Page 57 - Electrical Equipment Handbook _ Troubleshooting and Maintenance

TRANSFORMERS

3.14 CHAPTER THREE

If the primary voltage is given by υ (t) V cos
t V, the resulting flux will be
P
M
1
V cos
tdt
N P M
V M
sin
t Wb

N
P
Figure 3.8b illustrates the variations of the current required to produce the flux in the
core. The following observations can be made:
1. The magnetization current is not sinusoidal. It has a higher-frequency component due
to magnetic saturation in the transformer core.
2. In the saturation region, a large increase in magnetizing current is required to provide a
slight increase in the flux.
3. The fundamental component of the magnetization current lags the applied voltage
by 90°.
4. The higher-frequency (harmonic) component of the magnetization current increases as
the core is driven into saturation.
The second component of the no-load current in the transformer is required to supply
the core losses. The largest eddy current losses occur when the flux passes through 0 Wb
because these losses are proportional to d /dt. The hysteresis losses are also the highest
when the flux passes through zero. Therefore, the greatest core loss occurs when the flux
goes through zero. Figure 3.9 illustrates the variations in the total current required to make
up for core losses.
The total no-load current is known as the excitation current. It is given by
i i i h e
m
ex
Figure 3.10 illustrates the total excitation current in a transformer.

THE DOT CONVENTION

Figure 3.11 illustrates a load supplied from a transformer. The dots on the windings of the
transformer help to determine the polarity of the voltages and currents in the core without
performing a physical examination. The dot convention states that a positive magnetomo-
tive force is produced when the current flows into the dotted end of the winding. A neg-
ative magnetomotive force is produced when the current flows into the undotted end of the
winding. Therefore, the magnetomotive forces will be subtracted if one current flows into
the dotted end of a winding and the second flows out of the dotted end.
The primary current shown in Fig. 3.11 produces a positive magnetomotive force
P
N i . A negative magnetomotive force N i is produced by the secondary current.
P P S S S
Therefore, the net magnetomotive force in the core is given by
N i N i
net P P S S
In well-designed transformers, the net magnetomotive force is negligible. Therefore,
N i ≈ N i
P P S S

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