Transformers

1
Chapter 14

• Transformers

2
Objectives

• Describe the components of an ideal transformer.
• Explain the relationship among the voltages,
  currents, and turns ratio in a transformer.
• Calculate the voltage, current, and power in a
  transformer.

3
Objectives

• Solve problems involving transformer losses and
  demonstrate the effect they have on efficiency.
• Show how to connect single-phase transformers to
  produce three-phase transformers.
• Apply special transformers such as
  autotransformers, current transformers, and
  potential transformers.

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14-1 Introduction
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14-2 The Ideal Transformer

• V1 / V2 N1 / N2
• a NHS / NLS
• V Vrated f / frated

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Simple transformer.
7
Transformer using high side and low side
designation.
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14-3 Transformer Power Losses

• Copper Loss
• Core Loss
• Hysteresis Loss
• Eddy Current Loss

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Copper Loss

• I2R power loss in the copper wire in the
  transformer windings.
• Proportional to the square of the winding
  current.
• Minimal when the transformer is operating with no
  load.
• Maximum copper loss occurs at rated load.

10
Core Loss

• Hysteresis Loss
• Frictional loss caused by the constant change in
  magnetic field polarity in the core.
• Increases with an increasing voltage or frequency
  applied to the transformer windings.
• Eddy Current Loss
• I2R loss in the core material caused by
  circulating induced currents in the core.
• Proportional to the square of the voltage and the
  square of the frequency applied to the
  transformer windings.
• Minimized by laminating the core.

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14-4 Transformer Efficiency

• ? Pout / Pin
• Pin Pout Plosses
• Plosses Pcu Pcore

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14-5 Effect of Power Factor on Transformer
Performance

• P V I cos ? V I x P.F.

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14-6 Impedance Reflection

• RL(HS) a2 RL(LS)

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Impedance reflection.
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14-7 Impedance Matching Transformers

• ZHS a2 ZLS

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14-8 Transformer Construction

• Shell
• Large
• Leakage flux
• E-Core
• Compact
• Leakage flux reduced

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Cores types, (a) shell and (b) E-core.
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14-9 Three-Phase Transformers

• Wye-to-Wye
• Wye-to-Delta
• Delta-to-Wye
• Delta-to-Delta

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Three-phase transformer wye and delta connection
possibilities.
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14-10 Autotransformers

• When wired as an autotransformer, the maximum
  current capacity of any winding of a transformer
  is the same as when it is used as a conventional
  transformer.
• The voltages, currents, and turns ratio still
  conform to the equations given.
• Although the autotransformer can deliver more
  apparent power (S, in volt-amperes) than the
  transformer alone, the transformer itself cannot
  safely deliver more apparent power than its
  rating.
• Because autotransformers can be connected in
  several different ways, rather than attempt to
  memorize the equations used to analyze each, it
  is easier to gain a fundamental understanding of
  how a basic autotransformer operates and then
  develop the governing equations as needed.

21
Autotransformer (boost connection).
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Autotransformer voltages and currents.
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Autotransformer buck configuration.
24
Variable autotransformer.
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14-11 Instrument Transformers

• Potential Transformer
• Current Transformer

26
Potential transformer and current transformer
application.
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14-12 Useful Transformer Tips

• The core losses in a transformer are determined
  by the applied voltage and frequency. Winding
  currents have no bearing on core loss. Reducing
  the load on a transformer will not reduce its
  core loss.
• The copper losses in a transformer are
  proportional to the squares of the winding
  currents and the square of the frequency. The
  applied voltage has no bearing on the copper
  loss.
• The maximum current that can be carried safely by
  a transformer winding is determined only by the
  wire gauge of the windings. The dimensions of
  the core and applied voltage have no bearing on
  maximum current capacity. Operating a
  transformer at a reduced voltage will not change
  its maximum current capability.
• The real power (watts) that can be delivered
  safely by a transformer is the volt-amp rating of
  a transformer times the power factor of the load
  it is powering. For example, a 1-kVA transformer
  can deliver only 700 watts to a 0.7-power-factor
  load.
• Transformers are designated to be most efficient
  when operated at full rated load (that is, rated
  voltage and rated current). Operating a
  transformer at reduced load current or reduced
  voltage reduces its efficiency.
• Transformers may be operated at lower frequencies
  if their voltage and apparent power ratings are
  derated by the same ratio as the frequency
  reduction.