Study on Dynamic Stability of Single Floating Pier Under Waves

Considering the upper structure restraint effect of the floating bridge, the diffraction effect and radiation effect of linear monochromatic waves, the dynamic response equation of floating pier is derived and the factors affecting the dynamic stability of the floating pier are analyzed in this paper. Based on the theory of potential flow, the calculation domain is divided into the interior region and the exterior region. The wave diffraction and radiation problems are solved by the matched eigenfunction expansion method (MEEM). After obtaining the wave excitation force, additional mass and radiation damping coefficient, considering the restraint effect of the upper structure of the floating bridge, the motion differential equation of the floating pier is established, and the response amplitude operator (RAOs) of the floating pier is obtained. The effects of span, mass and stiffness of upper structure, as well as the draft depth, size and net height of floating pier on dynamic stability of floating pier under wave are analyzed. The results show that the increase in the span of upper structure will significantly increase the peak RAOs of sway and heave, and the increase in stiffness is helpful to reduce the peak RAOs of sway and heave. The increase of the floating pier radius can reduce the heave RAO, and the net height on the water surface of the floating pier increases the heave and roll.

Wave Excitation Force Estimation for a Multi-DoF WEC via a Cubature Kalman Filter: Design and Preliminary Results

This paper presents the design and implementation of a wave excitation force estimator based on the cubature Kalman filter (CKF) for a CETO 6, a submersed wave energy converter controlled using three power take-off systems attached to the tether lines. Wave excitation force estimation is required by many advanced wav energy converter (WEC) control approaches. However, contrary to the single degree-of-freedom (1-DoF) case, the literature on the design of wave estimators is quite scarce for devices with multiple degrees-of-freedom. The advantages of CKF wave estimator described in the paper are its performance and ease of tuning when working with a high-order system, as it is the case for the 6-DoF linear model used for the design. Preliminary results for all the 6 directions are presented in nominal conditions and also in mismatch conditions, where the estimator is applied to a full nonlinear model of the system, under the action of long-crested and short-crested waves.

Real-Time Wave Excitation Forces Estimation: An Application on the ISWEC Device

Optimal control strategies represent a widespread solution to increase the extracted energy of a Wave Energy Converter (WEC). The aim is to bring the WEC into resonance enhancing the produced power without compromising its reliability and durability. Most of the control algorithms proposed in literature require for the knowledge of the Wave Excitation Force (WEF) generated from the incoming wave field. In practice, WEFs are unknown, and an estimate must be used. This paper investigates the WEF estimation of a non-linear WEC. A model-based and a model-free approach are proposed. First, a Kalman Filter (KF) is implemented considering the WEC linear model and the WEF modelled as an unknown state to be estimated. Second, a feedforward Neural Network (NN) is applied to map the WEC dynamics to the WEF by training the network through a supervised learning algorithm. Both methods are tested for a wide range of irregular sea-states showing promising results in terms of estimation accuracy. Sensitivity and robustness analyses are performed to investigate the estimation error in presence of un-modelled phenomena, model errors and measurement noise.

Experimental Assessment of the IFPEN Solution to the WEC Control Competition

This paper describes the experimental assessment of the solution developed by IFP Energies nouvelles (IFPEN) for the WEC Control Competition (WECCCOMP), a benchmark devised to compare energy-maximizing controllers for wave energy converters (WECs). For the first round of the competition, carried out in simulation with WEC-Sim, IFPEN had submitted an MPC-based solution, which eventually scored best among the contestants, with respect to the energy-related criterion defined by the organizers and computed on a set of six irregular waves. For the second round of the competition, the performance of this MPC solution has been assessed in a tank test situation, on the same Wavestar-like scale device that had been simulated in WEC-Sim. The paper first recalls the features of the control solution implemented for the competition, an offline-tuned weighted-QP MPC algorithm using short-term prediction from present and past wave excitation force estimates. Then, the major steps of the test plan are described and control design choices are explained. Finally, the experimental results in closed loop are presented. Despite noise and an imperfectly controlled PTO actuator, IFPEN’s MPC solution proves efficient and robust: its experimental performance in terms of harvested electrical energy is in accordance with the nominal results obtained in simulation using the linear design model, and this, for different realizations of each sea state. This performance has allowed the IFPEN team to win the competition also at the experimental stage.