The analysis and control of ocean Wave Energy Converters (WECs) requires time domain models that often lack certainty. In many advanced control strategies, the wave excitation force is key to determining the control input. However, it is often difficult to measure the excitation force acting on a WEC. The use of Kalman filters to estimate the wave excitation force based on readily available measurement data can potentially fill the gap between the development of WEC control strategies and the data that is available. This work attempts to reduce the barriers to WEC deployments through validating methods of estimating and predicting the wave excitation force and through the development of systematic methods of system identification for WECs.
An extended Kalman filter (EKF) is implemented for observing the dynamic states and estimating the viscous drag coefficient of a heaving WEC float in irregular waves. Numerical data was generated to recreate the conditions of a wave tank test performed on a 1:10 scale wave energy conversion system to validate the identification of the viscous drag coefficient. Three lumped parameter models were evaluated for use in the EKF. A systematic estimate of the process noise covariance based on the steady state response of the heaving object and the incident wave was implemented.
The EKF is then applied to experimental wave tank data for a heaving semi-submerged float to assess the ability of the Kalman filter to estimate wave excitation force. Two different estimation methods are described. The first method relies on directly including the excitation force as a state in the first order dynamics—which allows the “random walk” of the Kalman filter to identify an estimate of the excitation force. The second method of estimation involves modeling the wave excitation force as a harmonic oscillator comprised of sinusoidal components. Both methods are evaluated for a variety of incident waves and additional sensitivity analyses are performed to investigate the susceptibility of these estimation methods to changes in the model, measurement noise, and sampling rate.
Autoregressive methods are utilized to predict the wave excitation force through the use of estimated wave excitation force data, since they can be implemented in real time to adapt to changing conditions. The two models evaluated in this work are AutoRegressive (AR) and AutoRegressive with eXogenous inputs (ARX) models, which describes the wave propagation between two devices. The EKF incorporated nonlinear heave models of each body to estimate the wave excitation force, which was formulated as a harmonic disturbance to each system.
The drag identification and state observation capabilities of an extended Kalman are shown to be effective with limited sampled data and imperfect estimations of the process noise covariance. Some simplified models are shown to be effective if only state identification is needed, but a detailed model is needed for parameter identification. With the use of a sufficiently detailed model the EKF is shown to be able to identify a time varying drag coefficient of a semi-submerged floating object. The autoregressive excitation force prediction methods are evaluated for a variety of incident waves and additional sensitivity analyses are performed to investigate the susceptibility of these estimation methods to changes in the model, measurement noise, and sampling rate. The combination of the EKF and the autoregressive models presents an opportunity to evaluate the prediction capabilities of what can be currently implemented on board WECs in real time. Therefore, there is no need for of-fline training or post-processed filtering of the incident wave. The ARX model incorporating excitation force data from other deployed bodies (the exogenous input) is shown to significantly improve the performance of the wave excitation force prediction. It is concluded that WECs in a wave farm may be able to improve their energy harvesting performance through enhancing their prediction capabilities by using wave estimation data gathered from other WECs.
Major contributions of this work include: experimental validations of various WEC models, implementation of a nonlinear Kalman filter with WEC models, and the experimentally validated estimation and prediction of the wave excitation force using methods that can be implemented on a deployed WEC.