Tranformer Design

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A

Design Report

On

Electrical System Design-I Submitted To

For Partial Fulfillment of the Academic Requirements for the Award of

Bachelor of Technology

In

Electrical Engineering

SUBMITTED BY

Arnab Nandi

Roll No: 16901613025

Reg. No: 131690110525 of 2013-14

UNDER THE GUIDANCE OF

Prof. Probal Mukherjee

Prof. Sandipan Misra

Department of Electrical Engineering

ACADEMY OF TECHNOLOGY

2016-2017

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I undersigned, Arnab Nandi declare that this report on Electrical System Design-I

(EE-782) is the result of my work carried out during the 7th Semester of the B.Tech

course.

This report has not been previously submitted to any other university / institutions

for any other examination and for any other purpose by any other person. I will not

use this project report in future to use as submission to any other university,

institutions or any publisher. I also promise not to allow / permit any other persons

to copy / publish any part /full material of this report in any form.

ARNAB NANDI

Electrical Engineering,

Academy of Technology

Roll No: 16901613025

Reg. No: 131690110525 of 2013-14

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With profound respect and gratitude, I take this opportunity to convey my heartfelt gratitude

towards the academic and governing board of our University for including this course in our

B.Tech curriculum. I also express my gratitude towards our college for proving us such an

opportunity to improve our skills by assigning us this project.

My special thanks goes to Prof. Probal Mukherjee and Prof. Sandipan Mishra for guiding us

through this course.

I am also thankful Prof. Sandip Saha Chowdhury (H.O.D, Department of Electrical

Engineering) and all professors of Department of Electrical Engineering who have guided and

enlightened us throughout the B.Tech curriculum, and helped us in developing a thorough

knowledge of the various subjects which has been a significant factor for the accomplishment of

this designing project.

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Objective .................................................................................................................................................................5

Assumptions............................................................................................................................................................5

Description ..............................................................................................................................................................6

Core Design.............................................................................................................................................................8

Window Dimensions ........................................................................................................................................9

Yoke Parameters .............................................................................................................................................10

Weight of Lamination ....................................................................................................................................10

Winding Design ....................................................................................................................................................11

Calculation of Current Magnitudes ................................................................................................................11

Calculation of Cross Section Area .................................................................................................................11

Calculation of Number of Turns ....................................................................................................................11

Calculation of Length of Secondary Winding ................................................................................................12

Calculation of Length of Primary Winding ....................................................................................................12

Calculation of Winding Loss ..........................................................................................................................12

Tank Design ..........................................................................................................................................................13

Cooling Tubes ................................................................................................................................................13

Electrical Parameters ..........................................................................................................................................14

Efficiency Calculation ..................................................................................................................................14

Data Sheet .............................................................................................................................................................15

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To design a distribution transformer meeting the specified conditions

Rated Power (Q) 200 kVA

Primary Voltage 6.6 kV

Secondary Voltage 440 V

Frequency 50 Hz

Phase 3

Phasor Group Dy

Type Core type

Type of Cooling Oil Immersed Natural Cooled

Maximum Temperature Rise 35oC

Parameter Symbol Value Unit

Voltage/turns Factor Kt 0.5 (mΩ)1/2

Stacking Factor Kf 0.9

Yoke cross-section factor Ky 1.15

Peak flux density in core Bm 1.3 Tesla

Density of Si-steel σFe 7600 kg/m3

Core loss density ρFe 2 W/kg

Winding space factor Kw 0.27

Window aspect ratio α 3

Current density in winding δ 3.2 A/mm2

Resistivity of copper ρ 2.1 µΩcm

Density of copper σCu 8900 Kg/m3

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Electrical transformer is a static device which transforms electrical energy from one circuit to another without

any direct electrical connection and with the help of mutual induction between two windings. It transforms

power from one circuit to another without changing its frequency but may be in different voltage level.

Most transformers used in commercial and industrial facilities fall in the middle ground Because these

transformers represent the majority, we should evaluate them carefully before choosing a unit for a specific

project and/or application.

There are three main parameters in choosing a transformer:

It must have enough capacity to handle the expected loads (as well as a certain amount of overload)

Considerations should be given to possibly increasing the capacity to handle potential load growth

The funds allocated for its purchase be based on a certain life expectancy (with consideration to an

optimal decision on initial, operational, and installation costs.)

Both capacity and cost relate to a number of factors that you should evaluate. These include:

Application of the unit

Choice of insulation type (liquid-filled or dry type)

Choice of winding material (copper or aluminum)

Possible use of low-loss core material

Regulation (voltage stability)

Life expectancy

Temperature considerations

Losses (both no-load and operating losses)

Shielding

Accessories

The main parts of a transformer are:

Laminated core

Windings

Insulating Materials

Transformer oil

Oil Tank

Conservator

Cooling tubes

Figure 1: Section through a Distribution Transformer

http://www.electrical4u.com/electrical-power-transformer-definition-and-types-of-transformer/

http://www.electrical4u.com/what-is-inductor-and-inductance-theory-of-inductor/#Mutual-Inductance

http://www.electrical4u.com/voltage-or-electric-potential-difference/

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Figure 2: Working Principle of Ideal Transformer Figure 3: Per phase Voltage and Current Relation

Figure 2: Isometric Projection of 200kVA Transformer

ARNAB NANDI ©

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The r.m.s value emf generated in transformer core is given as:

E=4.44fNAeBm where Ae = effective cross-section area of limb

N = number of turns in the winding

Bm = peak flux density in core = 1.3 Tesla

E/N = 4.44fAeBm = et -----(i) is the voltage induced per turn

Again, et = Kt √Q -----(ii) where Kt =voltage/turns factor = 0.5 (mΩ)1/2

Q= kVA rating of transformer = 200kVA

et = 0.5* √200 = 7.07 V/turns

Substituting et in (i) we get Ae = 7.07

4.44∗50∗1.3 = 244.9 cm2= KfAg where Ag is the gross-core area

Ag = 0.02449/0.9 = 0.0272m2

Ag= a1dc + b1b2 + c1c2 = dc

2 cos θ1 + dc2 cos θ1(sinθ2 – sin θ1) + a2 dc(cosθ1 – sin θ2)

For maximum condition: 𝜕Ag

𝜕θ1 =

𝜕Ag

𝜕θ2 = 0

Ag = 0.668dc2 . Solving the above two equations we get θ2 = π/4 and θ1= 25o

Figure 5: Elevation of Transformer Core

Figure 6: Cross-section of Core Limb

From geometry, we get:

a1 = dc cosθ1 a2= dc sinθ1 b1=dc cos θ1 b2= dc (sinθ2 – sin θ1) c1=a2 c2=dc (cosθ1 – sin θ2) Ag= a1 a2 + b1b2 + c1c2

ARNAB NANDI ©

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Figure 7: Elevation of Cross-Section of 3-stepped core

Substituting θ1 and θ2 Substituting dc

a1 = 0.906dc a1 = 18.282 cm

a2= 0.424dc a2= 8.56 cm

b1=0.707dc b1= 14.266 cm

b2= 0.283dc b2= 5.71 cm

c1=0.42dc c1= 8.56 cm

c2= 0.199dc c2= 4.01 cm

Ag = 0.668dc2

dc = √Ag

0.668 = √

272

0.668 = 20.1788 cm

Throughput equation of transformer is given as:

Q*103 = 3.33 Kf Kw f Bm δ Ag Aw

Aw = Q∗103

3.33Kf Kw f Bm δ Ag

= 200∗103

3.33∗0.9∗0.2732∗50∗1.3∗0.0272∗3.2∗106

= 561.68 cm2 = Window Area

Window Dimensions: Let: Hy = Height of Yoke

Hw = Height of Window

Ww= Width of Window

α = Hw / Ww = Aspect Ratio = 3

Then Aw = Hw *Ww = α Ww 2

561.68 cm2 = α Ww 2

Ww = 13.68 cm

Hw = 41.049 cm

Figure 8: Vertical and Horizontal Cross-Section of Core

ARNAB NANDI ©

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Yoke Parameters:

Yoke Factor Ky = Yoke Area

Ag = 1.15 Yoke Area= Ky* Ag = a1* Hy

Hy = 17.11 cm

Volume of Yoke = 2* Hy * Kf*D where D= 3dc +2Ww = 87.8964 cm

Volume of Yoke = 2707.033 cm3

Volume of Limb = 3* Hw* Ag* Kf = 30146.38 cm3

Mass of Core = 229.78 kg

Core loss= 2W/kg

Total loss = 459.561W = 0.4595 kW

% loss = 0.4595∗100

200 = 0.229%

Weight of Lamination

Step-1

SEGMENT LENGTH L(cm) WIDTH (cm) STACK (cm) COUNT MASS (kg)

1 Hw + Hy = 58.159 a1= 18.282 a2= 8.56 3 186.76

2 d= 33.86 Hy= 17.11 a2 = 8.56 2 40.43

3 2d- a1 = 22.0756 Hy= 17.11 a2 = 8.56 1 22.115

Step-2

1 Hw + Hy = 58.159 b1= 14.266 b2= 5.71 3 97.214

2 d= 33.86 Hy= 17.11 b2= 5.71 2 45.254

3 2d- b1=53.46 Hy= 17.11 b2= 5.71 1 35.72

Step-3

1 Hw + Hy = 58.159 c1= 8.56 c2= 4.01 3 40.964

2 d= 33.86 Hy= 17.11 Hy= 17.11 2 31.78

2 2d- c1= 59.16 Hy= 17.11 Hy= 17.11 1 27.76

Total Mass of Lamination 527.997

Figure 9: Segments of Individual Laminations

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Calculation of Current Magnitudes

Secondary Current Is = Q∗103

√3∗Vs =

200∗103

√3∗440 = 262.43 A

Primary Current Ip = Q∗103

Vp=

200∗103

6.6∗103 = 10.10 A

Calculation of Cross-section Area

Secondary Cross sectional area: asec = Is

δ = 82 mm2

Primary Cross sectional area: apri = Ip

δ = 3.156 mm2

Calculation of Number of Turns

Number of turns in secondary winding: Ns= Vs

√3∗et = 32.664 ≈ 33

Number of turns in primary winding: Np= Vp

et = 933.52 ≈ 934

Figure 10: Arrangement of Windings on Limb

Figure 11: Cross-Section through the Windings

ARNAB NANDI ©

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Calculation of Length of Secondary Winding

Let: ls = number of layers in secondary winding = 2

ps= number of parallel sections = 2

tis= insulation thickness = 0.2mm

ts= thickness of secondary conductor = 2mm

tf = thickness of former = 3mm

tps = inter-layer insulation thickness = 0.5mm

Thickness of secondary winding: tsw = ps* ls*( ts+2 tis) + 0.5*( ls-1) = 10mm

Inner diameter of secondary winding: IDsec = dc +2tf = 207.788 mm

Outer diameter of secondary winding: ODsec = IDsec +2tsw = 227.788 mm

Mean diameter of secondary winding : MDsec = 217.788 mm

Length of secondary winding: Ls = π * MDsec * ps * (Ns/ ls) = 45.157 m

Mass/phase = ls* ws* ts*density *(10-6 ) = 17.686 kg

Calculation of Length of Primary Winding

Thickness of primary winding: tpw = 0.5mm

Thickness of duct: td = 10mm

Inner diameter of primary winding: IDpri = ODsec +2td = 247.788 mm

Outer diameter of primary winding: ODpri = IDpri +2tpw = 248.788 mm

Mean diameter of primary winding : MDpri = 248.288 mm

Length of primary winding: Lp= π * MDpri * Np = 727.7 m

Calculation of Winding Loss

Let resistivity ρ= 20nΩm.

Resistance/phase of secondary winding: Rs = 0.00513 Ω/ph

Resistance/phase of primary winding: Rp = 0.005 Ω/ph

Loss in secondary winding = 3*Is2*Rs = 1.06 kW

Loss in secondary winding = 3*Ip2*Rp = 1.53 W

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Let CH = clearance along height = 50 cm

CL = clearance along length = 5cm

CW = clearance along width = 5cm

d = Ww + dC = 33.8588 cm

dPo = ODpri = 24.8788 cm

Tank height: H = Hw + Hy + 2CH = 175.31 cm

Tank length: L = 2d + dPo +2CL = 102.59 cm

Tank width: W= dPo + 2Cw = 34.8788 cm

Cooling Tubes Heat transfer area: St = 2H(L+W) = 4.819 m2

Convection coefficient: λC = 6W/m2/oC

Radiation coefficient: λR = 6.5W/m2/oC

Heat transfer factor: θT = (λC + λR)*St = 60.2375 W/oC

Temperature rise: ∆TM = (core+copper loss) / θT

= 24.8 oC

Tube factor: ζ = 30%

Area of Tubes: Stu = (

loss

∆TM)−θT

(1+ζ )∗ λC = 2.29m2

Let height of tube h=170.31 cm and diameter φ = 5cm

Number of tubes = Stu / (π *h* φ) = 8.75 ≈ 9

NOT TO SCALE

Figure 12: Cross section of Core and Winding Figure 13: Schematic diagram of Core and Tank

ARNAB NANDI ©

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Inductance of primary winding: Lp = μo NP2 MDpri∗ (

𝑡𝑝3

+ 𝑡𝑑2

ℎ𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑝𝑟𝑖𝑚𝑎𝑟𝑦) = 3.683 mH/m

Inductance of secondary winding: Ls = μo Ns2 MDsec∗ (

𝑡𝑠3

+ 𝑡𝑑2

ℎ𝑒𝑖𝑔ℎ𝑡 𝑜𝑓𝑠𝑒𝑐𝑜𝑛𝑑𝑎𝑟𝑦) = 6.7913 μH/m

Let: R1 = Primary winding resistance/ph =Rp/3

X1 = Primary winding reactance/ph = jω(Lp/3)

R2’= Secondary winding resistance/ph referred to primary = (Np2/3Ns

2)Rs

X2’= Secondary winding reactance/ph referred to primary = jω(Np2/3Ns

2)Ls

Total Resistance/ph = Rp/3 + (Np2/3Ns

2)Rs = 1.3715 Ω

Total Inductance/ph = Lp/3 + (Np2/3Ns

2)Ls = 3.04 mH

Primary side impedance: Zp = Vp/3Ip = 217.8217Ω

% Resistance: εR = (1.3715/217.8217)*100 = 0.6296%

% Reactance: εX = 0.4384%

Core loss current/ph: Icore= PFe

3𝑉𝑝 = 0.023 A

Primary Magnetizing current/ph: Imag = 3.933A

Efficiency Calculation

Total winding Loss: PCu = 1034.57 W

Total core Loss: PFe = 459.561 W

Full load Loss: PL = PCu + PFe = 1494.131 W

Assume operating power factor: cosφ = 0.8

Efficiency at full load: η = 𝑄cosφ

𝑄cosφ+PL = 99.074%

Maximum efficiency Load fraction = √PFe

PCu = 66.684%

Maximum efficiency at unity power factor: ηmax = 99.5425 %

Figure 14: Equivalent circuit of Transformer referred to Primary

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SPECIFICATIONS


kVA Rating Q 200 kVA

Frequency f 50 Hz

Phases φ 3

Primary Vector Y Star

Secondary Vector ∆ Delta

Type Core

Primary Voltage VP 6600 Volt (V)

Secondary Voltage VS 400 Volt (V)

ASSUMPTIONS


Volts/turn factor Kt 0.5 (mΩ)1/2

Stacking factor Kf 0.9 Hz

Yoke factor Ky 1.15

Peak flux density Bm 1.3 Tesla

Density of Steel σFe 7600 kg/m3

Core loss density ρFe 2 W/kg

Winding space factor Kw 0.27

Window aspect ratio α 3

Current density in winding δ 3.2 A/mm2

Resistivity of copper ρ 2.1 µΩcm

Density of copper σCu 8900 Kg/m3

CORE DESIGN


Volts/turn Et 7.07 Volt

Net core area Ai 244.9 cm2

Gross core area Ag 272 cm2

Diameter of Circle dc 20.1788 cm

First step width a1 18.282 cm

Second step width b1 14.266 cm

Third step width c1 8.56 cm

First step stack a2 8.56 cm

Second step stack b2 5.71 cm

Third step stack c2 4.01 cm

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WINDOW DESIGN


Window area Aw 561.6 cm2

Window width Ww 13.68 cm

Window height Hw 41.09 cm

YOKE DESIGN


Gross yoke cross-section area Agy 318.5 cm2

Volume of yoke VY 2707.033 cm3

Depth of yoke DY 18.281 cm2

OVERALL CORE DIMENSIONS


Limb-to-limb distance d 33.86 cm

Total width of core W 34.88 cm

Total height of core H 41.09 cm

Mass of core MCore 229.78 kg

Core loss PCore 459.56 Watt (W)

Mass of lamination Mlami 527.997 kg

WINDING DESIGN


Secondary turns/phase NS 33

Primary turns/phase NP 934

Secondary current IS 262.43 A

Primary current IP 10.10 A

Secondary area aS 82 mm2

Primary area aP 3.156 mm2

Secondary turns/layer nS 16.5

Number of parallel sections lS 2

Width of section WS 22 mm

Thickness of section tS 2 mm

Secondary internal diameter IDS 207.788 mm

Secondary outer diameter ODS 227.788 mm

Primary internal diameter IDP 247.788 mm

Primary outer diameter ODP 248.788 mm

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EFFICIENCY CALCULATION


Total winding loss PCu 1034.57 W

Total iron loss PFe 459.561 W

Full load loss PFL 1494.131 W

Operating power factor Cosφ 0.8

Efficiency at full load η 99.047 %

Maximum efficiency load fraction ξ 66.648 %

Maximum efficiency at UPF ηmax 99.5425 %

TANK DESIGN


Height clearance CH 50 cm

Length clearance CL 2 cm

Width clearance CW 5 cm

Tank Height HTk 175.31 cm

Tank Length LTk 102.59 cm

Tank Width WTk 34.8788 cm

Heat dissipation area ST 4.819 m2

Convection coefficient λC 6 W/m2/oC

Radiation coefficient λR 6.5 W/m2/oC

Allowed temperature rise ∆T 35 oC

Maximum temperature rise ∆TM 24.8 oC

Number of cooling tubes ntu 9

ELECTRICAL PARAMETERS


Free space permeability µo 4π*10-7 H/m

Primary winding inductance LP 3.683 mH/m

Secondary winding inductance LS 3.6836.7913 µH/m

Equivalent resistance/phase ReqP 1.3715 Ω

Equivalent inductance/phase LeqP 3.04 mH

Percentage resistance εR 0.6296 %

Percentage reactance εX 0.4384 %

Percentage impedence εZ 0.76722 %

Core loss current/phase IO 0.023 A

Fault current If 2.283 kA

Open circuit current IOC 6.813 A

Primary magnetizing current Im 3.933 A

Peak mmf in yoke Hy 235 AT/m

Peak mmf in limb HL 395 AT/m

Peak mmf in core Hm 550.72 AT

Tranformer Design

Engineering

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