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Differential Protection

Analyze transformer differential (87T) protection with operate/restraint characteristics.

What This Tab Does

The Differential tab analyzes transformer differential (87T) protection by computing operate and restraint currents from HV and LV side measurements. It plots each time sample on an operate/restraint scatter chart to show whether the operating point falls inside the trip zone (internal fault) or the restraint zone (through-fault / load).

Access the Differential tab by clicking the scale icon in the left sidebar. The tab requires sign-in.

Differential Analysis

ComputeExisting

2AllABC

5AIdiff=1.800Ibias=1.200ratio=150.0%BIdiff=0.100ratio=4.0%

Settings

Channels

Phase A

Side 1IA (A)

Side 2Ia_LV (A)

Add windingAdd phase

Signal

Bias Factor

0.5Half1.0Full

CT Polarity

I1−I2I1+I2

Transformer

Enable compensation

Rated MVA100

HV kV132

LV kV11

TV kV33

Vector GroupDyn11 (+30°)

TV Vector GroupYy0 (0°)

Compensate sideAuto (LV)

Zero-seq filter

HVLVTV

Characteristic

Show on chart

Relay TypeRET670 / RET615 / RET630

IdMin (pu)0.30

EndSection1 (pu)1.00

SlopeSection2 (%)40

EndSection2 (pu)3.00

SlopeSection3 (%)80

IdUnre (pu)10.00

Trip Signal

DetectedTrip - HS BKRTrip - LS BKR

Add other channelChoose...

Classification

A: Internal Faulthigh

B: Through Faulthigh

Mode toggle — “Compute” calculates from raw channels; “Existing” uses relay’s pre-computed Idiff/Ibias. Always visible.

Phase selector — View all phases overlaid or isolate a single phase.

Settings toggle — Gear icon opens/closes the settings panel. Mobile: drawer with backdrop.

Scatter chart — Ibias (X) vs Idiff (Y). Dashed characteristic curve separates operate/restraint zones. U87P threshold shown as horizontal dashed line.

Readout bar — Per-phase peak Idiff, Ibias, and ratio at chart bottom.

Channels — Per-phase Side 1/Side 2 dropdowns. “+ Add winding” for tertiary. “+ Add phase” for multi-phase.

Signal — Bias factor and method (sum or max, auto-set by relay type) and CT polarity. Hidden in 3-winding mode.

Transformer — MVA, HV/LV/TV voltages with computed taps, vector groups, compensate side, zero-seq filter per winding.

Characteristic — Relay type selector grouped by manufacturer (SEL, Schneider, Siemens, ABB/Hitachi, GE) with relay-specific parametric editors. Settings auto-populate with manufacturer defaults.

Trip Signal — Auto-detected trip channels (checkboxes) plus manual dropdown. “T” badges appear on the scatter chart at the trip assertion point.

Classification — Per-phase fault verdict with confidence badge and stats.

Settings Reference

All settings are accessible from the gear icon in the chart header. They are organized into collapsible sections in the right-hand settings panel.

Channels

Setting	Description
Data Source	Toggle between Compute (calculate from raw channels) and Existing (use pre-computed Idiff/Ibias). Always visible in the chart header.
Channel Pairs	Per-phase Side 1 / Side 2 current channel dropdowns. Auto-detected from COMTRADE naming patterns.
Add Winding	Per-phase button to add a tertiary (Side 3) channel for 3-winding transformers.
Add Phase	Add additional phase pairs (up to A, B, C).

Signal (Compute mode only)

The entire Signal section is hidden in 3-winding mode — polarity is forced to summation and the bias factor applies as-is.

Setting	Description
Bias Factor	Scalar multiplier for sum-based bias. Common values: 0.5 (half-sum, Schneider/SEL-587) or 1.0 (full-sum, SEL-787/Siemens 7UT6x). Auto-set when a relay type is selected. Disabled when the selected relay uses max-based bias (Siemens 7UT87, ABB/Hitachi, GE T60).
CT Polarity	Subtractive (I1−I2) or additive (I1+I2). Auto-detected from pre-fault waveform analysis.

Transformer (Compute mode only)

Setting	Description
Enable Compensation	Master toggle for TAP normalization and vector group correction.
Rated MVA	Transformer rated apparent power. Used with winding voltages to compute TAP values.
HV / LV / TV Voltage (kV)	Rated winding voltages. TV voltage appears when 3-winding channels are configured.
Vector Group	HV-to-LV vector group (11 options). Determines the phase-shift compensation matrix.
TV Vector Group	HV-to-TV vector group. Appears only for 3-winding configurations.
Compensate Side	Which side receives the phase-shift matrix: Auto (LV), Side 1 (HV), or Side 2 (LV).
Zero-Seq Filter	Per-winding checkboxes (HV, LV, TV). Auto-defaulted based on vector group grounding.

Characteristic Curve

Setting	Description
Show on Chart	Toggle the characteristic curve overlay on the scatter chart.
Relay Type	Grouped by manufacturer (SEL, Schneider, Siemens, ABB/Hitachi, GE) with 9 built-in relay families plus Custom piecewise-linear. Selecting a relay auto-populates its default settings and sets the correct bias method.

Trip Signal

Setting	Description
Detected	Checkboxes for digital channels auto-detected by matching "trip" in the channel name (case-insensitive). All detected channels are pre-selected.
Add other channel	Dropdown to manually select any digital channel not auto-detected (e.g., CB52a breaker contacts).
Remove	Trash icon on manually-added channels to remove them from the overlay.

Reading the Results

Operate/Restraint Scatter Chart

The main visualization is a scatter chart plotting differential current ( $I_{\text{diff}}$ ) on the Y-axis against bias current ( $I_{\text{bias}}$ ) on the X-axis. The percentage bias characteristic curve divides the chart into two regions:

Red points above the curve — operate region, indicating internal fault conditions where the differential current exceeds the bias threshold.
Green points below the curve — restraint region, indicating through-fault or normal load conditions.

The percentage bias characteristic shape depends on the selected relay type: most use a dual-slope or triple-slope curve with a flat minimum pickup at low bias levels, progressively steeper slopes at higher bias levels for CT saturation stability, and an optional unrestrained threshold shown as a dashed horizontal line.

When trip signals are selected in settings, colored “T” badges appear on the scatter chart at the trajectory point where each digital channel first changed state. Each trip channel is assigned a distinct color. The badges are playback-aware — they only appear once the animation reaches the trip time.

Compute Mode vs Pre-computed Mode

Compute mode — Select raw current channels for each side. Detego applies TAP normalization, vector group phase shift, and polarity correction to compute the differential and bias quantities from scratch.

Pre-computed mode — Select differential and bias channels directly from the COMTRADE channel list. This uses the relay's own internal calculations as-is. The Compute/Existing toggle is always available in the chart header — useful when auto-detection does not find pre-computed channels but you know they exist in the file.

Polarity Auto-Detection

Detego automatically detects CT polarity using cross-correlation analysis between HV and LV current waveforms. Positive correlation means currents flow in the same direction (subtractive polarity); negative correlation means opposite directions (additive polarity).

If auto-detection produces incorrect results (e.g., very low load current or unusual CT wiring), you can manually toggle the polarity in the settings.

In 3-winding mode, polarity auto-detection is disabled and the Signal section is hidden — all three winding currents are always summed.

3-Winding Transformers

Each phase pair has an + Add winding button that opens a Side 3 (tertiary) channel dropdown. When all phases have tertiary channels assigned, the tab enters 3-winding mode:

The Signal section is hidden — polarity is forced to summation of all three winding currents.
A TV voltage input appears in the Transformer section alongside the HV and LV voltage fields.
A TV Vector Group dropdown appears for the HV-to-TV phase relationship.
The zero-sequence filter gains a TV checkbox.

If any phase is missing its tertiary channel, the tab falls back to 2-winding behavior for all phases.

Relay Characteristic Presets

The Relay Type dropdown is grouped by manufacturer. Selecting a relay auto-populates default settings from the relay manual and sets the correct bias method (sum or max). Each relay family uses its native setting names so values can be entered directly from the relay's settings printout.

SEL

SEL-787 / SEL-587 — Dual-slope with knee point (O87P, SLP1, IRS1, SLP2) and unrestrained threshold (U87P). Slopes pass through the origin. U87P creates a flat-top cap and is drawn as a dashed threshold line. Bias: sum of magnitudes.
SEL-487E / SEL-487B — Adaptive single-slope from origin (O87P, SLP1, SLP2, U87P). No knee point — the relay switches between SLP1 (normal) and SLP2 (high-security) at runtime; Detego draws SLP1. Bias: sum of magnitudes.

Schneider

P40x / P54x / P64x — Dual-slope with pickup and knee (Is1, K1, Is2, K2). Slopes pass through the origin. Bias: half-sum of magnitudes.

Siemens

7UT612 / 7UT613 / 7UT63 — SIPROTEC 4 dual-slope with base points. Slopes are additive on top of the pickup floor (not through the origin). Two configurable base points set where each slope region begins. Bias: sum of magnitudes. Unrestrained threshold (I-DIFF>>) shown as dashed line.
7UT87 — SIPROTEC 5 dual-slope with base points. Same curve shape as 7UT6x but uses max-based bias (max of winding magnitudes instead of sum). Different default slopes to account for the changed bias method.
7SD87 / 7SD86 / 7SD82 / 7SL87 — SIPROTEC 5 line differential with adaptive self-stabilization. Only one setting (Threshold) — the restraint is internally computed by the relay from CT error estimates. Characteristic is a 45-degree line above the threshold. Bias: approximated as sum for visualization.

ABB / Hitachi Energy

RET670 / RET615 / RET630 — Transformer differential with triple-slope characteristic (three sections, not two). Flat pickup (IdMin), then two progressively steeper slope sections. Slopes are additive on IdMin. Bias: max of winding magnitudes. Unrestrained threshold (IdUnre) shown as dashed line.
RED670 / RED650 / RED615 / REX640 — Line differential using the same triple-slope shape with different defaults optimized for line protection. Bias: max of magnitudes.

T60 — Transformer differential with dual-slope and a smooth cubic transition between Break 1 and Break 2 (instead of a sharp knee point). Slopes pass through the origin. Bias: max of magnitudes.

Custom

Custom (piecewise-linear) — Define any arbitrary characteristic by adding individual line segments. Useful for relays not yet in the built-in registry.

Classification

When a characteristic curve is configured, per-phase verdict cards appear in the settings panel showing one of three classifications:

Internal Fault — Operating points exceeded the characteristic curve during the event.
Through Fault — All operating points remained in the restraint region throughout.
Indeterminate — Points are close to the boundary or the data is insufficient for a clear verdict.

Practical Tips

Always enter accurate transformer MVA and voltage ratings — incorrect values cause a systematic mismatch that appears as a standing differential current under load.
Check the vector group setting carefully. A wrong vector group introduces a 30° or 60° phase error that produces false differential current even under balanced load.
If the operating points cluster near the characteristic curve boundary, try adjusting the bias factor to better match the relay's actual settings.
For recordings from numerical relays, try pre-computed mode first — it shows the relay's own view without recomputation errors from estimated parameters.
Check the compensate-side setting — most relays compensate the LV side, but some configurations may require HV compensation.
When changing the vector group, the zero-sequence filter checkboxes auto-update based on the grounding notation. Review them to confirm they match your relay settings.
For 3-winding transformers, ensure all three phases have tertiary channels assigned before interpreting results — partial assignment falls back to 2-winding behavior.

How it works

For the mathematical theory behind differential protection — including operate/restraint formulas, CT ratio compensation, vector group phase shift tables, and the percentage bias characteristic — see the Differential Protection Theory page.

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