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.
3 | ANSYS Conference, September 2011
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
4 | ANSYS Conference, September 2011
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
5 | ANSYS Conference, September 2011
Ultra-Fast FEA – Concept [2]
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
6 | ANSYS Conference, September 2011
Ultra-Fast FEA – Concept [3]
• 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%
7 | ANSYS Conference, September 2011
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!
8 | ANSYS Conference, September 2011
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.
9 | ANSYS Conference, September 2011
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
10 | ANSYS Conference, September 2011
Optimization Method Review - Surrogate Models
• Objective: approximate the input-output relationship by a computationally-efficient model
• Popular approaches:
• Design space reduction
• Response surface
11 | ANSYS Conference, September 2011
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
12 | ANSYS Conference, September 2011
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
13 | ANSYS Conference, September 2011
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
14 | ANSYS Conference, September 2011
Comparison of search algorithms
DE: Differential Evolution
Results of Contest on Evolution Computation
15 | ANSYS Conference, September 2011
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
16 | ANSYS Conference, September 2011
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
17 | ANSYS Conference, September 2011
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
18 | ANSYS Conference, September 2011
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
19 | ANSYS Conference, September 2011
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
20 | ANSYS Conference, September 2011
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
21 | ANSYS Conference, September 2011
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