Environmental Engineering Reference
In-Depth Information
L
1
L
2
R
1
R
2
N
1
N
2
V
2
L
m
V
1
Ideal transformer
Figure 4.10
The transformer equivalent circuit
R
t1
= R
1
+ R
21
X
t1
= X
1
+ X
21
V
1
X
m
Ideal transformer
Figure 4.11
Simplifi ed transformer equivalent circuit
The equivalent circuit of Figure 4.10 can be further simplifi ed if the
R
2
and
I
2
are transferred
to the primary so that the primary and secondary resistances and inductances could be lumped
into just two series components. This can be done through the conservation of energy prin-
ciple. The transferred resistance from the secondary (2) to primary (1), which can be called
R
21
, should have such a value that when it carries
I
1
should dissipate the same amount of
power as
R
2
when carrying
I
2
, i.e.
RR
22
I
2
=
I
2
. Substituting the number of turns for currents
21 1
from Equation (4.12) we get:
2
RR
N
N
⎛
⎜
⎞
⎟
1
=
(4.13)
21
2
2
Similar logic based on the reactive power conservation principle (Appendix A) can be
applied for the transfer of the secondary winding reactance to the primary:
2
XX
N
N
⎛
⎜
⎞
⎟
1
=
(4.14)
21
2
2
A new equivalent circuit incorporating these changes is shown in Figure 4.11. Here
R
t1
and
X
t1
are the total winding resistance and reactance respectively referred to the primary
winding. In this circuit the magnetizing reactance
X
m
is connected across the mains with
little loss in accuracy because it can be shown that the voltage drops across
R
t1
and
X
t1
are small. This equivalent circuit is frequently used to calculate the effect of a transformer
in a power network and will be used later to develop an equivalent circuit for the asyn-
chronous generator.
