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PAPER
Design, Modeling and Optimization of an
Ocean Wave Power Generation Buoy
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AUTHORS
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Carlos Velez
Department of Mechanical
and Aerospace Engineering,
University of Central Florida
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Zhihua Qu
Department of Electrical
Engineering and Computer Science,
University of Central Florida
Kuo-Chi Lin
Department of Mechanical
and Aerospace Engineering,
University of Central Florida
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Shiyuan Jin
Department of Electrical
Engineering and Computer Science,
University of Central Florida
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Introduction
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R
esearch into safe and clean energy
harvesting from renewable sources has
become popular in response to the
current energy crisis and growing environmental awareness. Renewable energy sources principally include solar,
wind, hydroelectric, ocean waves, etc.
Wind and solar power are restricted
to specific geographic regions; wind
power is only useful in windy areas,
and solar power is effective in only
sunny ones. Ocean wave power is especially promising because more than
two thirds of the Earth’s surface is covered by ocean, which should allow wise
access across the globe. Nature offers
large amounts of kinetic energy in the
form of ocean waves, and it is estimated that if 0.2% of the untapped
energy of the ocean could be harvested,
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ABSTRACT
Ocean waves provide an abundant, clean, and renewable source of energy. Existing systems, typically hydraulic turbines powered by high-pressure fluids, are very
large in size and costly. Additionally, they require large ocean waves in which to operate. This paper details the design, development, and laboratory prototype testing of
a wave power generation system comprising a buoy that houses a set of mechanical
devices and a permanent magnetic generator. The buoy, floating on the surface of the
ocean, utilizes the vertical movement of ocean waves to pull on a chain anchored to
the ocean floor. The linear motion is translated into rotation, which rotates a shaft to
move armature coils within the generator to produce an electric current. The amount
of energy generated increases with wave height and input frequency. The flywheel
inertia, shaft rotation speed, and electrical load are optimized to provide maximize
electricity production. The paper addresses the design, analysis, and implementation
of mechanical and electrical systems, together with resistive load control, system optimization, and performance analysis. Both simulation and experimental results are
provided and compared.
Keywords: buoy, ocean wave energy, permanent magnetic generator, load control,
wave power generation
it could provide power sufficient for the
61 entire world (Falnes, 2002).
62
This paper presents the novel design,
63 development, and laboratory prototype
64 testing of the wave power generation
65 system, shown in Figure 1, in which a
66 set of mechanical devices and a perma67 nent magnetic generator are installed
68 inside a buoy. The buoy floats on the
69 surface of the ocean and utilizes the ver70 tical movement of ocean waves to gen71 erate electric power. Specifically, when
72 the buoy moves from the trough to
73 the crest, the buoyancy force and hydro74 dynamic force pull upon the chain an75 chored to the ocean floor and rotates
76 the shaft to move armature coils of the
77 generator to produce electricity; mean78 while, the coiled spring in the reel is
79 pulled and tightened. Similarly, when
80 the buoy moves from the crest to the
60
trough, the reel rewinds the cable, and
the system returns to its original state.
The project thus far can be broken
into three stages:
1. Before implementing the laboratory prototype, a Matlab simulation
was used to simulate the hydrodynamics and the mechanical and
electrical models. The simulation
process aided the optimization of
the system’s electric power output.
2. Next, the laboratory prototype was
constructed and selected data were
measured.
3. Finally, the prototype results were
analyzed. Laboratory prototype data
were compared with simulation data
and identified discrepancies were
analyzed.
This design incorporates many technically challenging components such
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FIGURE 1
Conceptual design, wave power generation.
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as the wet-dry interface of the cable,
mooring design, hazardous environmental effects such as biofouling,
and multidirectional buoy motion.
These components are needed for
field installation but are not currently
considered as they are outside the
scope of this theoretical mechanical
study. The objective of this paper is
to study and optimize solely the internal mechanical components within
the buoy for a one-dimensional oscillating wave motion. System optimization was done by integrating the
hydrodynamic model along with the
mechanical and electric models. Additionally, load control was applied
to vary the electrical load on the output of the generator and to regulate the
rotor rpm in the case of irregular wave
motion.
The remainder of the paper is organized as follows:
■
Existing Wave Power Generation Technologies introduces existing ocean wave power generation
technologies.
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143 ■
Laboratory Prototype Design introduces conceptual and laboratory
prototype designs.
Mathematical Model provides the
mathematical equations and theoretical analysis.
System Optimization addresses system optimization (including simulation and prototyping test results).
Results and Discussion provides
experimental results and discussion
of voltage output, tension measurement, RPM, and electrical power
output.
Conclusion concludes the paper.
144
Existing Wave Power
146 Generation Technologies
145
Compared with other forms of gen148 eration of electricity such as wind and
149 hydro power, research on wave energy
150 is still in its infancy. Wave energy
151 development is a field that requires
152 multidisciplined, cooperative efforts
153 including technologies in hydro147
Marine Technology Society Journal
dynamics, mechanical engineering, in
addition to control and power systems.
There is much to improve in system efficiency, cost, reliability, and scalability
to make the extraction of wave energy
practical for consumer use. A few typical wave energy development examples are listed below.
■ Conceptual Wave Park by Oregon
State University (Brekken et al.,
2009): OSU is the pioneer in
research and development of wave
energy in the United States. It is
reported that a network of about
500 buoys could power the business district of downtown Portland.
Its linear generator using linear
translational motion harvests energy from one directional motion
of a buoy.
■ JAMSTEC, Japan (Osawa et al.,
2002): This system contains three
air chambers that convert wave energy into pneumatic energy. Wave
action causes the internal water
level in each chamber to rise and
fall, forcing a bidirectional airflow
over an air turbine. The turbines
drive three induction generators to
produce a three-phase AC output
at 200 Volts. More research has
been done by Cunha et al. (2009),
Elwood et al. (2010), Haniotis et al.
(2002), Kimoulakis et al. (2008),
Leijon et al. (2005), Mueller and
Baker (2002), Rhinefrank et al.
(2006), and Wolfbrandt (2006).
These systems all share the same difficulty in converting the oscillatory
motion of waves to the rotation of
a permanent magnet generator. The
proposed concept utilizes a buoy to
convert its linear height displacement
into electrical energy. The vertical displacement of the buoy will enable a
chain to rotate the shaft of a generator installed within the buoy itself.
Through the use of a pulley system,
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the rotation of the generator shaft
will be amplified with respect to the
actual buoy displacement. Incorporating these components will lead to
a small, inexpensive, light-weight and
consistent form of producing energy
for the applications including the
powering of nearby coastal regions
or offshore platforms.
Laboratory Prototype
Design
224
The prototype mechanical system
has been designed and constructed
and can convert the kinetic energy developed from the heaving forces generated by ocean waves into electrical
energy. The internal mechanism of
the buoy is designed to translate the
vertical oscillations of a buoy into rotational energy that will power a generator. Figure 2 is a snapshot of wave
power generation system inside the
buoy.
225
Mechanical Components
226
In Figure 2, a single long chain
wraps around two sets of sprockets
on the rotor shaft (connected to the
generator) and then loops downward
and is wrapped around two rotational
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FIGURE 2
Prototype wave generation system.
bearings fixed to the laboratory floor.
There are two loops made by a single
233 chain connecting the moving rotor
234 with the fixed rotor. This double
235 loop design multiplies the chain veloc236 ity at the second loop/sprocket by a
237 factor of 4. Additionally, the double
238 loop design allows for unidirectional
239 rotation of the main rotor (shown in
240 Figure 2) independent of the direction
241 of motion of the chain/buoy. In effect,
242 even if the buoy is oscillating up and
243 down, it will only incur a clockwise di244 rectional torque on the generator shaft.
245 In order for the chain to loop around
246 and drive the rotor shaft, two sprockets
247 are required. The first sprocket is lo248 cated at the first chain loop where
249 clockwise rotation will drive the rotor;
250 during counter-clockwise rotation,
251 it will spin freely around the main
252 rotor. The second sprocket is located
253 where the chain loops around the
254 rotor for the second time. This sprocket
255 is reversed and operates opposite to the
256 first sprocket. When the buoy moves
257 upward, the first sprocket drives the
258 generator and the second sprocket
259 spins freely. The opposite is true for
260 the downward motion of the buoy,
261 resulting in unidirectional rotation of
262 the rotor with bidirectional motion of
263 the buoy/chain. One end of the chain
231
232
is attached to a constant torque rotational spring, which acts to keep tension in the chain, and the other end
of the chain is fixed to the moving
buoy. This rotational spring also helps
drive the shaft in order to ensure the
continued rotation of the shaft. The
shaft is coupled to a permanent magnet
generator, which extracts power from
the rotating motion of the shaft. To increase the inertia of the shaft assembly,
three steel flywheels are fastened onto
the driven shaft.
In order to test the performance of
the mechanical system, a 6-DOF motion table is utilized to simulate the
motion of a wave. The motion of the
platform is prescribed to follow a sinusoidal path in the vertical direction
only. The mechanism is placed on top
of the platform with the chain fixed to
the floor, simulating a mooring to the
ocean floor. The platform was programmed to move at various frequencies ranging from 0.1 to 0.3 Hertz and
at amplitudes of 5–15 cm.
264
Electrical Components
290
In order to analyze the performance
of the mechanism, several parameters
were measured during the experiments.
■ An optical sensor was used to measure the instantaneous RPM of the
shaft.
■ A potentiometer was used to measure the instantaneous location of
the platform.
■ A strain gauge was placed on one
of the links in the chain in order
to constantly measure tension in
the chain.
■ A Data Acquisition Board (DAQ)
measured the power output from
the generator; the three leads of the
generator are brought out and connected to a diode rectifier.
A program constructed in
LABVIEW controlled a relay switch.
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The relay switch position is dependent
on the shaft RPM and position of the
platform. When load is applied, the
load current flows inside the generator,
inducing a voltage drop across the
internal circuit resistance. Applying
additional resistance increases the
torque of the generator, thereby reducing the RPM.
Design Issues Regarding
Optimal Performance
Components within the mechanical system can be optimized to improve overall system performance.
The optimal performance is intended
to produce the largest amount of
power, while preventing the system
from experiencing any large peak
or cyclical stresses that would greatly
limit the life span of the mechanism.
The amount of inertia contributed
by the flywheels is one simple way to
optimize the efficiency of the system.
By increasing the inertia of the shaft,
one raises the potential energy in
the rotating shaft. Consequently, the
torque needed to rotate the shaft at
a set RPM is increased because of the
increase in inertia. The proper amount
of shaft inertia is determined by the
size of the ocean waves, and this will
subsequently drive the dimensions of
the buoy. Additionally a gear train
may be implemented to convert excess
torque into an increased RPM of the
shaft; increasing the gear ratio will proportionally increase the shaft speed.
Thus, the gear ratio should be optimized to increase the RPM of the
shaft while not limiting the motion
of the buoy too much through the increase in mass. The dimensions of the
sprockets can also be optimized to improve the performance of the overall
system. Reducing the radius of the
sprocket increases the shaft RPM and
reduces the amount of torque created
4
by the buoy. The method in which
the generator extracts energy from
361 the rotating shaft can be selected to
362 conserve the momentum of the fly363 wheels. Varying the electrical resis364 tance or load on the generator can
365 allow one to control the required torque
366 needed to drive the generator. A de367 tailed analytical solution is developed
368 to optimize the system components
369 and is addressed at the optimization
370 section of this paper.
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Mathematical Model
372
Laboratory Prototype Model
The system can be represented by
374 three models: hydrodynamic model,
375 generator motion model, and buoy
376 model, as illustrated in Figure 3.
377
The relationship between mechan378 ical and electrical torques and angular
379 acceleration can be represented by the
380 following equation:
373
dω
Tm − Te ¼ I
dt
ð1Þ
where Tm is the mechanical torque, Te
382 is the electromagnetic back-torque, I is
383 the moment of inertia of the system,
384 and ω is the angular velocity of the
385 shaft. The mechanical torque is created
386 by both the tension from the tethered
381
Marine Technology Society Journal
FIGURE 3
Hydrodynamic and buoy system model.
cable as well as system frictional force.
The electrical torque is developed by
the rotor of the generator as it rotates
in the magnetic field with a resistive
load applied to the generator.
387
Hydrodynamic Model
392
The ocean wave motion is transferred into rotational motion for the
permanent magnetic generator via the
motion imparted on the floating buoy.
Wave forces consist of both rotational
and heaving forces. In this paper, only
the one-dimensional heaving force
is considered in the hydrodynamic
model. The equation of motion is
modeled by the following:
393
mz̈ ¼ Fb þ Fexcite − Fdrag − mg − T
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402
ð2Þ
where m is the total mass of the buoy
including all components inside it, z is
the vertical displacement of the buoy,
F B is the buoyance force acting on
the buoy, Fexcite is the vertical wave
excitation force which is described
shortly, F drag is the hydrodynamic
drag force acting on the buoy, and T
is the tension force of the cable which
tethers the buoy to ocean floor (Sarpkaya
& Isaacson, 1981). FB , Fdrag , T, and
Fexcite can be calculated as follows.
Fb ¼ ρw gVsubmerged
388
ð3Þ
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where w is the water density and Vsubmerged is the submerged volume of the buoy.
When a spherical buoy is in hydrostatic equilibrium, the weight of the buoy is balanced by the buoyancy force. Assuming that the water level reaches a height of y0
above the center of the sphere, then the overall static buoyancy force experienced
by the buoy is governed by the following equation
2
1
Fb ¼ ρw g πR 3 þ π R 2 yo − yo3
3
3
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422
where ρw is the density of the water (displaced fluid) and R is the radius of the spherical buoy.
Next, the drag force (FD) in equation (2) is expressed analytically as
Fdrag
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ð4Þ
1
¼ − ρw Cd Ab jżjjżj
2
ð5Þ
where Cd , set to 0.75, is the drag coefficient of the buoy and Ab is the area of the
submerged surface of the buoy projected on a plane normal to the z-direction. The
drag coefficient, Cd , is a function of the geometry of the buoy and the Reynolds
number of the fluid, but for convenience purposes it will be modeled as a constant
for this paper (Leonard et al., 2000). The drag force contributes the least of the five
forces due to its low velocity (ż).
The cable tension force (T ) in equation (2) is expressed as
T ¼ To þ Dcoupled
Cload ¼
Dcoupled ¼
Cgen ω Iα
Cload þ
r
r
1 if load is on
0 if otherwise
1
0
Coupled
Uncoupled
ð6; 7; 8Þ
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where Cload represents the electrical load state, Cgen is the generator back-torque
coefficient (generation load), Dcoupled represents the coupled/uncoupled state of
the mechanical system discussed shortly, α is the angular acceleration of the
shaft, and r is the radius of the sprocket.
The last force in equation (2) is the wave excitation force. The excitation
force of a wave acting on a body can be separated into three components: the
Froude-Krylov force, the diffraction force, and the radiation force (Patel, 1989).
The Froude-Krylov force, realized as wave momentum, is imparted onto a submerged body, and the diffraction and radiation forces come from the disturbances
to the surrounding fluid. The size of the buoy was considered significantly smaller
than the length of the surface waves; as a result, the diffraction and radiation forces
were considered negligible. Thus, the wave excitation force is equated to the FroudeKrylov force, as detailed below:
Fexcite ¼ −ρw
∯
dФi
nb dSsubmerged :
dt
ð9Þ
In the above equation, the surface integral is taken over the submerged
surface of the buoy. The normal vector to the surface is denoted by b
n;
since the simulation investigates
one-dimensional motion, only the
z-component of the normal vector is
used.
Equations (4)–(9) can be combined together into equation (2) to create the governing equation of motion.
It is impractical to solve analytically;
instead numerical methods are used
to calculate the position, velocity, and
acceleration of the buoy at each timestep. The resulting data can be used to
determine the RPM of the shaft, the
tension in the cable, and the expected
power output for a given generator
model (Cgen).
In order to simulate the system as
accurately as possible, it is necessary
to analyze the system in three separate
stages.
■ Stage I: Decoupled stage (upper
half of upstroke)—On the upper
half of upstroke, the buoy deaccelerates. The sprocket decouples from
the shaft, that is, the angular velocity of the shaft exceeds that of the
sprocket; the pulling force of the
buoy cable does not contribute
work to the flywheel. Only the resistive force of the generator and
friction exert forces on the shaft.
■ Stage II: Down-stroke stage—On
the down-stroke, there is no pulling
force at the cable tethered in the
buoy. The resistive load force of
the generator is not applied as well,
for the consideration of load control to keep flywheel momentum
which forces the system to run continuously, although the frictional
force (is proportional to angular velocity) slows the shaft.
■ Stage III: Coupled stage (lower half
of upstroke)—On the low half of
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upstroke, the pulling force/torque
accelerates the system until to the
equilibrium point when the angular
velocity of the shaft no longer increases. In addition to the pulling
force, the resistive force of the generator and friction force also apply
to the shaft, countering the pulling
force/torque. The maximum tension is applied right after the lowest
turning point.
adjusted to increase the power output of the system. The objective is to
534 choose values for these parameters
535 from their feasible ranges in an optimal
536 way in order to get maximum power
537 output. Of course the optimum values
538 are dependent on the design of the
539 buoy, and even more importantly,
540 the wave conditions; the result is that
541 in order to achieve truly optimum out542 put, the parameters would have to
543 dynamically adjust based on the con544 stantly changing wave conditions.
545 This is impractical, and instead the
Generator Model
The simulation of the system inte- 546 design parameters should be optimized
grated the hydrodynamic force of the 547 based on the estimated average wave
buoy into the mechanical and electrical 548 characteristics.
models. For the experimental portion
of this project, a GL-PMG-500A per- 549 Matlab Simulation
manent magnet generator, manufac- 550 A simulation was run in Matlab to
tured by Ginlong Technologies, Inc., 551 determine the estimated power output
was utilized. This model has the ad- 552 using the one-dimensional scheme devantage of a low start up torque (due 553 tailed in the previous section. In order
to low cogging and resistive torque 554 to solve the differential equation given
design) and high efficiency. The resis- 555 in equation (2), a fourth-order, explicit
tor load in this experiment is 1:6, 556 Runge-Kutta algorithm was implewhich matches the resistive load tested 557 mented. The simulation is executed
by the generator’s manufacturer. Ac- 558 for a 60-s duration with a time-step
cording to the generator specification, 559 of 0.05 s; initial conditions of dynamic
the power output can be represented as 560 equilibrium was imposed. The buoy is
561 modeled simply as a sphere of radius R
follows:
562 and the surface wave is a perfect sinu
2
563 soid. Each design parameter may be
w 60
564 adjusted independently within the
2π
ð10Þ
P¼
565 simulation so as to determine the effect
16:6
566 on the power output. The average power
where w is the RPM of the shaft.
567 output is given for the 60-s simulation
568 and used for comparison. Table 1 de569 tails the values of all of the constants
System Optimization
570 used within the Matlab simulation.
As mentioned previously, given a 571 The Matlab simulation is capable
fixed wave amplitude and frequency, 572 of outputting the instantaneous values
the optimal power output P max de- 573 of several system variables, including
pends on several factors. The radius 574 the tension in the mooring cable, the
of sprocket, r, the inertia of the fly- 575 RPM of the shaft, and the generator
wheel(s), I, the ratio of the gear set 576 output power. The simulation is run
used, GR, and the controlled electrical 577 utilizing the inputs given in Table 1
load added to the generator, L, may be 578 (except for a 20-s duration).
6
532
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Marine Technology Society Journal
The simulation is useful for predicting the average power output for
given system inputs. Because the simulation uses arbitrary values for the
parameters to be optimized, the results
of this method are only suboptimal.
To determine the actual optimal values, all parameters need to be varied
simultaneously. For simplicity, only
three design parameters are investigated here: flywheel inertia (I ), the
gear ratio (GR), and the load control
threshold (L).
Flywheel Inertia
Optimization
Without adequate inertia on the
shaft, the flywheel may not continuously rotate throughout the complete
wave cycle. With excessive inertia, on
the other hand, the angular acceleration of the shaft will suffer as a result
of increased chain tension, as seen in
equations (6) and (2). As such, the inertia of the shaft should be optimized
so that the motion of the shaft is continuous while limiting the effect on
the buoy motion. Given a fixed wave
amplitude and frequency, reasonable
flywheel inertia can be chosen to maximize electrical power output. The
value of the shaft inertia is varied in
the Matlab simulation for values between 0.05 and 0.5 kg m2; with increments of 0.01 kg m2. The power
output corresponding to the peak
power is a function of the other parameters, but for the given inputs the optimal inertia for the shaft is found to
be 0.25 kg m2.
Gear Ratio Optimization
The generator detailed in the simulation is relatively small, with a low
back-torque coefficient and ideal shaft
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580
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617
618
619
620
621
t.1
TABLE 1
t.2
Simulation parameter values for the optimization model.
t.3
Parameter
Value
Description
t.4
Aw
1
Amplitude of wave [m]
t.5
F
0.2
Frequency of wave [1/s]
t.6
R
0.5
Radius of buoy [m]
t.7
m
200
Mass of buoy [m]
t.8
ρw
997.0
Density of water at 25 °C [kg/m3]
t.9
μ
0.001
Dynamic viscosity of water at 25 °C [kg/ms]
t.10
Cd
0.45
Drag coefficient of sphere [unit-less]
t.11
g
9.81
Gravitational acceleration [m/s2]
t.12
To
100
Spool tension [kg m/s2]
t.13
Tfin
60
Duration of model [s]
t.14
δt
0.02
t.15
Cgen
6.36
Time step for model [s]
h
i
2
Back-torque coefficient kg ms
t.16
βfric
0.5
Mechanical friction coefficient [kg m2/s]
t.17
Tstart
5
2
Start-up torque for generator [kg m/s ]
2
t.18
I
0.1
Moment of Inertia of system [kg m ]
t.19
GR
1.0
Gear ratio [unit-less]
t.20
L
0
Load control threshold [RPM]
t.21
R
0.05
Radius of sprocket [m]
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
input of around 275 RPM. To achieve
this ideal speed, the gear ratio is likely
to be on the order of, but greater than,
unity. In the Matlab simulation, the
gear ratio is a multiplier acting on the
speed of the shaft and it acts to transmit the resulting large back-torques to
the tension of the mooring line, as detailed in equation (6). The gear ratio is
varied from 0.5 to 5, with increments
of 0.1 in the simulation. Figure 4 illustrates the relationship between GR and
the resulting average power output for
the system.
to prevent the shaft from slowing to a
standstill. Intuition suggests that the
load should be applied while the shaft
RPM is high above some threshold,
and it should be disconnected while
it becomes low. Furthermore, the electrical load should be controlled such
that:
1. least load is applied in the down
stroke when there is no wave force
and
2. the oscillating velocity of the
system is in phase with the wave’s
excitation force acting on the
system (Kimoulakis & Kladas,
2008).
Usually the oscillating velocity of the
buoy is out of phase with the wave’s
excitation force. Therefore, to maximize the electrical output power, the
electrical load should be controlled in
a way to make the buoy operate synchronously with the wave. The implementation of load control can be
enhanced by selecting a threshold
for which the load is disengaged. For
FIGURE 4
Electrical power output vs. gear ratio.
Electrical Load
Control Optimization
By adjusting the timing at which
the load is applied, continuous power
extraction may be sacrificed in order
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example, if the RPM of the shaft
drops below the threshold the load
is reduced and then reengaged when
the RPM rises above it. This load
control threshold (LC) was a parameter in the Matlab simulation and
varied from 0 to 200 RPM, at increments of 5 RPM.The suboptimal
value for the load control threshold
is found to be 170 RPM. Using this
point as the threshold value, the electrical load is disconnected from the
generator when the shaft speed falls
below 170 RPM.
mal values. For instance, when
running the overall optimization simu2
715 lation, values near 0.25 kg m inertia,
716 2.0 gear ratio, and 170 RPM load
717 threshold should be investigated
718 as one or more may lie close to the
719 actual system’s optimum. The system
720 scheme was done by brute force, a
721 range around each of the aforemen722 tioned values was selected, and each
723 scenario with that range was inspected
724 to determine the highest power out725 put. This method is effective, but
726 highly inefficient. Nevertheless, opti727 mum values were discovered for the
Optimization of the
728 given inputs for the defined buoy sysSprocket Radius
729 tem and wave characteristics. The opThe radius of the sprocket is di- 730 timal parameters resulted in an inertia
rectly related to the shaft RPM. The 731 of 0.18 kg m2, a gear ratio of 2.2, and
smaller the radius, the greater the 732 load control of 190 (RPM).
RPM, but this also increases chain
tension. The simulation did not demonstrate a clear relationship between 733 Results and Discussion
sprocket size and power output; it ap- 734 Simulated Wave
peared that the smaller the sprocket 735 In the laboratory prototype test,
radius, the greater the power. It may 736 an electrical 6-DOF motion system is
be possible that a very small sprocket 737 used to mimic the movement of ocean
would provide an optimum size, but 738 waves. The motion system consists of
this would be impractical. Instead, 739 a motion platform, a base frame, a
the chosen sprocket is the smallest, 740 motion control cabinet, and a mocommercially available unit that is suf- 741 tion computer that can simulate the
ficiently large enough to support the 742 very complicated movements (i.e., a
stresses induced by the peak chain 743 combination of lateral and vertical
tension.
744 movements) of a buoy. Figure 1 is a
745 simplified view of wave power generaOverall System Optimization
746 tion system concept. All mechanical
The suboptimal values found for 747 assemblies including the generator
the flywheel inertia, gear ratio, and 748 (shown at the upper right corner) are
the load control threshold are not 749 mounted to the motion platform. A
very useful by themselves because 750 chain is routed through a hole in the
of the arbitrary selection of values for 751 platform, and one end is attached to
the other parameters. To find the ac- 752 a pull-box directly tethered to the
tual optimal values, all three parameters 753 ground. The other end is fixed to the
must be optimized simultaneously to 754 moving table. When the platform
account for system interdependencies. 755 moves up, it pulls the chain to run
The three suboptimal values may serve 756 over the sprockets to rotate the shaft;
as guidelines for where to inspect each 757 when the platform moves down, the
of the parameters for the actual opti- 758 pull-box tightens the chain.
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Marine Technology Society Journal
Sensor Devices
and Measurements
759
In the laboratory prototype testing,
the following sensors are used to perform measurements to aide in optimizing the system. A strain gauge is
used to measure the tension in the
chain. This measurement is important
in the design of the buoy to reduce the
probability of a chain breaking due
to excessive stress. An RPM encoder
is used to measure the instantaneous
RPM of the flywheel and generator.
A displacement sensor is attached to
the motion platform to measure the
instantaneous height of the platform.
This sensor is used in conjunction
with a relay switch to automatically
apply the electrical load at the most
potent sections of the up-strokes.
761
Measurement of Voltage,
Load Control, and RPM
779
The measurement of voltage, load
control, and RPM under a frequency
of 0.3 Hz and amplitudes (platform
movement) of 10 cm and 12 cm were
performed. After calculation, the average power output under the amplitude of 10 cm was 113.37 W. At
an input amplitude of 12 cm, the system generated 136.13. Shaft RPMs
were 188.60 and 221.42, respectively.
This results in a 17.40% increase
in RPM and a 20.08% increase in
power (W) for experiments run with
a flywheel with moment of inertia
of 0.10 kg m2.
781
A Comparison of Simulation
and Experimental Results
796
Comparisons (RPM and power
output) were made between the
Matlab simulation and laboratory
prototype results, at the same input
torque; that is, the input torque based
on the measured tension force in the
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prototype was used as the input torque
to the Matlab simulation model.
Figure 5 shows the RPM data from
both the simulation and the prototype
unit. The experimental RPM is not
smooth as the platform moves down;
however, both datasets show similar
patterns—RPMs increase quickly as
the platform moves up and decrease
slowly as the platform moves downward, a direct effect of the load control.
When the RPM drops below the set
threshold, the relay switch turns off,
decreasing the electrical load. The
momentum of the flywheels engages,
and the shaft RPM decreases slowly
as the energy stored in the flywheel
momentum is depleted. Compared
with the experimental results, the RPM
in the simulation model drops more
quickly at the beginning in the downstroke and then decays more slowly.
It should be noted that the electrical
load (its resistive torque) is much
greater than the frictional torque in
the mechanical system.
Several factors can cause the observed discrepancies. For example, it
is difficult to measure the friction of
the mechanical system or accurately
simulate the generator model and its
resistive torque. Furthermore, the mo836 tion platform can create a sinusoidal
837 movement similar to a wave, but it is
838 difficult to mimic the complex hydro839 dynamic buoy model, which includes
840 several, more complex forces.
834
835
841
Conclusion
This paper introduces an innovative design, development, and labo844 ratory prototype of a light-weight,
845 low-cost, small-size wave power gener846 ation system which includes a buoy, a
847 set of mechanical devices, and a perma848 nent magnetic generator. Prior to pro849 totype setup, a hydrodynamic model,
850 buoy model, and a generator model
851 were analyzed, and a Matlab system
852 simulation was conducted. The fly853 wheel inertia, shaft rotation speed, and
854 electrical load are optimized to maxi855 mize electricity production. The cur856 rent laboratory prototype is capable
857 of generating an average of 136 W
858 under the movement of a motion plat859 form with 12 cm in amplitude, 0.3 Hz
2
860 frequency, and 0.10 kg m moment
861 of inertia, and 206 W with 10 cm in
842
843
FIGURE 5
Comparison of RPM from Matlab simulation and prototype experimentation.
amplitude, 0.3 Hz frequency, and
0.25 kg m2 moment of inertia. System
performance regarding the mechanical
power input and electrical output was
analyzed based on experimental data
such as tension of the chain, shaft
RPM, and voltage output. Both simulation and experimental results are
provided and compared to verify the
laboratory prototype design with reasonable correlation between them.
The success of this mechanical system
and optimized design could promise
a clean, safe, and abundant energy
source to satisfy a significant portion
of society’s energy needs in the future.
Corresponding Author:
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Carlos Velez
Department of Mechanical and
Aerospace Engineering,
University of Central Florida
4000 Central Florida Boulevard,
Orlando, FL 32826
Email: [email protected]
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