2014 matlab ansys fem based ipmsm optimization

7/23/2019 2014 Matlab Ansys Fem Based Ipmsm Optimization

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Zeszyty Problemowe – Maszyny Elektryczne Nr 4/2014 (104) 99

Rafał Piotuch, Ryszard PałkaWest Pomeranian University of Technology Szczecin

Department of Power Systems and Electrical Drives

FEM BASED IPMSM OPTIMIZATION

OPTYMALIZACJA MES MASZYNY SYNCHRONICZNEJ Z MAGNESAMI

ZAGNIEŻDŻONYMI

Abstract: The work presented in this paper relates to the Interior Permanent Magnet Synchronous Motor

( IPMSM ) optimization procedure programed in Matlab and Maxwell environments. The stator of the machine

is an mass-produced one with concentrated winding. In the first optimization stage geometry of IPMSM

machine was considered, concerning average torque value maximization and cogging torque minimization

with physical and technological constraints. By combining Matlab software and Maxwell application authors

used genetic algorithm for Finite Element Model optimization. Moreover Ld and Lq inductances were estimated

for evaluation of CPSR machine capabilities and selection for the best geometry among Pareto Front solutions.

Streszczenie: Artykuł podejmuje temat optymalizacji maszyn synchronicznych z magnesami zagnieżdżonymi

z wykorzystaniem narzę dzi Matlab i Maxwell. Dokonano optymalizacji geometrii wirnika maszyn o zadanychparametrach stojana, z uwzglę dnieniem maksymalizacji wartości średniej momentu elektromagnetycznego

i minimalizacji momentu zaczepowego oraz ograniczeń geometrycznych i technologicznych. W programie

Matlab zaimplementowano algorytm genetyczny użyty do optymalizacji modelu MES stworzonego

w programie Maxwell. Ponadto wyznaczono indukcyjności w osiach d oraz q dla wybranych struktur wirnika

wskazanych frontem Pareto w celu wyboru optymalnego rozwią zania zapewniają cego szeroki zakres pracy

maszyny przy stałej mocy.

Keywords: PM electrical machines, IPMSM optimization, FEM, Pareto front

Słowa kluczowe: Maszyny z MT, optymalizacja, MES, Pareto front

1. Introduction

Thanks to the rapid advancement in the field of

power electronics, digital signal processors and

control algorithms PM excited and Switched

Reluctance Motors are finding more and more

applications and have replaced traction systems

of most present hybrid electrical vehicles

(HEVs) because they offer high performance

over other DC and AC machines [1, 2, 3].

In particular, owing to development of rare-

earth magnets with high energy product, it is

possible to develop high power densitymachines with high overall efficiency.

Furthermore, extended high speed capabilities,

demanded in a highway cycle, are achieved

thanks to proper rotor geometry design, and

field weakening control strategies [3, 4, 5, 6].

Surface and radially-laminated Interior PM

synchronous machines with conventional

structure have limited or zero flux-weakening

capability [5, 7]. Properly designed IPMSMs

are capable of operating in CPSR (Constant

Power Speed Region) – such machines perform

also inverse saliency – that is q-axis inductance

is larger than d -axis inductance. Consequently,

it has an additive torque value, so called

reluctance torque, that may be exploited to

extend CPSR. Other positive feature of IPM

rotor is that centrifugal forces cannot damage

the magnet, thus whole construction is

mechanically robust, especially for high speeds.

To protect environment, there is a strong

demand to develop highly efficient motors with

high torque/mass ratio. Small cogging torque

reduces noise and mechanical vibrations which

cause increased reliability [8, 9, 10]. All theserequirements can be fulfilled by appropriately

designed PM motors [7, 11, 12]. Proposed

geometry has segmented magnet poles oriented

in the radial direction and iron bridges between

magnets that provides additional flux canals to

give the rotor inherent capability of flux

weakening. Such structures are referred as

Segmented IPM machines [5, 7]. Optimization

procedure with genetic algorithm has been

implemented in Maxwell and Matlab tools. The

final geometry has been analyzed regarding

inductances and air-gap magnetic flux density.




2. PMSM mathematical model

Torque developed in IPM motor can be divided

into PM-caused component and reluctance

torque as shown in Fig. 2. Mathematical model

of IPM machines can be described as follows:

( )3

2em b PM q d q d q

T p I L L I I Ψ = ⋅ ⋅ ⋅ + − ⋅ ⋅ (1)

The first term in the equation (1) is the PM

generated torque, and the second term is the

reluctance torque which is proportional to the

difference in stator inductances, Ld and Lq. In

the analyzed IPMSM, Lq is higher than Ld (due

to the lower reluctance in q-axis direction),

because the magnetic flux flowing along the

d -axis has to cross through the magnet cavities

in addition to the rotor air gap, while the

magnetic flux of the q-axis crosses only the airgap. The d -axis is also basically magnetized

with PM [13, 14]. Such difference increases

torque and extends CPSR. Mathematical model

for IPM machines is presented by following

equation set:

d

d d b m q

d U RI p

dt

Ψ= + − Ω Ψ (2a)

q

q q b m d

d U RI p

dt

Ψ= + + Ω Ψ (2b)

d d d PM L I Ψ = + Ψ (2c)

q q q L I Ψ = (2d)The control strategy applied for such motors

meets several limitations:2 2 2

d q N U U U + < (3a)

2 2 2

d q N I I I + < (3b)

For the high speed regions flux from magnets

gives high electro-motive force, which exceeds

supply voltage. Using field weakening

method, main flux is decreased by d -axis

negative current (2c) and thus it is possible to

stay in the voltage limit (3a). Optimum

flux-weakening condition can be written as:

PM rated

d

I L

Ψ = (4)

Such designs are called optimal field-

weakening IPM motor designs and theoretically

exhibit unlimited CPSR. Poles segmentation

provides physical reduction of the air-gap

magnet flux -PM

Ψ - during flux-weakening,

thus very high ratio of Lq to Ld is not crucial to

extend CPSR. Authors try to consider Lq / Ld

ratio, and PM decrease in the high current

regions.

3. Design problem

The case of study is represented by a 4-pole

segmented IPMSM with fixed stator geometry

and winding parameters. Rotor is equipped with

NdFeB magnets ( Br = 1.23 T, 3x7x40 mm).Most important motor dimensions are presented

in Table 1. Before the optimization process

implementation, classical and segmented

IPMSM geometries were considered.

According to the literature [4, 5] fractional

magnets arrangement may provide very wide

flux-weakening range with high overall

performance parameters. In such structures

d -axis current is still used for PM

demagnetization but it is also used to alter PM

flux-paths. The demagnetizing current causes

some part of PM flux to be canalized into therotor iron section between magnet poles.

In such a way PM flux passing through the air-

gap is efficiently reduced, while the PM-flux is

mostly preserved.

Initial design has been pre-optimized with

simple iterative process. Selected design

variables have been chosen according to the

geometrical constraints, and are presented in

Table 2. Analyzed geometry design variables

are also depicted in Fig. 1.

Fig. 1. Initial geometry cross-section

Table 1. Machine parameters

Rotor Outer

Diameter

[mm]

Air gap

length

[mm]

Stator

OuterDiameter

[mm]

Magnet

Thickness

[mm]

70 1 120 3.25




Table 2. Design variables constraints

x1 [mm]

Flux BarrierX position

x2 [mm]Flux

Barrier

Y position

x3 [mm]Flux

Barrier

Radius

x4 [mm]Magnet

Inset

Radius

4-8 20-25 2-3 20-27

4. Optimization process

In the optimization procedure authors used

heuristic technique based on struggle between

individuals commonly known as Genetic

Algorithm (GA). GA mimics natural selection

process were the strongest individuals survive

and non-important features fades away during

struggle between genes – according to present

demanding [12, 15]. Details of used genetic

algorithm have been described in detail in [16].

4.1. First optimization stageThe problem presented in the paper is a

Multiobjective Optimization Problem (MOP)

subject to a set of constraints. For the proposed

geometry the following objective functions

should be minimized, and are defined as:

( )1 cogg f ( x ) max(T t )= (4a)

2 em f ( x ) mean(T )= − (4b)

After solving the MOP a set of optimal non-

dominated solutions were generated, creatingPareto front shown in Fig. 4. It is a set of

models that acts as area for selection of best

individual. The final selection should be made

taking into account other features that the motor

should have [1].

4.2. Second optimization stage

For obtained set of models Ld and Lq

inductances values has been evaluated using

method presented in [13]. It is based on

Lagrange formalism, which, according to

Sobczyk [17], may be applied to PM excitedmachines. A model with the highest ratio

of Lq / Ld has been selected for the final analysis.

Whole optimization algorithm has been

presented in Fig. 2 and has been described in

detail in [12, 15].

Fig. 2. Optimizatiom algorithm workflow

5. Results

The direct problem has been solved using a 2D

FE model of the motor; torque has been

calculated with the virtual work principle.

GA used 10 generations with 70 models

in population. First optimization stage lasted for

about 6 hours on typical performance PC

(I5, 8GB RAM, Windows 7). The mesh of the

model consisted of a few thousand of elements.

-3.6 -3.4 -3.2 -3 -2.8 -2.6 -2.4 -2.20.05

0.055

0.06

0.065

0.07

0.075

0.08

m a x ( T

c o g g

) ( N m )

-mean(Tem

) (Nm)

Pareto Front

Pareto optimalFinal model

Initial model

Fig. 3. Pareto front for optimal geometrie

In the second optimization stage all

Pareto-Optimal geometries were compared

considering Lq / Ld ratio. The final geometry is

presented in Fig. 7 ( Lq / Ld = 1.8).




0 6 12 18 24 300

1

2

3

4

5

electrical angle (deg)

T o r q u e ( N m )

Torque waveforms

Final Model

Initial Model

Fig. 4. Torque waveforms comparison

0 3 6 9 12 15-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

mechanical angle (deg)

T o r q u e ( N m )

Torque waveforms

Final Model

Initial Model

Fig. 5. Cogging torque waveforms comparison

0 15 30 45 60 75 90-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

mechanical angle (deg)

B ( T )

Air gap magnetic flux density

Bnormal

Btangent

Fig. 6. Magnetic flux density waveforms (no-load

condition) – final geometry

Fig. 7. Final geometry cross-section; magnetic flux

denisty distribution

6. Summary

Maxwell and Matlab tools were combined for

the rotor geometry optimization process of

Segmented Interior Permanent Magnet

Synchronous Motor. The connection between

these two packages allowed flexible FE model

geometry definition and analysis as well as

effective results evaluation. The whole

optimization process has improved average

torque value significantly with the same

cogging torque value prior to initial geometry.

The simulation points out the benefits of the

optimization using a genetic algorithm.

Non ideal torque waveforms and higherharmonics (Fig. 6) in the air-gap magnetic flux

density make sinusoidal phase currents

improper for such IPM motors. Simple power

supply system applied during simulations

causes high torque ripples. It should be

emphasized that Maxwell can be connected

with Simplorer, therefor whole analysis of

a drive system, may be properly evaluated [18]

with cascade control structure commonly used

in practical applications. During simulations

there were encountered several problems.

The first one was proper mesh settings in orderto shorten whole optimization process, and

assure correct FEM calculation results.

Particularly, mesh should be more dense in the

air gap region, and in the stator core could be

thinner.




The second problem was to select proper

control angle for each model to produce the

highest torque from the available current. The

control angle in each model was constant, thus

torque evaluation exhibit minor error (current in

each phase was sinusoidal with

1.6 A rms value). Lq / Ld ratio for Pareto-optimal

models varied slightly, but the ratio was not

evaluated for other analyzed models.

Accurate procedure needs proper power angle

evaluation for each model during

GA optimization which strongly extends

calculation time with proposed inductance

estimation procedure. Future work will be

focused on Ld and Lq saturated parameters

calculation, because nonlinear IPM motor

characteristics may affect CPSR performance.7. Literature

[1]. Di Barba P., Mognaschi M. E.: Industrial design

with multiple criteria: shape optimization of

a permanent-magnet generator , IEEE Transaction

on Magnetics, vol. 45, no. 3, pp. 1482-1485, (2009)

[2]. Paplicki P., The new generation of electrical

machines applied in hybrid drive car , Electrical

Review, R. 86, no. 6, pp. 101-103, (2010)

[3]. May H., Pałka R., Paplicki P., Szkolny S.,

Wardach M.: Comparative research of different

structures of a permanent-magnet excited

synchronous machine for electric vehicles, ElectricalReview, no. 12a/2012, pp. 53-55, (2012)

[4]. Di Barba P., Mognaschi M. E., Pałka R.,

Paplicki P., Szkolny S.: Design optimization of

a permanent-magnet excited synchronous machine

for electrical automobiles, International Journal of

Applied Electromagnetics and Mechanics, IOSPress, vol. 39, no. 1-4, pp.889-895, (2012)

[5]. Stumberger B, Hamler M., Trlep M., Jesenik

M.: Analysis of Interior Permanent Magnet

Synchronous Motor Designed for Flux Weakening

Operation, IEEE Transaction on Magnetics, Vol. 37,

No. 5, pp. 3644-3647, (2001)

[6]. Pałka R., Paplicki P., Piotuch R.,Wardach M.: Maszyna z magnesami o regulowanym wzbudzeniu–

wybrane wyniki prac projektowych, Prace Naukowe

Instytutu Maszyn, Napę dów i Pomiarów

Elektrycznych Politechniki Wrocławskiej, Vol 66,

no. 32, pp. 128-133 (2013)

[7]. Dutta R.: A Segmented Interior Permanent

Magnet Synchronous Machine with Wide Field-

Weakening Range, The University of New South

Wales, PhD thesis, (2007)

[8]. Keyahani A., Murthy S. K., Studer C. B.,

Sebastian T.: Study of cogging torque in permanent

magnet machines, Electric Machines and Power

Systems”, no. 27, pp. 665-678, (1999)

[9]. Wardach M.: Cogging torque reducing in

electric machine by poling modification of magneticcircuit , Electrical Review, No. 2, pp. 131-133,

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[12]. Caramia R. Piotuch R. Pałka R.: Multiobjective

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(2013)




Authors

M.A. Rafał Piotuch, [email protected]

Prof. Ryszard Pałka, [email protected]

West Pomeranian University of TechnologySzczecin, Department of Power Systems and

Electrical Drives,

ul. Sikorskiego 37, 70-313 Szczecin,

tel.: +48 91 449 48 73

Acknowledgment

This work has been created with the support of

the Ministry of Education and Science, Poland,

under grant N N510 508040.

2014 matlab ansys fem based ipmsm optimization

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