Energy-maximising control of wave energy converters using a moment-domain representation

Abstract

A B S T R A C TWave Energy Converters (WECs) have to be controlled to ensure maximum energy extraction from waves while considering, at the same time, physical constraints on the motion of the real device and actuator characteristics. Since the control objective for WECs deviates significantly from the traditional reference ''tracking'' problem in classical control, the specification of an optimal control law, that optimises energy absorption under different sea-states, is non-trivial. Different approaches based on optimal control methodologies have been proposed for this energy-maximising objective, with considerable diversity on the optimisation formulation. Recently, a novel mathematical tool to compute the steady-state response of a system has been proposed: the moment-based phasor transform. This mathematical framework is inspired by the theory of model reduction by moment-matching and considers both continuous and discontinuous inputs, depicting an efficient and closed-form method to compute such a steady-state behaviour. This study approaches the design of an energy-maximising optimal controller for a single WEC device by employing the moment-based phasor transform, describing a pioneering application of this novel moment-matching mathematical scheme to an optimal control problem. Under this framework, the energy-maximising optimal control formulation is shown to be a strictly concave quadratic program, allowing the application of well-known efficient real-time algorithms. (N. Faedo). minimise the risk of damage, such an optimisation strategy must take into account the physical limitations of the whole conversion chain. Such an optimisation procedure can be achieved by designing an optimal controller that accomplishes such objectives.A considerable number of optimal control formulations and methods have been studied and developed to maximise the energy extraction process from WECs, with extensive reviews available, for example in Ringwood, Bacelli, and Fusco (2014). One particular popular wave energy control strategy is Model Predictive Control (MPC). The success of MPC on the energy-maximising control is mainly due to its ability to handle physical constraints systematically and within a finite horizon optimisation process. While MPC applied to WECs also involves a mathematical model, a typical receding horizon strategy, and can deal with system constraints, the objective function contrasts significantly with the one related to the usual set-point tracking objective. Rather, a converted energy-maximising objective, consistent with the definition https://doi.

Moment-based constrained optimal control of an array of wave energy converters

“…Recently, a novel energy-maximising optimal control framework for a single WEC has been presented in [1]. This formalism is based on the concept of moment (discussed in Section II), and allows mapping the original optimal control problem into a concave Quadratic Program (QP).…”

“…Then, a computationally efficient calculation of the optimal control law is achieved by state-of-the-art QP solvers [8]. Though [1] accomplishes the energy-maximising objective subject to motion constraints, the mathematical formalism considers only the single-input, single-output (SISO) case, hindering the application of the strategy to the case where an array of WECs is considered. Note that, though one can apply the SISO case of [1] to each isolated device of the array (ignoring the interactions between the WECs composing the farm), this has been already shown to be suboptimal in [7].…”

“…Though [1] accomplishes the energy-maximising objective subject to motion constraints, the mathematical formalism considers only the single-input, single-output (SISO) case, hindering the application of the strategy to the case where an array of WECs is considered. Note that, though one can apply the SISO case of [1] to each isolated device of the array (ignoring the interactions between the WECs composing the farm), this has been already shown to be suboptimal in [7]. In fact, [7] shows that a significant improvement in power absorption can be achieved by considering the corresponding hydrodynamic interactions between devices in the control problem.…”

“…Following the roadmap for a successful WEC commercialisation, and given the desirable properties of the momentbased strategy, we present an extension of the moment-based energy-maximising optimal control framework of [1] to the multiple-input, multiple-output (MIMO) case, for which the hydrodynamic interactions between devices are exploited to extract the maximum energy from a given wave field, subject to both state and input constraints. We show that the desirable properties of the moment-based strategy discussed in [1] are retained in the WEC array case.…”

Model Predictive Control Tuning by Inverse Matching for a Wave Energy Converter

“…In Scruggs et al [6] the optimal controller was found by solving a nonstandard linear quadratic Guassian optimal control problem. Various other control algorithms have been also applied, including dynamic programming [7], pseudo-spectral methods [8], fuzzy logic control [9], shape-based control [10], moment matching [11], and model predictive control [12].…”