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School of Electrical, Electronic and Computer
Engineering
Electrical Design 3 (ENEL3EA)
Transformer Design
Group 12
Due date: 20 July 2020
NAME STUDENT NUMBER
LINDOKUHLE NSELE 218023059
LINDOKUHLE YAKA 218016772
NKOSIYENZILE PHUNGULA 218017570
FANELESIBONGE MSWELI 218012788
i | P a g e
DECLARATION
Group 12 of Electrical design 3
Hereby declare that the project entitled Transformer design has been written and compiled
by our combined effort and has in no parts been plagiarized without citation or reference.
iii | P a g e
NOMENCLATURE
Et voltage per turn
Ф m
maximum flux in core
B m
maximum flux density in core
A i
net core area
K i
stacking factor
A gi
gross core area
K w
Window space factor
A w
Area of window
H w
height of window
W w
width of window
V p
voltage at primary winding
V s
voltage at secondary winding
I p
current at primary winding
I s
current at secondary winding
σ s
current density of secondary windings
σ p
current density of primary windings
A s
Area of secondary windings
A p
Area of primary windings
N s
Number of turns in primary
N p
Number of turns in secondary
iv | P a g e
Table of Contents
DECLARATION .......................................................................................................................................... i
Abstract ................................................................................................................................................... ii
NOMENCLATURE.................................................................................................................................... iii
Introduction
The transformer works on the principle of electromagnetic induction. A transformer is an
electrical device, having no moving parts, which by mutual induction transfers electric energy
from one circuit to another at the same frequency, usually with changed values of voltage and
current [1].
Transformer losses:
(a) Hysteresis loss (b) Eddy current loss
Uses of Transformers:
- Used in power distribution for residential and commercial use.
- Used to step-up or step-down voltage from transmission grids to distribution grids.
- Used in several types of electrical equipment’s.
Working Principle of a Transformer
The transformer link together two or more electrical circuits using a common oscillating
magnetic circuit which is produced by the transformer itself. A transformer operates on the
principles of ‘’electromagnetic induction’’, in the form of Mutual Induction. Mutual
induction is the process by which a coil of wire magnetically induces a voltage into another
coil located near it. Then we can say that transformers work in the ‘’transform’’ one voltage
or current level into another [2].
Transformer Theory
Figure 1 represents the essential elements for a transformer- a magnetic core, with a
primary and secondary coil wound on the limbs of the magnetic core.
Figure 1 A Basic Transformer
An alternating voltage applied to the PRIMARY creates an alternating current through the
primary. This current produces an alternating magnetic flux in the magnetic core. This
alternating magnetic flux induces a voltage in each turn of the primary and in each turn of
the SECONDARY [3].
The alternating current through the winding produces a continually changing and
alternating flux that surrounds the winding. If another winding is brought close to this
winding, some portion of this alternating flux will link with the second winding. As this flux is
continually changing in its amplitude and direction, there must be a changing flux linkage in
the second winding or coil. According to Faraday’s law of electromagnetic induction, there
will be an EMF induced in the second winding. If the circuit of this secondary winding is
closed, then a current will flow through it. This is the basic working principle of a
transformer.
The winding which receives electrical power from the source is known as the ‘primary
winding’. The winding which gives the desired output voltage due to mutual induction is
commonly known as the ‘secondary winding’.
A transformer that increases voltage between the primary to secondary windings is defined
as a step-up transformer. Conversely, a transformer that decreases voltage between the
primary to secondary windings is defined as a step-down transformer.
Whether the transformer increases or decreases the voltage level depends on the relative
number of turns between the primary and secondary side of the transformer. If there are
more turns on the primary coil than the secondary coil than the voltage will decrease (step
down). If there are less turns on the primary coil than the secondary coil than the voltage
will increase (step up) [3].
Figure 3 Three Phase Transformer
Advantages of Three Phase Transformer
- The cost of three phase transformer is around 15% less than single phase
transformer bank
- It is weightless and occupies less space
- The bus bar structure, switch gear and other wiring for a three-phase installation are
simple
- It can be more easily transported
- The amount core material required is less.
Transformer Construction Types
Core Type Transformer
Here the windings surround a considerable part of core as shown in the below figure and
has only one magnetic path [6]. It has two limbs for the two windings and is made up of two
L-type stampings as shown in figure 4 below.
Figure 4 Core Type Transformer
Shell Type Transformer
Here the core surrounds the considerable part of windings as shown in figure 5 below. The
two windings are carried by central limb. The core is made up of E and I stamping (figure 5 )
and has three limbs. It has two parallel paths for magnetic flux.
The coils used are of multilayer disc type and are former wound in the form of pancakes.
Each layer is insulated from each other by paper [6].
Figure 5 Shell Type Transformer
Transformer Efficiency
Under ideal conditions the voltage and current change by the same factor for any
transformer, which explains why the primary power value is equal to the secondary power
value for each case in the above table. As one value decreases the other increases to keep
at a constant equilibrium power level. Transformers can be extremely efficient. High-power
transformers can reach the 99% mark of efficiency, as a result of successes in
minimizing transformer losses. However, a transformer will always output a slightly lower
power than its input, as losses cannot be eliminated completely. There is some transformer
impedance [7].
Air Cooled and Dry Type Transformer
This classification pertains to the transformer cooling system used within the transformer. In
oil cooled transformers, the cooling medium is transformer oil. Whereas in the dry type
transformer, air cooling is used instead [2].
Core area
Magnetic flux density is directly proportional to the core area. Increasing the magnetic flux density
decreases the core area resulting in saving conductor cost.
Ø𝑚
Values of the magnetic flux density may differ depending on the material, value of the voltage and
the type of transformer.
Magnetic flux density (Bm) for hot rolled silicon steel:
- Distribution transformer: 1.1 – 1.35 Wb/𝑚
2
- Power transformer: 1.25 – 1.45Wb/𝑚
2
Magnetic flux density (Bm) for cold rolled silicon steel:
- Voltage(<132kV): 1.55Wb/𝑚
2
2
2
Gross area of the core
Core cross-section
Core type
For core type transformer the cross-section may be rectangular, square, or steeped. Rectangular are
used for small power transformer and the ratio of depth to width varies between 1.4 to 2.
Square Core-Section
Used for small sized core type transformer, notice on figure 6 for square core section lots of space is
wasted and the mean length of the winding is increased as a result the are more copper losses.
Gross area is given by the formula below:
2
2
Stepped Core-Section
Used for large core type transformers, notice on figure 6 for the Stepped core section less space is
being wasted and the length of the winding is smaller as a result fewer copper loss. Gross are is
given by the following formula:
2
2
Window dimension design
Figure 6 Transformer Window Dimensions
Window space factor
Window space factor is the ratio of copper in the window area. The window space factor depends on
the KVA rating, insulation and copper provided.
- For rating between 50 to 200KVA: 𝐾𝑤 =
10
30 +𝐾𝑉
- For rating of 1000KVA: 𝐾𝑤 =
10
30 +𝐾𝑉
- For rating of 20KVA: 𝐾𝑤 =
8
30 +𝐾𝑉
Area of the window
OR
𝐴𝑤 = 𝐻𝑤 × 𝑊𝑤 ( 7 )
Rating of 3-phase transformer
𝑄 = 3. 33 𝑓𝛽𝑚𝛿𝐾𝑤𝐴𝑖 × 10
− 3
Distance between adjacent limb
Design of insulation
5 + 0. 9 × 𝐾𝑉
- KV - Is the kilovolt voltage between windings and the core and between LV and HV windings.
Resistance of winding per phase
𝑅 = 𝑅𝑜[ 1 + 𝛼(𝑇 − 𝑇𝑜)] ( 19 )
DESIGN SPECIFICATIONS
Given a 3-phase core-type distribution transformer rated 11kV/400V, 45 KVA, plane tank, 50
Hz, star-star. Design its core dimensions and its primary and secondary windings. Ensure that
the necessary clearance between adjacent HV windings and between HV windings and core
are met for the transformer. Given that the resistivity of copper at 20°C is 0.17241x10-7 Ωm
and the temperature coefficient α is 0.0039 1/°C, determine the resistance of the both the
HV and LV windings per phase given that the operating temperature of the transformer is
40°C. Finally draw the approximate equivalent circuit of the transformer referred to primary
and determine the efficiency and voltage regulation of the transformer when it is operating
at full load, at an operating temperature of 40°C with a power factor of 0.8 lagging.
CORE DESIGN
Calculating voltage per Turn 𝐸
𝑡
Where K is a constant and Q is the 𝟑∅ kVA rating.
𝑡
= 0.45x
𝑏
Calculating the core area:
∅
𝑡
02
44 𝑥 50
= 13.60 x 10
− 3
Operating at a frequency of 50 Hz.
𝑖
∅ 𝑚
𝐵
𝑚
- 60 x 10
− 3
- 2
=11.33 x 10
− 3
2
Where 𝑩
𝒎
Chosen to be 𝟏. 𝟐
𝑾 𝒃
𝒎
𝟐
𝑔𝑖
𝐴
𝑖
𝑘
- 33 x 10
− 3
- 9
= 12.60 x 10
− 3
2
DIMENSIONS OF THE CORE
Ratio of gross core area to area of circumscribing circle:
2
𝜋 𝑥 𝑑
2
4
Now Calculating the diameter of the cruciform winding:
𝑔𝑖
𝜋 𝑥 𝑑
2
4
= 0.
2
=
- 60 x 10
− 3
d = 0.143m
Calculating the dimensions of the cruciform core:
a = 0.85d
b = 0.53d
∴ Substituting the known value of (d = 0.143)
a = 0.85(0.143) =0.1216m
b = 0.53(0.143) =0.0758m
Approximate the values of a and b to ±𝟓𝒎𝒎
𝑤
𝐴
𝑤
3
- 19 𝑚𝑚
2
3
𝑤
DESIGN OF YOKE
𝑦
𝑔𝑖
2
𝑦
= 1.20 x (12.60 x 10
− 3
2
2
𝑦
𝐴
𝑦
𝐷
𝑦
- 12 𝑚𝑚
2
120mm
𝑦
OVERAL DIMENSIONS
𝑤
3
𝑤
𝑦
DESIGN OF WINDINGS
𝑝(𝑙𝑖𝑛𝑒)
𝑠(𝑙𝑖𝑛𝑒)
𝑝(𝑝ℎ𝑎𝑠𝑒)
𝑠(𝑝ℎ𝑎𝑠𝑒)
𝑝ℎ𝑎𝑠𝑒
Current Calculations:
𝑝ℎ𝑎𝑠𝑒
𝑝
𝑝
15000
- 85
𝑠
15000
- 94
Number of turns calculations:
𝑠
𝑠(𝑝ℎ𝑎𝑠𝑒)
𝑚
𝑖
- 94
( 4. 44 )( 50 )( 1. 2 )( 11. 33 x 10
− 3
)
𝑝
𝑝(𝑝ℎ𝑎𝑠𝑒)
𝑠(𝑝ℎ𝑎𝑠𝑒)
× 𝑁
𝑠
85
94
× 77 = 2118 𝑡𝑢𝑟𝑛𝑠
𝑝
𝑝(𝑝ℎ𝑎𝑠𝑒)
2
𝑠
𝑠(𝑝ℎ𝑎𝑠𝑒)
2
Low voltage winding calculations
Since 𝒂 𝒔
= 𝟑𝟔. 𝟎𝟖𝟒 we use Table 17.1 to extrapolate and thus find values for the thickness and
width of the coil.
- Thickness = 2.8mm
- Width = 13mm
= 5 + 0. 9 ×
𝑤
1
08
5
𝑠
1
𝑅𝑎𝑑𝑖𝑎𝑙 𝑑𝑒𝑝𝑡ℎ 𝑜𝑓 𝐿𝑉 𝑤𝑖𝑛𝑑𝑖𝑛𝑔 = 𝑛𝑜. 𝑜𝑓 𝑙𝑎𝑦𝑒𝑟𝑠 × 𝑟𝑎𝑑𝑖𝑎𝑙 𝑡ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 + 0. 5 × 𝑛𝑜. 𝑜𝑓 𝑙𝑎𝑦𝑒𝑟𝑠 − 1
= 3 ×
+ 0. 5 × 2
