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Ocean Renewable Energy

Design, Analysis, and Evaluation of the UC-Berkeley Wave-Energy Extractor

[+] Author and Article Information
Ronald W. Yeung1

Department of Mechanical Engineering,  University of California at Berkeley, Berkeley, CA, 94720rwyeung@berkeley.edu

Antoine Peiffer2

Department of Mechanical Engineering,  University of California at Berkeley, Berkeley, CA, 94720antoine.peiffer@gmail.com

Nathan Tom

Department of Mechanical Engineering,  University of California at Berkeley, Berkeley, CA, 94720nathan.m.tom@gmail.com

Tomasz Matlak3

Department of Mechanical Engineering,  University of California at Berkeley, Berkeley, CA, 94720tmatlak@gmail.com

From [18]: $X3¯=X3/πρga2$, $m0¯=kH$, $d¯=d/a$, $μ33¯=μ33/πρa3$, $λ33¯=λ33/πρσa3$, $σ¯=σa/g=ka.$

The use of circuit theory, in the absence of inductance and capacitance, will reveal that the optimal condition would be R = r.

1

Correspondence author. Director, Computational Marine Mechanics Laboratory (CMML), Univ. of California at Berkeley.

2

Current address: Marine Innovation & Technology, Berkeley CA 94710.

3

Current address: Schlumberger Ltd, Houston, TX 77056.

J. Offshore Mech. Arct. Eng 134(2), 021902 (Dec 06, 2011) (8 pages) doi:10.1115/1.4004518 History: Received May 02, 2010; Revised March 08, 2011; Published December 06, 2011; Online December 06, 2011

Abstract

This paper evaluates the technical feasibility and performance characteristics of an ocean-wave energy to electrical energy conversion device that is based on a moving linear generator. The UC-Berkeley design consists of a cylindrical floater, acting as a rotor, which drives a stator consisting of two banks of wound coils. The performance of such a device in waves depends on the hydrodynamics of the floater, the motion of which is strongly coupled to the electromagnetic properties of the generator. Mathematical models are developed to reveal the critical hurdles that can affect the efficiency of the design. A working physical unit is also constructed. The linear generator is first tested in a dry environment to quantify its performance. The complete physical floater and generator system is then tested in a wave tank with a computer-controlled wavemaker. Measurements are compared with theoretical predictions to allow an assessment of the viability of the design and the future directions for improvements.

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Figures

Figure 1

Wave power (kW/m) as a function of significant wave height and period

Figure 2

Schematic for a wave-energy extraction system, showing relevant forces and the definitions associated with the incident wave

Figure 3

The UC-Berkeley generator design: (a) Detailed view of the stator, (b) Detailed view of the rotor, (c) Diagram showing the dimensions and electrical wiring of the linear generator

Figure 4

Comparison of voltage generated by a moving magnet: (a) Predicted shape of the voltage v(t) of three different phases of the generator, over one period. The horizontal axis represents t/T. The vertical axis represents voltage per unit Bm ζ·3(t)/τ, (b) Time history of the voltage v(t) of one column of teeth on the generator over one period T.

Figure 5

Global view of the assembled floater-generator system

Figure 6

Comparison of the normalized heave wave-exciting force X3¯ as a function kd, at the resonance period of 1.7 s

Figure 7

Heave RAO of the floater as a function of angular frequency σ, for a wave amplitude of 6.1 cm (2.4 in). The resonance frequency is observed around σ = 3.7 rad/s or T = 1.7 s. Comparison with the theoretical RAO, based on Eq. 18, when the total damping λT is 15 kg/s at this incident-wave amplitude A.

Figure 8

Force Fg  = Fc applied by the motor on the generator, over two periods, with an infinite resistive load R. The force signal Fc is smoothed and modeled with the experimental generator coefficients Kg , Bg , and μg , based on Eq. 16.

Figure 9

Comparing the smoothed and reconstructed force time history over two periods, for Fc (with no R) and Fg  = Fc  + Fem (with R = 3 Ω)

Figure 10

Generator coefficients as a function of frequency σ. “Spring-inertia” is the expression (Kg – σ2 μg ).

Figure 11

Power characteristics as a function of the load R

Figure 12

Quantification of power flow versus angular frequency σ

Figure 13

Comparison between predicted and measured heave RAO and average electrical power Pel as a function of the resistive load R, for a resonance period of 1.7 s and a wave amplitude A of 12.2 cm. Both methods of predictions are shown.

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