Optimal Control of Wave Energy Converters

In this dissertation, we address the optimal control of the Wave Energy Converters. The Wave Energy Converters introduced in this study can be categorized as the single body heaving device, the single body pitching device, the single body three degrees of freedoms device, and the Wave Energy Converters array. Different types of Wave Energy Converters are modeled mathematically, and different optimal controls are developed for them. The objective of the optimal controllers is to maximize the energy extraction with and without the motion and control constraints. The development of the unconstrained control is first introduced which includes the implementation of the Singular Arc control and the Simple Model Control. The constrained optimal control is then introduced which contains the Shape-based approach, Pseudospectral control, the Linear Quadratic Gaussian optimal control, and the Collective Control. The wave estimation is also discussed since it is required by the controllers. Several estimators are implemented, such as the Kalman Filter, the Extended Kalman Filter, and the Kalman-Consensus Filter. They can be applied for estimating the system states and the wave excitation force/wave excitation force field. Last, the controllers are validated with the Discrete Displacement Hydraulic system which is the Power Take-off unit of the Wave Energy Converter. The simulation results show that the proposed optimal controllers can maximize the energy absorption when the wave estimation is accurate. The performance of the unconstrained controllers is close to the theoretical maximum (Complex Conjugate Control). Furthermore, the energy extraction is optimized and the constraints are satisfied by applying the constrained controllers. However, when the proposed controllers are further validated with the hydraulic system, they extract less energy than a simple Proportional-derivative control. This indicates the dynamics of the Power take-off unit needs to be considered in designing the control to obtain the robustness

A control system for a constrained two-body wave energy converter

Wave energy can be used to power oceano-graphic buoys. A new switching control strategy is developed in this paper for a two-body heaving wave energy converter that is composed of a floating cylinder and two rigidly connected submerged hemispheres. This control strategy is designed to prevent excessive displacement of the floating buoy that may occur due to the actuator force. This control strategy switches the control between a multi-resonant controller and a nonlinear damping controller, depending on the state of the system, to account for displacement constraints. This control strategy is developed using a one-degree-of-freedom dynamic model for the relative motion of the two bodies. Estimation of the relative motion, needed for feedback control, is carried out using a Kalman filter. Numerical simulations are conducted to select the proper mooring stiffness. The controller is tested with stochastic models of irregular waves in this paper. The performance of the controller with different sea states is discussed. Annual power production using this control strategy is presented based on real data in 2015 published by Martha’s Vineyard Coastal Observatory

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

Pseudo-spectral method to control three-degree-of-freedom wave energy converters

The invention provides optimal control of a three-degree-of-freedom wave energy converter using a pseudo-spectral control method. The three modes are the heave, pitch and surge. A dynamic model is characterized by a coupling between the pitch and surge modes, while the heave is decoupled. The heave, however, excites the pitch motion through nonlinear parametric excitation in the pitch mode. The invention can use a Fourier series as basis functions to approximate the states and the control. For the parametric excited case, a sequential quadratic programming approach can be implemented to numerically solve for the optimal control. The numerical results show that the harvested energy from three modes is greater than three times the harvested energy from the heave mode alone. Moreover, the harvested energy using a control that accounts for the parametric excitation is significantly higher than the energy harvested when neglecting this nonlinear parametric excitation term.https://digitalcommons.mtu.edu/patents/1143/thumbnail.jp

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

Model predictive control of parametric excited pitch-surge modes in wave energy converters

A parametric excitation dynamic model is used for a three degrees-of-freedom (3-DOF) wave energy converter. Since the heave motion is uncoupled from the pitch and surge modes, the pitch-surge equations of motion can be treated as a linear time varying system, or a linear system with parametric excitation. In such case the parametric exciting frequency can be tuned to twice the natural frequency of the system for higher energy harvesting. A parametric excited 3-DOF wave energy converter can harvest more power, for both regular and irregular waves, compared to the linear 3-DOF. For example, in a Bretschneider wave, the harvested energy in the three modes is about 3.8 times the energy harvested in the heave mode alone; while the same device produces about 3.1 times the heave mode energy when using a linear 3-DOF model.https://digitalcommons.mtu.edu/patents/1147/thumbnail.jp

A Numerical Simulation of a Variable-Shape Buoy Wave Energy Converter

Wave energy converters (WECs) usually require reactive power for increased levels of energy conversion, resulting in the need for more complex power take-off (PTO) units, compared to WECs that do not require reactive power. A WEC without reactive power produces much less energy, though. The concept of Variable Shape Buoy Wave Energy Converters (VSB WECs) is proposed to allow continuous shape-change aiming at eliminating the need for reactive power, while converting power at a high level. The proposed concept involves complex and nonlinear interactions between the device and the waves. This paper presents a Computational Fluid Dynamics (CFD) tool that is set up to simulate VSB WECs, using the ANSYS 2-way fluid–structure interaction (FSI) tool. The dynamic behavior of a VSB WEC is simulated in this CFD-based Numerical Wave Tank (CNWT), in open sea conditions. The simulation results show that the tested device undergoes a significant deformation in response to the incoming waves, before it reaches a steady-state behavior. This is in agreement with a low-fidelity dynamic model developed in earlier work. The resulting motion is significantly different from the motion of a rigid body WEC. The difference in the motion can be leveraged for better energy capture without the need for reactive power

Control of Wave Energy Converters Using A Simple Dynamic Model

© 2018 IEEE. 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 suboptimal. 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