Giorgio Bacelli

Numerical Optimal Control of Wave Energy Converters

Energy maximizing control for wave energy converters (WECs) is a nonstandard optimal control problem. While the constrained optimal control problem for WECs has been addressed by model-predictive control strategies, such strategies need to employ cost function modifications due to convexity problems and the algorithms are computationally complex, making real-time implementation difficult. The recently developed family of direct transcription methods offer a promising alternative, since they are computationally efficient and a convex problem results. Moreover, constraints on both the device displacement and velocity, and power take off force, are easily incorporated. Both single-body and multibody device models can be used, as well as arrays of single-body or multibody devices.

Control-Informed Optimal Array Layout for Wave Farms

Somewhat similar to wind farms, commercial wave energy will be realized using farms of devices. However, for wave farms, both constructive and destructive interference may occur between individual devices; whereas, for wind farms, only destructive interference occurs. In order to maximize constructive interference, the layout of the wave farm must be optimized. In addition, power absorption may be improved by applying a control system technology to the farm of devices. As with many applications, there is a tendency in wave energy to separate the design of the array layout from the design of an energy maximizing control system. In this paper, we show that integrating the activities of optimal array layout design and control design are crucial if the full potential of the wave farm is to be realized. In particular, we show that a layout optimized without knowledge of the control system to be used can be inferior to the extent of recovering 40% less energy than a farm layout optimized with knowledge of the control system. This loss is significantly more than the difference in performance between a simple and a very complex control strategy.

Multibody Modelling of Wave Energy Converters Using Pseudo-Spectral Methods With Application to a Three-Body Hinge-Barge Device

Multibody wave energy converters are composed of several bodies interconnected by joints. Two different formulations are adopted to describe the dynamics of multibody systems: the differential and algebraic equations (DAEs) formulation, and the ordinary differential equations (ODEs) formulation. While the number of variables required for the description of the dynamics of a multibody system is greater in the DAE formulation than in the ODE formulation, the ODE formulation involves an extra computational effort in order to describe the dynamics of the system with a smaller number of variables. In this paper, pseudo-spectral (PS) methods are applied in order to solve the dynamics of multibody wave energy converters using both DAE and ODE formulations. Apart from providing a solution to the dynamics of multibody systems, pseudo-spectral methods provide an accurate and efficient formulation for the control of multibody wave energy converters. As an application example, this paper focuses on the dynamic modeling of a three-body hinge-barge device, where wave-tank tests are carried out in order to validate the DAE and ODE models against experimental data. Comparison of the ODE and DAE PS methods against a reference model based on the straightforward (Runge-Kutta) integration of the equations of motion shows that pseudo-spectral methods are computationally more stable and require less computational effort for short time steps.

Estimation of excitation force on wave energy converters using pressure measurements for feedback control

Many of the control strategies for wave energy converters (WECs) that have been studied in the literature rely on the availability of estimates for either the wave elevation or the exciting force caused by the incoming wave; with the objective of addressing this issue, this paper presents the design of a state estimator for a WEC. In particular, the work described in this paper is based on an extended Kalman filter that uses measurements from pressure sensors located on the hull of the WEC to estimate the wave exciting force. Simulation results conducted on a heaving point absorber WEC shows that the extended Kalman filter provides a good estimation of the exciting force in the presence of measurement noise combined with a simplified model of the system, thus making it a suitable candidate for the implementation in an experimental set-up.

Estimation of excitation forces for wave energy converters control using pressure measurements

ABSTRACT Most control algorithms of wave energy converters require prediction of wave elevation or excitation force for a short future horizon, to compute the control in an optimal sense. This paper presents an approach that requires the estimation of the excitation force and its derivatives at present time with no need for prediction. An extended Kalman filter is implemented to estimate the excitation force. The measurements in this approach are selected to be the pressures at discrete points on the buoy surface, in addition to the buoy heave position. The pressures on the buoy surface are more directly related to the excitation force on the buoy as opposed to wave elevation in front of the buoy. These pressure measurements are also more accurate and easier to obtain. A singular arc control is implemented to compute the steady-state control using the estimated excitation force. The estimated excitation force is expressed in the Laplace domain and substituted in the control, before the latter is transformed to the time domain. Numerical simulations are presented for a Bretschneider wave case study.

Multiresonant Feedback Control of a Three-Degree-of-Freedom Wave Energy Converter

For a three-degree-of-freedom wave energy converter (heave, pitch, and surge), the equations of motion could be coupled depending on the buoy shape. This paper presents a multiresonant feedback control, in a general framework, for this type of a wave energy converter that is modeled by linear time invariant dynamic systems. The proposed control strategy finds the optimal control in the sense that it computes the control based on the complex conjugate criteria. This control strategy is relatively easy to implement since it is a feedback control in the time domain that requires only measurements of the buoy motion. Numerical tests are presented for two different buoy shapes: a sphere and a cylinder. Regular, Bretschnieder, and Ochi–Hubble waves are tested. Simulation results show that the proposed controller harvests energy in the pitch-surge-heave modes that is about three times the energy that can be harvested using a heave-only device. This multiresonant control can also be used to shift the energy harvesting between the coupled modes, which can be exploited to eliminate one of the actuators while maintaining about the same level of energy harvesting.