Abstract
We present models and algorithms for choosing optimal locations of wave energy conversion (WEC) devices within an array, or wave farm. The location problem can have a significant impact on the total power of the farm due to the interactions among the incident ocean waves and the scattered and radiated waves produced by the WECs. Depending on the nature of the interference (constructive or destructive) among these waves, the wave energy entering multiple devices, and thus the power output of the farm, may be significantly larger or smaller than the energy that would be seen if the devices were operating in isolation. Our model chooses WEC locations to maximize the performance of a wave farm as measured by a well known performance measure called the q-factor, which is the ratio of the power from an array of N WECs to the power from N WECs operating independently, under the point absorber approximation. We prove bounds for the q-factor based on the eigenvalues of an important data matrix, and provide an analytical optimal solution for the 2-WEC problem. We propose an iterative heuristic for the general problem and discuss the WEC location problem under uncertainty.