Chicago UGM-8_ANSYS Conference - 08292011

2011 ANSYS, Inc. November 23, 2014

1

Scripting in Maxwell 2D for Computationally Efficient FEA with Optimization Algorithms

Gennadi Sizov and Peng Zhang

Marquette University Electrical and Computer Engineering

advisors: Professors Demerdash and Ionel


2

Introduction Model-based optimization

difficulties choice of a modeling approach

Computationally Efficient Finite Element Analysis (CEFEA) Electric circuit symmetry

vector potentials, flux linkages, induced voltages

Magnetic circuit symmetry core loss calculation

Torque calculation

Design Optimization Objective function selection (single weighted

function vs. multi-objective) Optimization algorithm

Differential Evolution

Optimization of 9-slot, 6-pole IPM Motor Design objectives Optimization study (10,000 candidate designs)

eleven independent stator and rotor variables

significant design improvements are achieved

Scripting Maxwell 2D RMxprt geometric primitives Simple interfacing of Maxwell 2D to Matlab Optimization of Toyota Prius IPM motor

Overview


3

Model-based optimization of electric machinery Difficulties:

Complex geometries (large number of geometric variables) Nonlinear material properties Multi-domain (physics) modeling (electromagnetic, thermal, stress, etc.) Multiple design objectives Population based design is problematic Search of large design spaces

Choice of modeling approach Tradeoffs

Speed vs. Accuracy Analytic/Lumped Parameter (MEC) vs. FEA

Computationally Efficient FEA [Trans. on IA 2010/2011, ECCE 2010, IEMDC 2011] Fast simulation of synchronous machinery Accurately estimates EMFs, average torques, cogging torque, on-load torque ripple, and

core losses.

Introduction


4

Maximum Torque per Ampere MTPA Optimum operating point depends on design

variables Every design requires additional model evaluations increasing computational time

Field Weakening Operation Depends on design variables. Requires further design evaluations increasing computational time Computational savings are possible by employing

solutions from MTPA search

Difficulties in Optimization of Interior-PM Machines

0

5

10

15

20

0 30 60 90 120 150 180

Ave

rage

torq

ue [N

m]

Torque angle, [deg. el.]

0

0.25

0.5

0.75

1

1.25

0 1 2 3 4 5 6

Torq

ue [p

u]

Speed [pu]

Field Weakening Operation

Maximum Torque per Ampere MTPA

MTPA

MTPA


5

10,000 designs in less than 51 hours! 6 static FE solutions (20 seconds/per design) CE-FEA (seconds) vs. time-stepping FE (minutes) several days vs. months! large scale FEA-based optimization studies

The fundamentals of CE-FEA fully exploits symmetries of electric and

magnetic circuits to reduce simulation time minimum number of magnetostatic solutions,

correlated with the maximum order of significant field harmonics

one-to-two orders of magnitude reduction of simulation time

suitable for most types of synchronous machines.

Computationally Efficient Finite Element Analysis (CEFEA)

5 10 15 20 250

5

10

15

20

25

30

35

Shaft Torque [Nm]

Torq

ue R

ippl

e [%

]

Goo

dnes

s [N

m/s

qrt(W

loss

)]

0.4

0.5

0.6

0.7

0.8

0.9

1


6

What is not included in CE-FEA?

Why is time-stepping (transient) FEA still needed? PM loss Eddy currents in conductors Current regulation in unconventional controllers (which may

require coupled simulations with 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



7

CE-FEA is applicable to design and analysis of both surface-PM and interior-PM machines.

Assumptions: Machine model is excited by instantaneous values of a set of

balanced three-phase sinusoidal currents. Assumption is well justified in motor-drive systems with well tuned

current regulators.

Principle: 2-D magnetostatic finite element formulation is utilized:

Instantaneous values of rotor position, mech, phase currents, iR, iY, iB,

are inputs to the model and the magnetic vector potentials (MVPs), A, are the outputs used in the post-processing stage to extract flux-densities, flux-linkages, energies (energy/co-energy).


PMJJyA

yxA

x=

+

11

Determination of number of solutions and rotor positions

FEA 2-D (static)

Post Processing: Flux linkages, emfs Flux densities Energies (energy/co-energy) Torques Losses

mechiR ()

A

iY () iB ()

CE FEA


8

Principle (flux linkages and back emfs): Symmetry of electric circuit results in the following:

where, A, is the average MVP in the coil side. Similar expressions can be developed for all the other coil sides.

From the coil side MVPs tooth fluxes, , and phase flux linkages, , can be estimated as follows:

where, lFe, is the effective stack length and, Nph, is the number of series turns per phase.


( ) ( ) ++ =+ YoR AA 60( ) ( ) ++ =+ BoR AA 120

( ) ( ) ( )( ) + = RRFeR AAl

( ) ( ) RphR N =

AY+

AB+

AR+

AR-

AR+

R


9

Principle (flux linkages and back emfs):

Flux linkages, , can be written in Fourier series form as:

Accordingly, resulting back emfs, e, can be written in Fourier series form as:

Here, the maximum harmonic order, vM, is related to the number of magnetostatic FE solutions, s, as follows:

Note: due to aliasing, the minimum number of FE solutions is limited by the highest harmonic present in the flux linkage waveform.


( ) ( )=

+=M

R

1cos

13 = sM

( ) ( )=

+==M

dtd

dde RR

1sin


10

( ) ( ) ++ =+ YoR AA 60( ) ( ) ++ =+ BoR AA 120

Principle (flux linkages and back emfs): Coil side MVP, AR+

-0.0100

-0.0080

-0.0060

-0.0040

-0.0020

0.0000

0.0020

0.0040

0.0060

0.0080

0.0100

0 20 40 60 80 100 120 140 160 180

[Wb/

m]

[deg. el.]

R+

Y+

B+

-0.01

-0.008

-0.006

-0.004

-0.002

1.2E-17

0.002

0.004

0.006

0.008

0.01

0 20 40 60 80 100 120 140 160 180

[Wb/

m]

[deg. el.]

R+

Y+

B+

-0.0100

-0.0080

-0.0060

-0.0040

-0.0020

0.0000

0.0020

0.0040

0.0060

0.0080

0.0100

0 20 40 60 80 100 120 140 160 180

[Wb/

m]

[deg. el.]

R+

Y+

B+


Five magnetostatic FE solutions

AY+

AB+

AR+

R

One magnetostatic FE solution


11

Principle (flux linkages and back emfs): Coil side MVP, AR+ 5 - solutions Assuming lack of even order harmonics (half-wave symmetry)


Five magnetostatic FE solutions

-0.0100-0.0080-0.0060-0.0040-0.00200.00000.00200.00400.00600.00800.0100

0 60 120 180 240 300 360

[Wb/

m]

[deg.el.]

Single magnetostatic FE solution yields six equally spaced points on MVP waveform! Using five static FE solutions yeilds thirty samples of MVP Flux EMF!


12

Principle (flux linkages and back emfs):

Selection of the number of static solutions Has to be chosen to avoid aliasing in Fourier series Example 9-slot, 6-pole IPM with 5-static FE solutions (no aliasing) Spectrum of back emf, eR Rated-load, 3600 r/min


0255075

100125150175200225250

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

EM

F H

arm

onic

Mag

nitu

de, |

e a| [

V]

Harmonic Order

Estimated from 5 solutions

No significant harmonic content

beyond 13th order

no aliasing


13

Principle (flux linkages and back emfs): Verification (5-solutions): With respect to time-stepping FE Phase flux-linkage, R, and back emf, eR Open-Circuit, 3600 r/min


( ) ( )=

+=M

R

1cos ( ) ( )

=

+==M

dtd

dde RR

1sin

-300

-200

-100

0

100

200

300

0.00 2.78 5.56 8.33 11.11 13.89 16.67Time, [ms]

EMF,

eR

, [V]

-300

-200

-100

0

100

200

3000 60 120 180 240 300 360

Rotor Position, [el. deg.]

TSFEeq. (3)

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.00 2.78 5.56 8.33 11.11 13.89 16.67Time, [ms]

Flux

Lin

kage

, R

, [W

b]

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.20 60 120 180 240 300 360


TSFEeq. (2)


14

Principle (flux linkages and back emfs): Verification (5-solutions): With respect to time-stepping FE Phase flux-linkage, R, and back emf, eR Rated-load, 3600 r/min


( ) ( )=

+=M

R

1cos ( ) ( )

=

+==M

dtd

dde RR

1sin

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.20 60 120 180 240 300 360

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.00 0.93 1.85 2.78 3.70 4.63 5.56

Rotor Position [deg. el.]

Flux

Lin

kage

, a

[Wb]

Time [ms]

TSFESamples (5 solutions)eq. (2)

-300

-200

-100

0

100

200

3000 60 120 180 240 300 360

-300

-200

-100

0

100

200

300

0.00 0.93 1.85 2.78 3.70 4.63 5.56

Rotor Position [el. deg.]

Indu

ced

Vol

tage

, ea

[V]

Time [ms]

TSFEeq. (3)


15

Principle (stator core flux densities): Magnetic circuit symmetry

Symmetry of magnetic circuit [PAS 1981, IAS 2011] results in the following relationships for elemental radial and tangential components of stator core flux-densities at different rotor positions:

where, k, is a positive integer, s, is the slot-pitch in electrical measure.


( )strstr krtBrktB

+=

+ ,,,, ,,


16

Principle (stator core flux densities): Magnetic circuit symmetry

Using the same magnetostatic solutions used for estimation of flux-linkages and back emfs and assuming the lack of even order harmonics (half-wave symmetry), Fourier series of elemental flux densities can be created:

Radial and tangential components of elemental flux densities will be used for estimation of stator core losses (efficiency).


-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 60 120 180 240 300 360

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0.00 2.78 5.56 8.33 11.11 13.89 16.67


Flux

Den

sity,

[T]

Time, [ms]

s 2s

e1

e2

e3

( ) ( )=

+=M

BB tr

1, cos


17

Principle (stator core flux densities): Magnetic circuit symmetry Verification (5-solutions):

With respect to time-stepping FE Flux densities at locations: 1, 2 Full-load, 3600 r/min


Location 1 (Yoke) Location 2 (Tooth-Yoke Junction)

-2

-1.5

-1

-0.5

0

0.5

1

1.5

20 60 120 180 240 300 360

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0.00 0.93 1.85 2.78 3.70 4.63 5.56


Flux

Den

sity

[T]

Time [ms]

B r TSFE magnify x10B r eq. (11) magnify x10B t TSFEB t eq. (11)

-2

-1.5

-1

-0.5

0

0.5

1

1.5

20 60 120 180 240 300 360

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0.00 0.93 1.85 2.78 3.70 4.63 5.56


Flux

Den

sity

[T]

Time [ms]

B r TSFE B t TSFEB r eq. (11) B t eq. (11)

4

3

2

1


18

Principle (stator core flux densities): Magnetic circuit symmetry Verification (5-solutions):

With respect to time-stepping FE Flux densities at locations: 1, 2 Full-load, 3600 r/min


Location 3 (Tooth) Location 4 (Tooth Tip)

-2.5-2-1.5-1-0.500.511.522.5

0 60 120 180 240 300 360

-2.5-2

-1.5-1

-0.50

0.51

1.52

2.5

0.00 0.93 1.85 2.78 3.70 4.63 5.56


Flux

Den

sity

[T]

Time [ms]

B r TSFEB t TSFE magnify x10B r eq. (11)B t eq. (11) magnify x10

-2.5-2-1.5-1-0.500.511.522.5

0 60 120 180 240 300 360

-2.5-2

-1.5-1

-0.50

0.51

1.52

2.5

0.00 0.93 1.85 2.78 3.70 4.63 5.56


Flux

Den

sity

[T]

Time [ms]

B r TSFE B t TSFEB r eq. (11) B t eq. (11)

4

3

2

1


19

( ) ( )=

+=W

mcogmstored N

1

cosWW

( )=

+=W

mcogcogm

stored NNd

d

1

sin WW

Principle (torque calculation): Creating a Fourier series of the energy stored in the magnetic circuit:

Taking the derivative:

Using flux-linkages obtained earlier the electromagnetic torque can be estimated using the following expression:


( ) ( ) ( ) ( )( ) ( ) ( )( )

( )

=

===

++

+++++=

++=

W

MMM

mech

oB

oYR

mech

storedBB

YY

RRem

W

iiiP

ddW

ddi

ddi

ddiPT

1

111

sin

240sin120sinsin2

2

alignment and reluctance cogging


20

Principle (torque calculation): Cogging torque With respect to time-stepping FE Open-circuit, 3600 r/min


16.7

16.8

16.9

17

17.1

17.2

17.3

17.40 10 20 30 40 50 60

-3-2.5

-2-1.5

-1-0.5

00.5

11.5

22.5

3

0 10 20 30 40 50 60

Stored E

nergy [J]

Cog

ging

Tor

que

[Nm

]


Cogging - TSFE Cogging - eq. (8)Energy (5 solutions) Energy - eq. (5)


21

Principle (torque calculation): On-load With respect to time-stepping FE Electromagnetic torque Open-circuit, half-load, rated-load (3600 r/min)


-5

0

5

10

15

200 60 120 180 240 300 360

-5

0

5

10

15

20

0 60 120 180 240 300 360

Torq

ue [N

m]


eq. (8)TSFE


22

Principle (torque calculation):

Average torque calculation Error in estimation of the average torque as a function of number of static FE

solutions. Compared to TSFE (based on Maxwell Stress Tensor)


-1-0.5

00.5

11.5

22.5

33.5

44.5

55.5

1 2 3 4 5 6 7 8 9 10

Ave

rage

torq

ue e

stim

atio

n er

ror [

%]

Number of magnetostatic FE solutions, s


23

Model-based optimization: Conflicting requirements on the modeling approach used for optimization

(accuracy vs. execution time). Need for search of very large design spaces to find optimum design. Large number of design variables (geometry, materials, etc.) CE-FEA can be used for fast and accurate evaluation of very large number of

candidate designs.

Design Optimization


24

Objective function selection: Single weighted objective function:

Pros: simple implementation Cons: choice of weights, wn, conflicting vs. non-conflicting objectives

Multi-Objective (Pareto-based Optimization)

Pros: meaningfully accounts for tradeoffs between multiple design goals, no weights, results in a family of best compromise designs

Cons: implementation

Design Optimization

=

=N

nnn fwf

11 )(x

FeCu

em

pkpk( em

PPT

f :maximize

Tf :minimize

+=

=

2

)1 min(Torque Ripple)

max(Goodness) measure of average electromagnetic torque with respect to total losses


25

][ qPPMPMTTSSTSi w, ,h , w, ,d ,d ,l , wg, ,D =x

9-slot, 6-pole IPM: 11 geometric variables

Only outer diameter is fixed 7Arms/mm2, 0.3 slot fill factor Search of MTPA for every design

Optimization of 9-slot, 6-pole IPM Motor


26

Optimization results: Generations = 100, Population = 100 Total of 10,000 candidate design evaluations

51 hours on a single core (single license) Search of maximum torque per amp (MTPA ) for every design


M-1

M-2 M-3

Typ

M-1: High Specific Torque

M-2: Compromise between Specific Torque and Ripple

M-3: Low Ripple

Typ: Machine of Normal Proportions


27

Optimized machines:


M-1: High Specific Torque

M-2: Compromise Specific Torque and Ripple

M-3: Low Ripple

Typ: Machine of Normal Proportions

max. Bmid-tooth = 1.75T, min. BPM = 0.76T





28

Electromagnetic Torque at Rated-Load (MTPA): Verified with time-stepping FEA (2nd order elements)


14

15

16

17

18

19

20

21

22

0 10 20 30 40 50 60

Elec

tro m

agne

tic to

rque

[Nm

]

Position [deg. el.]

M-1 Tem = 20.84Nm, Ripple = 4.93%

M-2 Tem = 18.55Nm, Ripple = 2.72%

M-3 Tem = 15.79Nm, Ripple = 0.45%

Typ Tem = 15.21Nm, Ripple = 10.64%


29

Electromagnetic Torque at Open-Circuit (Cogging): Verified with time-stepping FEA (2nd order elements)


-1.00

-0.75

-0.50

-0.25

0.00

0.25

0.50

0.75

1.00

0 10 20 30 40 50 60

Elec

tro m

agne

tic to

rque

[Nm

]

Position [deg. el.]

M-1 Tpk-pk = 0.41Nm M-2 Tpk-pk = 0.29Nm M-3 Tpk-pk = 0.19Nm Typ Tpk-pk = 1.87Nm


30

7.5Hp rating (15Nm, 3600 r/min) axial-length is scaled to achieve the desired rating


Axial length PM Mass

0.931.05

1.25

1.00

0

0.25

0.5

0.75

1

1.25

1.5

M-1 M-2 M-3 Typ.

PM M

ass

[pu]

0.75 0.810.92

1.00

0

0.25

0.5

0.75

1

1.25

M-1 M-2 M-3 Typ.

Tota

l Mac

hine

Mas

s [pu

]

Total Mass

0.730.82

0.96 1.00

0

0.25

0.5

0.75

1

1.25

M-1 M-2 M-3 Typ.

Axia

l Len

gth

[pu]


31

Separation of Losses 7.5Hp rating (15Nm, 3600 r/min) Equal split between copper and core losses for optimized designs


182.7 167.4 170.8 206.1

164.9 170.5 184.0167.2

050

100150200250300350

M-1 M-2 M-3 Typ.

Pow

er L

oss

[W]

Copper

Core

347.6W 337.9W 354.8W 373.3W

Note a 9.5% reduction of losses with optimized machine M-2!


32

RMxprt geometric primitives Large number of predefined parameterized

geometries: Stator slot shapes Rotor topologies (various interior-PM and

surface-PM layouts) Primitives are accessible through scripting Custom geometries can be created through low-

level primitives such as lines, arcs, etc.

Simple interfacing of Maxwell 2D to third party software Communicates to any software that uses

Common Object Module (COM) Matlab, MS Office Excel, Visual Basic, etc.

Optimization exercise for Toyota Prius IPM type motor 48-slot, 8-pole, V-shaped IPM rotor topology Three parameters:

PM width, PM length, V depth

Scripting Maxwell 2D


33

Advice/hint: Use Tools\Record Script To File to get an idea of how to write your own script!

ENABLE Record Script To File PERFORM the functions using Graphical User Interface (GUI)

THEN look at the recorded text file to get an idea how to script.

Opening Maxwell from Matlab environment Create COM object, open Maxwell, start new Maxwell 2D project, select transient

solver % Maxwell COM object: iMaxwell=actxserver('AnsoftMaxwell.MaxwellScriptInterface'); Desktop=iMaxwell.GetAppDesktop(); % remove set from the object definitions Desktop.RestoreWindow % Create project in Maxwell or open an existing project Project=Desktop.NewProject; invoke(Project,'Rename','C:\Users\labadmin\Desktop\Optimization

Project\Scripting\ANSOFT\Scripting\IPM2.mxwl',true) invoke(Project,'InsertDesign','Maxwell 2D','Design1','Transient','') Design=Project.SetActiveDesign('Design1'); invoke(Design,'SetSolutionType','Transient','XY') Editor=Design.SetActiveEditor('3D Modeler'); invoke(Editor,'SetModelUnits',{'NAME:Units Parameter','Units:=','mm','Rescale:=',false}) %

Setup units [mm]



34

Execution of Maxwell models from Matlab environment Changing Maxwell params. from Matlab

% Input parameters Imax=250; % Imax: the magnitude of phase currents Thet_deg=20; % Thet_deg: the load angle in degree, initial value: 20deg O2=7.28; % O2: Distance form duck bottom to shaft surface TM=6.48; % TM: Magnet thickness WM=32; % WM: Total width of all magnet per pole

Passing values to Maxwell using invoke/ChangeProperty commands Make sure to add units to all dimensions (using Matlabs strcat function). Also change all numerical values to strings (using Matlabs num2str function) before passing

them to Maxwell. O2S=strcat(num2str(O2),'mm');TMS=strcat(num2str(TM),'mm');WMS=strcat(num2str(WM),'mm'); % Change these 5 parameters: invoke(Design,'ChangeProperty',{'NAME:AllTabs',{'NAME:LocalVariableTab',{'NAME:PropServers','LocalVariab

les'},... {'NAME:ChangedProps',{'NAME:Imax','Value:=',num2str(Imax)}}}}) invoke(Design,'ChangeProperty',{'NAME:AllTabs',{'NAME:LocalVariableTab',{'NAME:PropServers','LocalVariab

les'},... {'NAME:ChangedProps',{'NAME:Thet_deg','Value:=',num2str(Thet_deg)}}}}) invoke(Design,'ChangeProperty',{'NAME:AllTabs',{'NAME:LocalVariableTab',{'NAME:PropServers','LocalVariab

les'},... {'NAME:ChangedProps',{'NAME:O2','Value:=',num2str(O2S)}}}}) invoke(Design,'ChangeProperty',{'NAME:AllTabs',{'NAME:LocalVariableTab',{'NAME:PropServers','LocalVariab

les'},... {'NAME:ChangedProps',{'NAME:TM','Value:=',num2str(TMS)}}}}) invoke(Design,'ChangeProperty',{'NAME:AllTabs',{'NAME:LocalVariableTab',{'NAME:PropServers','LocalVariab

les'},... {'NAME:ChangedProps',{'NAME:WM','Value:=',num2str(WMS)}}}})



35

Execution of Maxwell models from Matlab environment Running the simulation

% Run program: invoke(Design,'Analyze','Setup1');

Extracting results (Post-processing) % Create reports of flux linkages, energy and torque: Module=Design.GetModule('ReportSetup'); % Create the report of three phase flux linkages: invoke(Module,'CreateReport','XY Plot 1','Transient','Rectangular Plot','Setup1 :

Transient',{'Domain:=','Sweep'},... 'Time:=',{'All'},'Poles:=',{'Nominal'},'Speed_rpm:=',{'Nominal'},'Thet_deg:=',{'Nominal'},'Imax:=',{'Nominal

'}},... {'X Component:=','Time','Y

Component:=',{'FluxLinkage(PhaseA)','FluxLinkage(PhaseB)','FluxLinkage(PhaseC)'}},{}) invoke(Module,'RenameReport','XY Plot 1','FluxLinkages') % Create the report of torque: invoke(Module,'CreateReport','Torque','Transient','Rectangular Plot','Setup1 :

Transient',{},{'Time:=',{'All'},'Poles:=,{'All'},'Speed_rpm:=',{'All'},'Thet_deg:=',{'All'},'Imax:=',{'All'}},{'X Component:=','Time','Y Component:=',{'Moving1.Torque'}},{})

% Calculate the energy: Module=Design.GetModule('FieldsReporter'); invoke(Module,'EnterQty','Energy') invoke(Module,'EnterVol','AllObjects') invoke(Module,'CalcOp','Integrate') invoke(Module,'AddNamedExpression','WEnergy','Fields') % Create the report of energy: invoke(Module,'CreateReport','XY Plot 2','Fields','Rectangular Plot','Setup1 :

Transient',{'Domain:=','Sweep'},... {'Time:=',{'All'},'Poles:=',{'Nominal'},'Speed_rpm:=',{'Nominal'},'Thet_deg:=',{'Nominal'},'Imax:=',{'Nomina

l'}, 'O2:=',{'Nominal'},'TM:=',{'Nominal'},'WM:=',{'Nominal'}},{'X Component:=','Time','Y Component:=',{'WEnergy'}},{})

invoke(Module,'RenameReport','XY Plot 2','Energy')



36

Execution of Maxwell models from Matlab environment

Saving results % Export all data to .csv files: invoke(Module,'ExportToFile','FluxLinkages','C:\Users\labadmin\Desktop\Optimization

Project\Scripting\ANSOFT\Scripting\Fluxlinkages.csv') % The file path can be changed invoke(Module,'ExportToFile','Energy','C:\Users\labadmin\Desktop\Optimization

Project\Scripting\ANSOFT\Scripting\Energy.csv') % The file path can be changed invoke(Module,'ExportToFile','Torque','C:\Users\labadmin\Desktop\Optimization

Project\Scripting\ANSOFT\Scripting\Torque.csv') % The file path can be changed

These basic step summarize show how to:

Create a Maxwell 2D model using RMxprt primitives Change model parameters from Matlab environment Solve using Maxwell Extract the results



37

Toyota Prius IPM type motor: Objective function: Single objective function:

Single constraint maintain torque of 243Nm Goal reduce PM usage while maintaining same torque!

Differential Evolution Optimizer Settings Three design variables (rotor only)

PM length, PM width, V-depth Strategy DE/best/1 with jitter, F = 0.85, Cr = 1 Np = 15 candidates per population Ng = 10 generations Total candidate design evaluations = Ng*Np = 150 designs Simulation time approximately 30 minutes

Optimization exercise

PM Mass :maximize 1

emTf =

PM length

PM depth


38



39

Toyota Prius IPM type motor:

Optimization results Original motor (Toyota)

PM mass = 2.1 kg @ 243Nm Optimized motor

PM mass = 1.75 kg @ 245Nm Possible reduction of up to 20% of PM mass


Original (Toyota) Optimized

min. BPM = 0.65 T min. BPM = 0.61 T


40

1. F. A. Fouad, T. W. Nehl, and N. A. O. Demerdash, Magnetic field modeling of permanent magnet type electronically operated synchronous machines using finite elements, IEEE Trans. on PAS, vol. PAS-100, no. 9, pp. 4125-4133, 1981

2. D. M. Ionel and M. Popescu, Finite element surrogate model for electric machines with revolving field - application to IPM motors, IEEE Trans on Ind. Apps., vol. 46, no.6, pp. 2424-2433, Nov/Dec 2010.

3. G. Y. Sizov, D. M. Ionel, and N.A.O. Demerdash, Modeling and design optimization of PM AC machines using computationally efficient finite element analysis, IEEE Energy Conversion Congress and Exposition ECCE, pp. 578-585, Atlanta, Georgia, September 2010, updated version accepted for publication at IEEE Transactions on IES.

4. G. Y. Sizov, D. M. Ionel, and N.A.O. Demerdash, Multi-Objective Optimization of PM AC Machines Using Computationally Efficient - FEA and Differential Evolution, IEEE International Conference on Electric Machines and Drives IEMDC, pp. 1537-1542, Niagara Falls, Canada, May 2011.

5. G. Y. Sizov, D. M. Ionel, and N.A.O. Demerdash, A Review of Efficient FE Modeling Techniques with Applications to PM AC Machines, IEEE Power and Energy Society General Meeting (PES-2011), Detroit, Michigan, July 24-28 2011.

6. G. Y. Sizov, P. Zhang, D. M. Ionel, N.A.O. Demerdash, and M. Rosu, Automated Multi-Objective Design Optimization of Integral-MW Direct-Drive PM Machines Using CE-FEA, IEEE Energy Conversion Congress and Exposition ECCE 2011, Phoenix, Arizona, September 2011.

7. K. V. Price, R. M. Storn, and J. A. Lampinen, Differential Evolution - A Practical Approach to Global Optimization, Springer-Verlag Berlin Heidelberg, 2005.

References

Scripting in Maxwell 2D for Computationally Efficient FEA with Optimization AlgorithmsOverviewIntroductionDifficulties in Optimization of Interior-PM MachinesComputationally Efficient Finite Element Analysis (CEFEA)Computationally Efficient Finite Element Analysis (CEFEA)Computationally Efficient Finite Element Analysis (CEFEA)Computationally Efficient Finite Element Analysis (CEFEA)Computationally Efficient Finite Element Analysis (CEFEA)Computationally Efficient Finite Element Analysis (CEFEA)Computationally Efficient Finite Element Analysis (CEFEA)Computationally Efficient Finite Element Analysis (CEFEA)Computationally Efficient Finite Element Analysis (CEFEA)Computationally Efficient Finite Element Analysis (CEFEA)Computationally Efficient Finite Element Analysis (CEFEA)Computationally Efficient Finite Element Analysis (CEFEA)Computationally Efficient Finite Element Analysis (CEFEA)Computationally Efficient Finite Element Analysis (CEFEA)Computationally Efficient Finite Element Analysis (CEFEA)Computationally Efficient Finite Element Analysis (CEFEA)Computationally Efficient Finite Element Analysis (CEFEA)Computationally Efficient Finite Element Analysis (CEFEA)Design OptimizationDesign OptimizationOptimization of 9-slot, 6-pole IPM MotorOptimization of 9-slot, 6-pole IPM MotorOptimization of 9-slot, 6-pole IPM MotorOptimization of 9-slot, 6-pole IPM MotorOptimization of 9-slot, 6-pole IPM MotorOptimization of 9-slot, 6-pole IPM MotorOptimization of 9-slot, 6-pole IPM MotorScripting Maxwell 2DScripting Maxwell 2DScripting Maxwell 2DScripting Maxwell 2DScripting Maxwell 2DOptimization exerciseOptimization exerciseOptimization exerciseReferences

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