1
Design of Three-Phase Multi-Stage Axial Flux Permanent Magnet Generator for
2
Wind Turbine Applications
3
Muhammad Mansoor ASHRAF1,*, Tahir NADEEM MALIK1
4
1
Electrical Engineering Department, University of Engineering and Technology,
5
Taxila (47050), Pakistan
6
*Correspondence: mansoor.ashraf@uettaxila.edu.pk
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Abstract: Presently, the axial flux permanent magnet machines are becoming popular
8
and are being deployed actively for low speed applications. The paper presents an
9
improved model of Multi-Stage Axial Flux Permanent Magnet Generator (AFPMG). The
10
multi-stage AFPMG consists of multiple stator and rotor discs. There are three identical
11
1-phase stator discs and four in-phase rotor discs in proposed multi-stage AFPMG. In this
12
research paper, 4 case studies have been analyzed on design of multi-stage AFPMG. First,
13
Phase Shift Model (PSM) positions the three 1-phase stator discs to behave as 3-phase
14
generator. Actually, PSM computes phases for three stator discs in order to establish
15
phase shift of 120° between each two phases. The implementation of presented model in
16
multi-stage AFPMG reduces the diameter of stator disc three times as compared to
17
conventional 3-phase AFPMG with identical rated specifications. Second, voltage
18
waveform of AFPMG has been analyzed for harmonic contents and the percentages of
19
3rd and 5th harmonics have been computed. The test results show that 3rd and 5th
20
harmonics have been reduced to 10.7% and 0.54% respectively in voltage waveform.
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Third, the proposed multi-stage AFPMG has been designed considering begin-to-end
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winding connections of stator disc. While adopting begin-to-end connection, the number
23
of poles of AFPMG are doubled which ultimately increases air-gap flux density and thus
24
terminal voltage of stator disc and operating shaft speed is halved. The test results show
1
1
that torque-to-weight ratio parameter of designed AFPMG has been improved by using
2
begin-to-end connection for stator disc. Fourth, the increased air-gap flux density also
3
improves the power density parameter of AFPMG with begin-to-end winding connection.
4
Moreover, a prototype model of 1200 W multi-stage AFPMG has been designed and
5
fabricated while following PSM and begin-to-end winding connection and tested. Thus
6
test results verify the proposed model of multi-stage AFPMG for wind turbine
7
applications.
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Key words: permanent magnet generator, axial flux generator, neodymium permanent
9
magnets, winding connection, wind energy systems, total harmonic distortion, multi-
10
stage generator, phase shift model, power density
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1.
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In this modern era, the renewable energy resources are replacing the conventional energy
13
sources for electricity production because of the tremendously increasing cost and rapidly
14
decreasing sources of fossil fuels. Out of various renewable energy resources, wind
15
energy represents one of the cheaper sources of electrical energy production. The wind
16
energy systems consisting of low speed electrical generators are getting immense
17
attention now-a-days [1-3]. The AFPMGs are being addressed extensively for low speed
18
applications such as wind turbines and small hydro turbines [4]. The AFPMG basically
19
has disc type structure in which stator disc is sandwiched between two rotor discs [4-7].
20
The strong neodymium permanent magnets are attached on rotor discs alternatively. The
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stator disc is prepared by casting the coils in epoxy resin for coreless construction [4, 5].
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This type of AFPMG is having a number of advantages as higher torque-to-weight ratio,
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higher power density, higher efficiency, free of cogging torque losses, compact structure,
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light weight and low operating shaft speed [4, 6, 8, 9].
Introduction
2
1
2.
Related Work
2
There are numerous topologies which are being addressed and used in literature. The
3
author [6] has reviewed different topologies for AFPMGs and discussed the various
4
advantages. The rotor type of machine basically classifies the topology of machine as:
5
axial flux induction machine, mounted permanent magnet machine and interior
6
permanent magnet machine with squirrel cage, surface mounted permanent magnet and
7
interior permanent magnet rotor structures respectively. The basic type of axial flux
8
machine is single-single topology consisting of one stator disc and one rotor disc. The
9
torus type axial flux machine consisting of one stator disc and two rotor discs which are
10
sandwiched while internal stator disc topology. The rotor discs of this machine are
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adjusted either in repulsion mode: with identical poles of permanent magnets front to each
12
other or in attraction mode: with different poles of permanent magnets front to each other.
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Besides, the stator disc may be iron cored, coreless, slotted and non-slotted. The torus
14
type axial flux machine consisting of two stator discs and one rotor disc with internal
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rotor type structure is also present. The permanent magnets are fitted on both sides of the
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rotor disc. The rotor disc of this machine is made of non-ferromagnetic material because
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in this topology, the flux does not pass through rotor disc. However, the stator of these
18
machines must be iron cored to facilitate the flux passage. The fourth topology of multi-
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stage axial flux machines is also getting enormous attention. The multi-stage axial flux
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machines are designed with multiple stator and rotor discs where rotor discs is always
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greater than stator discs by one. The windings of all stator discs can either be connected
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in parallel or series to enhance the current or voltage rating respectively. The permanent
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magnets are fitted on one side and both sides of sided rotors and internal rotors
24
respectively. The rotor discs may be adjusted while considering permanent magnets either
3
1
in attraction mode or repulsion mode. A hybrid machine is also addressed which was
2
proposed by Dr. Hsu. This machine is having axial as well as radial fittings of permanent
3
magnets on double sided rotor structure. The last and new machine addressed in this
4
article consists of DC field windings as well as permanent magnets for controlled
5
machine. The machine is single stator and double rotor topology.
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A single phase permanent magnet generator has been presented with double sided stator
7
and two rotors exhibiting axial as well as radial directed flux (specially designed core) to
8
reduce cogging torque [9]. A micro wind energy system consisting of small wind turbine
9
coupled with single-phase, single-stage, 8 pole AFPMG has been presented and power
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density parameter of AFPMG has been improved [4]. The AFPMGs has been fabricated
11
by using magnets from redundant materials like hard disks and performance of AFPMGs
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has also been evaluated [10]. An AFPMG having single-stator single-rotor topology with
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coreless stator disc has been proposed [11]. A five-phase AFPMG composed of two rotors
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and one coreless stator has been designed which feeds the rectified load [5]. A novel axial
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field flux switching permanent magnet generator has been introduced which is having
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permanent magnets and winding on stator and toothed rotor [12]. A torus type AFPMG
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has been optimized with multiple stators and rotors [13]. Another topology of AFPMG
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with multiple stator and rotors has been proposed to reduce cogging torque loss [14]. The
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different topologies of 3-phase, 5-phase and 9-phase AFPMGs have been discussed and
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their performances have been evaluated by 3-dimensional finite element analysis [15]. A
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two rotor and one stator topology of AFPMG has been considered for analysis with back
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iron on rotor plates [16]. A time saving analysis method of 2-dimensional finite element
23
analysis along with analytical tools has been presented for design analysis of AFPMGs
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[17]. The design considerations as; wound concentrated coils, design features, sizing
4
1
equations and sensitivity analysis regarding AFPMGs has been discussed [18]. The
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different AFPMG results as; power density, active mass, torque, torque-to-weight ratio
3
and cost analysis of different types of AFPMGs has been computed and discussed [8]. An
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experimental kit consisting of small scale wind turbine and wind tunnel has been proposed
5
for indoor operation of wind energy system [19].
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3.
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In this research paper, a 3-phase and multi-stage AFPMG has been addressed and
8
designed. The Phase Shift Model (PSM) positions the three 1-phase stator discs angularly
9
to establish phase shift of 120°. The coils of stator discs are connected in begin-to-end
10
connection. This pattern of end winding connection doubles the number of poles and also
11
enhances the air-gap flux density and voltage of AFPMG. This aspect increases the
12
electromagnetic torque of AFPMG for the same size and mass of machine as a
13
consequence the torque-to-weight ratio parameter and power density have been
14
improved. Thus designed AFPMG is having improved value of torque-to-weight ratio
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parameter (8.194 Nm/kg) using begin-to-end connection as compared to simple AFPMG
16
topology (5.940 Nm/kg) addressed in Ref [8]. The output voltage waveform of AFPMG
17
has been viewed and Fourier analysis has been conducted to determine harmonic contents.
18
The designed AFPMG is having reduced 3rd harmonic (10.7%) than AFPMG with
19
rectangular magnets [17] (12.5%) in output voltage waveform. The voltage of fabricated
20
AFPMG is also having significantly reduced value of 5th harmonic (0.54%) than AFPMG
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with rectangular magnets [17] (16%). The three stator and four rotor topology of proposed
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AFPMG is shown in Figure 1. There are 4 rotor discs R1, R2, R3, R4 and 3 stator discs
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S1, S2, S3 sandwiched alternatively. The Figure 1 shows the axial view of multi-stage
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AFPMG.
Proposed Work
5
1
Figure 1
2
The 3-dimensional view of generator topology presented in Figure 2. The light grey color
3
shows the permanent magnets, dark grey color shows the rotor disc core and brown color
4
shows the copper coils of stator discs.
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Figure 2
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The rotor discs R1, R2, R3, and R4 are mounted on the same shaft for in-phase rotor discs
7
while the stator discs will be displaced angularly to establish phase shift according to
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PSM. The suitable air gap is adjusted between stator and rotor discs to combine the
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assembly of multi-stage AFPMG as shown in Figure 3.
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Figure 3
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From Figure 3, it can be seen that 4 rotor discs are in-phase while 3 stator discs are
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angularly displaced to produce phase shift.
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4.
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A number of design requirements and satisfying electrical as well as mechanical
15
constraints, are two essential steps of electrical machine design [20]. The name plate
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ratings of line voltage, maximum current carrying capacity, phase voltage, machine
17
power rating, shaft speed and poles, are to be presented before commencing the design
18
procedure of AFPMG [20, 21]. The name plate ratings are given in Table 1.
Design of Multi-Stage AFPMG
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Table 1
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The number of coils, number of magnets, winding type, coil pitch and end winding
21
connection type according to specified number of poles, are those design considerations
22
which are taken into account and being focused for designing AFPMG.
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4.1.
The Phase Shift Model
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1
The multi-stage machine consisting of multiple stator and rotor discs is addressed [6] in
2
which stators of multi-stage machine are to be connected either in series or parallel.
3
According to Phase shift model, the stator discs of multi-stage AFPMGs are to be
4
connected either in star (γ) or delta (Δ) connection and three stator discs and four rotor
5
discs topology behaves as a single 3-phase generator. The topology of prototype multi-
6
stage AFPMG for implementation of phase shift model is shown in Figure 2 and Figure
7
3. The Phase shift model computes the three phases for angular displacement of three
8
stator discs to establish the phase shift of 120° between each two phases and connect three
9
1-phase stator discs either in star or delta configuration. The sine waves of 3-phase
10
voltages are considered by plotting the instantaneous voltage values for each phase. The
11
3-phase instantaneous voltages are analyzed and shown in Figure 4. At t=0 sec instant,
12
phase A is at zero value while phase B and C are at 86.6% of the peak values but with
13
opposite polarity. At the same instant of time, the values of phase B and C are increasing
14
towards negative peak and decreasing from positive peak respectively.
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Figure 4
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For computation of phases through Phase shift model, a generalized framework consisting
17
of design structure and terminology has been established. The Figure 5(a) shows a
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differential portion of one axial flux stator disc. The shown differential portion is called
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segment (θseg) which is defined as (1/Nc)th portion of stator disc where Nc is number of
20
coils per stator disc or arc portion of stator disc consisting of four identical imaginary
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slots. The imaginary slot (θs) is defined as (1/4)th arc portion of segment of stator disc.
22
The coil angle (θc) is angular displacement which is covered by placement of one coil of
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stator disc at certain position.
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1
The specific position of coil within stator disc is represented by coil pitch parameter
2
which is expressed in terms of imaginary slots. While considering Phase shift model,
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there are only two possible aspects of coil pitch parameter as: 1-3 and 1-4 slots. In this
4
research paper, the former aspect of coil pitch parameter of 1-3 slots has been considered.
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The placement of coil within slots for stator disc while following Phase shift framework,
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is shown in Figure 5(b).
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8
Figure 5 (a, b and c)
The segment arc of stator disc is given by:
θ seg =
9
(1)
π
2N c
rad
(2)
The coil arc representing coil placement within stator disc is given by:
θc =
11
rad
The slot arc of stator disc is given by:
θs =
10
2π
Nc
3π
2N c
rad
(3)
The number of magnets on each rotor disc is given by:
N m = 2N c
(4)
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The permanent magnets on the rotor plates are placed in alternate polarity of North South
13
poles consecutively. The angle between two adjacent magnets on rotor disc is represented
14
as inter-magnet displacement and is given by:
θm =
2π
Nm
rad
(5)
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The inter-magnet displacement is shown in Figure 5(c). The two permanent magnets are
16
shown with alternate polarity facing upward North and South sides respectively. The dark
8
1
grey color represents North face whereas the light grey color represents South face. The
2
size and shape of the permanent magnets for rotor discs are computed and finalized
3
according to the width of coil limb, air gap width and coil pitch in terms of slots while
4
considering Phase shift framework.
5
The white circles on the permanent magnets show the magnet number on a specific rotor
6
disc so that there may be precise track of magnets while rotating the rotor disc and
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analyzing in accordance with certain phase of stator disc. The rotor plate is rotated
8
counter-clockwise direction while performing animation and analysis. The angle of rotor
9
disc at a specific instant while performing animation with respect to horizontal line (x-
10
axis) in counter-clockwise direction is represented as rotor animation angle and step of
11
rotor animation angle is denoted by θa which is given by:
θa =
1
π
θ seg =
12
6Nc
rad
(6)
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The position of the segment portion is specified by an angle within stator disc with respect
13
to rectangular coordinate system. The angle is called ‘Segment Reference’ angle and is
14
denoted by θrs. If the leading North Pole and lagging South Pole overlap the leading and
15
lagging coil limbs in counter-clockwise direction, the positive value of induced emf in
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the coil is depicted as convention and vice versa. The value of induced voltage depends
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on extent of overlapping between coil limbs and permanent magnets.
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The differential portion of one segment is considered with rotor disc as shown in Figure
19
6. From Figure 6(a), it is shown that first North magnet is at 2nd slot of segment and first
20
South magnet is at one slot before segment at present instant of rotor disc. There does not
21
exist overlapping between coil limbs and magnets: thus voltage will not appear across the
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coil terminals called zero crossing of phase ‘A’ and this can be shown in Figure 4 at t=0
9
1
sec instant. The 1st stator disc segment is placed at reference of x-axis which is also the
2
angle of angular displacement for 1st stator disc and its value is 0 rad.
3
Figure 6 (a, b and c)
4
The 2nd stator disc for phase B is considered at same instant of time t=0 sec and with
5
identical second rotor disc which is in-phase with other rotor discs. From the Figure 4, it
6
is shown that the value of voltage at t=0 sec instant is 86.6% of negative peak value which
7
is decreasing at t=0+ sec instants. The segment for 2nd stator disc (Phase B) must be
8
positioned in way in accordance with rotor disc that leading South Pole and lagging North
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Pole overlap 86.6% of the leading and lagging coil limbs in counter-clockwise direction
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in increasing pattern of overlapping and this arrangement of segment for phase B stator
11
disc is shown in Figure 6(b). While keeping the identical and in-phase rotor disc, the
12
segment portion for stator disc B has to be displaced angularly to fulfill the conventions.
13
The segment reference angle for phase B can be measured and its value is -2θseg/3 and -
14
8θs/3 in terms of segment arc portion and slots respectively. Similarly, the segment
15
reference angle for phase C can be measured and its value is -4θseg/3 and -16θs/3 in terms
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of segment arc portion and slots respectively.
17
The phase of stator disc is the angle at which the whole stator disc is rotated angularly.
18
The expressions showing the segment reference angles in terms of number of coils will
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be represented as respective phases for phase A, B and C on 1st, 2nd and 3rd stator discs
20
respectively. The set of angles comprising of θA, θB and θC for three stator discs is called
21
Phase shift Model and is given by:
θ A = 0 rad
θB = −
4π
3
 1

 Nc

 rad

(7a)
(7b)
10
θC = −
8π
3
 1

 Nc

 rad

(7c)
1
2
4.2.
Winding of Stator Discs
3
The end winding connection in which begin and end limbs of one coil are connected with
4
end and begin limbs of adjacent coil respectively while connecting coils within stator
5
disc, generally referred as begin-to-end winding connection. Begin-begin is the type of
6
the connection in which begin and end limbs of one coil are connected with begin or end
7
limbs of adjacent coil. The configuration of begin-to-end and begin-to-begin winding
8
connection for six coils is shown in Figure 7 and Figure 8 respectively.
9
Figure 7
10
Figure 8
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The begin-to-end connection requires stair winding with 1-3 coil pitch in which number
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of magnets is twice than number of coils on rotor and stator discs respectively and is also
13
equal to number of poles of machine. The stator disc of AFPMG using begin-to-end and
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begin-to-begin connections are shown in Figure 9(a) and Figure 9(b) respectively.
15
Figure 9 (a and b)
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Comparatively, for large number of poles, the machine wound with stair winding is
17
heavier in mass than machine wound with begin-to-begin connection. But double number
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of magnets contribute to improve power density and torque-to-weight ratio in two ways:
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first air gap flux density is increased and second shaft speed of AFPMG is halved. The
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stator and rotor discs of AFPMG showing begin-to-end connection and stair winding type
21
is shown in Figure 10(a). The red and blue blocks represent the North and South poles of
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permanent magnets respectively. The Block winding is the type of winding design of coils
11
1
within stator disc in which coils are arranged and interconnected while following begin-
2
to-begin connection. This winding arrangement is shown in Figure 10(b).
Figure 10 (a and b)
3
4
4.3.
Design Computation
5
Assuming negligible leakage inductance and resistance, the main dimensions of AFPMG
6
are computed [8]. For given peak values of air-gap current and air-gap emf, the rated
7
power of AFPMG is expressed as given by: [8, 12]
T
m
Pr = η ∫ e(t ) i (t )dt
T 0
(8)
8
Where e(t) and i(t) are instantaneous voltage and current of AFPMG. Evaluating the
9
expression, power of AFPMG is given by:
Pr = ηmE p I p K p
(9)
10
Where η is the generator efficiency, m the number of phases, Ep the peak voltage of rated
11
per phase voltage, Ip the peak current of rated per phase current and Kp is the electrical
12
power waveform factor.
13
The expression for peak value of rated per phase voltage is given by: [4, 6, 8]
E p = K e N t Bg
f
( Do2 − Di2 )
p
(10)
14
Where Ke is the emf factor which also incorporates the winding distribution factor Kw, Nt
15
the number of turns of coil, Bg the air-gap flux density (T, Wb/m2), f the supply frequency
16
(Hz), p the number of pole pairs, Do the outer diameter of stator disc (m) and Di is the
17
inner diameter of stator disc (m).
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The expression for peak current of rated per phase current is given by: [4, 6, 8]
12
Ip =
1
1 + λ Do
K i Aπ
1 + Kφ
2 2m1 N t
(11)
1
Where Kϕ is the ratio of electrical loading on rotor and stator of generator, Ki the current
2
waveform factor, A the electrical loading in ampere conductor per meter of stator disc
3
(A/m), λ the ratio of inner to outer diameter of stator disc and m1 is the number of phases
4
per stator disc.
5
The initial design considerations are specified before computing the design parameters
6
and dimensions of AFPMG. The usage of permanent magnets sets the value of Kϕ=0 [8].
7
The values of m1 and m are selected on basis of stages and phases of AFPMG respectively.
8
The emf, current and power waveform factors are specified by their values from data of
9
typical prototype waveforms against sinusoidal voltage waveform of AFPMG [22]. The
10
design procedure has been followed and the design parameters have been computed
11
which are given in Table 2.
12
Table 2
13
The three identical independent single phase stator discs with described specifications
14
have been designed. These three stator discs have been placed angularly according to the
15
phases computed from set of equations (7a, 7b, 7c) representing Phase shift Model. The
16
computed phases for three stator discs and different design specifications of multi-stage
17
axial flux generator are listed in Table 3.
Table 3
18
19
5.
Fabrication of Multi-Stage AFPMG
20
The generator model has been fabricated according to the dimensions and design
21
parameters listed in Table 2 and Table 3. Fabrication of generator model includes the
22
construction of stator discs, rotor discs and generator assembly.
13
1
The stator construction included specific design considerations. The 6 coils have been
2
placed in stator disc template with 1-3 coil pitch. The epoxy resin was filled in the
3
template and three identical stator discs were casted. These three stator discs have been
4
casted while considering single phase design configuration. Thus casted stator discs
5
represent 1-phase three generators which will be later connected as 3-phase to form a
6
single generator. The coils of each stator disc have been connected in series. The six
7
terminals from three stator discs have been connected in star (γ) configuration to make 3-
8
phase single generator. The set of three stator discs fitted within generator assembly is
9
shown in Figure 11(a).
10
The rotor discs of generator have been designed by casting four rotor plates. The slots for
11
permanent magnets have been carved and neodymium permanent magnets have been
12
placed within rotor slots. Each rotor disc contains 12 magnets with alternate polarity. The
13
set of four rotor discs with permanent magnets is shown in Figure 11(b).
14
The three stator and four rotor discs have been placed alternatively and fitted within
15
generator assembly. The generator assembly consists of two square shaped aluminum
16
plates along with bearings and shaft. The generator model is shown in Figure 11(c) and
17
11(d). For testing purpose, the generator has been fitted in testing bench, coupled with
18
DC motor.
Figure 11 (a, b, c, and d)
19
20
6.
Testing of Multi-Stage AFPMG and Results Discussion
21
After fabrication, the AFPMG model has been placed in machine testing bench. The
22
machine testing bench consists of a variable speed DC motor which has been coupled
23
with AFPMG model as prime-mover. The testing bench is fitted with tachometer to
14
1
measure shaft speed and a multi-meter to measure the single-phase voltage, current and
2
frequency. Thus complete testing bench is ready for testing shown in Figure 12.
Figure 12
3
4
6.1.
Testing of Phase Shift Model
5
A three-phase measurement module has been placed with testing bench to measure the
6
AFPMG and DC motor parameters accurately. An oscilloscope has also been connected
7
with AFPMG output terminals which shows the voltage waveform of AFPMG.
8
Figure 13 (a, and b)
9
The Figure 3 shows that angular displacement in stator discs of multi-stage AFPMG
10
establishes the phase shift of 120° between each two phases.
11
6.2.
12
The generator is run at its rated parameters of shaft speed and frequency. At rated
13
parameters of shaft speed (500 rpm) and frequency (50 Hz), the output voltage waveform
14
of AFPMG is shown in Figure 14.
Harmonic Analysis of Voltage Waveform
15
Figure 14
16
The output voltage waveform of AFPMG model has been viewed and analyzed in
17
MATLAB. The Fourier analysis of output voltage waveform has been conducted. The
18
fundamental, 3rd and 5th harmonics of voltage waveform have been extracted as shown in
19
Figure 15.
20
Figure 15
21
The harmonics are analyzed and manipulated in terms of percentage presence of
22
individual and total harmonics. Technically, these terms are called individual harmonic
23
distortion and total harmonic distortion in literature [23]. Computing the percentage
24
presence of one harmonic at a time with respect to fundamental, is known as Individual
15
1
Harmonic Distortion (IHD) [23]. The net deviation of waveform from original sinusoidal
2
waveform due to all harmonics at a time may be referred as Total Harmonic Distortion
3
(THD) [23]. The values of individual harmonic distortion due to 3rd and 5th harmonics
4
and value of total harmonic distortion have been computed. The percentage presence of
5
3rd and 5th harmonics have been reduced in designed AFPMG as compared to AFPMG
6
with rectangular magnets addressed in Ref. [17]. The comparison is listed in Table 4.
7
Table 4
8
The fundamental, 3rd and 5th harmonics of voltage waveform have been rescaled to
9
compare harmonic contents of designed AFPMG model with AFPMG with rectangular
10
magnet [17] graphically. From the graphical results, it is clear that 3rd harmonic has been
11
reduced while the presence of 5th harmonic has been reduced significantly on rescaled
12
values. The result comparison is shown in Figure 16.
Figure 16
13
14
6.3.
Torque-to-Weight Ratio
15
The one of the important parameters of AFPMG testing is torque-to-weight ratio of
16
machine. The parameter torque-to-weight ratio is the measure of AFPMG torque against
17
mass active mass of machine. The higher value of torque-to-weight ratio parameter
18
reflects the minimization of machine’s active mass while maximizing the electromagnetic
19
torque of machine. Once the output voltage and full load current is known at pure resistive
20
load, the electromagnetic torque (Te) of AFPMG is given by: [17]
Te =
1
ωm
[va (t ).ia (t ) + vb (t ).ib (t ) + vc (t ).ic (t )]
(12)
21
Where va(t), vb(t) & vc(t) are instantaneous voltages of three phases, ia(t), ib(t) & ic(t) are
22
instantaneous load currents of three phases of AFPMG and ωm is the mechanical shaft
16
1
speed of AFPMG in rad/sec. The AFPMG model is run at its rated parameters of shaft
2
speed and frequency. The output voltage waveform of AFPMG has been taken from
3
oscilloscope and analyzed in MATLAB. The instantaneous voltage waveform, and
4
computed electromagnetic torque of AFPMG are shown in Figure 17 and Figure 18
5
respectively.
6
Figure 17
7
Figure 18
8
The electromagnetic torque of AFPMG is measured which comes out to be 18.584 Nm
9
(mean value). The torque-to-weight ratio parameter is computed which shows that active
10
mass of AFPMG has been reduced while improving the electromagnetic torque. The coils
11
of fabricated and designed AFPMG have been connected in series while following begin-
12
to-end winding pattern which increases the active mass of machine and also the air gap
13
flux density which in turn improves the electromagnetic torque. Due to which, the torque-
14
to-weight ratio parameter has been improved as compared to AFPMG with begin-to-
15
begin end winding pattern addressed in Ref. [8]. The comparison is listed in Table 5.
Table 5
16
17
6.4.
Power Density
18
The important parameter of AFPMG results is the power density which is the measure of
19
power rating of machine against active mass of machine. The higher value of power
20
density reflects the minimization of machine’s active mass while maximizing the power
21
rating [2]. The coils of fabricated and designed AFPMG have been connected in series
22
while following begin-to-end winding pattern which increases the mass of machine and
23
air gap flux density. Due to which, the power density parameter of AFPMG has been
17
1
improved as compared to AFPMG with begin-to-begin winding pattern addressed [4].
2
The comparison is presented in Table 6.
Table 6
3
4
6.5.
No-Load and Load Tests
5
The no-load test has been conducted on designed AFPMG model and observations have
6
been recorded. The no-load voltage characteristics of machine against variable shaft
7
speed is presented and shown in Figure 19.
8
Figure 19
9
The load test has been performed on AFPMG model. The voltage regulation of AFPMG
10
has been computed which is 17%. The voltage characteristics of AFPMG at load
11
conditions is shown in Figure 20 at constant load of 800W.
Figure 20
12
13
6.6.
Power and Efficiency Test
14
The multi-stage AFPMG has been tested for power and efficiency. The experimental
15
arrangement to test generator powers is shown in Figure 21.
16
Figure 21
17
In this test, the generator supplies the variable electrical load at constant shaft speed. Here
18
the variable electrical load represents the ohmic load at unity power factor [9]. The
19
variable electrical load (5 – 25 ohm) has been applied on generator terminals at various
20
values of shaft speed. The output powers of multi-stage AFPMG at various shaft speeds
21
(300, 500, 800 and 1000 rpm) have been recorded and shown in Figure 22. It is obvious
22
that multi-stage AFPMG supplies the maximum load at 9.5 ohm at different shaft speeds.
23
This test is basically the reflection of Thevenin’s Theorem that generator delivers the
24
maximum power to the load when winding resistance of generator equals the value of
18
1
ohmic load. Hence the multi-stage AFPMG delivers the optimal power to the loads when
2
ohmic value of the load is near winding resistance as shown in Figure 22.
3
Figure 22
4
Figure 23 shows the efficiency of multi-stage AFPMG against shaft speed at different
5
values of electrical loads as 9.5, 5.0 and 15.2 ohm. Analyzing the power and efficiency
6
characteristics of multi-stage AFPMG shown in Figure 22 and 23 respectively, the near
7
optimal operating zone can be proposed for the generator. The efficiency of multi-stage
8
AFPMG exceeds 95% while supplying the load of 9.5 ohm at 1000 rpm as evident from
9
Figure 23. Hence the rated parameters of multi-stage AFPMG can be defined as supplying
10
the load near 9.5 ohm at shaft speed near 1000 rpm, the generator exhibits near optimal
11
performance.
Figure 23
12
13
7.
Conclusion
14
In this paper, a Phase shift Model has been presented for design of multi-stage axial flux
15
machine while considering begin-to-end connection of stator disc. The axial flux
16
machines used to have large diameter of stator disc causing the occurrence of large
17
attractive forces at edges of rotor discs due to strong neodymium permanent magnets
18
which may tend to twist rotor plates axially inward. In this context, the presented design
19
improvement in axial flux machines has been incorporated by which the stator diameter
20
has been reduced to 1/3rd approximately for large number of poles. The analysis of voltage
21
waveform reveals that 3rd and 5th harmonics have been reduced in output voltage
22
waveform of designed AFPMG. The test results of AFPMG show that power density and
23
torque-to-weight ratio parameter has been improved while using begin-to-end connection.
24
Thus generator design has been improved and higher value of power density and torque19
1
to-weight ratio parameter exhibits the promise of generator design. Moreover the power
2
and efficiency test highlights the near optimal region of operation for designed multi-
3
stage AFPMG.
4
8.
5
The authors strongly acknowledge their institution, University of Engineering and
6
Technology Taxila, Pakistan for providing the financial support for the completion of this
7
research project under Grant: UET/ASR&TD/60.
8
References
9
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23
1
2
Figure 1. Multi-Stage topology of AFPMG
3
4
Figure 2. Stator and rotor discs of multi-stage AFPMG
24
1
2
Figure 3. Assembly of multi-stage AFPMG
3
4
Figure 4. The 3-phase instantaneous voltage waveform
5
25
1
(a)
(b)
(c)
Figure 5. (a) Differential segment arc portion of stator disc; (b) Differential segment arc
2
portion of stator disc showing coil placement according to 1-3 coil pitch; (c) Inter-magnet
3
displacement
4
(a)
(b)
(c)
Figure 6. Segment portions of stator discs: (a) Phase A stator disc; (b) Phase B stator
5
disc; (c) Phase C stator disc
6
7
Figure 7. Begin-to-end winding connection
26
1
2
Figure 8. Begin-to-begin winding connection
3
(a)
(b)
Figure 9. (a) Begin-to-end winding connection for stator disc of AFPMG; (b) Begin-to-
4
begin winding connection for stator disc of AFPMG
5
(a)
(b)
Figure 10. (a) Coil-magnet overlapping for begin-to-end connection of AFPMG; (b)
6
Coil-magnet overlapping for begin-to-begin connection of AFPMG
7
27
(a)
(b)
(c)
(d)
1
Figure 11. (a) Angularly displaced three casted stator discs of Phases A, B and C; (b) Set
2
of four in-phase rotor discs with permanent magnets; (c) Generator assembly consisting
3
of four rotor discs and three stator discs; (d) Multi-Stage AFPMG model
28
1
2
Figure 12. Multi-Stage AFPMG testing bench
3
(a)
(b)
Figure 13. (a) 1-phase voltage waveform of AFPMG model; (b) Voltage waveform of 2
4
phases of AFPMG model
29
1
2
Figure 14. No-load output voltage of AFPMG at rated parameters
3
4
Figure 15. Harmonic contents of AFPMG output voltage
30
1
2
Figure 16. Comparison of harmonics of AFPMG
3
4
Figure 17. 3-phase voltage waveform of AFPMG model
31
1
2
Figure 18. Electromagnetic torque developed by AFPMG model
3
4
Figure 19. No-load test
32
1
2
Figure 20. Load test
3
4
Figure 21. Multi-Stage AFPMG testing bench
33
1
2
Figure 22. Output power of AFPMG at different shaft speed
3
4
Figure 23. Efficiency of AFPMG at different electrical load
5
6
7
8
9
34
Table 1. Name plate ratings of AFPMG
1
Sr. #
Rating
Value
1
Power
1200 Watt
2
Voltage
220 / 127 Volt
3
Frequency
50 Hz
4
Max. Current
3.2 Amp/Phase
5
Shaft Speed
500 rpm
2
Table 2. Design Parameters of AFPMG model
3
Sr. #
Specification / Dimension
Aspect / Value
1
Number of poles
12
2
Number of coils of stator disc
6
3
Number of magnets per rotor disc
12
4
Outer diameter of stator disc
304.8 mm
5
Inner diameter of stator disc
132.1 mm
6
Number of turns of coil
7
Length of Magnet
25.4 mm
8
Width of Magnet
25.4 mm
9
Thickness of Magnet
10 mm
10
Rotor disc diameter
254 mm
11
Axial length of stator disc
10 mm
12
Axial length of rotor disc
15 mm
13
Segment Arc
230
1.047 rad
35
14
Slot Arc
0.261 rad
15
Coil Arc
0.786 rad
16
Inter-magnet Displacement
0.524 rad
17
Active Mass of AFPMG (per phase)
2.268 kg
1
Table 3. Design specifications of AFPMG model
2
Sr. #
Specification
Aspect / Value
1
Number of stator discs
3
2
Number of rotor discs
4
3
Winding connection type
4
Conductor size
SWG 21
5
Coil pitch
1-3 coils
6
Winding type
7
Phase A Stator Disc (Reference Phase)
8
Phase B Stator Disc (w.r.t Phase A)
-0.698 rad
9
Phase C Stator Disc (w.r.t Phase A)
-1.396 rad
Begin-end
Stair winding
0 rad
3
4
Table 4. Comparison of Generator Results
Harmonic Distortion
Designed AFPMG
AFPMG with
Model
rectangular magnets [17]
Harmonic distortion due to 3rd harmonic
10.7 %
12.5 %
Harmonic distortion due to 5th harmonic
0.54 %
16.0 %
Total harmonic distortion (THD)
10.7 %
20.3 %
5
36
1
Table 5. Comparison of AFPMG results
2
Parameter
Designed AFPMG with
AFPMG model with begin-
begin-to-end connection
to-begin connection [8]
8.194
5.94
Torque-to-weight ratio
(Nm/kg)
3
Table 6. Comparison of AFPMG results
4
Parameter
Designed AFPMG with
AFPMG model with begin-to-
begin-to-end connection
begin connection [4]
167.55
113.82
Power Density
(W/kg)
5
37