UC Berkeley

The wave power resource along the U.S. shelf edge is enormous. It was estimated that in the U.S. the total recoverable wave resource, more than 40% of the total available wave power, could cover around 30% of the electricity used in the country each year. A large variety of wave-energy extraction technologies has been proposed, with relatively few designs reaching commercial scales. Wave farm, an array of wave-energy converters (WECs), has been proposed as a solution for commercializing the wave-energy extraction technology. However, wave-interaction effects among the WEC devices in the farm introduce uncertainties in the estimation of the power production from the wave farm and hence the levelized cost of energy (LCOE). This can present hurdles in promoting wave-energy extraction technology.

This dissertation focuses upon the realistic estimation of the optimal power generation for a wave farm. A semi-analytical method based on potential-flow theory is developed to efficiently obtain the hydrodynamic properties of the devices in a WEC array with the “exact" wave-interference effects taken into account. The newly-derived Haskind relation is applied to multiple floating bodies to obtain the diffraction properties of individual bodies based on the solution to the radiation problem. With the knowledge of the hydrodynamic properties of individual devices, maximal power production from the WEC array is computed for arrays of different configurations in waves of all frequencies and incident angles. However, physical constraints on the system are not able to be accounted for in this phase of modeling.

To investigate the optimal power production of a WEC array in constrained conditions, a constrained optimal control method using model-predictive control (MPC) is developed for an array of heaving point absorbers. Wave-interaction effects among the devices are included in the dynamic model. The cost function of the proposed optimization model for this WEC problem is developed to be convex, which enables the efficient computation of the optimal control outputs for multiple coordinated devices. The proposed MPC is demonstrated for real-time implementation on a single point absorber and applied to a point-absorber array. Results show that with constraints on the motion amplitudes of the devices and the power take-off forces considered, the array would produce less power than the case that they were operated individually in isolation in the majority of wave conditions. Effects of the spacing among devices, wave-incidence angle, and array configurations on the power performance are discussed and compared to those predicted by the frequency-domain analysis where constraints were not applied.

Furthermore, a method is proposed to implement the optimal control force obtained by the MPC, using an in-house designed permanent magnetic linear generator (PMLG). The proposed MPC needs to use the PTO force as the optimizing variable to attain the convex formulation of the optimization problem, which results in reactive power defined as the power flowing from the PTO system to the absorber. This would require the PTO to be both a generator and a motor and would significantly complicate the PTO design. To resolve this issue, an additional constraint is added to the PTO force in the optimization problem such that the reactive power can be eliminated and the convexity of the problem can be retained. The optimal PTO force obtained by this modified MPC is then realized by using the PMLG with a time-varying damping. Simulation results are presented for a three-device array with the optimal PTO forces implemented by the PMLG, operated in irregular sea states at seven sites in the west coast of the U.S.

In conclusion, this dissertation developed a set of tools to reduce uncertainties in evaluating the annual power production of a WEC array. Results show that wave-interaction effects appear to be destructive for common sea states in the west coast of the U.S., with physical constraints of the systems considered. The loss of absorbed power caused by the wave-interference effects is less than 5% when the spacing among devices is larger than 3 body diameters. Considering the permitted area of occupancy, mooring-line arrangements, and reduction of production cost with the increase of the array size, we conclude that a relatively close-spacing wave farm consisting of more than 10 devices can be beneficial to the commercialization of the wave-energy extraction technology.