Wave-actuated power

109 Pages·2013·3.9 MB·English

Project DE-EE0004565: Wave-actuated power take-off device for electricity generation
FINAL REPORT
Project research questions
The investigation conducted under this program and documented herein addressed the following principal
research question regarding RME’s power take off (PTO) concept for its 3D-WEC:
Is RME’s winch-driven generator PTO concept, previously implemented at sub-scale and tested at the
Ohmsett wave tank facility, scalable in a cost-effective manner to significant power levels—e.g., 10
to 100kW? In particular:
1. Can helical springs, of sufficient turns and torque capacity to provide the requisite tether
restoring force, achieve a service fatigue life of at least 5 years or more?
2. Can a reliable tether winching scheme be realized that will avoid potential for fouling?
3. What order of efficiency can be attained by the spring-generator system?
Background
Since 2008, Resolute Marine Energy, Inc. (RME) has been engaged in the development of a rigidly
moored shallow-water point absorber wave energy converter, the "3D-WEC," depicted in Figure 1.

Buoy Waves

Tether

Anchor and

PTO Seabed

Figure 1 - The 3D-WECTM (Goudey, 2008)
RME anticipated that the 3D-WEC configuration with a fully buoyant point absorber buoy coupled to
three power take off (PTO) units by a tripod array of tethers would achieve higher power capture than a
more conventional 1-D configuration with a single tether and PTO. This advantage was prompted by the
finding that the theoretical maximum capture width of a WEC responsive to both heave and surge wave
actions is three times that of one absorbing only in heave mode [1]. Moreover, RME, in conjunction
with Dr. Jeffrey Scruggs at Duke University also theorized that 3D-WEC power capture could be further
improved via a causal dynamic control of tether reaction forces as a function of velocity versus the more
conventional viscous loading policy wherein reaction force is in fixed proportion to velocity.
1
Prior Research
RME proposed to explore these hypotheses and was awarded a DOE SBIR Phase I grant for this purpose.
Key findings of the completed Phase I investigation [1] supported RME’s and Scruggs’ expectations. In
particular:
1. Sub-scale model testing at the Ohmsett wave tank facility demonstrated that a spherical buoy with
three tethers and PTOs captured significantly greater power than the same buoy configured with
only one tether and PTO
2. Analysis revealed that the power capture advantage of 3D-WEC is due to the fact that it captures
energy across two widely separated frequency modes--the higher mode related to heave excitation
(high hydrostatic stiffness) and the lower mode related to surge excitation (low hydrostatic
stiffness)
3. Model tank testing and analysis revealed that when the 3D-WEC anchors are aligned with the
wave propagation direction as depicted below in Figure 2, the “head” tether-PTO unit delivers
90% or more of the developed mechanical power. This suggests that where units are deployed in
wave climates characterized by a prevailing propagation direction—e.g., near-shore—a single
head PTO may suffice—the others simply providing passive tether spring bias—perhaps with
elastic mooring bungees
4. For a single 3D-WEC, optimal control of tether reaction force may increase power capture by as
much as 2.5 times relative to simple viscous loading
5. Preliminary investigation of optimal control for arrays of 3D-WECs indicated potential for
significant increase of power capture over that contributed by the same number of isolated units
These findings were very encouraging and motivated further development of the 3D-WEC technology.
Sub-scale 3D-WEC model testing at the Ohmsett facility was conducted as diagrammed in Figure 2. To
simplify test procedures, the PTO units of Figure 3 were not submerged and, instead, were mounted on
the wave tank work bridge as shown in Figures 2A and 2B.

Figure 2A – Plan view of RME 3D-WEC test apparatus deployed at the Ohmsett wave tank
2
Prior Research - continued

Figure 2B – Elevation view of RME 3D-WEC test apparatus deployed at the Ohmsett wave tank

Figure 3 - Power take off configuration for 3D-WEC test at the Ohmsett wave tank
The electric PTO units of Figure 3 accommodated peak power generation up to 50W using off-the-shelf,
gear-driven permanent magnet brushed DC motors serving as generators and provided tether bias tension
on the order of 100N with off-the-shelf constant force springs. Simple viscous loading of the tethers was
provided by manually selected resistive loads applied to the PTO DC generators.
Bias tension in each tether was provided by a constant-force, coiled-tape spring depicted in Figure 3
which kept the buoy submerged at a preferred mean depth and maintained tension on the tether under
dynamic conditions. Bias tension equal to peak dynamic tension from generator reaction is essential to
enable power generation over an entire wave cycle. During these tests the peak dynamic tension was
typically less than half that to maintain the buoy submerged to its equator when at rest.

3
Program overview
Under this DOE-sponsored program we designed, built and tested a proof-of-concept (POC) fully
enclosed, fluid-filled and pressure-balanced PTO assembly suitable for submerged ocean deployment
with direct-drive, gearless generator power capacity on the order of 1,000W supporting typical tether bias
tension on the order of 2,000N. Additionally we estimated the PTO manufacturing materials cost for a
3D-WEC unit at various power scales..
In the developed PTO, tether excursions induced by buoy motion are directly converted to electrical
power by a rotary electrical generator and spool arrangement similar to the test unit depicted in Figure 3.
It is anticipated that use of high strength, low density and fatigue-resistant Dyneema cordage and the
careful attention that was paid to its interface with the spool will provide 5 years or more unattended
service life. The linear constant force spring employed in the model test PTO was replaced with a spiral
spring providing approximately constant bias torsion directly coupled to the spool-generator system.
RME believes that the developed PTO configuration is potentially advantageous compared to alternatives,
which have been, and continue to be explored for point absorber WEC devices. For example an
envisioned hydraulic link between linear tether motion and a rotary generator would require a very long-
stroke cylinder—with means to protect the rod from corrosion—coupled to a hydraulic motor to drive a
rotary generator. Bias tension would be provided by means of an accumulator. However, the efficiency
of such apparatus would be compromised by high losses—perhaps as much as 33%.1
The direct-drive rotary permanent magnet generator (PMG) avoids significant difficulties posed by linear
PMGs, which are widely under investigation for point absorber wave energy converters, e.g., [4-5]. For
example, the moving element of a rotary machine is supported by conventional bearings which readily
accommodate radial loading due to residual unbalanced magnetic forces on the rotor whereas, in the
linear machine, the moving element requires a relatively complex, difficult-to-lubricate, linear bearing
carriage. Attaining sufficient stiffness in the stator and mover of a linear machine to assure maintenance
of a uniform air gap is more difficult than for a rotary generator. Provision of water tight packaging and
sealing of the mover interface with the mechanical prime-mover is also more difficult to implement than
in the case of a rotary generator. Then, too, the linear machine is burdened with the significant
disadvantage that only a small portion of either the stator or mover is engaged in power conversion while
in a rotary machine all electromagnetic material defining the air gap is productive.
An off-the-shelf gear-driven permanent magnet DC brushed motor was employed as a generator for short-
term model tests at Ohmsett. However, lessons-learned from the wind turbine industry--where even at
today’s stage of maturity, costly gear transmission failures persist—recommended a direct-drive, gearless
solution. Indeed, a gear transmission would be subject to even more challenging service under the
oscillating load regime of a WEC and it would not be readily accessible for annual or more frequent
inspections and oil changes. Hence, while the advantages of generator size, weight and cost reduction
enabled by a geared speed increaser are appealing, we rejected this option and are encouraged by the
technical and commercial success of kilowatt to megawatt scale direct-drive wind turbines, which
incorporate either permanent magnet or electromagnetic field excitation.
Since size, weight and cost attributes of generators are primarily determined by torque rating, only
electric machines, such as permanent magnet designs, with very high weight-specific torque performance

1 For example, Henderson [3] reported up to 20% losses in the primary piston hydraulic link to an accumulator in the
Pelamis attenuator WEC. Secondary conversion losses—rotary hydraulic motor and generator—were cited to be up
to 20% as well. Assuming the generator would be responsible for 7% of the secondary loss, the hydraulic loss
contribution would be 13%. Hence the primary and secondary hydraulic loss in this example could be as high as
33%.

4
Program overview - continued
were deemed suitable candidates. In particular we leveraged findings of prior studies related to low
speed, direct-drive permanent magnet generators—e.g., [6-8]—as well near off-the-shelf rotor and stator
components to expedite implementation of the proof-of-concept PTO.
Before moving on to a detailed discussion of the program a schematic of the envisioned prototype PTO
package and a photo of the finished unit are presented in Figure 4 to provide the reader with a better idea
of the undertaking.
Generator stator

core and windings
Removable shear bolt to
free spool for set up
Field magnets

Magnet back iron

Rotor hub

0.030” air gap

Mounting base

Bearing and seal Commercial 1.5” food Lovejoy disk
cartridges service, corrosion- shaft coupling
resistant flanged sealed
bearing package

Figure 4 – Original schematic vision of the proof-of-concept PTO and the finished unit
5
Description of research tasks
Task 1 – Requirements definition and allocation
Requirements for principal PTO components were identified at the outset of the program including:
1. Tether extension-retraction range to accommodate variations in wave dynamics and tide
2. Spool diameter – # of rotations for tether extension-retraction range, impact generator and spring
3. Generator – peak reaction torque and losses
4. Bias torque spring – bias torque, number of operating turns, fatigue-life
5. Rotary seals and enclosure – pressure-balanced, liquid-filled
6. Tether material – sizing for fatigue endurance, minimum spool/tether diameter ratio
7. Enclosure flooding fluid type – dielectric, non toxic, bio-degradable
These requirements were interactive e.g., spool diameter determined required spring torque and number
of turns to be accommodated. Spool diameter also impacted the peak generator reaction torque
requirement, which, in turn, directly affected its size, weight and cost which are largely driven by torque
rather than power. Hence, rather than prematurely fixing specific values in these cases, tradeoff
relationships were identified.
Some requirements might have been allocated to other subsystems. For example, it may be the case—as
it was for the sub-scale Ohmsett wave tank test—that the bias force provided by the spring to maintain the
tether in tension over the complete crest-to-trough wave cycle at peak dynamic generator load is
substantially less than that necessary to keep the buoy at a preferred mean submergence depth. In this
case, to reduce the cost of the generator-coupled torsion spring, a portion of spring capacity might be
allocated to another spring device not coupled to the generator—e.g., a lower- cost mooring bungee
linking the buoy directly to the anchor.
Special requirements of WEC operation must also be considered in setting requirements. For example the
cyclic nature of generator shaft speed requires accommodation of a peak torque, which may exceed twice
the average required to develop equivalent power under constant speed conditions, and dominant “copper
losses” must be assessed in consideration of this mode of operation. In a prospective follow-on to this
program, the impact of such losses would be assessed on an annualized basis in consideration of sea-state
conditions for a prospective installation applying the methodology recommended by the E21 EPRI
Specification or similar procedure [9].

Task 2 – Acquire design data via model simulation using existing tools
To facilitate the PTO design we utilized a numerical model previously developed by Dr. Jeffrey Scruggs,
of Duke University, during the course of a previous DOE Phase I SBIR program [2] to generate time-
series tether tension and displacement data. The displacement data was of particular importance to
assessment of the helical spring which provides tether bias tension.
Time-series data at 100s/s for a periods of approximately 11 minutes were generated for a sea-state
condition defined by Pierson-Moskowitz significant height (Hs) and peak power period (Tp) parameters
representative of a prospective shallow water test site at the village of Madakat on the southerly shore of
Nantucket Island. These parameters were obtained from historical data gathered by a NOAA data buoy
56NM SE of Nantucket identified in Figure 5 as this was the closest available data buoy south of
Nantucket. We generated 4 data sets--one each for January, April, July and October, to get a fair
representation of annual conditions.

6
Task 2 – Acquire design data via model simulation using existing tools

Figure 5 – Description of NOAA data buoy selected to provide Hs and Tp model parameters
An illustrative displacement data file for representative April conditions is shown below in Figure 6.
X = tether displacement (m).

2
1.112
1
X 0
1
1.073 2
0 100 200 300 400 500 600
0 t 650
Figure 6 – Illustrative tether displacement analysis results
Salient model parameters for this run were as follows:

From http://www.ndbc.noaa.gov/view_climplot.php?station=44008&meas=wh
Mean wave period (averaged for April from 8/1982-12/2008), Tp=6s
Significant wave height (averaged for April from 8/1982-12/2008), Hs=1.9 m
Recoil spring, Kg = 0 N-m/rad (constant tension spring)
Rotational viscous damping, Bg = 1 N-m-s/rad
Rotational inertia, Jg = 0.50 N-m-s^2/rad
Linear-to-rotational conversion, rg = 0.08 m (spool radius)
Viscous damping, c0 = 10 kg/s
Generator back-EMF constant, Ke =21.2 V/rad/s
Stator coil resistance, Rs=4.96 Ohms
Generator load resistance for optimum energy production, R = 21 Ohms
7
Task 2 – Acquire design data via model simulation using existing tools
In each case the generator load was adjusted for maximum energy production over the simulation
interval. In practice we would employ a “Power Matrix” of optimum load values according to real-time
observations of Hs and Tp with a bottom-mounted wave pressure sensor to automatically adjust the load
for best performance. Power Matrix values would be initially developed by model analysis and then
adaptively improved by a real-time “hill-climbing” adjustments of matrix values.
Since the start of this investigation RME has been engaged in ocean testing of its SurgeWEC Oscillating
Wave Surge Converter (OWSC) device on the Outer Banks of North Carolina at Jennette’s Pier in Nags
Head and at the U.S. Corps of Engineers (USCOE) Field Research Facililty (FRF) pier. The capabilities
of the FRF are particularly well-suited to WEC testing and RME envisions that initial ocean trials of its
3D-WEC with the prototype PTO developed under this program might be conducted at this site rather
than the Madaket Nantucket location originally envisioned.

Task 3 – Set requirements for a proof-of-concept PTO
Froude scaling of prior sub-scale PTO Ohmsett wave tank tests
We set the requirements of the prototype PTO at a scale judged to be affordable within the budget
constraints of the TRL-3 program. An initial rough estimate of prototype requirements at reasonable
scale were determined by Froude scaling of results obtained during tank testing of a 3D-WEC model with
0.45m diameter buoy at the Ohmsett wave tank facility [2] . Performance data for one of the highest
power test cases (Run 39) is presented in Table 1 below along with assumed scaling law and projected
results for Froude scaling of the Ohmsett 0.45m diameter buoy to a 1.0m diameter. Note that for this
Ohmsett trial waves approached the array as depicted in Figure 2a above and the “head” PTO delivered
most of the power. The peak line velocity and peak mechanical power reported below are those
associated with this PTO.

Parameter Ohmsett value Scale factor Scaled value
Buoy diameter 0.45m 2.222 1.0m
Half displacement force 2 241N (54.2 lbf) 2.2223 = 11 2,650N (596 lbf)
Static line tension force 3 114N (25.6 lbf) 2.222 3 = 11 1,250N (280 lbf)
Wave period 2s 2.222 0.5 = 1.49 3.0s
Wave amplitude 0.2m 2.222 0.44m
Peak line velocity 0.6m/s 2.222/(2.222 0.5) = 1.49 0.89m/s 4
Peak mechanical power 31.4W 2.222 3.5 = 16.4 515W
Peak dynamic line force 5 52.3N (11.8 lbf) peak power/peak velocity 580N (130 lbf)
Table 1 - Froude scaling of Ohmsett test results for proof-of-concept PTO preliminary sizing
These illustrative preliminary estimates are for monochromatic wave excitation and are constrained to the
period and wave amplitude determined by Froude scaling. Peak power on the order of 1kW is projected
for more energetic waves than were generated in the Ohmsett tank tests and average power would be
approximately half of peak. These results were considered at proposal time in making preliminary cost
estimates for the proof-of-concept prototype components.

2 At half submergence, 1,030 kg/m3 sea water density, 9.087 m/s2 gravitational acceleration
3 To maintain the buoy at half submergence with mooring lines at 45 degrees from the vertical
4 Velocity increased by dimension scale which increases wave amplitude and buoy displacement and reduced by 1/T
5 Peak dynamic line tension= peak mechanical power / peak line velocity
8
Task 3 – Set requirements for a proof-of-concept PTO

While the 0.44m scaled wave amplitude may be representative of a real, but modest, ocean wave climate
the 3s period is 1/2 to 1/3 of what might be encountered. Other than the scaled tether bias tension
required to keep the buoy at half submergence under static conditions these results provided limited
guidance in determining dynamic tether load, tether velocity and generator power for the prototype
design.

The results reported in Table 1 are representative for the case where waves approach the mooring array as
depicted in Figure 2a above. This would frequently be the case for a shallow water installation where the
approach of waves is normal to the shore. Under this condition we observed that the head PTO generated
most of the power but this may be peculiar to testing with monochromatic waves in a tank.

Estimating tether loading and power

To estimate tether loads and power we used the results of the numerical model of the system which were
developed based on typical wave conditions reported by the above described NOAA data buoy for
months of January, April, July and October. Table 2 summarizes the significant wave height Hs and peak
power period Tp for each case.

Month Hs Tp (s) Incident Tether 1 Tether 2 Tether 3 Total Capture
(m) wave generator generator generator generator width
power power power power power ratio
(W) (W) (W) (W) (W)
January 2.5 6.0 19.9 471 236 236 943 0.047
April 1.9 6.0 11.5 272 136 136 545 0.047
July 1.2 5.8 4.4 111 55 55 221 0.051
October 1.8 5.9 10.2 240 119 119 478 0.047
Averages 11.5 274 137 137 547 0.048

Table 2 – Numerical model run results

The generator stator winding resistance per phase assumed in these runs was twice that of the machine we
ultimately selected and so the above generator output results are understated due to higher than expected
winding “copper loss”. Although the model assumed waves normal to Tether 1 we see here that the
flanking tethers are contributing a significant portion of the total power which is not the situation we
observed during sub-scale model wave tank testing at the Ohmsett facility. Due to constraints of budget
and schedule we were not able to investigate the cause of this performance difference. It may be due to a
model deficiency or a consequence of monochromatic wave tank conditions.

The theoretical maximum capture width CW for a point absorber responding to heave and surge is 3/2
[1]. For a 6s period in shallow water as typical of cases we modeled wave length  is approximately 40m
and so the theoretical CW = 19m and capture width ratio CWR for the modeled 1 m buoy would be 19—
approximately 380 times that indicated by our model results in Table 2. However, theoretical value is for
monochromatic excitation without a practical limit on buoy excursion. Some confirmation that our CWR
model results are reasonable is provided by the findings of numerical analyses reported by Babarit et al.
[23]. In particular the authors modeled a single tether version of our 3D-WEC and found a CWRs in the
range of 0.021 to 0.042. Figure 6A below depicts the modeled configuration and results.

9
Task 3 – Set requirements for a proof-of-concept PTO

Estimating tether loading and power - continued

Figure 6A – Results of numerical model of single tether configuration – by Babarit, et al. [23]
10