Output Equations Of Transformer And Design

Output Equations Of Transformer And Design

1. Output Equations OF Transformer
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2. Output Equations OF Transformer
•Single phase core type transformer
•Voltage per turn
•Window in a single phase transformer one primary winding and one
secondary winding
•Total copper area of the window



•Current density in the primary and secondary winding is same
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3. Output Equations OF Transformer
•Total conductor area in window
• (1)
•Window factor - (2)
•Conductor / copper area of window Ac,
•From (1) & (2) (3)
•Rating of the transformer in kVA

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4. Output Equations OF Transformer
•Rating of the transformer in kVA



(4)
Three Phase Transformer
In three phase transformer,
Each winding consists of two
Primary winding and two
secondary winding
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5. Output Equations OF Transformer
•Total conductor area in each window

• (5)
•Total conductor area = =
•Ating of the transformer in KVA



• (6)
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6. Output Equations OF Transformer
•Output equation - volt per turn
•KVA Rating of the 1phase transformer
• (7)

•The ratio for a given transformer
•Let where r is a constant


• (8)

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7. Output Equations OF Transformer
•Voltage per turn Et
• (9)


• (10)

•Where K =

•As the ratio depends up on the type of the transformer
•K is also constant depends upon the type and service of transformer

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K

8. Output Equations OF Transformer
•Values of K for different type of transformer

Type of transformer K
Single phase shell
1.0 – 1.2
Single phase core
0.75 – 0.83
Three phase shell
1.3
Three phase core (Power)
0.6 – 0.7
Three phase core (Distribution)
0.45
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9. Output Equations OF Transformer
•Ratio of iron loss to copper loss
•Copper loss per
•Resistivity of copper 2.1 x 10
-8
Ωm at 75 degree
density as 8.9 x 10
3
kg/m
3

•Specific copper loss ( Copper loss at 75 degree )

• δ – current density
•Consider Stray loss Gc- 5 to 25 % of copper loss
•Total copper loss Wc = Pc Gc


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10. Output Equations OF Transformer
Total iron loss per kg – specific iron loss Wi
Wi = Pi Ii
Ratio of Iron loss to copper loss (11)
Design of Core
In core type distribution transformer, small power transformer with
moderate voltage - Rectangular shaped core section is used.
In core type, the ratio of width to depth of the core is 1.0 to 1.2
In shell type of ratio of width to depth of the core is 2.0 to 3.0

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11. Core of Transformer


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12. Core of Transformer
•Square and Stepped Core
•Circular coils are required for high voltage distribution and power
transformers – square and stepped cores are used





•In large transformer cruciform core is used for better space factor

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square core section
Cruciform core

13. Core of Transformer
•Square core
•Gross area of the core

•Net area of core
•
•
• =0.58

•= 0.64
•
13
Ai = stacking factor x gross iron area = 0.9x0.5d
2
= 0.45d
2

14. Core of Transformer
•Two Stepped Core
•Gross core area



•Agi = 2 d
2
sinθ cos θ - d
2
sin
2
θ
• = d
2
(sin 2θ - sin
2
θ )
•Differentiating w. r . t. to θ
• = (2 cos 2 θ – 2 sinθ cos θ )
• For maximum area = 0 , θ = 31.45 degree
•
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15. Core of Transformer
• , a = 0.85d , b = d sin 31.45 = 0.53 d
•Agi = 2ab - b
2
=

0.618 d
2
•
Net core area = 0.9 Agi
= 0.56d
2


•

•


•
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16. Core of Transformer


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17. Core of Transformer
•Variation of core diameter
•If the core diameter is higher - cross sectional area increases
•Increase the voltage per turn – reduce the number of turns in windings
•Reactance of the winding
It is directly proportional to the number of winding turns and diameter
of the coil
Inversly proportional to voltage per turn and coil depth
So a coil have a specified percentage reactance, the coil depth is
decreased when increase the coil dimension
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18. Core of Transformer
•Stepped core cross section is preferred for obtain the optimum core
area within circumscribing circle
•Core area determined by
1.Number of steps
2.Grade of steel
3.Insulation and Lamination
4.Type of clamping
•Selection of type core depends upon
1.Rating and operation duty
2.Transport limitation
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19. Design winding of Transformer
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The number of turns in primary winding
The number of turns in Secondary winding
The number of Low voltage winding turns per phase is an integer
The current in primary winding per phase is an integer

20. Design winding of Transformer
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•Copper loss in primary =

•Copper loss in secondary =

•Total copper loss

•Differentiating w.r.t

•For minimum loss

21. Design winding of Transformer
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Selection of type of winding
•Type of winding is depends on
•Electrical characteristics and adequate mechanical strength.
•Simplicity in constructional features
Types of high voltage windings are
1.Cylindrical winding with circular conductors
2.Cross over winding with either circular or small rectangular
conductors
1.Continuous type winding with rectangular conductors
The cylindrical and cross over winding are used for 100KVA 33KV
transformer

22. Design winding of Transformer
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•Disk type of windings are used for transformers from 200 KVA to tens
of MVA and voltage above 11KV
•The low voltage winding – two types
1. Cylindrical winding
2.Helical Winding

23. Design winding of Transformer
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Types of winding
 Cylindrical winding with circular conductors





Cylindrical winding with rectangular conductors


Cylindrical windings are low voltage windings used up to 6.6 kV for kVA up
to 600-750, and current rating between 10 to 600 A.

24. Design winding of Transformer
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•Cross-over windings.
•Cross-over windings are used for currents up to 20 A so they are
suitable for h.v. winding of small transformers.
• Cross-over coils are wound over formers and each coil consists of a
number of layers with a number of turns per layer.
•The complete winding consists of a number of coils connected in
series.
•Two ends of each coil are brought out, one from inside and one from
outside.
• The inside end of a coil is connected to the outside end of the
adjacent coil.

25. Design winding of Transformer
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•Ranges of different winding types ae given below

Type of
Winding
Rating KVA Voltage KV Minimum
Current
Conductor/A
Conductor
cross section
mm
2

No. of
conductors
(Strips in
parallel)
Cylindrical
Circular
conductor
5000-
10000
Up to 33 Up to 80 Up to 30 1 to 2
Cylindrical
Rectangular
conductor
5000- 8000 Up to 6.0 1.600 5-20 1 to 4
Cross over Up to 1000 Up to 33 Up to 40 Up to 15 1
Helical From 160
to tens of
thousands
Up to 15 but
sometimes
up to 33
From 300 and
above
75 to 100 and
above
4 to 16
Continuous
Disc
From 200
to tens of
thousands
3.33 to 220 12 and above From 4 to 200
and above
1 to 4

26. Design winding of Transformer
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•Position of winding relative to core




•LV windings are placed at inner side nearer to the core with H V
winding on out side because
1.PD b/w lv winding and the core is very low Insulation between the
core and lv winding has small thickness
2.HV winding is placed around the core - insulation b/w the LV and HV
winding is thick and mean turn length is large

27. Design of insulation for Transformer
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•Design insulation of TFR - fundamental concept
•Arrange the core, winding and insulation to obtain satisfactory electrical,
mechanical and thermal characatristics during the steady state as well as
transient condition
•Basic consideration in the design insulation
1.Electrical consideration
•The insulation structure is determined from the magnitude and nature of
voltages
•between the individual turns
•between the Coil or layers
•between the Windings
•between the Windings to core

28. Design of insulation for Transformer
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2.Eddy current loss
•The winding should be design with small stray loss
•Stray loss includes
1.the eddy current loss in conductors and connectors
2.the eddy current loss between tank walls and clamping structure
3.Leakage reactance
 The arrangement of core and winding determines leakage
reactance of the winding
The leakage reactance is controlled by changing the winding
configuration

29. Design of insulation for Transformer
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•Mechanical Consideration – two types
•Insulation must be capable of
with standing the mechanical stress imposed on it during the
manufacturing process
with standing the mechanical stress developed in the winding due
to electromagnetic phenomenon
•Thermal Consideration
•Thermal aspects of design of insulation depends on
1. Type of insulation material,
2.Selection of safe maximum operating temperature
3.Type of cooling method employed

30. Design of insulation for Transformer
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Thickness of major insulation of H V winding up to 33KV
( All dimension in mm)

31. Design of insulation for Transformer
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Thickness of major insulation of L V winding up to 33KV
( All dimension in mm)

32. Yoke designOF Transformer
•Area of the yoke is taken as 15 to 25 % of core – hot rolled steel
•hot rolled steel – reduce the flux density obtained in tnhe yoke – reduce
the iron loss and magnetising current
•Cold rolled silicon steel – area of yoke is equal to area of core
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33. Yoke designOF Transformer
•Rectangular section yoke
•Ay – area of yoke
•Ay = Depth of Yoke x Height of Yoke
•Ay = Dy x Hy
a = width of largest stambing
d = dia of circumscribing circle
D – distance b/w centres of adjacent limbs
Ww – Width of window
Hw – height of window – length of limb
H – overall height of the frame transformer

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34. Yoke designOF Transformer
• D = d +Ww
• Dy = a
• H = Hw + 2 H y
•
• W = D +a
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35. Yoke designOF Transformer

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