# Inverse-Time Overcurrent Relay Setting (IEC 60255-151)

Compute the operating time of an inverse-time overcurrent relay per IEC 60255-151: t = TMS·(k/((I/I_s)^α − 1)). Supports Standard Inverse (SI), Very Inverse (VI), Extremely Inverse (EI) and Long-Time Inverse (LTI) curves, and samples a T-I characteristic.

> Canonical page: https://elysiatools.com/en/tools/relay-setting-calculator

- **Category:** Math & Numbers

- **Keywords:** overcurrent relay, IEC 60255, inverse time, TMS, pickup current, SI, VI, EI, LTI, protection, fault current, electrical engineering

## Overview

Calculate the operating time of inverse-time overcurrent protection relays according to the IEC 60255-151 standard. This calculator supports Standard Inverse (SI), Very Inverse (VI), Extremely Inverse (EI), and Long-Time Inverse (LTI) curves, allowing electrical engineers to determine trip times and generate T-I characteristic data points using pickup current, fault current, and time multiplier settings.

## Inputs

- **Curve Type** (select)
- **Pickup Current I_s (A)** (number): Relay pickup (setting) current, primary side.
- **Time Multiplier TMS** (number): Time multiplier setting, typical 0.05 – 1.0.
- **Fault Current I (A)** (number): Applied fault current. Must exceed pickup (I > I_s) for the relay to operate.
- **Curve Sample Points** (number): Number of points sampled on the T-I curve (11–41).
- **Decimal Places** (number)

## When to use

- Designing electrical protection coordination schemes for power distribution networks.
- Verifying relay trip times during commissioning or periodic maintenance testing.
- Generating T-I (Time-Current) curve data points to plot protection characteristics in engineering reports.

## How it works

- Select the IEC 60255-151 curve type (Standard, Very, Extremely, or Long-Time Inverse) to define the curve constants k and alpha.
- Input the primary pickup current (I_s), the applied fault current (I), and the time multiplier setting (TMS).
- Specify the number of curve sample points and decimal precision to generate the detailed T-I characteristic dataset.
- Run the calculation to obtain the exact relay operating time and the sampled curve points in JSON format.

## Use cases

- Calculating the trip time of a feeder relay under a specific short-circuit fault current.
- Determining the grading margin between upstream and downstream relays to prevent nuisance tripping.
- Generating data points to model relay characteristics in power system simulation software.

## Frequently asked questions

### What is the formula used for the calculation?

It uses the IEC 60255-151 standard formula: t = TMS * (k / ((I / I_s)^alpha - 1)), where I is the fault current and I_s is the pickup current.

### What curve types are supported by this calculator?

It supports Standard Inverse (SI), Very Inverse (VI), Extremely Inverse (EI), and Long-Time Inverse (LTI) curves.

### Why does the calculator require the fault current to exceed the pickup current?

An overcurrent relay only initiates its timing sequence when the fault current (I) is strictly greater than the pickup current (I_s).

### What is the typical range for the Time Multiplier Setting (TMS)?

The TMS typically ranges from 0.05 to 1.0, which scales the overall operating time of the relay.

### What output format does the calculator provide?

It outputs a JSON object containing the calculated operating time, input parameters, and a sampled array of points along the T-I curve.

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