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