4.4. The Real Transformer Model 4.
Transformers
to cause the insulation around the wire to break down. If this happens, the transformer may be
permanently damaged.
The power-handling capacity of a transformer is dependent upon its ability to dissipate heat. If
the heat can safely be removed, the power-handling capacity of the transformer can be increased.
This is sometimes accomplished by immersing the transformer in oil, or by the use of cooling fins.
The power-handling capacity of a transformer is rated in apparent power (VA) rather than active
power (kW) since the active and reactive current components both produce heat in the transformer.
Transformer wiring does exhibit resistance and thereby I 2 R losses in the windings, known as
copper loss, and some of the magnetic flux developed in the primary does not couple to the secondary
(and vice versa) and leaks from the magnetic circuit, known as leakage flux. The core of the
transformer has eddy current and hysteresis losses, requires excitation current to magnetize the
core, and may saturate. Eddy current loss is a result of induced currents circulating in the core.
Hysteresis loss is that energy lost by reversing the magnetic field in the core as the magnetizing AC
rises and falls and reverses direction. These real phenomena can be represented by lumped passive
circuit parameters.
For a given voltage, the transformer’s frequency of operation determines the flux in the core (see
Faraday’s law), as flux is proportional to the ratio of voltage to frequency, known as the volts-per-
hertz ratio. If the frequency applied to a transformer is lower than it’s nameplate frequency, the
volts-per-hertz ratio will exceed the nameplate value and magnetic saturation may occur. When
magnetic circuit saturation occurs, a large change in magnetizing current will produce very little
change in magnetic flux in the core. This condition can lead to overheating and cause damage.
Transformers should never be applied at frequencies lower than their rated frequency. Applying
frequencies higher than rated frequency will result in an increase of the winding inductive reactance
and a corresponding increase in voltage drop across the transformer (i.e., its impedance increases).
Since both hysteresis and eddy current losses are related to the applied frequency, those losses will
increase as well.
Putting many of these concepts together, a real single-phase transformer model is shown in
Figure 4.21.
R1 L1 R2 L2
RC LM
Figure 4.21: A lumped-parameter circuit model of a real transformer
The primary and secondary wiring resistances are represented by series resistors R1 and R2 ,
respectively. The primary and secondary flux leakages are represented by series inductances L1 and
L2 , respectively. These series components account for the impedance rating of the transformer.
This is an important rating, as an increase in the impedance rating increases the voltage drop across
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