Revisiting Theoretical Limits for One-Degree-of-Freedom Wave Energy Converters: Article No. JERT-20-1777

Nathan Tom

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5 Scopus Citations


This work revisits the theoretical limits of one degree-of-freedom wave energy converters (WECs). This work considers the floating sphere used in the OES Task 10 WEC modeling and verification effort for analysis. Analytical equations are derived to determine bounds on displacement amplitude, time-averaged power (TAP), and power-take-off (PTO) force. A unique result found shows that the TAP absorbed by a WEC can be defined solely by the inertial properties and radiation hydrodynamic coefficients. In addition, a unique expression for the PTO force was derived that provides lower and upper bounds when resistive control is used to maximize power generation. For complex conjugate control, this same expression only provides a lower bound, as there is theoretically no upper bound. These bounds assist in comparing the performance of the floating sphere if it were to extract energy using surge or heave motion. The analysis shows because of differences in hydrodynamic coefficients for each oscillating mode, there are different frequency ranges that provide better power capture efficiency. The influence of a motion constraint on TAP while utilizing a nonideal power take-off is examined and found to reduce the losses associated with bidirectional energy flow. The expression to calculate TAP with a nonideal PTO is modified by the electrical conversion efficiency and the ratio of the PTO spring and damping coefficients. The PTO spring and damping coefficients were separated in the expression, allowing for limits to be set on the PTO coefficients to ensure net power generation.
Original languageAmerican English
Number of pages9
JournalJournal of Energy Resources Technology, Transactions of the ASME
Issue number9
StatePublished - 2021

NREL Publication Number

  • NREL/JA-5700-77709


  • Ocean Energy Systems Task 10
  • optimal control
  • resistive control
  • theoretical limits
  • wave energy converter


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