1

Prototype of a Linear Generatorfor Wave Energy Conversion in the AWS

Goncalo F. Beirao 1,2, Antonio F. Dente 2, Gil D. Marques 2

Abstract—Wave energy conversion has been challengingengineers and scientists for the last decades. In this paperit is described the design and construction of a transverseflux linear generator, where some mechanical and electricalaspects are referred. The main goal is to deliver a contri-bution in knowledge and technical data for future develop-ments of the modeling and design methods.

Index Terms—Transverse Flux Linear Generator, Perma-nent Magnets, Electromotive Force

I. Introduction

OCEAN waves represent a form of renewable energycreated by wind currents passing over open water.

Capturing the energy of ocean waves in offshore locationshas been demonstrated as technically feasible [1]. Wave en-ergy devices are at various stages of development, rangingfrom demonstration to requiring significant R&D. There isconsiderable work already underway on all these aspects inmany countries [2]. One of those devices is the ArchimedesWave Swing (AWS) shown in Fig. 1. The AWS consists ofan upper part (the floater) of the underwater buoy movesup and down in the wave while the lower part (the base-ment or pontoon) stays in position. The periodic changingof pressure in a wave initiates the movement of the up-per part (Fig. 1(a)). The floater is pushed down under awave top (Fig. 1(b)) and moves up under a wave trough(Fig. 1(c)). To be able to do this, the interior of the sys-tem is pressurized with air that serves as an air spring. Theair spring, together with the mass of the moving part, isresonant with the frequency of the wave. The mechanicalpower required to damp the free oscillations is convertedto electrical power by means of a Power Take Off system(PTO). The PTO consists in a linear electrical genera-tor [2]. This paper presents the description of a prototypefor a PTO propose.

Fig. 1. Archimedes Wave Swing

1 Master Degree Dissertation - Electrical Machinery Laboratorye-mail: goncalo.beirao@ist.utl.pt

2 Electrical Engineering Department, Instituto Superior Tecnico,TULisbon, Lisbon

II. Configuration of the Transverse FluxMachine

This section describes the working principle and config-uration of the transverse flux machine (TFM). In Fig. 2it is shown a single pole of the machine where its work-ing principle can be understood. The machine’s statorhas two laminated iron pieces, one U shaped and anotherI shaped. Between them are two neodymium permanentmagnets placed the way shown in Fig. 2. Having a vari-able flux density in the iron core, i.e. the magnets changingtheir polarity, an electromotive force is generated on a Nturn winding.

Fig. 2. Pole morphology and Magnetic Flux Density Plot

In Fig. 3 is shown the design of the prototype with a 4pole pairs stator, p = 4, U and I shaped blocks, and the32 permanent magnets translator.

Fig. 3. TFM CAD model

2

III. Modeling

To drive the prototype in the laboratory it was useda induction machine, connected to a gear box that, bymeans of a two arm shaft, converts the rotary into linearmovement (Fig. 4).

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))

v(t) = −raω sin(2π tTmec

)− rb dγ(θ)dt sin(γ(θ))

(1)The electromotive force is determined by the Flux Lawmodulated by the displacement (eq. 1) on eq. 2.

E(t) = −dψm(z)dt =−dψm(z)

dzdzdt =−dψm(z)

dz v(t) ⇔

⇔ E(t) = −v(t)(ψm)max2πp 1L sin(2πp z(t)L )

(2)The prototype’s internal impedance is given by a resis-tance in series with an inductor, where the resistance isdetermined by the length (LCu) and cross section (SCu) ofthe cooper winding and the inductor is determined by themagnetic flux leakage of each winding:

RCu = ρCuLCu

SCu[Ω] ⇔

⇔RCu = 0.0178×3000.75 = 7.12Ω

LCu = 38.2 mH

IV. Prototype Construction

The build process of the prototype follows several as-pects. The guidelines to build a robust prototype, to with-stand the forces due to magnetic flux leakage and to main-tain 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 weaklinks (translator)

- Heavy duty glues (fix the translator’s magnets)

A. Stator - Iron Core

The stator’s iron core consists in a series of alternatedstacked iron plates, U and I shaped, respectively, insertedin 4 threaded brass rods, separated by acrylic rings andfixed by brass nuts (Fig. 5).

Fig. 5. One side of the Iron Core

B. Stator - Winding

The winding of a transverse flux machine is particularlydifferent from a general winding. This fact lead to a com-plete manufacture of two windings, each on each side ofthe iron core. A acrylic mold with flaps holds the windingwhile 250 turns are made (Fig. 6)

Fig. 6. Winding

C. Translator

The translator was one of the most difficult parts tobuild in previous projects [4]. In order to eliminate thisconcern, a acrylic plate with 2 cm deep and 32, 2×2 cm2,sockets for the magnets, was ordered (Fig. 7(a)). To thisplate, 32 magnets with alternated polarity were glued intothe sockets. Then, 2 ’V’ guides were fixed, with brassscrews, to the top and bottom of the plate to finish thetranslator (Fig. 7(b)). The translator was put into 4 cars,fixed to the prototype’s anchorage, where the ’V’ guidesslide (Fig. 7(c)).

BEIRAO: PROTOTYPE OF A LINEAR GENERATOR FOR WAVE ENERGY CONVERSION IN THE AWS 3

Fig. 7. Translator

D. Structure Anchorage

To anchor all the prototype’s components it is used aniron frame in handy material. In particular, to hold downthe stator against the forces due to magnetic flux leak-age, numerous attempts were made, until a final structuremade 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 towithstand a minimum air gap of g = 1 cm.

Fig. 8. Stator anchor system

V. Prototype Testing

After the prototype was built and before testing it, theinternal generator’s impedance for each winding was mea-sured by a LCR Meter (ISO-TECH LCR819):

R1 = 5 ΩR2 = 4.6 ΩL1 = 94.966 mHL2 = 79.767 mH

Adjusting the system to fit a better approximation to real-ity is one of the aspects that lead to several speed tests. Byspeeding the induction machine up to 40 Hz the transla-tor’s linear oscillating period is Tmec = 2.54 s; which is themost suitable velocity for the machine. At this oscillatingperiod it is measured a no load RMS voltage of:

ERMSlab= 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

voltage is:

ERMSthe= 18.65 V

The voltage difference between this values happens due tothe magnetic flux leakage, which is not taken into accountby the theoretical model, i.e.:

φlab = Kφthe

Where K can be given by:

K =ERMSlab

ERMSthe⇔

⇔K ≈ 0.6

Adding the contribution of K into eq. 2, and replacing thevalues of the internal impedance by the ones measured, thetheoretical model can make a better description of reality.

A. Testing Apparatus

As it was said before a induction motor (Fig. 9(b)) con-nected to a gear box (Fig. 9(c)) is used to power up the lin-ear generator (Fig. 9(f)). The motor’s speed is tunned byan ALTIVAR (Fig. 9(a)) in V/f mode, which gives a hightorque at low speed. To measure the translator’s position itis used a ultrasound sensor (Fig. 9(d)) that converts the po-sition of the translator into a voltage 0< Vsensor < 10 [V ].The windings are connected in series and all the data ismeasured and recorded by a digital oscilloscope (Fig. 9(e)).

Fig. 9. Prototype’s Testing Apparatus

B. No Load Test

The results, both theoretical and experimental, are plot-ted in the graphs of Fig. 10 and Fig. 11. By comparing theresults it can be seen that both electromotive forces, fromthe theoretical and experimental, are similar, having aboutthe same tempo. As the theoretical results have taken intoaccount the contribution of K there is no difference in thevoltage RMS value. The most notorious difference relies

4

on the noise seen in Fig. 10. It can be explained has thetheoretical calculations do not take into account the forcesalong the z axis (Fz(z)) and, while testing, those forceswere very significant.

Fig. 10. Electromotive Force and displacement evolution in time(experimental)

Fig. 11. Electromotive Force and displacement evolution in time(theoretical)

C. Load Test

To test the prototype in a load state it was connected toaRl = 5 Ω resistor. The acquired data is plotted on Fig. 12.In Fig. 13 their are plotted the results of the theoreticalcalculations for the same situation, while in Table I theirare shown the results of load voltage, current and averagepower for both situations, measured and calculated; as wellas the error for each calculation.

TABLE I

Voltage and Current RMS Values and Average Power

URMS [V ] IRMS [A] Pav [W ]Experimental 3.10 0.64 1.95Theoretical 3.62 0.72 2.62|δ| 14.4% 11.1% 25.5%

Fig. 12. Electromotive Force, Current and Displacement evolutionin time with Rl = 5 Ω (experimental)

Fig. 13. Electromotive Force, Current and Displacement evolutionin time with Rl = 5 Ω (theoretical)

D. Load Test With Rectifier Bridge

In a real life situation, before handling power to the elec-tric network grid, a generator like this is connected to arectifier bridge and then to an inverter, so that the outputvoltage has the grid frequency and constant peak value. OnFig. 15 and 14 their are shown the evolution of the load’svoltage and current after a diode rectifier bridge, while inTable II their are shown the results of load voltage, cur-rent and average power for both situations, measured andcalculated; as well as the error for each calculation.

TABLE II

Voltage and Current RMS Values and Average Power

URMS [V ] IRMS [A] Pav [W ]Experimental 2.89 0.60 1.72Theoretical 3.62 0.72 2.62|δ| 20.2% 16.7% 34.3%

BEIRAO: PROTOTYPE OF A LINEAR GENERATOR FOR WAVE ENERGY CONVERSION IN THE AWS 5

Fig. 14. Load Voltage, Load Current and Displacement evolution intime with Rl = 5 Ω after a Diode Rectifier Bridge (experimental)

Fig. 15. Load Voltage, Load Current and Displacement evolution intime with Rl = 5 Ω after a Diode Rectifier Bridge (theoretical)

The errors shown on Table II are larger than the onesshown in Table I as the theoretical calculations do no takeinto account the power loss in the diodes.

VI. Conclusion

This work’s objective was to built and model a prototypeof a linear transverse flux electrical generator with the re-sources, economical and physical, available. On chapter IIIthe system was modeled by an electromotive force in serieswith a synchronous impedance, which lead to the theo-retical results shown on chapter V. The building processespresented on chapter IV was where this work had its focus;that’s why every construction process detail is describedand all the malfunctions and prototype fails are pointed.Chapter V shows the tests done to the prototype as wellas the results of a more accurate theoretical calculation.

In this area, projects don’t often get to the prototypestage. In this work a functional prototype was built, whichcan be useful for future studies as it can be studied or itcan serve as an example for future prototypes.

References

[1] Minerals Management Service - U.S. Department of the InteriorRenewable Energy and Alternate Use Program Wave EnergyPotential on the U.S. Outer Continental Shelf, page 2, May2006.

[2] WaveNet Results from the work of the European ThematicNetwork on Wave Energy, European Community - EESD En-

ergy, Environment and Sustainable Development, pages 2-3; 9-10,March 2003.

[3] A. E. Fitzgerald, Charles Kingsley Jr., Stephen D. Umans Elec-tric Machinery, McGraw-Hill, 6th Edition 2002.

[4] Paulo A. S. Prieto, Construcao de um Oscilador Electromecanicopara o Aproveitamento da Energia das Ondas, Master Thesis,October 2008.

[5] Antonio F. Dente; Sistemas Electromecanicos I, Instituto Supe-rior Tecnico (IST) – Department of Electrotechnical Engineeringand Computers (DEEC) / Energy, 2007/08.

[6] Filipa A. Marques, Goncalo F. Beirao, Joao T. Mestre, WaveEnergy: Generator and Grid Integration, Norwegian Universityof Science and Technology (NTNU), 2008.

Goncalo F. Beirao (S’04) was born in Lisbonin 1986. He received the B.Eng. degree in elec-trical engineering with distinction from Tech-nical University of Lisbon, Portugal, in 2007.From August 2008 to February 2009, he wasan Exchange Student at Norwegian Universityof Science and Technology (NTNU), Norway.He is currently a M.S. degree at Technical Uni-versity of Lisbon, doing his thesis on electricmachinery under the supervision of ProfessorAntonio F. Dente & Professor Gil D. Marques.