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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. 

Wave Energy Converters (WEC) are deployed in arrays to improve the overall quality of the delivered power to the grid and reduce the cost of power production by minimizing the cost of design, deployments, mooring, maintenance, and other associated costs. WEC arrays often contain devices of identical dimensions and modes of operation. The devices are deployed in close proximity, usually having destructive inter-device hydrodynamic interactions. However, in this work, we explore optimizing the number of devices in the array and concurrently, the dimensions of the individual devices (heterogeneous) to achieve better performance compared to an array of identical devices (homogeneous) with comparable overall submerged volume. A  techno-economic objective function is formulated to measure the performance of the array while accounting for the volume of material used by the arrays. The power from the array is computed using a time-domain array dynamic model and an optimal constrained control. The hydrodynamic coefficients are computed using a semi-analytical method to enable computationally efficient optimization. The Hidden Gene Genetic Algorithm (HGGA) formulation is used in this optimization problem.  During the optimization, tags are assigned to genes to determine whether they are active or hidden. An active gene simulates an active WEC device in the heterogeneous array, while the hidden gene results in a reduction in the total number of devices in the array compared with the homogeneous array. The volume of the heterogeneous array is constrained to be close to that of the homogeneous array. These hidden tags do not exclude the associated devices from the optimization process; these devices keep evolving with the active devices as they might become active in subsequent generations. Heterogeneous arrays were found to perform better than homogeneous arrays.