Chapter one – INTRODUCTION

While the world’s development has reached its maximum and the energy sources used

today are facing imminent depletion, new energy sources are required. Amongst them, the

renewables seem to provide the solution to this problem. The main candidates are the wind,

solar, geothermal and ocean energy, our focus being on the last category. The easiest way to

harvest and transport the ocean’s mechanical energy is to convert it to electricity; most of the

wave energy converters use rotational generators, but this thesis is focused on the use of linear

electric generators in WECs.

The last couple of decades were marked by the development of wind and solar renewable

energies sectors, most of the developed countries having their own programs for replacing the

classic energy sources with new ones. Just by considering that 60% of the Earth’s surface is

covered by oceans and that water density is 800 times greater than air’s it is obvious that the

energy in the oceans is enormous, so solutions must be searched there as well.

Wave Energy Converters

Many solutions for harvesting the ocean energy were proposed, and while some of them

disappeared in time, some have turned into viable commercial solutions or are tested in site. The

most important WECs are:

- Salter’s Duck

- Oscillating Water Column devices

- Floating joint-devices: PELAMIS

- Over-toping devices: Wave Dragon

- Water-column pressure devices: AWS

- Systems with linear generators and buoys

Chapter two– LINEAR ELECTRIC GENERATORS

All rotating machines can be transformed into linear machines, most of them being

suitable for working as generators, but not all have good performances. Depending on the

excitation source and its location, linear machines can be mobile-coil, mobile-iron or mobile-PM

linear machines. The thesis focused on the following machine types as solutions for WECs:

- Linear synchronous machines

- Permanent magnet linear synchronous machines

- Permanent magnet variable reluctance machines

- Transverse flux machines

- Linear hybrid Vernier machines

- Air-cored linear tubular machines

- Iron-cored linear tubular machines

Each of these machines provides advantages or disadvantages, so a comparison was

made, considering the shear stress maximum value that can be obtained for each machine type.

The best values are obtained for the TFM, but the structure of such a machine is far more

complicated than the others. All the machines using rear-earth permanent magnets provide high

values, so in the end it was a matter of choosing between the VHM and air-cored or iron-cored

structures. Based on the literature and the manufacturing capabilities the air/iron cored structures

were considered for further studies.

Chapter three– LINEAR GENERATOR DESIGN

A Finite Element Method software, JMAG Studio, was used for simulating the

performances of the generator topologies. The program provides 2D, 3D and axis-symmetric

modules for static and dynamic simulations; the axis-symmetric module is ideal for tubular

structures, such as the ones considered here.

Air-cored vs. Iron-cored linear tubular generator

Two structures were considered with similar geometric dimensions, one with an air-cored

tubular stator, the other with a stator made of magnetic material. The comparative study focused

on the magnetic flux density repartition in the structure and in the airgap, stator coil flux and

induced voltages and magnetic and Lorentz forces.

Figure 1 – Induced voltages for the air-cored and iron-cored structures

As it can be seen in figure 1, the voltage obtained in the second case if 14 times bigger

that the one obtained in the air-cored structure. Similar results are obtained for the current, power

or coil flux. The main drawbacks of the iron-cored generator are the appearance of important

electromagnetic forces and a weight increase. Considering these and the major improvements in

all categories the iron-cored structure will be studied in this thesis.

Because the rapid flux variation in the stator it is required to use laminations to limit the

iron losses. Building a stator of laminations mounted in planes parallel to the movement

direction so that the flux lines could close could prove very difficult, so other solutions were

studied. Other authors proposed structures with 2 or more linear stators mounted around the

translator. By increasing the number of stators the structure is closer to a tubular one, but the

manufacturing costs increase and so are the problems that can occur. We opted for a four-sided

generator, searching a compromise between a tubular or a many stators structure and an easy-to-

construct structure.

A comparative study was performed to see the differences between a tubular and a four-

sided structure. Stationary simulations were performed to see the magnetic flux density

repartition and dynamic simulations were performed for coil flux and induced voltage

comparison.

Figure 2 – Magnetic flux density in the two structures

The results regarding magnetic flux repartition were similar, and the computed airgap

flux values were identical. As a result, so were the coil flux and induced voltage time variations.

Differences appeared regarding the medium coil turn length, 27.5% longer, and the total iron

volume required, 32.1% bigger for the four-sided structure, both with negative influence on the

overall generator losses.

Linear electric generator design

The wave motion is generally approximated by a sinus, so we started the generator design

from this motion, approximated by a crank-rod system. Based on the movement equations the

peak and mean speed values were determined. Starting from the speed and some input values

reported in the literature we determined the geometric dimensions of the four-sided linear

generator.

Figure 3– Four sided electric generator structure

The first step was to determine the stator tooth length and width, the stator slot length

width, depth and length, the number of turns/coil and the total number of teeth and slots. Next

the required permanent magnet volume was calculated and the non-magnetic shaft was

dimensioned. The final step was to determine the translator poles width and length and the

permanent magnet dimensions. The resulted structure is shown in figure 3.

Once all these value were calculated the next step was to validate them using a magnetic

equivalent circuit. After all the reluctances were determined and the materials nonlinearities were

took into account, the magnetic flux densities in the airgap and the other components were

determined the values were similar to those obtained in FEM calculations and the design

procedure.

Pole width influence on the induced voltage

In order to determine the pole width influence on the induced voltage a set of simulations

are performed with the translator pole width near the airgap varied from 7 mm, the value

obtained from the calculations, to 3.5 mm, half a millimeter shorter than the stator tooth.

Once the pole width is reduced the induced voltage wave form gets deformed in the

maximum and minimum values zones. For each case the THD and RMS are calculated and the

FFT determined.

Figure 4 – Induced voltage and FFT for the 5.5mm width pole

Based on these values we considered that the best case is the one with a pole width of

5.5mm, so this value was used for the simulations and prototype construction.

Chapter four – FINITE ELEMENT SIMULATION OF THE

LINEAR ELECTIC GENERATOR

Armature reaction

When the generator is connected to a load the armature reaction phenomenon appears

causing a voltage drop. Resistive, inductive and capacitive loads are considered and their

influence determined for aligned, unaligned and partially aligned positions. The results are

confirmed using the magnetic equivalent circuit used before, modified to take into account the

supplementary mmf.

Four-sided linear generator behaviour working in WEC conditions

For these simulations 16 cases were considered with different stroke lengths, movement

frequencies, load status and winding topologies. The induced voltages, currents and generated

powers were studied

No load and load induced voltages Rectified voltages

Resistive and inductive load currents Generated power, inductive load

Figure 5 – Simulated voltage, current and power

The cogging force and electromagnetic forces were also determined and solutions for

limiting their effect were presented. The chapter ends with the stator winding inductivities

calculation.

Chapter five – PROTOTYPE CONSTRUCTION AND

EXPERIMENTAL RESULTS

The prototype parts and the test-bed

The four sided linear generator parts were manufactured and assembled in the laboratory.

Various problems appeared in the assembling process, due to the presence of the permanent

magnets on the translator. The total prototype weight is around 30 kg, the larges amount being

the coils and the stator laminations.

Figure 6 – The translator and the test-bed

The induced voltages and currents were measured using a DAQ system. Some wave

forms are presented in figure 7. The best results were obtained for the highest linear speed

available with the test-bed configuration and for the cases when all the stator coils remain active

for the entire translator stroke.

No-load induced voltage No-load voltage, with condenser

Inductive load current Generated power

Figure 7 – Experimental wave forms

Chapter six – CONCLUSIONS

Considering the global trend of searching for new ways to convert the raw renewable

energies into usable forms the present thesis concentrates on the study of a permanent magnet

linear electric generator suitable for wave energy converters. Based on the information found in

the literature a tubular linear generator structure is considered. After a series of simulations a

four sided structure is preferred because it eliminates the manufacturing problems of the tubular

structure and offers similar results.

The geometric dimensions of the generator are determined based on a set of input values

and are then confirmed using a FEM based software and a magnetic equivalent circuit. A study

on the pole width influence on the induced voltage is performed, resulting that while the pole

gets narrower the voltage is more deformed. An optimal case is selected, taking into account the

peak voltage, THD and RMS values and FFT harmonic components. The armature reaction is

studied for resistive, inductive and capacitive loads seeking for the reason why the voltage

decreases when a load is connected to the generator terminals; besides the armature reaction this

voltage drop is determined by the high internal generator resistance. Next simulations in real-life

conditions are performed using a movement profile similar to those met in WEC. Results show

that for better generator performances higher speed values are required. The best results were

obtained when all the stator coils were active for the entire translator stroke.

Based on the dimensions determined the prototype parts are constructed and assembled.

The generator is mounted on a test-bed containing an induction machine fed trough a frequency

converter, a fix ratio gearbox, a crack-rod system, the generator and a DAQ system for

visualizing and measuring the voltage and current wave forms. The results are similar to those

obtained in the simulations with peak voltages limited by the maximum speed available using the

test-bed. Because the high cogging torque and mechanical imperfections the motion profile was

different than the one used in simulations, so the voltage wave forms varied.

As far as the scientific contribution of the author is concerned, the work aimed three

aspects: creating an analytical design procedure for a four-sided permanent magnet linear

generator, finite element based simulations for confirming the results and improving the

generator performances. The third aspect is regarding the manufacturing of all the generator

components, mounting them and testing the prototype on the test stand to confirm the theoretical

results.

The current PhD thesis offers a series of perspective for continuing the research in the

renewable energy domain in general and in the electric liner generator domain in particular:

improving the four-sided linear generator performances through one or several methods: limiting

the number of inactive coils at the stroke ends, building a translator with a higher number of

poles or developing a system that disconnects the inactive coils; modifying the test-bed so that it

can provide linear speeds higher than the 0.5 m/sec limit to test the generator in the specific

WEC speed range; building a generator with a similar structure but with reduced dimensions that

can be incorporated in a portable electric device; transforming the linear generator into a rotating

one to eliminate the down sides of the stroke ends; developing the electronic component required

so that the generator could be connected to the electric grid; analyzing a multi-phase structure.