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Optimum Permanent Magnets Configuration in Flat-Quasi Linear Permanent Magnet Generators

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p>Flat-quasi type of linear permanent magnet generators (LPMGs) have been considered to be applied for several applications, such for wave energy conversion and free piston combustion engine. One of the important issues concerning LPMG is the permanent magnets configuration, due to its effects to the generator’s excitation performance. In this paper, a 1 kW flat-quasi LPMG would be designed and built. During the process, optimum permanent magnets configuration was required and researched. The optimum configuration considered the output power and resulted cogging force. Invetigation was then conducted by modifying several variables, including poles’ arrangement, pole length, number of pole, and pole skewing angle. The modification constraints were total permanent magnets’ volume and generator dimension. The results showed that permanent magnet configuration with halbach arrangement, pole length equals 55% of the slot pitch length, and 61.19<sup>o</sup> skewing angle produced the optimum output values.</p
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International Journal of Electrical and Computer Engineering (IJECE)
Vol. 6, No. 6, December 2016, pp. 2589~2602
ISSN: 2088-8708, DOI: 10.11591/ijece.v6i6.11966 2589
Journal homepage: http://iaesjournal.com/online/index.php/IJECE
Optimum Permanent Magnets Configuration in Flat-Quasi
Linear Permanent Magnet Generators
Fransisco Danang Wijaya, Budi Azhari, Harnoko Stephanus
Department of Electrical Engineering and Information Technology, Gadjah Mada University, Yogyakarta, Indonesia
Article Info
ABSTRACT
Article history:
Received Jul 27, 2016
Revised Sep 20, 2016
Accepted Oct 4, 2016
Flat-quasi type of linear permanent magnet generators (LPMGs) have been
considered to be applied for several applications, such for wave energy
conversion and free piston combustion engine. One of the important issues
concerning LPMG is the permanent magnets configuration, due to its effects
to the generator’s excitation performance. In this paper, a 1 kW flat-quasi
LPMG would be designed and built. During the process, optimum permanent
magnets configuration was required and researched. The optimum
configuration considered the output power and resulted cogging force.
Invetigation was then conducted by modifying several variables, including
poles’ arrangement, pole length, number of pole, and pole skewing angle.
The modification constraints were total permanent magnets’ volume and
generator dimension. The results showed that permanent magnet
configuration with halbach arrangement, pole length equals 55% of the slot
pitch length, and 61.19o skewing angle produced the optimum output values.
Keyword:
Cogging force
Linear generator
Optimum configuration
Output power
Copyright © 2016 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
Budi Azhari,
Department of Electrical Engineering and Information Technology,
Universitas Gadjah Mada,
2nd Grafika street, Mlati, Sleman, Yogyakarta, Indonesia.
Email: budi.azhari@mail.ugm.ac.id
1. INTRODUCTION
Linear permanent magnet generators (LPMGs) have attracted interest of many scientists and
engineers around the world [1]. This generator, as shown in Figure 1(a) have been used for many
applications, such for sea wave energy conversion and free piston internal combustion engine [2-3]. The
characteristics of the sea wave are having high peak force and low speed [4], which all support the use of this
generator. Furthermore, unstable wave energy problems could be solved by utilizing energy storage system to
maintain the output voltage and frequency [5]. On the other hand, the use of the LPMG in free piston
combustion is considered due to its ability to produce higher combustion efficiency, higher power density,
and work for various fuels [6].
Differ from common rotary model, LPMG generates electric energy by driving linear motion
without any medium components, such as gears, screws, or crankshafts [7-8]. Generally, several advantages
could be gained from this model, such as simpler structure, higher efficiency and longer lifetime compared to
rotary ones [8]. Besides, the elimination of the medium components also reduces initial cost and simplifies
the structure of the machine.
Based on the geometrical shape, linear generators could be separated into tubular-type and flat-type.
Tubular type has cylindrical body, while the flat ones have prism shape. Recent studies show that for various
load, flat-type LPMG have easier and cheaper design, and higher values of efficiency and output power than
the tubular ones [9-10]. Furthermore, the use of permanent magnets for the generator excitation is because of
its simpler design, higher flux density in air gap, and higher efficiency [11].
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The flat-type LMPGs could be further classified based on the shape of its stator core. There are flat
tricore which has triangular-shaped stator and flat-quasi with its rectangular-shaped stator [12]. Both types
are shown in Figure 1(b). The last type has been proved to have larger flux density and induced voltage in
various low speeds [12].
(a)
(b)
Figure 1. (a) Linear Permanent Magnet Generator (LPMG) Model and (b) Several Model of Flat Type Linear
Generator: Flat-Tricore (left) and Flat-Quasi (right).
One of the important issues in all generators is the excitation system. This system would determine
the output voltage and output power [13]. In permanent magnet generators, including LPMGs, the excitation
performance is determined by configuration of the permanent magnets. Besides, the configuration of the
permanent magnets could also contribute to disruptive output parameter’s value, such as cogging force [14].
In this paper, a 1 kW flat-quasi LPMG would be designed and built. During the process, optimum
permanent magnets configuration was required and investigated. To obtain the desired result, modeling and
simulation were conducted. Those things, however are important for preliminary analysis, as they could
reduce the cost and spending time of any research which means to design certain tools or systems [15]. The
optimization in this case used pole modification method. The overall dimension of the machine was fixed,
while the modification were applied to the permanent magnet units.
Previous researches have tried to find out the optimum design of linear permanent magnet generator.
In tubular LPMG, optimization was conducted to obtain minimum electrical losses and maximum efficiency.
It is performed by changing the length ratio of radial magnets and axially magnet, and the ratio of translator
diameter and stator diameter [16].
Different tests had also been conducted to tubular LPMG. This tests were meant to optimize the
output power, cogging force, and the weight of the machine [17]. In this case, several variables, such as the
stator core height, air gap, magnets height, and the number of the pole were tested based on the 2D model of
the machine.
Other researcher investigated the optimum design on flat LPMG. The optimization was aimed to
minimize the cogging force. The research only used commercially available permanent magnets Therefore
the size of the magnets were fixed and the size modification was only applied to the teeth and slot. Several
variables, such as magnet and gap dimension, magnet skewing angle, and semislot dimension were modified
and tested [18].
All researches above investigated the optimum design of the LPMG. However, there are different
variables and/or optimized parameters among those researches. In this paper, the optimization was focused
on the permanent magnet variables, and was meant to optimize the output power and cogging force. The
variables that were modified are the arrangement, unity length, number, and skewing angle of the permanent
magnets. The total volume of the permanent magnets, translator, and the overall dimension of the machine
were kept constant.
First, a three phase 1 kW flat-quasi LPMG model was presented. The model was then simulated
using Finite Element Method (FEM) software of FEMM. During the simulation, the configuration of the
permanent magnet was modified. In each test, the output power and resulted cogging force were examined
and noted. The configuration that produces maximum output power and minimum cogging force was chosen
for the next tests. At the end of the paper, the optimization result was examined and discussed.
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2. RESEARCH METHOD
2.1. Proposed LPMG Model
A 1 kW flat-quasi LPMG was modeled. In this paper, two-sided LPMG, as shown in Figure 2 (a),
representing four-sided LPMG, as shown in Figure 2(b). Permanent magnets for excitation were placed on
the translator, while the electrical output could be extracted from the stationary part (stator). The permanent
magnets were made of rare-earth material (NdFeB 40) and were initially arranged in radial arrangement. This
initial arrangement of the permanent magnet was illustrated in Figure 3.
The stator had salients on its end. These salients were aimed to maximize the flow of the magnetic
flux from the magnets and to reduce the cogging force [19]. American Wire Gauge (AWG) 11 was used as
the stator wire, because expected full load current that could be generated from the LPMG was 10 A.
Furthermore, the stator winding used concentrated winding model.
Several equations were considered to design this generator [20]. The power rating of the generator
was approached using the following equation,
IVmP T..
(1)
The value of expected terminal voltage, VT next lead to the value of expected electromotive force (emf), by
using the following equation,
)( jXRIVE TA
(2)
Then, the value of the emf was used to determine the width of the stator. The equation is shown below,
avgTts
A
svBNM E
W... 2
(3)
Meanwhile, the desired value of rated current would determine the size of coil wire. For certain kind of wire
with typical diameter, the size of slot follows the equation below,
wt
t
ls
N
D
s.6.0
.
2
2
(4)
The actual width of air gap could be determined using equation below,
gKg Ceq .
(5)
where KC is Carter coefficient. The value of KC could be calculated using equation below.
2
)5( )5(
wtwtt
wtt
Cssg sg
K
(6)
Figure 2. (a) Two-Sided Flat LPMG; (b) Four-Sided Flat LPMG.
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Table 1. Parameter Data of LPMG Model
Symbol
Quantity
Unit
Value
Ls
stator total length
mm
330
Ws
stator width
mm
120
tl
stator teeth length
mm
90
tw
stator teeth width
mm
20
sw
salient width
mm
30
sh
salient height
mm
10
sl
slot length
mm
80
swt
slot width
mm
30
τt
slot pitch
mm
50
τp
pole length
mm
27.5
τw
pole thickness
mm
20
Sbw
stator back iron width
mm
30
so
slot opening
mm
20
m
number of phase
-
3
p
number of pole
-
12
q
slot/pole/phase
-
0.5
Hc
PM coercivity
A/m
979,000
σ
PM electrical conductivity
MS/m
0.667
Nt
turns per slot
-
300
Br
PM magnetic flux density remanant
T
1.24
σ-s
stator wire electrical conductivity
MS/m
58
D
stator wire diameter
mm
0.20378
R
stator wire resistance
Ω/km
4.13
Figure 3. One-Sided of flat-quasi-type LPMG model with radial configuration.
Slot pitch (τt) is defined as the length of slot width (swt) plus the length of tooth width (tw). After deciding its
value, the length of stator could be calculated using the following equation:
wts tmqpL ...
(7)
The value of pole length (τp) then could be calculated using the following equation.
p
Ls
P
(8)
More detail information about the generator model is shown in Table 1, which refers to Figure 3.
Finite element method with open source software FEMM was then used. This software could be controlled
by Lua scripts to extract desirable quantities, such as flux linkage and resulted cogging force [21]. In this
paper, the simulation was conducted in two-sided model. However, the results of the induced voltage and
cogging force values of the four sided design were assumed linear with the two sided’s. The initial design of
the generator in FEMM is shown in Figure 4 (right).
2.2. Optimization Procedure
After modeling and simulating the desired LPMG model, the permanent magnets configuration was
then modified. The modification was conducted sequentially. First, the pole arrangement was modified. Then
the pole length was modified while keeping the total length and volume of the translator. After that, the
magnets were skewed with certain skewing angle. When the magenets were skewed, the size of each magnet
was also kept constant. In each modification, the optimum design was determined by using a fitness function.
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The output power was noted at full load condition. For obtaining the output power, single phase
analysis could be conducted. First, no-load induced voltage for each phase was examined. In this test, the
simulation only gave the flux linkage values. The Faraday’s law equation could be used to convert that value
to induced voltage value.
)(.. tv
dz
d
dt
dz
dz
d
dt
d
(9)
where variable v(t) shows that the velocity is time-varying. However, in this paper, the velocity was assumed
contant.
Table 2. Meaning of Several Symbols Used in this Paper
Symbol
Meaning
Unit
ε
no-load induced voltage
V
λ
flux linkage
Wb
t
time variable
s
z
translation position
m
v
translation speed
m/s
Z
coil impedance
Ω
I
full load current
A
RL
load resistance
Ω
X
coil reactance
Ω
f
frequency
Hz
L
coil inductance
H
Rline
coil resistance
Ω
PT
output power
W
n
constant for deciding the output frequency
-
P
output power from simulation
W
FC
output cogging force from simulation
N
Pmin
minimum output power from certain test
W
FC_max
maximum cogging force from certain test
N
Assuming that there was only resisitive load of RL, the value of load resistance could be determined.
lineL RX
I
R
2
2
(10)
The value of X was determined by the output frequency. It could be calculated using equation below.
LfX ...2
(11)
Meanwhile, the output electrical frequency was analytically affected by the pole configuration.
n
v
f
(12)
The value of n=4 for halbach magnetic array n=2 for radial or axial magnetic array. Meanwhile, the value of
line resistance could be calculated using equation below.
)(2...2 whlbwsttline gstsWNR
(13)
Usually, second term is relatively small compared to first term, thus its effect is not significant. The full load
output power was then calculated by using equation below.
LT RIP ..3 2
(14)
Equation (10) and (14) has urged to set the maximum current below the full load current in case the
full load current was less than 10 A. If both values are equal, the value of RL would be zero and so would the
output power. In other words, all input power are dissipated in coil resistance as power loss.
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Another consideration was cogging force. It is undesired force that is resulted from the attractive
interaction between permanent magnets in translator and stator teeth, which was made of ferromagnetic
materials [22-23]. The presence of cogging force could cause mechanical oscillation during translator
movement. Thus, the value of the cogging force should be minimized.
Single phase equivalent circuit in this test is shown in Figure 4 (left). Meanwhile, list of symbols
used in this paper, complete with their meanings and units are in Table 2. Since three phase generator was
used, there were self and mutual inductances. The total inductance was the sum of both inductances’ values.
The effect of modification to the size of the generator and the investment cost were neglected.
Earth’s gravitation and air friction force were also neglected. The optimum design in each modification was
chosen based on the value of fitness function (F) below. Larger the value of fitness function, a design was
said to produce optimum or better output.
maxmin Fc
Fc
PP
F
(15)
Figure 4. Single Phase Equivalent Circuit of the LPMG Model (left); Generator Model in FEMM (right)
3. RESULTS AND ANALYSIS
3.1. Optimum Poles’ Arrangement
As mentioned earlier, the initial configuration at first using radial permanent magnets arrangement.
The arrangement was then varied, while other parameters’ values were kept constant. Overall, the
configurations used in this test were radial, axial, and halbach. All of these arrangements are shown in
Figure 5(a)-5(c).
Radial arrangement in this configuration was shown in the left side of Figure 5(a). In this
arrangement, two adjacent magnets have alternating magnetization, with one points out the stator and another
points out the opposite direction. This arrangement is relatively simple and low-cost assembly. However, for
more than one-sided permanent magnet arrays, magnetic yoke is needed to maintain the distance among
those arrays. This yoke would then cause several consideration, such as eddy current loss and increase of the
generator weight.
Axial arrangement in this configuration was shown in Figure 5(b). It does not have to be sticked on
magnetic yoke. In this arrangement, each magnet have magnetization that is perpendicular to the surface of
the stator teeth. The adjacent magnets would naturally repel each other due to their magnetization setting, so
they might be tied to hold their position. This arrangement could be assembled with or without any distance
pieces between two magnets.
The magnetic field resulted from radial and axial magnetic arrays are shown in the right side of
Figure 5(a) and Figure 5(b) successively. It could be seen that both arrangement result magnetic field in both
sides of each array. The consequences is that the magnetic field through the yoke would be quite large, which
then generates quite large eddy current losses. Besides, the magnetic flux that flows to the coil would
decrease, so the output power would not be optimum.
Halbach arrangement in this configuration is shown in the left side of Figure 5(c). It consists of
alternating radial and axial magnets. In this case, there are four directions of magnetization, which yield
nearly sinusoidal magnetic flux output. Moreover, this configuration would augment the magnetic field on
one side of the permanent magnets array, and cancel the field up to nearly zero on the other side. This array
properties could increase the efficiency of the generator, since the magnetic flux from the permanent magnets
could be focused to one side. However, the investment cost of this arrangement is quite high.
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The magnetic field from halbach arrangement is shown in the right side of Figure 5(c). In this
arrangement, the magnetic field through the magnetic yoke is lesser than the previous arrangements.
Therefore, this arrangement could reduce the eddy current loss. Moreover, the magnetic flux that flows to
stator would be larger than the previous arrangement. It would then increase the induced voltage and the
output power of the generator.
(a)
(b)
(c)
Figure 5. Arrangement Model: (a) Radial, (b) Axial, (c) Halbach.
Figure 6. Frequency and Impedance of Various
Arrangement
Figure 7. The Values of Induced Voltage, Terminal
Voltage, and Cogging Force from Various
Arrangement
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(a)
(b)
Figure 8. (a) Output Power, and (b) Fitness Function of Various Configuration
The simulation used 1 m/s as the translation speed, and was assumed constant. In halbach
arrangement, one period of electrical wave would be generated in coil after four adjacent poles passing a
stator tooth where that coil lies. Meanwhile in both radial and axial array, same amount of wave could be
generated after two adjacent poles passing the tooth. Because the translation speed was same for all
arrangements, then the electrical frequency resulted from halbach arrangement would less than the electrical
frequency of both axial and radial arrangement. The electrical frequency then determines the inductance,
reactance, and thus impedance of the coil. The frequency and the impedance of all arrangement are shown in
Figure 6. Halbach arrangement results lower electrical frequency, thus lower impedance than the other two
arrangements.
On the other hand, focussed magnetic flux of halbach array induces larger voltage than the other
arrays. Then with lower coil impedance, the terminal voltage of the halbach array would become the largest,
and so is the output power. The values of the induced voltage and output power of all arrangements are
shown in Figure 7 and Figure 8(a) respectively.
The arrangement also affect the cogging force. From Figure 7, halbach arrangement suffers the
largest cogging force. This is due to the strongest magnetic field resulted from this arrangement, compared to
the other two. On the other hand, radial arrangement suffers the lowest. In this arrangement, the accumulation
of the flux density on the edges of the permanent magnet decreases.
From Figure 8(b), halbach arrangement produces the largest fitness function. In other words, this
arrangement gives the optimum output. This configuration would then be used as initial configuration for
next tests.
3.2. Optimum Pole Length
The dimension of the pole at first followed what are mentioned in Table 1. Then the value of pole
length per slot pitch length pt) was varied, with other parameters’ values were kept constant. Because the
translator total length and the magnets’ total length and volume were kept, the change in pole length was then
compensated by changing the number of poles. Longer the pole length (τp), the number of the pole would be
fewer, and vice versa. Furthermore, the initial translation speed in this test was set 1 m/s.
The results show that the value of τpt would affect the value of the induced voltage and terminal
voltage, as shown in Figure 10(a). The length of each permanent magnet affects the relative position of any
magnet toward the stator. It then affects the instantaneous value as well as the rate of change of the flux
linkage in the coil. The latter parameter, would determine the value of induced voltages.
The length of the magnet on the other hand, is inversely proportional to the output electrical
frequency. This frequency would then affect the impedance of the coil. Figure 11(a) shows the values of the
electrical frequency and the coil impedance for various values of τpt. The values of the induced voltage and
coil impedance would determine the terminal voltage, which is directly proportional to the output power of
the generator.
The length and number of the magnets also determines the cogging force, as shown in Figure 10(b).
In this case, if each magnet has equal size, thus they produce equal magnetic field. Moreover the total
translator volume and length were also constant. However, different size of single magnet results in different
cumulative interactions in an array, and thus different force resultant. Then the average cogging force would
differ among different pole length, for equal total length.
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The interaction which shows the cogging force could be described through the magnetic flux’s lines
which are resulted from each configuration. More intense the continuous flux’s lines from the magnet to the
stator teeth means stronger the interaction. However, the average cogging force value in this paper considers
the interaction at all positions. So, the magnetic flux intensity in all relative position (during the translator
movement) of the translator and stator would influence the result. Figure 9(a) to 9(d) shows the different
magnetic flux’s lines and intensity among several configuration at the same position.
(a)
(b)
(c)
(d)
Figure 9. Different Magnetic Flux Intensity Relates to the Strength of Interaction of Flat-Quasi LPMG with,
(a) 18 Poles; (b) 13 Poles; (c) 9 Poles; (d) 6 Poles, at same Position
(a)
(b)
Figure 10. (a) Values of Induced Voltage and Terminal Voltage for Various τpt; (b) Values of Output Power
and Cogging Force for Various τpt.
Figure 10(b) also shows that the configuration where the pole length equals 2.75 cm or τpt=0.55
results the largest fitness function. Then different values of translation speed were tested. It is purposed to
check its influence to the value of fitness function. The results were tabulated in Figure 11(b). It could be
seen that larger the value of the translation speed, the value of the fitness function would increase. However,
the trend of the fitness function values are same for every value of speed. Figure 11(b) shows that the
optimum output was obtained when τp=2.75 cm or τpt=0.55, for all values of translation speed.
Further tests were then conductedby modifying some other parameters. In these test, the width of
stator tooth’s salient and the pole thickness were modified. In several values of the both quantities, all values
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of τpt were re-tested. The results were then tabulated and compared. These tests were meant to check
whether these two parameters affect the output values. This is because these two dimension in this test were
decided manually.
(a)
(b)
Figure 11. (a) Values of Resulted Electrical Frequency and Coil Impedance for Various τpt; (b) Values of
Fitness Function for Various τpt and for Several Values of Translation Speed.
(a)
(b)
Figure 12. (a) Output Power and (b) Cogging Force Values from Various Values of τpt and Different Salient
Width.
(a)
(b)
Figure 13. (a) Output power and (b) cogging force values from various τpt and different pole thickness
The output power and cogging force values from several values of salient width are shown
in Figure 12(a) and 12(b). Meanwhile, the values both parameters for several values of pole thickness are
shown in Figure 13(a) and 13(b). From those graphs, the output power is directly proportional to the width of
salient and pole thickness. However, the trend of the output power is same for all values of thickness.
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Meanwhile the cogging force slightly decreases if the width of salient is increase and slightly increases if the
pole thickness increases.
If the fitness function values from all salient widths and pole thicknesses are tabulated, the result is
shown in Figure 14. From that graph, the trend and the values of the fitness function is nearly same for all
values of both quantities. Besides, Figure 14 also shows the pole length equals 2.75 cm or τpt = 0.55
produces the largest fitness function, for all values of both quantites. This configuration, with initial value of
salient width and pole thickness would be used for next test.
Figure 14. Fitness Function from Various Values of τpt.
3.3. Optimum Pole Skewing
The optimum configuration from previous test was brought for skewness test. Here, the permanent
magnets were skewed with certain angles. However, other parameters’ values were still kept constant. The
illustration of the skewed poles is shown in Figure 15.
In this test, input variable of the skewing angle was set by shifting the outer side of the permanent
magnets, each by 1 mm. The skewing of the permanent magnets by this method would not change the total
volume of the translator. However, the skewing might change the total length of the translator and modify its
shape, which may need certain treatment in certain application. The skewing would also change the total
surface area of the magnetic array. In this case, the skewing angles that were applied were limited between
45o to 90o.
Figure 15. Illustration for Skewed Permanent Magnets
The change of surface area of the magnetic arrays would affect the induced voltage and cogging
force. Different surface area, as well as shape, would affect the intensity of the magnetic flux that is resulted
by the permanent magnets. On the other hand, the contact area between the magnet and the stator would also
change for different skewing angle. Figure 16(a) shows the values of induced voltage and output power for
several skewing angles. Meanwhile, the resulted cogging force and the fitness function are shown in and
Figure 16(b).
Coil
PM
Yoke
Stator
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As it could be seen, the output voltage at first increases as the skewing angle decreases. It then
reaches peak value at skewing angle=63.44o, before going down as the skewing angle decreases. In this
modification, change in skewing angle does not change the output frequency. This is because neither pole
number nor pole length changes. Hence, the impedance of the coil is also constant. Then the output power is
directly proportional to the induced voltage. It is proved from the trend of the output power which is same as
the trend of induced voltage.
From Figure 16(b), the value of fitness function is inversely proportional to the value of cogging
force. It could be seen that the trend of the fitness function is the reflection of the cogging force’s trend. This
result is valid in other designs with same treatment. It could be concluded that for an LPMG with skewed
permanent magnet and for given fitness function, the trend of the cogging force is the reflection of the fitness
function trend.
(a)
(b)
Figure 16. (a) Induced Voltage and Output Power from Various Skewing Angle; (b) Cogging Force and
Fitness Function Values from Various Skewing Angle
In this test, the configuration where skewing angle equals 61.19o results the optimum output. This
configuration was then declared as the optimum one. The parameter values of the optimum configuration are
tabulated in Table 3.
Table 3. Parameters’ Values of Resulted Optimum Configuration of 1 kW Flat-quasi LPMG
Parameters
Unit
Value
Induced voltage
Vrms
79.225
Coil resistance
Ω
0.778
Coil reactance
Ω
5.826
Coil impedance
Ω
5.878
Rated current
A
10
Terminal voltage
Vrms
20.445
Frequency at rated speed
Hz
9.091
Output power
W
1,376.999
Cogging force
N
3.508
PM skewing angle
-
61.19o
4. DISCUSSION
The optimization test was conducted for 1 kW flat-quasi LPMG design. The initial design of the
generator considered several parameters and equations which are commonly used for designing typical
machine. Furthermore, the optimization was focused on the permanent magnets of the generator.
In part of poles arrangement analysis, the dimension of the permanent magnets in each arrangement
was same. This causes the number of the pole in each arrangement was same. In other words, this part only
analyzed the arrangement, and not also investigated the number of the permanent magnet.
In pole length and pole number optimization analysis, it should be noted that the stator and the
translator in this paper have equal length. Moreover, the modification did not change both total surface area
ISSN: 2088-8708
IJECE Vol. 6, No. 6, December 2016 : 2589 2602
and volume of the permanent magnets. It would be beneficial to further investigate the effect of these two
parameters if the translator length is not constant.
In pole skewing angle analysis, the skewing angle was limited from 45o to 90o. Larger angle is
impossible to design. Meanwhile, smaller angle is not recommended due its uncommon design, manufacture
difficulties, and larger cost of manufacturing.
Other similar optimization researches of LPMG have also conducted. However, those researches
investigated either different objective parameter, or different method of optimization. Therefore, this research
could be an additional reference for optimum design of LPMG.
5. CONCLUSION
The optimization of the permanent magnet’s configuration for flat-quasi linear permanent magnet
generator has been performed using 1 kW generator model. Pole modification methos was used to optimize
the generator. The variables were the arrangement, pole length, and skewing angle of the permanent magnets.
The constraints was the total permanent magnets’ volume and size of the generator. The optimization
considered the output power and resulted cogging force. It were shown that the permanent magnets with
configuration of halbach arrangement, pole length equals 55% of the slot pitch length, and was skewed with
skewing angle of 61.19o resulted the optimum output. It was also proved that the salient width and the pole
thickness might affect the output power and resulted cogging force. However, they did not affect the
optimum level of the configuration based on given fitness function.
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Optimum Permanent Magnets Configuration in Flat-Quasi LPMGs (Fransisco Danang Wijaya)
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BIOGRAPHIES OF AUTHORS
Fransisco Danang Wijaya, born on February 1974 in Sleman, Indonesia. He received his
Bachelor and Master degree, both from Electrical Engineering Major, Gadjah Mada University
in 1997 and 2001 respectively. He then got his Doctor of Engineering in Tokyo Institute of
Technology in 2009. He is currently Associate Professor at the Department of Electrical
Engineering and Information Technology, Gadjah Mada University. His research is specialized
in power system engineering, energy conversion, also transmission and distribution system. He
is also expert in power system control technique using Magnetic Energy Recovery Switch
(MERS).
Budi Azhari was born on December 1994 in Bantul, Indonesia. He received his Bachelor
degree of Electrical Engineering from Department of Electrical Engineering and Information
Technology, Gadjah Mada University in 2016. His research topics are focused on design and
analysis of electrical machine. He is currently conducting research about linear permanent
magnet generator to be applied in South Coast of Yogyakarta, Indonesia.
Harnoko Stephanus, born on December 1953 in Yogyakarta, Indonesia. He got his Bachelor
and Master degree, both from Electrical Engineering Major, Gadjah Mada University. He is
currenly a lecturer at the Department of Electrical Engineering and Information Technology,
Gadjah Mada University. His research is specialized in Energy management System, Electrical
Energy Conservation, Distributed System.
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