0
Research Papers: Ocean Renewable Energy

Nonlinear Model Predictive Control Applied to a Generic Ocean-Wave Energy Extractor1

[+] Author and Article Information
Nathan Tom

Ocean Engineering Major Field Group
Department of Mechanical Engineering,
University of California at Berkeley,
Berkeley, CA 94720
e-mail: nathan.m.tom@gmail.com

Ronald W. Yeung

American Bureau of Shipping
Inaugural Chair in Ocean Engineering,
Director of Computational Marine Mechanics
Laboratory (CMML),
Department of Mechanical Engineering,
University of California at Berkeley,
Berkeley, CA 94720
e-mail: rwyeung@berkeley.edu

Paper presented at the 2013 ASME 32nd International Conference on Offshore Mechanics and Arctic Engineering (OMAE2013), Nantes, France, June 9–14, 2013, Paper No. OMAE2013-11247.

2Present address: National Renewable Energy Laboratory, 15103 Denver W Pkwy, Golden, CO 84101.

3Corresponding author.

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received March 27, 2013; final manuscript received May 4, 2014; published online July 31, 2014. Assoc. Editor: Longbin Tao.

J. Offshore Mech. Arct. Eng 136(4), 041901 (Jul 31, 2014) (12 pages) Paper No: OMAE-13-1027; doi: 10.1115/1.4027651 History: Received March 27, 2013; Revised May 04, 2014

This paper evaluates the theoretical application of nonlinear model predictive control (NMPC) to a model-scale point absorber for wave energy conversion. The NMPC strategy will be evaluated against a passive system, which utilizes no controller, using a performance metric based on the absorbed energy. The NMPC strategy was setup as a nonlinear optimization problem utilizing the interior point optimizer (IPOPT) package to obtain a time-varying optimal generator damping from the power-take-off (PTO) unit. This formulation is different from previous investigations in model predictive control, as the current methodology only allows the PTO unit to behave as a generator, thereby unable to return energy to the waves. Each strategy was simulated in the time domain for regular and irregular waves, the latter taken from a modified Pierson–Moskowitz spectrum. In regular waves, the performance advantages over a passive system appear at frequencies near resonance while at the lower and higher frequencies they become nearly equivalent. For irregular waves, the NMPC strategy leads to greater energy absorption than the passive system, though strongly dependent on the prediction horizon. It was found that the ideal NMPC strategy required a generator that could be turned on and off instantaneously, leading to sequences where the generator can be inactive for up to 50% of the wave period.

FIGURES IN THIS ARTICLE
<>
Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.

References

Falnes, J., and Lovseth, J., 1991, “Ocean Wave Energy,” Energy Policy, 19(8), pp. 768–775. [CrossRef]
Yeung, R. W., Peffier, A., Tom, N., and Matlak, T. J., 2010, “Design, Analysis, and Evaluation of the UC-Berkeley Wave-Energy Extractor,” ASME J. Offshore Mech. Arct. Eng., 134(2), p. 021902. [CrossRef]
Tom, N., and Yeung, R. W., 2013, “Performance Enhancements and Validations of a Generic Ocean-Wave Energy Extractor,” ASME J. Offshore Mech. Arct. Eng., 135(4), p. 041101. [CrossRef]
Budal, K., and Falnes, J., 1975, “A Resonant Point Absorber of Ocean-Wave Power,” Nature, 256, pp. 478–479. [CrossRef]
Rhinefrank, K., Schacher, A., Prudell, J., Stillinger, C., Naviaux, D., Brekken, T., von Jouanne, A., Newborn, D., Yim, S., and Cox, D., 2010, “High Resolution Wave Tank Testing of Scaled Wave Energy Devices,” Proceedings of the 29th ASME International Conference on Ocean, Offshore, and Arctic Engineering (OMAE-10), Shanghai, China, June 6–11, pp. 505–509.
Grilli, A., Merrill, J., Grilli, S., Spaulding, M., and Cheung, J., 2007, “Experimental and Numerical Study of Spar Buoy-Magnet/Spring Oscillators Used as Wave Energy Absorbers,” Proceedings of the 17th International Society of Offshore and Polar Engineers (ISOPE-07), Lisbon, Portugal, July 1–6, pp. 489–496.
Elwood, D., Yim, S., Prudell, J., Stillinger, C., von Jouanne, A., Brekken, T., Brown, A., and Paasch, R., 2010, “Design, Construction, and Ocean Testing of a Taut-Moored Dual-Body Wave Energy Converter With Linear Generator Power Take-Off,” Renewable Energy, 35(2), pp. 348–354. [CrossRef]
Oprea, C., Martis, C., Biro, K., and Jurca, F., 2010, “Design and Testing of a Four-Sided Permanent Magnet Linear Generator Prototype,” Proceedings of the 19th International Conference on Electrical Machines (ICEM-10), Rome, Italy, Sept. 6–8, pp. 1–6.
Leijon, M., Bernhoff, H., Agren, O., Isberg, J., Berg, M., Karlsson, K. E., and Wolfbrandt, A., 2005, “Multiphysics Simulation of Wave Energy to Electric Energy Conversion by Permanent Magnet Linear Generator,” IEEE Trans. Energy Convers., 20(1), pp. 219–224. [CrossRef]
Stalberg, M., Waters, R., Danielsson, O., and Lejion, M., 2008, “Influence of Generator Damping on Peak Power and Variance of Power for a Direct Drive Wave Energy Converter,” ASME J. Offshore Mech. Arct. Eng., 130(3), p. 031003. [CrossRef]
Falcão, A., 2007, “Modelling and Control of Oscillating-Body Wave Energy Converters With Hydraulic Power Take-Off and Gas Accumulator,” Ocean Eng., 34(14–15), pp. 2021–2032. [CrossRef]
Falnes, J., 2002, “Optimum Control of Oscillation of Wave-Energy Converters,” Intl. J. Offshore Polar Eng., 12(2), pp. 147–155.
Bjarte-Larsson, T., and Falnes, J., 2006, “Laboratory Experiment on Heaving Body With Hydraulic Power Take-Off and Latching Control,” Ocean Eng., 33(7), pp. 447–477. [CrossRef]
de Falcão, A. F., 2008, “Phase Control Through Load Control of Oscillating-Body Wave Energy Converters With Hydraulic PTO System,” Ocean Eng., 35(3–4), pp. 358–366. [CrossRef]
Henriques, J. C., de Falcão, A. F., Gomes, R. P., and Gato, L. M., 2012, “Latching Control of an OWC Spar-Buoy Wave Energy Converter in Regular Waves,” Proceedings of the 31st International Conference on Ocean, Offshore and Arctic Engineering (OMAE-12), Rio de Janeiro, Brazil, July 1–6, pp. 641–650.
Valerio, D., Beirão, P., and da Costa, J. S., 2007, “Optimisation of Wave Energy Extraction With the Archimedes Wave Swing,” Ocean Eng., 34, pp. 2330–2344. [CrossRef]
Yavuz, H., Stallard, T. J., McCabe, A. P., and Aggidis, G. A., 2007, “Time Series Analysis-Based Adaptive Tuning Techniques for a Heaving Wave Energy Converter in Irregular Seas,” J. Power Energy, 221(1), pp. 77–90. [CrossRef]
Babarit, A., and Clement, A. H., 2006, “Optimal Latching Control of a Wave Energy Device in Regular and Irregular Waves,” Appl. Ocean Res., 28, pp. 77–91. [CrossRef]
Clement, A. H., and Babarit, A., 2012, “Discrete Control of Resonant Wave Energy Devices,” Phil. Trans. R. Soc. A, 370, pp. 288–314. [CrossRef]
Hals, J., Falnes, J., and Moan, T., 2011, “A Comparison of Selected Strategies for Adaptive Control of Wave Energy Converters,” ASME J. Offshore Mech. Arct. Eng., 133, p. 031101. [CrossRef]
Eidsmoen, H., 1998, “Tight-Moored Amplitude-Limited Heaving-Buoy Wave-Energy Converter With Phase Control,” Appl. Ocean Res., 20(3), pp. 157–161. [CrossRef]
Falnes, J., 2002, Ocean Waves and Oscillating Systems, Cambridge University, New York.
Rossiter, J. A., 2003, Model-Based Predictive Control: A Practical Approach, CRC Press, New York.
Brekken, T. K. A., 2011, “On Model Predictive Control for a Point Absorber Wave Energy Converter,” Proceedings of the 2011 Trondheim PowerTech Conference, Trondheim, Norway, June 19–23, pp. 1–8.
Hals, J., Falnes, J., and Moan, T., 2011, “Constrained Optimal Control of a Heaving Buoy Wave-Energy Converter,” ASME J. Offshore Mech. Arct. Eng., 133, p. 011401. [CrossRef]
Cretel, J. A. M., Lightbody, G., and Thomas, G. P., 2010, “An Application of Model Predictive Control to a Wave Energy Point Absorber,” Proceedings of the IFAC Conference on Control Methodologies and Technology for Energy Efficiency, Vilamoura, Portugal, Mar. 29–31, pp. 1–8.
Cretel, J. A. M., Lightbody, G., Thomas, G. P., and Lewis, A. W., 2011, “Maximisation of Energy Capture by a Wave-Energy Point Absorber Using Model Predictive Control,” Proceedings of the 18th IFAC World Congress, Milano, Italy, Aug. 28–Sept. 2, pp. 3714–3721.
Richter, R., Magana, M., Sawodny, O., and Brekken, T., 2013, “Nonlinear Model Predictive Control of a Point Absorber Wave Energy Converter,” IEEE Trans. Sustainable Energy, 4(1), pp. 118–126. [CrossRef]
Nocedal, J., and Wright, S., 2006, Numerical Optimization, Springer, New York.
Cummins, W. E., 1962, “The Impulse Response Function and Ship Motions,” Schiffstechnik, 9, pp. 101–109.
Yeung, R. W., 1981, “Added Mass and Damping of a Vertical Cylinder in Finite-Depth Waters,” Appl. Ocean Res., 3(3), pp. 119–133. [CrossRef]
Kung, S. Y., 1978, “A New Identification and Model Reduction Algorithm via Singular Value Decompositions,” Proceedings of the 12th IEEE Asilomar Conference on Circuits, Systems and Computers, Pacific Grove, CA, Nov., pp. 705–714.
Kristiansen, E., Hijulstad, A., and Egeland, O., 2005, “State-Space Representation of Radiation Forces in Time-Domain Vessel Models,” Ocean Eng., 32(17–18), pp. 2195–2216. [CrossRef]
Taghipour, R., Perez, T., and Moan, T., 2008, “Hybrid Frequency-Time Domain Models for Dynamic Response Analysis of Marine Structures,” Ocean Eng., 35(7), pp. 685–705. [CrossRef]
Yu, Z., and Falnes, J., 1996, “State-Space Modelling of a Vertical Cylinder in Heave,” Appl. Ocean Res., 17(5), pp. 265–275. [CrossRef]
Wchter, A., and Biegler, L. T., 2006, “On the Implementation of a Primal-Dual Interior Point Filter Line Search Algorithm for Large-Scale Nonlinear Programming,” Math. Program., 106(1), pp. 25–57. [CrossRef]
HSL, 2011, “A Collection of Fortran Codes for Large Scale Scientific Computation,” http://www.hsl.rl.ac.uk
Kelman, A., Vichik, S., and Borrelli, F., 2012, “BLOM: The Berkeley Library for Optimization Modeling and Nonlinear Model Predictive Control,” http://www.mpclab.net/Trac/
Wehausen, J. V., and Laitone, E. V., 1960, “Surface Waves,” Encycl. Phys., IX, pp. 446–778, Available online at http://coe.berkeley.edu/SurfaceWaves/
Faltinsen, O. M., 1990, Sea Loads on Ships and Offshore Structures, Cambridge University, Cambridge, NY.

Figures

Grahic Jump Location
Fig. 1

Schematic of the physical system under investigation

Grahic Jump Location
Fig. 2

Nondimensional hydrodynamic coefficients [31] versus nondimensional frequency. Nondimensional added mass, μ¯33 = μ33/πρa3, wave damping, λ¯33 = λ33/πρσa3, wave-exciting force, X¯3 = |X3|/gπρa2, phase of wave-exciting force, ϕ, and frequency, σ¯ = σ(a/g)1/2.

Grahic Jump Location
Fig. 3

Kr(t) from IFT versus reduced SSn model generated from imp2ss where Xr ∈ Rn×1. (a) Time history of Kr(t) and (b) error of Kr(t) approximations.

Grahic Jump Location
Fig. 4

Screen shot from Simulink using Berkeley Library for Optimization Modeling (BLOM) function blocks for the present problem

Grahic Jump Location
Fig. 5

Normalized capture width versus angular frequency after doubling Hp

Grahic Jump Location
Fig. 6

Performance metrics versus wave angular frequency. Bg represents linear damping for a passive system (left Bg|max = 50, right Bg|max = 100). (a) Time averaged power, (b) response amplitude operator (RAO) where RAOmax = 10, and (c) normalized capture width Cw /D.

Grahic Jump Location
Fig. 7

Time history of floater and PTO system with Hp = Tt. (a) ζ3(t) and ζ0(t), (b) ζ·3(t) and ζ0(t), (c) Bg(t) and ζ0(t), (d) fgen(t) and fe(t), and (e) P(t).

Grahic Jump Location
Fig. 8

NMPC time histories of fgen and fe with Hp = Tt

Grahic Jump Location
Fig. 9

NMPC time histories of Bg and ζo with Hp = Tt

Grahic Jump Location
Fig. 10

Comparison of floater and PTO time histories between NMPC and passive strategies with Hp = Tt. (a) ζ3(t) and ζ0(t), (b) ζ·3(t) and ζ0(t), (c) Bg(t) and ζ0(t), (d) fgen(t) and fe(t), and (e) P(t).

Grahic Jump Location
Fig. 11

Random wave time series comparison between NMPC and passive strategies. (a) ΣE(t), (b) P(t), (c) ζ3(t) and ζ0(t), (d) ζ·3(t), (e) Bg(t), and (f) fgen(t) and fe(t).

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In