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Control-Oriented Wave to Wire Model of Oscillating Water Column

  • R. SuchithraEmail author
  • Abdus Samad
Conference paper
Part of the Lecture Notes in Civil Engineering book series (LNCE, volume 23)

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.

Keywords

Oscillating water column Wave to wire model Model reduction Wells turbine Doubly fed induction generator 

Nomenclature

Abbreviation

DFIG

Doubly fed induction generator

OWC

Oscillating water column

PTO

Power take-off

ROM

Reduced-order model

WEC

Wave energy converter

Symbols

a

Wave amplitude

Vc

Volume of the air chamber

B

Damping coefficient

bt

Rotor blade height

C

Hydrostatic stiffness

Ca

Input power coefficient

Cd

Discharge coefficient

Cs

Speed of sound

Ct

Torque coefficient

d

Draft of the OWC

Dt

Diameter of the turbine

D

System drag

Edq

Transient voltage

Fa

Added mass force

FFK

Froude–Krylov force

FΔpair

Air force on water column

g

Acceleration due to gravity

h

Water depth

H

Wave height

ha0

Height of the water column

idq

Direct quadrature axis current

J

Moment of inertia of motor generator set

k

Wave number

K

Stiffness coefficient

Kt

Turbine constant

L

Wavelength

lr

Chord length of rotor

M

Water column mass

Rc

Radius of the water column

R

Resistance

rt

Mean radius of the turbine

Ti

Time period

Te

Electromagnetic torque

To

Transient open circuit time constant

Tt

Turbine torque

Ur

Circumferential velocity

vdq

Direct quadrature axis voltage

vx

Mean axial velocity

X

Reactance

X

Transient impedance

z

Internal free surface elevation

Z

Impedance

zt

Number of blades

γ

Heat capacity ratio of air

Δp

Pressure drop between the chamber and atmosphere

ζ

Damping coefficient

η

Water surface elevation

θr

Torsional displacement of the rotor

ρa

Density of air

ρs

Density of water

ύ

Water particle velocity

ϕ

Phase angle of the wave

ϕt

Flow coefficient

ω

Wave angular frequency

ωr

Rotor angular frequency

ωs

Generator angular frequency

m

Mass of air inside the chamber

Ma

Added mass

Nr

Rotor speed

p

Number of generator poles

pc

Chamber pressure

q

Volume flow rate

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Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Wave Energy and Fluids Engineering Lab, Ocean Engineering DepartmentIndian Institute of Technology MadrasChennaiIndia

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