Transformer Design

A transformer transfers electric power from one circuit to another circuit without change in frequency. It contains primary and secondary winding. Primary winding is connected to main supply and secondary to required circuit. In our project circuit we have taken design of low power (10 KVA) single phase 50 hertz power transformer as per our requirement in the project.

Transformer is basically of three types:

  1. Core Type
  2. Shell Type
  3. Toroidal

In core type windings surround a part of core where as in shell type core surrounds windings. In Core type there are two main types namely E-I type and U-T type. In this transformer design we used E-I core type. We chose E-I core as winding is much easier when compared to toroidal, but efficiency is very high (95%-96%). It is so because flux loss is very less in toroidal cores comparatively.

The transformers employed in the project are

  1. Series transformer:  To provide required boost or buck voltage  and
  2. 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 following specifications 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)

Winding data on Enameled copper wire

(@ 200A/cm²)

Max. Current Capacity (Amp.)

Turns/Sq. cm

SWG

Max. Current 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

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 Number

Tongue Width (cm)

Window Area (Sq. cm)

Type Number

Tongue Width (cm)

Window Area (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:-

  • 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
  •  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

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
  • 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.

20 Comments

  1. JD Dhinesh says:

    Dear sir.
    Thanks for ur valuable information ,please help us to find EI core selection calculation and to find the Stack calculation sir..,

  2. Very good post on transformer design. I also have an article regarding types of CTs on my page if anyone is interested in learning more about Current Transformer Theory. Cheers!

  3. Dear sir.
    Thanks for ur valuable information ,please help us to find EI core selection calculation and to find the core area of a line and load inductors

  4. Hello sir,
    This site is very informative and I learn a lot . thank you for sharing the design in detail.
    One doubt sir in example 1 and 2 how you select turn per ratio 0.5
    Hope to listen from you soon regards

  5. really very useful in our industry

      1. having any calculation formula for design

  6. Akash Tiwari says:

    use full information but i can’t understand what is 4.44*10 to the power minus 4 please reply its urgent.

  7. K. Mohinder says:

    this is very useful information.. Thnx A ton for sharing… Its very helpful…

    1. Team ElProCus says:

      Dear Mahinder, Thank you so much for your valuable feedback about this post, we love to help you with more great posts, please subscribe into our newsletter you will get regular updates via direct mail.
      Please visit our website once https://www.elprocus.com
      For any assistance or for customization of projects please email us on team@elprocus.com

  8. JEEVAN SINGH says:

    Its very useful to learn any transformer Design.

  9. Useful information. I bookmarked it…

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