1. Energy Conversion and Transport George G. Karady & Keith Holbert
EEE 360
Energy Conversion and Transport
George G. Karady & Keith Holbert
Chapter 5
Transformers
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360 Chapter 5 Transformers

2. Lecture 9
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3. 5.1 Construction
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4. Transformers 5.1 Basic components of single phase transformer
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5. Transformers 5.2 Single phase transformer arrangement 4/12/2019
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6. 5.3 Polarity for transformer
Transformers
5.3 Polarity for transformer
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7. Transformers
5.4 Small transformer construction a) Lamination, b) Iron core with winding
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8. Transformers 5.5 Winding Construction 4/12/2019
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9. Transformers Figure 5.6 Dry-type three-phase transformer 4/12/2019
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10. Transformers Figure 5.7 Oil Insulated and cooled transformer 4/12/2019
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11. Transformers Figure 5.8 Porcelain transformer bushing 4/12/2019
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12. Transformers Figure 5.9 Large Oil cooled high voltage transformer
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13. 5.2 Magnetic circuit
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14. Figure 5.10 B(H) Magnetization curves
Transformers
Figure 5.10 B(H) Magnetization curves
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15. Figure 5.11 B(H) Magnetization loss curves
Transformers
Figure 5.11 B(H) Magnetization loss curves
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16. Transformers Ampere law Permeability and flux density Flux
Fig 5.12 Magnetic circuit
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17. Transformers Induced voltage
The substitution of the above equations give
Modified Induced voltage
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18. Transformers Inductance Magnetic energy 4/12/2019
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19. Transformers 5.22 Magnetic circuit analysis Dimension of the core
w = 3in, h = w, a = 1in, b = 1.5in
Im = 2A, Nm = 20, f = 60Hz,
Magnetic path length and area
Lm = 2 (w + a) + 2 (h + a)
Acore = a b
Magnetic field intensity
Fig 5.13 Magnetic circuit
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20. Transformers 5.22 Magnetic circuit analysis Magnetic flux density ,
Permeability of free space
Magnetic flux density from B(H)
Fig 5.13 Magnetic circuit
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21. Transformers 5.22 Magnetic circuit analysis Magnetic flux ,
After substitution
Magnetizing curve is sinusoidal)
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22. Transformers 5.22 Magnetic circuit analysis
Magnetic flux time function ,
Maximum flux is:
Flux time function
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23. Transformers 5.22 Magnetic circuit analysis Induced voltage
rms. voltage value
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24. Transformers 5.22 Magnetic circuit analysis
Simplified induced voltage equation
Derivation of inductance
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25. Transformers 5.22 Magnetic circuit analysis Inductance equations
Derivation of inductance
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26. Transformers 5.22 Magnetic circuit analysis Inductance equations
Derivation of inductance
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27. Transformers 5.23 Magnetic energy Instantaneous power Energy 4/12/2019
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28. Transformers 5.2.4 Magnetization curves B (H)
The linear region, where the permeability of the material is a constant
The transition or knee region, where the material permeability reaches saturation; and
The saturation region.
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29. Figure 5.14 B(H) Magnetization curves and relative permeability
Transformers
Figure 5.14 B(H) Magnetization curves and relative permeability
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30. Transformers
Figure Magnetization curve regions and relative permeability of a high-silicon transformer steel.
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31. Transformers 5.2.5 Magnetic circuit with air gap
a = 3cm, b = 2cm, c = 4cm, g = 0.2cm, w = 10cm
h = 11 m, Bgap = 0.8T, Im = 8A
Dimensions of iron core
Lvert = (h –b) + (h-b-g) Lvert = 17.8 cm
Avert = c a Avert = 12 cm2
Lhorz = 2 (w –a) Lhorz = 14 cm
Ahorz = c b Ahorz = 12 cm2
Fig 5.16 Magnetic circuit with air gap
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32. Transformers 5.2.5 Magnetic circuit with air gap Gap flux = Total flux
Flux density in the horizontal and vertical sections
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33. Transformers 5.2.5 Magnetic circuit with air gap
Magnetic field intensity in the gap
Magnetic field intensity in the vertical and horizontal sections from Fig 5.17
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34. Figure 5.17 B(H) Magnetization curves
Transformers
Figure 5.17 B(H) Magnetization curves
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35. Transformers 5.2.5 Magnetic circuit with air gap
Number of turns using Ampere law
Inductance calculation
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