skip to main content


The NSF Public Access Repository (NSF-PAR) system and access will be unavailable from 10:00 PM ET on Friday, December 8 until 2:00 AM ET on Saturday, December 9 due to maintenance. We apologize for the inconvenience.

This content will become publicly available on September 2, 2024

Title: A time domain approach for the optimal control of wave energy converter arrays
Wave energy converters typically use various control methods to extract energy from ocean waves. The objective of the control system is to optimize the energy extraction process, taking into account the dynamics of the system and the wave conditions. The task of deriving the optimal control laws of wave energy converter arrays for regular and irregular waves using the Pontryagin minimum principle was previously investigated in the literature. The result is a combination between the singular arc and bang-bang control laws. For irregular waves, some complexity arises due to the radiation state-space representation, which requires ignoring the hydrodynamic coupling terms related to the added mass and radiation-damping coefficients; this reduces the computational complexity of the control force but adversely affects the solution's accuracy. Also, the derived control laws are specific to a particular wave condition. Recently, the optimal control of a flexible buoy wave energy converter was derived using the convolution representation for the radiation force. In this work, the optimal control laws of flexible buoy wave energy converters are modified to simulate wave energy converter arrays; then, the results are compared to those obtained by dropping the hydrodynamic radiation coupling terms. Although using a convolution representation adds computational complexity to the optimal control problem, it generates an equation that is generic to any wave condition, can be used with any wave spectrum, and provides an expression for the switching condition.  more » « less
Award ID(s):
Author(s) / Creator(s):
Date Published:
Journal Name:
Proceedings of the European Wave and Tidal Energy Conference
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. null (Ed.)
    A novel Variable-Shape Buoy Wave Energy Converter (VSB WEC) that aims at eliminating the requirement of reactive power is analyzed in this paper. Unlike conventional Fixed Shape Buoy Wave Energy Converters (FSB WECs), the VSB WEC allows continuous shape-changing (flexible) responses to ocean waves. The non-linear interaction between the device and waves is demonstrated to result in more power when using simple, low-cost damping control system. High fidelity numerical simulations are conducted to compare the performance of a VSB WEC to a conventional FSB WEC, of the same volume and mass, in terms of power conversion, maximum displacements, and velocities. A Computational Fluid Dynamics (CFD) based Numerical Wave Tank (CNWT), developed using ANSYS 2-way fluid-structure interaction (FSI) is used for simulations. The results show that the average power conversion is significantly increased when using the VSB WEC. 
    more » « less
  2. This paper derives a control law within the context of optimal control theory for a heaving wave energy converter (WEC) and presents its implementation procedure. The proposed control assumes the availability of measurements of pressure distribution on the buoy surface, buoy position, and buoy velocity. This control has two main characteristics. First, this control is derived based on a simple dynamic model. The forces on the WEC are modeled as one total force, and hence there is no need to compute excitation or radiation forces. Second, this control can be applied to both linear and nonlinear WEC systems. The derived control law is optimal, yet its implementation requires estimation of some force derivatives which render the obtained control force sub-optimal. Numerical testing demonstrates in this paper that the proposed simple model control can achieve levels of harvested energy close to the maximum theoretical limit predicted by singular arc control in the case of linear WEC systems. 
    more » « less
  3. null (Ed.)
    The wave excitation force is required in some control algorithms of wave energy converters. Excitation force is not, however, directly measurable. Therefore, to obtain excitation force information for control implementation, a number of excitation force estimators have been developed. The estimation performance is usually validated by low-fidelity simulations. This paper assesses the performance of a wave estimator in a Computational Fluid Dynamics (CFD) based Numerical Wave Tank (CNWT), where the estimator collects necessary measurements in-line with the high-fidelity simulation. The proposed simulation framework can be directly applied for a controlled wave energy converter. Numerical simulations are conducted on the implemented estimator, and the estimated excitation force is compared with a benchmark force that is extracted from a diffraction test. 
    more » « less
  4. This paper discusses wave-by-wave near-optimal control of a wave energy device in irregular waves. A deterministic propagation model is used to predict the wave elevation several seconds into the future at the device location. Two prediction approaches are considered. The first is based on a time series being measured over an advancing time window at a particular up-wave location. This approach is here utilized in long-crested irregular waves. The second approach uses successive snapshots of wave elevation measurements over an up-wave area. This approach is found more convenient for multi-directional waves, and is here applied in a bi-directional wave irregular wave field. A small, heaving vertical cylinder reacting against a deeply submerged (i.e. assumed to undergo negligible oscillations) mass is studied under wave-by-wave control. The non-causal feedforward control force required for optimum velocity under a swept-volume constraint is based on the past, current, and predicted wave elevation at the device. Results for time-averaged converted power and displacement/force maxima are obtained for a range of irregular wave conditions. Also presented in addition are energy conversion results with a feedback-alone control force using a multi-resonant control technique. 
    more » « less
  5. The model of a three-degree-of-freedom Wave Energy Converter can be simplified as a linear time-varying system. In this model, the heave mode parametrically excites the pitch mode, which in turn excites the surge mode. The heave mode, however, is independent to the other two modes when the motion is small. The purpose of this paper is to design a controller to maximize the energy harvested over a receding time horizon. We also want to demonstrate that, with proper design of the control, it is possible to exploit this nonlinear coupling between the modes so as to harvest more energy. The controller selected is the linear quadratic Gaussian optimal control. The prediction of excitation forces is constructed based on the estimation where the estimations are obtained by using extended Kalman Filter. The prediction of excitation force is fed into the controller to compute the time-varying linear quadratic optimal control. Constraints on the WEC motion are accounted for in computing the control. The results show that the energy captured by three-degree-of-freedom Wave Energy Converter is 3:56 times the energy extracted in heave mode only. Higher energy harvesting is demonstrated when the linear time-varying model is used in control design. 
    more » « less