In a transformer, both primary and secondary currents
produce flux. The flux Ф which links both
the windings is the useful flux and is called mutual flux.
However, primary current would produce some flux Ф1
which would not link the secondary winding. Similarly, secondary winding would
produce Ф2 that would not link the primary winding.
The flux such as Ф1 or Ф2 which
links only one winding is called leakage flux, shown below.
Why
does flux leak in a transformer ?
This is due to parallel magnetic circuit. Lets take
primary winding alone for simplicity.
The flux through the air is given by
The mmf is same for both. Therefore, flux becomes inversely
proportional to reluctance. Since air reluctance is high (as compared to core
reluctance), therefore, a small flux takes path through air.
On the other hand, core reluctance is small, therefore, a large flux
passes through the transformer core.
So, to make leakage flux zero, we must increase the air
reluctance to infinite, which is not possible. Hence, there always exists a
leakage flux in machine.
Representation
of Leakage flux in equivalent transformer circuit
Leakage flux is represented by inductive reactances in
series with winding resistances as shown below.
Lets see how we reached this conclusion.
The mmf N1I1
would produce leakage flux Ф1 which
would be in phase with the current I1 , shown by the magnetisation
curve of the air.
Let Ф1= Фm sinwt and I1=
Im sinwt . The flux Ф1
would induce emf in primary given by
(1)
and (2) show that induced emf is proportional to the rate of change of current
and leads current by 900. But these are the properties of an inductor.
Hence, leakage flux is represented by an
inductive reactance in transformer equivalent circuit.
Methods
of Reducing Leakage Flux
(1)
By increasing window height :-
For a given window area,
if window height is increased, the leakage flux path becomes more. This has the
effect of increasing the reluctance offered to the leakage flux paths and for a
given mmf, leakage flux is reduced.
(2) By arranging primary and secondary windings
concentrically
Since the primary and
secondary windings are more close to each other, leakage flux is reduced.
(3) By sandwiching primary and secondary windings
:-
As shown above, winding 1
has four sections and winding 2 has two sections. On each leg, winding 2 is
sandwiched by two sections of winding 1. Sandwiching is done to arrange
windings as close as possible, so that leakage flux is reduced.
(4) Using shell-type construction :-
In shell-type
construction, iron surrounds both the windings. Therefore, the fluxes produced
by the windings tend to follow the least-reluctance iron-path around them,
rather than the high reluctance air path.
Related concepts :-
