Preliminary Study on Permanent Magnet Generator Prototypes

for Wave Power

by

Lars Yde, B.Sc.E.E, Project Manager Jacob Bugge, M.Sc.M.E

Prof. Boris V. Sidelnikov, D.Sc.Eng. Prof. Galina S. Rogachevskaya, D.Sc.Eng

Anna S. Shelygina, Engineer Vadim L. Kunaev, Engineer

April 2002

Danish Folkecenter for Renewable Energy Kammersgaardsvej 16, DK-7760 Hurup Thy.

www.folkecenter.dk This project has been supported by the Danish Energy Agency Project J.No. 51191/00-0029

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Preliminary Study on

Permanent Magnet Generator Prototypes for

Wave Power

by

Lars Yde, B.Sc.E.E, Project Manager Jacob Bugge, M.Sc.M.E

Prof. Boris V. Sidelnikov, D.Sc.Eng. Prof. Galina S. Rogachevskaya, D.Sc.Eng

Anna S. Shelygina, Engineer Vadim L. Kunaev, Engineer

FC-print April 2002 ISBN 87-7778-140-6

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CONTENTS THE RESOURCE ................................................................................................................................................. 4

GENERAL.......................................................................................................................................................... 4 CHARACTERISTICS OF A SEA STATE ........................................................................................................ 4 WAVE TRAIN OR SEA STATE................................................................................................................................. 5 ONE WAVE.......................................................................................................................................................... 6 DESIGN BASIS ................................................................................................................................................. 6 REFERENCE VALUES..................................................................................................................................... 7 SCALING OF PARAMETERS.......................................................................................................................... 8 TYPES OF WAVE ENERGY ABSORBERS.................................................................................................... 8

WAVE POWER MACHINES SUITED FOR PM ............................................................................................. 9

POINT ABSORBER DRIVING A LINEAR GENERATOR (1A) .................................................................... 9 INTERACTION BETWEEN WAVE ABSORBER AND PMG. .................................................................... 11

CALCULATION OF POWER OUTPUT FROM POINT ABSORBER........................................................ 13

AUTOMATIC LATCHING ............................................................................................................................... 19

WAVE PLUNGER................................................................................................................................................ 19 ALTERNATIVE DESIGN OF POINT ABSORBER FOR PMG ..................................................................................... 20

RAW DESIGN OF PMG PROTOTYPE .......................................................................................................... 22

10 KW RAW ELECTRICAL DESIGN............................................................................................................. 24

GRID CONNECTION ........................................................................................................................................ 27

RAW MECHANICAL DESIGN OF 10 KW PMG .......................................................................................... 29

RAW ELECTRICAL DESIGN OF 0.1 KW PMG........................................................................................... 31

RESULTS CALCULATED FOR LINEAR GENERATORS ........................................................................................... 33

NAME ................................................................................................................................................................... 33

VALUE ................................................................................................................................................................. 33

RAW MECHANICAL DESIGN OF THE 0.1 KW GENERATOR ............................................................... 34

PRICES ................................................................................................................................................................ 34

CONCLUSION.................................................................................................................................................... 35

REFERENCES

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The resource

GENERAL Ordinary waves are created by the wind. Like wind energy, wave energy fluctuates although slower and with a certain delay. On a small time scale wave heights, wavelengths, and wave direction vary; not two waves are identical, high and low, short and long waves follow one another in an irregular pattern. However, the average condition changes slowly, so over a few hours a certain distribution of wave heights and wavelengths may be defined. This is called a sea state. A sea state may be described by a Rayleigh distribution. On a large time scale, the variation corresponds to the variation of the mean wind speed, and the whole spectrum of sea states from calm to heavy sea occur. The spectrum may be described by a Weibull distribution.

CHARACTERISTICS OF A SEA STATE The wave height H is the full amplitude between crest and trough. A sea state or wave train is characterised by the significant wave height: Hs: Significant wave height in m equalling the average of the highest third

of all the waves measured over a certain period of time. Statistically it can be foreseen which fraction of the time waves at a given sea stage will be smaller or equal to a certain wave height h. P(H≤h) = 1 - exp[-2(h/Hs)2].

Distribution of Wave Heights

00.10.20.30.40.50.60.70.80.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6Significant Wave Height

Prob

abili

ty

From the graphic it can be seen that:

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About 50% of the waves will exceed 0.6 * Hs. 5% of the waves will exceed 1.2 * Hs. 1% of the waves will exceed 1.5 * Hs. Hm: Average wave height in m: Tz: Average wave period in s. Tp: Peak wave period in s, related to the highest waves. Pw: Available wave energy flux or power per m of wave front in kW/m. Other definitions which are used in the Danish Wave Energy programme [REF.1] : Hm = 0.625 * Hs. For a fully developed sea, which is a steady state after a long time with a certain average wind speed, Tz = 3.55 * Hs

1/2 Generally, Tz is approximately proportional to 1* Hs

1/2 For a fully developed sea: Pw = 0.577 * Hs

2 * Tz. Generally Pw is approximately proportional to Hs

2.5 for a certain wave energy converter. Near the surface, the water particles almost move in circles with a tangential velocity vT: vT = (π * H)/T, where H and T are the actual height and period of one wave.

Wave train or sea state The power in the waves expressed as kW/m wave front can be calculated as: Pw= 0.557(Hs)2 ∗ Tz Hs = (1/0.625) Hm

Pw= 0.557(1/0.625 *Hm)2 ∗ Tz Pw= 1.426(Hm)2 ∗ Tz Where Hm and Tz is the average wave height and period. The rated power Pr, which is defined as the average power at a sea stage Hs= 5 m, absorbed by the wave converter, is directly proportional to the water plane area of the absorber.

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Owing to the fact that the output from a linear PMG is proportional to the speed, the power output will also be proportional to the height of the waves, because the vertical speed of the water surface is proportional to the height of the wave. Hp is the height of the 5% highest waves of a wave train and can be calculated as: Hp = Hs ∗ 1.2 Hm is the average wave height of a wave train and can be calculated as: Hm = Hs ∗ 0.625 From this it can be seen that the ratio between the peak waves and the average waves is about one to two. Hp / Hm = 1.92 This corresponds to each wave in a wave train which varies between zero and maximum and therefore has half the maximum value as average.

One Wave It is important to distinguish between a sea state, which contains waves of many different sizes and one wave with a specific height. During the passage of one wave, the vertical speed of the water surface will vary from zero at the trough to maximum at the middle and to zero at the top. The inclination of the tangent to the wave will indicate the velocity in each point. From this it can be calculated that the ratio between the maximum and the average speed is π/2 =1.57. Since the power is the force multiplied by the velocity the power ratio Pp/Pm will be the same if the force is constant.

DESIGN BASIS In order to obtain a cost-effective conversion of the wave energy, the whole system must undergo a total optimisation. This has to include efficiency in the whole range of operational conditions, annual number of operation hours, and overall price of the wave energy power plant. The power plant may consist of a large number of individual converters. Since the overall price includes power transmission to the shore, the optimisation of different systems may lead to different properties and positions at different distances from the shore. The Danish Wave Power Programme has chosen a location 100 km from the Danish west coast of the North Sea where the sea is 50 meter deep as a standard location. Wave power converters can be located at a shorter distance from land if the water depth is sufficient. As some examples it can be mentioned that only 5 km north of Skagen the depth is 70 meter, 10 km north and west of Hanstholm the depth

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is 30 meter and in Scotland on a cliff coast a converter has been placed on land. Depending upon the optimisation, the size and capacity of a wave energy conversion system may be adapted to different ranges of sea states. In any case, the occurrence of very large waves makes it necessary generally to confine the absorber movements and the loads to certain limits. It is important to state that the figures and calculations are based upon rough estimates; a more refined analysis would require further information and experience which may be expected during the continued work in the Danish Wave Power Programme.

REFERENCE VALUES A proposed reference position for ocean wave energy in the Danish part of the North Sea within the Danish wave energy programme is a position about 100 km west of the Danish coastline with a depth of 50 m. The following distribution of significant wave heights in meters, average wave periods in seconds, and energy fluxes in kW/m, applies to this position: REFERENCE POSITION Hs [m] 0.5 1 2 3 4 5 5.5 Hm [m] (Hs x 0.625) 0.3 0.6 1.3 1.9 2.5 3.1 3.4 Hp [m] (Hs x 1.2) 0.6 1.2 2.4 3.6 4.8 6 6.6 Tz [s] 4 5 6 7 8 8.3 Tp [s] 5.6 7 8.4 9.8 11.2 Vm = Hm / 1/2 x Tz [m/s] 0.31 0.5 0.63 0.714 0.78 Vp = Hp / 1/2 x Tp [m/s] 0.43 0.69 0.86 0.98 1.07 Velocity in % 40 64 81 92 100 Lp [m] 49 76 110 150 195 Pw [kW/m] 2.1 11.6 32 65.6 114 145 % of Pr 2 10 28 56 100 % of time 11 46.8 22.6 10.8 5.1 2.4 1.3 Number of hours 964 4100 1980 946 447 210 114 Energy [MWh] 0 9 23 30 29 24 17 Accumulated MWh 0 9 32 62 91 115 132 Accumulated MWh in % 0 7 24 47 69 87 100

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It has to be underlined that the figures are wave data and are not reflecting the output of a wave power converter. It can be seen that the power varies with a factor of 114/2,1 = 54, whereas the velocity only varies with a factor of 0.78/0.31= 2.5 for Hs between 1 and 5 meter. This is a very important point, because the output of a PMG is proportional to the velocity.

SCALING OF PARAMETERS Scale models for preliminary testing of wave energy concepts have the same linear proportions as the full-scale converters. In order to compare models and full-scale wave energy converters, the Froude model law applies. The following scaling of parameters applies to a linear scaling factor s: Scale factor Length s Area s2 Volume, Force s3 Time s0.5

Speed, linear and peripheral generator speed s0.5

Power s3.5 According to a report by the Danish Hydraulic Institute, DHI, the Folkecenter test site in Nissum Bredning, with a depth of 2 to 5 m, has approximately the same distribution of significant wave heights corresponding to a 1:10 scale of the reference position. Other scales, such as 1:5 may apply to scale models tested in open sea positions.

TYPES OF WAVE ENERGY ABSORBERS There is a number of working principles of absorbers, many of them included in the Danish wave energy programme: 1) Point absorber: Heaving-floating device with a vertical movement of

the absorber driven by its buoyancy. The energy may be transformed in three ways:

a) Directly from the vertical movement by a linear generator; b) Through the rotation of a propeller on a shaft near the bottom

where the vertical movements of the water are small; the relative flow drives the propeller which drives a normal generator system;

c) Through a mechanical, pneumatic, or hydraulic system, which drives a normal generator system. In this case, the design of the generator depends entirely upon the configuration of this system.

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2) Pitching floating devices with an angular absorber movement, either relative to the mooring system or between floats which meet the waves successively with different phases in the angular movement. In both cases, the energy is transformed through a pump system, either hydraulic or pneumatic. The design of the generator depends entirely upon the configuration of this system including the amount of energy accumulation.

3) Damming devices where the water is lifted above sea level and let out

through a hydraulic system like a low head hydro power station. The design of the generator depends entirely upon the configuration of the turbine.

4) Oscillating water column. Fixed or floating hollow device where the

internal water column rises and falls with the waves. In most cases it drives an airflow through a pneumatic system. The design of the generator depends entirely upon the configuration of the system.

5) Other systems including combinations of 1) and 2), many of which

have not been sufficiently developed to form the basis of a preliminary design of the energy transformation system. Turning fixed device with a rotation about a vertical axis driven by the vertical movements of the water which turn a propeller near the surface; as in 1b) the rotation drives a normal generator system.

In terms of a direct electrical energy conversion (PMG) without use of hydraulic, pneumatic, or mechanical transformation systems including various types of turbines and gearboxes, only the types 1a), 1b), and 5) are relevant at present. If a pneumatic and a hydraulic transmission are considered also 2, 3 and 4 can utilise the use of PMG�s.

Wave power machines suited for PM

POINT ABSORBER DRIVING A LINEAR GENERATOR (1a) A point absorber follows the rise and fall of the water with a phase delay of about 1/10 to 1/4 of the wave period; the damping and the absorber's diving is caused by the power extraction. In order to maintain the maximum stroke the diving of the absorber has to be kept at a minimum. Therefore the absorber has to be as flat and light as possible if resonance is not considered. An example is the Point Absorber PA9801 in the Danish Wave Power Programme which is shown below, the present design includes a tight, flexible mooring. The model testing of this absorber is described in [REF.2], which has formed a significant part of the data basis for this section.

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If the effective natural frequency of the point absorber is in resonance with the wave period or if the phase of the absorber movement is delayed, it is possible to obtain a longer stroke and thereby a higher absorber velocity. Approximately 40% increase of both parameters has been obtained in tests. The result is a doubling of the energy absorption by point absorber, because the diving and thereby the buoyancy also increases. So this is an obvious optimisation parameter. The improved system, which has not yet been tested in automatic operation, is termed an intelligent point absorber. Two versions may apply:

1) It may be possible to obtain different degrees of resonance in a certain sea state by means of varying ballast adjusted to the current average wave height and wavelength.

2) A delay of the phase may be obtained by a short fixation of the point

absorber in the bottom position, and if the support is stiff, also in the top position; this is termed latching, and it may prove practicable to adjust it to the individual waves for optimum amplification. When released, the absorber rises and falls with an increased force caused by increased gravity and increased buoyancy respectively. To build the latching function into a linear generator system will require a PMG strong enough to dive the absorber.

The Point Absorber PA9801 has a full-scale volume of 200 m3, and an expected rated absorbed power of 80 kW at Hs = 5 meter. The overall design and the rated absorbed power as a function of the sea state are shown below. As it appears, the height of the absorber is 2.5 m whereas the diameter is 10 m; since the generator has to be placed on top of the absorber, alternative shapes may be considered within the practical limits.

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With the figures mentioned above, a maximum power during passage of a peak wave will be in the order of 2 times 80 kW ( Hp/Hm = 2). Therefore a PMG should be of 160 kW if applied. The power figures mentioned above are for ordinary absorbers without resonance or latching.

INTERACTION BETWEEN WAVE ABSORBER AND PMG. A linear PMG can provide a force against the movement of the point absorber of about 10 kN/m2 air gab between the inductor and the stator. A 10 kW PMG will have an air gap area of about 1.5 m2. Ten generators will therefore give a force of 10x1.5x10 = 150 kN equal to the displacement of 15m3 of water. Since the 9801-absorber has an area of 78 m2 the generators on average will cause it to dive 15m3/78m2 = 0.19 m. The height of the absorber is 2.5 m which means that it will only dive 8.5% because of the PMG power take-off if mounted on the 9801. Therefore it can be concluded that without resonance or latching, the horizontal movement of the absorber will be almost equal to the height of the waves. In order to determine a reasonable stroke for a linear PMG it has to be remembered that the generator also will utilise a part of the waves, which is higher than the stroke of the generator. This can be compared to when a wind turbine goes into stall. 87% of the wave energy is found in the waves up to Hm = 3 m corresponding to Hs = 5 m. Therefore a stroke of 3 m seems like a reasonable choice. Latching requires a power take-off system strong enough to dive the absorber, which is not possible even with 100 kW PMG mounted on the 9801 which has a volume of 200 m3. From above it can be seen that with a PMG, only 8.5% of the absorber volume is actually used for power production (15m3/200 m3).

12

Only 15 m3 are necessary to create the force needed to drive the generator. If 10 PMGs of 10 kW and 500 kg each are considered, a floater volume of 5 m3 are needed to float them (5 tonne). The weight of the 9801 point absorber is 60 ton. That is 0.3 ton per m3. In the down stroke the weight of the absorber and the generators must be at least 15 ton in order to be able to drive the generator. Therefore the weight of the absorber must be at least 15�5 ton equal to 10 ton. That is equal to 33 m3 if 0.3 ton/m3 are considered. With 10 m in diameter and an area of 78 m2 the thickness of the PMG absorber will be 33 m3/78 m2 = 0.42 m, only 17% of the size of the absorber with the hydraulic power take-off system. The test results of 9801 shove that about 20% of the absorber volume are used for pretension of the anchor wire equal to 40 m3. Because it is using an anchor rope, not a stiff mast, it can only utilise the upstroke from the trough to the crest. If the volume used for pretension, the anchor rope and the volume used for power production were separated, then it would be possible also to utilise the down stroke. As the PMG is a relatively expensive machine it is considered as not economically only to use the upstroke. This is probably not the case with a hydraulic system, which is relatively inexpensive. In this case it might be more economical to increase the size of the hydraulic system and the absorber to the double compared to the extra costs of a more complex system also able to use the down stroke. A design with an anchor rope and utilisation of up and down stroke on deep water is shown below. In order to be able to lift the floating absorber in the down stroke the dived floater must be larger than the floating absorber. On more shallow water a stiff mast could be used.

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Calculation of power output from point absorber. The power production from a PMG can be expressed as: P = F! V F = The force at which the generator damps the movement of the absorber. V = The linear velocity of the generator shaft. If the buoyancy on the absorber is larger than the maximum damping force of the generator, then F is constant and P will be proportional to V. The following graphic�s shows the vertical movement of the water surface, the vertical velocity (which is the gradient to each point on the movement curve) and the power output from a PMG. The movement curve is sinus shaped and varies from zero to maximum. Therefore the average is equal to half the maximum. The average of the velocity is equal to (2/π) Vp

Vm = (2/π) Vp or Vp = 1.57 Vm

While the velocity can be defined as positive and negative, the power output of the generator will always be positive and as for the velocity the ratio between the maximum and the average is π/2 = 1.57. Therefore a PMG that produces 10 kW on average will produce 15.7 kW at its maximum, which occurs at the middle of the wave between trough and crest.

14

15

If eight 10 kW PMGs of the FC design are connected to the 9801 absorber the output in average waves of 3.1 meter will be 85 kW on average, and 85xπ/2 = 133 kW in the middle of each wave. A calculation for all five sea states is given in the table below. The output of the PMG is calculated as follows and assuming that the efficiency of the generator is constant at all sea states and 100%. PPMG = F∗ Vm Vm = (Hm � (2∗ Diving)) / (Tz /2) Eight generators of each 10 kW will create a force against the movement of 120 kN and can therefore displace 12 m3 of water. The area of the absorber is 78 m2. Therefore the diving can be calculated as:

Diving = 12m3 / 78m2 = 0.15 m Power Output from 80 kW PMG Hs [m] 0.5 1 2 3 4 5 5.5 Hm [m] (Hs x 0.625) 0.3 0.6 1.3 1.9 2.5 3.1 3.4 Hp [m] (Hs x 1.2) 0.6 1.2 2.4 3.6 4.8 6 6.6 Tz [s] 3 4 5 6 7 8 8.3 Diving [m] 0.15 0.15 0.15 0.15 0.15 0.15 0.15 Vm of absorber [m/s] 0.01 0.16 0.38 0.53 0.63 0.71 0.76 F [kN] 120 120 120 120 120 120 120 PPMG [kW] 1 20 46 63 75 85 91

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Number of hours 964 4100 1980 946 447 210 114 Energy [MWh] 80 90 60 34 18 10 Accumulated MWh 80 170 230 264 281 292 Accumulated MWh in % for PMG 27 58 79 90 96 100 Accumulated MWh in % for WAVE 7 24 47 69 87 100 By comparing the accumulated energy output from the PMG in percent with the accumulated energy in the waves in percent it can be seen that the PMG has a good ability to utilise the lower sea states. Therefore, e.g. 90% of the possible utilisation of the wave power is reached at a lower sea state than should be expected from looking at the accumulated energy in the waves at different sea states. Measurements on the 9801 point absorber have given the results shown in the table below as �Hydraulic power take-off�. By using an efficiency of 72% the electrical output have been calculated. Measured Power Output from Hydraulic Power Take-off Hs [m] 0.5 1 2 3 4 5 5.5 Hydraulic power take-off [kW] 0 4 19 42 65 78 85 Eectric. generator [kW] 0 3 14 30 47 56 61 Number of hours 964 4100 1980 946 447 210 114 Energy [MWh] 0 12 27 29 21 12 7 Accumulated MWh 12 39 67 88 100 107 By applying the same calculating method to the point absorber with the hydraulic system as used above for the point absorber with the PMG the following table has been elaborated. The hydraulic system is only utilising the upstroke. Therefore the stroke efficiency nstroke equal to 0.5 is applied. Power Output from 61 kW Hydraulic Electric Power Take-off

Hs [m] 0.5 1 2 3 4 5 5.5 Hm [m] (Hs x 0.625) 0.3 0.6 1.3 1.9 2.5 3.1 3.4 Hp [m] (Hs x 1.2) 0.6 1.2 2.4 3.6 4.8 6 6.6

Tz [s] 3 4 5 6 7 8 8.3

Diving [m] 0.04 0.08 0.15 0.23 0.3 0.38 0.41 Vm of absorber [m/s] 0.16 0.24 0.38 0.48 0.54 0.59 0.63 F [kN] 28.7 57.3 115 172 229 287 315 Phy [kW] 5 14 44 82 124 170 198 nupstroke 0.50 0.50 0.50 0.50 0.50 0.50 0.50

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ntransmission 0.72 0.72 0.72 0.72 0.72 0.72 0.72 Phyel [kW] 2 5 16 29 45 61 71 Number of hours 964 4100 1980 946 447 210 114 Energy [MWh] 2 20 31 28 20 13 8 Accumulated MWh 22 53 81 101 113 122 Accumulated MWh in % 18 43 66 83 93 100 By using a diving of 12% of Hm the best matching between measured and calculated values was found. The graphing below shows the two power curves. By this it is validated that it is reasonable to use the applied calculation method. The following table shows the calculations for the power production from a point absorber equipped with PMGs with an efficiency equal to 85%. Power Output from 61 kW PMG Hs [m] 0.5 1 2 3 4 5 5.5 Hm [m] (Hs x 0.625) 0.3 0.6 1.3 1.9 2.5 3.1 3.4 Hp [m] (Hs x 1.2) 0.6 1.2 2.4 3.6 4.8 6 6.6

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Tz [s] 3 4 5 6 7 8 8.3

Diving [m] 0.15 0.15 0.15 0.15 0.15 0.15 0.15 Vm of absorber [m/s] 0.01 0.16 0.38 0.53 0.63 0.71 0.76 F [kN] 120 120 120 120 120 120 120 Ppmg [kW] 1 17 39 54 64 72 77 nupstroke 1 1 1 1 1 1 1 ntransmission 0.85 0.85 0.85 0.85 0.85 0.85 0.85 Ppmgel [kW] 1 14 33 46 54 61 66 Number of hours 964 4100 1980 946 447 210 114 Energy [MWh] 1 58 65 43 24 13 7 Accumulated MWh 58 123 166 190 203 211 Accumulated MWh in % 27 58 79 90 96 100 The rated power, which is the output power at Hs = 5 m is the same for the two systems as well as the diameter of the absorber which is equal to 10 m and 78 m2. The diving for the hydraulic system is 12% of the average wave height, which gives the best matching to the measured power. The diving of the absorber with the PMG is constant and equal to 12 m3 because 8 generators are used, each able to displace 1.5 m3 of water equivalent to 15 kN.

The following graphic shows the two power curves.

Measured and Calculated Power for Pointabsorber with Hydraulick Power Take-off

0

10

20

30

40

50

60

70

80

0 1 2 3 4 5 6 Hs

kW

Measured Calculated

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The output from the PMG will be 211 MWh, which is about 73% more than the 122 MWh from the hydraulic system. Tests have shown that latching can increase the power output by 50% in regular waves and 4 to 8% in irregular waves. Since regular waves only exist in wave tanks the increase in power due to latching in the sea will be in the range of 4 to 8%. Automatic latching The PMG will be grid connected through a 4-quadrent inverter. If the inverter is run in constant force mode, the absorber will not move before the diving increases by 0.15 m. In this way automatic latching is created. Because the power is proportional to the velocity, latching will not increase the average output power. The output will just be zero for a longer period at trough and crescent and higher between.

Wave plunger

Calculated Power from Hydraulic Driven Generator and PMG

0

10

20

30

40

50

60

70

80

0 1 2 3 4 5 6 Hs

kW

Phyel [kW] Ppmgel [kW]

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The Wave Plunger in the Danish Wave Energy Programme shown above is a type related to a point absorber but has a 2.5 times higher efficiency regarding the energy transmission from wave to absorber. Basically, the Wave Plunger slides along a 450 inclined hinged spar, which comprises the mooring; it has weather vanes which means that the front of the absorber always faces the waves. The peak wave stroke is 3.2 m which corresponds to a maximum linear speed of 0.9 m/s. The outer cross section is a rectangular triangle with a hypotenuse of 5.6 m along the spar, the other sides being 4 m each. The possibility of further optimisation by intelligent absorber operation has not been investigated. In contradiction to the point absorber the plunger can utilise both up and down stroke without modifications. The velocity of the generator shaft will, because of the geometry of the hinge system, be higher than the vertical velocity of the waves. How much depends on the final design, but a factor equal to square root two can easily be obtained. As the power output from a PMG is proportional to the shaft speed, it will be possible to use an e.g. square root two smaller generator and get the same annual production compared to the size needed if applied to a point absorber. The conclusion is that the Plunger will be very well suited for a PMG.

Alternative design of point absorber for PMG One method of utilising both up and down stroke on deep water has already been presented. An alternative to dividing the absorber into two parts, a submerged and a floating one, could be to use springs to deliver the force for

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the down stroke as shown on the drawing below. On shallow water a stiff mast can be used and thereby the total absorber volume may be halved, because the absorber shown below has to drive both the springs and the generators in the upstroke.

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Raw design of PMG prototype St. Petersburg State Technical University was given the task to elaborate raw electrical designs for four different 10 kW linear PMGs, suited for the standard site defined by the Danish Wave Energy Programme, as well as for one test and measurement generator of 0.1 kW suited for the Folkecenter�s test site at Nissum Bredning. For the 10 kW machine the standard conditions from the Danish Wave Energy Programme were used to determine a reasonable stroke and average speed and for the 0.1 kW wave heights calculated on basis of wind data for Nissum Bredning were used, [REF 3]. See graphic below.

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Wawe Periods at Testsite

0

0,5

1

1,5

2

2,5

0 0,1 0,2 0,3 0,4Wave Heights in Meters

Sec.

Heaving Speeds at Testsite

0,000,05

0,100,15

0,200,25

0,300,350,40

0,45

0 0,1 0,2 0,3 0,4Wave Heights in Meters

m/s

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On the basis of these data it was decided to design the 10 kW generator for 3 meter stroke and an average speed of 0.71 m/s and the 0.1 kW for 0.3 meter stroke and 0.3 m/s. 10 kW raw electrical design The design data presented in the table shows four prototypes of machines with a plane double-stator structure. In the first version, the driving rod from the wave absorber is directly connected to the generator inductor: The velocity and length of the inductor are equal to those of the rod stroke. In the second and third versions, the rod is connected to the inductor through the reduction gearbox: the velocity of the inductor and its length are equal to the double velocity and length of the rod stroke. In the fourth version, an inductor-stroke stop-gear is applied alongside the reduction gearbox. Its velocity is equal to the double velocity of the rod, while the length of the inductor stroke, and accordingly, the linear dimension of the device are reduced by 40% as compared to those in the second and third versions. Results presented in the table are a preliminary evaluation of the feasibility to manufacture the wave generators providing Pr = 10 kW. They may be used for a comparative analysis of the power units providing the wave parameters specified. It is advisable to conduct a more detailed design together with development of the arrangement layout and assembly power unit, taking into consideration the wave absorber. Attention should be drawn to the disproportion between the principal dimensions of the machines. The greater length due to the rod stroke length specified, together with the small width and thickness of the generators causes a lot of problems associated with assemblage of the unit, its mechanical strength and stability. The reliable mounting of the components is needed while maintaining the same requirements to the vibration properties and geometry stability, in particular, the uniform air gap, the latter being relatively small. A considerable increase in the mass of purely structural units is expected in comparison to that of the active core of the generators as presented in the Table, and consequently, in the volume of construction work. Assuming the minimum advisable frequency of current, fav = 15 Hz, we manage to use the tooth-like-layer generator stator. Application of the reduction gear design, according to the data in the table (versions 2 and 3), enables us to reduce the specific mass of magnets by 1.6 to 1.9 times and the specific mass of the active core of the generators by 1.4 to 1.5. Also, we manage to raise the output frequency (version 3), which has a

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positive effect on the quality of electric power being generated. No doubt, it involves an advantage of the reduction drive. Meanwhile, the essential drawback of such a design is the greater length of the generator due to increasing the stroke of the inductor twofold. Technological and designing problems associated with this factor hinder the production process execution of such a project. The length of the inductor stroke and, consequently, the linear dimension of the generator on the whole may be reduced by means of an inductor-stroke stop-gear. Thanks to it, the inductor will not strictly follow the motion of the driving rod of the wave absorber. At the marginal points and at the low velocity of the rod, the inductor remains immovable. Naturally, at the same time the generator output power is decreasing. For instance, in version 4 proposed, when reducing the length by 40%, approximately 81% of wave energy will be utilized with more stable parameters of electric power being generated. The generator mass remains unchangeable. The less its length, the greater its width. Thus, the proportions of the active core become more favorable. In order to soften the impact loading on the drive, a damper should be added to the gear stop. Similarly, the length of the generator equipped with a direct (no-gear) drive may be reduced.

Version №

Name 1 2 3 4

1 Rated power, Pr [kW]

10 10 10 10

2 Average frequency, fav [Hz] 15 15 25 25 3 Number of poles, 2p 126 126 210 126 4 Number of phases, m 3 3 3 3 5 Circuit arrangement of phase

windings star star star star

6 Pole pitch, τ [cm] 2.38 4.76 2.86 2.86 7 Active length of the inductor, Lr[cm] 300 600 600 360 8 Length of the stator part with

winding, L [cm] 500

1000

1000

600

9 Total width and thickness of the plane generator, l/b [cm]

48.3/5

12.1/6

14.8/5.3

24.7/5.3

10 Total air gap, δ [mm] 1.5 1.5 1.5 1.5 11 Effective rated linear voltage, Ur [V] 118 118 120 120 12 Effective rated phase current, Ir [A] 49 49 48 48 13 Number of active turns in the

winding phase, W 252

504

420

252

14 Total number of phase turns, Wc 420 840 700 420 15 Design current density in the

winding, j [A/mm2] 4

4

4

4

26

16 Length of the stator winding turn, lw [cm]

103.2

37.5

37.6

57.4

17 Maximum phase voltage/emf, idle operation [V]

136/190

136/190

139/194

139/194

18 Magnetic flux, Фm [10-2, Wb]

0.512 0.257 0.189 0.315

19 Maximum inductance in the gap, Bδ [Tesla]

0.7

0.7

0.7

0.7

20 Linear current load, A/cm 123.5 123 100.7 100.7 21 Type of the magnets applied NdFeB NdFeB NdFeB NdFeB 22 Summarized mass of the magnets,

mm [kg] 41.5

21

25

25

23 Mass of stator winding copper, mCu [kg]

142 103 84 77

24 Dimensions of the winding lead, [mm*mm]

3.5x3.5

3.5x3.5

3x4

3x4

25 Mass of the inductor, mi [kg] 50 25 30 30 26 Approximate active core mass of the

generator, mG [kg] 587

420

390

384

27 Specific mass of the magnets, γm [kg/kW]

4.15

2.1

2.5

2.5

28 Specific mass of the generator, γG [kg/kW]

58.7

42

39

38.4

On the basis of the calculations it was decided to choose version no 1. The increased length and complexity of the generator design 2, 3 and 4 cannot be justified by the reduction in weight. In order to save weight the concept with reduced stroke was also chosen. Further weight reduction in relation to the figures given in the table can be obtained by making the inductor longer than the stator, instead of the opposite as indicated in the table. This will reduce the weight from 587 to about 400 kg, equal to 30%. It can bee seen from the drawing below that the stroke of the generator is 3 meter but only 2 meter of the stroke will be 100% active. Because the velocity in the crest and trough of the waves is relatively small, it is more efficient to concentrate the use of material at the middle of the stroke where the velocity is much higher.

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Grid connection The frequency from the generator is varying from zero to maximum 30 Hz within every stroke. At the same time the amplitude changes from nil at the start and end of the stroke to maximum at the middle thus following the frequency. In order to convert this output from the PMG to 230/400 50Hz to be fed into the grid, a 4-quadrant inverter can be used. The ACS611 from ABB seems to be a good choice. It can handle input frequencies from 0 to 300 Hz and voltage from 0 to 400 V. It also has a feature called ID-run, which means automatic impedance matching.

28

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Two different control strategies have been investigated. One way could be to detect the shaft velocity by a separate sensor and use the signal as a continuously changing control signal for adjusting the frequency at which the inverter should operate. Another control strategy could be to run the inverter in constant moment mode. Then the inverter will automatically cause the PMG to create a constant force against the movement of the shaft. Raw mechanical design of 10 kW PMG As mentioned above a double stator concept is applied. It gives the advantages of the magnetic forces being balanced and thus minimises the forces acting on the bearings. Also the width of the inductor is reduced by this concept, thus giving a more compact design. See drawings below.

30

31

Raw electrical design of 0.1 kW PMG As input data, the following are adopted: • The rated power of the generator, Pr = 100 W. • The average velocity of the inductor movement, Vav = 0.3 m/s. • The maximum movement of the inductor (stroke length), Lst = 0.3 m. For the multipole generator the phase voltage may be represented as a total of sinusoids with time-varying amplitudes, mmA T/tsinUU π= , where: Tm is half the wave period. In our case, Tm = 1 s. Such being the case, the design effective phase voltage of the generator is equal to 2/U2/UU mAph == . In case of the active symmetric loading, the effective phase current, I, relative to its maximum, Imax, is determined from the equation: 2/maxII = . To obtain electrical power of the quality required, the average frequency of the emf being generated should be not lower than fav = 15 � 25 Hz. Given the

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minimum value of the values indicated is fav = 15 Hz, the pole pitch of the linear generator proves to be equal to:

01.01523.0

f2V

av

av =⋅

==τ m.

By increasing the frequency, τ is decreasing. Thus, within the portion of the length, τ = 1 cm, it is necessary to place the m-phase winding coils. If m = 3, each coil maintains τ/m = 3.33 mm. It is one of the main problems of designing the generator under the conditions given. In the version proposed for development, the wave parameters are very unfavourable, which considerably reduces the specific mass-size and cost indices in comparison to the generators previously studied. Further, the results calculated for the linear synchronous electromagnetically-excited machine are applying modern rare-earth magnets Nd-Fe-B (Br = 1.25 Тesla, Hc = 900 kА/m). Each of the generators under study has its certain inherent advantages and disadvantages. The final choice of the option requires not only comparative evaluation of the performance properties, but also the conditions of assemblage compatibility with the wave motor, as well as the priorities distribution concerning the cost, technological advantage, mass of the moving parts, etc. Linear Generator with a Plane Stator

For very small pole pitch (τ = 1 cm) it is impossible to make the magnetic circuit (core) of the stator as tooth-like and also dropping the three-phase winding into slots. Two ways of solving the problem were considered, namely: • Reducing the number of phases to m = 2 with dropping each phase

winding on a separate stator; • Applying a no-slot design with the three-phase winding being mounted on

the surface of the stator core. In the first case, with lower consumption of materials, especially permanent magnets, the output voltage wave shape gets impaired, the technology complicated, and the cost of preproduction increases, as well as the losses in the inductor increase on account of oscillations of the stator magnetic field. Therefore, in spite of increasing the active materials consumption, as a working option we adopted the no-slot version with m = 3 and the glued winding. The length of the inductor�s active part filled with magnets is assumed to be equal to the stroke length, Lr = Lst = 0.3 m. Aiming at maximum utilisation of the wave energy, and simultaneously, if possible, reducing the active materials consumption, the length of the stator part with the winding is as follows:

L = 0.5 m. In such a way, the possibility of demagnetisation of the magnets is essentially diminished, while the wave energy is to be utilised up to 98%.

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Some results calculated for the machine equipped with a plane stator are tabulated.

Results Calculated for Linear Generators

Value №

Name Plane

Stator

1 Rated power, Pr [W]

100

2 Average frequency, fav [Hz] 15 3 Effective rated linear voltage, Ur [V] 115 4 Effective rated phase current, Ir [A] 0.51 5 Maximum phase voltage, idle operation,

Em [V] 160

6 Number of phases, m 3 7 Circuit arrangement of phase windings Star 8 Number of poles, 2p 30 9 Pole pitch, τ [cm] 1.0 10 Active Length of the Rotor, Lr [cm] 30 11 Length of the stator part with winding, L [cm] 50 12 Total width and thickness of the plane

generator, l/b [cm] 50/3

13

14 Equivalent air gap, δ [mm] 2x1.8 15 Number of active turns in the winding phase, W

480

16 Total number of phase turns, Wc 800 17 Length of the stator winding turn, lw [cm] 102.8 18 Design current density in the winding,

j [A/mm2] 4.01

19 Diameter of the winding lead, d [mm] 0.4 20 Maximum inductance in the gap, Bδ [Tesla] 0.71 21

Magnetic flux, Фm [10-2, Wb] 0.22

22 Type of the magnets applied NdFeB 23 Summarized mass of the magnets, mm [kg] 4.9 24 Mass of stator winding copper, mCu [kg] 2.75 25 Mass of the inductor, mi [kg] 5.9 26 Approximate mass of the generator mass,

mG [kg] 33

27 Specific mass of the magnets, γm [kg/kW] 49 28 Specific mass of the generator, γG [kg/kW] 330

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As for the 10 kW generator weight reduction can be obtained by shifting the dimensions of the stator and the inductor. Raw mechanical design of the 0,1 kW Generator The same concept as for the 10 kW generator is applied, where the inductor is moving as a carrier on two rails between the two stators. Instead of laying down the windings in slots, they are winded around the stator. It gives larger air gab, which are compensated for by thicker magnets.

Prices In [REF. 2] prices for concrete for ballast and steel for construction are in given as 500 DKK and 25,000 DKK respectively. If the absorber weight can be reduced from 60 ton of steel to10 ton, the saving would be 50 ∗ 25,000 DKK = 1,250,000 DKK. The size of the ballast is set to 150% of the maximum buoyancy. Therefore a 33m3 needs ballast of 50 ton concrete. The 9801 absorber has ballast of 300 ton. The savings will therefore be 250∗ 500 DKK = 125,000 DKK.

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The total potential for savings is then 1,375,000 DKK which will be the amount that is available to pay for the extra costs of the eight 10 kW PMGs. Conclusion The power that the take-off system can utilise can be expressed as: P = F ∗ V The velocity V is determined by the wave height and period. When the height of the waves increases, also the wave period will increase. Therefore the vertical velocity only varies by a factor of about two when the wave height changes from one to five meters. The force F is determined by the dynamic diving of the absorber. That is the diving caused by the power take-off system. The dynamic diving can as maximum be as deep as the wave height, but in that case the velocity will be zero and the power production also zero. From this it can be seen that if F is increased, V will decrease. As the price of a PMG is inversely proportional to the nominal shaft speed, it is necessary to design for maximum speed which means a point absorber as flat as possible. A power system that utilises the speed rather than the force, will be better to utilise the low wave heights compared to a hydraulic system which performs better in high waves. The study has shown that by using a permanent generator power take-off it is possible to reduce the volume of the wave absorber from 200 m3 to about 33 m3 compared to the 9801 point absorber utilising a hydraulic power take-off system. This indicates a potential for savings on the absorber and mooring system since the forces acting and the prices will be roughly proportional to the volume of the absorber. There is no doubt that the PMG system will be more expensive than the combined hydraulic generator power take-off system, but it is too early to say whether the savings can pay for the extra costs, though it seems likely.

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References REF. 1. Bølgekraft � Forslag til forsøg og afrapportering.

Forslag til systematik i forbindelse med afprøvning af bølgekraftanlæg. Marts 1999 Bølgekraftudvalgets Sekretariat

REF. 2. Bølgekraftprogram.

Forslag til systematik i forbindelse med sammenligning af bølgekraftanlæg og status år 2000 Januar 2000 Bølgekraftudvalgets Sekretariat

REF. 3. Bølgeforhold ved Helligsø Teglværk, Nissum Bredning Februar 1998