Abstract
Spectral control is an accurate and computationally efficient approach to power-maximising control of wave energy converters (WECs). This work investigates spectral control calculations with explicit derivative computation, applied to WECs with non-ideal power take-off (PTO) systems characterised by an efficiency factor smaller than unity. To ensure the computational efficiency of the spectral control approach, it is proposed in this work to approximate the discontinuous efficiency function by means of a smooth function. A non-ideal efficiency function implies that the cost function is non-quadratic, which requires a slight generalisation of the derivative-based spectral control approach, initially introduced for quadratic cost functions. This generalisation is derived here in some detail given its practical interest. Two application case studies are considered: the Wavestar scale model, employed for the WEC control competition (WECCCOMP), and the 3rd reference model (RM3) two-body heaving point absorber. In both cases, with the approximate efficiency function, the spectral approach calculates WEC trajectory and control force solutions, for which the mean electrical power is shown to lie within a few percent of the true optimal electrical power. Regarding the effect of a non-ideal PTO efficiency upon achievable power production, and concerning heaving point-absorbers, the results obtained are significantly less pessimistic than those of previous studies: the power achieved lies within 80–95% of that obtained by simply applying the efficiency factor to the optimal power with ideal PTO.
Highlights
Power-maximising control is a promising path to improve the economic competitiveness of wave energy converters (WECs) [1]
Recent years have witnessed a growing interest for model predictive control (MPC) strategies [2], whereby an optimisation problem is solved in real-time to update a prescribed control input, or a reference trajectory to be followed by the WEC
For the WECCCOMP model, the cut-off frequency for the control solution is set to 4 Hz
Summary
Power-maximising control is a promising path to improve the economic competitiveness of WECs [1]. Recent years have witnessed a growing interest for model predictive control (MPC) strategies [2], whereby an optimisation problem is solved in real-time to update a prescribed control input, or a reference trajectory to be followed by the WEC. MPC strategies take profit from wave excitation predictions They can, in theory, handle nonlinear WEC models, through the use of nonlinear optimisation algorithms, as well as constraints on the WEC dynamics, control force or instantaneous power. First introduced in [3] for WEC control applications, spectral and pseudo-spectral MPC methods discretise the wave inputs and optimisation variables by means of basis functions, typically Fourier [4,5] (when a periodic wave input is considered), or Chebyshev-like [6] (to handle directly the non-periodic wave signal, seen within the receding-horizon control window).
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