Design of Transformers
By
Prof. (Dr.) J. G. Jamnani
Associate Professor
Department of Electrical Engineering
School of Technology, PDEU, Gandhinagar
jg.jamnani@sot.pdpu.ac.in
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Types of Transformers
Transformers can be categorized on the following basis:
According to construction
1. Core type
2. Shell type
According to voltage transformation ratio
1. Step-up
2. Step-down
According to type of supply
1. 1-Phase
2. 3-Phase
According to type of service
1. Distribution
2. Power
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Types of Transformers
Core type Transformer
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Types of Transformers
According to construction, there are two main types of
transformers namely:
Core type Transformers
In this type, the windings surround the iron core. Both the windings
are divided and half of each winding is placed on each limb, so that
the two windings can be closely coupled together to keep the
leakage flux and hence leakage reactance low.
The low voltage (LV) winding is wound on the inside nearer to the
core while the HV winding is wound over the LV winding away from
the core in order to reduce the amount of insulating materials
required and also the insulation of LV winding is easy.
The removal or repair of the HV winding, which is more liable to
faults than the LV winding, is easy and convenient.
Small transformers have core of square or rectangular crosssection but for large size transformers stepped or cruciform core is
used.
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Types of Transformers
Shell Type Transformer
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Types of Transformers
Shell type Transformers
In this type, the windings are put around the central limb and the
flux path is completed through two side limbs.
The central limb carries total mutual flux while the side limbs
forming a part of a parallel magnetic circuit carry half the total flux.
Consequently, the cross-sectional area and hence width of the
central limb is twice that of each of the side limbs.
The sandwich type of winding is used in which the sections of the
primary winding are sandwiched in between the sections of the
secondary winding, therefore the leakage flux is reduced and hence
leakage reactance will be low.
To minimize the amount of high voltage insulation, low voltage coils
are placed adjacent to the iron core.
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Comparison between Core and Shell type Transformers
Construction
Core type transformers can be assembled and dismantled more
easily compared to shell type.
Repair
Repair is easy in core type because more portion of the windings is
accessible. Core type transformer can be dismantled easily for
repair.
Cooling
In case of core type transformer, the windings surround the core.
The windings are exposed and therefore the cooling is better in
windings than in core.
In shell type, the core is exposed and therefore cooling is better in
the core than in windings.
The most vulnerable part of a transformer is the insulation of the
windings, therefore core type construction affords better heat
dissipation.
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Comparison between Core and Shell type Transformers
Leakage reactance
Leakage reactance of shell type transformers is smaller compared
to core type, because of better linkage between LV and HV
windings.
Application
Shell type transformer is better for low voltages and large output.
Core type transformer is better for high voltages and comparatively
smaller output.
Core type transformers are commonly used because of
much better heat dissipation facilities. Core type
transformer has more space for insulation so it is
preferred for high voltages.
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Step-up and Step-down Transformers
When the transformer raises the voltage i.e. when the output
voltage of a transformer is higher than its input voltage, it is called
step-up transformer.
When the transformer lowers the voltage i.e. when the output
voltage of a transformer is lower than its input voltage, it is called
step-down transformer.
If N2>N1 then K>1 and the transformer is known as step-up
transformer
If N2<N1 then K<1 and the transformer is known as step-down
transformer
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Distribution and Power Transformers
Distribution Transformers
Transformers which are used to step down the distribution voltages
to a standard service voltage or from transmission voltage to
distribution voltage are called distribution transformers.
They are kept in operation all the 24 hours in a day whether they
are carrying any load or not. So energy is lost in iron losses
throughout the day whereas Cu losses occur only when the
transformer is supplying current to the load. Therefore distribution
transformers should have iron losses small as compared with full
load Cu losses.
Hence the distribution transformers are designed to have maximum
efficiency at load much lower than full –load (About 45-50%)
In order to reduce iron losses and increase all-day efficiency, the
distribution transformers are designed for a lesser value of flux
density( 1.4T to 1.5T)
They have a rating upto about 1000kVA.
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Distribution and Power Transformers
Power Transformers
Transformers which are used in generating stations and substations
for stepping up or down the voltage are called power transformers.
They are put in operation during load periods and are disconnected
during light load periods. Therefore power transformers are
designed to have maximum efficiency at or near full load
In order to have maximum efficiency at or near full-load and to
make iron losses equal to full load copper losses, the power
transformers are designed for comparatively higher value of flux
density( 1.5T to 1.8T)
They have a rating above 1000kVA.
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Aim in Designing Transformer
To obtain the complete dimensions of various parts of the
machine, based on given specifications and using the available
materials economically and to furnish these data to the
manufacturer.
To obtain the following information by using the given specifications:
Main dimensions of the magnetic circuit i.e. core, yoke and
window
Design details of Electrical circuit (Design of LV and HV
windings)
Performance characteristics
Design details of the tank
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To determine above design information, designer needs:
Specifications
Limiting values of performance characteristics
Design equations
Choice of various design parameters
Level of insulation at different places
Materials available for various parts
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Design Equations
EMF equation
EMF per turn equation
Output equation
The ratio of cross-sectional area of the core and the copper area
of the windings is constant for a particular transformer. i.e.
Ai/Ac = Constant.
EMF/turn, Et = k Q
Where
k = 4.44 fr × 103
r=
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IT
= Const.
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Design Equations
Factor k basically depends upon the ratio, Ai/Ac = constant
For the identical transformers, shell type will require more
magnetic material than the core type. Therefore, k will be higher
for shell type.
1-Φ core type transformer will require more magnetic material than
3-Φ core type on per phase basis. Therefore, k will be higher for
1-Φ core type.
k will be lesser for distribution transformer compared to power
transformers.
Values of k for different types of transformers
1-Φ shell type: 1 to 1.2
1-Φ core type: 0.75 to 0.8
3-Φ shell type: 1.3
3-Φ core type (Distribution): 0.45
3-Φ core type (Power): 0.6 to 0.7
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Types of core sections
Rectangular core
Square core
Stepped or cruciform core
In case of small transformers, rectangular or square core is
used. For large transformers stepped core is used.
As the space utilization is better with cruciform cores, the
diameter of circumscribing circle is smaller than with square
core of the same area. Therefore the length of mean turn of
copper is reduced. Therefore reduction in cost of copper.
However, with larger number of steps, a larger number of
sizes of laminations have to be used. That results in higher
labour charges for shearing and assembling different types
of laminations.
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Types of core sections
Rectangular core
Square core
Stepped or cruciform core
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Types of core sections
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Choice of Design Parameters
Flux density Bm
Basically depends upon the steel grades used for the core
and yoke.
Advantages with higher flux density in core
1. Reduction of core section for the same output
2. Reduction in length of mean turn of windings, Therefore,
saving in copper material.
3. Reduction in weight of transformer
4. Reduction in overall cost
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Choice of Flux density Bm
Disadvantages with higher flux density in core
1. Increased magnetizing current (Large AT requirement)
2. Higher No load losses
3. Saturation of magnetic material
4. Lower efficiency
5. Higher temperature rise
Higher Bm should be chosen to achieve an economical
design. But the performance of transformer is affected by the
choice of higher Bm.
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Choice of Flux density Bm
As a guide line, usual values of Bm considering the economics
and performance:
Transformers using hot rolled silicon steel:
Power Transformers: 1.2 to 1.4T
Distribution Transformers: 1.1 to 1.3T
Transformers using cold rolled grain oriented silicon steel:
Power Transformers: 1.5 to 1.7T
Distribution Transformers: 1.4 to 1.5T
Lower values should be used for small rating transformers.
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Choice of Design Parameters
Current density δ
Generally highest temperature rise is observed in the HV
winding. Permissible δ in the windings is limited by local
heating and efficiency.
Advantages with higher current density in windings
1. Reduction of cross-sectional area of the conductor for the
windings
2. Saving in copper material, therefore cheaper design.
Therefore, Economics of the transformer suggests higher δ
for the windings.
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Choice of Current density
Disadvantages with higher current density
1. Higher resistance of the windings
2. increased copper losses
3. Lower efficiency
4. Higher temperature rise, this may cause breakdown of the
insulation
δ for HV winding is taken comparatively higher, compared to
LV winding, because cooling conditions are better in the HV
winding.
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Choice of Current density
As a guide line, usual values of δ :
Distribution Transformers: 2 to 2.5 A/mm2
Power Transformers: 2.5 to 3.5 A/mm2
Large Transformers with forced circulation of oil or with water
cooling coils: 5 to 6 A/mm2
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Choice of Design Parameters
Window Space Factor
It is the ratio of copper area to the total area in the window.
KW = Copper area in window/total window area
The window space factor depends upon the relative amounts
of insulation and copper provided, which in turn depends
upon the voltage rating and output of transformers.
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Window Space Factor
Formula for Estimating KW
1. For Transformers of rating 50kVA,
KW =
8
30+kV
10
30 + kV
12
3. For Transformers of rating 1000kVA, KW =
30 + kV
2. For 50 to 200kVA Transformers,
KW =
Space factor is larger for large outputs and smaller for small
outputs.
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Design of core
Single Phase Core type Transformer
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Design of core
Three Phase Core type Transformer
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Design Problem
Finding Main Dimensions of Core, Yoke and Window
Determine the main dimensions of the core and window for a
250kVA, 50Hz, 1-Phase core type transformer based on the
following information of design parameters:
Maximum flux density in the core Bm= 1.2T
Current density = 2.5 A/mm2
Window space factor = 0.33, Use a 2-stepped core
Emf per turn = 15V, Stacking factor = 0.9
Distance between the centers adjacent limbs = 1.6 times the
width of largest lamination
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Design Problem
Finding Main Dimensions of Core, Yoke and Window
Determine the main dimensions of the core and window for a
315kVA, 11/0.433kV, 50Hz, 3-Phase core type distribution
transformer based on the following information of design
parameters:
Maximum flux density in the core Bm= 1.4T
Current density = 2.5 A/mm2
Window space factor = 0.32, Use a 3-stepped core
Ratio of height to width of window = 2.5
Emf per turn = 15V, Stacking factor = 0.9
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Selection of Winding
Both the windings (LV and HV) must be designed to
achieve:
Better electrical performance characteristics
Adequate mechanical strength to withstand the stress due
to short circuit
Proper ventilation to limit the temperature rise of the
windings within permissible value.
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Types of Windings used for HV and LV
For HV Winding :
1. Cylindrical winding with circular conductors
2. Cross-over winding with either circular or small rectangular
conductors
3. Continuous disc winding with rectangular conductors
Cylindrical and Cross-over windings are used for
transformers of ratings up to 1000kVA and 33kV.
Disc type winding is used for higher ratings transformers
(200kVA to tens of MVA, Voltages above 11kV.
For LV Winding :
1. Cylindrical winding with rectangular conductors (up to
800kVA, 433V)
2. Helical winding with rectangular conductors (up to tens of
MVA, 33kV)
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Types of Transformer Windings
1. Cylindrical winding
These windings are layered type and uses either rectangular
or round conductor
The layered winding may have conductors wound in one,
two or more layers and is therefore accordingly called on,
two or multilayer winding
The two layers are separated by an oil duct
They are wound on a solid paper Bakelite cylinder
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Types of Transformer Windings
2. Helical Windings
A helical winding consists of rectangular strips wound in the
form of a helix.
The strips are wound in parallel radially and each turn
occupies the total radial depth of winding.
Suitable for LV windings of large transformers
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Types of Transformer Windings
3. Crossover Windings
The width of coils is 25 to 50mm. In cross-over windings, the
conductors are paper covered round wires or strips. Each coil
consists of a number of layers with a number of turns per layer.
The winding is divided into several coils and these coils are separated
from each other by insulating materials.
This is done to reduce the insulation requirement between adjacent layers.
Compare to cylindrical windings this winding exhibits more mechanical
strength, however, it has more labour cost. This winding is used in high
voltage winding of low rating transformers
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Types of Transformer Windings
4. Continuous Disc Windings
Disc Windings are used for high capacity transformer. The winding
consists of a number of flat coils or discs in series or parallel. The coils are
formed with rectangular strips wound spirally from the center outwards in
the radial direction
The discs are separated from each other with press-board sectors.
The vertical and horizontal spacers provide radial and axial ducts for the
free circulation of oil which comes in contact with every turn.
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Design of Windings
Design of LV Winding
No. of turns per phase
T2 = V2/Et
V2 = Voltage rating of LV winding per phase
Current rating of LV winding
I2 = kVA per Phasex103/ V2
Cross-sectional area of conductor
a2 = I2 /δ2
Choice and dimensions of conductor
Rectangular conductor is chosen for LV winding because of
higher current density.
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Design of Windings
Design of LV Winding
Length of mean turn lmt2= π Dm2
Where, Mean diameter of LV Winding Dm2 = (Di2+ Do2)/2
Di2= Inner diameter of LV winding
Do2= Outer diameter of LV winding
Hot resistance per phase of LV winding
r2 = (ρ lmt2/a2).T2
Where, ρ =Specific resistance value at 750C=0.02 Ω/m/mm2
I2R loss in LV winding = I22r2
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Design of Windings
Design of HV Winding
No. of turns per phase
T1 = T2. V1/V2
V1 = Voltage rating per phase of HV winding
No. of turns for +5% tapping = T2. V1/1.05V2
No. of turns for -2.5% tapping = T2. V1/0.975V2
Current rating of LV winding
I1 = I2. V2/ V1
Cross-sectional area of HV conductor
a1 = I1 /δ1
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Design of Windings
Design of HV Winding
Choice and dimensions of conductor
For small and medium transformers with lesser conductor
section, circular conductors are used.
For large transformers, Rectangular conductors are preferred
because of higher current rating.
Length of mean turn lmt1= π Dm1
Where, Mean diameter of HV Winding Dm1 = (Di1+ Do1)/2
Di1= Inner diameter of HV winding
Do1= Outer diameter of HV winding
Hot resistance per phase of HV winding
r1 = (ρ lmt1/a1).T1
I2R loss in HV winding = I12r1
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Design Problem
Determine the (i) Cross-sectional areas of LV and HV
windings (ii) Number of LV and HV turns per phase (iii)
Number of HV turns for ±5% tappings for 1250kVA,
33/6.6kV, 50Hz, 3-phase delta/star core type power
transformer. Assume suitable values for various design
parameters.
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Voltage Regulation
When a transformer is loaded with a constant primary voltage, its
secondary terminal voltage changes because of its internal
resistance and leakage reactance of the windings.
Regulation is defined as “change in secondary terminal voltage
from no-load to full-load, expressed as % of secondary no-load
voltage” the primary applied voltage is assumed constant.
% Voltage regulation = (V2nl –V2fl) / V2nl
V2nl = No-load secondary voltage
V2fl = Secondary voltage at load
The secondary terminal voltage on load decreases for lagging
power factor load. Therefore, the regulation of the transformer will
be positive for lagging p.f. load.
For leading power factor load, the secondary terminal voltage on
load is higher than at no-load. Therefore the regulation of the
transformer will be negative for leading p.f. load.
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Voltage Regulation
Voltage regulation of transformer can also be expressed in
terms of primary values
% VR = (IpRO1cosΦ± IpXO1sinΦ)/Vp x 100
Where RO1 = equivalent resistance referred to primary
XO1=equivalent leakage reactance referred to primary
Vp = Primary side voltage
Ip = current on primary side
+ sign for lagging p.f.
- sign for leading p.f.
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Voltage Regulation
Leakage reactance of Winding
Total leakage reactance of the transformer per phase referred
to primary side
Xp = 2πfµ0TP 2 Lmt / Lc (a + (bp+bs)/3)
Lc= axial height of windings
a = width of radial duct
bp and bs = radial width of primary and secondary
windings respectively
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Design Problem
Estimate per unit regulation at full load and 0.8 power factor
lagging for a 500kVA, 50Hz, 11/0.433kV, 3-phase, delta/star, core
type transformer. The data given is
HV Winding: Outside diameter = 0.5m, Inside diameter = 0.4m,
Area of conductor = 6 mm2
LV Winding: Outside diameter = 0.35m, Inside diameter = 0.25m,
Area of conductor = 180 mm2
Length of coils = 0.6m, Voltage/turn = 10V, Resistivity = 0.021
Ω/m/mm2
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Estimation of No-load current
Estimation of No-load current
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Estimation of No-load current
Single phase, 230V, 50Hz, transformer is built from stampings
having relative permeability of 1000. The length of the flux path is
2m, the area of cross-section of the core is 2x10-3 m2 and the
primary winding has 450 turns. Estimate the maximum flux and
no-load current of the transformer. The iron loss at the working
flux density is 2 W/kg. Density of the iron 7.8x103 kg/m3. stacking
factor =0.9.
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Temperature Rise in Plain walled Tanks
Temperature rise Equation
Modes of Heat Dissipation
Design of Tank with Tubes
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Design of Tank with Tubes
A 250kVA, 6600/433V, 3-phase Core type transformer has a
total loss of 4800W at full load. The transformer tank is
1.25m in height and 1m x 0.5m in plan. Design a suitable
scheme for tubes if the average temperature rise is to be
limited to 350C. The diameter of tubes is 50mm and are
spaced 75mm from each other. The average height of tubes
is 1.05m.
Specific heat dissipation due to radiation and convection is
respectively 6 and 6.5 W/m2.0C. Assume that convection is
improved by 35% due to provision of tubes. Also show the
arrangement of the cooling tubes.
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Performance Characteristics of the Designed
Transformer
Performance regarding magnetic frame
1. No load current
2. No load losses (Iron losses)
Performance regarding windings
1. Cu losses
2. Regulation under loaded conditions
Performance regarding magnetic frame and windings
Efficiency, All day efficiency, Maximum efficiency
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∆
1. No load current
Performance limitation:
In small transformers 3 to 5% of rated current
medium transformers 1 to 3% of rated current
large transformers
0.5 to 2% of rated current
In case, no-load current I0 of the designed
transformer is more than the limiting value, the
design of the magnetic frame may be changed in
order to have no load current within the limit.
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∆
2. No load losses
No load losses = Hysteresis losses + Eddy current losses
= ηVfBm1.6 + kBm2 f 2t 2V
Performance limitation:
To have a better efficiency and to maintain the
temperature within specified limit of the designed transformer
Iron losses in small transformers 0.5 to 1 % of rated output
medium and large transformers 0.2 to 0.5% of rated output
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∆
3. Copper losses
Cu losses occur in LV and HV windings
Performance limitation:
To have a better efficiency and to maintain the
temperature within specified limit of the designed transformer
Cu losses in small transformers 1 to 1.5 % of rated output
For medium and large transformers 0.3 to 1% of rated output
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∆
4. Efficiency
η = Output power / output power + losses
Performance limitation:
For small transformers 98%
For medium and large transformers 98 to 99.2%
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∆
5. Regulation
Regulation in terms of equivalent resistance and
reactance referred to HV, load current and power
factor,
I1(R1 cosϕ± X1 sinϕ)
Regulation =
×100
ES
+ sign for lagging p.f.
- sign for leading p.f.
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THANK YOU
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