ISSN (Online) 2581-9429

IJARSCT
International Journal of Advanced Research in Science,, Communication and Technology (IJARSCT)
International Open-Access,
Access, Double-Blind,
Double Peer-Reviewed,
Reviewed, Refereed, Multidisciplinary Online Journal
Impact Factor: 7.301 Volume 3, Issue 1, October 2023

Design Parameters of Transformer

Chinmayi Satish Thakare
Final Year B.E. Electrical Engineering
Jawaharlal Darda of Engineering and Technology,
Technology Yavatmal, Maharashtra, India
cthakare002019@gmail.com

Abstract: Transformers are used to change ac voltage levels, as well as to provide galvanic isolation
between circuits. Single and three phase transformers are extensively employed in the world's power
distribution system. This chapter considers the design of single phase power transformers. It reviews the
classic transformer equivalent circuit and also considers its use in steady state phas
phase or analysis. The
chapter focuses on single phase transformers. Single phase transformers are often classified as being either
core type or shell type. The chapter discusses
discusses transformer performance considerations such as the
calculation of transformer parameters, regulation, magnetizing current, operating point analysis, and
inrush current, all in general terms. It also focuses on one specific class of transformer, develo
develop an
Magnetic Equivalent Circuit, and ultimately a design approach. Core loss is a significant contributor to
overall transformer loss and dominates no load losses.

Keywords: Road hypnosis, Driver behavior, Safety warning, Monotonous

Mon city effect.

I. INTRODUCTION
A transformer transfers electric power from one circuit to another circuit without a change in frequency. It contains
primary and secondary winding. The primary winding is connected to the main supply and secondary to the required
circuit. In our project circuit,, we have taken the design of low power (10 KVA) single phase 50 hertz power transformer
as per our requirement in the project.
The transformer is basically of three types:
 Core Type
 Shell Type
 Toroidal
In core, type windings surround a part of the core whereas in shell type core surrounds windings. In the Core type, there
are two main types namely E-II type and U-T U type. In this transformer design, we used E-II core type. We chose E
E-I core
as the winding is much easier when compared to toroidal, but efficiency is very high (95%-96%).
(95% 96%). It is so because flux
loss is very less in toroidal cores comparatively.
Example of coree type transformer looks like :- :

Fig.1: Three phase transformer(6 type core winding)

Copyright to IJARSCT DOI: 10.48175/568 227
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 ISSN (Online) 2581-9429
IJARSCT
International Journal of Advanced Research in Science, Communication and Technology (IJARSCT)
International Open-Access, Double-Blind, Peer-Reviewed, Refereed, Multidisciplinary Online Journal
Impact Factor: 7.301 Volume 3, Issue 1, October 2023

The transformers employed in the project are

 Series transformer: To provide the required boost or buck voltage and
 Control transformer: For sensing the output voltage and for power supply.

Design Formulas:
Here we take the reference of winding data on enameled copper wire table and dimensions of transformer stampings
table to select input and output windings SWG and core of the transformer for given specifications.
The design procedure is followed assuming that the following specification of a transformer are given:-
 Secondary voltage (Vs)
 Secondary current (Is)
 Turns ratio (n2/n1)
From these given details we calculate Tongue width, stack height, core type, window area as follows:-
 Secondary Volt-Amps (SVA) = secondary voltage (Vs) * secondary current(Is)
 Primary Volt-Amps (PVA) = Secondary Volt-Amps (SVA) / 0.9 (assuming efficiency of the transformer as
90%)
 Primary voltage (Vp)= Secondary voltage(Vs)/ turns ratio(n2/n1)
 Primary current (Ip) = Primary Volt-Amps(PVA)/ Primary voltage(Vp)
The require cross-sectional area of the core is given by:-
 Core area (CA) = 1.15 * sqrt (Primary Volt-amps(PVA))
 Gross core area (GCA) = Core area(CA) * 1.1
The number of turns on the winding is decided by the ratio given as:- Turns per volt (Tpv) = 1/(4.44 * 10-4 * core area*
frequency * flux density)bh

Winding data on Enameled copper wire

Max. Current Max. Current

Capacity (Amp.) Turns/Sq. cm SWG Capacity (Amp.) Turns/Sq. cm SWG
0.001 81248 50 0.1874 711 29
0.0015 62134 49 0.2219 609 28
0.0026 39706 48 0.2726 504 27
0.0041 27546 47 0.3284 415 26
0.0059 20223 46 0.4054 341 25
0.0079 14392 45 0.4906 286 24
0.0104 11457 44 0.5838 242 23
0.0131 9337 43 0.7945 176 22
0.0162 7755 42 1.0377 137 21
0.0197 6543 41 1.313 106 20
0.0233 5595 40 1.622 87.4 19
0.0274 4838 39 2.335 60.8 18
0.0365 3507 38 3.178 45.4 17
0.0469 2800 37 4.151 35.2 16
0.0586 2286 36 5.254 26.8 15
0.0715 1902 35 6.487 21.5 14
0.0858 1608 34 8.579 16.1 13
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 ISSN (Online) 2581-9429
IJARSCT
International Journal of Advanced Research in Science, Communication and Technology (IJARSCT)
International Open-Access, Double-Blind, Peer-Reviewed, Refereed, Multidisciplinary Online Journal
Impact Factor: 7.301 Volume 3, Issue 1, October 2023

0.1013 1308 33 10.961 12.8 12

0.1182 1137 32 13.638 10.4 11
0.1364 997 31 16.6 8.7 10
0.1588 881 30

Dimension of Transformer stampings (Core table):

Type Tongue Window Area Type Tongue Window Area

Number Width (cm) (Sq. cm) Number Width (cm) (Sq. cm)
17 1.27 1.213 9 2.223 7.865
12A 1.588 1.897 9A 2.223 7.865
74 1.748 2.284 11A 1.905 9.072
23 1.905 2.723 4A 3.335 10.284
30 2 3 2 1.905 10.891
1.588 3.329 16 3.81 10.891
31 2.223 3.703 3 3.81 12.704
10 1.588 4.439 4AX 2.383 13.039
15 2.54 4.839 13 3.175 14.117
33 2.8 5.88 75 2.54 15.324
1 1.667 6.555 4 2.54 15.865
14 2.54 6.555 7 5.08 18.969
11 1.905 7.259 6 3.81 19.356
34 1.588 7.529 35A 3.81 39.316
3 3.175 7.562 8 5.08 49.803
For operation on mains supply, the frequency is 50HZ, while the flux density can be taken as 1Wb/sq cm. for ordinary
Steel stampings and 1.3Wb/sq cm for CRGO stampings, depending on the type to be used.
Hence
Primary turns (n1) = Turns per volt(Tpv) * Primary voltage(V1)
Secondary turns (n2) = Turns per volt(Tpv) * secondary voltage(V2) * 1.03 (Assume that there is 3% drop in
transformer windings)
The width of the tongue of laminations is approximately given by:-
Tongue width (Tw) = Sqrt * (GCA)
Current density
It is the current carrying capacity of a wire per unit cross sectional area. It is expressed in units of Amp/ cm². The above
mentioned wire table is for a continuous rating at current density of 200A/cm². For non-continuous or intermittent mode
of operation of transformer one can choose a higher density up to 400A/cm² i.e., twice the normal density to economize
the unit cost. It is opted as, the temperature rise for the intermittent operational cases are less for the continuous
operational cases.
So depending on the current densities choosen we now calculate the values of primary and secondary currents that are
to searched in wire table for selecting SWG:-
n1a = Primary current (Ip) calculated / (current density/200)
n2a = Secondary current (Is) calculated / (current density/200)
For these values of primary and secondary currents we choose the corresponding SWG and Turns per sqcm from the
wire table. Then we proceed to calculate as follows:-
Copyright to IJARSCT DOI: 10.48175/568 229
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 ISSN (Online) 2581-9429
IJARSCT
International Journal of Advanced Research in Science, Communication and Technology (IJARSCT)
International Open-Access, Double-Blind, Peer-Reviewed, Refereed, Multidisciplinary Online Journal
Impact Factor: 7.301 Volume 3, Issue 1, October 2023

Primary area(pa)= Primary turns(n1) / (Primary turns per sqcm)

Secondary area(sa)= Secondary turns(n2) / (Secondary turns per sqcm)
The total window area required for the core is given by:-
Total area (TA) = Primary area (pa) + Secondary area (sa)
Extra space required for the former and insulation may be taken as 30% extra space of what is required by the actual
winding area. This value is approximate and may have to be modified, depending on the actual winding method.
Window area (Wacal) = Total area (TA) * 1.3
For the above calculated value of tongue width, we choose core number and window area from the core table ensuring
that the window area chosen is greater than or equal to the Gross core area. If this condition is not satisfied we go for a
higher tongue width ensuring the same condition with a corresponding decrease in the stack height so as to maintain
approximately constant gross core area.
Thus we get available tongue width (Twavail) and window area ((avail)(aWa)) from the core table
Stack Height = Gross core area / Tongue width ((available) (atw)).
For commercially available former size purposes, we approximate stack height to tongue width ratio to the nearest
following figures of 1.25, 1.5, 1.75. At the worst case we take the ratio equal to 2. However any ratio till 2 can be taken
which would call for making ones own former.
If the ratio is greater than 2 we select a higher tongue width (aTw) ensuring all the conditions as above.
Stack height(ht) / tongue width(aTw) = (some ratio)
Modified stack height = Tongue width(aTw) * Nearest value of standard ratio
Modified Gross core area = Tongue width (aTw) * Modified stack height.
Same design procedure applies for control transformer, where in we need to ensure that stack height equals Tongue
width.
Thus we find core number and stack height for the given specifications.
Designing a transformer using an example:
The given details are as follows:-
Sec. voltage(Vs) = 60V
Sec current(Is) = 4.44A
Turns per ratio (n2/n1) = 0.5
Now we have to calculations as follows:-
Sec.Volt-Amps(SVA) = Vs * Is
= 60 * 4.44
=266.4VA

Prim.Volt-Amps(PVA) = SVA / 0.9

= 296.00VA

Prim.Voltage (Vp) = V2 / (n2/n1)

= 60/0.5
= 120V

Prim.current (Ip) = PVA/Vp

= 296.0/ 120
= 2.467A

Core Area(CA) = 1.15 * sqrt(PVA)

= 1.15 * sqrt(296)
= 19.785 cm²

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 ISSN (Online) 2581-9429
IJARSCT
International Journal of Advanced Research in Science, Communication and Technology (IJARSCT)
International Open-Access, Double-Blind, Peer-Reviewed, Refereed, Multidisciplinary Online Journal
Impact Factor: 7.301 Volume 3, Issue 1, October 2023

Gross core area(GCA) = CA * 1.1

= 19.785 * 1.1
= 21.76 cm²
Turns per volt(Tpv) = 1 / (4.44 * 10-4 * CA *frequency * Flux density)
= 1 / (4.44 * 10-4 * 19.785 * 50 *1)
= 2.272 turns per volt
Prim.Turns(N1) = Tpv * Vp
= 2.276 * 120
= 272.73 turns
Sec.Turns(N2) = Tpv * Vs * 1.03
= 2.276 * 60 * 1.03
= 140.46 turns
Tongue width(TW) = Sqrt*(GCA)
= 4.690 cm
We are choosing the current density as 300A/cm², but the current density in the wire table is given for 200A/cm², then
Primary current search value = Ip / (current density/200)
= 2.467 / (300/200)
= 1.644A
Secondary current search value = Is / (current density/200)
= 4.44 / (300/200)
= 2.96A
For these values of primary and secondary currents we choose the corresponding SWG and Turns per sqcm from the
wire table.
SWG1=19
SWG2=18
Turn per sqcm of primary = 87.4 cm² turns per sqcm of secondary =60.8 cm²
Primary area(pa) = n1 / turns per sqcm(primary)
= 272.73 / 87.4
= 3.120 cm²
Secondary area(sa) = n2 / turns per sqcm(secondary)
= 140.46 / 60.8
= 2.310 cm²
Total area(at) = pa + sa
= 3.120 + 2.310
= 5.430 cm²
Window area (Wa) = total area * 1.3
= 5.430 * 1.3
= 7.059 cm²
For the above calculated value of tongue width, we choose core number and window area from the core table ensuring
that the window area chosen is greater than or equal to the Gross core area. If this condition is not satisfied we go for a
higher tongue width ensuring the same condition with a corresponding decrease in the stack height so as to maintain
approximately constant gross core area.
Thus we get available tongue width (Twavail) and window area ((avail)(aWa)) from the core table:
So tongue width available (atw) = 3.81cm
Window area available (awa) = 10.891 cm²
Core number = 16
Stack Height = gca / atw
= 21.99 / 3.810
= 5.774cm
Copyright to IJARSCT DOI: 10.48175/568 231
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 ISSN (Online) 2581-9429
IJARSCT
International Journal of Advanced Research in Science, Communication and Technology (IJARSCT)
International Open-Access, Double-Blind, Peer-Reviewed, Refereed, Multidisciplinary Online Journal
Impact Factor: 7.301 Volume 3, Issue 1, October 2023

For performance reasons, we approximate stack height to tongue width (aTw) ratio to the nearest following figures of
1.25, 1.5, and 1.75. At the worst case we take the ratio equal to 2.
If the ratio is greater than 2 we select a higher tongue width ensuring all the conditions as above.
Stack height(ht) / tongue width(aTw) = 5.774 / 3.81 = 1.516
Modified stack height = Tongue width(aTw) * Nearest value of standard ratio
= 3.810 * 1.516 = 5.715cm
Modified Gross core area = Tongue width (aTw) * Modified stack height
= 3.810 * 5.715
= 21.774 cm²
Thus we find core number and stack height for the given specifications.
Design of a small control transformer with example:
The given details are as follows:-
Sec. voltage(Vs) = 18V
Sec current(Is) = 0.3A
Turns per ratio (n2/n1) = 1
Now we have to calculations as follows:-
Sec.Volt-Amps(SVA) = Vs * Is
= 18 * 0.3
= 5.4VA
Prim.Volt-Amps(PVA) = SVA / 0.9
= 5.4 / 0.9
= 6VA
Prim. Voltage (Vp) = V2 / (n2/n1)
= 18/1
= 18V
Prim. current (Ip) = PVA/Vp
= 6 / 18
= 0.333A
Core Area(CA) = 1.15 * sqrt(PVA)
= 1.15 * sqrt(6)
= 2.822 cm²
Cross core area(GCA) = CA * 1.1
= 2.822 * 1.1
= 3.132 cm²
Turns per volt(Tpv) = 1 / (4.44 * 10-4 * CA *frequency * Flux density)
= 1 / (4.44 * 10-4 * 2.822 * 50 *1)
= 15.963 turns per volt
Prim. Turns(N1) = Tpv * Vp
= 15.963 * 18
= 287.337 turns
Sec.Turns(N2) = Tpv * Vs * 1.03
= 15.963 * 60 * 1.03
= 295.957 turns
Tongue width(TW) = Sqrt*(GCA)
= sqrt * (3.132)
= 1.770 cm
We are choosing the current density as 200A/cm², but the current density in the wire table is given for 200A/cm², then
Primary current search value = Ip / (current density/200)
= 0.333 / (200/200) = 0.333A
Copyright to IJARSCT DOI: 10.48175/568 232
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 ISSN (Online) 2581-9429
IJARSCT
International Journal of Advanced Research in Science, Communication and Technology (IJARSCT)
International Open-Access, Double-Blind, Peer-Reviewed, Refereed, Multidisciplinary Online Journal
Impact Factor: 7.301 Volume 3, Issue 1, October 2023

Secondary current search value = Is / (current density/200)

= 0.3 / (200/200)
= 0.3A
For these values of primary and secondary currents we choose the corresponding SWG and Turns per Sq. cm from the
wire table.
SWG1=26
SWG2=27
Turn per Sq. cm of primary = 415 turns
Turns per Sq. cm of secondary = 504 turns
Primary area(pa) = n1 / turns per sqcm(primary)
= 287.337 / 415
= 0.692 cm²
Secondary area(sa) = n2 / turns per sqcm(secondary)
= 295.957 / 504
= 0.587 cm²
Total area(at) = pa + sa
= 0.692 + 0.587
= 1.280 cm²
Window area (Wa) = total area * 1.3
= 1.280 * 1.3
= 1.663 cm²
For the above calculated value of tongue width, we choose core number and window area from the core table ensuring
that the window area chosen is greater than or equal to the Gross core area. If this condition is not satisfied we go for a
higher tongue width ensuring the same condition with a corresponding decrease in the stack height so as to maintain
approximately constant gross core area.
Thus we get available tongue width (Twavail) and window area ((avail)(aWa)) from the core table
So tongue width available (atw) = 1.905cm
Window area available (awa) = 18.969 cm²
Core number = 23
Stack Height = gca / atw
= 3.132 / 1.905
= 1.905cm
Hence the control transformer is designed.

II. CONCLUSION
A procedure for the optimal transformer. A transformer is a passive electrical device that can change the voltage in an
alternating current (AC) electric circuit. Transformers are used to increase or decrease the operating voltage levels
between circuits.

REFERENCES
[1]. Lowdon, E., Practical Transformer Design Handbook, McGraw-Hill, Inc., 2nd edition, 1989.
[2]. McLyman, W.T., Transformer and Inductor Design Handbook, Dekker, New York, USA, 3rd edition, 2004.
[3]. Rubaai, A., “Computer aided instruction of power transformer design in the undergraduate power engineering
class”, IEEE Trans. on Power Systems, Aug 94, v. 9, No. 3, pp. 1174-1181.
[4]. H.L. Garbarino, “Some properties of the optimum power transformer design,” Power Apparatus and Systems,
Part III. Transactions of the American Institute of Electrical Engineers, vol.73, no.1, pp. 675-682,Jan. 1954.
[5]. T.H. Putman, “Economics and power transformer design,” IEEE Transactions on Power Apparatus and
Systems, vol.82, no.69, pp.1018-1023, Dec. 1963.

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