Nonlinear model reduction for wave energy systems: a moment-matching-based approach

Wave energy converters (WECs) inherently require appropriate control system technology to ensure maximum energy absorption from ocean waves, consequently reducing the associated levelised cost of energy and facilitating their successful commercialisation. Regardless of the control strategy, the definition of the control problem itself depends upon the specification of a suitable WEC model. Not only is the structure of the model relevant for the definition of the control problem, but also its associated complexity: given that the control law must be computed in real-time, there is a limit to the computational complexity of the WEC model employed in the control design procedure, while there is also a limit to the (analytical) complexity of mathematical models for which a control solution can be efficiently found. This paper presents asystematicnonlinear model reduction bymoment-matchingframework for WEC systems, capable of providing control-oriented WEC models tailored for the control application, which inherently preserves steady-state response characteristics. Existence and uniqueness of the associated nonlinear moment for WECs are proved in this paper, for a general class of systems. Given that the definition of nonlinear moments depends upon the solution of a nonlinear partial differential equation, an approximation framework for the computation of the nonlinear moment is proposed, tailored for the WEC application. Finally, the use and capabilities of the framework are illustrated by means of case studies, using different WEC systems, under a variety of wave conditions.