ECAI 2016 - International Conference – 8th Edition
Electronics, Computers and Artificial Intelligence
30 June -02 July, 2016, Ploiesti, ROMÂNIA
Electromagnetic Optimization of a Permanent
Magnet Synchronous Generator
Erol KURT
Halil GÖR
Electrical and Electronics Engineering
Faculty of Technology, Gazi University
Ankara, Turkey
ekurt52tr@yahoo.com
Electrical and Electronics Engineering
Faculty of Engineering, Hakkari University
Hakkari, Turkey
halilgor@hakkari.edu.tr
Abstract – In the present paper, the optimization studies
of a new permanent magnet synchronous generator
(PMSG) are presented. The PMSG has two rotors at
both sides and a inertial stator and operates as a threephase machine. The optimization studies have been
carried out by a finite element analysis (FEA) code for
various airgaps. Although some distortions are seen in
the waveform at lower rotor speeds such as 100 rpm, the
higher speeds exhibit good waveforms.
Keywords-synchronous generator; permanent magnet;
finite element; optimization
I.
INTRODUCTION
According to the literature, two distinct PMG
groupings, namely axial flux and radial flux PMGs
exist. Considering the flux passes through the coils in
radial direction, it is called as radial flux generator, on
the other hand, if the flux passes parallel to the axial
direction, then it is called as axial flux machine (AFM)
[1]. The AFM can be used worldwidely in robotics,
electrical vehicles, wind turbines. The rotor speed and
power density do not give a basic correlation in those
machines whereas, AFM are frequently known as their
high power densities from p= 6 kW/m3 to 700 kW/m3
[2].
As in every machine design and optimization, the
design and optimization steps of a AFM should get
high attention in order to reach good efficiency and
output power. One can divide the optimization studies
in two main fields: Mechanical and electrical. As the
task of an electrical engineering, the designs of the
electrical parts by considering the magnet shape,
airgap, flux density, core shape, winding type,
insulator and conductor parts become great tasks to
achieve a good machine [3]. For the design of the
mechanical part, all moving parts and air circulation
inside the machine get much attention as the tasks of
mechanical engineering. Indeed all parts must be
durable and undamaged at medium and high rotations,
when the design is completed [3].
Although AFMs have lower cogging torque, high
power density, easy maintanance, high efficiency,
lower volume and cost [4-9], the engineers and
physicists still aim to produce much efficient machine
and to obtain higher electrical power density.
In a previous paper, Li and his colleagues [7]
informed that higher power densities cause heating
problems. As mentioned above, a useful design should
be carried out to cool down the machine especially at
higher speeds. There exist a number of ways to do it:
The optimization of the airgaps [10] and the shapes of
the cores can be mentioned in that manner. Those also
play an important role to minimize the cogging torque
and mechanical vibrations [11]. On the other hand, the
losses should also be examined for a new machine.
For instance, Vansompel et al [12] explored the
efficiency of the generator terms of core mass, shape
and lamination under FEA. They proved that the
varying air gap decreased the core losses by giving a
rate of 8% [13].
In the present paper, some design features and
optimization steps are mentioned. While the design
aspects are given in the next section, the optimization
findings are presented in Sec. III. Finally, the
concluding remarks are stated in the last section.
II.
ELECTROMAGNETIC DESIGIN OF AN AFPMG
In the design process, the finite element analysis
(FEA) is realized. After the determination of the
simulation volume and machine units, reliability of the
meshes is tested. The material characteristics are
determined to all units such as magnets, cores, airgaps,
coils, rotors and stator. The features are given in Table
1.
TABLE I. DESIGN PARAMETERS OF THE MACHINE
Components
Inner radius of rotor R2 (mm)
Outer radius of rotor R2 (mm)
Inner radius of rotor R1 (mm)
Outer radius of rotor R1(mm)
Inner radius of stator disc (mm)
Outer radius of stator disc (mm)
Thickness of backirons (mm)
Radial width of backirons (mm)
Coil inner diameter (mm)
Small coil outer diameter (mm)
Large coil outer diameter (mm)
Phase
Winding turns for large coil
Winding turns for small coil
Coil number
Wire diameter (mm)
Magnet type
Magnet shape
Magnet number
Features
75
105
120
150
70
155
5
40
30
46.4
69.6
3
300
200
24
0.75
NdFeB
Circular
16
Erol Kurt, Halil Gör
2
Magnet diameter (mm)
Magnet thickness (mm)
Core material
Core type
Core number
Air gap (mm)
30
5
M19
Axially/radially
laminated
12
0.6 – 1.4
According to Table 1, the airgap is adjusted as 5
mm due to the elimination of the frictional problems in
experimental, whereas various airgaps have been
examined during the optimization. The cross-sectional
view of the PMSG is shown in Fig. 1.
Figure 3. The design of the core and coils
It was stated in our previous study that this shape
assisted to decrease the cogging torque [14,15]. The
adjacent core tips and magnets are situated on the
stator and rotor with an electrical angle of 22.5 degrees
in order to maintain a 3 phase output. The magnets are
30 mm in diameter and 5 mm in thickness.
III.
Figure 1. Sectional view of the AFPMG
The rotors are located on the upper and lower parts
of the machine. The cores and the location of sample
magnets are also given in the same figure. In the
design, the rotors can move easily and the stator at the
middle is subjected to be inertial. The machine has 24
windings and 32 magnets in total. In the design, the
cores assist to decrease the total reluctance. Since the
laminated cores are used, the core losses are
minimized, too [12].
OPTIMIZATION
Since the airgap, core shape and the distances of
successive magnets become innovative, the flux
topology of the machine differs from the earlier ones.
The magnetostatic analysis of magnetic flux density is
given in Fig. 4(a,b). The flux densities of two rotors
and the cores are shown clearly. After each 22.5
degrees, four magnets would come to the same angular
position with the cores. Therefore these regions have
the maximal flux on the cores. Note also that maximal
flux densities are found around 1.5 T.
The meshed forms of stator and rotor are shown in
Fig. 2. While 66934 mesh cells are used in stator,
45778 mesh cells are used in rotors.
(a)
(b)
Figure 2. The meshed view of the PMSG
A sample core is shown in Fig. 3. The machine has
12 cores in total with a separate core geometry.
Figure 4. Magnetic flux densities on (a) the back iron and cores
and (b) a sample core (airgap=0.8mm).
Electromagnetic Optimization of a Permanent Magnet Synchronous Generator
3
In the core, the flux densities have different values
from 0.8 T to 1.6 T depending on the local geometry
for 0.8 mm airgap. If two magnets move near the tips,
the maximal fluxes are obtained at the tips (Fig. 4(b)).
The flux density gives the maximal value of 0.5 T in
the airgap near the magnets.
The parametrical analyzes have also been realized
on the cogging torque. The maximal cogging torque
value has been found as 4.5 Nm, whereas this value
could be decreased to 3.5 Nm as in Fig 5(a).
Figure 6. Magnetic flux density on a single core (airgap=0.6 mm).
Fig. 7 shows the output waveforms for all phases,
when a electrical load of 60 ohms are added to the
terminals. The amplitude of each phase is obtained
with the phase shift of 120 degrees as usual. At this
speed (i.e. 1000 rpm), the maximal peak to peak
voltage is found as Vpp = 700 V.
(a)
Figure 7. Phase voltages for 60 ohm load in the case of 1000 rpm
rotor speed.
(b)
Figure 5. The variation of cogging torque with respect to the rotor
angle and airgap.
When the airgap decreased from 1.4 mm, initially
the cogging torque is increased substantially from 3.8
Nm to 4.4 Nm (Fig. 5(b)). It reaches to the highest
value for 1 mm. Then, it decreases substantially for
much lower airgaps. It is interesting that it decreases to
3.55 Nm for the airgap of 0.6 mm. Since the flux
density increases for small airgap values, one expects
a higher cogging torque value, however the flux lines
at the tip of the cores deviates to larger rotor angles
and it leads to lower torque. According to the previous
analyzes [11,14], the phase number of a machine also
affects the maximal cogging torque values.
Although the simulations have been performed
upto 1000 rpm, the waveforms have preserved its
sinusoidal shape and the phase shift, perfectly. This
indicates that the machine design is stable for each
phase. According to the simulations, while the rotor
speed increases, the amplitude also increases.
Flux density optimizations have also been carried
out for different airgaps (Fig. 8(a,b)). The maximal
flux density (i.e. B = 1.15 T) is obtained for 0.6 mm. It
gradually decreases, when the airgap is decreased till
1.4 mm. The minimal value (i.e. B = 1.0 T) is obtained
at the largest distance.
Fig. 6 presents a representative flux density. Note
that there exists a perfect symmetry in the waveform,
which proves the accuracy of the flux topology.
(a)
Erol Kurt, Halil Gör
4
[3]
[4]
[5]
(b)
Figure 8. The variation of flux density with respect to (a) rotor
angle and (b) airgap.
According to Fig. 8(b), the maximal flux density
decreases smoothly from 1.14 T to 1 T. Therefore the
optimized value for the airgap can be adjusted as 1.2
mm in terms of cogging torque and flux density
values.
IV.
CONCLUSIONS
The design and some optimization steps of a new
axial flux machine have been reported. The new
machine has an innovative flux topology with the
separated cores, which helps to decrease the core
loses. The airgap flux density is estimated as 0.5 T for
the studied gap. However, this value may decrease for
larger airgap values. The estimated power is found to
be 4.3 kW. The cogging torque optimization convinces
us to adjust 1.2 mm airgap by considering the
magnetic flux.
[6]
[7]
[8]
[9]
[10]
[11]
[12]
ACKNOWLEDGMENT
This research has been supported by The Scientific
and Technological Research Council of Turkey
(TUBITAK) under grant No. MAG-315M483. The
machine has been patented by Turkish Patent Institute
under Nos. 2013/13062 and 2015/04164.
[13]
[14]
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