Model Predictive Control of Buoy Type Wave Energy Converter

Abstract

The paper introduces the Wavestar wave energy converter and presents the implementation of model predictive controller that maximizes the power generation. The ocean wave power is extracted using a hydraulic electric generator which is connected to an oscillating buoy. The power generator is an additive device attached to the buoy which may include damping, stiffness or similar terms hence will affect the dynamic motion of the buoy. Therefore such a device can be seen as a closed-loop controller. The objective of the wave energy converter is to harvest as much energy from sea as possible. The straight forward solution to this maximization problem is achieved by maximizing the instantaneous range of motion of the buoy. The buoy as a single degree of freedom oscillator will undergo its maximum movements when it is in resonance with the sea state. Hence the best solution to the problem is achieved by forcing this condition. In the paper the theoretical framework for this principal is shown. The optimal controller requires information of the sea state for infinite horizon which is not applicable. Model Predictive Controllers (MPC) can have finite horizon which crosses out this requirement. This approach is then taken into account and an MPC controller is designed for a model wave energy converter and implemented on a numerical example. Further, the power outtake of this controller is compared to the optimal controller as an indicator of the performance of the designed controller.

Model Predictive Control of a Wave Energy Converter with Discrete Fluid Power Power Take-Off System

“…Recently, WPEA's based on the idea of Model Predictive Control (MPC) have attained increasing focus from the wave energy research community, see e.g., [4][5][6][7][8][9][10][11], and initial results are encouraging: MPC may lead to increased energy output of a WEC compared to e.g., reactive control WPEA. In the early work of [4,6,8], a linear MPC has been developed and simulated on ideal PTO systems harvesting energy of point absorber WEC's.…”

“…In the early work of [4,6,8], a linear MPC has been developed and simulated on ideal PTO systems harvesting energy of point absorber WEC's. These papers acknowledge that practical constraints imposed by the PTO system must be studied to a greater extent.…”

A Study about Performance and Robustness of Model Predictive Controllers in a WEC System

“…Although, since the last decade, more complex controllers like MPC (model predictive control) are being employed. The interest in implementing MPCs in WEC systems is motivated by the need to increase the productive/economic viability of these systems; due to the fact that these controllers allow them to minimize mechanical fatigue in their structures (limiting the operating ranges) and to focus the control strategy on the maximization of the extracted power directly.Actually, several authors have developed predictive controllers for WECs [7][8][9][10][11][12][13][14][15][16][17]. These MPCs can be grouped according to the characteristics of the cost function optimized.…”

“…On one side, in [9][10][11]13,14], a reduced model was used for the design, which did not consider the dynamics of the radiation force. Meanwhile,in [7,8,12,13,[15][16][17], such dynamics were considered in the design model. Moreover, the previous works did not consider the dynamics of the power take-off system (PTO), neither in the evaluation, nor in the design of the MPCs.…”

“…Finally, the treatment carried out in the case of non-feasibility when solving the cost functions with restrictions should be highlighted. In this aspect, the works in [9,10,13] considered a more complete approach by adding soft constrains in the case of non-feasibility.This paper analyses the main approaches of MPCs applied to PAW systems [8][9][10][11][12][13][14][15][16][17]. In addition, a new design is proposed: MPC based on a model with an embedded integrator for controllers that follow a setpoint for the speed of oscillation of the PAW.…”