Nonlinear model reduction for wave energy systems: a moment-matching-based approach
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ORIGINAL PAPER
Nonlinear model reduction for wave energy systems: a moment-matching-based approach Nicolás Faedo · Francisco Javier Dores Piuma Giuseppe Giorgi · John V. Ringwood
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Received: 25 June 2020 / Accepted: 13 October 2020 © Springer Nature B.V. 2020
Abstract 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 a systematic nonlinear model reduction by momentmatching framework for WEC systems, capable of providing control-oriented WEC models tailored for the control application, which inherently preserves steadyN. Faedo (B) · J. V. Ringwood Centre for Ocean Energy Research (COER), Department of Electronic Engineering, Maynooth University, Kildare, Ireland e-mail: [email protected] F. J. Dores Piuma Departamento de Ciencia y Tecnología, Universidad Nacional de Quilmes, Bernal, Argentina G. Giorgi Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Turin, Italy
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. Keywords Nonlinear model reduction · Momentmatching · Wave energy conversion · Nonlinear hydrodynamics
1 Introduction Control system technology can impact many aspects of wave energy converters (WECs) design and operation, including device sizing and configuration, maximising energy extraction from waves, and optimising energy conversion in the power take-off (PTO) actuator system [23,33]. To be precise, the central problem in WEC control is to find a technically feasible way to ‘act’ on the device (via the PTO system), so that energy absorption from waves is maximised while minimising the risk of component damage. It is already clear that control technology can enhance WECs performance in a wide range of sea conditions, hence substantially reducing
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the associated levelised cost
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