Abstract — High speed brushless permanent-magnet
generators (HSBPMGs) may be the most suitable choice for small
solar co-generation systems due to a variety of merits. For
instance, they offer substantial reduction in size, and thermally
excellent high-power density, which reduces the running costs with
good performance and reliability. Moreover, high efficiencies i.e.
over 90%, light-weight, low operating temperature, high
insulation, no brushes/slip rings and almost negligible cogging
torque make HSBPMGs ideal for co-generation systems. However,
because of the very high rotor speed and high stator frequency, the
design of HSBPMG is quite different from designing a
conventional generator with low speed and low frequency. As the
speed increases, the losses and temperature go up, and thus careful
attention is needed while selecting the design parameters and
material for the machine. This paper is aimed to use the basic
design process for HSBPMGs running at 60,000rpm, with 6.6kW
capacity keeping the losses minimum by using an appropriate
material and cooling method. Finite element analysis of the
machine is carried by using Motor-CAD simulation software, and
modeling of a prototype machine is presented.
Keywords—high speed brushless permanent magnet generators
(HSBPMG); Co-generation; Motor-CAD.
In past few years, increasing demand of green energy and to
minimize the dependence on fossil fuels have provide a route to
worldwide combination of renewable energy generation. Mainly
there are two main technologies which are mostly focused: -
wind and solar. Concentrated solar thermal power (CSP)
integrated with co-generation system is one of the promising
solutions for distributed power generation as discussed in . In
regions with low transmission capabilities smaller power plants
are better idea than to a large power plant due to their cost
effectiveness. In electrical machines theory, the output power is
directly proportional to the speed of rotor, higher speed, would
lead to higher output power with reduced size. Permanent
magnet machines with high rotor speed operations are the best
candidates for small co-generation system as they have simple
structure and higher power density as discussed in .
Designing high speed brushless permanent magnet (BPM)
generator is quite different from designing a conventional
generator. In high speed operations, the frequency and the
temperatures of the rotor are very high which leads to higher
losses and need careful attention while selecting the design
parameters as discussed in .
Different design topologies of high speed BPM generator
were presented by the researchers in past few years presented in
[4-6]. Different design features of HSBPMG have been
investigated in [7-9]. The potential and limits of HSBPM
machines, selection of magnet, rotor and stator material, rotor
and stator topologies and advantages of using retaining sleeves
are illustrated in . Reference  presented the design
solution of high speed permanent magnet (PM) machine for a
flywheel application, also rotor losses reduction techniques are
discussed. A high speed PM machine which operates in elevated
temperature environments with specification of 23kW, 84krpm
with a torque density of 50kNm/m
is discussed in . Different
materials for high speed PM machines are discussed in . In
high speed operations, liquid cooling method is more effective
than air cooling, but liquid
in jackets alone cannot effectively
cool the inner rotor and windings, so self-ventilation may be
needed along with liquid cooling. In  effective cooling
method is presented and also thermal analysis for different rotor
types are discussed.
The design approach demonstrated in this study is elaborated
for a particular type of high speed PM machine. Basic machine
specifications are set to required power of 660kW, required
speed of 60,000 rpm, and output voltage of 700V. Geometry of
the machine is set to 24 stator slots and 2 poles, and 3-phase
machine. The number of slots per pole per phase is q = 2. There
are number of options that can be set for the rotor topology in
Motor-CAD, U-shaped magnets are used with circular ducts in
this design which help to reduce the high temperature and losses.
Concentrated winding is used to achieve the shortest possible
length of the machine; winding is set to double layer overlapping
and the number of turns per coil is 8 with 224 conductors per
slot. Magnet material used in this design is 6.5%SiFe, which is
excellent to reduce the iron losses and has a very good operating
temperature range. In thermal analysis, water jackets are used in
housing for cooling and windings are set to self-ventilate.
Electromagnetic and thermal analysis of the machine is carried
by using Motor-CAD simulation software. Finally, all the results
are verified by finite element analysis.
Designing high speed BPM generator is more
complicated than designing a conventional generator. Because
of high frequency and high losses, all the parameters need to be
In this paper 6.6kW/60,000rpm HSBPM generator is
designed. In first step, basic requirements of the module need to
be decided, secondly selection of rotor and stator is done. Two
common topologies of stator which are mostly used in high
speed applications: slotted stator, slotless stator. Slotted stators
offer high torque density and high acceleration, selected for the
design. Radial flux interior permanent magnets (IPM) rotor is
selected, as it offers low cogging torque and higher peak-to-
peak ripple torque. Selection of material is very critical in high
speed BPM generator design. A material which offers low
losses and has capability to stand with higher temperature needs
to be chosen. Selection of pole number, number of slots, number
of phases, number of slots per pole per phase and winding
layout are very important constraints which affects the overall
efficiency of designed generator.
Finite element analysis (FEA) is done using Motor-CAD.
Motor-CAD provides the ability to quickly and easily perform
electromagnetic and thermal performance tests on prototype
designs. Results are matched and verified with calculated
values. Finally, thermal analysis is done and temperatures are
calculated. If the results are not verified machine calculated
dimensions, rotor and stator structure and selected material
would be modified.
Design of High Speed Permanent Magnet
Generator for Solar Co-Generation System Using
Faculty of Engineering & IT, University of Technology Sydney, Australia.
University of KwaZulu-Natal, South Africa.
978-1-5386-3246-8/17/$31.00 © 2017 IEEE
Radial flux buried magnets rotor topology is selected for this
design as they are capable in heat removal and appropriate
cooling and high power and speed applicability as discussed in
. The rotor aspect ratio defined as length-to-diameter (L/D)
should not be very low it will cause high stiffness and larger
diameter. To keep the rotor radial size minimum, the optimum
value of L/D is kept 2.51. Rotor tip speed is calculated by rotor
radius and rotational speed; its value lies in 50-200 for PM
A. calculation of rotor parameters
• Number of poles is critical factor that affects the structure
and performance of the machine. It mainly depends on
the speed, N (rpm) of the machine and electrical
frequency, f (Hz) as shown below.
N⋅ (2p) = 120⋅f
If number of poles is higher, frequency will be high
which causes high losses. Moreover, number of slots per
pole per phase reduces which causes less sinusoidal
waveform. So, number of poles is kept lower i.e. 4 in this
• Air gap flux density depends on magnetic height (h
magnetic remnant flux density (B
Magnet losses can be reduced by using smaller magnets,
i.e. small magnet height. To keep the magnetic field
uniform, magnetic height is greater than the air gap by a
• Number of phases (q) can be determined by the following
equation and it affects machine’s power (P), current (I)
and voltage (V) ratings.
3 phase machines has been selected for this design as it
is the most common form and mostly used in industry
also we get balanced torque in 3-phase machine.
• Once number of slots (N
) are known pole pairs (p) and
number of phases (q), slots per pole phase (m) can be
calculated as below.
• To get a sinusoidal voltage waveform and reduced
machine harmonics the number of slots/pole/phase can
Basically, there are two main stator topologies; slotted and
slot-less stator. Slotted motors are good for high torque density
and high acceleration, while slot-less motors are better option for
and good linearity when operating in a servo
control system. Cogging torque will vary greatly with different
motor designs and steps are typically taken to minimize its
impact, like skewing the magnet or stator laminations. Both
technologies offer large through holes and can be designed for
low profile direct drive applications. Slotted stators are good at
higher acceleration as compared to the slot-less stator which are
not good choice for high speed applications despite some
advantages, slotted stator topology is selected for this design.
Slotting helps to get a narrow air-gap and keeps the main field
winding conductors close to the field magnets to get maximum
flux linkage also provides a limited thermal resistance which
helps to get proper cooling of field windings.
A. Stator windings
Since there are an infinite number of possibilities for pole
and slot count combinations and winding layouts, assumptions
are required to focus or limit the scope so that desirable windings
can be found . The assumptions considered here are machine
has three phases, all slots are filled, each slot has two coil sides
or double layer windings, only balanced windings are considered
all coils have the same number of turns and all span the same
number of slots.
Number of stator slots is 24 (N
= 24), number of poles is 4
= 4), motor constant is 0.7 (K
= 0.7), minimum skew
required to eliminate cogging torque is 1 (α
= 1). Fig 1 shows
the winding layout of the machine.
Fig 1. Winding layout of the machine
Winding type is selected as overlapping; the winding definition
is defined by wire size, which is set to be 0.885mm and 0.800mm
from the metric table, and the material between the liner and
lamination is set as air as shown in picture. Number of strands in
hand is set to 14 and conductor separation is 0.025mm.
Conductor/ slot and conductor/ slot drawn should be same.
OTOR AND STATOR MATERILA SELECTION
Kind of material selected for rotor and stator of
HSPMG is very critical as it affects the losses and overall
efficiency of the machine. Selection of the material depends on
the application of the machine plus cost, saturation flux,
permeability and core losses. We need the material which offers
minimum losses at high-speed operation to be selected for this
6.5%SiFe is selected as a rotor and stator material, the potential
benefits are reduced iron losses,
Low Magneto-striction, high
permeability, stable quality, non-oriented and operating
temperature range on high speed operation. Table below shows
some features of 6.5%SiFe also known as JNEX core material.
Saturation flux density 1.6 Tesla.
Typical core loss (50kHz, 100mT) 650mW/cm
Curie temperature 700°C.
Operating temperature range -30°C to 200°C.
Table 1. Properties of 6.5%SiFe
OSSES CALCULATION IN MACHINE
Basic losses in HSPMG can be categorised as follows as
1. Stator losses
2. Rotor eddy current losses
3. Winding losses
Stator losses Stator losses made up of copper losses and iron
losses. Copper losses consist of conventional I
R loss and stray
losses which are due to the skin effect and proximity effect.
losses can be calculated by the following equation.
Stray losses consist of (a) skin effect causing because of the same
source conductors and (b) proximity effect which is because of
the electromagnetic field induced in two adjacent conductors
sharing the one slot.
The intensity of skin effect can be analysed
by skin depth which is a measure of a distance of a current flow
along the surface of the material and reduces in amplitude by a
factor 1/e, where e = 2.71828. Skin depth can be calculated by
the formula given below.
Losses because of proximity effects of the conductor can be
estimated based on the equation below as given below.
Iron losses include hysteresis and eddy current losses,
loss per unit volume in terms of maximum flux density and
frequency can be analysed by the following formula.
The eddy current loss per unit volume at lower frequencies
is given by the following equation.
Eddy current loss further divided into two classes (a)
classical eddy current and (b) excess eddy current for more
accurate calculation. So, for a given frequency, the iron losses of
the machine are calculated as below.
Rotor eddy current Losses
Eddy current losses can be
divided into three categories as below. (a)No-load rotor eddy
current losses caused by the presence of stator slots, (b)On-load
rotor eddy current losses caused by winding’s harmonics (space
harmonics), (c)On-load rotor eddy current loss induced by the
time harmonics of the phase currents (PWM). Generally,
following relationship can be used to calculate the eddy current
Since rotor loss caused by time harmonics is dominant in most
applications, increasing the switching frequency and using
external line inductance to reduce current THD is a very
effective way to reduce rotor loss.
Winding Losses winding in air cause losses as well, power
is needed to control the drag resistance of rotor cylinder.
Different gases or fluids are also used in between rotor and
stator, so winding losses is a function different operating
conditions such as temperature, density, the pressure of these
fluids/gases and the rotational speed of the shaft. Winding loss
can be estimated by the following equation.
There are frictional losses as well because of surface roughness
of rotor and stator should also be taken into account for the more
precise calculation of overall losses.
S BASIC MODEL AND SIZING
We can model our machine as a phasor circuit as follows. As
the machine is assumed to be balanced so the parameters for one
phase can be determined and applied to other two phases. The
phasor diagram of the machine is shown in figure 2.
Fig 2. Phasor circuit of the machine
Where Ra is the winding’s resistance, Xs is the inductance of
winding, Ea is the back electromotive force (emf) and Va is
terminal voltage of the machine.
Winding resistance is calculated analytically by using the
Flux in the machine is calculated as
By using Faraday’s law we can determine the back emf as given
The air gap inductance is given as
Slot leakage inductance is given as
End turn inductance per phase is given as
Total inductance is the sum of three inductances
Machines are basically sized for rated torque capability
rather than power, output torque is proportional to product of
rotor volume and shear stress, air-gap shear stress is proportional
to the product of air-gap electrical and magnetic loading. Shear
stress is calculated as.
Typically for liquid cooled machines the value of shear stress
is 10-20Psi, we will use 15Psi for our design. We have discussed
the tip speed previously, with the assumed value of 200m/s. we
higher odd phases
can use the following fundamental power equation to find out
the stack length and rotor radius.
We will assume the L/D ratio to be 2.5, air-gap flux density to
be 0.8T, slot height 15mm and slot fill fraction to be 0.5. We can
calculate all design parameters using MATLAB code and given
in table 2.
The phasor relationship between internal voltages (
) and the synchronous voltage drop is used to get the
terminal voltage and current of the machine as shown below.
Once the basic parameters are known in depth analysis is done.
To get a better understanding pre-existing database of the same
kind of machines need to have a look. These data bases are
helpful to choose input parameters. This data can be collected
from several firms including ATE in Germany, Rueland electric
in the USA and E und A in Switzerland given in the appendix,
from all these databases and analysing different machines the
following input parameters are developed.
Table 2. Detailed sizing parameters of the machine
A. Machine’s geometry and windings
Geometry of the machine is set as; housing is round, slot
type parallel tooth in stator. Rotor topology is set to u-shaped
inner magnets with circular rotor ducts for ventilation. Stator
and rotor dimensions in radial view as calculated in matlab. The
resulted geometry is shown in fig 1. Winding type is selected as
overlapping; the winding definition is defined by wire size,
which is set to be 0.885mm and 0.800mm from the metric table
and the material between the liner and lamination is set as air.
Fig 3. Radial and axial view of the machine
MMF harmonics of the machine are analysed, no odd harmonics
are detected in this design which depicts voltage waveform is
symmetric about the centre of the rotor flux. Secondly winding
factor is analysed. Because of the almost sinusoidal counter-
electromotive force (CEMF), the PM machines work very well
with distorted stator magneto-motive force (MMF), where the
high winding factor is of highest priority . In figure 5 it can
be seen that winding factor value is 0.96 which is good to
maximise the torque, avoid unbalanced magnetic pull and to
minimize the rotor losses.
Fig 4. Winding factor of the machine
B. Electromagnetic analysis of the machine
Electromagnetic model is solved and results are analyzed
and compared. Output current and terminal voltage is shown in
the following figures.
The terminal voltage waveform is close to sinusoidal, although
some torque ripples can be observed because of harmonic
contents of line-line voltage and skew effect in air-gap flux
density, it shows a good agreement between analytical and FEA
Machine Diameter = 0.195 m Machine Length = 0.257 m
Rotor radius = 0.032 m Active length = 0.160 m
Slot Avg Width = 8.050 mm Slot Height = 25.000 mm
Back Iron Thick = 11.200 mm Tooth Width = 8.050 mm
Power Rating = 660.0 kW Speed = 60000 RPM
Va (RMS) = 417 V Current = 527.9 A
Ea (RMS) = 430 V Arm Resistance = 0.00246 ohm
Synch Reactance = 0.194 ohm Synch Induct = 0.015 mH
Stator Cur Den = 1049.3 A/cm2 Tip Speed = 201 m/s
Efficiency = 0.993 Power Factor = 1.000
Phases = 3 Frequency = 2000.0 Hz
Number of Slots = 24 Num Arm Turns = 8
Breadth Factor = 0.966 Pitch Factor = 0.966
Tooth Flux Den = 1.14 T Back Iron = 0.81 T
Slots/pole/phase = 2.00
Magnet Height = 25.00 mm Magnet Angle = 50.0 degm
Air gap = 4.00 mm Pole Pairs = 2
Magnet Remanence = 1.20 T Air Gap Bg = 0.57 T
Magnet Factor = 1.203 Skew Factor = 0.995
Core Loss = 1.5 kW Armature Loss = 2.1 kW
Windage Loss = 1.3 kW Rotor Loss = TBD kW
Core =14.06 kg Shaft = 3.96 kg
Magnet = 2.30 kg Armature = 9.98 kg
Services = 4.55 kg Total = 34.85 kg
Fig 5. Output current
Fig 6. Terminal Voltage
Cogging torque harmonic spectrum is analysed, it can be seen
that the dominant harmonics are 48, 96 and then 144 which are
well below 1 % of the rated torque. Although cogging torque is
very low still there is a possibility to reduce cogging torque by
changing width of stator slot opening and to skew stator slot.
Fig 7. Harmonic spectrum of cogging Torque
By solving the e-magnetic model, the flux distribution in rotor
and stator of the machine can be analysed. It is verified that flux
lines are leaving the rotor polar piece nearly perpendicularly
which means that the main field components are radial and
tangential are neglected. Tooth and stator yoke have the flux
density value within the calculated range which is 1.8T. Also
tooth and stator yoke dimensions are good to get the design
Fig 8. Open circuit flux distribution
Open circuit losses are analysed as well, we can verify that the
losses in rotor and stator teeth are well below within the
calculated range. Higher losses can be observed in stator yoke
due to some harmonics present in current going through the
armature winding, another cause of these losses may the skin
effect resulting from the same source conductors.
A 3-phase balanced current is injected in armature winding to
get a sine-wave drive. Phasor diagram in figure 27 is used here
to calculate the required terminal voltage. By knowing the value
of impedance and current voltage can be calculated which has a
sinusoidal waveform which verifies the analytical results.
In on-load flux distribution, it can be verified that machine is
highly saturated, the value of flux density is about 2.2T as can
be seen in the figure below. It confirms that the dimensions of
tooth width and stator yoke are good. Losses are also within the
C. Thermal analysis
Compared with common permanent magnet (PM) machine,
the high-speed PM machine has smaller size and larger power
density. However, owing to high-speed high frequency and
small volume, the PM rotor is more easily to become overheated
so that irreversible demagnetization of the PM is induced.
Traditional cooling methods of machine directly cool the
machine stator; the temperature rise of rotor is reduced through
heat exchange among stator, air gap and rotor. Owing to rapid
temperature rise of high speed PM machine rotor, the method
of indirect cooling rotor does not effectively protect PM rotor
Aluminium is selected for housing and end-caps to keep the
overall machine light in weight. Liquid cooling is used as a main
cooling method, water jackets are in housing of the machine to
extract heat from active windings and end windings in the end
space region as well. To directly reduce the temperature,
increase in winding and rotor of the machine self-ventilated
method is used to control the winding temperature.
In thermal analysis, the main cooling options are defined and
the final results are obtained using the lumped thermal circuit at
steady state as shown in fig 12. Duty cycle operation is a
specialized feature, directed to analyse specific exploration
regimes. To perform the necessary sensitivity analyses and
check the important cooling paths is more easy and quick to
look at steady state operation. Then, since the cooling is
defined, the duty cycle analysis can be performed.
The thermal network for Motor-CAD is quite sophisticated with
32 nodes. This is shown in Fig.13; the five nodes below
represent the nodes closest to the measured nodes and were
chosen as being suitable for comparison.
Fig 9. Steady state temperatures
The predicted average winding temperature is 112 °C. The
predicted magnet temperature is 107 °C. These values are below
the initial estimated values of temperatures.
D. Slot FEA
In motor-CAD calibration can be done by the conduction heat
transfer in the stator slot. Figure shows the result with
minimum, average and maximum winding temperature of
105°C, 107°C, and 112°C respectively. We can verify that there
is a relatively good match of temperatures in the slot with
minimum, average and maximum winding temperature shown
in figure, we got after solving the slot FEA. Slightly different
results are observed if we distribute the conductors differently
in the slots. We will get large average and maximum
temperature giving a closer match to the analytical solution as
the conductor touching the slot liner move towards the slot
Fig 10. Steady state temperature in stator slots
E. Performance charts
. Efficiency map is very useful to get the ideal region of
efficiency where the design is laying. At high speeds operations,
we may get a larger spectrum of efficiency. This is because
copper losses are higher at lower speeds. Therefore, at high
speeds the losses are decreased and efficiency increases, as can
be seen in losses map in figure. As we can see that efficiency of
94% can be achieved in a larger spectrum between the speed of
30,000rpm and 60,000rpm.
Fig 11. efficiency map of the machine
in this paper importance of high speed PM machines in
renewable sector is highlighted. Design strategies and problems
are analyzed. A special design topology is presented to
overcome high cost problem in solar co-generation system. The
HSBPMG running at 60,000rpm having four poles, 24 stator
slots and tooth coil winding is modeled to get comprehensive
and cost-effective manufacturing keeping the electromagnetic
losses as low as possible. 6.5% SiFe is selected as a rotor and
stator material as it offers lowest losses. Losses are kept
minimized by using air-gap length, tooth tip optimization and
FEA is done by using motor-CAD and all the
results show good accord with calculated values. Presented
topology is suitable to use in small co-generation system on
high speed application, this design is able to get design targets,
comprehensive, cost effective and low electromagnetic losses.
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