DESIGN OF TRANSFORMER

Classification of transformer
Depending upon the type of construction used:
I. Core type
II. Shell type
2

Comparison of core type and shell type
transformers:-
I. Construction:- Core type transformers are much
simpler in design and permit easier assembly and
insulation of winding.
II. Mechanical forces:- The forces produced between
windings is proportional to the product of the currents
carried by them. Very large electromagnetic forces are
produced when secondary winding is short circuited.
Since the windings carry currents in opposite direction,
there exists a force of repulsion between them. Hence,
the inner winding experiences a compressive force and
outer winding experiences a tensile force.
3

In a shell type transformer, windings have greater
capability of withstanding forces produced under short
circuit as these windings are surrounded and supported
by the core. But in a core type transformer windings
have a poorer mechanical strength.
4

III. Leakage reactance:- In core type transformer large space
required between the high and low voltage winding, it is
not possible to subdivided the winding, while, in shell type
transformer the windings can be easily subdivided by using
sandwich coil. So it is possible to reduce the leakage
reactance of shell type transformers.
IV. Repairs:- The winding of core type transformer is
completely accessible so coils can be easily inspected. And
also core type transformer is easy to dismantle for repair. In
shell type transformer, the coils are surrounded by core,
therefore difficulty in inspection and repair of coils.
V. Cooling:- In core type transformer windings are exposed
and therefore the cooling is better in winding than core. In
case of shell type transformer core is exposed therefore
cooling is better than winding.
5

7
CORE TYPE SHELL TYPE
1. Easy in design and
construction.
1. Comparatively complex.
2. Has low mechanical strength
due to non- bracing of windings.
2. High mechanical strength.
3. Reduction of leakage reactance
is not easily possible.
3. Reduction of leakage reactance is
highly possible.
4. The assembly can be easily
dismantled for repair work.
4. It cannot be easily dismantled for
repair work.
5. Better heat dissipation from
windings.
5. Heat is not easily dissipated from
windings since it is surrounded by
core.
6. Has longer mean length of core
and shorter mean length of coil
turn. Hence best requirement
6. It is not suitable for EHV (Extra
High voltage) requirement.

Classification on the basis of type of service:
I. Distribution transformer
II. Power transformer
Classification on the basis of power utility:
I. Single phase transformer
II. Three phase transformer
8

Construction of transformer
I. Transformer core
II. Winding
III. Insulation
IV. Tank
V. Bushings
VI. Conservator and breather
VII. Tapping and tap changing
VIII.Buchholz Relay
IX. Explosion vent
X. Transformer oil
9

• The most important function performed
by transformers are,
– Changing voltage and current level in an electric
system.
– Matching source and load impedances for
maximum power transfer in electronic and
control circuitry.
– Electrical isolation.
10

Nomenclature
11
Vp , Vs = terminal voltages at primary and Secondary
winding respectively, V
Ep, Es = emf induced in the primary and secondary
windings per phase, V
Et = emf per turn, V
Tp, Ts = number of primary and secondary turns per phase
Ip, Is = primary and secondary currents per phase , A
ap, as = area of the primary and secondary winding
conductors, m2
Φm –=main flux in weber = AiBm
Bm = Maximum value of the flux density = Φm / Ai tesla

12
Ai – Net iron area of the core or leg or limb (m2)= KiAgi
Ki – Iron or stacking factor = 0.9 approximately
Agi – Gross area of the core, m2
Ac – area of copper in window, m2
Aw – window area, m2
D – distance between core centers, m
d= diameter of circumscribing circle, m
Kw – window space factor
δ - Current density (A/m2). Assumed to be same for both LV
and HV winding.

Output Equation of Transformer
13
 The equation which relates the rated kVA output of a
transformer to the area of core and window is called output
equation.
 In transformers the output kVA depends on flux density and
ampere-turns.
 The flux density is related to core area and the ampere-turns
is related to window area.
 The low voltage winding is placed nearer to the core in order
to reduce the insulation requirement.
 The space inside the core is called window and it is the space
available for accommodating the primary and secondary
winding.
• The window area is shared between the winding and their
insulations.

The simplified cross-section of core type and shell type
single phase transformers
14
Core Type Transformer Shell Type Transformer

Single phase core type transformer
15
The induced emf in a transformer,
Emf per turn,
The window in single phase transformer contains one primary and
one secondary winding.
The window space factor Kw is the ratio of conductor area in window
to total area of window.
Conductor area in window,
The current density is same in both the windings. Therefore Current
density =

16
Area of cross - section of primary conductor,
Area of cross - section of secondary conductor,
If we neglect magnetizing mmf then primary ampere turns is
equal to secondary ampere turns. Therefore ampere turns,
Total copper area in window,
Ac = Copper area of primary winding + Copper area of secondary
winding
= (Number of primary turns x area of cross-section of primary
conductor) + (Number of secondary turns x area of cross -
section of secondary conductor)

17
On equating the above equations, we get,
Therefore Ampere turns,

18
The kVA rating of single phase transformer is given by,
on substituting for E and AT from equations we get,
The above equation is the output equation of single phase core
type transformer

Single phase shell type transformer
19
Emf per turn,
The window in single phase transformer contains one primary and
one secondary winding.
The window space factor Kw is the ratio of conductor area in window
to total area of window.
The current density is same in both the windings. Therefore Current
density =

20
Area of X - section of primary conductor,
Area of X - section of secondary conductor,
Since there are two windows, it is sufficient to design one of the
two windows as both the windows are symmetrical. Since the
LV and HV windings are placed on the central leg, each
window accommodates Tp and Ts turns of both primary and
secondary windings
Copper area in window Ac

21

22
The kVA rating of single phase shell type transformer is given by,
The above equation is the output equation of single phase shell
type transformer

Three phase core type transformer
23
• Core type three phase transformer has three limbs and two
windows as shown in figure.
• Each limb carries the low voltage and high voltage winding of
a phase.

24
Emf per turn,
In case of three phase transformer, each window has two
primary and two secondary windings.
window space factor Kw is
The current density is same in both the windings. Therefore
Current density =

25
Area of cross - section of primary conductor,
Area of cross - section of secondary conductor,
Total copper area in window, Ac = (2 x Number of primary turns
x area of cross-section of primary conductor) + ( 2 x Number
of secondary turns x area of cross - section of secondary
conductor)

26

27
The kVA rating of three phase transformer is given by,
The above equation is the output equation of three phase
transformer

Three phase shell type transformer
28
Rating of the transformer in
Q = VpIp x 10-3 = EpIp x 10-3 kVA
= 4.44 Φm f Tp x Ip x 10-3 kVA
Since there are six windows, it is sufficient to design one of the
six windows, as all the windows are symmetrical. Since each
central leg carries the LV and HV windings of one phase, each
window carries windings of only one phase.

30
Copper area in window Ac =

31
on substituting AT in kVA rating,
Q = 3 x 4.44 AiBmf x (AwKwδ/2) x 10-3 kVA
Q = 6.66 f δ AiBm AwKw x 10-3 kVA

Output equation of transformer
Single phase core type & shell type transformer :-
Three Phase core type transformer :-
Three Phase shell type transformer :-
Q = 6.66 f Bm δ KwAw Ai . 10-3 kVA
32

33
Usual values of flux density
Normal Si-Steel 0.9 to 1.1 T
(0.35 mm thickness, 1.5%—3.5% Si)
HRGO 1.2 to 1.4 T
(Hot Rolled Grain Oriented Si Steel)
CRGO 1.4 to 1.7 T
(Cold Rolled Grain Oriented Si Steel)
(0.14---0.28 mm thickness)

This depends upon cooling method employed
Natural Cooling: 1.5---2.3 A/mm2
AN Air Natural cooling
ON Oil Natural cooling
OFN Oil Forced circulated with Natural air cooling
Forced Cooling : 2.2---4.0 A/mm2
AB Air Blast cooling
OB Oil Blast cooling
OFB Oil Forced circulated with air Blast cooling
Water Cooling:5.0 ---6.0 A/mm2
OW Oil immersed with circulated Water cooling
OFW Oil Forced with circulated Water cooling
34
Usual values of current density

35
Emf per turn equation
To solve the output equation,
kVA = 2.22 or 3.33 or 6.66 f δ AiBm AwKw x 10-3 having two
unknowns Ai and Aw , volt per turn equation is
considered.
Rating of the transformer per phase
Q = VpIp x 10-3 = EpIp x 10-3 kVA (Vp ≈ Ep)
= 4.44 Φm f Tp Ip x 10-3
The term Φm is called the magnetic loading and I1T1 is
called the electric loading. The required kVA can be
obtained by selecting a higher value of Φm and a lesser of
IpTp or vice-versa.

36
As the magnetic loading increases, flux density and hence the
core loss increases and the efficiency of operation decreases.
Similarly as the electric loading increases, number of turns,
resistance and hence the copper loss increases. This leads to
reduced efficiency of operation. It is clear that there is no
advantage by the selection of higher values of IpTp or Φm. For an
economical design they must be selected in certain proportion.
Let, ratio of specific magnetic and electric loading be,
Considering the primary voltage and current per phase
kVA rating of transformer:

Design of Cores
Rectangular core: It is used for core type distribution
transformer and small power transformer for moderate and low
voltages and shell type transformers.
In core type transformer the ratio of depth to width of core varies
between 1.4 to 2.
In shell type transformer width of central limb is 2 to 3 times the
depth of core.
Square and stepped cores: For high voltage transformers, where
circular coils are required, square and stepped cores are used.
40

Two Stepped Core for Cruciform Core
45

Cross-section and dimensions of Stepped cores
49
Area %age of
circumscribing circle
Square Cruciform Three
stepped
Four
Stepped
Gross core area, Agi
Net core area, Ai
64
58
79
71
84
75
87
78
Net core area
Ai=kcd2, kc
0.45 0.56 0.6 0.62

Window Space Factor: It is the ratio of copper area in the
window to the total window area.
Kw = 10/(30+kV) for transformer rating 50 to 200kVA
Kw = 12/(30+kV) for rating about 1000 kVA
Kw = 8/(30+kV) for rating about 20 kVA
50

Window dimensions:
The area of window depend upon total conductor area and
window space factor.
Area of window Aw = total conductor area/ window space factor
= 2.ap Tp/Kw for 1-ph transformer
= 4.ap Tp/Kw for 3-ph transformer
Aw = height of window x width of window = Hw x Ww
The ratio of height to width of window, Hw /Ww is b/w 2 to 4.
51

Design of Yoke: The section of yoke can either be taken as
rectangular or it may be stepped.
In rectangular section yokes,
depth of the yoke = depth of core
area of yoke Ay = Dy x Hy
Dy = depth of yoke= width of largest core stamping
= a
Ay = 1.15 to 1.25 of Agi for hot rolled steel
= Agi for CRGO
52

d= diameter of circumscribing circle
D= distance b/w centers of adjacent
limbs
H= overall height
W= length of yoke
Hw= height of window
Ww= width of window
a = width of largest stamping
Hy = height of yoke
53
Overall Dimensions

1-Φ Core Type Transformer
D = d + Ww
Dy = a
H = Hw + 2Hy
W = D + a
Width over two limbs = D + outer diameter of hv winding
Width over one limb = outer diameter of hv winding
3-Φ Core Type Transformer
D = d + Ww, Dy = a
H = Hw + 2Hy
W = 2D + a
Width over three limbs = 2*D + outer diameter of hv winding
Width over one limb = outer diameter of hv winding
55

56
1-Φ Shell Type Transformer
Dy = b
Hy = a
W = 2Ww + 4a
H = Hw + 2a

Estimation of no of turns :
Primary no of turns Tp = Vp / Et
Secondary no of turns Ts = Vs / Et
Estimation of sectional area of windings
Primary current Ip = Q*10-3 /3Vp
Secondary current Is = Q*10-3 /3Vs
Sectional area of primary winding ap = Ip / δ
Sectional area of primary winding as = Is / δ
57

Resistance of Transformer
Resistant of the primary winding/phase rp = (ρLmt) Tp /ap ohm
Mean length of turn of the primary winding Lmt_p= π x mean
diameter of the primary winding
Resistant of the secondary winding/phase rs = (ρLmt) Ts /as ohm
Mean length of turn of the Secondary winding Lmt_s= π x mean
diameter of the secondary winding
Resistance of the transformer referred to primary / phase
Rp = rp + rs
‘ = rp + rs (Tp/Ts)
Resistance of the transformer referred to primary / phase
Rs = rs + rp
‘ = rs + rp (Ts/Tp)
58

Reactance of Transformer
Useful flux: It is the flux that links with both primary and
secondary windings and is responsible in transferring the energy
Electro-magnetically from primary to secondary side. The path of
the useful flux is in the magnetic core.
Leakage flux: It is the flux that links only with the primary or
secondary winding and is responsible in imparting inductance to
the windings. The path of the leakage flux depends on the
geometrical configuration of the coils and the neighboring iron
masses.
59

If xp and xs are the leakage reactances of the primary and
secondary windings, then the total leakage reactance of the
transformer referred to primary winding
Xp = xp + xs' = xp+ xs (Tp/Ts)2
and total leakage reactance of the transformer referred to primary
winding
Xs = xs + xp' = xs+ xp (Ts/Tp)2
60

Voltage Regulation
V .R. = Is RsCosΦ2 ± Is Xs SinΦ2 *100
Es
= RsCosΦ2 * 100 ± Xs SinΦ2 *100
Es / Is Es / Is
= %RsCosΦ2 ± %Xs SinΦ2
61

No-load current of transformer
The no-load current I0 is the vectorial sum of the magnetizing
current Im and core loss or working component current Ic.
[Function of Im is to produce flux Φm in the magnetic circuit and
the function of Ic is to satisfy the no load losses of the
transformer].
62

No load input to the transformer/ph = V1I0 Cosϕo = V1Ic
No load losses as the output is zero and input = output + losses.
Since the copper loss under no load condition is almost negligible,
the no load losses can entirely be taken as due to core loss only. Thus
the core loss component of the no load current
Ic = core loss/ V1 for single phase transformers
Ic = core loss/ 3V1 for three phase transformers
RMS value of magnetizing current Im =
63

The magnetic circuit of a transformer consists of both iron and air
path. The iron path is due to legs and yokes and air path is due to the
unavoidable joints created by the core composed of different shaped
stampings. If all the joints are assumed to be equivalent to an air gap
of length lg , then the total ampere turns for the transformer magnetic
circuit is equal to ATfor iron + 800,000lgBm.
ATo = ATfor iron + 800,000lgBm
ATfor iron = 2 atc lc + 2aty ly for single phase transformer
ATfor iron = 3 atc lc + 2aty ly for three phase transformer
lc, ly = length of flux path through core and yoke respectively
atc , aty = mmf/m for flux densities in core and yoke respectively
64

1. In case of a transformer of normal design, the no load current will
generally be less than about 2% of the full load current.
2. No load power factor Cosϕo = Ic/Io and will be around 0.2.
3. Transformer copper losses:
a) The primary copper loss at no load is negligible as Io is very less.
b) The secondary copper loss is zero at no load, as no current flows in the
secondary winding at no load.
4. Core or iron loss:
Total core loss = core loss in legs + core loss in yokes.
Core loss in leg = loss/kg in leg * weight of leg in kg
= loss / kg in leg * volume of the leg (Ai*Hw) * density of
steel or iron used
Core loss in yoke = loss/kg in Yoke * volume of yoke (Ay * mean length of
the yoke) * density of iron used
65

Temperature rise of Transformer
•The losses developed in the transformer cores and windings are
converted into thermal energy and cause heating of corresponding
transformer parts.
•The heat dissipation in transformer occurs by Conduction,
Convection and Radiation.
The paths of heat flow in transformer are the following
1. From internal most heated spots of a given part (of core or
winding) to their outer surface in contact with the oil.
2. From the outer surface of a transformer part to the oil that cools
it.
3. From the oil to the walls of a cooler, eg. Wall of tank.
4. From the walls o the cooler to the cooling medium air or water.
66

•In the path 1 mentioned above heat is transferred by conduction.
•In the path 2 and 3 mentioned above heat is transferred by
convection of the oil.
•In path 4 the heat is dissipated by both convection and radiation.
In small capacity transformers the surrounding air will be in a
position to cool the transformer effectively and keeps the temperature
rise well with in the permissible limits.
As the capacity of the transformer increases, the losses and the
temperature rise increases. In order to keep the temperature rise with
in limits, air may have to be blown over the transformer. This is not
advisable as the atmospheric air containing moisture, oil particles
etc., may affect the insulation. To overcome the problem of
atmospheric hazards, the transformer is placed in a steel tank filled
with oil.
67

Further as the capacity of the transformer increases, the increased
losses demands a higher dissipating area of the tank or a bigger
sized tank. This calls for more space, more volume of oil and
increases the cost and transportation problems. To overcome these
difficulties, the dissipating area is to be increased by artificial
means with out increasing the size of the tank. The dissipating
area can be increased by
1. fitting fins to the tank walls 2. fitting tubes to the tank
3. using corrugated tank 4. using auxiliary radiator
tanks
Since the fins are not effective in dissipating heat and corrugated
tank involves constructional difficulties, they are not much used
now a days. The tank with tubes are much used in practice.
68

Heat goes dissipated to the atmosphere from tank by radiation and
convection. It has been found by experiment that a plain tank
surface dissipate 6.0W and 6.5W/m2–oC by radiation and
convection respectively. Thus a total loss dissipation is
12.5W/m2–oC.
Temp rise θ
St = Heat dissipating surface of tank
69
Plain Walled Tanks

Design of Tank with Tubes
If the temperature rise of plain tank exceeds the permissible limit
of about 50 degree centigrade, then cooling tubes are to be added
to reduce the temperature rise. With the tubes connected to the
tank, dissipation due to radiation from a part of the tank surface
screened by the tubes is zero. So there is no change in surface as
far as dissipation of heat due to radiation is concerned. Because
the oil when get heated up moves up and cold oil down,
circulation of oil in the tubes will be more. Obviously, this
circulation of oil increases the heat dissipation by convection
about 35%.
70

The diameter of tubes, normally used, is 50 mm and they are spaced
at 75 mm
72

Cooling of Transformer
The coolants used in transformers are air and oil.
Transformers using air as coolant are called Dry type transformers
while transformers which use oil as coolant are called Oil immersed
transformers.
Methods of Cooling of Transformers: the choice of cooling method
depends upon the size, type of application and the type of conditions
of installation sites.
The symbols designated these methods depend upon medium of
cooling used and type of circulation employed.
Medium:- Air-A, Gas-G, Oil-O, Water-W, Solid insulation-S
Circulation:- Natural-N, Forced-F
73

Cooling of Dry-type transformer
Air Natural (AN), Air Blast (AB)
Cooling of oil immersed transformer
Oil Natural (ON)
Oil Natural Air Forced (ONAF)
Oil Natural Water Forced (ONWF)
Forced Circulation of Oil (OF)
i. Oil Forced Air Natural (OFAN)
ii. Oil Forced Air Forced (OFAF)
iii. Oil Forced Water Forced (OFWF)
74

DESIGN OF TRANSFORMER

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