A time domain approach for the optimal control of wave energy converter arrays

Abstract

Wave energy converters typically use various control methods to extract energy from ocean waves. The objective of the control system is to optimize the energy extraction process, taking into account the dynamics of the system and the wave conditions. The task of deriving the optimal control laws of wave energy converter arrays for regular and irregular waves using the Pontryagin minimum principle was previously investigated in the literature. The result is a combination between the singular arc and bang-bang control laws. For irregular waves, some complexity arises due to the radiation state-space representation, which requires ignoring the hydrodynamic coupling terms related to the added mass and radiation-damping coefficients; this reduces the computational complexity of the control force but adversely affects the solution's accuracy. Also, the derived control laws are specific to a particular wave condition. Recently, the optimal control of a flexible buoy wave energy converter was derived using the convolution representation for the radiation force. In this work, the optimal control laws of flexible buoy wave energy converters are modified to simulate wave energy converter arrays; then, the results are compared to those obtained by dropping the hydrodynamic radiation coupling terms. Although using a convolution representation adds computational complexity to the optimal control problem, it generates an equation that is generic to any wave condition, can be used with any wave spectrum, and provides an expression for the switching condition.