Abstract
To facilitate the commercialization of wave energy in an array or farm environment, effective control strategies for improving energy extraction efficiency of the system are important. In this paper, we develop and apply model-predictive control (MPC) to a heaving point-absorber array, where the optimization problem is cast into a convex quadratic programming (QP) formulation, which can be efficiently solved by a standard QP solver. We introduced a term for penalizing large slew rates in the cost function to ensure the convexity of this function. Constraints on both range of the states and the input capacity can be accommodated. The convex formulation reduces the computational hurdles imposed on conventional nonlinear MPC. For illustration of the control principles, a point-absorber approximation is adopted to simplify the representation of the hydrodynamic coefficients among the array by exploiting the small devices to wavelength assumption. The energy-capturing capabilities of a two-cylinder array in regular and irregular waves are investigated. The performance of the MPC for this two-WEC array is compared to that for a single WEC, and the behavior of the individual devices in head or beam wave configuration is explained. Also shown is the reactive power required by the power takeoff system to achieve the performance.
Highlights
In the broad subject of wave-energy extraction, various control strategies have been proposed and implementedArticle Highlights Model-Predictive Control (MPC) is developed for an array of dual coaxial-cylinder WEC. Adding a penalty to the machinery force convexifies the controller objective function. Operation of 2 WECs in proximity is modeled with wave interaction and model-predictive control (MPC) considered. Wave-interaction effects on absorption performance is analyzed in various sea states. MPC is shown to yield a widening of the absorption bandwidth of the WEC array studied.Presented at the 3rd ICNAME, Marine Renewable Energy Forum, Qingdao, China, 7-9 September, 2017.on single or stand-alone wave-energy converters, including resistive control, approximate complex-conjugate control, and phase control by latching or clutching (see for example, Bacelli et al (2016) and Hals et al (2011a))
A nonlinear MPC (NMPC) was developed and used by these authors for the single WEC, where the PTO damping function was used as the optimizer
It was shown that by tuning the penalty weight r, the current MPC strategy can achieve a better performance in both regular and irregular waves in terms of its ability to broaden bandwidth of the capture width, while simultaneously saves computational time and power because of the convex formulation of the optimization problem
Summary
In the broad subject of wave-energy extraction, various control strategies have been proposed and implemented. In order to apply the theory for obtaining the optimal operating condition, hydrodynamic properties including wave-exciting forces, radiation damping coefficients, etc., for each individual device in the array configuration are needed. Li implemented decentralized, centralized, and distributed model predictive control (MPC) to an array of two WECs (Li and Belmont 2014a, b) with the point-absorber theory mentioned above to account for wave-interaction effects. The problem was recast as a quadratic programming (QP) problem, for which convexity can be guaranteed by tuning the weight of the penalty term on slew rates of the control input in the cost function; the problem can be solved efficiently by a standard QP solver In this paper, such an MPC (Zhong and Yeung 2017) is applied to an array of WECs, in both regular and irregular waves. As the MPC requires that a wave-prediction unit be simultaneously incorporated to predict the dynamics of the system, we will assume in this work that there exists a wave predictor (Fusco and Ringwood 2012; Morris et al 1998), which can estimate the wave elevation at a designated location for a certain future period
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