Page 55 - Electrical Equipment Handbook _ Troubleshooting and Maintenance

TRANSFORMERS

3.12 CHAPTER THREE

The voltage in the secondary coil is expressed as
d
υ (t) N S
S S dt
d d
LS
M
N N
S
S
dt dt
e (t) e (t)
S
LS
The mutual flux is
e (t) d e (t)
S
M
P

N P dt N S
Therefore,
e (t) N
P
P a
e (t) N
S S
This equation indicates that the ratio of the primary voltage caused by the mutual flux
to the secondary voltage caused by the mutual flux is equal to the turns ratio of the
transformer.
In well-designed transformers, and ; the ratio of the total voltage on
M LP M LS
the primary to the total voltage on the secondary is approximately
υ (t) N
P
P
≈ a
υ (t) N
S S
THE MAGNETIZING CURRENT IN A REAL
TRANSFORMER
When the ac power source is connected to a transformer, a current flows in the primary
winding, even when the secondary winding is open-circuited. This is the current required to
produce the flux in ferromagnetic core. It consists of these components:
1. The magnetization current i . The current required to produce the flux in the core of the
m
transformer.
2. The core-loss current I . The current required to make up for the hysteresis and eddy
h e
current losses.
Figure 3.8a illustrates the magnetization curve of a transformer core. The magnetization cur-
rent can be determined if the flux in the core is known. If we assume that the leakage flux is
negligible, the average flux in the core will be given by

1
υ (t) dt
N P P

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