Optimal control and model reduction for wave energy systems: A moment-based approach

Following the sharp increase in the price of traditional fossil fuels, in combination with issues of security of supply, and pressure to honor greenhouse gas emission limits, much attention has turned to renewable energy sources in recent years. Ocean wave energy is a massive and untapped resource, which can make a valuable contribution towards a sustainable, global, energy mix. Despite the fact that ocean waves constitute a vast resource, wave energy converters (WECs) have yet to make significant progress towards commercialisation. One stepping stone to achieve this objective is the availability of appropriate control technology, suchthatenergyconversionisperformedaseconomicallyaspossible,minimisingthedelivered energy cost, while also maintaining the structural integrity of the device, minimising wear on WEC components, and operating across a wide range of sea conditions. Suitable energy-maximising control technology depends upon the availability of two fundamental ‘pieces’: A control-oriented dynamical model, describing the motion of the WEC, and a model-based optimal control framework, able to efficiently compute the corresponding energy-maximising control law, subject to a set of constraints, defined according to the physical limitations of the device. FollowingtherequirementsforsuccessfulWECcontrol,andbothusingandextendingkeytools arising from the framework of model reduction by moment-matching, this thesis presents two main contributions. Firstly, this monograph proposes a comprehensive moment-based model reduction framework, tailored for WEC systems, addressing linear and nonlinear model reduction cases, providing a systematic method to compute control-oriented models from complex target structures. These approximating models inherit steady-state response characteristics of the target system, via the proposed moment-matching reduction framework. Secondly, by recognising that, besides being a powerful model reduction tool, the parameterisation of the steady-state response of a system in terms of moment-based theory can be explicitly used to transcribe the energy-maximising control problem to a finite-dimensional nonlinear program, a comprehensive moment-based optimal control framework, tailored for WEC systems, is proposed. This framework considers both linear and nonlinear optimal control cases, while also including robust solutions with respect to both system, and input uncertainty, providing an efficient method to compute the energy-maximising control law for WECs, under different modelling assumptions. Throughout this thesis both model reduction, and optimal control frameworks, are presented for a general class of WEC devices, and their performance is analysed via multiple case studies, considering different devices, under different sea state conditions

Hydrodynamic Model Fitting for Wave Energy Applications Using Moment-Matching: A Case Study

Several methods have been developed to identify a parametric model thatrepresents the radiation force convolution term in Cummins’ equation.The reason behind such an approximation is twofold: obtaining a modelwith less computational (effort) requirements, and easing model-basedcontrol design procedures. In this paper, a case study on the paramet-ric approximation of such a convolution term using frequency-domaindata is considered, based on recent advances in model order reductionby moment-matching. Both the force-to-motion and radiation impulseresponse dynamics are considered. The advantages of a moment-basedstrategy are discussed, while providing a comparison with well-knownexisting methods

A control design framework for wave energy devices

This paper presents an integrated framework for the design of wave energy control systems, considering the totality of the design process as well as any ancillary functions required, such as model reduction, excitation force estimation, etc. In particular, we propose the moment-based mathematical framework as an integrated environment which allows a smooth transition between modelling and control activities, as well as providing a framework to consider optimal rejection of modelling errors or errors in excitation force estimation. The paper provides an overview of the framework, also containing an illustrative case study to demonstrate a likely pathway through the framewor

A Critical Comparison Between Parametric Approximation Methods for Radiation Forces in Wave Energy Systems

Within the ocean engineering literature, and, particularly, within the wave energy research and hydrodynamic fields, different methods can be found that aim to identify a finite-order parametric model to represent the radiation force convolution term of the well-known Cummins’ equation. Such an approximation process is required for several reasons: firstly, to obtain a mathematical representation that requires low computational effort and, secondly, to ease the model-based control/estimation design procedures. Recently, a new Matlab toolbox has been released to obtain a parametric approximation of such a convolution term based on moment-matching. This paper aims to compare this new moment-matching-based application, with other well-established software. This comparison is based not only on the quality of the approximation, but also on the preservation of the intrinsic physical properties of radiation forces. Three different case studies are used as a basis for the comparison

Passivity preserving moment-based finite-order hydrodynamic model identification for wave energy applications

The dynamics of a Wave Energy Converter (WEC) are described in terms of an integrodifferential equation, particularly, of the convolution class. This convolution term, which is associated with fluid memory effects of the radiation forces acting on the WEC, represents a major drawback both for simulation, analysis and control design for WECs. Recently, a moment-matching based method to approximate this convolution term by a parametric model was presented in (Faedo et al. 2018). Such a technique allows the computation of a model that can match exactly the frequency response of the original system at a set of chosen frequencies. Though the models computed by this strategy are almost always inherently passive, the proposed method does not specifically ensure passivity, which is one of the main physical properties of the radiation subsystem. This paper describes an extension of the moment-based methodology presented in (Faedo et al. 2018) which guarantees a passive finite-order representation for the radiation kernel based on moment-matching. Moreover, we illustrate the applicability of the method by the means of a numerical example with a particular WEC

Parametric representation of arrays of wave energy converters for motion simulation and unknown input estimation: A moment-based approach

When it comes to parameterisation of dynamical models for arrays of Wave Energy Converters (WECs), the most used approach, within the wave energy literature, provides a state-space representation whose order (dimension) increases quadratically with the number of devices composing the WEC array. This represents a major drawback for key WEC design elements, such as motion simulation and unknown input estimation, being the latter essential to effectively maximise energy extraction from ocean waves. We present herein a multi-input, multi-output (MIMO) parameterisation strategy based on a system-theoretic interpretation of moments. The state-space representations computed with this moment-based approach exactly match the steady-state behaviour of the target WEC system at specific (user-selected) interpolation points, providing efficient low dimensional models that can accurately represent the input-output dynamics of WEC arrays. Moreover, we show that there exists an intrinsic connection between wave excitation force estimation strategies and the moment-based parameterisation method proposed in this paper. We exploit this mathematical correlation to provide low order models that deliver the same degree of wave excitation force estimation accuracy to that obtained by implementing the currently-used parameterisation methods, with mild computational requirements. The performance of the strategy is analysed in terms of a case study, considering a WEC array composed of state-of-the-art CorPower-like devices, for both WEC motion simulation and wave excitation force estimation scenarios

Simple Controllers forWave Energy Devices Compared

The design of controllers for wave energy devices has evolved from early monochromatic impedance-matching methods to complex numerical algorithms that can handle panchromatic seas, constraints, and nonlinearity. However, the potential high performance of such numerical controller comes at a computational cost, with some algorithms struggling to implement in real-time, and issues surround convergence of numerical optimisers. Within the broader area of control engineering, practitioners have always displayed a fondness for simple and intuitive controllers, as evidenced by the continued popularity of the ubiquitous PID controller.Recently, a number of energy-maximising wave energy controllers have been developed based on relatively simple strategies, stemming from the fundamentals behind impedance-matching. This paper documents this set of (5) controllers, which have been developed over the period 2010?2020, and compares and contrasts their characteristics, in terms of energy-maximising performance,the handling of physical constraints, and computational complexity. The comparison is carried out both analytically and numerically, including a detailed case study, when considering a state-of-the-art CorPower-like device.Fil: García Violini, Diego Demián. Universidad Nacional de Quilmes. Departamento de Ciencia y Tecnología; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Faedo, Nicolás Ezequiel. Politecnico di Torino; ItaliaFil: Jaramillo Lopez, Fernando. Maynooth University; IrlandaFil: Ringwood, John V.. Maynooth University; Irland

Wave Energy Control Systems: Robustness Issues

While traditional feedback control systems enjoy relatively good sensitivity properties, energy maximising wave energy converter (WEC) control systems have particular characteristics which challenge the application of traditional feedback and robust control methods. In particular, the relationship between plant and controller is largely defined by the need to maximise power transfer, and the controller contains a feedforward component which is difficult to robustify. Typically, WEC control systems are based on linear model descriptions, but this belies the true nonlinearity of WEC hydrodynamics (particularly under controlled conditions) and the associated power take-off (PTO) system. This paper examines two popular WEC control structures and examines the sensitivity of these structures to parameter variations, both in terms of closed-loop transfer functions and power absorbed. Some recommendations are also given on which WEC parameters need to be modelled with high accuracy

Data-based modelling of arrays of wave energy systems:Experimental tests, models, and validation

One of the key steps towards economic feasibility of wave energy conversion technology concerns scaling up to farms of multiple devices, in the attempt to reduce installation costs by sharing infrastructure, and a consequent drop in levelised cost of energy. Moreover, whenever wave energy systems are deployed in proximity (in so-called arrays), the exploitation of the hydrodynamic interactions between single devices is fully enabled, potentially increasing the final energy outcome. To achieve this in real (operational) time, the employed energy-maximising control strategies require control-oriented array models, able to efficiently describe the dynamics of these interconnected systems in a representative fashion. This can be, nonetheless, a difficult task when considering first principles alone, under small motion assumptions, for modelling purposes. Recognising the uncertainty associated to array numerical models obtained from the linearisation of simplified system equations around their equilibria, this paper presents models of several array configurations identified following a frequency domain approach on the basis of experimental data. Tailored tests on laboratory-scale devices have been designed and conducted in the Aalborg University (Denmark) wave tank facility, with the purpose of performing representative system identification of the wave energy systems arrays. The obtained models are validated on different representative sea states configurations, in controlled and uncontrolled motion operational conditions. The validation results are fully discussed and analysed in terms of standard error measures and time lag, while the obtained models are made freely accessible via a linked repository (named OCEAN), in the attempt to openly provide validated models for different array configurations.</p

A Broadband Time-Varying Energy Maximising Control for Wave Energy Systems (LiTe-Con+): Framework and Experimental Assessment

Motion of wave energy converters (WECs) is usually exaggerated as a consequence of the application of control strategies for energy absorption maximisation. With the aim of preserving the physical integrity of the devices, constraint handling mechanisms, as part of the underlying control strategies, are considered a key component. Recent developments in wave energy control include a linear time-invariant-based controller presented in the literature as LiTe-Con, which provides a simple constraint handling mechanism. However, this handling method can lead to conservative performance in certain scenarios. To overcome such limitations, this study presents a time-varying methodology for an online adaptation of the constraint handling mechanism in LiTe-Con, while preserving its original simplicity and efficiency. Experimental assessment of the presented control methodology is provided in this study, using a broad range of operating conditions. Results show that the presented control strategy (LiTe-Con+) exceeds the performance achievable with the original LiTe-Con. Additionally, the benefits of LiTe-Con+, such as low computational demand, technical versatility, and impressive performance level are highlighted.Fil: García Violini, Diego Demián. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Quilmes. Departamento de Ciencia y Tecnología; Argentina. Maynooth University; IrlandaFil: Pena Sanchez, Yerai. Universidad del País Vasco; EspañaFil: Faedo, Nicolás Ezequiel. Politecnico di Torino; ItaliaFil: Ferri, Francesco. Aalborg University; DinamarcaFil: Ringwood, John V.. Maynooth University; Irland