TRANSFORMER EFFICIENCY

Go to electrical engineering school. When done, read old papers or books on electrical machines i a resarcvh library.

It is usually covered in Transformers 101 and thus is all good EE theory books.

Or they buy from a builder manufacturer's catalogue.

I have no quarrel with what you say. Transformer manufacturers must use first principles. But sticking to first principles would not be enough to get highest efficiency in the old days, and probably, not now.

These days, with relatively large computing power available on your desktop, it might be possible to model the nitty gritty electrical, thermal, and magnetic parts of a transformer in great detail. I do not know if anyone has done that. I think of first principles as something in a textbook that allows a competent engineer to get reasonable proficiency to do something. That is a long cry from obtaining the high transformer efficiency needed to minimize power dissipation in truly high power transformers. The losses in small electronic equipment are trivial in comparison to what happens in gigawatt transmission systems. The wart power supplies we all use with are little electronic devices are very power wasteful. Individually, however, the cost to users like us is not much to worry about. With probably more that a billion of these in use in North America, it amounts to much waste.

Using computers, we are able to go to first principles that are "firster" than the first principles of a couple of decades ago.

In 1953 I had a course in machine design, including transformers and while the design methods were not up to the present, it was reasonable to have transformers in the MVA range with efficiencies over 99%. Design parameters did require balancing copper and iron losses as well as cost to optimize for the particular application- This is not to say that I disagree with you. The computer has proven effective as a tool as it made feasible many methods of analysis which were simply not practical in those days. I have tested small transformers built in the 70' and a cheap 3KVA transformer had a peak efficiency of 98% + and >95% over most of the load range, and large transformers would be pushing 99.9% (guaranteed). Getting

99.99+% is possible but becomes expensive (superconductive windings need refrigeration and low loss cores have their limitations). Some 20 years ago there was an IEEE paper on such an experimental transformer- economically impractical at the time and possibly still so. There is a balance between the capital costs of improvements and the cost of the losses in the lifetime of the equipment.

As for power system losses, very rarely does a power system load flow model include transformer resistance or core losses as they are negligible compared to line losses (typically 5% or thereabouts) and mechanical/ thermal losses in generation. A paper I heard many years ago did look at the cumulative losses in national power systems.

Now, I wonder whether the losses due to the inefficiency of all the power supplies and electronic devices might, on the whole exceed the losses in transmission systems. Isn't that a factor in new wall warts which have to meet certain efficiency standards (still a low 70% or so)?

Don

99.9% is pretty damn good. I'll bet that in doing so, the designers must have checked out where the losses were pretty carefully on a previous version. I find it difficult to believe that any designer could do so from first principles.

I once worked on a pulsed doppler radar system transformer. Quite a few people contributed to its development. I started using ferrite cores, but the eddy current losses heated up the cores into thermal runaway, temperatures above the curie point, and breakage. The cores broke. I got the cores "laminated" using slices made with diamond wheels. That reduced losses to where there was no thermal runaway. Someone els figured out that that the laminations could be separated with copper sheet to to conduct heat out. The copper did not add much eddy current loss. That shrank the transformer even more. Someone figured out how to use water cooling for even a smaller size. No way could that have been done using first principles.

Of course the designer looked at previous designs and tweaked them. Take what works and improve on it or correct what didn't work. Mtallurgists looked at better core materials. EHV transformers are quite different in design than lower voltage transformers as other factors came into being. For example some old insulation ideas (more at the HV end and less at the ground end -which actually worsened the surge voltage distribution) were proven faulty and newer designs considered the whole balance of RLC in order to have a more uniform voltage distribution when a surge occurred. The use of laminated cores came from way back( essentially Steinmetz) but the copper sheet idea is novel and is an adaption to the purpose and limitations involved. In the middle ages, people built Gothic cathedrals which are amazing solutions to the problems faced, even with our present knowledge of stress patterns. We are looking at engineering rather than physics -but basing the engineering on physics +"the perversity of inanimate objects"(Kipling)