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A low cost and highly efficient TFM generator for
wave power
Anders Hagnestål#1
#1Electric Power and Energy Systems, Royal Institute of Technology (KTH)
Teknikringen 33, 100 44 Stockholm, Sweden
1hagnes@kth.se
Abstract— A force-dense and very efficient direct drive
transverse flux generator aimed for wave power applications is
being developed at the Royal Institute of Technology in Sweden.
The machine is specialized for low speeds, and the design of a
linear version is presented in this paper. The basic
electromagnetic design is given as well as an overview of the
mechanical design. The benefits of such machines at low speeds
are described in detail. The challenges that the machine type
have are also presented, and suggestions are made on how they
can be handled. Geometrical and calculated performance data is
given for a prototype machine that is to be constructed during
2017. The possibility of using the machine type for control
methods such as reactive control is also discussed. The machine
is predicted to have an efficiency of 97-98% at speeds as low as
0.7 m/s, and a shear stress of 100-120 kN/m², corresponding to
200-240 kN/m² if only half the active area is counted as active
which is custom for such machines.
Keywords— Wave power, point absorbers, transverse flux
generator, power take-off, efficient
I. INTRODUCTION
Wave power is a promising future alternative for renewable
energy conversion, where the global resource is estimated to
about 2.11 TW [1], corresponding to perhaps 5-15% of the
world’s energy demands today depending on how large
fraction of that resource that can be harvested. Although this
looks promising, wave power has still not been
commercialized at large scale due to the difficulties to convert
the energy at sufficiently low cost and at the same time
making the energy conversion devices durable enough so that
they survive at the harsh conditions at sea. One of the key
challenges is that wave energy is delivered with low speeds
and large forces compared to other renewable energy sources
such as wind power. Since the size and cost of the Power
Take-Off (PTO) units and mechanical structures are related to
force rather than power, this is unfavourable. This challenge is
further complicated by the fact that maintenance is likely to be
very expensive at sea, and has the potential to further increase
the cost of wave power substantially.
Since gear boxes and hydraulic systems require
maintenance, direct driven generators first seem to be a viable
option for the PTO system since they can be made
maintenance free with a proper bearing design, and even
magnetic bearings can be considered. If demagnetization of
the magnets in the generator is avoided, only the bearings
suffer from wear since the force carrier, the magnetic fields in
themselves do not wear. However, the slow speed makes the
generators inefficient since the resistive losses in the copper
windings become unusually large compared to the power
production, especially for the case with smaller waves. At
airgap speeds below 1 m/s, it is hard to build a generator
which is both force dense and efficient. For typical generators
the low speed would give a low induced voltage compared to
the winding resistance, which would cause large resistive
losses. The more common machine types such as longitudinal
or radial flux permanent magnet synchronous machines or
induction machines will therefore operate in a suboptimal
regime at these speeds.
These unusual operating conditions call for a machine type
that is specialized for the task. The author has therefore
invented/developed a machine that is specialized for these low
speeds, and that has very low losses and very high force
density. In an ongoing project a linear version of this
generator is being developed, as well as a rotating generator of
a similar electromagnetic design. A linear prototype which is
aimed for a damping force of about 200 kN will be built in the
lab at KTH during 2017. The power rating is speed dependent,
and the speeds ranges from 0.1-3 m/s which corresponds to
20-600 kW. The machine type is a double-sided Transverse
Flux Machine (TFM) with flux-concentrating setup, which has
transformer-like design features which reduces losses and
increases the power factor compared to other types of TFM.
The machine is suitable for all direct drive solutions where the
speed is low. It is however intended for point absorbers, which
is a rather popular wave power concept where the heaving
movements of a buoy at the surface are used to extract energy.
This machine will combine a high force density with a for the
speed range extremely good efficiency and a high power
factor compared to other machines of the same type (0.5-0.7
seems possible).
The machine presented here will also be suitable for control
of buoy movement in point absorbers due to the extremely
low losses. The low efficiency of existing generators has been
a major roadblock for implementing such control by
controlling the force in the generator, i.e. the current. This
generator may therefore open up a new window for buoy
control.
Linear transverse flux machines for direct driven wave
power were first suggested by H. Polinder et. al [2]. More
recently, one group in Portugal [3] and one Italian group [4-5]
have suggested transverse flux machines for wave power. In
previous work, the main reason in general for selecting a
transverse flux machine has been to reduce the generator size
and cost. A 10 kW rotating prototype has been built in a by a
Portuguese team [3]. A linear prototype of a similar machine
from the same machine family, a Vernier Hybrid Machine
(VHM), was built by Markus Mueller’s group in the
beginning of this century [6]. The machine presented here is
in some ways of a similar design, but is of another type. In
principle, the VHM machine is simpler to construct but has
lower performance than the machine presented here in terms
of shear stress, power factor and efficiency. It is therefore in
some sense a trade-off between a PSMG and a TFM.
The paper is organized as follows. In section II, a brief
explanation of the problems with using machines like PMSGs
for speeds in the range of 1 m/s or lower is given, and it is
explained how these problems are avoided with a transverse
flux machine. In section III, the machine geometry is given, in
section IV the performance is calculated and in section V the
current control system is briefly described. In section VI, the
possibilities of using the presented generator for control of
buoy movement in point absorbers will be discussed. Section
VII gives the discussion and section VIII concludes the paper.
II. LIMITATIONS OF PMSGS AT LOW SPEED
At airgap speeds below 1 m/s, it is hard to build a
generator which is both force dense and efficient. This is in
some sense well known, but is often not given sufficient
attention. It is simply and well described by Polinder et al. [7],
and is so important that it is repeated here for clarity and is
described more in detail. A high force density requires a high
current density in the windings, which will require a rather
large electric field in the winding to overcome the resistivity.
The electric field in the winding can be found from Ohms law,
yielding
res
EJ
r
=
where
res
E
is the modulus of the electric
field in the winding,
r
is the resistivity of the conductor, J is
the modulus of the current density and it is assumed that the
conductor is sufficiently thin so that the skin effect and
proximity effect is negligible as well as contributions from
eddy currents. For annealed copper with a resistivity of
8
1.72 10
−
×
at 20 °C and a current density of 5 A/mm², this
yields
0.086 V/m.E=
At an operating temperature of 120°C
for the winding which may be reasonable for such a current
density, the resistivity and the electric field is about 40%
larger, i.e.
0.12 V/m.E=
It is well known that the induced
electric field in the winding in a longitudinal flux Permanent
Magnet Synchronous Generator (PMSG) can be approximated
by the motional EMF if the end windings are neglected [7].
Note that this is not true for TFMs. This yields
ind avg
E vB=
,
where
ind
E
is the induced electric field where the flux from
the current is neglected (i.e. the inductance is neglected), v is
the airgap speed and
avg
B
is the average magnetic flux density
in the airgap. The average flux density
avg
B
is usually about
0.9 T. For
1v=
m/s, this yields
0.9 V/m,
ind
E=
which at 5
A/mm and a winding temperature of 120°C yields a copper
loss ratio of
/ 0.133.
res ind
EE=
The workhorse generators in
the power grid such as hydropower operates at efficiencies of
about 97-98%. A ratio of 13.3 % copper losses in a generator
(with end windings and cable connections neglected) is very
high. To this, the iron losses should be added, and the machine
would probably end up having an efficiency of 80-85% at this
speed if it is well designed. What then can be done is to lower
the current. This reduces the fraction of copper losses for two
reasons. First, the copper losses are proportional to I² while
the power is proportional to I, which means that the fraction of
copper losses (i.e. copper losses in % of total power) is
proportional to current for this reason only. Second, the
temperature in the winding becomes lower when the current
density is decreased which lowers the resistance and thereby
the copper losses further. To lower the current density of the
machine has however two important consequences. First,
since the space for windings in the slots is limited, the total
current of the machine is limited. If operation is outside the
saturation region of the iron, which is typically the case, the
shear stress (the useful force density) is proportional to the
current. This means that the machine will have a low shear
stress if the current is reduced, and consequently the machine
will become unnecessarily large for a certain power rating.
Second, in such machines the majority of the magnetic flux
comes from the magnets or rotor windings, which is
independent of the stator current. This means that the iron
losses in the machine are largely independent on current.
However, the fraction of iron losses (i.e. in % of total power)
is proportional to 1/I, since the power is proportional to I.
Thereby, by lowering the current density in the windings, the
copper losses decrease but the iron losses instead increase,
which limits the total efficiency of the machine.
It is clear that for speeds below 1 m/s, the common types
of generators have some rather unattractive features. The
machines will have either low force density which makes the
generators very large and expensive for their power rating,
low efficiency which decreases revenues for sold electricity or
a combination of the two which is often the case. Note that the
low efficiency does not only decrease the maximum allowable
cost of the generator, but of all the components and parts in
the wave power device. Note also that direct driven generators
always become very large for their power rating since the size
of the generator is more or less proportional to force or torque,
not power. Power is force times speed, and generators
operating at speeds that are in the range of 10-100 times lower
than typical machines naturally become 10-100 times larger
for their power rating. However, some system anyhow needs
to deal with that force, and that system, perhaps a gearbox,
will also be rather large and expensive. It is therefore not
obvious that the idea of direct driven systems is bad.
The main problem for low speed machines is the large
winding resistance compared to the induced voltage. The
winding resistance is
l
RA
r
=
(1)
where
l
is the total length of the winding and
A
is the cross
sectional area of the winding. In a standard machine, the cross
sectional area is limited since there is a competition in space
between the winding and the iron. Further, due to geometry
the winding length becomes quite long. This is illustrated in
Fig. 1b, which shows a cross section of the airgap at the stator
side where the winding is located. The reason is that the
winding has to encircle every other pole in the machine,
which creates a zig-zag winding pattern. In Fig. 1a, the
winding on a TFM machine is shown. In a TFM, the machine
is arranged in such a way that the flux in all poles on the stator
side for one phase goes in the same direction at any instant.
This makes it possible to wind around the whole phase in the
stator instead of around each individual pole, which makes the
stator winding several times shorter for the same amount of
enclosed flux if there are many poles which there usually is.
This also means that the resistance per unit induced voltage
becomes several times lower in the TFM for this reason only,
since the resistance is proportional to the winding length.
Fig. 1 A cross section of the stator of a TFM (a) and a PSMG (b), illustrating
the difference in winding patterns.
A second advantage gained with the TFM geometry is that
there is no longer a competition in space between the iron and
the winding, since the winding is located outside the airgap.
Thereby, there is sufficient space to make the winding thicker
or to add more turns. Since the winding becomes much shorter,
it can be made much thicker without adding much to cost. If
the amount of winding material is kept constant, the winding
becomes as many times thicker as it becomes shorter, and the
resistance becomes proportional to the winding length squared.
For example, it is easily seen from Fig. 1 that with 18 poles
per phase and a square shape of the active area, this would
approximately yield a 5 times shorter winding and a resistance
in the TFM that is 25 times smaller than in the PSMG and
other machine types with this type of geometry. There is also
a possibility to compact the iron core of the TFM into a
massive iron block. If this block has a circular cross section,
the winding becomes optimally short for the amount of flux in
the machine, which gives an additional factor of about 2-3 on
the winding resistance. This transformer-like layout is
employed on the machine presented in next section. This large
reduction of the winding resistance will have a profound
impact on the performance of the machines in low speed
applications, and with a TFM it is fully possible to have both a
very high force density and a very high efficiency even at low
speeds.
III. MACHINE GEOMETRY
To motivate the machine geometry, the well-known
challenges associated with TFMs are first described as well as
the geometrical alternatives for implementing them. In general
TFMs have very beneficial properties for low speeds. The
losses can be made very low, and the machine type can
achieve very high shear stresses (force densities) of about
100-120 kN/m² which corresponds to 200-240 kN/m² if only
half the active area is considered as active which is custom for
such machines [8]. This should be compared with force-dense
PMSGs, which can reach shear stresses of about 40-50 kN/m²
[9]. The disadvantages of TFMs are the following:
1. They are difficult to design and construct. This is
perhaps the most important disadvantage, and it also
discourages many scientists to try to build them.
2. They have a low power factor. This increases the size
of and the losses in the power converter, and is an
important property to address.
3. The cogging forces may become large.
4. TFMs have fluctuating normal forces, which is
unfavourable for the bearings.
When selecting geometry, a single-sided or double-sided
approach can be made where a single-sided machine with
surface mounted magnets is shown in Fig. 2a and a double-
sided machine with flux-concentrating setup is shown in Fig.
2b.
Fig. 2 A single-sided linear TFM generator with surface mounted magnets in
(a) and a double-sided linear TFM generator with flux-concentrating setup in
(b). In the figure, 1 represents translator iron, 2 represents magnets, 3 is the
winding and 4 is the stator iron.
The main difference is that for single sided devices, either
the flux from both north and south poles are extracted from
the same side, or the flux from only one of the pole types is
extracted. For double-sided devices, the fluxes from the
different pole orientations are extracted from different sides.
For single-sided devices, the leakage fluxes become high, both
the leakage flux from the magnets which gives a low induced
voltage and, at least if the flux from both poles are extracted,
the leakage flux from the current which gives a high
inductance. This is since the iron parts that extract the flux
from one of the poles are close to the poles of the other type.
This combined gives a very low power factor. For double-
sided machines, the leakage fluxes become much smaller
since the iron parts that extract the fluxes from different poles
are located on different sides. These machines therefore in
general have higher power factor, but on the other hand they
are more difficult to construct and it seems that most scientists
choose single-sided configurations for this reason. In this
project, a double-sided machine is chosen due to the power
factor benefits.
The magnet configuration can basically be either surface
mounted magnets or a flux-concentrating setup. With surface
mounted magnets, both the north and south pole magnets will
create a flux, but that flux is larger for the magnets if the stator
iron parts that carry the flux is in front of the magnet. The net
flux in d axis position (in the d-q frame) will be the difference
of the fluxes from the aligned magnets of one polarity and the
fluxes of the non-aligned magnets of the other polarity. This
lowers the power factor. In a flux concentrating setup, the flux
always has an iron path to follow, which reduces leakage
fluxes. The flux-concentrating setup is however more difficult
to build. In this design, a flux-concentrating setup is chosen.
The disadvantages of the TFMs are important to address in
the design. Concerning the power factor, the machine
topology that gives the best performance is chosen. Further,
the machine has been designed in a transformer-like way to
make the coils as compact as possible. This reduces the
leakage flux to some extent, and thereby also increases the
power factor. The machine is designed for a small airgap, 1
mm, which also increases the power factor since the leakage
fluxes are decreased but again makes the machine
considerably more difficult to build.
The cogging forces have been analysed in detail. The
machine is designed as a three-phase machine with the three
phases arranged on top of each other. This cancels out the
cogging forces to a large extent, and they become ideally
about 1-3% of the total rated force with the tooth with that is
selected. However, since the iron at some parts of the machine
will go into deep magnetic saturation at high loads, the
cogging force will not be independent on current. Further,
deterioration of iron properties from manufacturing processes
and inaccuracies in airgaps, especially differences between
airgaps in different phases, will cause problems. Therefore,
the cogging will be handled by current control. A force vs
current and position mapping will be calculated, and currents
controlled so that the total force will be constant. This requires
a small tweak of the sinusoidal wave forms for the current.
This might potentially lower the power factor of the machine.
However, at maximum speed cogging compensation is not
considered to be as important, and sinusoidal currents can then
be used at maximum speed. Thereby, the power factor of the
machine is not affected by the cogging compensation. Perhaps
it will also be necessary to characterize each machine after
construction, i.e. to measure this mapping.
The normal forces will be fluctuating. However, the normal
forces are relatively small in the machine if it can be built with
symmetry, since the shear stresses are large in comparison to
the normal forces. In the first prototype, roller bearings will be
used. They have a considerably higher force limit where the
rollers do not suffer from fatigue compared to ball bearings.
For a linear machine, the linear bearings will nonetheless be a
costly component, partly since the travel life of the bearings
needs to be very long.
The most complex part of the machine is the mechanical
design, and it will be presented in more detail in a separate
publication later on. However, the main characteristics will be
given here as an overview. A top view of the design is given
in Fig. 3, which shows some of the special features of the
design.
Fig. 3 A top view of the linear TFM machine. The translator is in the center
of the picture, where 6 active and two passive airgaps are connected in series
magnetically. The layout is like a three-phase transformer, where a thinner
extra iron connection is added between the magnetic sides to allow for non-
symmetric fluxes. The winding is not shown in the picture, but is wound
around the round iron core parts close to the translator. Note that all magnets
are placed in the stator, in the green sections in the picture.
First, 6 active airgaps and two passive airgaps are
connected in series. Thereby, the extra amount of iron that
comes from the transformer design is used on many airgaps,
which gives a relatively low mass of iron per unit active area.
This means that three internal stator segments are fitted inside
the translator, which complicates the design. These stationary
segments contain all the magnets in the machine, and the
translator contains only iron and structure material. Since the
translator can be several times longer than the stator, this
reduces the amount of magnets required several times. It
however introduces 2 extra airgaps at the transformer cores,
which are passive. The internal stator segment is shown in Fig.
4, where the three phases are clearly seen.
Fig. 4. An internal stator segment. The green parts here are structural blocks
of glass fibre, and the three phases are clearly seen.
The transformer core, shown in Fig. 5, looks like a three-
phase transformer, with an extra connection part that allows
for non-symmetric fluxes. Just like in a transformer, the
transformer core is made of grain oriented iron which reduces
the iron losses in the core with a factor of 3-4. Although most
of the magnetized iron in the machine at any instant is located
in the transformer core, a large fraction of the iron losses will
be in the translator and the internal stator.
Fig. 5. The transformer core of the machine, where the three-phase
transformer layout is apparent. Windings will be placed around the sections
with round cross sections.
A 2D cross section of the stator and translator parts is given
in Fig. 6, which shows one phase of the machine.
Fig. 6. A cross section of one phase of the machine. Neodym magnets are in
red, grain-oriented and non-oriented laminated iron is in black and glass fibre
is in green.
To make this machine sufficiently strong mechanically, to
be able to maintain the small airgaps and to avoid mechanical
resonance frequencies below the maximum electrical
frequencies, several mechanical tricks have to be employed.
The translator and internal stator parts are slightly flexible so
that they can bend slightly sidewise in Fig. 6, and they are
separated by linear bearings which are adjusted properly.
Thereby, they are slightly deformed by the bearings to fit
properly. This allows for small airgaps but introduces need for
support bearings of translator parts outside the stator to avoid
low mechanical resonance frequencies which would be
harmful for the bearings in the stator. The bearing wheels will
be located in the stator, and the guideways will be located on
the translator.
The internal stator parts are difficult to make sufficiently
stiff mechanically to avoid the elastic deformation associated
with the magnetic forces. Note here that the bearings are
located on the sides of the structure, i.e. on the grey beams in
Fig. 4, and that the whole structure will bend elastically if the
airgaps on the different sides of the structure are unbalanced,
which is always the case to some extent. The problem is
solved by integrating a grid of structure material, primarily
glass fibre, in the magnet stacks and combining this with very
stiff phase blocks between the phases. This can keep the
maximum elastic deformation below 0.2 mm, which is
regarded as sufficiently stiff since we used a worst case-
approach. The translator at first seems easier to make
sufficiently stiff, since there is a lot of space for structure
material in it (the green parts in Fig. 6). However, here there
are no phase blocks, and the worst case elastic deformation is
actually of similar size as for the internal stator parts.
The magnetic forces were calculated in the FEA program
Comsol Multiphysics. The mechanical analysis was
performed in Ansys. The geometrical data is shown in Table I.
TABLE I
GEOMETRICAL DATA OF THE DESIGN
Property
Value
Airgap
1 mm
Pole width
25 mm
Magnet height
10 mm
Inner stator depth
51.5 mm
Active airgap width
270 mm
No active airgaps
6
Poles per phase
15
Phase block height
208.3 mm
Mass grain-oriented iron
2 ton
Mass active non-oriented iron
400 kg
IV. APPROXIMATE MACHINE PERFORMANCE
The approximate machine performance is shown in Table II.
In general the values depend on speed, and values for 0.7 m/s
and 3 m/s are shown. The calculations are based on some
simplifying assumptions. Iron losses are calculated using the
mass of iron involved, and assuming that it is close to fully
magnetized which is close to reality. The grain-oriented parts
are in large sheets, and are expected to have a performance
that is close to the Epstein test values given by the
manufacturer. The non-oriented iron is stamped in small parts
using dies, and is expected to perform worse than the Epstein
test values. The losses given by the manufacturer is here
multiplied with 2. The iron losses are separated into hysteresis
losses and Eddy current losses for simplicity, where values for
50 Hz are given by the manufacturer. This means that effects
of excess losses is ignored. The hysteresis losses are scaled as
f/50 and the Eddy current losses are scaled by (f/50)², where f
is the electric frequency. For the non-oriented steel it is
assumed that the hysteresis losses are 2.5 W/kg and the Eddy
current losses are 1.5 W/kg at 50 Hz (Epstein values). For the
grain-oriented steel it is assumed that the hysteresis losses are
0.7 W/kg and the Eddy current losses are 0.3 W/kg at 50 Hz.
For the winding, about 100 kg aluminium winding wire is
used per phase. Since the machine is transformer-like the
voltage can be chosen freely within some constraints, and will
be adapted to the power electronic system. The performance
of the generator itself is not affected by that choice. Loss
values are calculated for 225 turns, 150 mm² aluminium wire
at 20-100°C. The winding consists of many thin (2x4mm)
rectangular wires that are twisted in a certain pattern in the
machine to avoid circulating currents. The phase winding is
256 m long and has a resistance of 45 mΩ. The phase current
at full load is then 85 A, giving a current density of 0.57
A/mm². At maximum current loading, the machine will
operate in deep magnetic saturation of the iron, which
increases losses and decreases the power factor. There is an
option to run the machine with lower current, and perhaps
20% lower force. This will potentially lower the losses even
further, but increase the size of the machine. Eddy current
losses in the magnets, winding and structure material are not
yet calculated. They are expected to be small, and are not
included in the losses given in this section. The magnets are
epoxy coated and split in three parts to laminate them and
decrease the Eddy currents by a factor of 9. The force
densities and magnetic fluxes are calculated with the FEA
program Comsol Multiphysics. The friction losses from the
bearings are currently not known, but it is expected that they
are below 1 %.
TABLE II
CALCULATED GENERATOR PERFORMANCE
Property
0.7 m/s
3 m/s
Electrical frequency
14 Hz
60 Hz
Shear stress
100-120
kN/m²
100-120
kN/m²
Force
200 kN
200 kN
Power
140 kW
600 kW
Resistive losses
0.9-1.2%
0.2-0.3%
Iron losses non-oriented iron
0.4 %
0.7 %
Iron losses grain-oriented iron
0.3 %
0.4 %
Total electromagnetic losses
1.6-1.9 %
1.3-1.4%
Power factor
0.5-0.7
0.5-0.7
V. CURRENT CONTROL
The current control is to be performed using a back-to-back
inverter, which in principle controls the current value at any
instant. There has been progress in the development of
efficient power electronic components during the last 10 years,
and converters with efficiencies of over 99.5 % have been
demonstrated [10]. Since the power factor of the machine is
low, the active rectifier has to be overrated by a factor of 1.5
to 2 to be able to give unity power factor at maximum speed.
The cogging compensation will be implemented in this
rectifier. A first version of the back-to-back inverter has been
designed in the project, and the details of this will be given in
a separate publication.
VI. REACTIVE CONTROL
Although the calculations of the efficiency of the machine
are of approximate nature, they clearly indicate that the
generator can be very efficient. In wave power using point
absorbers, it is most likely necessary to apply a control system
for the buoy movement to get an economical wave power
plant, since several times more energy can be extracted from
the sea with a proper control system compared to simple linear
damping. The most effective control method is to cancel out
the hydrostatic stiffness of the buoy, i.e. to supply forces that
accomplish reactive control in one way or another. One way
of applying that force is to control the force in the generator
by controlling the current. There are however two major
problems with this:
1. The generator needs to be overrated in size several
times to be able to provide the required forces. This
requires a very force dense machine to keep costs
down.
2. The generator is partly run in motor mode during parts
of the wave period. The power gain is the difference in
the accumulated energy extracted in generator mode
and the energy spent in motor mode. The losses,
however, accumulate in both modes. The rated losses
(in percent) are therefore to be multiplied by
approximately a factor 4-5 to find out the real losses in
percentage of the extracted power. This requires a
generator with very high efficiency, and is regarded as
unfeasible since the appropriate technology does not
exist [11].
The generator that is proposed here in principle meets both
these requirements, and if the rated losses are 2-3% reactive
control is feasible, provided that the power electronic system
and the electric storage system is efficient. Therefore, the
generator has the potential to open up a new window for
reactive control.
VII. DISCUSSION
The generator presented here has great performance in
theory, but is complex to construct. It is however not expected
that it will be complex and time-consuming to build a second
unit if a working prototype is built, which is an important
property for mass production. The machine is however not
built yet, and numerous problems may arise during
construction. The machine is very complex, especially
concerning the mechanical design, and it is always a risk that
the prototype project will fail. However, the machine has very
suitable properties for wave power, and is probably – at least
in theory – more efficient than any PTO system that has been
built for wave power. The idea has therefore some potential
for the future, and there is currently no known problem with
the machine that does not have a solution in theory.
VIII. CONCLUSIONS
A TFM for wave power has been presented, which is
specialized for low speeds. It is predicted to have an
efficiency of 97-98% at speeds as low as 0.7 m/s, and a shear
stress of 100-120 kN/m², corresponding to 200-240 kN/m² if
only half the active area is counted as active which is custom
for such machines. The power factor is predicted to be over
0.5. A mechanical design of a linear machine has been
outlined but is not presented in detail. The machine is
predicted to be suitable for reactive control, since it is force
dense and has very low losses. A linear prototype will be built
during 2017.
ACKNOWLEDGMENT
The Swedish Energy Agency and J. Gust. Richerts
foundation are acknowledged for financing the project, where
the project number at the Swedish Energy Agency is P-40430-
1. Oskar Wallmark, Juliette Soulard, Hans-Peter Nee and
Simon Nee at KTH are acknowledged for useful discussions.
The master thesis students Gustaf Falk Olsson, Rickard
Holmgren, Erling Guldbrandzén, Manthan Shah and
Harvinder Singh Gill are also acknowledged for their
contribution to the project.
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