A practical approach to wave energy modeling and control

Abstract

The potential for control design to dramatically improve the economic viability of wave energy has generated a great deal of interest and excitement. However, for a number of reasons, the promised benefits from better control designs have yet to be widely realized by wave energy devices and wave energy remains a relatively nascent technology. This brief paper summarizes a simple, yet powerful approach to wave energy dynamics modeling, and subsequent control design based on impedance matching. Our approach leverages the same concepts that are exploited by a simple FM radio to achieve a feedback controller for wave energy devices that approaches optimal power absorption. If fully utilized, this approach can deliver immediate and consequential reductions to the cost of wave energy. Additionally, this approach provides the necessary framework for control co-design of a WEC, in which an understanding of the control logic allows for synchronous design of the device control system and hardware.

Importance of drivetrain optimisation to maximise electrical power from wave energy converters

“…Due to the cumbersome equations that define the MPC, the algorithm, including the discretisation of the continuoustime system, system prediction and formulation of the objective function, are outlined in the Appendix. In general, at each time step, the controller uses predicted values of the excitation force F exc as well as the dynamic wave-to-wire model of the WEC, Equations ( 11)- (12), and attempts to find values of the generator voltage V sq such that the average electrical power generated by the WEC over the prediction horizon T h is maximised. For this study, the prediction process of the wave excitation force is assumed to be perfect.…”

“…To fill this gap, a number of studies have developed and validated wave‐to‐wire models experimentally for WECs with different PTO systems [10]. Thus, it has been shown that relatively simple electro‐mechanical models of electrical generators and power converters can capture most power losses [11] and are suitable to be used for the WEC design optimisation [12, 13]. In direct mechanical drive power take‐off systems, the WEC is connected to a rotary generator through a drivetrain that converts the linear motion of a buoy into the angular rotation of the generator shaft [14].…”

Power maximising control of a heaving point absorber wave energy converter

“…Frequency-domain approach is often used to investigate and tune the performance of feedback control from a stability and control bandwidth perspective [9]. Substituting the PID control force in Equation (11) into the WEC equation of periodic motion (under harmonic oscillation) in Equation ( 5), and applying Lorenz linearisation [27] to approximate the nonlinear viscous drag effects following that in [28,29], the linearised model of the WEC feedback control system is obtained.…”

“…It is possible to avoid the acausality issue in the WEC control design if the impedance matching is achieved not across all frequencies simultaneously, but covering only a limited range of dominant wave frequencies. Controllers built using this philosophy are sub‐optimal in irregular waves but can produce power close to optimal conditions [9]. There are a number of ways to design a causal approximation of CCC leading to simple and reliable control strategies.…”

“…The most widely used control law for point absorbing WECs is a spring‐damper controller, sometimes called proportional–integral (PI), using WEC velocity as a basis, where stiffness and damping coefficients are tuned to achieve impedance matching at one dominant frequency [10]. Depending on the WEC dynamics and considered sea states, PI control can achieve up to 77–93% of the theoretical power limit [9]. As PI control is narrow‐banded by nature and optimal for one wave condition only, a self‐tuning PI strategy, where control parameters are adjusted in real‐time according to the wave environment, has been tested in [11].…”