How is hot-spot temperature calculated?

IEC 60076-7 adds to ambient the top-oil temperature rise and the winding-to-oil gradient times a hot-spot factor. For load factor K, oil rise grows with the loss ratio to the power x and winding gradient with K to the power y. With rated oil rise 52 K, winding gradient 26 K and 20 °C ambient, the hot spot is 98 °C at rated load.

How much does a small temperature rise shorten life?

For non-thermally-upgraded paper the ageing rate is 1 at a 98 °C hot spot and doubles every 6 K. At 20 °C ambient, 1.2 times load gives 120 °C and 13 times the ageing; 1.5 times gives 157 °C and about 930 times, using about 2.5 years of life in a day. At 30 °C ambient, rated load already gives 108 °C and 3.2 times.

Hot Spot Analysis of Transformers

Q: What is a transformer hot spot?

The hottest point in the winding, usually near the top where oil is hottest and eddy-current losses concentrate. Transformer life is set by how fast the paper insulating the winding degrades with heat, which depends on hot-spot temperature, making it the most important value when setting loads.

Category: Coupled Analysis – Electromagnetic-Thermal | Revised 2026-10-01

Theory: from losses to temperature to life

Overview

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How much does running a transformer slightly over rating affect its life?

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More than you'd think. Transformer life is set by how fast the paper insulating the windings degrades and becomes brittle with heat, and that rate depends exponentially on temperature: for non-upgraded paper it doubles every 6 K. More load raises copper loss with current squared, lifting both oil temperature and the winding-to-oil gradient. Computing the hottest point (hot spot) tells how fast life is consumed. Detailed work finds loss distribution by electromagnetic analysis and oil flow and temperature by CFD, but start with the IEC 60076-7 equations for a feel.

Hot-spot temperature and ageing rate

$$ \theta_h = \theta_a + \Delta\theta_{or}\left(\frac{1 + R K^2}{1 + R}\right)^{x} + H g_r K^{y},\qquad V = 2^{(\theta_h - 98)/6} $$

θ_a is ambient, Δθ_or rated top-oil rise (52 K), R the ratio of load to no-load loss at rating (6), K load factor, H hot-spot factor (1.3), g_r rated average winding-to-oil gradient (20 K), x = 0.8 and y = 1.3 (natural oil and air cooling example). V is the relative ageing rate of non-thermally-upgraded paper.

Coffee Break Trivia

The 6 K doubling rule

That insulation-paper degradation accelerates with temperature was shown experimentally by Montsinger in the 1930s, spreading the rule of thumb that life halves every 6–8 K. It rests on the Arrhenius idea that reaction rates rise exponentially with temperature. IEC 60076-7 now uses a doubling every 6 K referenced to 98 °C for non-upgraded paper, with a different formula and higher reference for thermally upgraded paper.

Worked examples

Example 1: 20 °C ambient

Load factor K	Top-oil temperature	Winding gradient	Hot spot	Ageing rate V
0.8	58.7 ℃	19.5 K	78.2 ℃	0.10
1.0	72.0 ℃	26.0 K	98.0 ℃	1.00
1.2	87.2 ℃	33.0 K	120.1 ℃	12.9
1.5	113.1 ℃	44.0 K	157.2 ℃	929

Example 2: 30 °C ambient

Load factor K	Hot spot	Ageing rate V
0.8	88.2 ℃	0.32
1.0	108.0 ℃	3.17
1.2	130.1 ℃	40.9
1.5	167.2 ℃	2,950

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At 1.5 times load you use two and a half years of life in a day. Surely that's not allowed?

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This is the steady state if 1.5 times load continued indefinitely. Real oil temperature rises slowly with a time constant of hours, so short overloads don't drive the hot spot this high. IEC guidance therefore computes temperature over time and sums low- and high-ageing periods through the day to assess life consumption; night-time hours at K 0.8 with ageing rate 0.1 can offset modest daytime overload. But if the hot spot gets too high, moisture in the paper can form bubbles and cause dielectric failure regardless of ageing, so temperature itself has limits. Ambient matters too: on a 30 °C day even rated load triples the ageing rate.

Analysis workflow

Set rated oil rise and winding gradient from heat-run test results.
Find winding eddy-loss distribution by electromagnetic analysis to locate the hot spot.
Use CFD of oil flow and winding temperature to confirm the hot-spot factor.
Compute temperature over time and life consumption from daily load and ambient profiles.
Calibrate against fibre-optic temperature measurements.

Coffee Break Trivia

“Top-oil temperature looked normal”

In one transformer top-oil temperature stayed below its alarm limit, yet inspection found paper at the top of the winding more degraded than expected. CFD showed a winding section with narrow oil ducts where oil barely flowed; there the winding-to-oil gradient exceeded design assumptions, equivalent to a hot-spot factor of about 1.6 rather than 1.3. Oil-guiding parts were added and fibre-optic sensors installed to monitor the hot spot directly.

Common mistakes

Mistakes and fixes

Mistake	Effect	Fix
Judging by top-oil only	Hot spot missed	Compute and monitor hot spot
Steady equations for short overloads	Ageing overestimated	Compute transient
Constant ambient	Summer ageing missed	Include seasonal variation
Fixed hot-spot factor	Local hot zones missed	Confirm with CFD
Confusing paper types	Wrong life	Choose formula by paper

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