# How does the efficiency of a transformer change with its load?

How does the efficiency of a transformer change when the load changes, and why is that so?

• I appreciate the "accept, but as nobody else has replied and I have no votes (yet :-) ) and it's been less than an hour since I replied, then waiting a while to see what else comes along may be a good idea. Some people get discouraged if an answer has already been accepted and may not reply, when they may have something very useful to add. | All that said you can always accept someone else's answer in place if mine if a better one come along :-) Thanks. Commented Dec 14, 2011 at 11:31

Increasing current causes increasing copper losses due to resistance.
Resistive loss is determined by current^2 x resistance. BUT,
Power is determined by voltage x current.

So if you increase power from 100% to 110% the copper losses rise by
(110%/100%)^2 = 1.1^2 = 1.21 ie losses increase by 21% for 10% more power.

Copper resistive energy loss is turned directly into heat.
A transformer will be designed to have a safe temperature rise at rated power in the worst case environmental conditions that it is guaranteed to work in.
Add 20% more heat and things may get "interesting"/ Short term failures may occur.
But, if not, inter-winding insulation will "cook" and perish, wire insulation may fail.

Iron losses due to hysteresis will also increase. Brain offers that this will be linear with current but brain may be wrong.

Increased temperature may affect magnetic property of the core steel. IF core permeability drops even slightly then flux will drop and inductance will drop and current per applied volt will rise and copper loss will increase and temperature will increase and ... .
Thermal runaway is not usually seen in domestic size transformers. Fortunately.

• Keeping a transformer as cool as possible is always a good idea. At elevated temperatures the life of the insulation is reduced, and the resistance also increases further because copper has a positive temperature coefficient of resistance.

• As the transformer gets hot, its resistance increases, increasing losses. This (naturally) leads to greater losses that cause the transformer to get hotter. There is a real risk of drastically reduced operational life (or even localised "hot-spot" thermal runaway) if any transformer is pushed too far - especially if there is inadequate (or blocked) cooling.

• It is generally accepted that any transformer will have one part of the winding that (for a variety of reasons) is hotter than the rest.
It's also a rule of thumb that the life expectancy of insulation (amongst other things) is halved for every 10°C (some claim as low as 7°C).
When these two factors are combined, it is apparent that any transformer operated at a consistently high temperature will eventually fail due to insulation breakdown. The likelihood of this happening with a home system is small, but it's a constant risk for power distribution transformers.

• Despite all this, mains frequency iron cored transformers typically outlast the product they are powering, and even recycled transformers can easily outlast their second or third incarnation. Once a transformer is over 50 years old I suggest that the chassis be earthed, as the insulation can no longer be trusted at that age.

Not directly asked about but related and worth noting: Transformer manufacturers seek to minimise cost (of course) and using as little lamination material as reasonably possible is a target. The core is usually designed to operate at the knee of its flux BH curve where increasing amp-turns start to give increasingly less flux per amp-turn as the core is driven further into saturation.
Transformers designed for 60 Hz operation can use usefully less core material due to the increased impedance at higher frequency (Z = 2.Pi.f.l).
However, operating a transformer designed for 60 Hz in a 50 Hz environment can lead to very substantial excess heating.
While this is not normally encountered it does happen. Two examples:

• People bringing equipment from eg the US to NZ not only need to adjust transformer tappings (if availaable) to accommodate the 100 VAC to 230 VAC change but also need to take account for the change from 60 Hz (USA) to 50 Hz (NZ)

• I once had a custom 500 watt mains power transformer would in New Zealand for use in a test box in a Taiwanese factory. Their mains is 110VAC and hours is nominally 230 VAC. I specified two primary windings that could be connected in series or parallel to allow operation in either country. In the specification I did not mention Taiwan but I did tell the manufacturer that it was for use in Taiwan, ultimately. He took it on himself, without asking or telling me, to design it for 60 Hz operation. NZ uses 50 Hz. While a 50 Hz design would have worked well in Taiwan, the opposite was not as true as I would have liked. In NZ on test it ran VERY hot - it took me a wee while to realise why.

• Typos galore: "dometic dize transformers. Firyunately." Commented Jul 29, 2016 at 0:55
• @immibis Och aye. Thanks. Revisiting my 2000+ answers for their generously allotted typos would be more than a full time job. | That was 4.5 years ago, the answer was accepted within an hour, it's useful as is and has 3 votes. If people valued it more it may be worth the effort. It's likely that people who find it useful will manage to find their way through the typos. And those who REALLY care are allowed to fix them. Just as long as they don't hack the answer about in the process. Commented Jul 29, 2016 at 1:17
• You clearly spent more time being annoyed by me pointing out typos than I did pointing out the typos. (And I believe trivial edits are discouraged except by the answer's original author) Commented Jul 29, 2016 at 1:23
• @immibis I did not say I was annoyed, and I wasn't. Not much anyway :-). I'd be more annoyed about more people who know about such things not voting up goodish answers so others who know less may see that they are worthwhile. That's not so I get more "rep" - I have enough :-) - and I nowadays try to add comments with pithy points in to educate to allow more benefit per effort. I agree with you about the typos. I am over messy and can usually find typos in my material. I was aware that the editing may be faster than the reply (and than this one) BUT what I said was true - I spend more time ... Commented Jul 29, 2016 at 1:28
• @immibis ... than I should or can afford on this site and others and other information related activities. | I appreciate people being considerate re editing. Fixing typos is welcome. What does annoy me is when people change style and grammar for no productive reason (often "correcting" my antipodean Queen's English" or 'laconic' bent) and often trampling on technical content in the process. BUT, 'just for you'. I will have a go at detypoing the answer. Do feel free to considerately detypo any of my other answers - many need it :-). Commented Jul 29, 2016 at 1:32

How does the efficiency of a transformer change with its load?

If an alternative voltage is applied to the primary, there will be a current through the primary regardless of whether a useful load is connected to the secondary. This current will have losses which is converted to heat.

When the secondary is open circuit, there is no useful load, but there are losses, so the efficiency is 0.

When the secondary is short circuit, there is no useful load, but there are the original losses, and also extra losses due to a larger current in the primary, and a current in the secondary. Again, losses, but no useful power given to a load, so the efficiency is again 0.

If the load resistance is varied from $$\\infty\$$ to 0, the efficiency will start at 0, climb to a relatively high value less than 100%. (95% or even more is not uncommon.) Then the efficiency will work its way back down to 0.

The major losses are due to

• resistance of the windings (so called copper losses)
• eddy currents in the core
• hysteresis in the core

While not directly losses, factors which affect losses include

• leakage inductance
• parasitic capacitance (not usually a significant factor in low frequency transformers.

Leakage inductance causes the secondary terminal voltage to sag as load on the secondary draws more current.