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7/23/2019 2014 Matlab Ansys Fem Based Ipmsm Optimization
http://slidepdf.com/reader/full/2014-matlab-ansys-fem-based-ipmsm-optimization 1/6
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.
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Zeszyty Problemowe – Maszyny Elektryczne Nr 4/2014 (104) 100
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
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Zeszyty Problemowe – Maszyny Elektryczne Nr 4/2014 (104) 101
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).
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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.
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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
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with multiple criteria: shape optimization of
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[2]. Paplicki P., The new generation of electrical
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synchronous machine for electric vehicles, ElectricalReview, no. 12a/2012, pp. 53-55, (2012)
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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.