I mean why we use 50/60 Hertz in houses why we dont use 400Hertz. i
know as we increase frequency losses increase but what is formula or
equation for that.
There are quite a few different factors to consider when deciding on
the "best" power distribution frequency. In general, the transformer
core size goes up proportional to the inverse of the frequency. So
400 Hz transformers are about 60/400=15% the size of those for 60 Hz.
This is an economic advantage for the higher frequency. But the
core loss goes up as the frequency does, in two ways. There are eddy
current losses (current that circulates in the core as if it were a
short circuited transformer secondary) that can be reduced by making
the laminations of higher resistivity material (most commonly, by
alloying silicon with iron) and by making it of stacks of insulated
laminations that are proportionately thinner.
There are also per cycle losses related to the energy lost each time
you reverse the direction of magnetization in iron, called hysteresis
losses. There is nothing you can do about those, as long as you use
iron for the core material. The exotic core materials with much lower
hysteresis losses are a lot more expensive than the silicon iron alloy
used for 60 Hz transformers.
There is also the problem of phase shifts over distance that gets
worse in proportion to the frequency. A wavelength at 60 Hz is
something like 3100 miles. At 400 Hz, that drops to about 470 miles.
You get into huge problems trying to connect a vast network of
generators and consumers with transmission lines when there are waves
of many phases propagating around all possible loops of the system,
some places aiding and some places canceling (called standing waves).
This makes it almost impossible to build a system with multiple
redundant energy paths, to handle all sorts of load shifts and
equipment failures. In effect, each state or city would have to have
its own independent 400 Hz grid.
I think those are the biggest factors in favor of lower frequency
transmission of power. There are quite a few more second and third
order factors, some of which may have applied more at the origin of
the grid than they might, now, with advances in technology.
