1
Prototype of a Linear Generator
for Wave Energy Conversion in the AWS
Gonçalo F. Beirão
1,2
, António F. Dente 2 , Gil D. Marques
Abstract—Wave energy conversion has been challenging
engineers and scientists for the last decades. In this paper
it is described the design and construction of a transverse
flux linear generator, where some mechanical and electrical
aspects are referred. The main goal is to deliver a contribution in knowledge and technical data for future developments of the modeling and design methods.
Index Terms—Transverse Flux Linear Generator, Permanent Magnets, Electromotive Force
I. Introduction
O
CEAN waves represent a form of renewable energy
created by wind currents passing over open water.
Capturing the energy of ocean waves in offshore locations
has been demonstrated as technically feasible [1]. Wave energy devices are at various stages of development, ranging
from demonstration to requiring significant R&D. There is
considerable work already underway on all these aspects in
many countries [2]. One of those devices is the Archimedes
Wave Swing (AWS) shown in Fig. 1. The AWS consists of
an upper part (the floater) of the underwater buoy moves
up and down in the wave while the lower part (the basement or pontoon) stays in position. The periodic changing
of pressure in a wave initiates the movement of the upper part (Fig. 1(a)). The floater is pushed down under a
wave top (Fig. 1(b)) and moves up under a wave trough
(Fig. 1(c)). To be able to do this, the interior of the system is pressurized with air that serves as an air spring. The
air spring, together with the mass of the moving part, is
resonant with the frequency of the wave. The mechanical
power required to damp the free oscillations is converted
to electrical power by means of a Power Take Off system
(PTO). The PTO consists in a linear electrical generator [2]. This paper presents the description of a prototype
for a PTO propose.
II. Configuration of the Transverse Flux
Machine
This section describes the working principle and configuration of the transverse flux machine (TFM). In Fig. 2
it is shown a single pole of the machine where its working principle can be understood. The machine’s stator
has two laminated iron pieces, one U shaped and another
I shaped. Between them are two neodymium permanent
magnets placed the way shown in Fig. 2. Having a variable flux density in the iron core, i.e. the magnets changing
their polarity, an electromotive force is generated on a N
turn winding.
Fig. 2. Pole morphology and Magnetic Flux Density Plot
In Fig. 3 is shown the design of the prototype with a 4
pole pairs stator, p = 4, U and I shaped blocks, and the
32 permanent magnets translator.
Fig. 1. Archimedes Wave Swing
1 Master Degree Dissertation - Electrical Machinery Laboratory
e-mail: goncalo.beirao@ist.utl.pt
2 Electrical Engineering Department, Instituto Superior Técnico,
TULisbon, Lisbon
2
Fig. 3. TFM CAD model
2
A. Stator - Iron Core
III. Modeling
To drive the prototype in the laboratory it was used
a induction machine, connected to a gear box that, by
means of a two arm shaft, converts the rotary into linear
movement (Fig. 4).
The stator’s iron core consists in a series of alternated
stacked iron plates, U and I shaped, respectively, inserted
in 4 threaded brass rods, separated by acrylic rings and
fixed by brass nuts (Fig. 5).
Fig. 4. Two arm shaft system
The translators displacement can be described by z(t)
and its velocity by v(t) = dz(t)
dt and it can be expressed by
eq. 1:

z(t) = ra cos (θ(t)) + rb cos (γ(θ))

ra sin (θ(t)) = rb sin (γ(θ))

t
) − rb dγ(θ)
v(t) = −ra ω sin (2π Tmec
dt sin (γ(θ))
(1)
The electromotive force is determined by the Flux Law
modulated by the displacement (eq. 1) on eq. 2.
E(t)
=
dψm (z)
(z)
m (z) dz
= − dψdz
v(t) ⇔
− dψm
dt
dt = − dz
⇔ E(t)
=
−v(t)(ψm )máx 2πp L1 sin(2πp z(t)
L )
Fig. 5. One side of the Iron Core
B. Stator - Winding
The winding of a transverse flux machine is particularly
different from a general winding. This fact lead to a complete manufacture of two windings, each on each side of
the iron core. A acrylic mold with flaps holds the winding
while 250 turns are made (Fig. 6)
(2)
The prototype’s internal impedance is given by a resistance in series with an inductor, where the resistance is
determined by the length (LCu ) and cross section (SCu ) of
the cooper winding and the inductor is determined by the
magnetic flux leakage of each winding:
RCu
=
ρCu LCu
SCu [Ω]
⇔ RCu
=
0.0178×300
0.75
LCu
=
38.2 mH
⇔
= 7.12Ω
Fig. 6. Winding
IV. Prototype Construction
The build process of the prototype follows several aspects. The guidelines to build a robust prototype, to withstand the forces due to magnetic flux leakage and to maintain a certain level of precision (i.e. air gap), were:
- Most of the materials having µR ≈ µ0 (brass, acrylic,
wood, aluminum)
- Use the maximum standardized components (rods,
guides)
- One piece uniform components, i.e. without weak
links (translator)
- Heavy duty glues (fix the translator’s magnets)
C. Translator
The translator was one of the most difficult parts to
build in previous projects [4]. In order to eliminate this
concern, a acrylic plate with 2 cm deep and 32, 2 × 2 cm2 ,
sockets for the magnets, was ordered (Fig. 7(a)). To this
plate, 32 magnets with alternated polarity were glued into
the sockets. Then, 2 ’V’ guides were fixed, with brass
screws, to the top and bottom of the plate to finish the
translator (Fig. 7(b)). The translator was put into 4 cars,
fixed to the prototype’s anchorage, where the ’V’ guides
slide (Fig. 7(c)).
BEIRAO: PROTOTYPE OF A LINEAR GENERATOR FOR WAVE ENERGY CONVERSION IN THE AWS
3
voltage is:
ERM S the
=
18.65 V
The voltage difference between this values happens due to
the magnetic flux leakage, which is not taken into account
by the theoretical model, i.e.:
φlab
Fig. 7. Translator
=
Kφthe
Where K can be given by:
D. Structure Anchorage
To anchor all the prototype’s components it is used an
iron frame in handy material. In particular, to hold down
the stator against the forces due to magnetic flux leakage, numerous attempts were made, until a final structure
made in handy and 8 mm threaded brass rods (Fig. 8(a))
and two aluminum guides fixed to the structure (Fig. 8(b))
dealt with those forces. In the end the structure is able to
withstand a minimum air gap of g = 1 cm.
K
⇔K
E
RM S lab
= ERM
⇔
S the
≈ 0.6
Adding the contribution of K into eq. 2, and replacing the
values of the internal impedance by the ones measured, the
theoretical model can make a better description of reality.
A. Testing Apparatus
As it was said before a induction motor (Fig. 9(b)) connected to a gear box (Fig. 9(c)) is used to power up the linear generator (Fig. 9(f)). The motor’s speed is tunned by
an ALTIVAR (Fig. 9(a)) in V /f mode, which gives a high
torque at low speed. To measure the translator’s position it
is used a ultrasound sensor (Fig. 9(d)) that converts the position of the translator into a voltage 0 < Vsensor < 10 [V ].
The windings are connected in series and all the data is
measured and recorded by a digital oscilloscope (Fig. 9(e)).
Fig. 8. Stator anchor system
V. Prototype Testing
After the prototype was built and before testing it, the
internal generator’s impedance for each winding was measured by a LCR Meter (ISO-TECH LCR819):
R1
R2
L1
L2
=
=
=
=
5Ω
4.6 Ω
94.966 mH
79.767 mH
Adjusting the system to fit a better approximation to reality is one of the aspects that lead to several speed tests. By
speeding the induction machine up to 40 Hz the translator’s linear oscillating period is Tmec = 2.54 s; which is the
most suitable velocity for the machine. At this oscillating
period it is measured a no load RM S voltage of:
ERM S lab
=
11.22 V
By the theoretical model explained by eq. 2 in chapter III,
with an oscillating period of Tmec = 2.54 s, the no load
Fig. 9. Prototype’s Testing Apparatus
B. No Load Test
The results, both theoretical and experimental, are plotted in the graphs of Fig. 10 and Fig. 11. By comparing the
results it can be seen that both electromotive forces, from
the theoretical and experimental, are similar, having about
the same tempo. As the theoretical results have taken into
account the contribution of K there is no difference in the
voltage RM S value. The most notorious difference relies
4
on the noise seen in Fig. 10. It can be explained has the
theoretical calculations do not take into account the forces
along the z axis (Fz (z)) and, while testing, those forces
were very significant.
Fig. 12. Electromotive Force, Current and Displacement evolution
in time with Rl = 5 Ω (experimental)
Fig. 10. Electromotive Force and displacement evolution in time
(experimental)
Fig. 13. Electromotive Force, Current and Displacement evolution
in time with Rl = 5 Ω (theoretical)
Fig. 11. Electromotive Force and displacement evolution in time
(theoretical)
C. Load Test
To test the prototype in a load state it was connected to
a Rl = 5 Ω resistor. The acquired data is plotted on Fig. 12.
In Fig. 13 their are plotted the results of the theoretical
calculations for the same situation, while in Table I their
are shown the results of load voltage, current and average
power for both situations, measured and calculated; as well
as the error for each calculation.
TABLE I
Voltage and Current RM S Values and Average Power
Experimental
Theoretical
|δ|
URM S [V ]
3.10
3.62
14.4%
IRM S [A]
0.64
0.72
11.1%
Pav [W ]
1.95
2.62
25.5%
D. Load Test With Rectifier Bridge
In a real life situation, before handling power to the electric network grid, a generator like this is connected to a
rectifier bridge and then to an inverter, so that the output
voltage has the grid frequency and constant peak value. On
Fig. 15 and 14 their are shown the evolution of the load’s
voltage and current after a diode rectifier bridge, while in
Table II their are shown the results of load voltage, current and average power for both situations, measured and
calculated; as well as the error for each calculation.
TABLE II
Voltage and Current RM S Values and Average Power
Experimental
Theoretical
|δ|
URM S [V ]
2.89
3.62
20.2%
IRM S [A]
0.60
0.72
16.7%
Pav [W ]
1.72
2.62
34.3%
BEIRAO: PROTOTYPE OF A LINEAR GENERATOR FOR WAVE ENERGY CONVERSION IN THE AWS
[3]
[4]
[5]
[6]
Fig. 14. Load Voltage, Load Current and Displacement evolution in
time with Rl = 5 Ω after a Diode Rectifier Bridge (experimental)
Fig. 15. Load Voltage, Load Current and Displacement evolution in
time with Rl = 5 Ω after a Diode Rectifier Bridge (theoretical)
The errors shown on Table II are larger than the ones
shown in Table I as the theoretical calculations do no take
into account the power loss in the diodes.
VI. Conclusion
This work’s objective was to built and model a prototype
of a linear transverse flux electrical generator with the resources, economical and physical, available. On chapter III
the system was modeled by an electromotive force in series
with a synchronous impedance, which lead to the theoretical results shown on chapter V. The building processes
presented on chapter IV was where this work had its focus;
that’s why every construction process detail is described
and all the malfunctions and prototype fails are pointed.
Chapter V shows the tests done to the prototype as well
as the results of a more accurate theoretical calculation.
In this area, projects don’t often get to the prototype
stage. In this work a functional prototype was built, which
can be useful for future studies as it can be studied or it
can serve as an example for future prototypes.
References
[1] Minerals Management Service - U.S. Department of the Interior
Renewable Energy and Alternate Use Program Wave Energy
Potential on the U.S. Outer Continental Shelf, page 2, May
2006.
[2] WaveNet Results from the work of the European Thematic
Network on Wave Energy, European Community - EESD En-
5
ergy, Environment and Sustainable Development, pages 2-3; 9-10,
March 2003.
A. E. Fitzgerald, Charles Kingsley Jr., Stephen D. Umans Electric Machinery, McGraw-Hill, 6th Edition 2002.
Paulo A. S. Prieto, Construção de um Oscilador Electromecânico
para o Aproveitamento da Energia das Ondas, Master Thesis,
October 2008.
António F. Dente; Sistemas Electromecânicos I, Instituto Superior Técnico (IST) – Department of Electrotechnical Engineering
and Computers (DEEC) / Energy, 2007/08.
Filipa A. Marques, Gonçalo F. Beirão, João T. Mestre, Wave
Energy: Generator and Grid Integration, Norwegian University
of Science and Technology (NTNU), 2008.
Gonçalo F. Beirão (S’04) was born in Lisbon
in 1986. He received the B.Eng. degree in electrical engineering with distinction from Technical University of Lisbon, Portugal, in 2007.
From August 2008 to February 2009, he was
an Exchange Student at Norwegian University
of Science and Technology (NTNU), Norway.
He is currently a M.S. degree at Technical University of Lisbon, doing his thesis on electric
machinery under the supervision of Professor
António F. Dente & Professor Gil D. Marques.