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WAVE ENERGY CONVERTER MODELING IN THE TIME DOMAIN: A DESIGN GUIDE BRET BOSMA
SUSTECH
8/1/2013
OCEAN WAVE ENERGY
• Ocean energy is a significant source in several forms
•Tidal
•Current
•Temperature gradient (OTEC and SWAC)
•Salinity
•Wave
• Compared to other renewables, wave energy has advantages:
•Higher availability
•More predictable and forecastable: up to 10 hours forecast time
•Low viewshed impact
• At present, wave energy is estimated at 20-30 cents per kWh. Coal and wind are 5 to 10 cents per kWh.
• Wave power is about 20-30 years behind wind, but it is predicted that wave power can catch up quickly.
WAVE ENERGY POTENTIAL
• 2010 OMAE (Assesing the Global Wave Energy Potential)
• 32400 TWh/year potential
• 2011 EPRI study
• United States
• 1170 TWh/year potential
• Oregon
• Inner shelf 143 TWh/year potential
• US Electricity use 2010
• 4143 TWh/year
WAVE POWER DENSITY (kW/m)
NORTHWEST NATIONAL MARINE RENEWABLE ENERGY CENTER (NNMREC) • Investigate technical, environmental, and social dimensions of
Marine and Hydrokinetics
• Advance Ocean Wave Energy Industry by assisting developers
• Device design
• Development
• Testing
• Evaluation
• Integration
• Lower Levelized Cost of Energy
• Time domain modeling
WAVE ENERGY CONVERTER (WEC) TIME DOMAIN MODELING
• MATLAB/Simulink
• Heave only
Time Domain Formulation and Analysis (Nonlinear) – Relatively moderate simulation time/More detailed analysis possible
Frequency Domain Parameters
Mooring Model (Linearized/Nonlinear)
PTO Model (Linearized/Nonlinear)
Wave Modeling and Simulation
Time Domain Modeling Tool
(eg. AQWA, MATLAB/SIMULINK,
OrcaFlex)
Motion Response
Mooring/PTO Forces
Power output
RAO (Response Amplitude Operator)
GENERIC WEC MODEL
FLUID FORCES ON STRUCTURE
Fluid Forces on Structure
Hydrodynamic
Hydrostatic
Diffraction
Froude-Krylov
f(ω)η (ω)
Wave Exciting
Force (Fe)
Radiation Force (Fr)
Radiation
Damping C(ω)
Added Mass
A(ω)
-ω2A(ω)Z(ω)
-iωC(ω)Z(ω)
KZ(ω)
HYDRODYNAMICS
0 0.2 0.4 0.60
2
4
6
8
10x 10
5
Frequency (Hz)
FK
+D
iff
(N/m
)
Float
Damper
Spar
0 0.2 0.4 0.6-200
-100
0
100
200
Frequency (Hz)
FK
+D
iff
(deg)
Float
Damper
Spar
0 0.2 0.4 0.60
2
4
6
8
10
12x 10
5
Frequency (Hz)
Added M
ass (
N/(
m/s
2))
Float
Damper
Spar
0 0.2 0.4 0.60
1
2
3
4
5
6x 10
5
Frequency (Hz)
Radia
tion D
am
pin
g (
N/(
m/s
))
Float
Damper
Spar
EQUATIONS OF MOTION
SIMULINK MODEL
EXCITATION IMPULSE RESPONSE FUNCTION
-5 -4 -3 -2 -1 0 1 2 3 4 5-5000
0
5000
10000
15000
Time [s]
Excitation I
RF
Float
Spar
-5 -4 -3 -2 -1 0 1 2 3 4 5-5000
0
5000
10000
15000
Excitation I
RF
Causal
NonCausal
EXCITATION FORCE
REGULAR WAVE OUTPUT
0 10 20 30 40 50 60 70 80 90 100-1
-0.5
0
0.5
1
Dis
pla
cem
ent
(m)
wave surface elevation
Float Displacement
Spar Displacement
0 10 20 30 40 50 60 70 80 90 100-4
-2
0
2
4x 10
5
Forc
e (
N)
PTO Force
0 10 20 30 40 50 60 70 80 90 1000
0.5
1
1.5
2x 10
5
time (s)
Pow
er
(W)
Pavg = 69645W
0 10 20 30 40 50 60 70 80 90 100-1
-0.5
0
0.5
1
Dis
pla
cem
ent
(m)
wave surface elevation
Float Displacement
Spar Displacement
0 10 20 30 40 50 60 70 80 90 100-2
-1
0
1
2x 10
5
Forc
e (
N)
PTO Force
0 10 20 30 40 50 60 70 80 90 1000
5
10
15x 10
4
time (s)
Pow
er
(W)
Pavg = 59416.4W
Introduction of system nonlinearities can identify significant power loss
not modeled in the frequency domain simulations.
IRREGULAR WAVE OUTPUT
0 10 20 30 40 50 60 70 80 90 100-2
-1
0
1
2
Dis
pla
cem
ent
(m)
wave surface elevation
Float Displacement
Spar Displacement
0 10 20 30 40 50 60 70 80 90 100-5
0
5
10x 10
5
Forc
e (
N)
PTO Force
0 10 20 30 40 50 60 70 80 90 1000
2
4
6x 10
5
time (s)
Pow
er
(W)
Pavg = 51459.2W
0 10 20 30 40 50 60 70 80 90 100-2
-1
0
1
2
Dis
pla
cem
ent
(m)
wave surface elevation
Float Displacement
Spar Displacement
0 10 20 30 40 50 60 70 80 90 100-1
-0.5
0
0.5
1x 10
5
Forc
e (
N)
PTO Force
0 10 20 30 40 50 60 70 80 90 1000
5
10
15x 10
4
time (s)
Pow
er
(W)
Pavg = 22635.8W
Similar nonlinearities could be added to the relative displacement and mooring.
CONCLUSIONS
• Time domain simulation of generic WEC
• Adaptable to geometry or device type
• Introduction of nonlinearities to model
• Results for any input waveform
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