inductor design 2 - Purdue University

E-Core Inductor Design

S.D. Sudhoff

Spring 2005

Spring 2005 EE631 2

A Design Approach

Spring 2005 EE631 3

Genetic Algorithms in a Nutshell

• Probabilistic Optimization Technique• Loosely Based in Principals of Genetics• First Developed By Holland, Late 60’s –

Early 70’s• Does Not Require Gradients or Hessians• Does Not Require Initial Guess• Operates on a Population

Spring 2005 EE631 4

A Gene As A Parameter

• Biological SystemsEach Gene Has Value From Alphabet {AT,GC,CG,AT} from Nitrogenous Adenine, Guanine, Thymine, CytosineEach Gene is Located on One of a Number of ChromosomesChromosomes May Be Haploid, Diploid, Polyploid

• Canonical Genetic AlgorithmEach Gene Has a Value From Alphabet (Normally Binary {0,1})Each Gene is Located on a Chromosome (Normally 1)Chromosomes Generally Haploid

• Non-Encoded Genetic Algorithms (GOSET)Each Gene Has A Range (Minimum Value, Maximum Value)Each Gene Has A Type (Mapping)

• Integer• Linearly Mapped Real Number• Logarithmically Mapped Real Number• Power Mapped Real Number

Each Gene is Located on One of a Number of ChromosomesChromosomes Are Haploid

Spring 2005 EE631 5

An Individual in GOSET

• A Collection of Genes on Chromosomes

• Fitness (Measures of Goodness)

• Region

Gene 1

Gene 2

Gene 3

Gene 4

Gene 5

Gene 6

Gene 7

Gene 8

Gene 9

Gene 10

Gene 11

Gene 12

Chromosome 1

Chromosome 2

Chromosome 3[ ]TNfff 21=f

Spring 2005 EE631 6

A Population In GOSET

iF

iFiF iF

iF

iFiF

Region 1

iF

iF

iF

iF

iF

iF

Region 2

iF iFiF

iF iF

iF

Region 3

Spring 2005 EE631 7

Evolution in GOSET

START

Initialization

Diversity Control

Scaling

Crossover

Mutation

Migration

Fitness evaluation

Elitism

Random search

END

STOP?

Randomly change somegenes in a chromosome

Report plot

Preservebest chromosomes

Prevent crowingin a specific region

Determine the scaledfitness

Move chromosomes fromone retion to another

Search the vincinity ofthe best chromosome

Draw report plots

Prepareinitial population

Evaluate the fitnessvalues of chromosomes

Exchanges genesbetween chromsomes

gap_defaultgainit unrndinitdownsize

mutate

elitism

divcon

scale

migrate

randsearch

reportplotdistplotparetoplot

evaluate

matingcrossover

Post-processing updatestat

Pre-processing Update objectiveweighting vector objwght

Selection Select chromosomesfor reproduction select

Update statistics

START

Initialization

Crossover

Mutation

Fitness evaluation

END

STOP?

Selection

Spring 2005 EE631 8

Example Operator:Single Point Crossover

Gene 1

Gene 2

Gene 3

Gene 4

Gene 5

Gene 1

Gene 2

Gene 3

Gene 4

Gene 5

Gene 1

Gene 2

Gene 3

Gene 4

Gene 5

Parent 1

Gene 1

Gene 2

Gene 3

Gene 4

Gene 5

Parent 2 Child 1 Child 2

Spring 2005 EE631 9

Advantages of Evolutionary Design

• Can Treat Large Unfriendly Search Space• Readily Automated• Does Not Require Same Degree of Model

SimplificationDesign Problem Formulated as Analysis Problem (Inversion Not Necessary)Readily Incorporate Domain Specific Knowledge

Spring 2005 EE631 10

Our Problem

• Parameter Vector

• Optimization

⎪⎩

⎪⎨⎧

≥+

<−++++=

=

1115

),,,,min(

54321

54321

cv

ccccccf

cccccc

ε

[ ]twwwiwdss wNdfffwffwdgxxf

uceww=

)(maximize


GOSET


Design Codes

• See inductor_fit.m

• See inductor_design.m


Evolution of Inductor Design

0 50 100 150 200 250 300 350 400 450 500-500

0

500

1000

1500

2000

2500

generation

fitne

ss

Fitness Versus Gopulation

best

mean

median


Final Gene Distribution

1 2 3 4 5 6 7 8 9 10 11 120

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Parameter Number

Nor

mal

ized

Val

ue

Final Chromosome Distribution


Design Summary

• Air Gap: 0.084207 mm• Slot Depth: 2.1996 cm• Slot Width: 0.85553 cm• Winding Depth: 2.1994 cm• Winding Width: 0.85552 cm• I-Core Width: 1.2824 cm• E-Core Width (Ends): 1.2081 cm• E-Core Width (Center): 2.4337 cm• E-Core Width (Bottom): 1.2217 cm• Core Depth: 13.289 cm

• Number of Turns: 16• Wire Type: 3• Overall Height: 4.7121 cm• Overall Width: 6.5609 cm• Overall Depth: 15 cm• Fitness: 2156.3908 m^-3• Constraints: 1 1 1 1 1• Incremental Inductance: 5 mH• Winding Resistance: 0.097955• Packing Factor: 0.7• Volume: 463.7378 cm^3


Flux Linkage Versus Currentof Final Design

0 0.5 1 1.5 2 2.5 3 3.5 40

0.005

0.01

0.015

0.02

0.025

Current, A

Flux

Lin

kage

, Vs


Comments on Speed

inductor design 2 - Purdue University

Documents

Transcript of inductor design 2 - Purdue University