The impact of energy extraction of wave energy converter arrays on wave climate under multi-directional seas

  • Zhi Yung TayEmail author
  • Vengatesan Venugopal
Research Article


This paper investigates the energy extraction of three types of wave energy converters (WEC) arranged in arrays and subjected to multi-directional seas of different wave spreading. The changes in the wave climate observed in the neighborhood of the arrays by their energy extraction were also reported. The hydrodynamic software, WAMIT, has been used to generate the performance of the WEC arrays in regular waves, whereas, a post-processing programming code developed in-house has been used to generate the device arrays’ performance in multi-directional seas characterized by single-peaked (JONSWAP and Bretschneider) and double-peaked (Ochi–Hubble) wave energy spectra. The results showed interesting findings on the WEC array performance and change in the wave environment around the devices, both strongly depend on the wave energy generation mechanism of the WECs and the wave spreading. The results obtained from the multi-directional seas with double-peaked wave spectrum showed significant differences in the energy production performance by the WEC arrays to those with single-peaked wave spectra. The uni-directional seas resulted in a larger q-factor. The q-factor differed with the peak wave periods, and at small wave periods, the q-factor for the terminator and attenuator WEC arrays are found to be higher than their counterparts for the point absorber WECs. With reference to the wave height modification in the neighborhood of the WEC arrays, the attenuator generated a greater wave disturbance followed by the terminator and point absorbers.


Multi-directional sea Wave energy converter array q-Factor Wave climate Double-peaked wave spectrum Energy extraction 



The authors are grateful for the financial support of the UK Engineering and Physical Sciences Research Council (EPSRC) through the EcoWatt2050 research consortium (EPSRC Reference: EP/K012851/1).

Supplementary material

40722_2019_127_MOESM1_ESM.pdf (386 kb)
Supplementary material 1 (PDF 386 kb)


  1. Babarit A, Hals J (2011) On the maximum and actual capture width ratio of wave energy converters. In: The 10th European wave energy conference, 5–9 September 2011, SouthamptonGoogle Scholar
  2. Borgarino B, Babarit A, Ferrant P (2012) Impact of wave interactions effects on energy absorption in large arrays of wave energy converters. Ocean Eng 41:79–88CrossRefzbMATHGoogle Scholar
  3. Bozzi S, Miquel AM, Antonini A, Passoni G, Archetti R (2013) Modeling of a point absorber for energy conversion in Italian seas. Energies 6:3033–3051CrossRefGoogle Scholar
  4. Bozzi S, Giassi M, Miquel AM, Antonini A, Bizzozero F, Gruosso G, Archetti R, Passoni G (2017) Wave energy farm design in real wave climates: the Italian offshore. Energy 122:378–389CrossRefGoogle Scholar
  5. Budal K (1977) Theory for absorption of wave power by a system of interacting bodies. J Ship Res 21:248–253Google Scholar
  6. Cruz J, Sykes R, Siddorn P, Eatock Taylor R (2010) Estimating the loads and energy yield of arrays of wave energy converters under realistic seas. IET Renew Power Gener 4:488–497CrossRefGoogle Scholar
  7. De Andrés A, Guanche R, Meneses L, Vidal C, Losada I (2014) Factors that influence array layout on wave energy farms. Ocean Eng 82:32–41CrossRefGoogle Scholar
  8. DNV (2010) Recommended practice DNV-RP-C205: environmental conditions and environmental loads. Det Norske Veritas, Det Norske Veritas, NorwayGoogle Scholar
  9. Duarte T, Gueydon S, Jonkman J, Sarmento A (2014) Computation of wave loads under multidirectional sea states for floating offshore wind turbines. In: ASME 2014 33rd international conference on ocean, offshore and arctic engineering. American Society of Mechanical Engineers, pp V09BT09A023–V09BT09A023Google Scholar
  10. Engström J, Eriksson M, Göteman M, Isberg J, Leijon M (2013) Performance of large arrays of point absorbing direct-driven wave energy converters. J Appl Phys 114:204502CrossRefGoogle Scholar
  11. Falcão AFDO (2010) Wave energy utilization: a review of the technologies. Renew Sustain Energy Rev 14:899–918CrossRefGoogle Scholar
  12. Falnes J (2002) Ocean waves and oscillating systems. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  13. Faltinsen OM (1993) Sea loads on ships and offshore structures. Cambridge University Press, CambridgeGoogle Scholar
  14. Goda Y (2010) Random seas and design of maritime structures. World Scientific, SingaporeCrossRefzbMATHGoogle Scholar
  15. Lee CH, Newman JN (2006) WAMIT user manual. WAMIT, IncGoogle Scholar
  16. Noad I, Porter R (2015) Optimisation of arrays of flap-type oscillating wave surge converters. Appl Ocean Res 50:237–253CrossRefGoogle Scholar
  17. Ochi MK, Hubble EN (1976) Six-parameter wave spectra. Coast Eng 1:301–328Google Scholar
  18. Renzi E, Abdolali A, Bellotti G, Dias F (2014) Wave-power absorption from a finite array of oscillating wave surge converters. Renew Energy 63:55–68CrossRefGoogle Scholar
  19. Retzler C (2006) Measurements of the slow drift dynamics of a model Pelamis wave energy converter. Renew Energy 31:257–269CrossRefGoogle Scholar
  20. Sarkar D, Renzi E, Dias F (2014) Wave farm modelling of oscillating wave surge converters. Proc R Soc Lond A Math Phys Eng Sci 470:20140118MathSciNetCrossRefzbMATHGoogle Scholar
  21. Sinha A, Karmakar D, Soares CG (2015) Effect of floater shapes on the power take-off of wave energy converters. In: Renewable energies offshore. Taylor and Francis Group, London, pp 375–382Google Scholar
  22. Soares CG (1984) Representation of double-peaked sea wave spectra. Ocean Eng 11:185–207CrossRefGoogle Scholar
  23. Tay ZY (2019) Energy extraction from an articulated plate anti-motion device of a very large floating structure under irregular waves. Renew Energy 130:206–222CrossRefGoogle Scholar
  24. Tay ZY, Venugopal V (2016) Optimization of spacing for oscillating wave surge converter arrays using genetic algorithm. J Waterw Port Coast Ocean Eng 143:04016019CrossRefGoogle Scholar
  25. Tay ZY, Venugopal V (2017) Hydrodynamic interactions of oscillating wave surge converters in an array under random sea state. Ocean Eng 145:382–394CrossRefGoogle Scholar
  26. Tay ZY, Wang CM, Utsunomiya T (2009) Hydroelastic responses and interactions of floating fuel storage modules placed side-by-side with floating breakwaters. Mar Struct 22:633–658CrossRefGoogle Scholar
  27. Tay ZY, Wei Y, Vakis AI (2018) Energy extraction of pontoon-type wave energy converter. In: ASME 2018 37th international conference on ocean, offshore and arctic engineering, Madrid. American Society of Mechanical Engineers, pp V010T09A037–V010T09A037Google Scholar
  28. Wang CM, Tay ZY (2010) Hydroelastic analysis and response of pontoon-type very large floating structures. In: Bungartz HJ, Mehl M, Schafer M (eds) Fluid structure interaction II. Springer, BerlinGoogle Scholar
  29. Wolgamot HA, Taylor PH, Eatock Taylor R (2012) The interaction factor and directionality in wave energy arrays. Ocean Eng 47:65–73CrossRefGoogle Scholar
  30. Yasukawa H (1990) A Rankine panel method to calculate unsteady ship hydrodynamic forces. J Soc Nav Archit Jpn 1990:131–140CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Engineering Cluster, Singapore Institute of TechnologySingaporeSingapore
  2. 2.Institute for Energy Systems, School of EngineeringThe University of EdinburghEdinburghUK

Personalised recommendations