Distance Protection Setting Assistant

Proposed zone reaches and times for a line distance relay from the line and network data: residual compensation k0, zones 1–3 and a reverse zone in primary and secondary ohms, resistive reaches limited by load, and checks for load encroachment, source impedance ratio and short lines.

Distance protection settings follow well-established rules — zone 1 under-reaches the remote end, zone 2 covers the rest of the line with a delay, zone 3 backs up the adjacent lines — but each rule has a limit set by the adjacent lines, the load and the source. Laying them out together, with the numbers in primary and secondary ohms, makes the setting sheet consistent and the compromises visible.

Standards followed

IEC 60255-121 (functional requirements for distance protection: reach accuracy, residual compensation)IEEE C37.113 (guide for protective relay applications to transmission lines)Common utility practice for zone reaches and times (80 % / 120 % / 0.3–0.4 s / 0.8–1.0 s)

What it can do

k0 = (Z0 − Z1) / 3Z1 and the line angle from the line constants.
Zone 1 = 80 % of the line; zone 2 = max(120 % of the line, line + 50 % of the shortest adjacent line), limited so it stays inside zone 1 of that line; zone 3 = 120 % of (line + longest adjacent line); reverse zone 15 %.
Resistive reach: earth faults 1.2 × 2 × fault resistance (allowance for remote infeed), phase faults 1.2 × arc resistance, both limited to 80 % of the minimum load resistance at 0.9 pu voltage and the load angle.
Secondary ohms = primary × (CT ratio / VT ratio); quadrilateral sketch; warnings for load encroachment of zone 3, SIR > 4 and short lines.

Example problem

A 40 km 132 kV line (Z1 = 0.08 + j0.40 Ω/km, Z0 = 0.25 + j1.20 Ω/km), CT 800/1, VT 132 kV/110 V, adjacent lines 25 and 60 km, maximum load 150 MVA.

Line 16.3 Ω ∠ 78.7°, k0 = 0.668 ∠ −0.7°.
Zone 1 13.05 Ω (8.70 Ω secondary), zone 2 21.42 Ω at 0.35 s, zone 3 49.0 Ω at 0.9 s.
Earth-fault resistive reach 24 Ω, well inside the 65 Ω load limit.

A consistent first setting proposal to check against the relay manual and the grading with the neighbouring relays.

This is a starting point for the setting study, not a replacement for it: infeed, mutual coupling of parallel lines, series compensation, power swings and teleprotection schemes need the full study and the relay manufacturer's guidance.

Line and network data

R1 (Ω/km)

X1 (Ω/km)

R0 (Ω/km)

X0 (Ω/km)

Protected line length (km)

Shortest adjacent line (km)

Its |Z1| (Ω/km)

Longest adjacent line (km)

Its |Z1| (Ω/km)

CT primary (A)

CT secondary (A)

VT primary (V)

VT secondary (V)

System voltage (kV)

Maximum load (MVA)

Load angle (°)

Source impedance (Ω, for SIR)

Earth-fault resistance to cover (Ω)

Phase-fault arc resistance (Ω)

Proposed zones — line 16.32 Ω ∠ 78.7°

Zone	Reach primary	Reach secondary	R earth / phase (prim.)	R earth / phase (sec.)	Time
Zone 1 80 % of the protected line (instantaneous; margin for CT/VT, line data and relay errors)	13.05 Ω	8.70 Ω	24.0 / 3.6 Ω	16.0 / 2.4 Ω	0 s
Zone 2 ≥ 120 % of the line, ≤ line + 50 % of the shortest adjacent line	21.42 Ω	14.28 Ω	24.0 / 3.6 Ω	16.0 / 2.4 Ω	0.35 s
Zone 3 120 % of line + longest adjacent line (remote back-up)	48.96 Ω	32.64 Ω	24.0 / 3.6 Ω	16.0 / 2.4 Ω	0.9 s
Zone 4 (reverse) 15 % reverse, for busbar back-up / blocking schemes	2.45 Ω	1.63 Ω	24.0 / 3.6 Ω	16.0 / 2.4 Ω	1.2 s

Minimum load impedance at 0.9 pu: 94.1 Ω; resistive reach limit 65.2 Ω · SIR 1.23.

Checks

NoteResidual compensation k0 = (Z0 − Z1) / 3Z1 = 0.668 ∠ -0.7°; line angle 78.7°. Secondary ohms = primary × CT ratio / VT ratio = primary × 0.6667.

Characteristics (earth-fault resistive reach, primary Ω)

Tool guide · know before you use

What this tool is, how it works and how far to trust it

A setting assistant that proposes distance relay zone reaches, times and resistive reaches for a line from the line and network data.

Read this before relying on a result. Every method, formula, assumption and limit is stated here, so you can check the answer yourself instead of accepting it blindly.

What it can do

Compute the line impedance, angle and residual compensation k0 from R1, X1, R0, X0 and the length.
Propose zone 1, zone 2, zone 3 and a reverse zone in primary and secondary ohms with their times and the rule behind each.
Propose earth-fault and phase-fault resistive reaches and limit them by the minimum load impedance at the load angle.
Warn for load encroachment, source impedance ratio above 4 and short lines; sketch the quadrilateral characteristics.

Why you need it

Each zone rule has a limit set by the adjacent lines, the load and the source; laying them out together keeps the setting sheet consistent.
Primary and secondary ohms side by side avoid the most common setting error — a wrong CT/VT ratio conversion.

Understand this first

Zone 1 under-reaches the remote end (80 %) so it can trip instantly without overreaching for errors in line data, CTs and VTs.
Zone 2 covers the rest of the line with a delay (0.3–0.4 s) and must not reach beyond zone 1 of the shortest adjacent line.
Zone 3 backs up the adjacent lines (0.8–1.0 s) and is the zone most at risk of tripping on heavy load.
Secondary ohms = primary ohms × CT ratio / VT ratio.

What you need before you start

Line R1, X1, R0, X0 per km and length; the shortest and longest adjacent lines.
CT and VT ratios, system voltage, maximum load and load angle, source impedance, fault resistances to cover.
A current browser (Chrome, Edge, Firefox or Safari). Nothing is installed and your data is never uploaded; it is processed on your own computer.

How to use it

Enter the line and network data (the defaults show the worked example).
Read the proposed zones and the checks; adjust the resistances or the reach rules if a check fails.
Transfer the values to the relay's setting sheet, using the relay's own settings for k0 and the characteristic.

What you get

A table of zones with reach in primary and secondary ohms, earth and phase resistive reaches and times.
Load impedance, resistive reach limit, SIR and checks; a quadrilateral sketch.

How to read the results

Zone 3 reaches into the load area: reduce the resistive reach or use load encroachment blinders.
SIR above 4: zone 1 accuracy suffers on a weak source — consider a lower zone 1 reach or a teleprotection scheme.
Very short line: zone 1 may be impractical; use line differential or a permissive scheme.

Technical basis

IEC 60255-121, IEEE C37.113 and common utility practice (80 % / 120 % / 0.3–0.4 s / 0.8–1.0 s).
Zone 2 = max(1.2 ZL, ZL + 0.5 Zadj,short), capped at ZL + 0.64 Zadj,short; zone 3 = 1.2 (ZL + Zadj,long); reverse 15 %; resistive reach 1.2 × 2 Rf (earth), 1.2 × Rarc (phase), ≤ 0.8 × Zload,min × cos(load angle).

Limits: when not to rely on it

A starting point, not the setting study: infeed, mutual coupling, series compensation, power swing and teleprotection schemes need the full study.
Relay-specific characteristics, k0 formats and angle conventions differ — follow the manufacturer's manual.

For preliminary engineering use. Results must be checked by a qualified engineer against the project's standards. How results are checked · Terms & disclaimer · Privacy · Build 7cfcbe2 · 2026-11-14