Modelling and geometry optimisation of wave energy

Transcription

Modelling and geometry optimisation
of wave energy converters
Adi Kurniawan
Supervisors: Prof. Torgeir Moan & Prof. em. Johannes Falnes
23 April 2013
Outline
Introduction
Modelling
Geometry optimisation
Geometry control
Conclusion
There is abundant power available from the waves
NatGeo TV, “Green DIY Riding radical wave power”
Any device will deliver some energy
What matters is the cost of energy
Ultimate problem
Given the waves, design a device that minimises the cost per unit
of delivered energy.
What matters is the cost of energy
Ultimate problem
Given the waves, design a device that minimises the cost per unit
of delivered energy.
Open questions
How does this device look like? Is there a systematic way to design
an economic device?
What do we need?
What do we need?
a model
What do we need?
a model
predict
power output &
device response
What do we need?
a model
predict
power output &
device response
an optimiser
What do we need?
a model
predict
power output &
device response
maximise energy &
minimise cost
an optimiser
What do we need?
a model
predict
power output &
device response
maximise energy &
minimise cost
an optimiser
Research questions
Modelling
How to develop more realistic wave energy converter (WEC)
models while at the same time reduce their simulation time?
Research questions
Modelling
Optimisation
How to incorporate the cost factor into the design problem and
thus design an economical WEC?
Assumptions
I
Linear hydrodynamics
I
Unidirectional incident wave
I
Uniform water depth
Outline
Introduction
Modelling
Geometry control
Conclusion
What is a WEC?
An oscillator in water
What is a WEC?
It has two main parts
What is a WEC?
primary interface
What is a WEC?
power take-off
(PTO)
primary interface
Oscillating-body WECs
Utilise relative motion
I
between a moving body and a fixed reference (e.g. sea bed)
Oscillating-body WECs
Utilise relative motion
I
between a moving body and a fixed reference (e.g. sea bed)
I
between several moving bodies
Oscillating-water-column WECs
Utilise the motion of a partially enclosed mass of water relative to
I
a fixed reference
I
a moving outer body
A WEC is faced with two inherent challenges
I
A WEC must work with large forces and low velocities
I
I
Current technology for electrical generation is more used to
low force, high speed motions
Large forces are inconvenient and expensive to handle
A WEC is faced with two inherent challenges
I
I
I
I
Current technology for electrical generation is more used to
low force, high speed motions
Large forces are inconvenient and expensive to handle
A WEC must deal with the stochastic nature of the waves
I
I
It has to absorb energy optimally from the most frequent waves
It has to survive the most extreme waves
Several energy conversion alternatives are available
Mechanical translation/rotation
Hydraulic piston
Mechanical system
Hydraulic
Hydraulic
Pneumatic
Water turbine
Hydraulic motor
Air turbine
Mechanical rotation
Electrical generator
Electrical
Hydraulic piston
Mechanical system
Hydraulic
Hydraulic
Pneumatic
Water turbine
Hydraulic motor
Air turbine
Mechanical rotation
Electrical
Hydraulic piston
Mechanical system
Hydraulic
Hydraulic
Pneumatic
Water turbine
Hydraulic motor
Air turbine
Mechanical rotation
Electrical
Hydraulic piston
Mechanical system
Hydraulic
Hydraulic
Pneumatic
Water turbine
Hydraulic motor
Air turbine
Mechanical rotation
Electrical
Hydraulic piston
Mechanical system
Hydraulic
Hydraulic
Pneumatic
Water turbine
Hydraulic motor
Air turbine
Mechanical rotation
Electrical
Hydraulic piston
Mechanical system
Hydraulic
Hydraulic
Pneumatic
Water turbine
Hydraulic motor
Air turbine
Mechanical rotation
Electrical
Research questions
Modelling
Research questions
Modelling
Bond graph modelling
Domain-independent; uses common notations across different
energy domains
I
Se
1
R
C
Port-based, modular
I
Se
1
R
C
Port-based, modular
I
Se
1
C
R
Se
I
C
I
1
0
1
R
R
C
Graphical and intuitive
20-sim Reference 4.3
Systematic derivation of model equations → automated simulation
Systematic derivation of model equations → automated simulation
Bond graph modelling in wave energy research
First allusion by Jefferys (1984), “Simulation of wave power devices”
Bond graph modelling in wave energy research
Otherwise, relatively recent
Nolan et al. (2003)
PTO of a WEC for electricity and potable water production
Marré (2006)
WEC consisting of a buoy connected to a semi-submersible
Engja and Hals (2007)
WEC consisting of a buoy connected to a semi-submersible
Bacelli et al. (2008)
hydraulic PTO
Hals (2010)
integrated WEC systems
Yang (2011)
hydraulic PTO
Single oscillating body
Hydrost.
Restoring
Exc. Force
Mass + m(∞)
C
I
1
Se
Coulomb
Damping
R
R
Quadratic
Damping
TF
Transformation
Ext. Restoring
C
R
Radiation
Impedance
0
1
P
R
Load
Resistance
Self-reacting bodies
Hydrost.
Restoring
C
Se
Mass + m(∞)
I
Quadratic
Damping
R
1
Coulomb
Damping
Exc. Force
Ext. Restoring
R
R
Radiation
Impedance
C
Se
1
Exc. Force
C
Hydrost.
Restoring
I
Mass + m(∞)
R
Quadratic
Damping
0
1
P
R
Load
Resistance
Self-reacting bodies
Hydrost.
Restoring
C
Se
Mass + m(∞)
I
Quadratic
Damping
R
1
Coulomb
Damping
Exc. Force
Ext. Restoring
R
R
Radiation
Impedance
C
Se
1
C
1
P
Mass + m(∞)
R
I
Load
Resistance
1
Exc. Force
I
Mass + m(∞)
R
Quadratic
Damping
R
Rad. Impedance
+ Ext. Damping
Se
Exc. Force
Hydrost.
Restoring
0
R
Load Resistance
C
Hyd. + Ext. Restoring
Oscillating water column (OWC)
The hydrodynamics of an OWC device may be modelled using
I
massless piston model
I
→ oscillating-body problem, approximate
I
I
pressure distribution model
I
I
pressure distribution model
→ accurate
Floating OWC
Floating OWC
Fj = fj A −
X
Zjj 0 Uj 0 − Hjp p,
j0
Q = qA − Y p −
X
j = 1, 2, . . . , 6
HjU Uj
j
fj
q
Zjj 0
Y
Hjp , HjU
excitation force coefficient
excitation vol. flow coefficient
radiation impedance
radiation admittance
radiation coupling coefficients
Three options are available to evaluate Hjp and Y
1. Modify the dynamic boundary condition on the internal free
surface by special coding
2. Use generalised modes
2. Use generalised modes
3. Use reciprocity relations
G = <{Y } =
k
8πρgvg
Z
π
−π
Hjp = −HjU
|q(β)|2 dβ
Fixed & floating OWC
C
0
1
R
Sf
Air Compressibility
P
R
Load
Resistance
Relief Valve
0
Exc. Vol. Flow
R
Ext. Damping
R
Radiation
Admittance
Fixed OWC
Hydrost.
Restoring
Exc. Force
Mass + m(∞)
C
I
1
Se
Coulomb
Damping
R
R
Quadratic
Damping
TF
Transformation
Ext. Restoring
C
R
Radiation
Impedance
0
1
P
R
Load
Resistance
Oscillating body
Hydrost.
Restoring
Exc. Force
Mass + m(∞)
I
C
Se
1
Coulomb
Damping
R
R
Quadratic
Damping
TF
Transformation
Ext. Restoring
C
C
R
Radiation
+ C(∞)
Coupling
TF
Radiation
Impedance
0
1
R
Sf
Air Compressibility
P
R
Load
Resistance
Relief Valve
0
Exc. Vol. Flow
R
Ext. Damping
R
Radiation
Admittance
Floating OWC
To be realistic, time-domain model is necessary
Assuming PTO force as linear enables frequency-domain analysis.
Fe (ω) = R(ω) + Ru + iω M + Mu + m(ω) − (Sb + Su )ω −2 U (ω)
However, since the PTO is nonlinear in reality, time-domain model
is necessary.
Fe (t) = [M + m(∞)]u̇(t) + k(t) ∗ u(t) + Sb s(t) + Fext (s(t), u(t), t)
Fe
s(t)
U (ω), u(t)
M
m(ω)
m(∞)
R(ω)
k(t)
Sb
Ru , M u , S u
Fext (s(t), u(t), t)
wave excitation force
body displacement
body velocity
structural inertia
added inertia
infinite-frequency added inertia
radiation damping
radiation impedance impulse response function (IRF)
hydrostatic stiffness
PTO damping, inertia, and spring
general nonlinear force which includes the PTO force
To be realistic, time-domain model is necessary
Assuming PTO force as linear enables frequency-domain analysis.
Fe (ω) = R(ω) + Ru + iω M + Mu + m(ω) − (Sb + Su )ω −2 U (ω)
However, since the PTO is nonlinear in reality, time-domain model
is necessary.
Fe (t) = [M + m(∞)]u̇(t) + k(t) ∗ u(t) + Sb s(t) + Fext (s(t), u(t), t)
Fe
s(t)
U (ω), u(t)
M
m(ω)
m(∞)
R(ω)
k(t)
Sb
Ru , M u , S u
Fext (s(t), u(t), t)
wave excitation force
body displacement
body velocity
structural inertia
added inertia
infinite-frequency added inertia
radiation damping
radiation impedance impulse response function (IRF)
hydrostatic stiffness
PTO damping, inertia, and spring
general nonlinear force which includes the PTO force
Force equations for a floating OWC
Frequency domain:
Fj = fj A −
X
Zjj 0 Uj 0 −Hjp p,
j0
Q = qA − Y p −
X
j = 1, 2, . . . , 6
HjU Uj
j
Time domain:
Fj (t) = Fe,j (t) −
X
[mjj 0 (∞)u̇j 0 (t) + kjj 0 (t) ∗ uj 0 (t)]
j0
+Cj (∞)p(t) + hj (t) ∗ p(t),
Q(t) = Qe (t) − y(t) ∗ p(t) −
X
j
j = 1, 2, . . . , 6
[Cj (∞)uj (t) + hj (t) ∗ uj (t)]
The convolution accounts for the system memory
Rt
The convolution k(t) ∗ u(t) ≡ 0 k(t − τ )u(τ ) dτ accounts for the
system memory, signifying the fact that waves radiated by the body
in the past continue to affect the body for all subsequent times.
Evaluation of the convolution term is problematic
It has to be re-evaluated at every time step.
Research questions
Modelling
Research questions
Modelling
Bond graph modelling,
assessment of alternatives to the radiation convolution term
Alternatives are available to avoid the convolution term
I
State-space model
A set of coupled linear ordinary differential equations
I
Constant-coefficient model
Replace frequency-dependent radiation coefficients by
constants
Three generic WECs
I
Single oscillating body
I
Fixed OWC
I
Floating OWC
Various nonlinearities are included in the models
I
Quadratic damping
I
Coulomb damping
osc. body
I
Quadratic damping
I
Coulomb damping
I
Air compressibility
I
Pressure relief valve
osc. body
fixed OWC
I
Quadratic damping
I
Coulomb damping
I
Air compressibility
I
Pressure relief valve
osc. body
fixed OWC
floating
OWC
State-space models are found to be accurate
error [%]
6
SS2
SS3
SS4
SS7
4
2
0
0
2
ω [rad/s]
4
6
Errors relative to frequency-domain model, for the body velocity of
a WEC without nonlinear terms
computation time [s]
State-space models save computation time
600
ode4
SS3
400
200
0
0
2000
4000 6000 8000 10000
simulation length [s]
Computation time of state-space radiation model of order 3 (SS3)
compared to direct convolution integration (ode4)
Application 1: Oscillating body with hydraulic PTO
Width
Draft
10
7.5
m
m
Two alternative hydraulic PTO systems
HP_accumulator
fluid_inertance
C
I
Se
Exciting_force
Body
TF
P
Primary conversion:
Hydraulic cylinder
0
1
Check valves
0
TF
R
pipe_resistance
C
LP_accumulator
Secondary conversion:
Hydraulic motor
P
R
R
Two alternative hydraulic PTO systems
pipe_resistance1
fluid_inertance1
I
R
Se
Exciting_force
Body
TF
P
C
1
Primary conversion:
Hydraulic cylinder
HP_accumulator
0
Check valves
0
1
TF
R
pipe_resistance2
I
fluid_inertance2
C
LP_accumulator
Secondary conversion:
Hydraulic motor
P
R
R
Simulation: 2-valve system, Tp = 11 s, Hs = 2 m
6
x 10
0
F
exc
[Nm]
5
−5
η [rad]
0.5
5
0
−0.5
7
[Pa]
3.4
x 10
p
HP
3.2
3
6
[Pa]
12
x 10
p
LP
10
8
u
P [kW]
150
100
50
0
0
100
200
300
time [s]
400
500
600
Simulation: 4-valve system, Tp = 11 s, Hs = 2 m
6
x 10
0
F
exc
[Nm]
5
−5
η [rad]
0.5
5
0
−0.5
7
[Pa]
3.4
x 10
p
HP
3.2
3
6
[Pa]
12
x 10
p
LP
10
8
u
P [kW]
150
100
50
0
0
100
200
300
time [s]
400
500
600
Application 2: Backward bent duct buoy (BBDB)
Length
Width
Draft
50
24
13
m
m
m
Bond graph model of the BBDB
Incident Wave Ampl.
Hydrost. + Ext. Mass + m(∞)
Ext. Damping
Restoring
C
file
input
MSe
I
1
Exc. Force
R
TF
R
body
TF
TF
Air Compressibility
C
Radiation Impedance
Radiation Coupling + C(∞)
0
R
P
Air Turbine
Sf
Radiation Admittance
R
Relief Valve
MSf
0
Exc. Vol. Flow
internal surface
R
Ext. Damping
Mass + m(∞)
With state-space models
Hydrost. + Ext.
Restoring
I
C
Exc. Force Data
f ile
input
Exc. Force
1
MSe
SSRadImp
Ext. Damping
R
body
TF
TF
MR
Rad. Imp.
Air Comp.
MSe
SSRadCF
C
Rad. Coupl. F
TF
C(∞)
0
Air. Turb.
MSf
SSRadCQ
R
P
Rad. Coupl. Q
R
Relief Valve
Rad. Adm.
AB
CD
MSf
y
f ile
input
Exc. Vol. Data
MSf
0
Exc. Vol. Flow
internal surface
R
Ext. Damping
Simulation: Tp = 8 s, Hs = 3 m
1200
P (t), unlimited p
u
mean Pu, unlimited p
Pu(t), limited p
800
mean Pu, limited p
600
u
P [kW]
1000
400
200
0
0
50
100
150
t [s]
200
250
300
Outline
Introduction
Modelling
Geometry control
Conclusion
A good wave absorber has to be a good wave maker
|H̄r opt (β ± π)|2
Pmax = λJ R 2π
2
0 |Hr opt (θ)| dθ
λ
J
Hr (β)
β
incident wavelength
wave-power level
radiation Kochin function
wave heading angle
To maximise power absorption, a system of WECs has to radiate
waves mainly opposite the incident wave direction, when the
system is forced to oscillate in time-reversal of its optimum motion,
in otherwise calm water.
A good wave absorber has to be a good wave maker
Jamie Taylor (1976)
But at what cost?
... a most important and urgent challenge is to develop a
feasible single unit of a WEC, a unit that maximises the power
output, not with respect to the free wave power that is
available in the ocean, but with respect to parameters related
more directly to the WEC itself (size, cost of investment and
maintenance, etc.).
Falnes and Hals (2012)
We need to maximise energy absorption and minimise cost
Maximise energy absorption
I
maximise power absorption
I
minimise losses
I
maximise design life
I
maximise capacity factor
Minimise cost
I
minimise capital expenditures
I
minimise operational expenses
I
minimise environmental impact
We need to maximise energy absorption and minimise cost
Maximise energy absorption
I
maximise power absorption
I
minimise losses
I
maximise design life
I
maximise capacity factor
Minimise cost
I
minimise capital expenditures
I
minimise operational expenses
I
minimise environmental impact
conflicting
objectives!
Example: Designing a bridge
The bridge is to carry as much load as possible and be as
lightweight as possible → conflicting objectives!
Wolfram (2007)
Example: Designing a bridge
The bridge is to carry as much load as possible and be as
lightweight as possible → conflicting objectives!
Wolfram (2007)
Possible solution strategies
I
Combine multiple objectives into one aggregate objective
function, e.g.
relative capture width =
capture width
device dimension
I
function, e.g.
capture width
device dimension
Drawbacks:
I
I
Need to know beforehand the relative importance of the
objectives
Returns only one optimum solution
I
function, e.g.
capture width
device dimension
Drawbacks:
I
I
I
Need to know beforehand the relative importance of the
objectives
Returns only one optimum solution
Multi-objective optimisation algorithms
I
I
Returns multiple optimum solutions to choose from
Provides insight into the behaviour of the solutions along the
optimal front
Research questions
Modelling
alternative modelling of the hydrodynamic radiation term
Optimisation
Research questions
Modelling
Optimisation
Multi-objective optimisation
The algorithm
The algorithm
The algorithm
The algorithm
The algorithm
The algorithm
The algorithm
The algorithm
The algorithm
The algorithm
Application 1: Composite circular cylinder
Optimisation objectives:
a2
θ
c
1. maximise absorbed power,
integrated over a wave
frequency range
a1
h
d1
d/2
Variable
d
d1
a1
a2
min [m]
max [m]
4
1
2
1
20
d/2 − 1
7
0.95 c
Pmax =
|Fe |2
,
4(R + |Zi |)
where
Zi = R+iω M + m − Sb ω −2
2. minimise total surface area
→ indicative of structural
cost
Progression of the ‘best’ solutions at the end of each
generation
1000
As
800
× initial
population
600
-◦- temporary
Pareto fronts
400
200
0
0
-◦- final Pareto
front
500
108 /
1500
R1000
Pmax dω
2000
Optimum geometries
−10
0
5
10
15
x [m]
6
z [m]
0
−5
−10
0
5
10
15
x [m]
0
0
5
10
−5
15
600
400
200
0
0
0
5
−5
0
5
10
15
0
5
x [m]
2
5
500
7
108 /
8
9
10
1500
R1000
Pmax dω
8
z [m]
5
−5
0
5
10
15
x [m]
0
−5
−10
−5
1
6
15
0
x [m]
3
4
10
x [m]
2000
10
15
5
0
−5
−10
5
−5
−10
−5
x [m]
800
7
−5
−10
5
−5
−10
−5
As
z [m]
−10
5
−5
z [m]
5
−5
5
4
0
9
z [m]
−10
−5
5
3
0
z [m]
z [m]
z [m]
−5
5
2
0
z [m]
5
1
0
z [m]
5
−5
0
5
10
15
10
15
x [m]
0
−5
−10
−5
0
5
x [m]
10
15
−5
0
5
x [m]
10
Optimum geometries
−10
0
5
10
15
x [m]
6
z [m]
0
−5
−10
0
5
10
15
x [m]
0
0
5
10
−5
15
600
400
200
0
0
0
5
10
15
x [m]
0
0
−5
5
10
15
z [m]
5
−5
0
5
10
15
x [m]
0
−5
−10
−5
x [m]
8
0
5
x [m]
10
15
5
0
−5
−10
5
−5
−10
−5
x [m]
800
7
−5
−10
5
−5
−10
−5
As
z [m]
−10
5
−5
z [m]
5
−5
5
4
0
9
z [m]
−10
−5
5
3
0
z [m]
z [m]
z [m]
−5
5
2
0
z [m]
5
1
0
z [m]
5
−5
0
5
10
15
10
15
x [m]
0
10
−5
−10
−5
0
5
x [m]
10
15
−5
0
5
x [m]
I Among the optimum geometries,
1
more power can be absorbed only
by increasing the surface area.
2
3
4
5
6
500
7
108 /
8
9
10
1500
R1000
Pmax dω
2000
Optimum geometries
−10
0
5
10
15
x [m]
6
z [m]
0
−5
−10
0
5
10
15
x [m]
0
0
5
10
−5
15
600
400
200
0
0
0
5
10
15
x [m]
0
0
−5
5
10
15
z [m]
5
−5
0
5
10
15
x [m]
0
−5
−10
−5
x [m]
8
0
5
x [m]
10
15
5
0
−5
−10
5
−5
−10
−5
x [m]
800
7
−5
−10
5
−5
−10
−5
As
z [m]
−10
5
−5
z [m]
5
−5
5
4
0
9
z [m]
−10
−5
5
3
0
z [m]
z [m]
z [m]
−5
5
2
0
z [m]
5
1
0
z [m]
5
−5
0
5
10
15
10
15
x [m]
0
10
−5
−10
−5
0
5
x [m]
10
15
−5
0
5
x [m]
1
2
3
4
I The radii of the central cylinder
5
6
500
tend to the maximum limit.
7
108 /
8
9
10
1500
R1000
Pmax dω
2000
Optimum geometries
−10
0
5
10
15
x [m]
6
z [m]
0
−5
−10
0
5
10
15
x [m]
0
0
5
10
−5
15
600
400
200
0
0
0
5
10
15
x [m]
0
0
−5
5
10
15
z [m]
5
−5
0
5
10
15
x [m]
0
−5
−10
−5
x [m]
8
0
5
x [m]
10
15
5
0
−5
−10
5
−5
−10
−5
x [m]
800
7
−5
−10
5
−5
−10
−5
As
z [m]
−10
5
−5
z [m]
5
−5
5
4
0
9
z [m]
−10
−5
5
3
0
z [m]
z [m]
z [m]
−5
5
2
0
z [m]
5
1
0
z [m]
5
−5
0
5
10
15
10
15
x [m]
0
10
−5
−10
−5
0
5
x [m]
10
15
−5
0
5
x [m]
1
2
3
4
I The radii of the central cylinder
5
6
tend to the maximum limit.
7
8
9
10
1500
R1000
108 / Pmax dω
500
I The radii of the larger cylinders
2000
are not maximized.
For geometries 6 to 10, a1 = 2 m,
the minimum limit.
Added inertia, Sb ω −2 − M , and absorbed power
5
1
z [m]
0
−5
−10
−5
0
15
4000
5
4
3
2
1
0
0.4
10
Pmax , Plim [kW]
m, Sω −2 − M [kgm2 ]
6
5
x [m]
8
x 10
0.6
0.8
ω [rad/s]
1
1.2
3000
2000
1000
0
0.4
0.6
0.8
ω [rad/s]
1
1.2
Added inertia, Sb ω −2 − M , and absorbed power
5
5
z [m]
0
−5
−10
−5
0
15
4000
10
5
0
0.4
10
Pmax , Plim [kW]
m, Sω −2 − M [kgm2 ]
15
5
x [m]
7
x 10
0.6
0.8
ω [rad/s]
1
1.2
3000
2000
1000
0
0.4
0.6
0.8
ω [rad/s]
1
1.2
Application 2: Cylinders with simple cross sections
l
l
l
p
p
h
p
h
b
h
O
O
d
O
e
e
e1
l
p
h
c
a
h
θ
a
X
c
a2
X
p
p
h
h
O
O
p
c
O
X
a3
a1
a4
O
e
Objective functions to be minimised
f1 (~x) =
f2 (~x) =
Z
ωmax
ω
Z ωmin
max
As /Pmax (ω)dω
FR max (ω)/Pmax (ω)dω,
ωmin
where
As submerged surface area
Pmax constrained maximum achievable power
FR max maximum dynamic reaction force at the hinge
Final Pareto fronts, ωmin = 0.4 rad/s, ωmax = 1.3 rad/s
submerged elliptical cyl.
surface-piercing circular cyl.
submerged circular cyl.
vertical flap
3
2.5
2
R
FR max /Pmax dω
3.5
1.5
1
0
1
R2
3
As /Pmax dω
4
5
−3
x 10
Optimum geometries, ωmin = 0.7 rad/s, ωmax = 1.3 rad/s
1.4
a1
a4
FR max /Pmax dω
1.2
1.1
1
0.9
0.8
O
0.7
0
0.5
1
R
1.5
2
0
0
−5
−5
−10
−15
−10
2.5
3
As /Pmax dω
z [m]
p
a3
R
h
1.3
c
X
z [m]
a2
−3
x 10
−10
−5
0
x [m]
5
10
−15
−10
−5
0
x [m]
5
10
Outline
Introduction
Modelling
Geometry control
Conclusion
Recall: The inherent challenges facing a WEC
I
I
A WEC must deal with the stochastic nature of the waves
What is required of a WEC to be economic?
Changing wave periods
A WEC must have a broad natural resonance bandwidth or
otherwise be able to artificially broaden its bandwidth (by adapting
itself from time to time to keep resonating with the waves).
Changing wave heights
A WEC must be able to avoid loads higher than the design limit.
Geometry control: Examples
I
Changing the orientation of a WEC relative to the incident
wave direction
I
Changing the inertia or inertia distribution of a WEC,
e.g. by ballasting
I
Changing the freeboard of an overtopping WEC
Wind turbines: Blade pitch control
Maintains stable power output and mitigates loads
Research questions
Modelling
Optimisation
Multi-objective optimisation,
Research questions
Modelling
Optimisation
adaptive geometry
Can we combine these two features into one device?
1.4
1.2
1.1
1
0.9
R
FR max /Pmax dω
1.3
0.8
0.5
1
R
1.5
2
0
0
−5
−5
−10
−15
−10
2.5
As /Pmax dω
z [m]
z [m]
0.7
0
3
−3
x 10
−10
−5
0
x [m]
5
10
−15
−10
−5
0
x [m]
5
10
Proposed WEC
2m
1.5 m
X
7m
20 m
O
Two flap angles are considered
θ = 0◦
θ = 90◦
Changing the flap angle changes its hydrodynamic
properties
7
1
0
−1
0.5
30
20
1
10
1.5
ω [rad/s]
2
m55 [kgm2 ]
m55 [kgm2 ]
9
x 10
2
x 10
10
0
0.5
1
10
1.5
9
d [m]
0
2
ω [rad/s]
7
x 10
x 10
30
1
20
1
10
1.5
ω [rad/s]
θ = 0◦
2
0
d [m]
R55 [Nms]
R55 [Nms]
20
d [m]
0
2
0
0.5
30
5
5
30
0
0.5
20
1
10
1.5
ω [rad/s]
θ = 90◦
2
0
d [m]
Varying the flap angle results in differing resonant
characteristics
C(ω) = −m55 (ω) − Ms +
8
5
Ss
ω2
8
x 10
4
x 10
C [kgm2 ]
C [kgm2 ]
3
0
2
1
0
−5
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
−1
0.4
0.6
0.8
1
1.2
1.4
ω [rad/s]
ω [rad/s]
θ = 0◦
θ = 90◦
1.6
1.8
2
Computed annual mean power output for different cases
θ = 0◦ (vertical flap)
θ = 90◦ (horizontal flap)
Pann [kW]
Case
Description
A
θ = 0◦ for all sea states
46.9
B
θ = 90◦ for all sea states
55.6
C
Best configuration for each sea state
57.2
D
θ = 0◦ for all sea states, with additional
restoring force for sea states 4 to 7
62.2
Maximum reaction force for cases C (solid) and D (dashed)
F R max [kN]
2000
1500
1000
500
0
1
2
3
4
5
6
7
8
Sea state
C
Best configuration for each sea state
57.2 kW
D
θ = 0◦ for all sea states, with additional
restoring force for sea states 4 to 7
62.2 kW
Outline
Introduction
Modelling
Geometry control
Conclusion
Research questions
Modelling
Optimisation
Research questions
Modelling
Optimisation
Research questions
Modelling
Optimisation
Research questions
Modelling
Optimisation
Research questions
Modelling
Optimisation
adaptive geometry
Further research directions
I
Bond graph modelling of overtopping and flexible WECs
I
Multi-objective optimisation of OWCs and other oscillating
bodies
I
Multi-objective optimisation of WEC arrays
I
WECs with adaptive geometries
Thank you

Modelling and geometry optimisation of wave energy

Transcription

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