New Method for Electrical Machine Design and Optimization · New Method for Electrical Machine Design and Optimization Yao Duan and Dan M. Ionel Vestas Technology R&D Americas, Inc

New Method for Electrical Machine Design and Optimization

Yao Duan and Dan M. Ionel Vestas Technology R&D Americas, Inc.

ANSYS User Conference, September 2011

2 | ANSYS Conference, September 2011

Outline

• Introduction

• Ultra-Fast FEA Method

• Review and Comparison of Design Optimization Methods

• Conclusion.


Introduction

Background

• Challenges in Machine Design Optimization: nonlinear, computationally-intensive, large number of design input variables, multi-objective, complicated trade-offs

• Significant progress in the last decade, including machine performance calculation and optimization methods.

Focus

• A novel ultra-fast FEA method

• An update-to-date review and comparison of optimization algorithms

• Use of Design Explorer environment for machine design optimization.

Problem formulation

•Select machine type, materials, basic configuration

•Define design input variables

•Define design constraints

•Define design objectives

Performance calculation

•Direct calculation: analytical, FEA, MEC, etc.

•Surrogate

•Challenge: Reduce computational effort without sacrificing accuracy

Optimization

•Deterministic

•Stochastic

•Challenge: finds the global optimal solution(s) with minimum evaluation of candidates

Decision Making

•Optimal design selection

•Detailed FEA


Ultra-Fast FEA – Concept [1]

• Objective: approximate the electromagnetic field at balanced steady state operation through a few magnetostatic FEA solutions

• Three magnetostatic FEA solutions at three rotor positions: 0o, 20o, 40o

• Flux linkage for phase R: Φ𝑅+𝑅− = 𝐴𝑅+ − 𝐴𝑅− (A: vector potential)

• Symmetry of balanced three phase operation

• Valid for both no load and on load conditions

𝐴𝑅+ 𝜃 = 𝐴𝑅+ 𝜃

𝐴𝑅+ 𝜃 + 60𝑜 = −𝐴𝑌+ 𝜃

𝐴𝑅+ 𝜃 + 120𝑜 = 𝐴𝐵+ 𝜃

𝜃 = 0𝑜, 20𝑜, 40𝑜(𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑎𝑙 𝑑𝑒𝑔𝑟𝑒𝑒)

Ref.: Io

nel, D

.M. a

nd P

opescu, M

., “Fin

ite-E

lem

ent S

urro

gate

Model fo

r Ele

ctric

Machin

es W

ith R

evolv

ing

Fie

ld—

Applic

atio

n to

IPM

Moto

rs” , In

dustry

Applic

atio

ns, IE

EE

Tra

nsactio

ns o

n, N

ov-D

ec 2

010



Vector potential of R+ Vector potential of R- Three Magnetostatic

FEA

Symmetry

between

phases

9 solution points of Φ over 180o

Half wave

symmetry

18 solution points of Φ over 360o

Fourier

Analysis

Flux linkage Φ waveform up to 7th

harmonic

Ref.: Io

nel, D

.M. a

nd P

opescu, M

., “Fin

ite-E

lem

ent S

urro

gate

Model fo

r Ele

ctric

Machin

es W

ith R

evolv

ing F

ield

—A

pplic

atio

n

to IP

M M

oto

rs” , In

dustry

Applic

atio

ns, IE

EE

Tra

nsactio

ns o

n,

Nov-D

ec 2

010



• Same concept is used to calculate flux density in stator tooth and yoke – core loss

Flux linkage Φ

waveform up to 7th harmonic

Stator current input

Electromagnetic Torque up to 6th

ripple

Back EMF waveform up to 7th harmonic

Power factor

Output power

Torque Ripple

Cogging

Torque

Flux density in tooth and core

Core Loss

Efficiency

0 0.005 0.01 0.015 0.020

500

1000

1500

2000

2500

3000

time(s)

Co

re loss(W

)

Core loss

Fast FEA

Transient

0 50 100 150 200 250 300 350190

195

200

205

210

215

220

225Electromagnetic Torque

theta(electrical degree)

Torq

ue

(N

m)

Fast FEA

Transient FEA

Avg. Error < 1%


Ultra-Fast FEA – Advantage and Implementation

Matlab

VBscript Maxwell

Optimization Algorithm

Strong scripting capability

Parametrized environment

Automatic meshing

Analytical calculation

Transient FEA

Ultra-fast FEA

Accuracy Low, difficult to model saturation

High Satisfactory

Typical computation Time

< 1 seconds 10 minutes 30 seconds

A powerful machine modeling tool for machine design optimization!


What Is Not Included in the Ultra-Fast FEA? Why is time-stepping (transient) FEA still needed?

• PM loss

• Eddy currents in conductors

• Current regulation in unconventional controllers (which may require Simplorer)

• Motor-drive-controller simulations

• Fault conditions

• Unbalanced operation

• Machine asymmetries, for example due to tolerances, e.g. air-gap eccentricity

• More detailed space (i.e. multiple points) and time (e.g. PWM switching) info for core losses.


Optimization Overview Problem formulation

•Define design input variables

•Define design objectives

Performance calculation

•Direct calculation: analytical, FEA, MEC, etc.

•Surrogate

•Challenge: Reduce computational effort without sacrificing accuracy

Optimization

•Deterministic

•Stochastic

•Challenge: finds the global optimal solution(s) with minimum evaluation of candidates

Decision Making

•Optimal design selection

•Detailed FEA

• More efficient performance calculation method – Ultra-Fast FEA

• Surrogate – Response Surface, etc.

• Identify optimization algorithms most suitable for machine design


Optimization Method Review - Surrogate Models

• Objective: approximate the input-output relationship by a computationally-efficient model

• Popular approaches:

• Design space reduction

• Response surface


Design Space Reduction – Statistical Screening

• Different statistical measures and approaches

• Analysis of Variance or Correlation

• Multi-regression

• Linear Correlation Analysis

Quadratic Regression

Example Sensitivity Study of Efficiency with design input parameters

for a 1 HP, 1050 rpm BLDC motor

(11 parameters, <200 candidates calculated)

Br

cov

Bso

hm Byks

skew

g Tw Hs0 Hs1 Rs

Br

cov

skew g Bso


Response Surface

• DoE: systematical sample generation

• Full factorial design

• Central Composite design

• Box-Behnken design

• Approximation functions

• 2nd Polynomial

• Kriging function

• Neural Network

Create approximation of output based on DoE results

Design of Experiments (DoE)

Define problem input/output

An example 12-parameter 4-level Central Composite design


Search Algorithms

• Single-objective: scalar-valued fitness function

• Deterministic methods

• Stochastic methods

• Genetic Algorithms

• Simulated Annealing

• Particle Swarm Optimization

• Differential Evolution

• Other methods: climbing terrain, bacterial forging, etc.

• Multi-objective: vector-valued fitness function

• Multi-Objective GA

• Multi-Objective PSO

• Multi-Objective DE

• Design of Experiments

• Other methods


Comparison of search algorithms

DE: Differential Evolution

Results of Contest on Evolution Computation


Benchmark Study [1]

• Benchmark study problem

• multi-objective design optimization of a 200 kW, 3600 rpm, Surface-Mount PM machine.

• Optimization methods compared

• Differential Evolution and Response surface

Five Independent Design Variables

Two Design objectives

W= 𝑘𝑚𝑊𝑚+𝑘𝑡𝑊𝑡

G= 𝑇𝑚

𝑃𝑙𝑜𝑠𝑠

𝐷/2

𝑙𝑚

𝑐𝑜𝑣

𝐵𝑡

𝐿𝑠𝑡

• Direct search – reference

• 7 incremental steps for each design variable

• 16,807 candidates evaluated


Benchmark Study [2]

Response surface-Second-order polynomial fitting

𝑓 𝑥 = 𝑐0 + 𝑐𝑘𝑥𝑘

𝑛

𝑘=1

+ 𝑐𝑘𝑗𝑥𝑘𝑥𝑗

𝑛

𝑗=𝑘+1

𝑛

𝑘=1

+ 𝑐𝑘𝑘𝑥𝑘2, 𝑛 = 5

𝑛

𝑘=1

0.6 0.7 0.8 0.9 16

8

10

12

1411

11.5

12

covhm(mm)

Go

od

ne

ss f

unction

(Nm

/W0

.5)

0.6 0.7 0.8 0.9 16

8

10

12

1411

11.5

12

covhm(mm)

Go

od

ne

ss f

unction

(Nm

/W0

.5)

Variation of Goodness function as design variables

Actual RS fitted Errors


Benchmark Study [3]

• Pareto front

150 200 25011

11.2

11.4

11.6

11.8

12

Weight function (kg)

Go

od

ne

ss f

unction

(N

m/W

0.5

)

Direct Search

DE2200

DE1024

DE240

DE45

RS1024

RS243

RS46

DE Population Iteration Selected for DE operation

45 15 5 7

240 40 15 15

1024 64 30 30

2200 100 25 80

RS Description

46 3-level Box-Behnken

243 3-level full factorial

1024 4-level Full Factorial


Benchmark Study [4]

• Comparison of DE and RS

RS-46 RS-243 RS-1024 DE-45 DE-240 DE-440 DE-1024DE-22000

0.2

0.4

0.6

0.8

1

Optimization Methods

No

rma

lized

Hype

rvo

lum

e

150 200 25011

11.2

11.4

11.6

11.8

12

Weight function (kg)

Go

od

ne

ss f

unction

(N

m/W

0.5

)

Direct Search

DE2200

DE1024

DE240

DE45

RS1024

RS243

RS46

No. of candidates

Comparison Result

Small Comparable

Medium DE better

Large DE better RS does not converge


Benchmark Study [5]

• Design space with higher dimension – 11 variables

• Benchmark function “SYMART” from the 2007 Contest on Evolution Computation

Method DE RS

No. of Candidates 180 20,100 188 177,147

Normalized Hypervolume

0.54 0.9 0.38 0.9


Optimal Design – Sensitivity and Six-Sigma Analysis

• Example study: Cogging torque vs Design input parameters

Br cov

Bso

skew

g Tw

Hs0 Hs1

Rs

hm Byks

Defects


Conclusion

• An ultra-fast FEA method has been developed to significantly reduce the computational effort while ensuring accuracy

• A review of the optimization methods over the last decade reveals a potential shift from Response Surface to Computational Intelligence methods

• An electrical machine design and optimization toolset for industrial applications was presented.

Problem formulation

• Define input variables, constraints, and objectives

Statistical screening

• Screen out insignificant input variables

DE Optimization with ultra-fast FEA

• Find the optimal design/Pareto front

Decision making

• Detail FEA on the optimal design

• Sensitivity/Six Sigma analysis

Design Explorer Maxwell/RMxprt

Maxwell VBscripting Matlab

Maxwell Design Explorer

Copyright Notice

The documents are created by Vestas Wind Systems A/S and contain copyrighted material, trademarks, and other proprietary information. All rights reserved. No part of the documents may be reproduced or copied in any form or by any

means - such as graphic, electronic, or mechanical, including photocopying, taping, or information storage and retrieval systems without the prior written permission of Vestas Wind Systems A/S. The use of these documents by you, or

anyone else authorized by you, is prohibited unless specifically permitted by Vestas Wind Systems A/S. You may not alter or remove any trademark, copyright or other notice from the documents. The documents are provided “as is” and

Vestas Wind Systems A/S shall not have any responsibility or liability whatsoever for the results of use of the documents by you.

Thank you for your attention

Documents

New Method for Electrical Machine Design and Optimization · New Method for Electrical Machine Design and Optimization Yao Duan and Dan M. Ionel Vestas Technology R&D Americas, Inc