Hello,
In one article I read that power transformer works very near
saturation area beause of better energy efficiency. It is well known

that magnetic flux - current characteristics is nonlinear, but there
is one area that can be considered linear. I wonder why is that, and
how working point near saturation area can provide better efficiency.
Thank you

It doesn't. Running high flux density as close to satruation as possible
allows a transformer to be as small and cheap as possibe, but it's
efficiency is not the best. The closer to saturation it runs, the higher the
magnetizing current, the higher the core losses, the higher the winding
losses and the hotter it runs. That's not the condition for high efficiency.
The B_H curve of the core material is the curve of the amount of flux
density you get, B for the amount of magnetizing force, H. This curve has a
relatively straight line portion at low values of H but curves off
flattening the flux density, B as you approach saturation. When fully
saturated, B = H and the core material acts like air. You don't want to run
there! The straight line portion is relatively linear.

| It doesn't. Running high flux density as close to satruation as possible
| allows a transformer to be as small and cheap as possibe, but it's
| efficiency is not the best. The closer to saturation it runs, the higher the
| magnetizing current, the higher the core losses, the higher the winding
| losses and the hotter it runs. That's not the condition for high efficiency.
What is the condition for highest efficiency?

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| Google Groups. If you want your postings to be seen by more readers |

the
efficiency.
Highest efficiency occurs when the core losses and the winding losses are as
low as possible. Core losses increase with core weight and flux density.
But, flux density decreases with larger core area. Therefore these things
are in opposition to each other.
Winding losses are due to I^2*R in the wire so the wire wants to be as large
in diameter as possible and as short in length as possible. High flux
density means a shorter wire but fatter wire means large core with more
space for wire. Again, these things oppose each other.
It can be shown mathematically that the highest efficiency occurs when the
core losses equal the winding losses at the maximum current. That's where
these opposing parameters balance one another.
In general, with modern silicon steel core materials, a flux density in the
region of 1.2 to 1.3 Teslas will result the highest efficiency. Exact
calculations based on core configuration, allowed temperature rise, desired
regulation and so on are required to get an exact answer.
If you are a glutton for punishment and want to get into a lot of
mathematics see: Transformer and Inductor Design Handbook by Col. Wm. T.
McLyman.

To supplement what Bob Eld has said:
Decreasing flux density by enlarging the core cross sectionwill reduce core
loss per unit volume of core. However, tthat also increases the core volume
so this tactic is a wash-and can increase the length of a turn of the
winding so the resistance loss rises. Increasing the number of turns will
reduce core loss and magnetising current but again the conductor I^2R loss
will rise. This can be countered by larger conductors but that will result
in some increase in core length.
For a given manufacturing cost then there is a balance between core and
copper losses and the maximum efficiency is where these are equal. For
something like a distribution transformer the average load is in the 50%
range so the balance should give maximum efficiency in this range. For a
large transformer the maximum efficiency should be near full load.
Large station transformers will have maximum efficiency in excess of 99%
while distribution transformers have max efficiency about 97-98% -- tis a
matter of $
Efficiencies can be increased by throwing more money at the problem but
there is a point where the increase in capital cost exceeds the decrease in
losses- and there isn't much room to increase. Going from 99% to 99.9%
efficiency would be very expensive.

--

Don Kelly snipped-for-privacy@shawcross.ca
remove the X to answer

The company I worked for a long time ago now, specified a $ value
for no-load losses (core and continuously energized pumps and/or
fans) and a separate $ value for load losses. The idea being that
the designer could make tradeoffs in the design to favor one or
the other. For example if fans and pumps were staged on/off at
different loading that would affect the load loss. A little more
or less copper might determine at what load a cooler would be
brought on line at some given standardized ambient temperature
and allow an evaluation to be made between more or less copper vs
running and extra pump or fan.
I don't have a copy of the old transformer spec or I'd look up
the wording but I seem to recall some sort of present worth of a
kW of loss over the life of the transformer adjusted somehow for
the load factor in the case of load losses.
Transformers were tested and money changed hands depending on
whether the loss guaranties were met or exceeded. This let the
designer improve the efficiency if he could make money doing so.
This was done on large generator step-ups and transmission system
transformers. I don't think we did heat runs on station auxiliary
and substation transformers at medium voltages. I suspect that
distribution transformers were type tested or sampled somehow.

--
Fred Lotte
snipped-for-privacy@nospam.stratos.net

Thanky you for the replies...
I have read that almost all power transformers work near saturation
area. From your reples, I think that is not true. Based on your
arguments, I agree that working point near saturation does not
provide good effeciency. Does it mean that power transformers (say 200
MVA) don't have working points on linear piece near saturation?

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