The motion of a Wave Energy Converter (WEC) can be described in terms of an integro-differential equation, which involves a convolution product. The convolution term, which accounts for the radiation forces, represents a computational and representational drawback both for simulation, and analysis/design of control strategies. Several studies attempt to find a suitable finite parametric form that approximates the radiation impulse response, to express the equation of motion in the time-domain by a state-space representation. Ideally, this approximated parametric model should behave as closely as possible to the system under analysis, particularly at key frequencies, such as the resonant frequency of the device. This study presents a method to obtain a parametric model of both the force-to-motion dynamics and/or the radiation force convolution term, based on moment-matching. Recent advances in moment-matching, allow the computation of a model that exactly matches the frequency response of the original system at the chosen frequencies, while enforcing specific physical properties of the device, depicting a robust and efficient method to compute a state-space representation for the dynamics of a WEC. The potential of the algorithm is illustrated by numerical examples, and the approximation error is shown to be monotonically decreasing with increasing model order.

The implementation of energy-maximizing control systems (EMCSs) can significantly increase the efficiency and economic viability of resonant wave-energy converters (WECs). To achieve optimal control and drive the WEC into resonance with the incoming wave field, knowledge of the wave excitation force is required. In operational conditions, this quantity is immeasurable and, thus, has to be estimated. This article presents a critical comparison of the available excitation force estimators found in the literature. A reference measurement of the excitation force is determined using computational fluid dynamics (CFD) simulation, allowing an absolute comparison of the different estimation strategies. The estimators are compared based on the required input data, achieved accuracy, computational delay, and estimation time. In total, 11 estimation strategies are compared, with three, in particular, emerging with relatively superior performance.

A Linear Time Invariant (LTI) energy-maximising control strategy for Wave Energy Converters (WECs) is proposed in this paper. Using the fundamental requirement of impedancematching, the controller is tuned to maximise the energy obtained under polychromatic wave excitation. Given the LTI nature of the proposed controller, the design and implementation procedure is significantly simpler than well-established energy-maximising controllers, including state-of-the-art numerical optimisation routines, which are predominant in this field. Additionally, a LTI constraint handling mechanism is provided. The effectiveness of both the LTI control strategy and the constraint handling mechanism are assessed using regular and irregular waves in unconstrained and constrained cases. The resulting performance is compared to those obtained using existing WEC optimal control strategies. Finally, the benefits, in terms of power production, for both the controller and the constraint handling mechanism are explicitly highlighted by means of an application case.

To maximise energy conversion, real-time control of a Wave Energy Converter (WEC) requires knowledge of the present and future excitation force (Fex) acting on the device, which is a non-measurable quantity. The problem of estimation and forecasting of Fex becomes more challenging when arrays of WECs are considered, due to the hydrodynamic interactions in the array. In this paper, a global Fex estimator for a complete WEC array is developed and compared to a set of independent estimators which utilise information local only to each device. A significant question is whether the array of measurements is sufficient to compensate for the greater complexity of the wave field, compared to the isolated body case. The paper shows that the global estimator is always more accurate than the independent estimator, improving up to 45% the estimation accuracy of the independent estimator. Regarding prediction, two different Fex forecasters for a WEC array are compared: a global forecaster, utilising Fex estimates from the full set of array devices, and an independent forecaster, utilising only a local Fex estimate. We demonstrate that the global forecaster achieves more accurate results, not only compared to the independent forecaster, but also compared to the isolated body case.

In this study, we address the issue of real-time energymaximising control for wave energy converters (WECs), by proposing a receding-horizon optimal control framework based on the concept of a moment. This approach is achieved by extending the so-called moment-based framework, recently published in the WEC literature, to effectively solve the associated optimal control problem within a finite time-horizon, allowing for real-time performance, and a straightforward inclusion of the wave excitation force F e estimation and forecasting requirements, which are intrinsic to the wave energy control application. We present a case study, based on a CorPower-like device, subject to both state and input constraints. We show that the proposed strategy can perform almost identically to the ideal performance case, where full knowledge of F e over the time-horizon is assumed available. Moreover, a sensitivity analysis is provided, addressing the impact of wave excitation force estimation and forecasting errors in the computation of the moment-based control input. Two main conclusions can be drawn from this analysis: Forecasting mismatch has a negligible impact on the overall performance of the strategy, while potential differences arising from estimating F e , in particular, phase errors, can substantially impact total energy absorption.