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Distance Protection

Configure impedance-based fault location on the R-X plane.

What This Tab Does

The Distance tab lets you overlay zone boundaries on an R-X impedance plane and plot measured fault impedance loci from your COMTRADE recording. It answers the key question: "Did the fault impedance fall inside a protection zone, and which zone would have operated?"

You configure the protected line's impedance, choose between Mho (circular) or Polygonal (quadrilateral) zone shapes, set per-zone reach values to match your relay settings, and then see the measured impedance trajectory traced against those zones in real time as you move the cursor through the recording.

Getting Started

Access the Distance tab by clicking the mho (circle) icon in the left sidebar. The tab requires 3-phase voltage and current channels (VA, VB, VC, IA, IB, IC). Configure line impedance, zone settings, and CT/VT ratios via the gear icon in the top-right corner of the panel.

Settings Reference

All settings are accessible from the gear icon in the Distance tab header. Each parameter is described below with its effect on the R-X display and impedance computation.

Line Impedance1

Z₁ mag10Ω

Z₁ ang80°

Z₀ mag30Ω

Z₀ ang70°

RCA75°

k₀ = 0.667 ∠ −10.0° = 0.657 − j0.116

Characteristic3

MhoPolygonal

4Directional clipping

Zones5

6Z1

X Ω8

ms0

Dir→ Fwd

α °75

7Rφ Ω4

Rg Ω5

σ °0tilt

X Ω12

ms350

Dir→ Fwd

α °75

Rφ Ω6

Rg Ω8

σ °0tilt

Load Encroachment9

Z_load0Ω

CT / VT10

CT ratio

1000/1A

VT ratio

110000/110V

Line impedance — Z1/Z0 magnitude and angle define the protected line; drives K0 and zone defaults.

K0 display — Auto-computed complex zero-sequence compensation factor (magnitude + angle + rectangular).

Characteristic type — Mho (circles through origin) vs Polygonal (quadrilateral with independent R/X reach).

Directional clipping — Polygonal-only checkbox; clips zones against a directional boundary through origin.

Zone array — Add/remove zones freely; each zone is a bordered card.

Zone badge — Color-coded (Z1=green, Z2=blue…) with reach, timer, direction, alpha angle. Reach label changes by characteristic: “|Z| Ω” for Mho, “X Ω” for Polygonal.

Polygonal-only fields — Rφ (phase R-reach), Rg (ground R-reach), σ (reactance tilt) — hidden in Mho mode.

Add Zone — Appends new zone with defaults derived from line impedance.

Load encroachment — Dashed amber circle on R-X plane at Z_load radius (0 = disabled).

CT/VT ratios — Scales impedance from secondary to primary quantities.

Line Impedance

These parameters define the protected line's electrical characteristics. They are the foundation for all zone reach calculations and the R-X plane orientation.

Parameter	Unit	Description
Z1 mag	Ohm	Positive-sequence line impedance magnitude. Sets the length of the dashed Z1 vector drawn on the R-X chart and is used for K0 computation. Typical values: 1-50 Ohm for transmission lines (secondary side).
Z1 ang	deg	Positive-sequence impedance angle (line angle). Controls the direction of the dashed Z1 vector on the R-X plane and serves as the default alpha when adding new polygonal zones. Typical values: 60-85 deg for overhead lines, 20-70 deg for cables.
Z0 mag	Ohm	Zero-sequence impedance magnitude. Only used to compute the K0 compensation factor for ground fault loops (AG, BG, CG). Does not affect zone shapes. Typically 2.5-4x Z1 for overhead lines, 1.5-2.5x for cables.
Z0 ang	deg	Zero-sequence impedance angle. Only used for K0 computation. Typically 5-15 deg less than Z1 angle.
RCA	deg	Relay Characteristic Angle. Serves as the default alpha when adding new Mho zones. Each zone now has its own alpha angle that can be set independently. Has no effect on polygonal zones. Typically set to Z1 angle minus 5 deg.

Per-Zone alpha Angle

Each zone has its own alpha angle. For Mho zones, alpha tilts the circle (defaulting to RCA). For polygonal zones, alpha tilts the resistance boundaries (defaulting to Z1 angle). You can set different alpha values per zone to match relay settings like the P437 alpha-n parameters.

Characteristic Type

Choose between two zone boundary shapes:

Mho -- Circular zones that pass through the origin, tilted at the RCA. Inherently directional. Good for phase faults on transmission lines. Limited resistance coverage.
Polygonal -- Quadrilateral zones with per-zone alpha (side tilt) and sigma (reactance boundary tilt). Independent R-reach and X-reach settings in ohms. Better resistance coverage for ground faults. Separate phase (R-phi) and ground (Rg) R-reach per zone.

Per-Zone Settings

Each zone is defined by the following parameters. Values are entered directly in ohms -- matching the settings sheet of any relay (Siemens P437, ABB REL670, GE D60, SEL-421, etc.). You can add or remove zones freely.

Parameter	Unit	Mode	Description
\|Z\| / X	Ohm	Both	Zone reach in ohms. In Mho mode this is the circle diameter (\|Z\| reach); in Polygonal mode it is the reactance reach (X-reach). Enter the value directly from the relay settings sheet.
Dir	--	Both	Zone direction: Forward or Reverse. Forward zones look into the protected line; reverse zones look behind the relay for busbar backup or blocking schemes.
alpha	deg	Both	Per-zone characteristic angle. In Mho mode, tilts the circle. In Polygonal mode, tilts the resistance boundaries. Defaults to Z1 angle (polygonal) or RCA (Mho) when a new zone is added.
ms	ms	Both	Trip time delay. 0 = instantaneous (Zone 1). Display label for reference -- does not affect zone geometry on the chart.
R-phi	Ohm	Polygonal	Resistance reach for phase-phase faults. Measured perpendicular to the alpha direction. Used when any phase-phase loop (AB, BC, CA) is active.
Rg	Ohm	Polygonal	Resistance reach for phase-ground faults. Used when any ground loop (AG, BG, CG) is active. Typically 1.3x the phase R-reach.
sigma	deg	Polygonal	Reactance boundary tilt angle. Tilts the top and bottom boundaries of the polygonal zone. 0 deg = horizontal boundaries (classic parallelogram). Negative values tilt the right side of the reactance boundary downward.

Phase vs Ground R-reach

The panel automatically selects R-phi or Rg based on which measurement loops are active. If ground loops (AG, BG, CG) are enabled, the zone shapes use the Rg value. If only phase-phase loops are active, R-phi is used. This means zone width on the R-X chart changes when you toggle loops -- this is expected behavior matching real relay settings.

Load Encroachment

The load encroachment circle shows the minimum expected load impedance boundary. Set Z_load to a positive value (in Ohm) to display a dashed circle centered at the origin on the R-X plane. If any zone boundary overlaps this circle, there is a risk of the relay tripping on normal load current.

Set Z_load to 0 (default) to disable the circle. This setting is found in the "Load Encroachment" section of the settings sidebar.

CT / VT Ratios

CT and VT ratios scale the computed impedance from secondary (relay) quantities to primary (system) quantities. The ratio VT/CT is applied to all impedance measurements. If your COMTRADE data is already in primary quantities, set both ratios to 1:1.

Zone Grading

Distance relays use multiple zones with progressively increasing reach and time delay to provide both fast clearance for close-up faults and backup protection for remote faults.

Zone	Typical Reach	Time Delay	Purpose
Zone 1	8 Ohm (~80% of Z1)	Instantaneous	Primary fast protection. Set below 100% of line impedance to prevent overreach from CT/VT errors and line parameter uncertainty.
Zone 2	12 Ohm (~120% of Z1)	350 ms	Covers the remaining line plus the remote bus. Time-graded to coordinate with Zone 1 of the adjacent line.
Zone 3	20 Ohm (~200% of Z1)	800 ms	Remote backup for adjacent line sections. Must be checked against minimum load impedance to avoid load encroachment trips.
Reverse	2 Ohm (reverse)	Instantaneous	Reverse-looking zone for busbar backup or blocking schemes. Covers faults behind the relay location. Shown with dashed lines on the R-X chart.

Load Encroachment

Long, heavily loaded transmission lines can present a load impedance that falls inside Zone 3 or higher zones. Enable the load encroachment circle (Z_load setting) to visualize the minimum load boundary. If any zone overlaps the circle, there is a risk of unwanted tripping during heavy load conditions.

Measurement Loops

A distance relay simultaneously monitors six fault loops to detect all possible fault types. Toggle loops on/off using the colored chips in the Distance tab header. The faulted loop (lowest impedance near fault time) is highlighted with a pulse animation.

Distance Protection

ABBCCA

AGBGCG

R-X impedance plane (zones + loci rendered here)

Loop Chip States

3AB

Active

White text on loop-coloured background

4BC

Inactive

Outlined border, muted text

5AG

Faulted

Active + animated pulsing glow shadow

Phase-phase loops — AB (red), BC (blue), CA (green) — toggle on/off to show or hide the corresponding impedance locus on the R-X plane.

Phase-ground loops — AG (orange), BG (purple), CG (cyan) — toggling changes the displayed zone width between ground reach (R g) and phase reach (R φ).

Active state — White text on the loop’s assigned colour background. The impedance locus for this loop is visible on the R-X plot.

Inactive state — Bordered outline with muted text. The loop’s impedance locus is hidden from the chart.

Faulted indicator — Animated pulsing box-shadow glow on the active chip. Auto-detected as the loop with the lowest impedance magnitude nearest the fault inception time.

Loop	Type	Fault Types Covered
AB	Phase	A-B and A-B-G faults
BC	Phase	B-C and B-C-G faults
CA	Phase	C-A and C-A-G faults
AG	Ground	A-G fault (uses K0 compensation)
BG	Ground	B-G fault (uses K0 compensation)
CG	Ground	C-G fault (uses K0 compensation)

Loop Selection and Zone Width

When ground loops are active, polygonal zones use the wider Rg R-reach. When only phase loops are active, zones use the narrower R-phi R-reach. This matches how real distance relays apply different resistance coverage for phase vs ground elements.

Reading the Results

The main chart shows the R-X impedance plane with zone boundaries and impedance loci. Key visual elements:

Zone overlays -- Filled polygons (or circles for Mho) showing each zone boundary. Forward zones are solid; reverse zones are dashed. Zones are layered largest-to-smallest so inner zones are visible.
Z1 vector -- Dashed line from origin at the Z1 angle showing the line impedance direction.
Load encroachment circle -- Dashed amber circle at the origin (when Z_load is set) showing the minimum load impedance boundary.
Impedance loci -- Colored dots for each active measurement loop, with color intensity fading over time. Click a point to move the cursor to that time.
Cursor marker -- Red X showing the impedance at the current waveform cursor position.

The readout bar at the bottom shows the numerical impedance (R, X, |Z|, angle) for each active loop at the cursor position, plus a zone indicator if the point is inside any zone boundary.

Tips for Common Configurations

Start with Mho zones for phase distance elements, then switch to Polygonal if you need independent R-reach control for ground faults.
Set Zone 1 reach to approximately 80% of Z1 to avoid overreach caused by CT/VT errors and line parameter uncertainty.
Always check Zone 3 against the load encroachment circle on long, heavily loaded lines.
Use the per-zone alpha angle to match your specific relay settings (e.g., Siemens P437 alpha-n parameters).
If your COMTRADE data is already in primary quantities, set both CT and VT ratios to 1:1.

How it works

For the mathematical theory behind impedance measurement, Mho and Polygonal characteristics, K0 compensation, and fault loop equations, see Theory: Distance Protection.

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