SLOTLESS, TOROIDAL WOUND, AXIALLY- MAGNETIZED PERMANENT
MAGNET GENERATOR FOR SMALL WIND TURBINE SYSTEMS
S.E. Skaar, O. Krovel, R. Nilssen and H. Erstad
Department of Electrical Power Engineering
Norwegian University of Science and Technology
Abstract
A toroidal wound three phase axially-magnetized, disc type, permanent magnet generator is
presented in this paper. For a novel wind turbine application the generator must have a low
reluctance torque and need to be direct-driven to reduce mechanical losses in the application.
For this purpose the stator winding is wound around a slotless ring core. The rotor disc has
18 surface mounted magnet poles. A test of a proto type generator will be presented.
1.
INTRODUCTION
Along the long coastline of Norway lighthouses and
smaller light signals used extensively. In the modern
society automated lights are chosen to reduce cost. At
the time the only good alternative for supplying power
to the lighthouses are solar cells. This becomes a
problem with the light conditions at the Norwegian
coast. At the northern latitudes there is polar night with
no sunlight for over two months at winter time, and
limited sunlight for the rest of the winter. To overcome
this obstacle the battery bank has to be fully charged
during summer time, and be dimensioned to supply the
lighthouse, without charging, throughout the polar night.
An alternative to solar cells is wind power. Small
conventional horizontal axial wind turbines along the
coastline have proven to fail from the stress of high- and
turbulent wind forces. Consequently, the need for a
robust vertical axial wind turbine was stated. Such
turbines are more expensive but may become very
robust. These turbines are independent on wind direction
and do not have to align up against the wind. A new
generator to be used in this application is needed. The
generator is direct-driven to reduce mechanical losses in
transmission. The application concept and the generator
are fully presented in [1]. A toroidal, axially-magnetized
permanent generator concept was chosen. The generator
must charge a 12 V battery bank and supply power to
the light bulb.
Figure 1. Generator concept
2.
DESIGN OF GENERATOR
When designing the generator, required rated power,
voltage and wind speed for start of charging was chosen
as main design parameters. In the following sections
calculation of induced voltage, flux distribution and
harmonics
presented.
2.1
from
winding
configuration
will
be
Induced voltage
The generator is designed as a disc type machine.
Permanent magnets (NdFeB) on the rotor discs are
placed with poles facing every other way giving a flux
path shown in figure 1. The generator is designed to
charge at rated power at a wind speed of 6 m/s. The
generator has 18 poles on each of the rotor discs, and
was designed for a rated speed of 230 rpm which results
in an electrical frequency of approximately 34 Hz.
Figure 1 is only is a principal sketch of the machine. It
does not show true magnet size nor the right number of
coils pr. pole. In the actual machine the number of coils
pr. pole are three. In the sketch the windings are shown
as square and circulare conductors to indicate the
changing winding direction needed to produce torque in
the machine.
In slotless machines, there should be no worries on slot
harmonics in the design. A wound ring in centre of the
machine may give a fixation problem towards the shaft.
To solve this problem the machine was given 54 slots
(teeth made of pressboard), whereas the term slot here
would be the actual space where the coil is wound, and
only 51 of these were wounded slots. This gives the
machine 51 distributed coils to constitute the three
phases. One coil covers a sector of 6 2/3º leaving three
empty, unwound spaces to provide mechanical fix of the
stator disc to the shaft. The three empty spaces can not
be made with a somehow symmetric 120º angular
displacement on the core, as this would lead to a
cancellation of three coils in the same phase. The
displacement was chosen to be at 0º, 126,67º and
233,33º, or slot number 1, 20 and 36. Each of the empty
spaces cancels one coil in each of the three phases. From
[2] induced fundamental phase voltage is calculated by:
E
N
2π
× N × f × Φ max × s
(1)
Erms = max =
N ph
2
2
N is number of turn pr. coil, Ns number of slots and Nph
is number of phases. f is electric frequency and Φmax is
peak value of the fundamental flux from the magnets,
calculated from:
Φ max = Amagn ⋅ Bmax
(2)
where Bmax is maximum fundamental air gap flux
density from the magnets. The magnet area is calculated
by:
Amagn =
π ⋅ (ro2 − ri 2 ) − τ f (ro − ri ) ⋅ N m
(3)
Nm
where ro is outer and ri is inner magnet radius, τf is
spacing between magnets and Nm is number of magnets.
Air gap flux density is calculated by:
l
Bmax = Br ⋅ m
(4)
lm + δ
Br is the remanent flux density of the magnet, lm is the
magnet length and δ is the air gap length between one
rotor disc and stator disc. This would give a rather
optimistic value of the air gap flux density. To get a
more realistic value an empirical correction factor of
0.75 is used. The air gap of the machine consists of the
area needed for the copper winding and a small physical
air gap to make clearing between rotor and stator. This
air gap should be minimized to achieve maximum air
gap flux density. The total air gap (including winding
region) is 4 mm and the magnet thickness is 8 mm. This
results a theoretical flux density in the air gap of 0.8 T.
After correcting this value with the correction factor a
maximum air gap flux density of 0.6 T is given. Using
the inner and outer radius from table I the calculated
magnet area becomes 7.7*10-4 m2 and maximum flux
from each magnet of 4.62*10-4 Wb. Using (1) the
number of turns to provide the needed charging voltage
can be calculated. For this machine 8 turns will induce
high enough voltage. The voltage will be 9.5 V pr phase,
with a line voltage of 16.5 V. Using a diode rectifier, the
DC-voltage [3] becomes:
U dc = 1.35U ac
(5)
This indicates a possible rectified voltage of 22.2 V
Outer radius
Inner radius
Magnet spacing
Number of magnets
Number of coils
Number of phases
Magnet thickness
Air gap
ro [mm]
ri [mm]
τf [mm]
Nm
Ns
Nph
lm [mm]
δ [mm]
92
59
3
18
51
3
8
4
Table I. Machine data
2.2
Flux distribution
To verify the assumption of the air gap flux density, a
2D model of the machine was generated in FEMLABTM.
Three cross-section models were made with radiuses ro,
ri and rm. Result of the middle cross-section is shown in
figure 2. In this model saturation of iron is not taken into
account. The parts of the machine being most
magnetically stressed are the yoke between the magnets.
In figure 2 these areas has a reddish colour.
Figure 3. Flux density in the middle section of the
machine
Figure 2. Flux density in the middle section of the
machine
The most stressed areas will only lightly saturate. A
graph of the flux density from one magnet in the middle
of the air gap was obtained by using FEM calculations.
The flux density is presented in figure 3. From the FEM
calculation the assumption of an air gap flux density of
0.6 T seems to be reasonable.
The models of the magnet at outer and inner radius both
gave simular results. From this it would be fair to
assume the model from the middle of the machine would
describe the field satisfactorily. From an optimization
point of view the end-effects should be taken into
consideration. However this was not done in this case.
2.3
Harmonic components
In [2] the fundamental flux value is used in the induced
voltage calculation. Later in this paper measurement will
show how small the contributions of sub-harmonics are
compared to the fundamental component in the induced
voltage.
From [2] both distribution factor and coil-span factor
must be taken into account when estimating the phase
e.m.f. The distribution factor for the fundamental
component from a phase spread of 60º is 0.955 using:
1
1
sin σ
sin nσ
2
2
km1 =
and kmn =
(6)
1
1
g 'sin (σ / g ')
g 'sin (nσ / g ')
2
2
where g’ is the number of coils pr phase and σ the phase
spread. From this the 5th harmonic is 0.192 and the 7th
harmonic -0.138.
The coil-span factor is given by:
1
1
ke1 = cos ε and ken = cos nε
(7)
2
2
where ε is the chording angel obtained from shortpitching the winding. In this machine there is no shortpitch and the chording angel is 0º. Resulting winding
factor is:
K wn = kmn ken
(8)
where ken is 1 for any n.
The harmonic contribution of the e.m.f. can now be
calculated by:
K B
E phn = E ph1 wn n
(9)
K w1 B1
The values of B1 and Bn are obtained from doing a
harmonic analysis of the field. From [2] the analytical
expression for this analysis is:
B1 = .086b1 + .167b2 + .236b3 + .289b4 + .323b5 + .167b6
B5 = .323b1 − .167b2 − .236b3 + .289b4 + .086b5 − .167b6
(10)
In (10) the b-values are calculated by:
lg
(11)
b = 100
l
where lg is the gap length from where the flux lines
leaves and enters iron and l is the length of the flux line.
Using this analysis with approximated values for the b’s
gives the expression:
E ph 5 = 0.0152 E ph1
(12)
(12) give an indication of the level of the 5th harmonic
e.m.f. The higher harmonics are not calculated since
these would give even smaller contributions. The low
value from (12) is the reason for using the fundamental
flux value when calculating induced voltage.
3.
PROTO TYPE BUILDING
The generator stator consists of a ring core with
thickness 10 mm. On each side of the core a 3 mm thick
pressboard was glued. 6 mm straight slots for placing
the winding were then milled out. After the stator was
wound the ring core with windings and the shaft was
cast in epoxy. A picture of the stator after casting is
shown in figure 4.
Figure 6. Assembled generator prototype
A HMB Torque Transducer connected between the two
machines measured the shaft torque. A Tektronix
TDS2014 oscilloscope was used to measure induced
voltage and to record curve forms. The oscilloscope was
connected to MatLabTM on a computer, providing an
easy data processing of the measurements and curve
forms. For the harmonic analysis a MatLabTM function
using a true Fourier's analysis (TFA) was used.
Figure 4. Stator disc and shaft cast in epoxy
The rotor discs yoke are made of solid steel. A picture of
one rotor disk with the magnets is shown in figure 5. A
picture of the prototype machine is presented in figure 6.
The proto type has an overall diameter of 200 mm and a
length of 55 mm, -shafts not included.
The generator was tested at no load, with a speed of 230
rpm giving an electrical frequency of 34 Hz. The phase
voltage rms value was measured to 7.74 V. This
indicates the correction factor of 0.75 used with the
calculation is to large. From the measured voltage it
should indicate an average flux density in the air gap of
0.5 T, giving a correction factor of 0.625. Still, the
induced voltage is satisfactory for the purpose of
charging the battery bank.
Figure 5. Rotor disc with magnets
4.
GENERATOR TESTS
The generator was tested in our laboratory. A 9.3kW
DC-machine was connected to the shaft as a drive unit.
Figure 7. Phase voltage compared to a sinusoidal
signal at same frequency and amplitude
Figure 7 show curve form of measured induced phase
voltage compared to a pure sinusoidal curve at the same
frequency and with same amplitude.
The curve of the phase voltage does not differ much
from a pure sinusoidal signal, doing a TFA of the
measured signal the result presented in figure 8 occur.
From the measurement a total harmonic distortion
(THD) of the voltage was calculated to 9.9%. At first
view this is a high THD. Connecting the generator in a
Y-connection would on the other hand eliminate the 3rd
harmonic and all its multiples. Taking this into account
when calculating THD gives the much better value of
1.7%
shown in figure 10, gives a THD of 1.8%. In figure 10
there is not a complete cancellation of the 3rd harmonics.
Not being able to get a complete cancellation with a Yconnection would imply unbalanced windings. There is
also the possibility of numerical errors in the data
processing.
Figure 10. Fourier analysis of measured line voltage
In figure 11 the odd harmonics of the phase voltage are
presented. In this figure the 1st and triple harmonic are
left out, to give a better view of the odd harmonics. The
measured 5th harmonics has a peak value of 0.187V
Figure 8. Fourier analysis of measured phase voltage
The line voltage between two phases and a sinusoidal
signal is presneted in figure 9.
Figure 11. Harmonic contribution, without 1st and
triple harmonics
while using (12) would give a calculated value of
0.163V.
Figure 9. Line voltage compared to a sinusoidal
signal with same frequency and amplitude
The almost matching curves of figure 9 show small subharmonic contribution. A TFA of the measured values,
Compared to the fundamental peak value on 10.7V it is
a good approximation to disregard the sub-harmonic
contributions in the calculations for this machine.
5.
LOAD TESTS
The machine was tested with different load situations at
constant speed. The test was run from no-load up to an
output power of 108W. Figure 12 show a plot of current
versus voltage. The load connected to the generator was
a resistive load. The winding resistance was measured to
0.2 Ω. The reactance can be calculated by:
X =
2
E ph
− (U + RI ) 2
(13)
I
Eph is the induced no load voltage, U and I is measured
at the given load situation and R is the winding
resistance.
With an output power of 108W, measured voltage was
6.42V and measured current was 5.6A, resulting in a
reactance of 0.31 Ω.
Figure 12. Current vs. voltage for different loads
At a frequency this low it would be a good
approximation to neglect core losses. The efficiency
could then be expressed by:
Pout
η=
(14)
Pout + PLosses + RI 2
A load test with an output power of 108W, a current of
5.6A and a total loss of 16.2W, would have an estimated
efficiency on 0.85. It was however not possible to verify
this estimation since the measure range of the shaft
torque is too coarse to ensure correct measurement. If
the measured no load losses, 33.5W, were used the total
losses would become 39.8W and the efficiency would
have dropped to 0.75
6.
CONCLUSION
The generator meets its requirements. It should be
possible to develop automatic winding techniques for
the stator, which is the only manufacture challenge of
the machine. The machine could be realized at a lowcost and would fit well into a package solution for
coastline lighthouses.
The behavior of the odd harmonic components in the
voltage is at acceptable low values. Verification in the
use of the fundamental flux when calculating induced
voltage has been proven. The generator has a stiff
voltage.
During tests of the machine too coarse equipment for
measuring torque ruined verification of the machine
efficiency.
7.
REFERENCES
[1]
H. Erstad, "Vindbasert elektrisk kraftforsyning
til Kystverkets lykter", (Wind based electric
power supply for the Norwegian Coastal
department’s lighthouses), Master thesis NTNU
2002
[2]
M.G. Say, "The performance and design of
alternating current machines", 2nd Ed, Pitman,
London, 1948, pp 181-237
[3]
Mohan,
Undeland,
Robbins,
"Power
electronics", 2nd Ed, Wiley, New York, 1995,
pp 103-114