With the advantages of low loss and flexible control, direct-drive wave energy converter (WEC) based on oscillating body structure has become a research hotspot in wave energy. Through mooring system, two-body direct-drive WEC, which is independent of off-shore fixed platforms, is a promising solution to wave energy utilization. However, the two-body WEC utilizes relative motion between upper and lower float to generate electricity, which makes modelling and optimal energy extraction control more difficult. Through equivalent method, a two-body WEC can be regarded as two power sources with different voltages and resistance paralleled to output electricity, furthermore, this two paralleled power source can be equivalent to a single source model, which is similar to a single-body WEC. Therefore modelling and energy extraction characteristic of two-body WEC are simplified and it can be concluded that stiffness of mooring has a great effect on maximum wave energy extraction. The results show that the mooring should be as stiffness as possible to avoid energy extraction loss and in this case two-body WEC can be totally equivalent to a single-body WEC: the upper float plays the role of harnessing wave energy and the lower float along with mooring system acts as a fixed base. And the design of two-body WEC with pretension mooring system is put forward.
Model predictive control (MPC) is the state-of-art method for optimal energy extraction in wave energy. Based on the equivalent model, MPC problem for maximizing wave energy extraction considering generator force and float displacement constraints is formulated. For the need of wave excitation force prediction, Kalman filter is used to achieve excitation force identification and autoregressive model is used for excitation force prediction. Considering the computation complexity for MPC solution, a fast solution algorithm is put forward, the core idea of this algorithm is to use the solution from previous step as the initial iteration of current step, thus only one iteration is required. Compared with conventional MPC that requires 3-5 interactions, the proposed fast solution algorithm can save up to 80% computing time.
A two-body direct-drive WEC prototype with upper float of 1.5m diameter is designed for experimental test in the wave tank lab with dimension of 100mx18mx5m. This lab can generate waves with periods from 2-3m and 0.25m maximum wave height. Different power control methods are conducted including resistive control, damping control, latching control, conventional MPC and proposed MPC. The results show that MPC can extract 70% more energy compared with traditional methods and the proposed MPC with fast solution algorithm have the same energy extraction efficiency while only 50% CPU operation time required.
The following conclusions can be drawn: (1) pretension mooring has no negative effect on energy extraction and two-body WEC can be equivalent to one-body WEC through equivalent circuit method, which will simplify control modelling significantly, (2) compared with conventional methods, MPC has more energy extraction efficiency by injecting reactive power to increase the oscillation amplitude while limiting it within preset constraints simultaneously, (3) the experimental results indicate that the proposed MPC is stable considering there exists modelling errors in experiment, besides, excitation force prediction is achieved by software algorithms, and the proposed MPC method only requires 50% computation time, which means the proposed method is promising for practical implementation without need of additionally sensors and high-performance control system.