Optimal Constrained Control of Arrays of Wave Energy Converters

Abstract

Wave Energy Converters (WECs) are designed to be deployed in arrays, usually in a limited space, to minimize the cost of installation, mooring, and maintenance. Control methods that attempt to maximize the harvested power often lead to power flow from the WEC to the ocean, at times, to maximize the overall harvested power from the ocean over a longer period. The Power Take-Off (PTO) units that can provide power to the ocean (reactive power) are usually more expensive and complex. In this work, an optimal control formulation is presented using Pontryagin’s minimum principle that aims to maximize the harvested energy subject to constraints on the maximum PTO force and power flow direction. An analytical formulation is presented for the optimal control of an array of WECs, assuming irregular wave input. Three variations of the developed control are tested: a formulation without power constraints, a formulation that only allows for positive power, and finally, a formulation that allows for finite reactive power. The control is compared with optimally tuned damping and bang–bang control.