second harmonic blocking because overexcitation is symmetric (not asymmetric like inrush), and the waveform is rich in odd harmonics with very little even harmonic content — there is essentially no ambiguity with internal faults.

4. REF (Restricted Earth Fault) Protection — The Complement to Differential

4.1 Why REF is Needed

A phase-to-ground fault on the transformer winding near the neutral point produces a fault current that is limited by the winding impedance. As the fault location moves closer to the neutral, the driving voltage decreases proportionally:

I_f = V_phase-to-neutral × (fraction of winding from neutral) / Z_fault

At 5% of the winding from the neutral, the driving voltage is only 5% of the phase-to-neutral voltage → the fault current is correspondingly small. The differential relay — with a minimum pickup of 20-30% of rated current — may not detect this fault.

REF protection uses a dedicated CT in the transformer neutral connection (or a residual connection of the phase CTs) that measures only the ground-fault current (zero-sequence). Because the REF element has no restraint from the phase CTs (it measures only the neutral current), it can be set much more sensitively — typically 5-10% of rated current.

4.2 REF vs. Differential Coordination

Feature	Differential (87T)	REF (64REF)
Protects	Phase-to-phase and phase-to-ground faults across the full winding	Phase-to-ground faults near the neutral end of the winding (typically the bottom 20-40%)
Sensitivity	Limited by CT ratio error and tap-position error (Slope1 ≈ 25%)	High sensitivity — typically 5-10% of rated, limited only by the neutral CT accuracy
Zones	Full winding (HV + LV, including the transformer itself)	The wye winding whose neutral is monitored by the REF CT
CT requirements	HV + LV main CTs (Class 5P or PX)	Neutral CT (Class 5P) — typically lower ratio (e.g., 400/1 for a 50 MVA transformer)
Coordination	The differential relay is the primary protection; REF fills the sensitivity gap near the neutral

Typical REF setting: Pickup = 0.05-0.10 × I_rated (secondary referred), instantaneous (no time delay). The REF element trips the transformer via the same lockout relay as the differential protection.

FAQ

Q: What is the difference between low-impedance and high-impedance differential protection?

Low-impedance (percentage-restrained) differential protection is the standard for numerical transformer relays. The relay measures the differential current and compares it to a percentage of the restraint current — the characteristic described in Section 1. High-impedance differential protection uses a stabilizing resistor in series with the differential circuit to raise the effective impedance of the differential path. This makes the scheme immune to CT saturation during through-faults (a saturated CT acts as a short circuit, but the high-impedance path requires a voltage to drive current through the differential element — and the saturated CT's terminal voltage is near zero, so no differential current flows through the high-impedance element). High-impedance schemes are simpler but less flexible (they require all CTs in the differential zone to have the same ratio and the same knee-point voltage) and are used primarily for busbar protection and for transformer differential schemes with dedicated Class PX CTs.

Q: Why does the differential relay sometimes trip on transformer energization despite second harmonic blocking?

Causes: (1) the second harmonic content of the transformer's inrush current is lower than the relay's setting — this is characteristic of modern low-loss core transformers (amorphous, Hi-B) where the second harmonic may be 7-12% of fundamental, below the standard 15% setting, (2) CT saturation during inrush — the inrush current contains a large DC component that can saturate the CT, and the saturated CT's output waveform has a different harmonic content (the third harmonic dominates), reducing the measured second harmonic, (3) cross-blocking is disabled and the relay uses phase-segregated blocking — if inrush occurs in two phases and a genuine fault exists in the third phase (energizing onto a fault), the third phase trips while the other two are blocked, and (4) the inrush current decays very slowly (long L/R time constant of a large transformer) and the harmonic measurement window in the relay (typically 2-3 cycles) captures a period when the second harmonic content has already dropped below the threshold. Mitigations: lower the second harmonic setting (to 10%), enable waveform recognition, or use flux-based restraint.

Q: How do I test the differential relay during commissioning?

The standard commissioning test sequence: (1) Inject balanced three-phase currents into the HV and LV CT inputs at rated values. Verify I_diff ≈ 0 and I_restraint ≈ I_rated on the relay's metering display. (2) Inject a single-phase current on the HV side only → I_diff should equal the injected current, I_restraint should equal half the injected current. (3) Ramp up the injected current until the differential element trips. Verify the trip occurs at the expected I_diff with the expected operating time. (4) Repeat for each phase and for the LV side. (5) Inject a second harmonic component on top of the fundamental and verify that the trip is blocked when I_2nd/I_fundamental exceeds the setting. (6) Inject a fifth harmonic and verify blocking for overexcitation. (7) Perform a stability test: inject through-current equal to 10× I_rated (simulating a severe through-fault) and verify the differential element does NOT operate — the restraint slope prevents false tripping. This test requires a high-current test set (e.g., Omicron CMC 356). If the CT secondary circuit includes any connections (terminal blocks, test switches), verify the wiring polarity at each connection — a single reversed CT polarity will cause a trip on load.

Q: What is the significance of the REF element for a resistance-earthed transformer?

On a resistance-earthed transformer (LV winding neutral earthed through a neutral earthing resistor, NER), the ground-fault current is limited to a controlled value (typically 100-1,000 A). Because the NER limits the fault current, a ground fault near the neutral end produces an even smaller fault current than on a solidly-earthed system — sometimes below the differential relay's minimum pickup. The REF element, connected to a CT in the neutral connection (where the full ground-fault current passes, regardless of the fault location on the winding), detects this low-level fault current with high sensitivity. For a resistance-earthed transformer, REF protection is not optional — it is the only protection that reliably detects ground faults in the bottom 30-50% of the winding.

Q: Can one differential relay protect a three-winding transformer?

Yes. Modern numerical differential relays (e.g., Siemens 7UT6, GE T60, SEL-787 with 3-winding option, ABB RET670) support up to 5 winding inputs (for three-winding transformers plus a tertiary plus a bus tie). The relay calculates the differential current as the vector sum of all winding currents (after ratio and phase-angle compensation for each winding individually). The restraint current is typically the maximum of all winding currents. The protection is extended to cover inter-winding faults between any two windings, and internal faults affecting all three windings. The harmonic blocking and REF protection are similarly extended.

Q: What is the "2-out-of-3" logic in differential protection?

2-out-of-3 (also called cross-tripping) logic: the differential element must detect a fault in at least 2 of the 3 phases before issuing a trip. This provides security against a single-phase CT circuit problem (loose connection, CT saturation) that causes a false differential current in only one phase. The logic delays tripping — if an internal single-phase fault occurs, only one phase has differential current, and the relay must wait for either: (1) a second phase to develop differential current (unlikely for a single-phase fault), or (2) an independent confirmation signal (neutral overcurrent, Buchholz gas alarm, or the differential element timing out and trip override). 2-out-of-3 logic is common in generator differential protection but less common in transformer differential because transformer internal faults often start single-phase and may not propagate to a second phase before catastrophic failure. For transformer protection, the increased security from 2-out-of-3 logic is typically NOT worth the cost in speed — use harmonic blocking, CT supervision, and the slope characteristic for security instead.

References / Standards

Reference	Title
IEC 60255-187-1:2021	Measuring relays and protection equipment — Part 187-1: Functional requirements for differential protection
IEC 60076-1:2011	Power transformers — Part 1: General
IEEE C37.91-2021	IEEE Guide for Protecting Power Transformers
IEEE C37.102-2023	IEEE Guide for AC Generator Protection
CIGRE TB 419	Protection of Power Transformers

*Authored by Du Fu, Production Engineer at ZY POWER. Transformer differential protection is a system — the relay, the CTs, the wiring, and the settings must all be correct. The most common cause of differential misoperation is not a relay setting error — it is a CT wiring polarity reversal. Always verify CT polarity during commissioning.*