K
Science and Technology
Development Fund
Central Laboratory for
Aquaculture Research
‫جام ـ عة ك ـفر ال ش ـ ـ ـ ـ يخ‬
afrelsheikh University
Kafrelsheikh
University
South Valley
University
Colon University of Applied
Sciences
Tanta University
Report WP4-A11
Work package
WP4
Activity
A11
Title
Create optimal model for energy and water management and the corresponding energy
management to be a design guide for turbine system selection
Work
Month
Planed
Gantt chart
Actual
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Schedule
Work Team
No
Name
Position
1
2
3
Dr. Mohamed El-Nemr
Dr. Said Allam
Eng. Mohamed Mamdouh
Researcher
Research Assistant
Research Assistant
Page: 1
Work
Group
TAN
TAN
TAN
Main Task
Literature Review and Modeling
Literature Review and Modeling
Literature Review and Modeling
K
Science and Technology
Development Fund
Central Laboratory for
Aquaculture Research
‫جام ـ عة ك ـفر ال ش ـ ـ ـ ـ يخ‬
afrelsheikh University
Kafrelsheikh
University
South Valley
University
Colon University of Applied
Sciences
Tanta University
Contents
Report WP4-A11 .......................................................................................................................... 1
Work package .......................................................................................................................... 1
Activity ..................................................................................................................................... 1
Title .......................................................................................................................................... 1
Schedule .................................................................................................................................. 1
Work Team .............................................................................................................................. 1
Table of Figures ........................................................................................................................... 3
Objectives .................................................................................................................................... 4
Descriptions ................................................................................................................................. 4
Preface ......................................................................................................................................... 5
Classifications of Permanent Magnet Synchronous Generator .................................................. 6
PM synchronous machines with different directions of flux path .............................................. 7
A.
Radial Flux Permanent Magnet (RFPM) machine .......................................................... 7
B.
Axial flux permanent magnet (AFPM) machine ............................................................. 7
C.
Transverse flux permanent magnet (TFPM) machines ................................................10
PM synchronous machines according to PM mounting ........................................................10
A.
Surface Mounted PM ...................................................................................................10
B.
Interior Mounted PM ...................................................................................................11
C.
Inset Mounted PM .......................................................................................................13
Page: 2
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Science and Technology
Development Fund
Central Laboratory for
Aquaculture Research
‫جام ـ عة ك ـفر ال ش ـ ـ ـ ـ يخ‬
afrelsheikh University
Kafrelsheikh
University
South Valley
University
Colon University of Applied
Sciences
Tanta University
Table of Figures
Figure 1: Radial-flux PM-machine configurations ....................................................................... 7
Figure 2: Axial-flux machine configurations ................................................................................ 8
Figure 3: Layout of Torus ............................................................................................................. 8
Figure 4: Rotor structure of surface-mounted PM machine .....................................................11
Figure 5: Rotor structure of interior-mounted PM machine ....................................................12
Figure 6: V-shape rotor structure of buried-mounted PM machine .........................................13
Figure 7: Rotor structure of interior-mounted PM machine ....................................................13
Figure 8: Outer rotor structure of PM machine (Single external rotor and internal stator) ....14
Figure 9: Double rotor with internal toroidally wound stator ..................................................15
Figure 10: Matlab utility for PMSG dynamics simulation in generator mode.......................... 17
Figure 11: Matlab utility for PMSG dynamics simulation in generator mode .......................... 17
Page: 3
K
Science and Technology
Development Fund
Central Laboratory for
Aquaculture Research
‫جام ـ عة ك ـفر ال ش ـ ـ ـ ـ يخ‬
afrelsheikh University
Kafrelsheikh
University
South Valley
University
Colon University of Applied
Sciences
Tanta University
Objectives
Investigate the different configuration configurations of PMSG suitable for low speed
applications with gearless coupling
Descriptions
The generator in wind energy systems is the main energy converter from mechanical energy
into electrical energy. This project focuses on permanent magnet synchronous generators
(PMSG). This type of generator has mainly six categories based on the arrangement of magnet
distribution and geometrical properties.
The researchers of Tanta University had performed a literature survey for the categories of
PMSG and their geometries and performance characteristics. A three dimensional drawing
library is produced to present different categories using Autodesk AutoCAD software. The
surface mounted PMSG is nominated as a suitable candidate for manufacturing visibility.
Dynamic model that present the load effect and voltage built-up process is developed using
MATLAB software. Such model should conclude the information required for the successful
cooperation between generator design team and energy-optimizer design team.
Page: 4
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Science and Technology
Development Fund
Central Laboratory for
Aquaculture Research
‫جام ـ عة ك ـفر ال ش ـ ـ ـ ـ يخ‬
afrelsheikh University
Kafrelsheikh
University
South Valley
University
Colon University of Applied
Sciences
Tanta University
Preface
Wind power is an energy source whose industrial application in the world has grown at the
fastest rate in the last 10–15 years. Installed capacity of wind power plants is continuously
growing at a level of annual rate exceeding 30%. The European power market has been the
main driving force in development of wind power industry for many years. In EU countries, a
record installation of more than 6,180 MW new wind power generators was achieved in 2005.
By the end of 2005, the capacity of wind energy generation reached a level of more than 40,500
MW in Europe and more than 59,300 MW worldwide. In Europe, the current targets of using
wind capacity are 75,000 MW by 2010, 180,000 MW by 2020, and 300,000 MW by 2030 [1].
Powerful grid-connected megawatt-scale wind generators, 0.5–5.0 MW per unit, are mostly
manufactured and installed as pollution-free sources of renewable energy in the world in last
years’. At the same time, many smaller wind turbines are required for certain installations and
local consumption as maintenance-free independent power suppliers. A small-scale wind power
turbine of the capacity 0.2–30 kW, with rotor diameters from 1 m up to 15 m may be used as a
flexible and vital alternative for local power demand in isolated regions or locations [2-4].
Recent study shows a great demand for small to medium rating (up to 20 kW) wind generators
for stand-alone generation-battery systems in remote areas. The type of generator for this
application is required to be compact and light so that the generators can be conveniently
installed at the top of the towers and directly coupled to the wind turbines [5].
Compared with a conventional, gearbox-coupled wind turbine generator, directly coupled
generators have a series of advantages, such as a much reduced size of the overall system, a
rather low installation and maintenance cost, a flexible control method, a quick response to the
wind fluctuation and load variations, etc. However, a directly coupled generator needs to have a
very low-speed operation to match the wind turbine speed and, at the same time, to produce
electricity in a normal frequency range (30–80 Hz). According to the electric machine design
principles, this implies a very bulky generator with a very big pole number [5].
Potentially, Permanent Magnet Synchronous Generators (PMSGs) offer a high efficiency in
operation and a simple and robust structure in construction because no field current and
winding are used. The attractiveness of PMSG generators is further enhanced by the availability
of high-energy PM materials such as neodymium-iron boron [5]. As a result, many different
configuration of PM generator have been developed and widely used.
Permanent magnet (PM) synchronous generators are one of the best solutions for smallscale wind power plants. Low-speed multi pole PM generators are maintenance-free and may
be used in different climate conditions [1]. It is possible to combine PM wind generators for
hybrid technologies such as wind-diesel, wind-photovoltaic etc.
Page: 5
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Science and Technology
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Central Laboratory for
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‫جام ـ عة ك ـفر ال ش ـ ـ ـ ـ يخ‬
afrelsheikh University
Kafrelsheikh
University
South Valley
University
Colon University of Applied
Sciences
Tanta University
The advantageous of PM machines can be summarized as follows:





Elimination of copper losses in the rotor winding
Higher efficiency, smaller size and lower weight
It has no brushes or slip rings so it has the same simple and rugged construction as
induction generator
Since PMSG operate at synchronous speed there are no copper losses in the rotor and an
increased efficiency of the order 5–10 % may be expected over induction generator
PM on the rotor supply the field excitation and there is no need for external dc source
for excitation
On the other hand, the disadvantages of the PM machines are:





High price of permanent magnet
Variation of permanent magnet characteristics with time
Strongly attractive nature of PM material tends to increase the difficulty of manufacture
PM synchronous generator excitation constant which reduce the ability of controlling
the terminal voltage
High cost due the initial cost of PM (this cost is decreasing rapidly with the development
of new PM material)
The introducing of Samarium-Cobalt magnets in 1963 and Neodymium-Iron-Born magnets in
1983 has changed the technology of the building PM machines drastically. These materials offer
extra ordinary PM characteristics. Therefore, they decrease the volume of the PM material
inside the machines [6].
Classifications of Permanent Magnet Synchronous Generator
Generally, the stator of permanent magnet synchronous machine is structurally similar to
that of the conventional synchronous machine, while, the rotor has permanent magnet instead
of wire-wound fields and its associated slip-rings and brush gears. PM synchronous machines
can be classified according to magnetization orientation (radial, axial or transverse), according
to PM mounting (surface mounting, inset or interior mounting) or according to rotor structure
(inner or outer). It should be noted that, the arguments are also typically overlapping and one
special type may belong to different groups.
The aim of this study is to compare different designs of Permanent Magnet (PM)
synchronous generators for low speed applications.
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Science and Technology
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Central Laboratory for
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‫جام ـ عة ك ـفر ال ش ـ ـ ـ ـ يخ‬
afrelsheikh University
Kafrelsheikh
University
South Valley
University
Colon University of Applied
Sciences
Tanta University
PM synchronous machines with different directions of flux path
A. Radial Flux Permanent Magnet (RFPM) machine
The Radial Flux Permanent Magnet (RFPM) machine is producing the magnetic flux in the
radial direction with PMs. The design of Radial Flux (RF) machines is simple and widely used. The
structural stability of RF machines is easy to make sufficient. Most of the low speed megawatts
wind generators are RF machines and these RF machines seem to be the most interesting
machine type for the large-scale direct-drive wind turbines. When using permanent magnets for
the direct drive generators, the generators can operate with good and reliable performance
over a wide range of speeds. In manufacture, the simple way of constructing the machine with
high number of poles is gluing PMs on the rotor surface. In RFPM machines, the length of the
stator and the air gap diameter can be chosen independently. If necessary, the radial-flux
machine can be made with a small diameter by using a long stator. Fig. 1 shows two
configuration of radial-flux PM-machine. RFPM machines have the advantages such as a better
torque density than the RF Electrically Excited Synchronous Machine (EESM), so that these
machines have been discussed in a number of literatures. However, the presence of PMs makes
the assembly more difficult and the structure more strong, especially in large machines.
Figure 1: Radial-flux PM-machine configurations
B. Axial flux permanent magnet (AFPM) machine
The Axial Flux Permanent Magnet (AFPM) machine is a machine producing magnetic flux in
the axial direction. Several axial-flux machine configurations can be found regarding the
stator(s) position with respect to the rotor(s) positions and the winding arrangements giving
freedoms to select the most suitable machine structure into the considered application.
Possible configurations of AFPM are shown in fig.2. Fig. 3 shows another configuration of AFPM
named 'Torus' [7]. The Torus machine is a slotless, toroidal-stator, double-sided, axial-flux, disctype, permanent magnet, brushless machine. The name Torus was adopted to indicate the
toroidal nature of both the stator core and the stator winding. AFPM machines built with 'Torus'
topology give twice the torque density of RFPM machines. On the other hand, the thickness of
the magnets used in 'Torus' machines makes the cost/torque twice that of RFPM machines with
surface mounting magnets.
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afrelsheikh University
Kafrelsheikh
University
South Valley
University
Colon University of Applied
Sciences
Tanta University
Figure 2: Axial-flux machine configurations
(a) Single-rotor – single-stator structure (b) Two-rotors – single-stator structure
(c) Single-rotor – two-stators structure, called hereafter also as AFIPM machine (Axial-Flux Interior rotor
Permanent-Magnet machine) (d) Multistage structure including two stator blocks and three rotor blocks
Figure 3: Layout of Torus
Page: 8
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Science and Technology
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‫جام ـ عة ك ـفر ال ش ـ ـ ـ ـ يخ‬
afrelsheikh University
Kafrelsheikh
University
South Valley
University
Colon University of Applied
Sciences
Tanta University
The salient features of the Torus machine can be summarized as follows:




The topology of the machine leads to a short axial length and thus to a high power-toweight ratio and makes it possible to integrate the generator directly with the wind
turbine to form a very compact generating set.
The disc rotors and magnets act naturally as fans, so good ventilation and cooling of the
stator winding are achieved even at low rotational speed and hence the machine can
operate with high electric loading.
The slotless, air-gap winding gives low values of mutual and leakage inductances. The
axially-directed end winding lengths are relatively short, yielding low resistance. Hence,
the voltage regulation under load is acceptable for the application.
The absence of the slots leads to a very low-noise machine with negligible cogging
torque. Vibration and high-frequency rotor losses associated with stator slot opening are
also eliminated
AFPM machines have the advantages compared to RFPM machines as the following:






Simple winding
Low cogging torque and noise (in slotless machine)
Allows construction of compact generator with large number of poles
Higher torque/volume ratio
They operate with similar magnetic flux density in all the magnetic circuit, which
translate to better utilization factor for the magnetic core. Also the axial flux
construction takes the advantage of the anisotropic characteristic of the oriented grain
silicon iron
Better efficiency
However, the disadvantages of AFPM machines compared to RFPM machines can be
summarized as the following.




Lower torque/mass ratio
Larger outer diameter, large amount of PM, and structural instability (in slotless
machine)
Difficulty to maintain air gap in large diameter (in slotted machine)
Difficult production of stator core (in slotted machine)
According to the survey on AFPM machines, a larger outer diameter, heavier mass than
RFPM machine and complicated slotted machines construction must be taken into account.
Therefore to apply AFPM machines in direct-drive application for large scale wind turbine, these
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afrelsheikh University
Kafrelsheikh
University
South Valley
University
Colon University of Applied
Sciences
Tanta University
disadvantages must be solved or even improved significantly, since those cause cost increase
and difficult manufacture.
C. Transverse flux permanent magnet (TFPM) machines
The transverse flux (TF) principle means that the path of the magnetic flux is perpendicular
to the direction of the rotor rotation. The major difference of TFPM machine compared to RFPM
and AFPM machines is that TFPM machine allows an increase in the space for the windings
without decreasing the available space for the main flux. TFPM machine can also be made with
a very small pole pitch compared with the other types.
The main advantages of TFPM machines can be summarized as follows compared to the
longitudinal machines:



Higher force density
Considerably low copper losses
Simple winding
Contrary to the advantages, the construction of TFPM machine is more complicated
compared to RFPM and AFPM machines, since TFPM machine has the flux path of three
dimensions. TFPM machine with large air gap seems to be no more attractive because its force
density is a little high or even low compared to RFPM machines.
In contrast to axial-flux machines, which are manufactured almost exclusively with surface
mounted magnets, several variations of assembling the magnets into the rotor of a radial-flux
machine are possible and reasonable.
PM synchronous machines according to PM mounting
According to the location of the magnets in the rotor, the different configurations of
permanent magnet synchronous machine can be classified. Mainly, there are three types of PM
machines being used in the industry. They can be briefly defined as follows:
A. Surface Mounted PM
In this type, the PM materials are mounted on the surface of the rotor. The simplicity of
building the rotor is one of the advantages of this machine type. Fig. 4 shows the rotor structure
of the surface-mounted PM machine and the definitions for the direct (d) and quadrature (q)
axes.
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University
(a) conventional surfacemounted PM
South Valley
University
Colon University of Applied
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(b) surface-mounted PM with
pole shoes
Figure 4: Rotor structure of surface-mounted PM machine
Surface-mounted structures are relatively simple to manufacture and assemble. If
permanent magnets are glued on the surface of the rotor, the rotation speed of the machine
must be limited so that centrifugal forces do not break the glue joint. In the case of low speed
wind applications, centrifugal forces on the surface mounted PM are very low because the
nominal speed is around 50 rpm. It is possible to improve the mechanical rigidity of the rotor
structure by adding a reinforcing belt around the rotor. The reinforcement may be a carbon
fiber or fiberglass band or a stainless steel cylinder. The first mentioned are, however, thermal
insulators causing additional difficulties in the rotor cooling. A reinforcement cylinder obtained
by using stainless steel involves a problem in terms of eddy currents since the material is
conductive.
A conventional surface-mounted PM structure is shown in fig. 4-a. Special arrangements
may be used in order to obtain a sinusoidal air-gap flux density waveform as well as mechanical
protection for the magnets. Rotor structure of surface-mounted PM machine with pole shoes is
shown in fig. 4-b.
B. Interior Mounted PM
In this type, the PM materials are mounted (buried) inside the rotor. This method increases
the durability of the machine but has hard manufacturing process. Fig. 6 shows the rotor
structure of the interior-mounted PM machine and the definitions for the direct (d) and
quadrature (q) axes.
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(a)
‫جام ـ عة ك ـفر ال ش ـ ـ ـ ـ يخ‬
afrelsheikh University
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University
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Colon University of Applied
Sciences
Tanta University
(b)
Figure 5: Rotor structure of interior-mounted PM machine
The buried magnet configuration exists in several variants as shown in fig.6-a and fig.6-b.
Although the rotor structure is somewhat more complex to manufacture it offers several
advantages over the surface-mounted structure. The usual advantages of the buried magnet
configurations compared to the surface PM designs are the possible flux concentration
generated by the magnets in the rotor. The required magnet shape is a rectangular
parallelepiped, which is simple to manufacture. No problems occur for the magnets to be fixed,
consequently higher rotation speeds may be allowed without using additional reinforcements. It
is possible to achieve a nearly sinusoidal air-gap flux density waveform and low cogging torque,
which thus improves the torque quality. The demagnetization risk of the permanent magnets is
reduced since the magnets are surrounded by ferromagnetic iron and fixed relatively far from
the air-gap. The surrounding material also protects the magnets against mechanical impacts,
wear and corrosion.
As a disadvantage, the structure suffers from the increased leakage flux in the ends of the
magnets since magnetic short-circuits may be formed due to the surrounding iron offers. The
leakage fluxes can be reduced by means of proper flux barriers or material selections but
leakage fluxes are difficult to diminish to a same level as in the case of a surface-mounted
structure. It is also stated that the demolition and recycling of the materials of the machine is
more difficult because it is awkward to remove the magnets from the rotor core. Considering
this, the surface-mounted structure is a simpler construction [8].
The tangentially magnetized PM rotor, shown in fig. 6-b, presents the drawback of many
iron and magnet pieces to be manipulated if the number of poles is high. Therefore, some
production difficulties can arise. However, it does not present any bridges and the flux leakage
is then very low.
Another rotor structure of the buried-mounted PM machine, named V-shape is shown in fig.
7. The drawbacks of the rotors with V-shape magnets are the iron bridges that cause a high
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afrelsheikh University
Kafrelsheikh
University
South Valley
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Colon University of Applied
Sciences
Tanta University
leakage flux. Furthermore, the V-shape rotor is not very adapted for high pole numbers. Indeed
the higher the pole number, the smaller the place for the magnets in V-shape, and the smaller
the angle between the two magnets. It can therefore easily get saturated between the magnets
if the angle is too little. Another drawback of the V-shape configuration is the high number of
magnets that increases the production cost [9].
Figure 6: V-shape rotor structure of buried-mounted PM machine
C. Inset Mounted PM
In this type, the PM materials are inset or partially inset into the rotor. The direct axes
inductance is less than the quadrature axes inductance. Fig. 8 shows the rotor structure of the
inset-mounted PM machine and the definitions for the direct (d) and quadrature (q) axes.
Another property that differs between the investigated rotors is the saliency of the buried PM
designs and of the inset PM designs. A reluctance torque can be produced in addition to the
torque produced by the magnets.
Fig. 8.
Figure 7: Rotor structure of interior-mounted PM machine
2.1. PM synchronous machines according to rotor structure (inner or outer)
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University
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University
Colon University of Applied
Sciences
Tanta University
Most of the RFPM machines have a conventional inner rotor design but some outer rotor
designs have also been presented in literature. The structure with external rotor and internal
stator, known also as drum motor, is an alternative configuration and shown in fig. 9.
Fig. 9.
Figure 8: Outer rotor structure of PM machine (Single external rotor and internal stator)
As can be noticed, the wound stator is stationary, located in the center of the machine while
the magnets are mounted evenly along the inner circumference of the rotating drum.
Several advantages can be identified easily from the illustrated outer-rotor structure, as
follows [5].




The blades of the wind turbine can be conveniently bolted to the front face of the drum
to realize the direct coupling between the wind turbine and the PM generator.
Because of the enlarged periphery of the out-rotor drum, the multipole structure can be
easily accommodated.
Due to the multipole structure, the total length of the magnetic path is reduced. This not
only effectively uses the PMs, but also offers a noticeable height reduction of the rotor
yoke, resulting in a significantly reduced total volume and weight.
The coil pitch equals the slot pitch so that the end winding is shorter, and
correspondingly, copper loss is lower than those in a long pole pitch machine.
Furthermore, with the ratio of the rotor diameter to the magnet width large enough, a
minor air gap between the inner arc of the drum and the flat magnet surface will not be
significant, resulting in a much simplified process of machining of the rotor yoke and mounting
of the permanent magnets. Therefore, a small pole pitch and larger pole number is favorably
accommodated by the outer-rotor structure, and a cost-effective, directly coupled PM
generator can be made. In the actual design, all of the radially magnetized magnets are squarely
shaped and evenly placed to the inner periphery of the rotor drum. While the generator is
running, the centrifugal force of the magnets applies a pressure to the bonding media. Thus, the
reliability of the glued joints becomes higher.
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As exposed to the natural wind flow, the outer rotor has a much reduced temperature rise
than does the stator. Additionally, the simple outer rotor structure makes the PM generator
compact, light, rugged, and easy to be installed at the top of a high tower.
Recently, Qu et al., introduced a machine structure with toroidally wound internal stator
and two rotors as shown in Fig. 10. The latter construction does not seem very practical since
the mechanical structure is more complicated and the heat removal from the internal stator
requires efficient air circulation inside the machine. The unique features of dual-rotor radial flux
machine include very short end windings, high overload capability, balanced radial forces, low
cogging torque and low material costs. Dual rotor radial flux machine is known for its high
torque density and efficiency over induction and other permanent magnet machines. It has
some meticulous features such as rotor-stator-rotor structure and double air-gaps due to
unique mechanical configuration. As the output torque is proportional to the air-gap surface
area for the constant electrical and mechanical loadings, torque density is improved. Since both
the working surfaces of the stator core are used machine efficiency gets boosted up [8,9].
Figure 9: Double rotor with internal toroidally wound stator
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‫جام ـ عة ك ـفر ال ش ـ ـ ـ ـ يخ‬
afrelsheikh University
Kafrelsheikh
University
South Valley
University
Colon University of Applied
Sciences
Tanta University
To allow productive cooperation the Tanta university group has developed a model that
presents the dynamics of PMSG. The following few paragraphs presents the used model and the
Matlab utility developed.
Rs
q
-
+
Lls
Rf
Rkd
Lmd
+
-
Vd
Llf
Llkd
Vfd
Lls
Rs
d
-
+
Rkq
+
-
Vq
Lmq
Llkq

2 
2  


sin  sin   sin    Va 
Vd 
2
3
3   




 Vb
V  
2

2



3
cos  cos   cos     
 q
V 

3 
3   c 


 d   ( L ls  L md ) i d  L md ( i fd  i kd )
 q   ( L ls  L md ) i q  L mq i kq



t
0
 ( t ) dt
 
0
Fig. 11: The PMSG in the rotor reference frame, including damper windings effect
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Figure 10: Matlab utility for PMSG dynamics simulation in generator mode
a) q component of armature current
b) developed terminal voltage
c) Mechanical torque
Figure 11: Matlab utility for PMSG dynamics simulation in generator mode
1. References
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[2] Grauers, A. Design of Direct-Driven Permanent-Magnet Generators for Wind Turbines //
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[3] Lampola, P. Directly Driven Low-Speed Permanent-Magnet Generators for Wind Power
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Electromechanics: Espoo, Finland, 2000. 62 pp.
[4] 4. Kilk, A. Design and Experimental Verification of a Multipole Directly Driven Interior PM
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[5] J. Chen, C.V. Nayar and L. Xu, “Design and finite-element analysis of an outer-rotor
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K
Science and Technology
Development Fund
Central Laboratory for
Aquaculture Research
‫جام ـ عة ك ـفر ال ش ـ ـ ـ ـ يخ‬
afrelsheikh University
Kafrelsheikh
University
South Valley
University
Colon University of Applied
Sciences
Tanta University
[6] Asghar Abedini, “Integration of permanent magnet synchronous generator wind turbines
into power grid,” Ph.D. dissertation the University of Wisconsin, December 2008.
[7] B. J. Chalmers, W. Wu and E. Spooner, “An axial-flux permanent-magnet generator for a
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[8] Parviainen, “Design of axial-flux permanent-magnet low-speed machines and performance
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F. Libert and J. Soulard, “Design Study of Different Direct-Driven Permanent-Magnet Motors
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Page: 18