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.

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Fig. 1

Schematic of the physical system under investigation

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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.

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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.

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Fig. 4

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

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Fig. 5

Normalized capture width versus angular frequency after doubling Hp

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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.

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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).

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Fig. 8

NMPC time histories of fgen and fe with Hp = Tt

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Fig. 9

NMPC time histories of Bg and ζo with Hp = Tt

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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).

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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).




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