UC Berkeley

This thesis considers the design, optimization, and control of a coupled cylindrical floater and permanent magnet linear generator for wave-energy conversion. The investigation begins with the construction of the time-domain equation of motion for a generic floating body. The construction of a physical cylindrical floater is followed by a description of the experiments completed to verify free-motion and wave-exciting force predictions. The time-domain equation of motion was compared against experiments where it was found that corrective terms needed to be added due to the presence of viscosity. Initial low motion amplitudes lead to evaluation of the hydrodynamic performance between a floater with a flat and rounded-hemispherical bottom. Experimental results demonstrated that motion amplitudes can be over predicted by a factor of 2 when neglecting the effects of viscosity.

Second, modifications to the design, fabrication process, and material of a permanent magnet linear generator (PMLG) will be discussed with the aim of increasing both power output and mechanical-to-electrical conversion efficiency. In order to evaluate the performance of the power-take-off unit a dry-bench test was completed which consisted of driving the armature of the PMLG at various frequencies with a fixed motion amplitude. The force signature from the bench test was used to extract the spring, damping, and inertia force coefficients due to the influence of the PMLG. The force coefficients were obtained for various speeds, resistive loads, and magnet coil gap widths. The floater equation of motion was modified to accommodate the influence of the PMLG to predict the coupled system performance. As the damping coefficient was the dominant contribution to the PMLG reaction force, the optimum non time-varying damping values were presented for all frequencies, recovering the well known impedance matching at the coupled resonance frequency. Model-scale tests of the coupled floater-generator system were performed at the UC-Berkeley Model Testing Facility to verify the optimum conditions for energy extraction.

In an effort to further maximize power absorption, nonlinear model predictive control (NMPC) was applied to the model-scale point absorber. The NMPC strategy was set up as a nonlinear optimization problem utilizing the Interior Point OPTimizer (IPOPT) package to obtain the optimal time-varying generator damping from the PMLG. This was accompanied by a latching damper that was allowed to periodically slow the floater velocity in an effort to increase power absorption. The emphasis on this work has been on sub-optimal strategies that limit the power-take-off unit to behave as a generator, thereby minimizing energy return to the waves. It was found that the ideal NMPC strategy required a PTO unit that could be turned on and off instantaneously, leading to sequences where the generator would be inactive for up to 60% of the wave period. Experimental validation of the NMPC included repeating the dry bench test in order to characterize the time-varying performance of the PMLG. This was achieved through the use of mechanical relays to control when the electromagnetic conversion process would be active. After the time-varying performance of the PMLG was characterized the experimental set-up was transferred to the wave tank. The on/off sequencing of the PMLG was tested under regular and irregular wave excitation to validate NMPC simulations using the control inputs obtained from running the controller offline. Experimental results indicate that successful implementation was achieved and the absorbed power was indeed maximized.