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

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

Optimization and Energy Maximizing Control Systems for Wave Energy Converters

In recent years, we have been witnessing great interest and activity in the field of wave energy converters’ (WECs) development, striving for competitiveness and economic viability via increasing power conversion while decreasing costs and ensuring survivability [...

Empowering wave energy with control technology: Possibilities and pitfalls

With an increasing focus on climate action and energy security, an appropriate mix of renewable energy technologies is imperative. Despite having considerable global potential, wave energy has still not reached a state of maturity or economic competitiveness to have made an impact. Challenges include the high capital and operational costs associated with deployment in the harsh ocean environment, so it is imperative that the full energy harnessing capacity of wave energy devices, and arrays of devices in farms, is realised. To this end, control technology has an important role to play in maximising power capture, while ensuring that physical system constraints are respected, and control actions do not adversely affect device lifetime. Within the gamut of control technology, a variety of tools can be brought to bear on the wave energy control problem, including various control strategies (optimal, robust, nonlinear, etc.), data-based model identification, estimation, and forecasting. However, the wave energy problem displays a number of unique features which challenge the traditional application of these techniques, while also presenting a number of control ‘paradoxes’. This review articulates the important control-related characteristics of the wave energy control problem, provides a survey of currently applied control and control-related techniques, and gives some perspectives on the outstanding challenges and future possibilities. The emerging area of control co-design, which is especially relevant to the relatively immature area of wave energy system design, is also covered

CLOSED LOOP ENERGY MAXIMIZING CONTROL OF A WAVE ENERGY CONVERTER USING AN ESTIMATED LINEAR MODEL THAT APPROXIMATES THE NONLINEAR FROUDE-KRYLOV FORCE

Wave energy converters (WECs) exploit ocean wave energy and convert it into useful forms such as electricity. But for WECs to be successful on a large scale, two primary conditions need to be satisfied. The energy generated must satisfy the network requirements, and second, energy flow from waves to the grid needs to be maximized. In this dissertation, we address the second problem. Most control techniques for WECs today use the Cummins\u27 linear model to simulate WEC hydrodynamics. However, it has been shown that under the application of a control force, where WEC motions are amplified, the linear model diverges from actual motions. Hence, it becomes necessary to model the nonlinear motion for realistic energy capture prediction. In this work, it is shown that a closed form energy optimal solution to the nonlinear model requires satisfaction of initial conditions that violate physical restrictions. Numerical optimization based controllers that use physical constraints as a necessary condition require large computation costs and are difficult to implement in real time. To mitigate computation costs for real-time implementation while precisely predicting nonlinear behavior, an efficient method of modelling WECs using an estimated linear model for computing the energy optimal control solution is presented. The estimated linear model is compared against the Cummins\u27 model for accuracy of motion during an uncontrolled case. It is also shown that, there exists a force which results in higher energy extraction than optimal force from Cummins\u27 model when applied to a nonlinear model. Additional analyses are also performed to evaluate the robustness of the proposed method in random and extreme sea states

Optimization and Energy Maximizing Control Systems for Wave Energy Converters

The book, “Optimization and Energy Maximizing Control Systems for Wave Energy Converters”, presents eleven contributions on the latest scientific advancements of 2020-2021 in wave energy technology optimization and control, including holistic techno-economic optimization, inclusion of nonlinear effects, and real-time implementations of estimation and control algorithms

Optimal control of wave energy converters

Wave Energy Converters (WECs) are devices designed to absorb energy from ocean waves. The particular type of Wave Energy Converter (WEC) considered in this thesis is an oscillating body; energy conversion is carried out by means of a structure immersed in water which oscillates under forces exerted by waves. This thesis addresses the control of oscillating body WECs and the objective of the control system is to optimise the motion of the devices that maximises the energy absorption. In particular, this thesis presents the formulation of the optimal control problem for WECs in the framework of direct transcription methods, known as spectral and pseudospectral optimal control. Direct transcription methods transform continuous time optimal control problems into Non Linear Programming (NLP) problems, for which the literature (and the market) offer a large number of standard algorithms (and software packages). It is shown, in this thesis, that direct transcription gives the possibility of formulating complex control problems where realistic scenarios can be taken into account, such as physical limitations and nonlinearities in the behaviour of the devices. Additionally, by means of spectral and pseudospectral methods, it is possible to find an approximation of the optimal solution directly from sampled frequency and impulse response models of the radiation forces, obviating the need for finite order approximate models. By implementing a spectral method, convexity of the NLP problem, associated with the optimal control problem for a single body WEC described by a linear model, is demonstrated analytically. The solution to a nonlinear optimal control problem is approximated by means of pseudospectral optimal control. In the nonlinear case, simulation results show a significant difference in the optimal behaviour of the device, both in the motion and in the energy absorption, when the quadratic term describing the viscous forces are dominant, compared to the linear case. This thesis also considers the comparison of two control strategies for arrays of WECs. A Global Control strategy computes the optimal motion by taking into account the complete model of the array and it provides the global optimum for the absorbed energy. In contrast, an Independent Control strategy implements a control system on each device which is independent from all the other devices. The final part of the thesis illustrates an approach for the study of the effects of constraints on the total absorbed energy. The procedure allows the feasibility of the constrained energy maximisation problem to be studied, and it provides an intuitive framework for the design of WECs relating to the power take-off operating envelope, thanks to the geometrical interpretation of the functions describing both the total absorbed energy and the constraints

NEURAL NETWORK BASED REACTIVE CONTROL OF POINT ABSORBER WAVE ENERGY CONVERTERS

The main objective of this work is to develop a neural-network-based Reactive Control (RC) system for wave energy converters. The ability to maximize the power output of WEC while maintaining operation constraints, which can be physical or thermal, is crucial to the development of deployable control strategies. Having a control method that is robust, which means it handles uncertainty and noise very well, is one of the main performance criteria in evaluating the method. Therefore, this work starts by deriving an averaged WEC model to be simulated in MATLAB/Simulink. Additionally, the concepts of resistive loading control and reactive control (approximate conjugate control) are discussed. A solution to sea state estimation is developed and explained which poses a contribution the current WEC research. This novel technique uses recurrent neural networks (RNNs) with time-series data input to estimate the sea state in real-time. The technique fills the gap of estimating forces based on peak frequencies and also the problem of calculating sea states based on periodical averaged statistical analysis. To complete the methodology, an optimization technique using feed forward neural networks is improved to perform optimization that is proposed to optimize the power output with respect to the sea states. This is done by using the neural network as a cost function while using the physical limitations of the system as a constraint. The neural networks in this work are developed, trained and tested using MATLAB’s Deep Network Designer and Deep Learning Toolbox then imported as a Simulink block to complete the simulation. The results are evaluated for each of the section. First, initial logging of the performance metrics, such as mean power, is done prior to the addition of any neural networks. The accuracy and robustness of the sea state estimation RNN is then discussed. Finally, a comparison between traditional reactive Control optimized and reactive Control is conducted. To summarize the outcome, after experimenting with different datasets and architectures, the RNN is able to estimate sea states in real-time under different initial conditions