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