UC Berkeley

This research demonstrates the design, optimization, and control of a dual coaxial-cylinder system as an ocean-wave energy converter (WEC). The coaxial-cylinder system consists of a tension-tethered vertical inner cylinder and an annular outer cylinder heaving along the outer surface of the inner cylinder. The relative heave motion between the two cylinders is used to extract energy from incoming waves. An "in-house developed" permanent-magnet linear generator (PMLG), consisting of an array of magnets mounted on the outer cylinder but moving relative to a set of coils installed inside the inner cylinder, is used to convert the mechanical movement into electrical current, thus functioning as a power take-off (PTO) unit. This research consists of the following phases.

First, the mathematical modeling, component design and fabrication of the WEC hardware, coupled with the PMLG, were developed. Verification of the predictability and viability of this coupling concept was conducted by comparing predictions with physical-model experiments of about 1:24 scale. The modeling is supplemented by relatively simple, experimentally determined, viscosity-related correction factors on theoretical hydrodynamic coefficients of damping and added mass. The wave-exciting force was well predicted. The modeling is successful for free motion of the cylinder in waves.

Second, a series of dry-bench tests on the PMLG unit was used to determine its electro-mechanical properties. The operating condition that enabled maximum useful power output at heave-motion resonance was investigated as a function of magnet-coil gap width and the output payload in the form of electrical resistance. Moreover, the bottom profile of the annular outer cylinder was modified into a curved shape similar to "The Berkeley Wedge" so as to reduce viscous losses and enhance the WEC performance. Viscous damping losses were reduced by as much as 70%, when compared to a flat-bottom shape. This simple change led to a three-fold increase in the heave amplitude of the outer cylinder and a two-fold increase in power output at resonance, when the WEC system was set at the optimal operating conditions.

Thirdly, to further maximize the energy-extraction capability for a wide operating range of sea-states, a nonlinear model predictive control (NMPC) methodology was developed for the coupled system. The mechanical to electrical power conversion efficiency of the PMLG, determined in Phase 2, was incorporated in this new control scheme. This NMPC process provided a strongly time-dependent PMLG damping profile in time as the control parameter. The typical optimal time-profile of this damping was found to consist of some intermediate value constrained within the specified damping capacity. To confirm the success of this NMPC strategy, this PMLG damping behavior was implemented electronically into the complete WEC system of Phase 1 and 2. The controller employs a solid-state relay based on a pulse-width modulation technique to mimic analog current flow. Experimental verification in regular and irregular sea waves confirmed this successful NMPC implementation. Peak values of energy capture and a broadened bandwidth were favorable compared to that using just passive control.

The present research, all integrated, is capable of producing a 300kW peak-power system in, say, 3m wave height of 8.8sec period using a 12m diameter WEC device. The estimated overall "wave-to-wire" capture-width efficiency is 32% relative to the diameter of the device, with the generator efficiency accounted for. The wattage goes up as the square of the wave amplitude.