On the State of the Art Design of Electric Machines and...

Dan M. Ionel, Ph.D., FIEEE | University of Illinois, Dec. 8, 2014 | 1

On the State of the Art Design of

Electric Machines and Drives

Dan M. Ionel, Ph.D., IEEE FellowChief Engineer – Regal Beloit Corp.

Research Professor – UWM and Marquette University

December 8, 2014

University of Illinois, Urbana Champaign, IL


Outline

• Introduction• The power of collaboration

• General design procedure and main challenges

•Design of electromechanical devices and systems• Wind turbines, HEV, EV cars … and all other EMD

• Multiple dimensions and objectives; “comparing apples and oranges”

•Multi-physics analysis• Coupled electromagnetic – mechanical – thermal – flow

• Ultra-fast or Computational Efficient FEA (CE-FEA)

•Optimization• Fundamental concepts: robust design and CI - DE

• Case studies

•Conclusion.


Outline








• Case studies

•Conclusion.


Electrical Engineering Story

Source: http://www.wikipedia.org

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Generic Design Procedure and Main Challenges

1) Establish specification

2) Select a topology

3) Initial sizing – “back of the envelope calculations”

4) (Optimal) design electromagnetic, thermal, mechanical• Incl. estimation of performance and cost

5) Study sensitivity to manufacturing, e.g.• Tolerances on materials and processes

• Noise and vibration

6) Compare topologies

7) Make decision

Not explicitly detailed, e.g.:• System to subsystem to component decoupling

• Dynamics – time variations (4D)

• Multiple performance indices (5D, etc)…


Outline








• Case studies

•Conclusion.


Vestas V-164 – World’s Most Powerful Wind Turbine

• Nacelle – 8x8x20 m 390 tones

• “medium – speed” drive train

• generator 710V AC and (AC/DC) rectifier

• Tower – DC power feeds down

• Base – 14 m high “E-module”

• internal power supply cabinets – 3rd floor

• the inverter DC/AC (line side) – 2nd floor

• Transformer & switchgear - 1st floor

• Multi MW wind turbines – more than 10,000 components and

many subsystems

• Just the power losses can be comparable with the output of a

smaller wind turbine!

Sources: MHI Vestas Offshore Wind

http://www.mhivestasoffshore.com/Products-and-

services/The-Turbines/V164 and

Wind Power Monthly Magazine

http://www.windpowermonthly.com/article/121105

6/close---vestas-v164-80-nacelle-hub


Skyscrapers and Vestas V-164

20x8x8 m

390 ton

nacelle

80 m 35 ton

blade

208 m top


From Wind to Electricity – Multi-System Multi-Physics Simulation

Sources: Valerio Viti et al., “Wind Energy Projects-

From Blade Design to Wind Farms”, ANSYS

Presentation, 2011.

Dan M. Ionel et al., “ANSYS Short Courses for

Industry”, 2011 to 2014, IEEE IEMDC 2013 and ECCE

2013 Conferences.

• Wind speed and electric power

variations

• Multiple systems and controls

• High level system simulation

• Low level – high fidelity

component simulation

• Design

• Fault analysis.


Power Electronics Reliability


Hybrid and Electric Vehicles

• Driving cycles

• US, EU etc

• Urban and highway

• Optimal design is different

depending of cycle

• Design changes also if “driving

experience” is a main

objective.

Source: Fatemi, Demerdash, Ionel, Nehl,

IEEE ITEC 2015.

0 50 100 150 200 250 3000

50

100

150

Speed(rad/s)

Torque(N.m)

0 100 200 3000

50

100

150

Speed(rad/s)

Torque(N.m)

70

70

80

80

85

85

87

87

89

89

90

90

91

91

92

92

92

93

93

93

94

94

94

95

95

96

96

97

Speed (RPM)

Torq

ue (

N.m

)

500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000

50

100

150

200

250

300

80

82

84

86

88

90

92

94

96

70

70

80

80

85

85

87

87

89

89

90

90

91

91

91

92

92

92

9393

9394

94

94

95

95

96

96

Speed (RPM)

Torq

ue (

N.m

)

500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000

50

100

150

200

250

300

80

82

84

86

88

90

92

94

96


See: "Electric Motor Drive Selection Issues for HEV Propulsion Systems: A

Comparative Study,“ IEEE Transactions on Vehicular Technology, 2006.

Example Motor Drive Comparison for HEV Traction


Systematic Optimal Design Comparison

• Ensuring a fair basis for comparison

• Thousands of candidate designs have to be analyzed

• Pareto front – collection of “best” (optimal/compromise) designs, e.g.

– cost vs. efficiency tradeoffs

• Study should include sensitivity to manufacturing tolerances. 13


A Generic Procedure for Systematic Design

1) Establish specification

2) Select a topology

3) Initial sizing – “back of the envelope calculations”

4) (Optimal) design electromagnetic, thermal, mechanical

- Incl. estimation of performance and cost

5) Study sensitivity to manufacturing, e.g.

- Tolerances on materials and processes

- Noise and vibration

6) Compare topologies

7) Make decision.


“Back of the Envelope Calculations” – Example “Stories”

• Initial sizing and/or scaling, including topology selection

• Performed by experts and novices � recommendations for the design process

• Many times, parts of the recommendations get lost in the communications

• “The 12 slot 10 pole configuration is very good (“the best”) for brushless PM

synchronous motors” – typical omissions in the communications

• Provided that the core losses are not significant because speed in relatively low, and high-

performance low-loss silicon steel is employed

• Provided that eccentricity can be maintained low due tight tolerance control

• Provided that the effect of high radial forces can be decoupled/dampened in the system

• “The synchronous reluctance motor can have higher specific torque and efficiency

than its induction motor counter part” – typical omissions in the communications

• Provided that the saliency ratio of the synchronous reluctance motor is very high with

values of 7-10

• Provided that the additional (stray-load) core losses are kept low through material selection

and process control

• In industrial practice many of the “provided that” conditions may actually be quite

difficult to achieve, to say the least…


Some of the Design Challenges

• Wind turbine objective

• Minimum Cost of Energy (COE)

• Reliability

• HEV (or EV) objectives

• Minimum Cost of Operation

• “Best Driving Experience”

• Typical electric machines and drives objectives

• Cost: materials, manufacturing, operating, total

• Performance: losses (efficiency), ripple, vibration-noise etc.

• Establish the trade offs cost vs. performance and “position” according to a strategy

• Many “truly” independent design variables, typically 10-20

• Multi-dimensional design problem: 2D, 3D, 4D, 5D…

• Problems are “weakly” coupled

• System – component

• Electromagnetic – mechanical – thermal

• Analysis is too slow, e.g. electromagnetic FEA is needed

• Optimization requires too many candidate designs

• … and the list can go on and on …


Outline








• Case studies

•Conclusion.


Brushless PM Motors and Power Electronics Drives

� Controls and PE

circuits

� Multi-physics

� Current regulation.


Coupled Field and Circuit Simulations


• Electromagnetic field and electric circuit equations

• Electromagnetic torque and motion equations.

Behind the Electromagnetic Field Animations


Multi-physics Analysis

Electromagnetic (2D)

Airflow Power losses Temperature (3D)


Ultra-fast or Computationally Efficient FEA (CE-FEA)

• The fundamentals of electromagnetic CE-FEA– sine-wave current regulated synchronous machines, brushless PM included

– steady-state operation

– 2D or 3D versions

– any geometry

– calculates all major performance indices and parameters

– induced voltage waveform, torque and torque ripple, core losses, PM losses, and

inductances

– fully exploits symmetries of electric and magnetic circuits to reduce simulation

time

– min. number of magnetostatic solutions, correlated with the max. order of

significant field harmonics

– multiple IEEE Transactions papers since 2010, including an award winner

• Main benefits– one-to-two orders of magnitude reduction of simulation time; days vs. months!

– thousands of designs in hours on state of the art workstation

– 10-20 seconds per design (e.g. 6 static 2D - FE solutions)

– enables large scale optimization studies.


( ) ( )θθ ++ −=+Y

o

RAA 60

( ) ( )θθ ++ =+B

o

RAA 120

-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+

• Coil side MVP, AR+

• Results also include: cogging and ripple torque, induced

voltage, (inductances), core and PM losses.

Five magnetostatic FE solutions

AY+

AB+

AR+

ΦR

One magnetostatic FE solution

Principles of CE-FEA (1/2)


Principles of CE-FEA (2/2)

• Harmonic calculations – flux linkage, back emf, and electromagnetic torque

• Flux density calculations based on symmetry

• Core loss calculation due to fundamental and low frequency harmonics

( ) ( )∑=

+=M

R

ν

ννν φνθλθλ

1

cos

( ) ( )∑=

+=−=M

dt

d

d

de

R

R

ν

ννν φνθνλω

θ

θ

λθ

1

sin


CE-FEA Hybrid Numerical and Analytical – Losses in PM

25/21

B11 B12 B13 B14


Coupling of Forces, Vibration and Noise

• Electromagnetic forces• Maxwell stress – electromagnetic

pressure in 3D

• Forces produce mechanical displacement

• Sound power calculated from displacement

• Noise is calculated from sound power

• “Strong” vs. “weak” coupling.

26


Magnetic Field

Structural Dynamics

Acoustic Field

ForcesDisplacements

ANSYS Short Courses for Industry

• Dearborn (Detroit), April 2013; Irvine and Santa Clara, November 2013

• Framingham (Boston), January 2014

• Dearborn (Detroit), August 2014, and Milwaukee, December 2014.

Electromagnetics to Vibration to Noise


CE-FEA and Electromagnetic Forces in BLPM Machines


Electromagnetic and Thermal Coupled Analysis


Example of Coupled Analysis – Motor-CAD

• Electromagnetics

• Ultra-fast 2D FEA in the abc

reference frame

• Seconds on a state of the art

PC workstation

• Analytical calculations for end

effects

• Thermal and air-flow

• Equivalent 3D networks

• Calculation time one order of

magnitude shorter than for

electromagnetics

• Coupling methods

• “Serial”, typ. 6 iterations for

each of Emag and thermal

• “Weak”, typ. only 2 iterations

for Emag and 6-10 for thermal

• Suitable for large-scale

optimization studies.


• EM analysis takes tens of seconds

• Thermal and air-flow problem

takes only seconds to solve

• Traditional approach typically

requires 6 or more iterations

• In synchronous motors the rotor

losses are typically low

• Variation of core losses with

temperature at given current is

relatively small.

Traditional approach New ultrafast approach

Traditional and Ultrafast Coupling Method


• Charging Simulation with High Performance Computing (HPC) – White Paper and IEEE Webinar by

Bradley Smith of GM Corp., and Scott Stanton of ANSYS Inc.

• “A 16x speed up on a computer farm delivers time and cost savings in the design of traction

motors for HEVs and EVS. “

HPC Implementation – GM and ANSYS Example


Multi-physics

EMAG

CFD

FEA

Fluid structure

interaction

Thermal

performance

Force coupling

Aero-acoustics

Optimization

Design exploration

DOE platform

Sensitivity Analysis

Regal Advanced Computational Engineering

HPC for Advanced Industrial R&D


Publically Available HPC

• Dell HPC cluster

• 46 servers and 520 cores

• Dell PowerEdge 1950 servers (dual quad-core Intel Xeon E5440)

• Dell PowerEdge r410 servers (dual quad-core Intel Xeon E5520)

• Dell PowerEdge r620 servers (dual eight-core Intel Xeon E5-2660)

• 160TB storage

• processors for a total of 29 nodes and 232 cores.

• Vizualization GPCPU/Cuda Server

• 12 CPU cores and 704 GPGPU cores

• Intel Xeon X5650 [Westmere] processors

• NVIDIA Quadro 4000 (256-core)

• NVIDIA Tesla C2075 (448-core).


Principles of Distributed Processing (Solving)


HPC – Mechanical, CFD, and Electromagnetics Examples


• 3D IPM synchronous machine with motion

• Mesh size: 120,000 tets – around 2 GB of RAM

• Machine: 4 x Xeon CPU [email protected] processors

• (32 cores total – 512 GB of RAM)

• Basic math for electromagnetic analysis only…

– 6,000 candidate designs – 1 minute/design – 100 core hours

– more than 4 days or…

HPC Solution – Example Model

Number of Cores Average Time per

Non linear Iteration (s)

Average Speed-up

Compared w/1 core

1 70 -

2 41 1.7

4 21 3.3

8 18 3.9

12 18 3.9


Outline








• Case studies

•Conclusion.


• Design of Experiments (DOE)

• Parameter correlation

• Response surface (RS)

• Estimated performance based on RS

• (Six) Sigma analysis

• Advantages

• Familiar engineering background

• Includes indications of input-output correlations and sensitivities.

Electric machine specification and initial design

Cost vs. performance characteristics � best designs

• Computational Intelligence

– Differential Evolution (DE);

others: GA, PSO etc

– Inspired from natural selection

– Generations /populations, each

with multiple individuals

• Advantages

– Minimal computational effort

for large scale optimization

studies (thousands of candidate

designs).

Methods for Automated Design Optimization


Which Method Is Better – RS or DE?

• Duan and Ionel (2011) paper - review

and benchmark problem

• Five independent variables, strong

non-linear output

• Two design objectives minimize

“weight” while maximizing “goodness”

• Design candidates evaluated on a

direct “reference” grid: 16,807

• RS vs. DE

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150 200 25011

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11.4

11.6

11.8

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Weight function (kg)G

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ess

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on

(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


� Differential Evolution:

� Initialization

�,�,� = ��(0,1) ∙ ( �_�� − �_�� ) + �_��

� Mutation

� Crossover

� Selection

� Stopping criterion: " = #�

� Definition of Variables:

� $ = 1, 2,⋯ ,�& ,

number of design variables, �& = 6.

� ( = 1, 2,⋯ ,)*,

number of individuals per generation

� ": index of current generation

� Typically for electric machine problems

� 10-20 independent variables

� 100-150 individuals (candidate designs) per

generation

� 60-80 generations per optimization study.

Differential Evolution Algorithm


Industrial Examples – RBC NEMA Range of IPM Motors

0.8 1 1.2 1.4 1.6 1.8

0.8

1

1.2

1.4

1.6

1.8

2

Losses, PCu

+ PFe

+ Ppm

+ Pme

[pu]

Co

st [p

u]

Co

st p

er

ou

tpu

t p

ow

er

[pu

]

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

M-1

M-2

M-3


Testing and Validation

89

9091

91

92

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93

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94

94

94

94.5

94.5

speed, pu

Shaft

torq

ue,

pu

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

85

90

95

efficiency map

2 Hp

4 Hp

6 Hp

8 Hp

10 Hp

Fan load

0 1 2 3 4 5 6 7-20

-10

0

10

20

Time [ms]

Th

ree p

has

e c

urr

ents

[A

]

0 1 2 3 4 5 6 7-500

0

500

Time [ms]

Thre

e p

hase v

oltages [

V]


Example 1 (Ex#1) – Optimal Design Proportions for PMSM

• Specified

• Generic 6 pole surface PM (PMSM) configuration with NdFe PMs

• Two slots per pole and phase

• Sample designs for distinct power ratings between 1kW and 1MW

• Fundamental frequency 120Hz, typical M19, ct. current density and slot fill factor

• Variables

• Eight (8) independent; relative to air-gap (stator ID) diameter

• Dependent: axial core length, adjusted in order to deliver rated power for given cross-section

• Objective

• Cost per point of efficiency at rated power; relative

• material costs [u.c./kg]: steel 1, copper 10, magnet (NdFeB) 100

• Constraints

• Max. torque ripple <20%

• Min. flux density in the NdFeB magnet >0.4T.

• Differential Evolution (DE) optimization process.

• For more details see: Duan Y., Ionel D. M., “Non-Linear Scaling Rules for Brushless PM Synchronous Machines Based on Optimal Design Studies for a Wide Range of Power Ratings”, accepted for publication in IEEE Trans. on Industry

Applications, Vol. 50, 2014, 9p, available in IEEExplore as DOI: 10.1109/TIA.2013.2277612.


Ex#1 – Parametric Model and Independent Variables

• Eight independent variables, relative to air-gap diameter and minimum gap

• Minimum physical air-gap [mm]:

• Slot pitch

• Pole pitch


Ex#1 – Evolution of Single-Objective DE

Evolution of the design variables and

objectives at different generations for

the 50kW example design

Evolution of design objective during DE

optimization

For more details see: Duan Y., Ionel D. M., “Non-Linear Scaling Rules for Brushless PM Synchronous Machines Based on Optimal

Design Studies for a Wide Range of Power Ratings”, accepted for publication in IEEE Trans. on Industry Applications, Vol. 50, 2014,

9p, available in IEEExplore as DOI: 10.1109/TIA.2013.2277612.


Ex#1 – Optimization Results (1/3)


Ex#1 – Optimization Results (3/3)

• Design proportions across a wide range of power ratings – confirmed many of the typical experienced based “rules of thumb” and reveled other insights

• More than 30,000 designs have been studied!

• Influenced of course by the optimization criteria considered and the relative cost of materials (Fe 1, Cu 10, NdFeB 100)

• Average value of magnet length (thickness) to air-gap ratio approx. 3 and increasing with power rating

• Pole arc approx. 0.65 to 0.7

• Tooth width to slot width 1:1 (equal split)

• Magnetic loading: stator tooth 1.65T, back iron 1.5T

• Split ratio air-gap diameter to outer stator approx. 0.55 to 0.6

• Rotor length to air-gap diameter approx. 1.1 to 1.4

• Percentage of copper loss to total loss variation 35% to 60%, decreasing with power rating

• Cost and performance

• Optimal designs very close to the 20% torque ripple imposed limit (indication of convergence from an engineering point of view)

• Efficiency in the range of 93.9% to 98.8%, increasing with power rating (not taking into account PM losses, and mechanical losses)

• Large machines dominated by NdFeB cost (approx. 50%); lower values for smaller machines

• Changes in the cost of materials will result in principle in different optimal designs.


Example 2 (Ex#2) – Comparison of IPM and Spoke

• Specified

• Morphing rotor configuration – from “flat bar” IPM to V-shape to spoke

• 3-phase PM synchronous motor 12 slots 10 poles

• NdFeB magnets, incl. for spoke

• Variables

• Nine (9) independent; relative to air-gap (stator ID) diameter

• Both stator and rotor dimensions can change

• Dependent: axial core length, adjusted in order to deliver rated power for given cross-section

• Objectives – three concurrent

• Minimum power losses at 10hp 1,800rpm rated load and

• Minimum torque ripple and

• Minimum cost of materials

• Constraints

• THD of the induced voltage at rated operation <5%

• Min. flux density in the NdFeB magnet >0.4T.

• Combined DOE and DE optimization process• For more details see: Zhang Peng, Ionel D. M., Demerdash N.A.O., “Morphing Parametric Modeling and Design

Optimization of Spoke and V-type Permanent Magnet Machines by Combined Design of Experiments and Differential Evolution Algorithms”, IEEE ECCE 2013, Denver (CO), Sept. 2013, pp.5056-5063.


Ex#2 – Morphing Rotor Topology from IPM to Spoke

• For more details see: Zhang Peng, Ionel D. M., Demerdash N.A.O., “Morphing Parametric Modeling and Design Optimization of

Spoke and V-type Permanent Magnet Machines by Combined Design of Experiments and Differential Evolution Algorithms”,

IEEE ECCE 2013, Denver (CO), Sept. 2013, pp.5056-5063.

12S10P Spoke12S10P V-SV IPM

12S10P “Flat Bar”

IPM

12S10P V-FV IPM


Ex#2 – RS and DE for Spoke Ferrite Designs


Ex#2 – Topology Comparison

• For NdFeB designs cost and performance are comparable regardless of rotor topology (see the Pareto fonts), for the rated load optimization (no variable speed nor variable torque criteria) and within the limits considered for the parametric models and cost structure

• The spoke rotor may be in this case at a disadvantage due to manufacturing complexity and in-situ magnetization challenges

• This is not to say that spoke rotors may not have great potential for designs employing ferrites nor that certain rotor topologies would have an advantage when used for designs operating in constant power – flux weakening mode.


Outline








• Case studies

•Conclusion.


•Multiple steps are involved in a systematic design process

•Special care should be taken with the initial topology selection and

design sizing, including “back of the envelope calculations”

•Multi-physics analysis electromagnetic-thermal-mechanical for

satisfactorily accurate or high-fidelity models

•The effect of manufacturing on performance and cost should be

quantified

•Automated design optimization can serve to study hundreds or

thousands of candidate designs and provide the “best” design, or

family of designs

•A “fair” evaluation of topologies and candidate designs should be

based on the results of optimal design studies.

Recommendations


Historical Evolution of Electrical Machines


The Impact of Electronics and Magnets

VSD Induction Motor

Higher Polarity (Speed)

New Gen. Improved Steel

Higher Efficiency

Aluminum Frame

50% Motor Part Reduction

IPM Motor

Even Higher Polarity (Speed)

Even Higher Efficiency

Similar Enclosure

Quieter Operation


Continuous Improvement…

•Not to forget that we made progress with the machines and drives

•But the design methods are in need for continuous improvement

•Things that we could not do, in terms of practical design

• One hundred years ago – …

• Ten years ago – 3D, large scale multi-objective optimization with high-fidelity models

• Last year – confirm through CI the “golden” design rules

•Among the many things that need improvement• “Stronger” coupling

• System – component

• Electromagnetic – mechanical – thermal

• Multiple dimensions: 2D, 3D, 4D, 5D…

•Interdisciplinary engineering and collaboration are vital.


Acknowledgments and Recent References

• Special thanks to the many collaborators at Regal, Vestas, ANSYS and MDL, and to

colleagues and students at Marquette University and University of Wisconsin –

Milwaukee.

• Recent papers and presentations• Novakovic B., Duan Y., Solveson M., Nasiri A., Ionel D. M., “Comprehensive Modeling of Turbine Systems from Wind to Electric Grid”,

accepted for publication in IEEE Trans. on Industry Applications, Vol. 51, 2015, 11p.

• Zhang Peng, Sizov G. Y., Li M., Ionel D. M., Demerdash N. A. O., Stretz S. J., Yeadon A. W., “Multi-Objective Tradeoff in the Design

Optimization of a Brushless Permanent-Magnet Machine with Fractional-Slot Concentrated Windings”, IEEE Trans. on Industry

Applications, Vol. 50, No. 6, Nov/Dec 2014, pp. 3285-3294.

• Ionel D.M., “The World’s Most Powerful Wind Turbine – Vestas V164”, Intl. Conf. on Renewable Energy Research and Applications

ICRERA 2014, Milwaukee (WI), Oct. 2014, invited panel presentation.

• Ionel D.M., “Design for Manufacturing Employing Automated Design Optimization and Multi-Physics Analysis – an Academic and

Industrial Point of View”, Special Session “Optimization of Electric Motors and Multi-Physics Analysis”, IEEE ECCE 2014, Pittsburgh

(PA), Sept. 2014, invited presentation.

• Wang Yi, Ionel D.M., Staton D.A., “Ultrafast Steady State Multi-Physics Model for PM and Synchronous Reluctance Machines”, Rec.

IEEE ECCE 2014, Pittsburgh (PA), Sept. 2014, pp.5152-5159.

• Duan Y., Ionel D. M., “Non-Linear Scaling Rules for Brushless PM Synchronous Machines Based on Optimal Design Studies for a Wide

Range of Power Ratings, IEEE Trans. on Industry Applications, Vol. 50, No.2, Mar/Apr 2014, pp. 1044-1052.

• Zhang P., Sizov G. Y., He J., Ionel D. M., Demerdash N. A. O., “Calculation of Magnet Losses in Concentrated-Winding Permanent

Magnet Synchronous Machines Using a Computationally Efficient – Finite Element Method”, IEEE Trans. on Industry Applications, Vol.

49, No. 6, Nov/Dec 2013, pp. 2524-2532.

• Sizov, G. Y., Zhang P., Ionel D. M., Demerdash N. A. O., “Automated Multi-Objective Design Optimization of PM AC Machines Using

Computationally Efficient-FEA and Differential Evolution”, IEEE Trans. on Industry Applications, Vol. 49, No. 5, Sept/Oct 2013, pp.

2086-2096.

• Duan Y., Ionel D. M., “A Review of Recent Developments in Electrical Machine Design Optimization Methods with a Permanent

Magnet Synchronous Motor Benchmark Study”, IEEE Trans. on Industry Applications, Vol. 49, No. 3, May/June 2013, pp. 1268-1275.

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