Research Papers: Ocean Renewable Energy

An Efficient Convex Formulation for Model-Predictive Control on Wave-Energy Converters1

[+] Author and Article Information
Qian Zhong

Department of Mechanical Engineering,
University of California at Berkeley,
Berkeley, CA 94720
e-mail: qzhong@berkeley.edu

Ronald W. Yeung

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

1Paper presented at the 2017 ASME 36th International Conference on Ocean, Offshore, and Arctic Engineering (OMAE 2017), Trondheim, Norway, June 25–30, 2017, Paper No. OMAE2017-62575.

2Corresponding 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 May 26, 2017; final manuscript received November 2, 2017; published online December 22, 2017. Assoc. Editor: Yi-Hsiang Yu.

J. Offshore Mech. Arct. Eng 140(3), 031901 (Dec 22, 2017) (10 pages) Paper No: OMAE-17-1082; doi: 10.1115/1.4038503 History: Received May 26, 2017; Revised November 02, 2017

Model-predictive control (MPC) has shown its strong potential in maximizing energy extraction for wave-energy converters (WECs) while handling hard constraints. However, the computational demand is known to be a primary concern for applying MPC in real time. In this work, we develop a cost function in which a penalty term on the slew rate of the machinery force is introduced and used to ensure the convexity of the cost function. Constraints on states and the input are incorporated. Such a constrained optimization problem is cast into a Quadratic Programming (QP) form and efficiently solved by a standard QP solver. The current MPC is found to have good energy-capture capability in both regular and irregular wave conditions, and is able to broaden favorably the bandwidth for capturing wave energy compared to other controllers in the literature. Reactive power required by the power-take-off (PTO) system is presented. The effects of the additional penalty term are discussed.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.


Bacelli, G. , Coe, R. , Wilson, D. , Abdelkhalik, O. , Korde, U. , Robinett, R. , and Bull, D. , 2016, “ A Comparison of WEC Control Strategies for a Linear WEC Model,” Sandia National Laboratories, Albuquerque, NM, Report No. SAND2016-4293 http://energy.sandia.gov/wp-content/uploads/dlm_uploads/2016/06/SAND2016-4293.pdf.
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(3), p. 031101. [CrossRef]
Eidsmoen, H. , 1996, “ Optimum Control of a Floating Wave-Energy Converter With Restricted Amplitude,” ASME J. Offshore Mech. Arct. Eng., 118(2), pp. 96–101. [CrossRef]
Evans, D. , 1981, “ Maximum Wave-Power Absorption Under Motion Constraints,” Appl. Ocean Res., 3(4), pp. 200–203. [CrossRef]
Mayne, D. , Rawlings, J. , Rao, C. , and Scokaert, P. , 2000, “ Constrained Model Predictive Control: Stability and Optimality,” Automatica, 36(6), pp. 789–814. [CrossRef]
Belmont, M. , Horwood, J. , Thurley, R. , and Baker, J. , 2006, “ Filters for Linear Sea-Wave Prediction,” Ocean Eng., 33(17), pp. 2332–2351. [CrossRef]
Fusco, F. , and Ringwood, J. , 2012, “ A Study of the Prediction Requirements in Real-Time Control of Wave Energy Converters,” IEEE Trans. Sustainable Energy, 3(1), pp. 176–184. [CrossRef]
Morris, E. , Zienkiewicz, H. , and Belmont, M. , 1998, “ Short Term Forecasting of the Sea Surface Shape,” Int. Shipbuilding Prog., 45(444), pp. 383–400.
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(1), p. 011401. [CrossRef]
Li, G. , and Belmont, M. , 2014, “ Model Predictive Control of Sea Wave Energy Converters—Part I: A Convex Approach for the Case of a Single Device,” Renewable Energy, 69, pp. 453–463. [CrossRef]
Cretel, J. , Lightbody, G. , Thomas, G. , and Lewis, A. , 2011, “ Maximisation of Energy Capture by a Wave-Energy Point Absorber Using Model Predictive Control,” IFAC Proc., 44(1), pp. 3714–3721. [CrossRef]
Tom, N. , and Yeung, R. , 2014, “ Nonlinear Model Predictive Control Applied to a Generic Ocean-Wave Energy Extractor,” ASME J. Offshore Mech. Arct. Eng., 136(4), p. 041901. [CrossRef]
Son, D. , and Yeung, R. , 2017, “ Optimizing Ocean-Wave Energy Extraction of a Dual Coaxial-Cylinder WEC Using Nonlinear Model Predictive Control,” Appl. Energy, 187, pp. 746–757. [CrossRef]
Tom, N. , and Yeung, R. , 2016, “ Experimental Confirmation of Nonlinear-Model-Predictive Control Applied Offline to a Permanent Magnet Linear Generator for Ocean-Wave Energy Conversion,” IEEE J. Oceanic Eng., 41(2), pp. 281–295. [CrossRef]
Son, D. , 2016, “ Performance Evaluation and Optimization of a Dual Coaxial-Cylinder System as an Ocean-Wave Energy Converter,” Ph.D. thesis, University of California at Berkeley, Berkeley, CA.
Bacelli, G. , Coe, R. , Patterson, D. , and Wilson, D. , 2017, “ System Identification of a Heaving Point Absorber: Design of Experiment and Device Modeling,” Energies, 10(4), p.472.
Wehausen, J. , 1971, “ The Motion of Floating Bodies,” Annu. Rev. Fluid Mech., 3(1), pp. 237–268. [CrossRef]
Yeung, R. , 1981, “ Added Mass and Damping of a Vertical Cylinder in Finite-Depth Waters,” Appl. Ocean Res., 3(3), pp. 119–133. [CrossRef]
Falnes, J. , 2002, Ocean Waves and Oscillating Systems: Linear Interactions Including Wave-Energy Extraction, Cambridge University Press, Cambridge, UK. [CrossRef]
Chau, F. , and Yeung, R. , 2012, “ Inertia, Damping, and Wave Excitation of Heaving Coaxial Cylinders,” ASME Paper No. OMAE2012-83987.
Wächter, A. , and Biegler, L. T. , 2006, “ On the Implementation of an Interior-Point Filter Line-Search Algorithm for Large-Scale Nonlinear Programming,” Math. Program., 106(1), pp. 25–57. [CrossRef]
Herceg, M. , Kvasnica, M. , Jones, C. , and Morari, M. , 2013, “ Multi-Parametric Toolbox 3.0,” European Control Conference (ECC), Zurich, Switzerland, July 17–19, pp. 502–510. http://ieeexplore.ieee.org/document/6669862/
Currie, J. , and Wilson, D. I. , 2012, “ OPTI: Lowering the Barrier Between Open Source Optimizers and the Industrial MATLAB User,” Foundations of Computer-Aided Process, Operations, N. Sahinidis and J. Pinto , eds., Elsevier, Savannah, GA.
Zhong, Q. , and Yeung, R. , 2016, “ Wave-Body Interactions Among an Array of Truncated Vertical Cylinders,” ASME Paper No. OMAE2016-55055.


Grahic Jump Location
Fig. 1

Impulse response of the radiation subsystem and damping coefficients with respect to wave frequency

Grahic Jump Location
Fig. 2

Averaged absorbed power by an unconstrained point absorber plotted over the angular frequency

Grahic Jump Location
Fig. 3

Time histories of ζ˙3 (solid), ζ3 (dash-dotted), and fe (dashed) on the left, and fm (dash-dotted) and fe on the right, for the absorber in regular waves with amplitude of 1 m and period of 9 s. Constraints, if any, are shown by dashed lines, values of which are set to ζ3,max=5 m, and fm,max=2 MN. Simulated cases are (a) no constraints, (b) constraints on the heaving motion, (c) constraints on the machinery force, and (d) constraints on both of the heaving motion and the machinery force.

Grahic Jump Location
Fig. 4

Schematic of the dual coaxial-cylinder system in Ref. [13]

Grahic Jump Location
Fig. 5

Comparisons of capture width by current method with those using NMPC

Grahic Jump Location
Fig. 6

Comparisons of RAO by current method with those using NMPC

Grahic Jump Location
Fig. 7

The ratio of the reactive power to the power flowing from the absorber to the PTO unit (so-called “active power”)

Grahic Jump Location
Fig. 8

Computational time for simulated cases of regular waves

Grahic Jump Location
Fig. 9

Time-averaged useful power in irregular waves

Grahic Jump Location
Fig. 10

The ratio of reactive power to “active power” in irregular waves

Grahic Jump Location
Fig. 11

Computational time for simulated cases of irregular waves

Grahic Jump Location
Fig. 12

Time histories of ζ˙3, ζ3, and fe on the left, and fm and fe on the right, for the absorber in irregular waves of Tp=2.2 s



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