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A promising direction toward improving the performance of wave energy converter (WEC) farms is to leverage a system-level integrated approach called control co-design (CCD), integrating geometric attributes, control parameters, and layout. However, the resulting optimization problem requires the estimation of hydrodynamic coefficients through computationally prohibitive numerical methods such as multiple scattering (MS). To mitigate this bottleneck, we construct data-driven surrogate models (SMs) using artificial neural networks and many-body expansion. To rectify errors in SMs, a hybrid optimization strategy, that involves solving an optimization problem with a genetic algorithm and SMs to generate a starting point which is then used by a gradient-based optimizer and MS, is devised. The effectiveness and efficiency of the proposed approach are demonstrated for a 5-WEC farm. For layout optimization study, the proposed framework offers a 91-fold increase in computational efficiency compared to the direct usage of MS. The framework also enables complex investigations, including concurrent geometry, control, and layout optimization of heaving cylindrical WEC devices in probabilistic irregular waves across various US coastal locations. The method’s scalability is assessed for a 25-WEC farm and the results indicate promising directions toward a practical framework for integrated WEC farm design with more tractable computational demands. 

Abstract A promising direction towards reducing the levelized cost of energy for wave energy converter (WEC) farms is to improve their performance. WEC design studies generally focus on a single design domain (e.g., geometry, control, or layout) to improve the farm’s performance under simplifying assumptions, such as regular waves. This strategy, however, has resulted in design recommendations that are impractical or limited in scope because WEC farms are complex systems that exhibit strong coupling among geometry, control, and layout domains. In addition, the location of the candidate site, which has a large impact on the performance of the farm, is often overlooked. Motivated by some of the limitations observed in WEC literature, this study uses an integrated design framework, based on simultaneous control co-design (CCD) principles, to discuss the impact of site selection and wave type on WEC farm design. Interactions among plant, control, and layout are also investigated and discussed using a wide range of simulations and optimization studies. All of the studies were conducted using frequency-domain heaving cylinder WEC devices within a farm with a linear reactive controller in the presence of irregular probabilistic waves. The results provide high-level guidelines to help the WEC design community move toward an integrated design perspective. 

This article explores various uncertain control co-design (UCCD) problem formulations. While previous work offers formulations that are method-dependent and limited to only a handful of uncertainties (often from one discipline), effective application of UCCD to real-world dynamic systems requires a thorough understanding of uncertainties and how their impact can be captured. Since the first step is defining the UCCD problem of interest, this article aims at addressing some of the limitations of the current literature by identifying possible sources of uncertainties in a general UCCD context and then formalizing ways in which their impact is captured through problem formulation alone (without having to immediately resort to specific solution strategies). We first develop and then discuss a generalized UCCD formulation that can capture uncertainty representations presented in this article. Issues such as the treatment of the objective function, the challenge of the analysis-type equality constraints, and various formulations for inequality constraints are discussed. Then, more specialized problem formulations such as stochastic in expectation, stochastic chance-constrained, probabilistic robust, worst-case robust, fuzzy expected value, and possibilistic chance-constrained UCCD formulations are presented. Key concepts from these formulations, along with insights from closely-related fields, such as robust and stochastic control theory, are discussed, and future research directions are identified. 

Wave energy converters (WECs) are a promising candidate for meeting the increasing energy demands of today’s society. It is known that the sizing and power take-off (PTO) control of WEC devices have a major impact on their performance. In addition, to improve power generation, WECs must be optimally deployed within a farm. While such individual aspects have been investigated for various WECs, potential improvements may be attained by leveraging an integrated, system-level design approach that considers all of these aspects. However, the computational complexity of estimating the hydrodynamic interaction effects significantly increases for large numbers of WECs. In this article, we undertake this challenge by developing data-driven surrogate models using artificial neural networks and the principles of many-body expansion. The effectiveness of this approach is demonstrated by solving a concurrent plant (i.e., sizing), control (i.e., PTO parameters), and layout optimization of heaving cylinder WEC devices. WEC dynamics were modeled in the frequency domain, subject to probabilistic incident waves with farms of 3, 5, 7, and 10 WECs. The results indicate promising directions toward a practical framework for array design investigations with more tractable computational demands.