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Transformer differential (87T) principle, operate/restraint characteristic, and vector group compensation.
In Detego
Differential protection operates on Kirchhoff's current law: under normal conditions, the current entering a protected zone equals the current leaving it. Any difference (the "differential current") indicates an internal fault, while through-faults produce equal and opposite currents that cancel in the differential measurement.
For power transformers, the basic differential principle is complicated by the transformer ratio, vector group phase shift, and magnetizing inrush current. The 87T relay addresses these challenges with CT ratio compensation, vector group correction, and percentage-biased characteristics with harmonic restraint.
The differential current is the vector sum of the currents from all sides of the protected zone, after CT ratio and vector group compensation. For a two-winding transformer with currents referred to a common base:
Differential current
Where
The sign convention depends on CT polarity. If CTs are connected so that through-fault currents subtract, the formula becomes |I₁ - I₂|. Detego auto-detects polarity via correlation analysis.
Under healthy conditions or through-faults, and are equal and opposite (after compensation), so is near zero. During an internal fault, the currents no longer cancel, producing a large differential current.
The bias current (also called restraint current) represents the through-fault current level. It is used to raise the operate threshold proportionally to the fault current magnitude, providing stability against CT saturation and ratio mismatch during heavy through-faults.
Bias current
Where
Some relay implementations use max(|I₁|, |I₂|) or (|I₁| + |I₂|) without the averaging factor. Detego uses the average with configurable bias factor.
Three-winding transformers extend the differential principle to include a tertiary (TV) winding. All three sides are normalized to the HV reference frame using individual TAP values and vector group compensation matrices.
3-winding differential current
Where
Polarity is always summation for 3-winding transformers — all CT currents flow into the protected zone.
3-winding bias current
Where
Each winding has its own vector group compensation matrix and optional zero-sequence filter, applied independently before the differential calculation.
The percentage differential characteristic plots against . The relay operates when the differential current exceeds the characteristic curve for the given bias level. The dual-slope design provides:
Percentage differential relay characteristic (dual-slope). Points above the curve cause relay operation (internal fault); points below are restrained (through fault or load).
Transformer HV and LV currents differ by the turns ratio. Before comparing them, both sides must be normalized to a common per-unit base. The transformer nameplate ratings are used to compute tap values:
CT tap normalization
Where
Each side's measured current is divided by its tap value before differential comparison.
The tap value represents the expected nominal current at each winding under rated conditions. Dividing the measured current by the tap value converts it to per-unit, making HV and LV currents directly comparable regardless of the transformer ratio.
Transformer vector groups (e.g., Dyn11, Yd1, YNyn0) introduce a phase shift between the HV and LV currents. This phase shift must be compensated before computing the differential current; otherwise, the uncompensated phase difference would appear as a false differential current even under balanced load conditions.
| Vector Group | Phase Shift | Compensation |
|---|---|---|
| Yy0, YNyn0, Dd0 | 0° | No phase correction needed |
| Yd1, YNd1, Dy1, Dyn1 | −30° | Compensated side rotated by +30° |
| Yd11, YNd11, Dy11, Dyn11 | +30° | Compensated side rotated by −30° |
The phase rotation is applied to the compensated side's current phasors before computing the differential and bias quantities. For a Dyn11 transformer, the LV currents lead the HV currents by 30°, so the compensation rotates the compensated phasors by −30° to align them with the reference frame. Note that delta (D/d) windings inherently block zero-sequence current, so only grounded star windings can carry zero-sequence components.
The phase-shift compensation matrix can be applied to either side of the transformer. Standard relay practice applies the matrix to the non-reference side (typically LV) to align its current phasors with the HV reference frame. In some configurations — such as when the HV side has a delta winding — it may be more appropriate to compensate the HV side instead.
Grounded star windings (Y with N grounding) can carry zero-sequence current during earth faults. Delta windings on the opposite side of the transformer do not pass zero-sequence current, creating a mismatch that appears as false differential current for external earth faults.
The zero-sequence filter removes this component by subtracting the average of all three phase currents from each individual phase before computing the differential:
Zero-sequence removal
Where
Applied independently per winding side before the vector group compensation matrix. The filter is typically enabled on grounded star windings paired with delta windings.
The CT polarity convention determines whether the HV and LV currents should be added or subtracted to compute the differential current. Incorrect polarity assignment causes the differential relay to see load current as a permanent internal fault.
Detego performs automatic polarity detection by analyzing the relationship between HV and LV current waveforms, automatically determining whether currents should be added or subtracted based on the CT connection convention.