Power Transformers
Dr. Akram I. Aly
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Definition and Construction
• A transformer is an electromagnetic device
having two or more stationary coils coupled
through a mutual flux.
• The basic components of a transformer are
the core, the primary winding N1, and the
secondary winding N2.
2
Construction
3
Construction
4
Construction
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Stepped transformer core cross
sections
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Construction
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Construction
Cutaway view of self-protected
distribution transformer typical of sizes
2 to 25 kVA, 7200:240/120 V.
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Oil
immersed
Trans.
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Dry
Type
Trans.
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Construction
A 660-MVA three-phase 50-Hz
transformer used to
step up generator voltage of
20 kV to transmission voltage
of 405 kV.
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The Ideal Transformer
The ideal transformer:
1- No losses
2- No leakage flux
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Transformer Theory
• Assume Ideal Transformer:
1. No losses:



No eddy currents → resistivity of the iron core = ∞
No hysteresis losses
No copper losses in the windings → resistivity of the
windings = 0
2. no leakage flux → permeability of iron core,
µr=∞
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The Hysteresis Loop
Hysteresis Losses
• Due to the residual magnetization, each time
the magnetization of a material is reversed an
amount of energy is lost.
• This loss is known as the hysteresis loss
• The loop shown above is known as the
hysteresis loop.
• The hysteresis losses per unit volume is
directly proportional to the area of the
hysteresis loop.
1.5→ 2.5
Ph = k h fBm
Watt/kg
Eddy currents Losses
• Ferromagnetic materials are also good
conductors, and a solid core made from
such a material constitutes a single
short-circuited turn throughout its
entire length.
• Eddy currents therefore circulate within
the core in a plane normal to the flux,
and are responsible for resistive heating
of the core material.
• Eddy current losses ≈ ke f 2 Bm2 t 2 Watt/kg
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Eddy Currents Losses
• To reduce eddy-current loss, a core
may be constructed of laminations,
or thin sheets, with very thin layers
of insulation alternating with the
laminations.
• The laminations are oriented
parallel to the direction of flux.
• The thickness of the lamination
varies from about 0.05 to 0.5 mm
in most electric machines.
Transformer Theory, cont’d
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Transformer Theory, cont’d
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Transformer Theory, cont’d
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Transformer Theory, (cont’d)
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Transformer Theory, (cont’d)
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Transformer Theory, (cont’d)
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Flux in an ideal transformer
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Flux in an ideal transformer
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Ideal transformer at load
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Ideal transformer at load
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Ideal transformer at load
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Ideal transformer at load
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Transformer Polarity
•
•
•
•
A transformer may have multiple windings that may be connected either in series
to increase the voltage rating or in parallel to increase the current rating.
Before the connections are made, it is necessary that we know the polarity of each
winding.
By polarity we mean the relative direction of the induced emf in each winding.
Since the induced emf e1 in the primary of an idealized transformer must be equal
and opposite to the applied voltage v1, terminal 1 of the primary is positive with
respect to terminal 2.
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Transformer polarity
•
•
•
•
the flux φ, in the core of the transformer must induce in the secondary winding an
emf e2 that results in the current i2 as indicated.
The direction of the current i2, is such that it produces a flux that opposes the
change in the original flux φ.
For the wound direction of the secondary winding as depicted in the figure,
terminal 3 must be positive with respect to terminal 4. Since terminal 3 has the
same polarity as terminal 1, they are said to follow each other.
terminals 1 and 3 are like-polarity terminals. To indicate the like-polarity
relationship, dots are placed at these terminals.
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Transformer Ratings
• Name plate of transformer:
– Apparent power
– Primary / secondary voltages
• Example:
– 5kVA, 220/110V
• The transformer is a step down transformer,
the primary voltage is 220V and the secondary
voltage is 110V
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Transformer Rating
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Part II
THE REAL TRANSFORMER AND
DEVELOPMENT OF THE EQUIVALENT
CIRCUIT
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