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.