Design of Control Transformer (Case Study)

Data

Voltage Rating= 230 V/ 24 V

Frequency, f= 50 Hz

Power Rating= 100 VA

Assumptions

Flux density in the core, B = 1 wb/m²

Stacking factor for Core lamination = 0.9

Current Density in the winding, J= 2.3 A/mm²

Turns per Volt, Te = 4.6

Efficiency of the Transformer= 0.95

Core Design

Flux in the core, Øm =1/ (4.44 f Te) =1/ (4.44*50*4.6) = 9.7924 * 10^-4 Wb

Net Core Area, Ai= Øm/Bm= 9.7924 * 10^-4 /1= 9.7924 * 10^-4  m²

Gross Core Area, A_G = Ai/ Stacking factor = 10.8804 cm²

A= √A_G = 3.2986 cm

                                        

A= 3.2986 cm ≈ 3.3 cm

D= A/2 = 1.6493 cm ≈ 1.65 cm

E=D ≈ 1.65 cm

C= 3A= 9.8958 ≈ 9.9 cm

F> E or D

F ≈ 1.8 cm

B= 2D+A+2F= 10.2 ≈ 10.2 cm

Window Area = ((B-2D-A)/2)*(C-2E) ≈ 11.88 cm²

Winding Design

Primary Current, Ip = VA/ (Eff.* Vp) = (100/0.95*230) =0.4577 A

Ap’=0.4577/2.3 = 0.199 mm²

dp’= √((4*0.199)/ᴨ) = 0.5035mm

Nearest Standard Wire Size, dp= 0.508 mm (25 SWG or 24 AWG)

Ap= (ᴨ*dp²)/4= 0.2026 mm²

Turns in Primary, Tp= Te* Vp= 4.6* 230= 1058 Turns

Turns in Secondary, Ts= Te* Vs= 4.6* 24= 110.4 = 111 Turns

5 % more turns for Secondary

Ts= 1.05 Vs* Te= 115.92= 116 Turns

Secondary Current, Is = VA/ Vs= 100/24 =4.1667 A

As’=4.1667/2.3 = 1.8116 mm²

ds’= √((4*1.8116)/ᴨ) = 1.5191 mm

Nearest Standard Wire Size, ds= 1.626 mm (16 SWG or 14 AWG)

As= (ᴨ*ds²)/4= 2.0754 mm²

Space required for Primary winding= (Tp*Ap)/Space factor

Space required for Secondary winding= (Ts*As)/Space factor

Total space= (Tp*Ap)/Space factor + (Ts*As)/Space factor

                      = (1058*0.2026)/0.8 + (116*2.0754)/0.8

                      = 568.8715 mm²

25 % additional space for insulation = 1.25*568.8715= 711.0894 mm²

                                                                       = 7.111 cm²

No. of Stamping                = A/ Thickness of Stamping = (3.33 cm/ 0.33 mm)

                                                                                        = 100.9090 = 101

Width of window on Core, W= Window area/ Length of winding

                                                       = 6.9488/ (C-2E) = 1.0774 cm

W/2= 0.5264 cm

Weight of Cu wire required = Mean length of turn * (Ap*Tp +As*Ts)* Density of Cu

Mean length of turn, Tav = 4 (A+ (W/2) + (W/2))

                                                 = 17.5312 cm

Wcu = 175.312*(1058*0.2026+ 116*2.0754)* 0.0089

        = 710.0776 gm= 750 gm