Maximum Torque Angle ▼
MTAMaximum Torque Angle — relay characteristic angle
°
Zone 1 Settings ▼
Z1 MagnitudePos-seq reach in secondary ohms
Ω
Z1 AngleLine impedance angle (matches MTA)
°
Z1 Reach %Typically 80–85% of protected line
%
Z1 TimerInstantaneous (0 ms typical)
ms
Zone 2 Settings ▼
Z2 MagnitudeCovers 100% line + 20% next line
Ω
Z2 AngleUsually same as Z1 angle
°
Z2 TimerTypical 200–400 ms delay
ms
Zone 3 Settings ▼
Z3 MagnitudeBack-up: covers remote bus + next line
Ω
Z3 Angle
°
Z3 TimerTypical 600–1000 ms delay
ms
Zero-Sequence Compensation ▼
Z0 MagnitudeZero-seq impedance (3–5× Z1 typical)
Ω
Z0 AngleUsually 5–10° more than Z1 angle
°
k0 (|Z0−Z1|/3Z1)Zero-seq compensation factor
CT / VT Ratios ▼
CT RatioPrimary : Secondary (e.g. 1200:5)
:1
VT RatioPrimary : Secondary (e.g. 115kV:115V)
:1

Distance Relay Settings

A distance relay (IEEE device 21) measures the apparent impedance from the relay point to a fault. It compares this measured impedance against a characteristic shape — the mho circle — drawn on the R-X impedance plane. When the measured Z falls inside the circle, the relay declares a fault in that zone.

Each setting below directly shapes the size, rotation, and position of the mho circles. As you adjust values on the left, the preview below updates instantly.

MTA — Maximum Torque Angle
The angle at which the relay produces maximum torque. Sets the tilt of the mho circle's diameter. Should match the protected line's impedance angle. Typical: 65–85°.
Z1 — Zone 1 Reach
Instantaneous trip zone. Deliberately under-reaches at 80–85% so infeed effects and CT/VT errors don't cause overreach into the next line. Set in secondary ohms.
Z2 — Zone 2 Reach
Time-delayed (200–400 ms). Reaches 100% of the protected line plus 20–50% of the shortest adjacent line. Provides backup for the remote end Z1 misses.
Z3 — Zone 3 Reach
Remote backup (600–1000 ms). Reaches beyond Z2. Must be checked against maximum load impedance to avoid unwanted operation during heavy load.
Z0 — Zero-Sequence Impedance
Ground faults use zero-sequence current which sees a different (usually 3–5×) impedance. The k0 compensation factor corrects the relay's apparent impedance for L-G faults.
CT / VT Ratios
The relay only sees secondary quantities. All impedance settings are in secondary ohms. Z_secondary = Z_primary × (CT ratio / VT ratio). Getting this wrong is the most common commissioning error.
Live Mho Preview (R-X Plane)
+jX (Inductive)
−jX (Capacitive)
−R
+R
HOVER TO READ R+jX · CLICK TO PROBE
The R-X Plane

What is the R-X Plane?

Every impedance Z = R + jX can be plotted as a point. Distance relays work in this plane — they measure the apparent impedance to the fault and check if it lands inside the mho circle.

The Mho Circle

A mho circle passes through the origin (the relay location) and has its diameter along the MTA direction. The far end of the diameter equals the zone reach magnitude. Any impedance inside = fault in zone.

Why Three Zones?

Z1 (fast, under-reaches) → Z2 (delayed, reaches remote end) → Z3 (backup, remote line). Each zone is a larger concentric circle shifted along the MTA direction.

Load Region

Heavy load appears at low angle near the R-axis. The relay must not see load as a fault — Z3 must clear the maximum load impedance (shown as the shaded region).

Zone Legend
Zone 1 — Instantaneous80–85% line reach, no intentional delay
Zone 2 — Time Delayed100% line + backup, ~300 ms
Zone 3 — Remote BackupFull back-up reach, ~800 ms
Load RegionNormal load impedance — must not trip
MTA Direction
MTA = 75° from R-axis
Circle diameter lies along this angle
Voltage Phasors (V ∠°)
Phase A
Phase B
Phase C
Current Phasors (I ∠°)
Phase A
Phase B
Phase C
Relay Element
Step-by-Step Derivation
—
Enter phasor values to see live derivation
Fault Point on R-X Plane
Zone Verdict
AWAITING COMPUTATION
Computed Impedance
|Z| Ω
—
∠Z °
—
R (Ω)
—
X (Ω)
—
CT/VT Correction
Configure CT/VT ratios in Module 1.
Z_primary = Z_sec × (VTR / CTR)
Fault History
No faults plotted yet.
Flashcards — Click to Reveal Quiz: 0 / 8

Each card tests a key concept. Click to flip. Then tackle the quiz to confirm your understanding.

What does the relay actually measure to detect a fault?
Apparent impedance Z = V/I. It compares R+jX to the mho circle boundary. If Z is inside → fault declared in that zone.
Why does Z1 only reach 80–85%?
To guard against overreach from infeed current, CT/VT errors, and system unbalance. Zone 2 covers the remaining 15–20% with a time delay.
What is the MTA and why does it match the line angle?
Maximum Torque Angle — the relay is most sensitive at this angle. Matching it to the line impedance angle means faults on the protected line produce the most relay torque.
How do you convert primary Ω to secondary Ω?
Z_sec = Z_primary × (CTR / VTR). Example: 10Ω primary, CTR=240, VTR=1000 → Z_sec = 10 × 240/1000 = 2.4 Ω.
Why is k0 needed for ground faults?
Ground faults return via earth, creating zero-sequence current. Z0 ≠ Z1, so without k0 compensation the relay's apparent Z would be wrong, causing under- or over-reach.
Where does a fault point appear during a bolted fault?
Near the origin (R≈0, X≈small). As fault resistance increases, the point moves rightward. As fault moves further away, |Z| grows — point moves outward from origin.
What is load encroachment?
Under heavy load, low-angle impedance (near R-axis) can fall inside Z3 and cause a false trip. Solution: use a load-blinder or lens characteristic to exclude the load region.
What does ∠Z = ∠V − ∠I tell you about a fault?
During a fault, current surges and lags voltage heavily (∠I ≈ −75° to −85°). So ∠Z is a large positive angle — the point plots high in Q1, well inside the mho circle.
Knowledge Check
Formula Cheatsheet

Core Equations to Memorize

Z = V∠θ / I∠φ
Relay apparent impedance — divide magnitudes, subtract angles
∠Z = ∠V − ∠I
Impedance angle — large positive value = inductive fault on line
R = |Z|·cos(∠Z)
Resistance — horizontal axis on R-X plane
X = |Z|·sin(∠Z)
Reactance — vertical axis, positive = inductive
V₁ = (Va + a·Vb + a²·Vc)/3
Positive-sequence voltage (a = 1∠120°)
Z_sec = Z_pri × CTR/VTR
Convert primary to secondary ohms for relay settings
k0 = (Z0 − Z1) / 3Z1
Zero-sequence compensation factor for ground fault reach correction
|Z_load| = V² / S
Minimum load impedance — Z3 must not reach this far at low angles