Multi-Objective Multidisciplinary Optimization of Wave Energy Converter Array Layout and Controls

Abstract

This study utilizes multidisciplinary design optimization (MDO) to design an array of heaving wave energy converters (WECs) for grid-scale energy production with decision variables and parameters chosen from the coupled disciplines of geometry, hydrodynamics, layout, motor-actuated reactive controls (with a force maximum constraint) and economics. We vary a WEC's dimensions, array layout, and control gain to minimize two objectives: the levelized cost of energy (LCOE) and the maximum separation distance. This multi-objective optimization approach results in a set of optimal design configurations that stakeholders can choose from for their specific application and needs. The framework yields a range of optimal (minimum) LCOE values from 0.21 to 0.23 \$/kWh and a separation distance ranging from 97 to 62 meters. The WEC radius of 4m is found to be optimal, and the q-factor for optimal designs are greater than 1 up to 1.06 for a rhombus-like layout. Additionally, a post-optimality global sensitivity analysis of a design shows that wave heading, wave frequency, WEC lifetime, amplitude and interest rate accounts for most of the variance. Different designs in the Pareto set may be appealing for different decision makers based on their trade-off analysis. To that end, regression model is developed for design heuristics.

Figures (19)

• Figure 1: xDSM diagram of the multidisciplinary model of WEC farms. This architecture couples the optimizer with the multidisciplinary analysis of all the relevant modules. The diagonals are the disciplines and off-diagonals are the coupling variables. The input design variables are shown passing from the top and output of each discipline is shown on the right. The optimal value for each discipline is shown with an asterisk(*) of the left after the optimizer converges. The grey line shows the data I/O and blue line shows the sequence of analysis.
• Figure 2: Plot showing the minimum space constraint and the SPACE$_{\text{max}}$ objective.
• Figure 3: Schematic of the WEC geometry and control design variables.
• Figure 4: The elevation of the radiated, diffracted, and total wave fields for an arbitrary 4-body WEC array.
• Figure 5: Block structure in influence matrices computed via full BEM resolution for any design.