A New methodology for frequency domain analysis of wave energy converters with periodically varying physical parameters




Mosher, Mark

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Within a wave energy converter's operational bandwidth, device operation tends to be optimal in converting mechanical energy into a more useful form at an incident wave period that is proximal to that of a power-producing mode of motion. Point absorbers, a particular classification of wave energy converters, tend to have a relative narrow optimal bandwidth. When not operating within the narrow optimal bandwidth, a point absorber's response and efficiency is attenuated. Given the wide range of sea-states that can be expected during a point absorber's operational life, these devices require a means to adjust, or control, their natural response to maximize the amount of energy absorbed in the large population of non-optimal conditions. In the field of wave energy research, there is considerable interest in the use of non-linear control techniques to this end. Non-linear control techniques introduce time-varying and state dependent control parameters into the point absorber motion equations, which usually motivates a computationally expensive numerical integration to determine the response of the device - important metrics such as gross converted power and relative travels of the device's pieces are extracted through post processing of the time series data. As an alternative, the work presented in this thesis was based on a closed form perturbation based approach for analysis of the response of a device with periodically-varying control parameters, subject to regular wave forcing, in the frequency domain. The proposed perturbation based method provides significant savings in computational time and enables the device's response to be represented in a closed form manner with a relatively small number of solution components - each component is comprised of a complex amplitude and oscillation frequency. This representation of the solution was found to be very concise and descriptive, and to lend itself to the calculation of gross absorbed power and travel constraint violations, making it extremely useful in the automated design optimization process; the methodology allows large number of design iterations, including both physical design and control variables, to be evaluated and conclusively compared. In the development of the perturbation method, it was discovered that the device's motion response can be calculated from an in nite series of second order ordinary differential equations that can be truncated without destroying the solution accuracy. It was found that the response amplitude operator for the generic form of a solution component provides a means to gauge the device's response to a given wave input and control parameter variation, including a gauge of the solution process stability. It is unclear as of yet if this is physical, a result of the solution process, or both. However, for a given control parameter set resulting in an unstable solution, the instability was shown to be, at least in part, a result of the device's dynamics. If the stability concerns can be addressed through additional constraints and updates to the wave energy converter hydrodynamic parameters, the methodology will expand on the commonly accepted boundaries for wave energy converter frequency domain analysis methods and be of much practical importance in the evaluation of control techniques in the field of wave energy converter technology.



Wave Energy, Perturbation Method, Point Absorber