Transformer Loss of Life Formulas

Transformer ageing formulas: the hot-spot temperature, the ageing acceleration factor from the IEEE loading guide and the life at a steady hot-spot temperature.

The formulas

θA is the ambient temperature, ΔθTO the top-oil rise over ambient and ΔθH the hot-spot rise over the top oil, all in °C or K as the case may be. The formula is the one of the IEEE loading guide C57.91 for thermally upgraded paper, and it takes the hot spot at 110 °C as the normal rate of ageing. Other insulation systems and other editions use other constants, and the temperatures come from the heat-run test and the loading calculation of the maker. The normal life of 180,000 h is the usual figure of the guide and is only an example here.

Worked example: 30 °C ambient, 55 K top-oil rise and 25 K hot-spot gradient

1. θH = 30 + 55 + 25 = 110 °C
2. FAA = exp(15000 / 383 − 15000 / (110 + 273)) = 1, so the insulation ages at the normal rate

Worked example: a hot spot of 130 °C held for a day

1. FAA = exp(15000 / 383 − 15000 / (130 + 273)) = 6.984
2. Hours of life used in 24 h = 24 × 6.984 = 167.6 h
3. With a normal life of 180,000 h, the life at this temperature is 180,000 / 6.984 = 25,770 h

Ageing factor and life by hot-spot temperature

Frequently asked questions

Why is 110 °C the reference?

The loading guide takes 110 °C as the hot-spot temperature at which thermally upgraded paper ages at the normal rate, so FAA is 1 there.

What does a factor above 1 mean?

The insulation is using up its life faster than normal. A factor of 7 means a day at that temperature costs about a week of life.

Can a cool period make up for a hot one?

Yes, in the sense that the ageing adds up over time. The equivalent ageing over a load cycle is the average of FAA weighted by time.

What defines the end of life?

The loading guide gives limits such as a fall in the strength of the paper. The normal life used here is an example, and the standard and the maker give the figures.

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