Skip to main content
SpringerLink
Log in

Control-Oriented Wave to Wire Model of Oscillating Water Column

  • Conference paper
  • First Online:
Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018)

Part of the book series: Lecture Notes in Civil Engineering ((LNCE,volume 23))

  • 1099 Accesses

Abstract

The interest in wave energy converters (WECs) is increasing, the study of grid connection of WEC along with the control system has become inevitable. WEC such as an oscillating water column (OWC) device involves conversions in various physical domains, thus a model describing the conversions at each stage and coupling between them should be accurate yet simple enough to reduce the computation time involved. The already existing models do not include all the components of wave to wire conversion. This paper presents a wave to wire model for control system studies. The model reduction technique is used to create a dynamically equivalent model for any large systems have more interconnecting stages. The dynamics involved in conversion stages are hydrodynamic and aerodynamic coupling at the capture chamber, aerodynamic and thermodynamic coupling inside the capture chamber, aerodynamic and rotor dynamic coupling in air turbine; and rotor dynamics and generator dynamics in the turbine generator coupling. Thus, a wave to wire model is represented to capture all the dynamics involved. It is observed that the model retains its fundamental physics, improves the computation time and reduces the number of unknowns to describe the state-space of OWC system. The accuracy and efficiency of the model is investigated through various static and dynamic analyses and found acceptable for OWC-WEC control system studies.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Abbreviations

DFIG:

Doubly fed induction generator

OWC:

Oscillating water column

PTO:

Power take-off

ROM:

Reduced-order model

WEC:

Wave energy converter

a :

Wave amplitude

Vc :

Volume of the air chamber

B :

Damping coefficient

b t :

Rotor blade height

C :

Hydrostatic stiffness

C a :

Input power coefficient

C d :

Discharge coefficient

Cs :

Speed of sound

C t :

Torque coefficient

d :

Draft of the OWC

D t :

Diameter of the turbine

D :

System drag

E ′ dq :

Transient voltage

F a :

Added mass force

F FK :

Froude–Krylov force

F Δpair :

Air force on water column

g :

Acceleration due to gravity

h :

Water depth

H :

Wave height

h a0 :

Height of the water column

i dq :

Direct quadrature axis current

J :

Moment of inertia of motor generator set

k :

Wave number

K :

Stiffness coefficient

K t :

Turbine constant

L :

Wavelength

l r :

Chord length of rotor

M :

Water column mass

R c :

Radius of the water column

R :

Resistance

r t :

Mean radius of the turbine

T i :

Time period

T e :

Electromagnetic torque

T o :

Transient open circuit time constant

T t :

Turbine torque

U r :

Circumferential velocity

v dq :

Direct quadrature axis voltage

v x :

Mean axial velocity

X :

Reactance

X ′ :

Transient impedance

z :

Internal free surface elevation

Z :

Impedance

z t :

Number of blades

γ :

Heat capacity ratio of air

Δp :

Pressure drop between the chamber and atmosphere

ζ:

Damping coefficient

η :

Water surface elevation

θ r :

Torsional displacement of the rotor

ρ a :

Density of air

ρ s :

Density of water

ύ :

Water particle velocity

ϕ :

Phase angle of the wave

ϕ t :

Flow coefficient

ω :

Wave angular frequency

ω r :

Rotor angular frequency

ω s :

Generator angular frequency

m :

Mass of air inside the chamber

M a :

Added mass

N r :

Rotor speed

p :

Number of generator poles

p c :

Chamber pressure

q :

Volume flow rate

References

  1. Falnes J (2007) A review of wave-energy extraction. Mar Struct 20:185–201. https://doi.org/10.1016/j.marstruc.2007.09.001

    Article  Google Scholar 

  2. Heath TV (2012) A review of oscillating water columns. Philos Trans R Soc A Math Phys Eng Sci 370:235–245. https://doi.org/10.1098/rsta.2011.0164

    Article  Google Scholar 

  3. Iturrioz A, Guanche R, Armesto JA, Alves MA, Vidal C, Losada IJ (2014) Time-domain modeling of a fixed detached oscillating water column towards a floating multi-chamber device. Ocean Eng 76:65–74. https://doi.org/10.1016/j.oceaneng.2013.11.023

    Article  Google Scholar 

  4. Brendmo A, Falnes J, Lillebekken PM (1996) Linear modelling of oscillating water columns including viscous loss. Appl Ocean Res 18:65–75. https://doi.org/10.1016/0141-1187(96)00011-9

    Article  Google Scholar 

  5. Alberdi M, Amundarain M, Garrido AJ, Garrido I, Casquero O, De la Sen M (2011) Complementary control of oscillating water column-based wave energy conversion plants to improve the instantaneous power output. IEEE Trans Energy Convers 26:1021–1032. https://doi.org/10.1109/TEC.2011.2167332

    Article  Google Scholar 

  6. Anand S, Jayashankar V, Nagata S, Toyota K, Takao M, Setoguchi T (2007) Performance estimation of bi-directional turbines in wave energy plants. J Therm Sci 16:346–352. https://doi.org/10.1007/s11630-007-0346-1

    Article  Google Scholar 

  7. Xie J, Zuo L (2013) Dynamics and control of ocean wave energy converters. Int J Dyn Control 1:262–276. https://doi.org/10.1007/s40435-013-0025-x

    Article  Google Scholar 

  8. Drew B, Plummer AR, Sahinkaya MN (2009) A review of wave energy converter technology. Proc IMech Part A J Power Energy 223:887–902. https://doi.org/10.1243/09576509JPE782

    Article  Google Scholar 

  9. Dean RG, Dalrymple RA (1989) Water wave mechanics for engineers and scientists. World Scientific Publishing Co., Pte. Ltd., Singapore

    Google Scholar 

  10. Gervelas R, Trarieux F, Patel M (2011) A time-domain simulator for an oscillating water column in irregular waves at model scale. Ocean Eng 38:1007–1013. https://doi.org/10.1016/j.oceaneng.2011.04.006

    Article  Google Scholar 

  11. Falcão AFO, Henriques JCC, Cândido JJ (2012) Dynamics and optimization of the OWC spar buoy wave energy converter. Renew Energy 48:369–381. https://doi.org/10.1016/j.renene.2012.05.009

    Article  Google Scholar 

  12. Setoguchi T, Santhakumar S, Maeda H, Takao M, Kaneko K (2001) A review of impulse turbines for wave energy conversion. Renew Energy 23:261–292. https://doi.org/10.1016/S0960-1481(00)00175-0

    Article  Google Scholar 

  13. Halder P, Samad A (2016) Optimal Wells turbine speeds at different wave conditions. Int J Mar Energy 16:133–149. https://doi.org/10.1016/j.ijome.2016.05.008

    Article  Google Scholar 

  14. Falcão AFO, Rodrigues RJ (2002) Stochastic modelling of OWC wave power plant performance. Appl Ocean Res 24:59–71. https://doi.org/10.1016/S0141-1187(02)00022-6

    Article  Google Scholar 

  15. Nunes G, Valério D, Beirão P, Sá da Costa J (2011) Modelling and control of a wave energy converter. Renew Energy 36:1913–1921. https://doi.org/10.1016/j.renene.2010.12.018

    Article  Google Scholar 

  16. Cummins WE (1962) The impulse response function and ship motions. Schiffstechnik 101–109

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Wave Energy and Fluids Engineering Lab, Ocean Engineering Department, Indian Institute of Technology Madras, Chennai, 600036, TN, India

    R. Suchithra & Abdus Samad

Authors
  1. R. Suchithra
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Abdus Samad
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to R. Suchithra .

Editor information

Editors and Affiliations

  1. Department of Ocean Engineering, Indian Institute of Technology Madras, Chennai, Tamil Nadu, India

    K. Murali

  2. Department of Ocean Engineering, Indian Institute of Technology Madras, Chennai, Tamil Nadu, India

    V. Sriram

  3. Department of Ocean Engineering, Indian Institute of Technology Madras, Chennai, Tamil Nadu, India

    Abdus Samad

  4. Department of Ocean Engineering, Indian Institute of Technology Madras, Chennai, Tamil Nadu, India

    Nilanjan Saha

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Suchithra, R., Samad, A. (2019). Control-Oriented Wave to Wire Model of Oscillating Water Column. In: Murali, K., Sriram, V., Samad, A., Saha, N. (eds) Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018). Lecture Notes in Civil Engineering , vol 23. Springer, Singapore. https://doi.org/10.1007/978-981-13-3134-3_52

Download citation

  • DOI: https://doi.org/10.1007/978-981-13-3134-3_52

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-3133-6

  • Online ISBN: 978-981-13-3134-3

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation