New Perspectives on Wave Energy Converter Control

This work examines some of the fundamental problems behind the control of wave energy converters (WECs). Several new perspectives are presented to aid the understanding of the problem and the interpretation of the literature. The first of these is a group of methods for classifying control of WECs. One way to classify control is to consider the stage of power transfer from the wave to the final energy carrier. Consideration of power transfer can also be used to classify WECs into families. This approach makes it possible to classify all WECs, including those that had previously eluded classification. It also relates the equations of motion of different classes of WECs to a generalised equation of motion. This in turn clarifies why some types of control are suited to some WECs, but not others. These classification systems are used to demarcate the boundary for the theoretical work that follows. The theory applies to WECs with governing equations of motion that are linear, and to control systems that are linear, aim to maximise power, and which regulate the PTO stage of power flow. Another important perspective is the new wet and dry oscillator paradigm, which is used to differentiate between frequency domain modelling and a commonly used technique, monochromatic modelling. This distinction is necessary background for many of the new ideas discussed. It is used to resolve an ongoing debate in wave energy research: whether frequency domain modelling can be applied to cases that are not monochromatic. It is the key to an extension to the theory of capture width, a widely used performance indicator. This distinction is also the rationale behind an improved method of presenting frequency domain results: the frequency responses due to both monochromatic and polychromatic forcing are represented on the same graph. These responses are different because the optimal control problem is acausal, a topic that is also discussed in depth. This visual tool is used to investigate and confirm various ideas about the control of WECs, and to demonstrate how the newly redefined capture width encapsulates the essential control problem of WECs. The optimal control problem is said to be acausal because information about the future is required to achieve optimal control. Another vantage point offered is that of the duration of the prediction interval required for optimal control. This is given by a new parameter emerging from this work, which has been termed the premonition time. The premonition time depends on the amount of knowledge required, which is determined by the geometry of the WEC, and the amount of information available, which is largely determined by the bandwidth of the sea state. The new perspectives introduced are the various systems of classification, the wet and dry oscillator paradigm, the presentation of monochromatic and polychromatic results on the same axes, premonition time, and the revised theory on capture width. These are all used to discuss the interrelationship between WEC geometry, the control strategy and the sea-state. The opportunities for, and limitations of, the use of intelligent control techniques such as artificial neural networks are discussed. The potential contribution of various control strategies and associated design principles is explored. This discussion culminates in a series of recommendations for control strategies that are suited to each class of WEC, and for the areas of research that have the potential to bring about the greatest reductions in the cost of harnessing energy from sea waves. Declaration of originality I hereby declare that the research recorded in this thesis and the thesis itself was composed and originated entirely by myself in the School of Engineering at The University of Edinburgh, unless otherwise stated. This work has not been submitted for any other degree or professional qualification.