Worked example · Device 49 · IEC 60255-149

The Same 1.5× Overload, Cold vs Warm — Why a Thermal Relay Has Memory

The identical overload trips a cold machine in 20.2 minutes and a warm one in 2.6 — about 8× faster, purely because the winding was already hot. A worked demonstration of the method, not a specific site installation.

Published 2026-08-03 · EI Portal

The same 1.5× overload trips a cold machine in 20.2 min — and a warm one in 2.6 min. That's ~8× faster, purely because the winding was already hot. A definite-time relay or a simple I²t fuse can't tell them apart. The thermal replica can. That is device 49 / IEC 60255-149.

The setup: a generic single-time-constant thermal replica with τ = 30 min, threshold k = 1.05, tripping when the thermal state reaches 100%.

θ_ss = (I_eq / k)² × 100%
      t    = −τ · ln[ (I² − k²) / (I² − I_p²) ]
      

I is the load multiple, I_p the preload multiple — and it trips only if I > k.

1.5× from cold

Push 1.5× rated from a cold start (preload I_p = 0). The steady-state target is θ_ss = (1.5/1.05)² × 100 = 204.1% — well over the trip line — so it trips. Time to reach 100%: 20.2 min. The cold winding has the full thermal headroom to burn through first.

The same 1.5× — but warm

Identical 1.5× overload, but now the machine was already running at 1.0× rated (preload I_p = 1.0). Same 204.1% steady-state target, but it starts part-heated — so it trips in 2.6 min. That's ≈ 8× faster (20.2 ÷ 2.6 ≈ 7.8) on the identical current. The I_p term — the prior load — is the bit fuses cannot model.

1.0× never trips

Hold 1.0× rated steady and the element never trips: the thermal state settles at θ_ss = (1/1.05)² × 100 = 90.7%. Alarm territory, but stable. And 2.0× from cold trips in 9.7 min — there the workspace pegs its steady-state display at its 250.0% ceiling, a display cap only. Overload protection isn't an on/off line — it's a thermal state.

One engine, every relay

The generic IEC 60255-149 replica is the rigorous core; vendor profiles are layered on top, vendor-faithful but bounded: Siemens 7SJ / 7SD5 / SIPROTEC 5, MiCOM P14x / P34x / P44x / P54x / P64x, ABB REX640 motor (MPTTR) and transformer (T2PTTR) — across motors, transformers, generators and cables. Negative-sequence rotor heating is in too: I_eq = √(I₁² + k_ns·I₂²).

The one-line takeaway

A thermal relay has memory. The thermal replica carries the winding's prior load forward, so the same overload trips a warm machine ~8× faster than a cold one, and 100% load never trips at all — it just sits at 90.7%. That's what θ_ss = (I_eq/k)² and t = −τ·ln[(I² − k²)/(I² − I_p²)] capture, and a fixed I²t curve cannot.