Optimal Active Control of a Wave Energy Converter

Abstract-This paper investigates optimal active control schemes applied to a point absorber wave energy converter within a receding horizon fashion. A variational formulation of the power maximization problem is adapted to solve the optimal control problem. The optimal control method is shown to be of a bang-bang type for a power take-off mechanism that incorporates both linear dampers and active control elements. We also consider a direct transcription of the optimal control problem as a general nonlinear program. A variation of the projected gradient optimization scheme is formulated and shown to be feasible and computationally inexpensive compared to a standard NLP solver. Since the system model is bilinear and the cost function is non-convex quadratic, the resulting optimization problem is not a convex quadratic program. Results will be compared with an optimal command latching method to demonstrate the improvement in absorbed power. Time domain simulations are generated under irregular sea conditions

Multi-resonant feedback control of multiple degree-of-freedom wave energy converters

Multi-resonant control of a 3 degree-of-freedom (heave-pitch-surge) wave energy converter enables energy capture that can be in the order of three times the energy capture of a heave-only wave energy converter. The invention uses a time domain feedback control strategy that is optimal based on the criteria of complex conjugate control. The multi-resonant control can also be used to shift the harvested energy from one of the coupled modes to another, enabling the elimination of one of the actuators otherwise required in a 3 degree-of-freedom wave energy converter. This feedback control strategy does not require wave prediction; it only requires the measurement of the buoy position and velocity.https://digitalcommons.mtu.edu/patents/1149/thumbnail.jp

A new latching control technology for improving wave energy conversion

Extracting wave energy from seas has been proven to be very difficult although various technologies have been developed since 1970s. Among the proposed technologies, only few of them have been actually progressed to the advanced stages such as sea trials or pre-commercial sea trial and engineering. One critical question may be how we can design an efficient wave energy converter or how the efficiency of a wave energy converter can be improved using optimal and control technologies, because higher energy conversion efficiency for a wave energy converter is always pursued and it mainly decides the cost of the wave energy production. In this first part of the investigation, some conventional optimal and control technologies for improving wave energy conversion are examined in a form of more physical meanings, rather than the purely complex mathematical expressions, in which it is hoped to clarify some confusions in the development and the terminologies of the technologies and to help to understand the physics behind the optimal and control technologies. As a result of the understanding of the physics and the principles of the optima, a new latching technology is proposed, in which the latching duration is simply calculated from the wave period, rather than based on the future information/prediction, hence the technology could remove one of the technical barriers in implementing this control technology. From the examples given in the context, this new latching control technology can achieve a phase optimum in regular waves, and hence significantly improve wave energy conversion. Further development on this latching control technologies can be found in the second part of the investigation

Optimal control for a self-reacting point absorber: A one-body equivalent model approach

International audienceThis paper deals with the optimal control of a self-reacting Wave Energy Converter (WEC) where the reaction force is obtained using a damping-plate. Model Predictive Control (MPC) is applied for unconstrained and constrained input control cases. Objective function attempting to optimise the power generation is directly formulated as an absorbed power maximisation problem and thus no optimal references, such as buoy and/or spar velocity, is required. Moreover, rather than using the full WEC model in the optimisation problem which can be time-consuming, and because of linear assumptions, we propose the use of a phenomenologically one-body equivalent model derived using the Thévenin 's theorem. Index Terms—wave energy converter, phenomenologically one-body equivalent model, optimal control, model predictive control

Optimal control of wave energy converters

A wave energy converter and method for extracting energy from water waves maximizes the energy extraction per cycle by estimating an excitation force of heave wave motion on the buoy, computing a control force from the estimated excitation force using a dynamic model, and applying the computed control force to the buoy to extract energy from the heave wave motion. Analysis and numerical simulations demonstrate that the optimal control of a heave wave energy converter is, in general, in the form of a bang-singular-bang control; in which the optimal control at a given time can be either in the singular arc mode or in the bang-bang mode. The excitation force and its derivatives at the current time can be obtained through an estimator, for example, using measurements of pressures on the surface of the buoy in addition to measurements of the buoy position. A main advantage of this approximation method is the ease of obtaining accurate measurements for pressure on the buoy surface and for buoy position, compared to wave elevation measurements.https://digitalcommons.mtu.edu/patents/1146/thumbnail.jp

Optimal damping profiles for a heaving buoy wave-energy converter

This paper explores optimal damping profiles for a heaving buoy wave energy converter (WEC). The approach is mathematical and the model of Eidsmoen (1995) is used as a basis. In order to permit analytical development, the model is initially simplified and an optimal damping profile is determined using numerical optimization. Having found the optimal damping profile, a semi-analytical solution methodology is developed to determine the optimal damping parameters. Finally, the procedure is validated on the original model and some aspects related to the control problem are addressed

Stochastic Control of Inertial Sea Wave Energy Converter

The ISWEC (inertial sea wave energy converter) is presented, its control problems are stated, and an optimal control strategy is introduced. As the aim of the device is energy conversion, the mean absorbed power by ISWEC is calculated for a plane 2D irregular sea state. The response of the WEC (wave energy converter) is driven by the sea-surface elevation, which is modeled by a stationary and homogeneous zero mean Gaussian stochastic process. System equations are linearized thus simplifying the numerical model of the device. The resulting response is obtained as the output of the coupled mechanic-hydrodynamic model of the device. A stochastic suboptimal controller, derived from optimal control theory, is defined and applied to ISWEC. Results of this approach have been compared with the ones obtained with a linear spring-damper controller, highlighting the capability to obtain a higher value of mean extracted power despite higher power peaks