Overcurrent protection (ANSI 50/51) — IDMT time-current characteristics

The guide on circuit breaker settings — L, S, I and G in the LSI(G) curve covers how a low-voltage power circuit breaker with a limited number of adjustable time and current bands is coordinated. This article covers the related, but not identical, principle used with medium-voltage protection relays: the inverse definite minimum time characteristic (IDMT) under ANSI 50 (instantaneous overcurrent) and ANSI 51 (time overcurrent with a time-dependent characteristic).

The difference between 50 and 51

• ANSI 50 — instantaneous overcurrent: trips without intentional delay as soon as the measured current exceeds a fixed, high pickup value. This element is typically set well above the maximum operating current and above the inrush current of connected transformers or motors, so that it only responds to an actual, severe fault close to the relay.
• ANSI 51 — time overcurrent with an IDMT characteristic: trips according to a curve where the trip time decreases as the measured current rises further above the pickup setting — hence "inverse". At a current just above the pickup setting, it takes relatively long before the relay trips; for a severe fault far above the pickup setting, the same relay trips much faster.

The IDMT curve families under IEC 60255-151

IEC 60255-151 (formerly IEC 60255-3) defines a set of standardised curve shapes, each with its own constants in the standard formula:

$$t = \text{TMS} \times \frac{K}{\left(\frac{I}{I_s}\right)^{E} - 1}$$

where t is the trip time, TMS the time multiplier setting, I the measured current, Iₛ the pickup setting, and K/E the curve-specific constants:

A curve with a higher exponent E (extremely inverse) responds relatively slowly to a slight overshoot above the pickup setting, but very quickly once the current is far above the pickup setting — suitable for applications with a wide spread between minimum and maximum fault current, such as motor feeders. A standard inverse curve gives a more even response across the whole range and is more commonly applied in general distribution networks.

Note: the TMS (or, in some manufacturers' implementations, the "time dial setting") scales the entire curve in the time direction without changing its shape. Two relays with the same curve type but a different TMS can therefore be made time-selective relative to each other without changing the current pickup setting itself — the main mechanism used to grade a chain of series relays (source → main distribution → outgoing circuit) so that the relay closest to the fault trips first.

Coordination between relays in series

When setting up a chain of 51 relays in series, an increasing TMS (and, where needed, an increasing pickup value) is chosen for each relay moving from the load back towards the source, so that a demonstrable time margin remains between the curve of each relay and that of the relay directly upstream at every fault current level — comparable in principle to zone-selective interlocking (ZSI) in low-voltage power circuit breakers, but achieved through time-curve separation rather than a communication signal between breakers.

Practical relevance

When drawing up or reviewing a selectivity study for a medium-voltage network, it is important to check not only the pickup value (Iₛ) of each 51 relay, but also the curve type and the TMS, and to verify that the associated 50 element is set high enough above the maximum continuous operating current and inrush current to avoid nuisance tripping under normal operation, while still responding fast enough to a fault close to the relay.

Common mistakes

1. Using the same curve type and the same TMS for every relay in a chain, without verifying an increasing time margin towards the source — this undermines selectivity between the relays.
2. Setting the 50 element too low, so it responds to normal inrush currents of transformers or motors and trips unnecessarily.
3. Choosing a curve type without regard for the spread between minimum and maximum fault current of the feeder in question, leading to an unnecessarily slow or unnecessarily fast response over part of the current range.
4. Treating the LSI settings of a low-voltage power circuit breaker and the IDMT settings of a medium-voltage relay as the same concept, when the underlying curve shape and setting logic differ substantially.

Related

• Circuit breaker settings — L, S, I and G in the LSI(G) curve
• Zone-selective interlocking (ZSI)
• Directional overcurrent protection (67)
• Circuit breaker characteristics B, C and D