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Proceedings ArticleDOI

Particle swarm optimization of air-cored axial flux permanent magnet generator for small-scale wind power systems

08 Apr 2014-pp 1-6
TL;DR: In this paper, the particle swarm optimization method is used in the design of an axial flux permanent magnet generator for small-scale wind power system, where five inter-dependent design parameters are adjusted simultaneously to achieve an optimal solution for the application.
Abstract: Axial flux permanent magnet synchronous machines with aircored configuration is particular suitable for small scale wind power system due to their advantages of low synchronous reactance, cogging torque free, high efficiency and high power factor. However, due to the number of machine parameters, with some tightly `coupled' with each other, optimisation of the design could become extremely challenging by conventional analytical means. Here, the particle swarm optimization method is used in the design of an axial flux permanent magnet generator for small-scale wind power system. Five inter-dependent design parameters are adjusted simultaneously to achieve an optimal solution for the application. Three-dimensional finite element analysis is employed to evaluate the electromagnetic performance for the optimization. The results show the proposed optimization method is efficient and with fast convergence.

Summary (3 min read)

1 Introduction

  • Whilst large-scale wind generators are now widely employed in centralized wind farms to provide electricity to the grid [2,3], the fast development of distributed electric generation means that the demand for small-scale to medium-scale generators will remain strong.
  • In the recent years, increasing number of researchers are applying PSO method to multiparameter, multi-objective optimal design of electric machines, as many of the parameters to be optimized are conflicting to each other during optimization.
  • Though with many inherent merits of this air-cored AFPM synchronous machine, there is a concern about the usage of permanent magnet (PM) materials hence the cost of the machine.
  • The results have revealed that PSO is a simple yet efficient method with fast convergence.

2 The AFPM generator

  • The air-cored AFPM synchronous machine with doubleouter-rotor-internal-stator configuration is illustrated in Fig.
  • The wind turbine can be directly attached to the outer rotor which can further reduce the system weight and cost.
  • Since saturation in back iron is not considered, the size and shape of PMs and coils are the key parameters which have great influences on the performance of the machine.
  • The design values of these parameters, such as pole pitch factor (αp), inner diameter (Di), thickness of PM (Hm), thickness of coil (Hc) and coil-band width (Wc), have great interaction, sometimes conflicting influence on one other.
  • They should be simultaneously optimized to achieve an optimal solution.

3 Application of PSO

  • PSO is a stochastic global optimization method.
  • Besides its fast convergence rates, another main advantage is simplicity.
  • Only two vectors are associated for each particle in PSO, position (Xi) and velocity (vi) respectively.
  • (3) where w is the initial weight, c1 and c2 are scaling factors, rand is function generating random numbers between 0 and 1, and pbest is best solution one particle ever achieved (personal pest), and gbest is the best solution all particle achieved so far (global best).
  • Much work has been done to achieve fast convergence on the selection of w, c1 and c2.

2.1 Define solution space

  • Generally in engineering applications, parameters are chosen in a certain range based on practical experience and theories.
  • (0.5,1)p Thickness of magnet (Hm): Thicker magnet will increase the flux density as well as cost PM material.
  • Nevertheless, thicker coils also enlarge the air gap and lower the flux density.
  • (0, /15) Population size also necessitates special attention.
  • Large population can explore solution space more thoroughly, with the cost of more time-consuming computations.

2.2 Boundary conditions

  • As there are random functions acting on the process of generating velocity, particles are likely to fly out of the defined solution space.
  • In the first two boundary conditions, particles are strictly restrained inside the solution space, while in invisible walls particles are allowed to go out of defined space.
  • Once a particle flies out, the position would not be calculated or evaluated, and the particle has to fly again until it is back within the defined region.
  • There is more freedom of the third boundary for particles to roam around, and thus their natural motion would not be interfered.
  • According to Robinson et al. in [11], invisible walls condition is faster and more consistent, and is thus adopted in this case.

2.3 Objective function

  • Each position of particles represents a possible design for the AFPM generator.
  • To evaluate the goodness of the designs explored by the particles, an objective function needs to be defined and linked to return fitness values.
  • In general, different weight coefficient choices represent different design goals.
  • Performance and the cost of the generator are the key criterion for optimization.
  • PMs are much more important and expensive than coils, and hence the value of km is much larger than kc.

2.4 Implement of PSO

  • The flow chart of the PSO program is illustrated in Fig.
  • After initialization, the process of each iteration can be divided into 4 steps.
  • The average fitness of particle positions, average fitness of personal best, and global best of each iteration is depicted in Fig.
  • It should be noted that all the design parameters stabilise after the 26 th iteration, with optimal solution obtained.
  • The trends of performance indexes are derived and depicted in Fig.5.

4 3-D FEA verification

  • To validate the performance of the final optimised design from PSO algorithm, simulation should be carried out by using the FEA method.
  • Because of the instinct structure of AFPM machines, 3-D FEA model is a used to obtain more accurate results.
  • Since only back iron, PM poles and coils matter in the electromagnetic simulation, housing and connection parts of the machine are not included in the 3-D FEA model.
  • The machine in 3-D model is illustrated in Fig.1, and the main design parameters are listed in Table 2.

4.1 No load characteristics

  • Firstly, the no-load characteristics of the machine are calculated.
  • The flux distributions of the back iron and the air gap are shown in Fig.
  • The back EMF is another most important parameter for the machine design.
  • For a three phase generator, sinusoidal wave form is preferred to avoid extra loss because of harmonic components.
  • Moreover, from Fig. 7(b), it can be seen that the output contains few harmonics.

4.2 On load characteristics

  • To simulated performances of the generator at different operating points, FEA models at different loads are also constructed.
  • And because of the influence of the electronic switches during commutation, distortion can be observed in the voltage wave form, and thus output DC voltage is fluctuating six times in one electrical period in terms of the six switches of the three-phase fullwave rectifiers, as is shown in Fig. 9(a) and 9(b).
  • Generally speaking, the trends of these two figures are quite similar.
  • In particular, it can be seen that the operating efficiency is above 81%, and the lowest efficiency appears at full load, which is because higher current leads to higher resistance loss.
  • Last but not least, for the small wind generator, the turbine is fixed and cannot be adjusted in terms of different wind speeds, which means that the energy captured by generator is changing all the time.

5 Conclusion

  • An AFPM synchronous machine with rated power of 500W at 300rpm is proposed for small-scale wind power applications.
  • A sophisticated multi-parameter and multi-objective PSO algorithm based on 3-D FEA is developed and employed to carry out optimization with a user defined objective function.
  • The performance of the final optimal machine has also been comprehensively evaluated by (a) phase voltage and current (b) loss, torque and power Fig.
  • Results reveal that the optimal design from PSO has a good performance under different load conditions and meets the requirements as a small-scale directdrive wind power system, and PSO method is a simple and efficient optimization algorithm with fast convergence.

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1
Particle Swarm Optimization of Air-cored Axial Flux Permanent
Magnet Generator for Small-Scale Wind Power Systems
B. Xia, P. C. K. Luk, W. Fei, L. Yu
Electric Power and Drive Group, School of Engineering, Cranfield University, UK
Keywords: Air-cored, axial flux permanent magnet, particle
swarm optimization, wind power.
Abstract
Axial flux permanent magnet synchronous machines with air-
cored configuration is particular suitable for small scale wind
power system due to their advantages of low synchronous
reactance, cogging torque free, high efficiency and high
power factor. However, due to the number of machine
parameters, with some tightly ‘coupled’ with each other,
optimisation of the design could become extremely
challenging by conventional analytical means. Here, the
particle swarm optimization method is used in the design of
an axial flux permanent magnet generator for small-scale
wind power system. Five inter-dependent design parameters
are adjusted simultaneously to achieve an optimal solution for
the application. Three-dimensional finite element analysis is
employed to evaluate the electromagnetic performance for the
optimization. The results show the proposed optimization
method is efficient and with fast convergence.
1 Introduction
Wind power will continue to contribute an increasingly
important fraction of the future energy mix in the U.K.
Among the most mature technology in renewable energy
industry, wind power has promising prospects to achieve an
economically sustainable and environment friendly solution
to energy challenge we face [1,2]. Whilst large-scale wind
generators are now widely employed in centralized wind
farms to provide electricity to the grid [2,3], the fast
development of distributed electric generation means that the
demand for small-scale to medium-scale generators will
remain strong. In particular, for some cities and towns in
windy area, small-scale wind generators can be built in
neighbourhoods and even clustered together to power
streetlights. Moreover, in some remote areas where power
grid is not available, small-scale off-grid power systems
become more crucial as the main energy source [4,5].
With the advantages of flat shape, compact structure, high
power and torque density, axial flux permanent magnet
(AFPM) synchronous machines are widely applied in various
applications such as wind power generation, electric vehicle,
aircraft and so on [6-8]. Air-cored AFPM synchronous
machines, which have no ferromagnetic material in the stator,
could eliminate iron loss as well as cogging torque. Moreover,
such an air-cored configuration could also deliver high
efficiency, light weight and low starting torque so that it will
be ideal for small-scale off-grid wind power applications. As
the air-cored AFPM synchronous machine has relatively large
magnetic air gap, more magnets are required for the sufficient
excitation. Nevertheless, the advantage of large air gap is that
no saturation occurs in the machine, and high harmonic
components of air gap flux density distribution can be
minimized. Importantly, the large effective air gap length also
results in low synchronous reactance and hence high power
factor.
The electromagnetic performance of an AFPM generator is
affected by many parameters, and some of them have strong
interactions with one another. This could present conflicting
requirements in the optimisation stage. Many optimization
methods, such as response surface methodology (RSM),
genetic algorithm (GA) and particle swarm optimization
(PSO), have been proposed for multi-parameter and multi-
objective problems to explore the design space and achieve
optimal designs to satisfy the objectives simultaneously [9-
11]. Among these methods, PSO is a relatively simple but
efficient evolutionary computation technique originated from
the movement around searching space of intelligent swarm
societies according to a user-defined fitness function. The
instinct merits such as simple parameter adjustment, short
computational time, derivative-free, and flexibility, make
PSO easily suit to different kinds of optimization problems
[11-13]. Although it was only first developed in 1995 [14,15],
PSO has already attracted more and more interests in a variety
of research areas and applications.
PSO method has been adopted successfully in electric power
systems for economic dispatch, reactive power control and
voltage regulations [10,12,16]. In the recent years, increasing
number of researchers are applying PSO method to multi-
parameter, multi-objective optimal design of electric
machines, as many of the parameters to be optimized are
conflicting to each other during optimization. Permanent
magnet synchronous machines (PMSMs) have been
optimized using PSO to achieve high efficiency and less
weight [17,18]. Moreover, the cogging torque of a transverse
flux permanent motor (TFPM) and the force of a linear TFPM
have been optimized in [9] and [19] respectively. An PSO-
based optimal design of axial laminated synchronous
reluctance motor (SynRM) has been used for traction
applications [20]. Moreover, designs of induction machines
using PSO method have also been reported [21].
This paper concerns the design of a 500W AFPM generator
for small-scale wind power system. Though with many
inherent merits of this air-cored AFPM synchronous machine,
Proceedings of the 7th IET International Conference on Power Electronics, Machines and Drives (PEMD 2014), Manchester, UK, 8-10 April 2014
DOI: 10.1049/cp.2014.0295
This paper is a postprint of a paper submitted to and accepted for publication in and is subject to Institution of Engineering and Technology Copyright.
The copy of record is available at IET Digital Library"

2
there is a concern about the usage of permanent magnet (PM)
materials hence the cost of the machine. Therefore, the inner
and outer diameters, pole pitch factor and thickness of PMs
should be carefully determined to obtain high power output
with minimum PM usage. Moreover, since no slot exists in
the stator, the coil configuration, which has a great influence
on the performance of the generator, needs to be optimized.
Three-dimensional (3-D) finite element analysis (FEA)
models are developed to carry out the optimization based on
PSO. Optimal design is achieved by factoring both the
performance and cost into the cost function. The
electromagnetic performance of the optimal design is
evaluated by 3-D FEA under different operational conditions.
The results have revealed that PSO is a simple yet efficient
method with fast convergence.
2 The AFPM generator
The air-cored AFPM synchronous machine with double-
outer-rotor-internal-stator configuration is illustrated in Fig. 1.
Surface-mounted PM poles have the merits of simple
structure and easy manufacture and assembly. The wind
turbine can be directly attached to the outer rotor which can
further reduce the system weight and cost. Since the gearbox
is no longer necessary, efficiency and reliability will further
improve [6]. Due to the relatively large magnetic air gap,
saturation is not considered in analysis. Therefore the main
design parameters lie on the dimensions of PM and coils.
According to its instinct flux distribution style, the sizing
equation of this AFPM synchronous machine can be obtained
2
23
(1 )(1 )
120
em p w g o
P mn K B A D
(1)
where P
em
is the electric power, α
p
is pole pitch factor, m is
the number of phases, n is rotating speed in resolution per
minute, K
w
is coil factor, B
g
is the air gap flux density, A is
the electric load, D
o
is the outer diameter, and γ is the ratio of
D
i
(inner diameter) over D
o
. Outer diameter is chosen as
250mm to meet the requirements.
The combinations of rotor poles and stator coils for such
AFPM machine have been discussed in [22]. The pole/coil
configurations of 16/12, 20/15 and 24/18 have large coil
factors and the power density of the machine with increase
with pole number. However, high pole number means strict
precision for pole location, which will increase mechanical
complexity and manufacturing cost. Therefore, a compromise
of 20/15 pole/coil configuration is adopted for the design.
The main active parts in the machine are PMs, coils and back
iron, as depicted in Fig.1. Since saturation in back iron is not
considered, the size and shape of PMs and coils are the key
parameters which have great influences on the performance of
the machine. However, the design values of these parameters,
such as pole pitch factor (α
p
), inner diameter (D
i
), thickness of
PM (H
m
), thickness of coil (H
c
) and coil-band width (W
c
),
have great interaction, sometimes conflicting influence on one
other. Consequently, they should be simultaneously optimized
to achieve an optimal solution.
3 Application of PSO
PSO is a stochastic global optimization method. Besides its
fast convergence rates, another main advantage is simplicity.
Only two vectors are associated for each particle in PSO,
position (X
i
) and velocity (v
i
) respectively. One position of a
particle is a candidate solution, and the next searching
position is determined by the velocity of the particle based on
the experience of the whole swarm. After one iteration,
position and velocity can be updated as follows [11]
( 1) ( ) ( 1)
i i i
X t X t v t
(2)
1
2
( 1) ( ) rand() ( )
rand() ( )
i i best i
best i
v t w v t c p X
c g X
(3)
where w is the initial weight, c
1
and c
2
are scaling factors,
rand() is function generating random numbers between 0 and
1, and p
best
is best solution one particle ever achieved
(personal pest), and g
best
is the best solution all particle
achieved so far (global best).
Much work has been done to achieve fast convergence on the
selection of w, c
1
and c
2
. According to [11,15], best choice for
c
1
and c
2
is 2.0 for both, and w should be between 0.4 and 0.9.
2.1 Define solution space
Generally in engineering applications, parameters are chosen
in a certain range based on practical experience and theories.
In PSO, particles are exploring the solution space for optimal
solution. Larger space means more time is required to explore
the area. Thus reasonable range should be given according to
different problem to save time for the optimization. For the
AFPM machine design, there are five key design parameters
having great influence on the machine performances:
Ratio of D
i
over D
o
(γ): Smaller D
i
is, longer the
effective length of conductors are. Yet smaller D
i
reduces the space for armatures in inner radius area.
(0.4,0.8)
Pole pitch factor (α
p
): Larger pole pitch not only can
increase the flux density in the air gap, but also
increase the amount of magnet usage and may cause
unwanted harmonics in flux distribution.
Fig. 1: Topology of air-cored AFPM machine.

3
(0.5,1)
p
Thickness of magnet (H
m
): Thicker magnet will
increase the flux density as well as cost PM material.
(2,12)
m
H
Ratio of H
c
over H
m
(β): Thicker coil means more
conductors can be used to generate higher power.
Nevertheless, thicker coils also enlarge the air gap
and lower the flux density.
Ratio of W
c
over R
i
(δ): Wider coil-band can contain
more conductors to generate higher torque, but more
conductors also can cause problems such as higher
armature resistance, higher loss, and thermal issues.
(0, /15)

Population size also necessitates special attention. Large
population can explore solution space more thoroughly, with
the cost of more time-consuming computations. However,
small population size of 10 to 20 can also provide sufficient
exploration through the solution space and effectively reduce
the optimization time [11]. Since the 3-D FEA evaluation is
quite time-consuming, 10 particles are set for this case.
2.2 Boundary conditions
As there are random functions acting on the process of
generating velocity, particles are likely to fly out of the
defined solution space. In order to address this problem,
boundary conditions are necessary to confine the particles.
Three boundary conditions are normally employed for PSO,
namely absorbing walls, reflecting walls and invisible walls.
In the first two boundary conditions, particles are strictly
restrained inside the solution space, while in invisible walls
particles are allowed to go out of defined space. However,
once a particle flies out, the position would not be calculated
or evaluated, and the particle has to fly again until it is back
within the defined region. There is more freedom of the third
boundary for particles to roam around, and thus their natural
motion would not be interfered. According to Robinson et al.
in [11], invisible walls condition is faster and more consistent,
and is thus adopted in this case.
2.3 Objective function
Each position of particles represents a possible design for the
AFPM generator. To evaluate the goodness of the designs
explored by the particles, an objective function needs to be
defined and linked to return fitness values. In order to meet
the required performance and at the same time reduce the
cost, five performance indexes, namely weight of magnet
(M
m
), weight of copper (M
c
), machine efficiency (η), volume
of the machine (V
g
) and power output (P
o
), are included in the
objective function. The weight coefficients are contained
before each performance index to indicate how much
influence of each performance index has on the overall design.
For the proposed machine, the objective function is defined as
follow
(1 )
m m c c v g po o
fitness k M k M k V k k P
(4)
where k
m
, k
c
, k
v
, k
,
and k
po
are corresponding weight
coefficients. In general, different weight coefficient choices
represent different design goals. In this case, performance and
the cost of the generator are the key criterion for optimization.
For instance, PMs are much more important and expensive
than coils, and hence the value of k
m
is much larger than k
c
.
Furthermore, small volume, high efficiency and power output
are preferred. Based on the design requirements and the range
of variation, the weight coefficients are chosen as listed in
Table 1, together with initial weight and scaling factors.
2.4 Implement of PSO
The flow chart of the PSO program is illustrated in Fig. 2.
After initialization, the process of each iteration can be
divided into 4 steps. Firstly, simulate and evaluate each
position (solution) of the iteration. And then update p
best
and
g
best
. Thirdly, the velocities and the positions of next iteration
are generated. At last, a judgement is carried out to make sure
all particles are searching within solution space for the next
iteration.
In this study, the fitness of objective function has been
successfully converged after 30 iterations. The average fitness
of particle positions, average fitness of personal best, and
global best of each iteration is depicted in Fig. 3. It is shown
that from 20
th
iteration, the personal bests are already
Initialization
Evaluations
Update p
best
and g
best
Generate and
update velocities
and positions
Within solution
space?
Record the
positions for the
next iteration
Yes
No
Iteration +1
Fig. 2: Flow chart of PSO program.
w
c
1
c
2
k
m
k
c
k
v
k
η
k
po
0.65
2.0
2.0
30.0
2.0
1000
150
0.15
Table 1: Values of factors and coefficients for PSO
Fig. 3: Fitness of objective function against iteration.

4
localized around their global best position in solution space.
After 30 iterations good convergence is achieved, and the best
solution found in iteration 26, is taken as the optimal design.
As shown in Fig. 4(a), after the first several iterations
fluctuation, the design parameters of H
m
, α
p
, and W
c
find their
corresponding optimal values, while D
i
has a great impact on
the value of H
c
with large fluctuations, as shown in Fig. 4(b).
It should be noted that all the design parameters stabilise after
the 26
th
iteration, with optimal solution obtained.
The trends of performance indexes are derived and depicted
in Fig.5. As expected, usage of PM has higher influence to the
evaluation. After an attempt to increase PM material, the
usage is reduced gradually from 7
th
iteration, while the usage
of copper is increased to maintain the output. Though this
brings out the issue of low efficiency and big in volume, the
benefit of smaller amount of PM thus lower in cost and high
power output makes the design a more practical choice.
4 3-D FEA verification
To validate the performance of the final optimised design
from PSO algorithm, simulation should be carried out by
using the FEA method. Because of the instinct structure of
AFPM machines, 3-D FEA model is a used to obtain more
accurate results. Since only back iron, PM poles and coils
matter in the electromagnetic simulation, housing and
connection parts of the machine are not included in the 3-D
FEA model. The machine in 3-D model is illustrated in Fig.1,
and the main design parameters are listed in Table 2.
4.1 No load characteristics
Firstly, the no-load characteristics of the machine are
calculated. The flux distributions of the back iron and the air
gap are shown in Fig. 6. As is seen from Fig. 6(a), the
magnitude of flux density in the air gap is between 0.5-0.6 T,
which is relatively low compared to machines with slotted
cores. For the back iron, its flux density should be at the knee
point of its B-H curve, which is about 2.0 T, to make full use
of the material as well as avoiding saturation. The back EMF
is another most important parameter for the machine design.
For a three phase generator, sinusoidal wave form is preferred
to avoid extra loss because of harmonic components. As is
shown in Fig. 7(a), the back EMF wave form of the machine
illustrates that the machine can achieve the output voltage
requirement. Moreover, from Fig. 7(b), it can be seen that the
output contains few harmonics. More specifically, the third
harmonic is less than 2%, which can be eliminated by using
the star armature connection. For other higher harmonics, the
magnitude of phase EMF is negligible. Therefore, such EMF
is perfect for three-phase generator.
4.2 On load characteristics
To simulated performances of the generator at different
operating points, FEA models at different loads are also
constructed. For small-scale off-grid generator, loads can be
classified into two categories, which are AC load for common
household appliances and DC load for battery charging. To
simulate the different conditions of these two loads, AC load
and DC load are connected respectively to assure the output
characteristics.
(a) (b)
Fig. 4: Trends of best design parameters against iteration.
(a) (b)
Fig. 5: Trends of performance indexes against iteration.
(a) air gap
(b) back iron
Fig. 6: Flux distribution density in the machine
Parameters
Value
Parameters
Value
P
o
(W)
500
D
o
(mm)
250
n (rpm)
300
D
i
(mm)
168
U
o
(V)
220
H
m
(mm)
7
m
3
α
p
0.75
p
20
H
c
(mm)
17.4
q
15
W
c
(mm)
16.8
Table 2: Parameters of final design from PSO.

5
Under the AC full load condition, both the induced voltage
and armature current are quite sinusoidal, and the power
output is over 520W with a smooth torque, as depicted in Fig.
8. In fact, the loss is mainly caused by copper loss, because
eddy current loss and core loss are eliminated due to the
absence of the stator core. Also, because of the large airgap
and thus low armature reaction, the iron loss in stator back
iron is negligible. Since more copper conductors are used,
107W is consumed by armature resistance. The resulting
efficiency is 82.9%.
Under DC load condition, a non-controllable three-phase
rectifier is connected to obtain DC output. And because of the
influence of the electronic switches during commutation,
distortion can be observed in the voltage wave form, and thus
output DC voltage is fluctuating six times in one electrical
period in terms of the six switches of the three-phase full-
wave rectifiers, as is shown in Fig. 9(a) and 9(b). In addition,
from Fast Fourier transform (FFT) analysis of the DC voltage
depicted in Fig. 9(c), it can be seen that there are only the 6th
harmonic and the harmonics which are multiple of six except
for DC component. Besides, greatly influenced by the
fluctuation from voltage, the output power and magnetic
torque also suffer from variations as shown in Fig. 9(d). The
fluctuation is up to 20% of the average value. With the
fluctuating currents, the copper loss is 9W higher than that
with DC load. Thus the efficiency at DC load is 81.2%, which
is lower than that under AC load. However, it should be noted
that no filter or control algorithm is used in the simulation. In
practical applications, power electronic circuit with controller
and filters should be applied to smooth the output voltage and
obtain a stable DC voltage. Due to the instability of wind
speed, the wind turbine should be designed to adapt all these
operating conditions at a wide wind-speed range. Thus,
simulations are necessary to carried out at various load
conditions to predict the output characteristics of the wind
generator. Generator voltage regulation and efficiency at
different load conditions with AC load and that with DC load
are illustrated in Fig. 10. Generally speaking, the trends of
these two figures are quite similar. In particular, it can be seen
that the operating efficiency is above 81%, and the lowest
efficiency appears at full load, which is because higher
current leads to higher resistance loss. In addition, the output
voltage and efficiency is linear against output power, which
means that the generator can be treated as a linear system.
Last but not least, for the small wind generator, the turbine is
fixed and cannot be adjusted in terms of different wind speeds,
which means that the energy captured by generator is
changing all the time. In other words, it is impossible for the
machine to operate at full load condition at all times.
Therefore, the average operating point is probably at around
400W, and the average efficiency should be about 87%.
In summary, according to PSO algorithm, a design with more
copper and less PM is chosen as the optimal design. 3D FEA
model is built and simulated under different load
circumstances. Simulation result reveals that the final design
has good performance with acceptable efficiency, and
achieves the design requirements for small wind power
systems. Furthermore, the usage of PM material for the
machine is reduced with approximately same output features,
which would minimize the cost of the machine.
5 Conclusion
In this paper, an AFPM synchronous machine with rated
power of 500W at 300rpm is proposed for small-scale wind
power applications. A sophisticated multi-parameter and
multi-objective PSO algorithm based on 3-D FEA is
developed and employed to carry out optimization with a user
defined objective function. The performance of the final
optimal machine has also been comprehensively evaluated by
(a) back EMF waveform (b) back EMF spectrum
Fig. 7: Phase back EMF waveform and spectrum.
(a) phase voltage and current (b) loss, torque and power
Fig. 8: Output characteristics at AC load
(a) phase voltage and current (b) DC voltage and current
(c) DC voltage spectrum (d) loss, torque and power
Fig. 9: Output characteristics at DC load power output.
(a) AC load (b) DC load
Fig. 10: Generator voltage regulation and efficiency at varied
loads

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TL;DR: In this paper, the authors proposed a particle swarm optimization (PSO) approach to optimize hot water injection process in heavy oilfields using a 2D heterogeneous reservoir with 13 wells and showed that optimal values exist for the water injection temperature of different wells.

52 citations

Journal ArticleDOI
TL;DR: In this article, a method based on a search and optimization approach is developed to solve the inverse natural convection problem of a two-dimensional heat source on a vertical flat plate.

25 citations

Proceedings ArticleDOI
01 Sep 2016
TL;DR: In this paper, the performance of coreless axial flux permanent magnet (AFPM) generators is investigated with the use of both neodymium and ferrite magnetic materials, applying particle swarm optimization (PSO) in the generator design process, while the final designs are verified and fine-tuned with finite element analysis (FEA) simulations.
Abstract: Locally manufactured small wind turbines are most frequently used in off-grid battery based renewable energy systems and typically utilize coreless axial flux permanent magnet (AFPM) generators. Due to reports of neodymium magnet corrosion, the performance of coreless AFPM generators is investigated with the use of both neodymium and ferrite magnetic materials. Generator designs are conducted for rotor diameters between 2.4 and 4.2m, applying a Particle Swarm Optimization (PSO) in the generator design process, while the final designs are verified and fine-tuned with Finite Element Analysis (FEA) simulations. Optimal magnet dimensions are derived for both magnetic materials and for each rotor diameter, while a ‘universal’ magnet design is compared with commercially available magnets. Experimental comparison of a ferrite and a neodymium magnet generator design for a 2.4m rotor is conducted, proving that ferrite magnet AFPM generators are suitable for locally manufactured small wind turbines, making them less prone to corrosion, but also heavier in weight.

19 citations

Journal ArticleDOI
TL;DR: In this paper, an optimal design of coreless axial flux permanent magnet (AFPM) synchronous generator using particle swarm optimization method based on sizing equations of the machine is performed in order to reduce the active material cost of the generator.
Abstract: This paper presents an optimal design of coreless axial flux permanent magnet (AFPM) synchronous generator using particle swarm optimization method based on sizing equations of the machine. The design optimization is performed in order to reduce the active material cost of the generator. General practical and mechanical limitations are considered as optimization constraints. A magnetic circuit model based on quasi three-dimensional (3-D) model of the coreless AFPM machine is taken into account to calculate the permanent magnet leakage flux (PMLF) accuracy. A computer-aided program is evaluated according to the proposed optimized design procedure that is used to design a 2-kW, 16-pole AFPM generator with two rotors and one coreless stator. Finally, the 3-D finite-element model (FEM) of the machine is prepared to confirm the validity of the proposed PMLF model and proposed optimized design algorithm.

16 citations


Cites background from "Particle swarm optimization of air-..."

  • ...Simple-parameter adjustment, flexibility, short computational time, and free of derivative are the other advantages of PSO [30], which makes it suitable for a variety of applications [31, 32]....

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Journal Article
TL;DR: In this paper, an improved design procedure of a coreless Axial Flux Permanent Magnet Synchronous Generator (AFPMSG) for wind turbine application is presented, where the reluctance of rotor back iron core is separated into two parts, which are calculated through the nonlinear iterative algorithm.
Abstract: This paper presents an improved design procedure of a coreless Axial Flux Permanent Magnet Synchronous Generator (AFPMSG) for wind turbine application. An analytical design approach is proposed based on sizing equations and a nonlinear Magnetic Equivalent Circuit (MEC) model of AFPMSG. The reluctance of rotor back iron core is separated into two parts, which are calculated through the nonlinear iterative algorithm. An optimal design of the coreless AFPMSG is performed using Partial Swarm Optimization (PSO) method in order to increase the Annual Energy Yield (AEY) of the generator. The statistical model of wind speed distribution and wind turbine characteristic are used for considering the generator performance over the whole operating wind speed range. In order to obtain the optimal values of design variables, the optimization procedure is provided for various number of pole pairs and coil numbers. The proposed procedure is used to design a double rotor-one coreless stator AFPMSG. Finally, 3-D Finite Element Analysis (FEA) is used to validate the design algorithm. Also, the generator performance is evaluated for different values of wind speed and load currents.

12 citations

References
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Proceedings ArticleDOI
04 Oct 1995
TL;DR: The optimization of nonlinear functions using particle swarm methodology is described and implementations of two paradigms are discussed and compared, including a recently developed locally oriented paradigm.
Abstract: The optimization of nonlinear functions using particle swarm methodology is described. Implementations of two paradigms are discussed and compared, including a recently developed locally oriented paradigm. Benchmark testing of both paradigms is described, and applications, including neural network training and robot task learning, are proposed. Relationships between particle swarm optimization and both artificial life and evolutionary computation are reviewed.

14,477 citations

Journal ArticleDOI
TL;DR: In this article, a unique axial-flux permanent-magnet synchronous generator (AFPMSG) is presented for both vertical-axis and horizontal-axis wind turbine generation systems.
Abstract: This paper presents a unique axial-flux permanent-magnet synchronous generator (AFPMSG), which is suitable for both vertical-axis and horizontal-axis wind turbine generation systems. An outer-rotor design facilitates direct coupling of the generator to the wind turbine, while a coreless armature eliminates the magnetic pull between the stationary and moving parts. The design and construction features of the AFPMSG are reviewed. The flux-density distribution is studied, with the aid of a finite element software package, in order to predict the generated e.m.f. waveform. The performance equations of the AFPMSG are derived, and the condition for maximum efficiency is deduced, for both constant-speed and variable-speed operations. The experimental results, in general, confirm the theory developed

208 citations

Proceedings ArticleDOI
30 Sep 2001
TL;DR: In this article, the windings of a multi-disc axial flux slotless construction were calculated using a finely meshed finite element model and a time-stepped approach.
Abstract: The stratospheric unmanned aircraft for the proposed European Union Helinet telecommunications infrastructure will use inverter/brushless AC motor drives for the propellers One form of machine being considered is of multi-disc axial flux slotless construction This has no iron losses due to the fundamental field but, since the windings are in the air-gaps, eddy current losses are present in the strands of the coil conductors These losses are calculated, using a finely meshed finite element model and a time-stepped approach The winding factors of the three types of winding without coil end-region overlaps are determined Design comparisons are drawn between axial flux and conventional radial flux designs

46 citations

Proceedings Article
01 Jan 2004
TL;DR: In this paper, a new TFPM with combined stator and concentrating flux rotor configurations is presented, and the related design parameters that reduce the cogging torque are investigated by using equivalent magnetic network method (MNM) for magnetic field analysis and particle swarm optimization (PSO) algorithm for optimization.
Abstract: Great emphasis is paid on transverse flux permanent motors (TFPM) in recent years especially in powerful propulsion system. However, the cogging torque in TFPM leads to mechanical vibration and noise inevitably. This paper presents a new TFPM with combined stator and concentrating flux rotor configurations. The related design parameters that reduce the cogging torque are investigated by using equivalent magnetic network method (MNM) for magnetic field analysis and particle swarm optimization (PSO) algorithm for optimization. The computation result shows the PSO can minimize the cogging torque substantially without deterioration the performance of TFPM

19 citations

Proceedings ArticleDOI
26 Dec 2007
TL;DR: In this article, an improved magnetic equivalent circuit (MEC) is applied to calculate the nonlinear magnetic field in an interior-type permanent-magnet (IPM) brushless DC (BLDC) motor.
Abstract: In this paper, an improved magnetic equivalent circuit (MEC) is applied to calculate the nonlinear magnetic field in an interior-type permanent-magnet (IPM) brushless DC (BLDC) motor. Compared with the finite element method, the MEC method is much more time efficient, whereas compared with the conventional MEC method, the improved MEC is more accurate since it takes the complicate topological structure of the motor into account. A rough design of the IPM BLDC motor was firstly conducted by the improved MEC method. The particle swarm optimization (PSO) algorithm is then employed to refine the design for optimal structural parameters that result in the lowest cost and highest performance.

12 citations

Frequently Asked Questions (1)
Q1. What have the authors contributed in "Particle swarm optimization of air-cored axial flux permanent magnet generator for small-scale wind power systems" ?

Here, the particle swarm optimization method is used in the design of an axial flux permanent magnet generator for small-scale wind power system.