Page 103 - Electric Machinery Fundamentals

TRANSFORMERS 79

....... - --., - - , ,
/ , /
/ \ \ / , <PM / / \ \
I
,
I - . \ / \ \ \ I I /~ I - Is \ \
I
Ip
,
\
I + \ \ I I I I • + \
I \ \ , , , \
I
I
I 1 \
I \ \ I I \
I \ \ ¢LP \ I <PLS I I
I \ I I I
I \ \ I I I
I
\
I Vp , , I I VS '
I ; ; I
I I I I I I
I I
I I I I
\ I I I I I
I
I
\ , , \ \ I
\ \ \ I
,
\ - I I I I \ \ - I I
\ I I \ \ \ \ J
\ I I I \ I
,
"
\ / I I \ \ /
, -- / '-./ , / <PM \ \ \>// " -- / /
FIGURE 2-10
Mutual and leakage fluxes in a transformer core.
This flux is present in the primary coil of the transformer. What effect does
it have on the secondary coil of the transformer? The effect depends on how much
of the flux reaches the secondary coil. Not all the flux produced in the primary
coil also passes through the secondary coil-some of the flux lines leave the iron
core and pass through the air instead (see Figure 2- 10). The portion of the flux
that goes through oue of the transformer coils but not the other one is called leak-
age flux. The flux in the primary coil of the transformer can thus be divided into
two components: a Inlltualjlux, which remains in the core and links both wind-
ings, and a smaU leakage flux, which passes through the primary winding but re-
turns through the air, bypassing the secondary winding:
(2-19)

where q,p = total average primary flux
<PM = flux component linking both primary and secondary coils
q,LP = primary leakage flux

There is a similar division of flux in the secondary winding between mutual flux
and leakage flux which passes through the secondary winding but returns through
the air, bypassing the primary winding:

I q,s = q,M + chs I (2-20)