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.

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Fig. 1

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

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Fig. 2

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

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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.

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Fig. 4

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

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Fig. 5

Comparisons of capture width by current method with those using NMPC

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Fig. 6

Comparisons of RAO by current method with those using NMPC

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Fig. 7

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

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Fig. 8

Computational time for simulated cases of regular waves

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Fig. 9

Time-averaged useful power in irregular waves

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Fig. 10

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

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Fig. 11

Computational time for simulated cases of irregular waves

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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




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