ptc slides 1 - ttu.ee · during the preparations students will add to their knowledge-base in the...

Elektriseadmete raalprojekteerimise kursuse kodune ettevalmistus ja slaidid: trafod

Metoodiline juhend üliõpilastele ja juhendajatele

Home assignments and slides in course on Numerical modelling and design of electrical devices: transformers

Guide for students and supervisors

Project 1.0101-0278

Application of interdisciplinary and international team and project based learning in Master Studies

IN 557

PROJECT 1.0101-0278

APPLICATION OF INTERDISCIPLINARY AND INTERNATIONAL TEAM

AND PROJECT BASED LEARNING IN MASTER STUDIES

IN 557

DESIGN, OPTIMIZATION AND PROTOTYPING OF POWER

TRANSFORMERS

COURSE ORGANIZERS Lecturing:

Avo Reinap e-mail: [email protected] eSkype: avo.reinap

Rando Pikner e-mail: [email protected]

Prototyping:

Michael Schmelzer e-mail: [email protected]

Rando Pikner e-mail: [email protected]

Main program coordinator at Tallinn University of Technology:

Juhan Laugis e-mail: [email protected]

COURSE PROGRAM

INDIVIDUAL PREPARATION Home preparation + Webinars + Feedback

W Event Preparation

42 First contact via e-mail Engineering challenges: How do design a power transformer? Prepare your individual work plan.

43 Correspondence via e-mail preparing to hold a webinar

Course compendium (a complementary material to classical text books) & Design specifications

44 Correspondence via e-mail or/and a webinar

Design model of a power transformer, parameterization, sensitivity, analytic vs numeric model


Transformer characteristics, sensitivity analysis and optimization


Starting a course report

TEAM WORK Design refinement + Prototyping

W Time Weekday: Mon-Tue-Wed-Thu-Fri

08:00-09:30

10:00-11:30

Design model of a power transformer

12:00-13:30

Arrival & Accom-modation Transformer

characteristics

14:00-15:30

Numeric field modelling

Transformer design with RALE

(Theoretical) Preparations for building prototypes

47

16:00-17:30

Presentation of preparations

Optimization of a power transformer

08:00-09:30

10:00-11:30

Arrival to Vändra MS Balti Trafo

12:00-13:30

14:00-15:30

Testing 48

16:00-17:30

(Practical) Preparations for building prototypes

Making windings

Making windings and core

Assembling and testing

Back to TUT

08:00-09:30

10:00-11:30

Handin report Preparing for presentation Farewell

12:00-13:30

14:00-15:30

Presentations

49

16:00-17:30

Completing the course report, conclusions

W – week number

Course on Design, Optimization and Prototyping of Power Transformers 2006-10-19 Introduction to Individual Preparations

COURSE ON DESIGN, OPTIMIZATION AND PROTOTYPING OF POWER TRANSFORMERS This course is a part of the application of interdisciplinary and international team and project based learning in master studies (Project 1.0101-0278).

OBJECTIVE The purpose of this page is to give an overview of the course and the course program.

COURSE DESCRIPTION The course focuses on electromagnetical energy conversion that takes place in a power transformer. The course is held in two parts, where the first part concentrates to an individual preparation and an actual teamwork takes place in the second part. The importance of the individual studies is to become acquainted with or/and to recall knowledge on

electromagnetic field theory,

magnetic materials and magnetic circuits,

circuit analysis,

phasor domain, single and 3-phase ac circuits.

During the preparations students will add to their knowledge-base in the fundamentals of electrical and computer engineering, knowledge about the solution procedures and computer utilization for solving practical applications related to electric and magnetic circuits, single and three-phase circuits, energy conversion principles, and basics of the transformer characteristics and operation. By solving project task, which is to design a power transformer and later actually to build it, possible solutions must be analyzed and among them the best solutions are to be selected. Therefore the theoretical preparations focus on

establishing a good design model and

using the model to find an optimal design.

The pre-established skills of problem solving and critical thinking are vital in the teamwork sessions when completing the design and making the actual prototype. During the preparation period there are weekly homework assignments that suppose to be handed in electronically before the next assignment will be announced. These assignments suppose to indicate engineer’s respectability and writing skills in clean organized presentation and clear decisions explanation manner. Later these assignments can efficiently be used to complete the individual course report.

COURSE PROGRAM – INDIVIDUAL PREPARATION During the next four weeks four home assignments will be given

drafting – gained ideas of how to design and to optimise a transformer and the actual time planning for the individual progress (W43),

Design model – starting to formulate a design model for a power transformer i.e. the mathematical description of the geometrical object and physical process (W44),

Analysis – the design parameter, number of phases (Nph), could be easily changed from 1 to 3 and backwards, investigate the sensitivity of the design model (W45),

Optimization – find the set of design parameters that gives the lowest weight, the losses, the cost of the transformer (W46).

It is expected that the assignment will be handed in on Thursdays (in the week shown in parentheses) for the further encouragements.

Course on Design, Optimization and Prototyping of Power Transformers 2006-10-26 Home Assignment 2 - model

HOME ASSIGNMENT 2 This is a home assignment in the course on design, optimization and prototyping of power transformers.

OBJECTIVE The purpose of the home assignment is to start building a mathematical model of an electromagnetic energy converter – a transformer.

MODEL The second assignment is a continuation to the first assignment that first of all bases on designer’s creativity. Concerning to the first home assignment, the course supervisor would like to know how a course participant interprets the word/action 'design' and 'optimization', and what software she/he thinks is suitable to develop such an environment where design and optimization of a power transformer is possible. So the main goal of the second home assignment is to start completing a mathematical design model of a transformer. To design an electrical device is an engineering challenge that usually includes the following steps: physical understanding, mathematical modelling, analysis, synthesis and optimization. The course material that could help you with the design process focused on transformers is not distributed yet. The reason for that is to encourage a course participant to think freely and creatively.

The task is to establish a mathematic description of a geometrical object and a physical process of an electromagnetic transformer. The parameters that specify the physical process are:

Rated primary (phase) voltage Up1=230 V,

Rated apparent power a) 1-φ S=1000 VA, b) 3-φ S=250 VA,

Rated secondary (phase) voltage Up2=48 V,

Full load voltage regulation sUp2=20%,

Winding temperature class B or F,

Natural cooling conditions aCu=8.9 W/Km2, aFe=21.3 W/Km2, Tamb=40OC,

Number of phases (φ) Nph=1 and Nph=3.

Please feel creative when designing a transformer start from establishing a good physical understanding then try to interpret the physics through mathematic. I would like to see your thoughts and progress in a couple of pages on Thursday 2nd of November!

Good Luck!

Avo R

Do you feel already hopeless? There will be a course material on numerical modelling and design of electrical devices. There you could see that your transformer model could be analytical or/and numerical. Apart from that there you can read my interpretation to the first home assignment about design and optimization. I prefer freeware to carry out the design task FEMM and Mirage for numeric field computation and SciLab for the rest. Actually in Tallinn we are going to use Matlab and this considers the ‘rest’ – analytical modelling, optimization and result visualisation. SciLab is quite the same as Matlab, nevertheless it is free and you can find the freeware by help of google.

Course on Design, Optimization and Prototyping of Power Transformers 2006-11-02 Home Assignment 3 - analysis


OBJECTIVE The purpose of the home assignment is to start analysing a transformer with the established mathematical model of an electromagnetic energy converter.

ANALYSIS The third assignment is a continuation to the second one as the second assignment was a ‘natural’ continuation to the first assignment. The assignments are focused towards participants’ professionalism on electrical engineering. The output from the second home assignment supposes to be a mathematic model that describes a geometrical object and a physical process of an electromagnetic transformer. The model consists of (design) parameters that specify the physical process related to the constructional geometry. The main purpose of this home assignment is to analyse the behaviour of the model and to see if it gives reasonable results. In addition

Change design parameter Nph from 1 to 3 and make it possible that you can run both models easily,

Introduce a parameter change in geometry and study the influence to transformer performance, losses, weight of copper and iron, etc,

Consider losses and magnetic saturation in the transformer model(s).

The physical properties of electromagnetic steel are attached to this document. Take material data (Surahammars Bruks AB) suitable for you. One way or another, the material input will be later different, i.e. given by MS Balti Trafo, try to introduce flexibility when making changes in model. Please feel creative when starting to use your model for analyses. Soon it is day ready (the fourth assignment) for synthesis and optimization. I would like to see your thoughts and progress in a couple of pages on Thursday 9nd of November!

Good Luck!

Avo R

Do you feel depressed? There will be an half of course material on design, optimization and prototyping of a power transformer. There you could see my interpretation of geometrical modelling and the equation system describing the transformer in a fixed frequency frame. This could be a complementary material to yours and the rest of references you have found so far.

Course on Design, Optimization and Prototyping of Power Transformers 2006-11-10 Home Assignment 4 - synthesis


OBJECTIVE The purpose of the home assignment is to complete the home preparation period by synthesising a transformer.

SYNTHESIS The fourth (last) assignment is a continuation to the sequence of the home assignments. The outcome of this homework is a transformer design that is “ready” for prototyping. A transformer construction can be proposed on the basis of the mathematic model that describes a geometrical object and a physical process of an electromagnetic transformer. Synthesis can be seen as an inversion to analysis. According to the performance requirements, which were described in the second home assignment, the transformer geometry has to be proposed. An additional design table will be provided where you specify the transformers that you have been designing. Fill as many cells in the table as you are able. The data will be summoned up in common table for comparison and presented in the opening session. In addition please be ready to make presentation, where

On a couple of slides you will give short overview of yourself, your curriculum and university,

There suppose to be one slide per home assignment, where you try to formulate the essence of your thoughts and achievements,

At least one slide about your expectations from the course.

See you in Tallinn on Monday 20th of November!

Good Luck!

Avo R

It is too late to be depressed. As far I have seen you have already made a good progress, you are well prepared and have some ideas about:

• What is design and which are the possible software to carry out the design task,

• How the transformer works and how this can be described mathematically,

• The specification of the transformers that we are going to work on,

I think this is a good starting point for teamwork!

Course on Design, Optimization and Prototyping of Power Transformers 2006-11-10 Home Assignment 4 - synthesis

quantity symbol unit A single phase

transformer A three-phase

transformer

rated apparent power S VA 1000 250

rated primary voltage (phase, rms value) Up1 V 230 230

rated secondary voltage (phase, rms value) Up2 V 48 48

full load voltage regulation sUp2 % 20 20

type of transformer - -

winding connection Δ/Y

height of transformer Htr mm

length of transformer Ltr mm

width of transformer Wtr mm

maximum flux density in the core Bc T

maximum current density in the primary winding Jc1 A/mm2

maximum current density in the secondary winding Jc2 A/mm2

the induced voltage per phase at 50Hz Ep V

cross-section area of primary electric circuit A1 mm2

cross-section area of secondary electric circuit A2 mm2

cross-section area of magnetic circuit (core) Ac mm2

copper filling factor in the primary winding Kf1 %

copper filling factor in the secondary winding Kf2 %

height of primary electric circuit (winding) Hw1 mm

height of secondary electric circuit (winding) Hw2 mm

Length of primary electric circuit (winding) Lw1 mm

length of secondary electric circuit (winding) Lw2 mm

the thickness of main insulation insl mm

number of turns in primary winding N1 turns

number of turns in secondary winding N2 turns

turn length of copper wire in primary winding Lc1 mm

turn length of copper wire in secondary winding Lc2 mm

diameter of copper wire in primary winding Dc1 mm

diameter of copper wire in secondary winding Dc2 mm

phase current rms value in primary winding Is1 A

phase current rms value in secondary winding Is2 A

the phase resistance in primary winding R1 Ohm

the phase resistance in secondary winding R2 Ohm

the phase inductance in primary winding L1 mH

the phase inductance in secondary winding L2 mH

thermal limit to the primary current Ith1 A

thermal limit to the secondary current Ith2 A

hot-spot temperature in primary winding ϑc1 °C

hot-spot temperature in secondary winding ϑc2 °C

copper losses Pcu W

ferrous losses Pfe W

the losses per cooling surface QP W/m2

weight of core Mrc Kg

weight of stator core Msc Kg

weight of copper Mcu Kg

Welcome!

Course on Design, Optimization and Prototyping of a Power Transformer

Course on design, optimization and prototyping of power transformers

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Program structure

• Project 1.0101-0278• Application of interdisciplinary and

international team and project based learning in Master Studies

• IN 557• Courses on Industrial automation, electrical

drives and power electronics, Computer aided design

• Course on Design, Optimization and Prototyping of a Power Transformer


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Course structure

• Individual preparation period (5 weeks)– meaning of design and optimization,

– design model – focus on a 1φ transformer

– Parameterisation and analysis – switch from 1φ to 3φ

– Synthesis and result presentation

• Team work sessions (2 weeks)– Design and optimization of two power transformers

– Prototyping of the designed transformers

• Design and course evaluation (2 days)


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Individual preparations

• Improve one’s knowledge-base for the further efficient collaboration,

• Establish a good contact with each course participant in order to support the improvements,

• Intensive program, communication via possible media simultaneously,


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Course program W47

Intro to software

16:00 17:30

E22 Optimi-zation

E12 FE modelling

Course start14:00 15:30

E42 Design specification

E32 Design comparison

12:00 13:30

E21 Cha-racteristics

E11 Design models

10:00 11:30

E41 Design specification

E31 Design with RALE

08:00 09:30

Friday 24-NOV-06

Thursday 23-NOV-06

Wednesday 22-NOV-06

Tuesday 21-NOV-06

Monday 20-NOV-06


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Course program W48

16:00 17:30

Back to Talinn

14:00 15:30

P1 Practical preparations for building the prototy-pes

12:00 13:30

P4Assembling and testing

P3 Making the win-dings and the core

P2 Making the win-dings and the core

10:00 11:30

P5 Testing Arrival to VändraMS BaltiTrafo

08:00 09:30

Friday 01-DEC-06

Thursday 30-NOV-06

Wednesday 29-NOV-06

Tuesday 28-NOV-06

Monday 27-NOV-06


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Course program W49

Farewell 16:00 17:30

C2Reporting, completing course doc

14:00 15:30

C4 Presen-tations, concluding session

12:00 13:30

C1 Post analysis

10:00 11:30

Farewell C3 handing in course report

08:00 09:30

Friday 08-DEC-06

Thursday 07-DEC-06

Wednesday 06-DEC-06

Tuesday 05-DEC-06

Monday 04-DEC-06


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Course Participants

• Piotr from Gdansk

• Edgars from Riga

• Andrius from Vilnius

• Roman from Tallinn

• Karl from Tallinn

Introduction to design and design environment

Course on numerical modelling and design of electrical devices


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Development

• Theory, experiment and simulation employed to understand the physical reality and put it into practice

comparison comparison

verification of the model by simulation

verification of the model by theory

computer simulation theory

computed data theoretical prediction

modelling mathematical model of the device

measurement

experimental data

real device


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Design• Design is a process of development

• In this course the development is focused on the field of electrical engineering – a power transformer

• Design based on a model – description of system and structure, that handles the complexity of PDE

• Designer seeks for / explores the optimal combination of structure and functionality of a device

• Cost efficient solution is usually more crucial than the technically optimal device

• Design will always remain stimulating and challenging engineering profession


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Computer Aided Design

• Efficient use of computation power and information

• CAD, CAE, CAM

Conceive DesignManufacture Develop

Validate Concept design

Product layout

Detailed device modelling

Tool design

Drawings

Analysis

CADIDEAS

Requirements

CAM

CAE


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Idea

• Knowledge – understanding of something

• Intention – purpose of doing something

• Principle – belief how something (is or) should be

• Suggestion – a plan for possible course of action

• Software suitable for design, any idea?

• What do design? no idea!?


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Design environment• The design environment is

established in Matlab– Approximate design model

– Analysis and optimization

– Visualization and administration

• Finite element modelling is performed by freeware

– Mirage – heat transfer

– FEMM – magnetics

APPROXIMATE DESIGN MODEL

NUMERICAL ANALYSIS

OPTIMIZATION


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Design task

• Find a minimal cost of a power transformer• Power transfer

– A single-phase 1000VA– A three-phase 250VA– At natural cooling conditions

• Power conditioning– Line voltage 230V / 48V– Voltage regulation 20%

• Laminations: M330-50A or M530-50A,• Winding insulation class, F or B


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Electromagnetic circuit

∑

∑

∑∫ ∫

=

=ℜ→=++

=++=++

==→=

2

0

000

000

2

1ggn

bb

bb

g

gg

mm

mm

bb

bg

gm

m

mbbggmm

fillslot

C A

BAF

NINIA

l

A

l

A

l

NIlB

lB

lB

lHlHlH

NIkJAHdldAJHdl

μ

φμμ

φμ

φμμ

φ

μμμμμ

• Ampere’s circuital law applied to magnetic circuit

• Maxwell stress concept – forces in magnetic field

Fn

+N·I -N·I

phi m-core

iron bar

air-gap


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Geometry parameterization

• Magnetic circuit is described by parameters: proportions, dimensions and numbers

• Parametric geometry input in electromagnetic circuit calculations

wsc

hsc wst

wst

ins

g

( )

( )( )inswssinshstA

wsthschst

Kwspwss

Kwspwst

KN

wscwsp

slot

s

s

ss

22

1

1

−−=−=⋅=−=−+

=


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Heat transfer

• Fourier’s heat conduction in the materials

• Newton’s convection boundary conditions

J2ρKf

qn=h(ϑ-ϑamb)

J2ρKf

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛−⋅−+=

⋅⋅⋅

=⋅=

⋅=⋅=

−t

ambmamb

ththth

thm

th

e

A

cVRC

A

PRP

τ

ϑϑϑϑ

αρτ

αϑ

1

2

2


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Electromagnetic circuit calculations

• Methods– Simple approach

– Equivalent circuit method (Magnetic EC, Thermal EC 1D elements describing 3D object)

– Finite element method (multiphysics 2D, 3D)

• Tools– Matlab (Design environment)

– FEMM (Magnetism) , Mirage (Heat transfer)


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Example in Matlab

• M-core dimensions, width 5.0 cm, height 4.0 cm

• M-core proportions, slot width = Ks*tooth pitch

% Matlab script for m-corex=[0 1 1 2 2 3 3 4 4 5 5 0 0];y=[0 0 3 3 0 0 3 3 0 0 4 4 0];figure(1); plot(x,y)A=polyarea(x,y);title(['region area ' …num2str(A,'%1.1f')])

0 1 2 3 4 5-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

(0.0,0.0) (1.0,0.0)

(1.0,3.0) (2.0,3.0)

(2.0,0.0) (3.0,0.0)

(3.0,3.0) (4.0,3.0)

(4.0,0.0) (5.0,0.0)

(5.0,4.0)(0.0,4.0)

(0.0,0.0)

region area 14.0


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FEMM Pre-Processor• Drawing the endpoints of the

lines and arc segments for a region,

• Connecting the endpoints with either line segments or arcsegments to complete the region,

• Defining material properties and mesh sizing for each region,

• Specifying boundaryconditions on the outer edges of the geometry.


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FEMM Post-Processor• Flux lines show magnetic

coupling between the magnetic conductive parts

• Flux density indicate magnetic loading

• Generally the forces are calculated by using weighted Maxwell’s stress tensor

• Flux linkage can be obtained from circuit-data


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FEMM and LUA Script• Femm functions are called by LUA Script

• Scripting is similar to Matlab, it is possible to create user-independent calculation loop


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Summary

• Course structure and plan

• Course participants

• Introduction to design and design environment

• Examples:– Design of electromagnetic/mechanic energy

converter,

– Intro to Matlab

– Intro to FEMM/Mirage

Model



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Design model and design process

• Multiple files used in Matlab– Listing ‘all’ equations determining the transformer

behaviour

– Selecting design variables and acceptable limits

– Setting performance criteria and comparison

• Design process– Select random values in order to study the ‘limits’ of

the model

– Evaluates device behaviour and checks for feasibility

– Compares to other designs and stores best designs


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Electromagnetic circuit calculations

• Methods– Simple approach

– Equivalent circuit method (Magnetic EC, Thermal EC 1D elements describing 3D object)

– Finite element method (multiphysics 2D, 3D)

• Tools– Matlab (Design environment)

– FEMM (Magnetism) , Mirage (Heat transfer)


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Equivalent circuit relations

ϑ=Q·RN·I=Φ·RU=I·ROhm’s Law

R=1/λ·l/AR=1/μ·l/AR=1/γ·l/AResistive element

Q=q·AΦ=B·AI=J·AFlow

ϑ=G·lN·I=H·lU=E·lPotential

Thermal circuit

Magnetic circuit

Electrical circuit

Relation


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Thermal circuit (A)

• Node points i, Qi [W], ϑi [K]1. Coil loss and temperature

2. Tooth loss and temperature

3. Yoke loss and temperature

4. Ambience temperature

• Thermal conductivity elements Gij [W/K]– From coil to tooth G12

– From coil to yoke G12

– From tooth to yoke G23

– From yoke to ambience G34

Gϑ13

Gϑ12

Gϑ34

Gϑ23

ϑ4

ϑ3

ϑ2 ϑ1


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Thermal circuit (B)• Topology matrix • Circuit formulation

ijji Gnodenodekelement:)T(k, =

34

23

13

12

434

323

312

211

G

G

G

G

T =

000

0

0

3

2

1

4

3

2

1

3434

343423132313

23231212

13121312

Q

Q

Q

GG

GGGGGG

GGGG

GGGG

=⋅

−−++−−

−+−−−+

ϑϑϑϑ

QG =ϑ

( )BBNNN

B giveninitially

ϑϑ

ϑ

⋅−=

−− GQG 1


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Thermal design

• Good estimate of losses – the distribution of heat sources

• Thermal characteristics of materials

• Heat dissipation – thermal circuit and cooling system

• Thermal limits at cooling capability


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Thermal limits

• Insulation lifetime is shortened radically if temperature exceeds the limit and that is due to accelerated oxidation process in the insulation material.

A E B F H0

20

40

60

80

100

120

140

160

180

insulation classes

tem

pe

ratu

re ϑ

[ °C

]

40

60

5

40

75

5

40

80

10

40

105

10

40

125

15ϑambmaxΔϑallow edΔϑsafety

140 160 180 200 220 240 260 28010

2

103

104

105

temperature ϑ [°C]

the

rma

l life

[h]

Class 200Class 155


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Modeling a winding

• Equivalent thermal conductivity of a winding is given by the filling factor of the conductor strands (copper in this example) and the thermal conductivity of the medium between the conductor strands

( ) ( )( )inscond

fcondfins

ins

f

cond

f

eff

kkLkLkLL

λλλλ

λλλ ⋅

−⋅+⋅⋅=

−⋅+

⋅=

11

( )fcondfins

inscondeff kk −⋅+⋅

⋅=

1λλλλλ


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Transient heat flow

• Steady state temperature

• Heating time constant

• Temperature rise during the transient heating

x

ϑ1 ϑ

α1

A

ϑamb

ϑhot

α2

l

QP QS QD

ϑ2

ϑαϑρ

ϑϑ

⋅⋅+⋅⋅=

+=

+=

2Adt

dcVP

Rdt

dCP

QQQ

thth

DSP

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛−⋅−+=

⋅⋅⋅

=⋅=

⋅=⋅=

−t

ambmamb

ththth

thm

th

e

A

cVRC

A

PRP

τ

ϑϑϑϑ

αρτ

αϑ

1

2

2


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Transport of heat

•Q - the required flow rate, m3/s, Ph -required cooling power, W, ρ - the density of the heat carrier, kg/m3, c - the specific heat capacity, J/kg°C, Δϑ - the temperature difference between incoming and outgoing temperature °C

•Natural convection

•Forced cooled plane surface by air speed v

•Empirical cooling capability

ϑρ Δ⋅⋅=

c

PQ h

2255

mK

W

⋅= Kα

78.06.0208.7 KK v⋅=α

25.21

m

kW

A

P

cool

loss K=


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Heat sources and hot-spot

• Specific heat loss of electric conductor depends on electric loading and resistivity

• Specific heat loss of magnetic conductor depends on magnetic loading, speed and ‘conductivity’,

• The temperature rise of a ‘conductor’ depends on the shape of the conductor and the thermal conductivity,

ρ2

2

1me Jq =

mmm kBq 22

2

1 ω=

42

2d

k

q

gλϑ =Δ


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Winding losses

• Resistive loss – energy wasted due to a material’s opposition to the flow of electric current

• A current displacement effect – due to the opposing induced currents– Proximity effect

– Skin effect


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Core losses• The reactive power loss associated with energy stored in

the magnetic core of a transformer,

• The active power loss is due to hysteresis loss and eddy current loss,

• Hysteresis loss – rate of change of energy used to affect magnetic domain wall motion,

• Eddy-current loss (macro eddy currents) is due to induced currents flowing in closed paths within magnetic material,

• Anomalous loss (micro eddy currents) eddy current loss due to magnetic domain wall motion


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Core losses

• Specific losses approach– Calculate Bm(x,y,z)– Estimate pfe(Bm,freq)

• Loss formulas approach– Calculate B(x,y,z,t)– Model (Steinmetz)

pfe=ChBhf+CeB2f2+CaB1.5f1.5

– Estimate pfe(B(t))

• Simultaneous electromagnetic and material modeling

0 0.5 1 1.5 20

1000

2000

3000

4000

5000

6000

7000

flux density B, [T]

rela

tive

mag

net

ic p

erm

eab

ility

μ, [-

] M 330 - 50 AM 530 - 50 A

0 0.5 1 1.5 20

1

2

3

4

5

6

7

8

spe

cific

loss

es

p c, [W

/kg

]

M 330 - 50 AM 530 - 50 A


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Reduction of losses

• Electric conductor: reduce ρ(ϑ), reduce eddy current effects (Litz wire, transposing, twisting, etc), reduce current loading (bigger slot for the same magneto-motive force)

• Magnetic conductor: Increase ρ(ϑ), reduce the cross section area of electric conductor (thinner lamination, iron powder, etc), reduce magnetic loading


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Magnetic circuit (A)• Loaded transformer

– Source flux φ1,

– Linked flux φ2,

– Leakage flux φσ,

Gμ1 Gμσ Gμ2

φ2

φ1

i1N1

u1 u2

i2N2


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Magnetic circuit (B)• Short-circuited ideal

transformer – R2=0Ω

– Ψ2=0Vs

– Lσ= Ψ1/i1

• Short-circuited ideal transformer– R2≠0Ω

– Ψ2=- Ψ20

Gμ1 Gμσ Gμ2

φ2

φ1

i1N1

u1

i2N2


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Electric circuit (A)

• Complete equivalent circuit for a transformer


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Electric circuit (B)

• Simplified equivalent circuit


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Summary

• The model of a transformer can be established either by starting from power transfer or power conditioning requirement

• It is important to get a good understanding in physics before formulating the problem in (advanced) mathematics

Optimization



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Construction of a transformer

• Intercoupled circuits: Electrical, magnetic and thermal


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Parameterisation of construction

• Length of transformer (Ltr), thickness of insulation (ins) and the geometrical proportions fully describes the construction


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Maximized cross-sections (A)

• The largest available cross-section area of electric and the magnetic ‘conductor’

( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟

⎟⎠

⎞⎜⎜⎝

⎛ −−

−==

p

sTHH

p

sTWW

pHW

sslfttr

tr

meptr N

kkk

N

kkk

Nkk

kkkkkl

V

AAkl

112

0.25 0.5 1 2 4 8

relative transformer width, kW

[-]

core type

00

0

2

2

2

2

22

24

4

4

4

46

6

6

8

8

101012

14

0.25 0.5 1 2 4 80.25

0.5

1

2

4

8


[-]

rela

tive

tra

nsfo

rme

r he

ight

, kH

[-]

shell type

0 0

22

22

2

2

2

4

4

4

4

4

6

6

68

8

10

10

1214


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Maximized cross-sections (B)

• The largest available cross-section area of electric and the magnetic ‘conductor’


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Power density of transformer

• Apparent power

• Transformed power density

memmmm AAJBIUS ω2

1

2

1==

ptrmmtr

klJBV

S ω2

1=


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Temperature rise in ‘conductor’• Plate

• Cylinder

• Temperature rise

d/2

Q=0

Q=0

ϑ=ϑs

ϑ=ϑs

q,λ

0.5dmin

0.5dmax

( ) ( ) ( )22

2xx

qxx s

xs −⋅+=

λϑϑ

( ) ( ) ( )22

4rr

qrr s

rs −⋅+=

λϑϑ

42

2d

k

q

gλϑ =Δ


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Minimal temperature rise

• According to the same loss density (W/m3) and thermal conductivity (W/mK)

0.25 0.5 1 2 4 8


[-]

core type

00

0

2

2

2

22

4

4

4

44

6

6

6

8

8

10

10

1214

16

0.25 0.5 1 2 4 80.25

0.5

1

2

4

8


[-]

rela

tive

tra

nsfo

rme

r he

ight

, kH

[-]

shell type

0 02 2

2

2

44

4

4

4

6

6

6

8

8 1010

12

14

16


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Optimization example

• Find maximum power transfer for a given geometry of a transformer

• Use Matlab

1

23

5

4

6

9

7

10 11

12

8

12

3

4

5

6

7

89

10

11

12 13

14 15

16


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Summary

• The example of the objective function of a transformer is rather established according to power transfer requirement and leaving the power conditioning requirement for the completion

ptc slides 1 - ttu.ee · during the preparations students will add to their knowledge-base in the...

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