According to calculations by scientists, the received energy from
fossil fuels will become gradually exhausted, and now therefore
looking for new energy sources is requisite. For Vietnam, the 2020
target is to become a country in which marine economics will
constitute over 50% of GDP. Therefore, the energy demand
supplying for general economics and particular marine economics is
very important. The research and fabrication of electrical generators
for sea wave energy are necessary. Moreover, the electrical energy
received from sea wave energy conversion is friendly to
environment, almost endless and is a clean energy source. The sea
wave energy is an important energy source of the world as well as
Vietnam in the future.
In addition, Vietnam has the advantage of being a country with a
coastline stretching over 3260 km, with more than 3000 islands and
over one million km2 of sea surface, it indicates that the energy
source from the sea is huge. In order to exploit the vast energy
resources of the sea, the author proposes a research of thesis of
building a device model to convert from sea wave energy to
electricity.

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MINISTRY OF EDUCATION
AND TRAINING
VIETNAM ACADEMY
OF SCIENCE AND TECHNOLOGY
GRADUATE UNIVERSITY SCIENCE AND TECHNOLOGY
----------------------------
Nguyen Van Hai
RESEARCH ON THE MECHANICAL MODEL AND
CALCULATING DESIGN OF AN ELECTRICAL
GENERATOR FOR SEA WAVE ENERGY
Major: Engineering Mechanics
Code: 9 52 01 01
SUMMARY OF MECHANICAL ENGINEERING AND
ENGINEERING MECHANICS DOCTORAL THESIS
HANOI – 2019
The thesis has been completed at: Graduate University of Science
and Technology - Vietnam Academy of Science and Technology
Supervisor: Prof. DrSc. Nguyen Dong Anh
Reviewer 1:
Reviewer 2:
Reviewer 3:
Thesis is defended at Graduate University of Science and
Technology
- Vietnam Academy of Science and Technology at, on
datemonth2019.
Hardcopy of the thesis be found at:
- Library of Graduate University of Science and Technology
- Vietnam National Library
1
INTRODUCTION
1. Reasons for choosing the topic
According to calculations by scientists, the received energy from
fossil fuels will become gradually exhausted, and now therefore
looking for new energy sources is requisite. For Vietnam, the 2020
target is to become a country in which marine economics will
constitute over 50% of GDP. Therefore, the energy demand
supplying for general economics and particular marine economics is
very important. The research and fabrication of electrical generators
for sea wave energy are necessary. Moreover, the electrical energy
received from sea wave energy conversion is friendly to
environment, almost endless and is a clean energy source. The sea
wave energy is an important energy source of the world as well as
Vietnam in the future.
In addition, Vietnam has the advantage of being a country with a
coastline stretching over 3260 km, with more than 3000 islands and
over one million km2 of sea surface, it indicates that the energy
source from the sea is huge. In order to exploit the vast energy
resources of the sea, the author proposes a research of thesis of
building a device model to convert from sea wave energy to
electricity.
2. Objective of the thesis
For the purpose of building a model of electrical generator for
sea wave energy, the device operates efficient and in suitable to
Vietnam's sea condition; Determining the optimal damping
coefficient of the generating motor, model parameters to received the
2
maximum output power; Design, fabrication of the electrical
generator with the output voltages are 12 VDC, 220 VAC frequency
50 Hz and pure sine wave.
3. Research method
The thesis uses analytical method, combining of the numerical
simulation and experiment for calculation, being specifically
described as follows:
- Determining the optimal damping coefficient of the generating
motor and model parameters by the analytical method.
- Using fourth-order Runge-Kutta and Simpson methods in
numerical simulation calculations, to determine the output power of
the device received from the sea wave energy and survey the device's
operation according to the sea wave conditions.
- Calculation, design, fabrication and experiment of the electrical
generator operates in sea.
4. Scientific and practical significance
- The thesis brings the electrical generator model for sea wave
energy, with the process of making the electrical generator device
from research to fabrication, the device operates effectively and
suitable to the actual conditions of Vietnam sea.
- The electrical generator can be used for signal buoys of seaway
and can supply the electrical power for lighthouses.
5. Structure of the thesis
The contents of the thesis include the introduction, 4 chapters,
the conclusion and proposition.
3
CHAPTER 1. OVERVIEW OF RESEARCHES ON THE
ELECTRICAL GENERATOR FOR SEA WAVE ENERGY
AND APPLICABILITY IN VIETNAM
1.1. Overview of researches on the electrical generator in the
world
In the world, the research and fabrication of the electrical
generator devices for sea wave energy source have been considered
for a long time. The received electrical energy source for wave
energy conversion has met some demands of society. Up to now,
the electrical generators from sea wave energy have been
investigated and fabricated in many countries, for example,
Britain, Canada, Denmark, France, Ireland, Japan, Norway, Spain,
Sweden, South Korea, the United States, The models are
researched in various forms such as the on-shore device, the device
fixed on the bottom of the sea, and the floating device on the sea
surface [1-19].
The analyses of models show that the electrical generator devices
have been researched and fabricated in many ways. In device
models, the generating motor is designed to operate in a rotational
motion or in a vertical up-down motion. Each device has different
advantages and disadvantages, depending on the fabrication
capabilities of each unit so that the research and fabrication devices
operate effectively and suitable to the actual use.
1.2. Overview of researches on the electrical generator in
Vietnam
In Vietnam, several research institutions have fabricated
electrical generators for sea wave energy. At National Research
4
Institute of Mechanical Engineering, the researchers have calculated
device model with Pelamis type, the device has been experimented in
Hon Dau - Haiphong sea and supplied the electrical power to the
border guards on the island to use [24]; At Vietnam National
University, the researchers have fabricated linear electrical
generators that operate and float on the sea surface in vertical
direction. The device has been tested in sea with the received output
power still limited [26,27]; At Institute of Energy Science - VAST
has fabricated an electrical generator device from sea wave energy,
the device is fixed on the sea surface. The fabricated device used the
vertical axis hydropower generator with 60 W power, the device has
been tested in sea with the output power received 50.92 W [28];
At Institute of Mechanics - VAST has carried out researches on
surveying the energy characteristics of floating wave energy
converters, to propose the design, calculation and fabrication of
energy conversion devices [30]. Moreover, since 2013, in the
professional work, the author has calculated a numerical simulation
of the electrical generator model from sea wave energy. The device
model is calculated with the linear electrical generator, directly
generating electricity and fixed on the seabed [31].
And more, the author has leaded the project "Study, design and
fabrication of the electrical power system from the renewable energy
sources, project’s code: VAST 02.04/11-12" [32]. The project has
designed and fabricated a power generation system with input energy
sources from solar panel, wind energy and sea wave energy. In
which, the input source from sea wave energy has been calculated
5
and designed to be integrated with the electrical generator for sea
wave energy will be studied and fabricated in the thesis.
1.3. Research on the ability to apply the electrical generator in
Vietnam and research orientation of the thesis
Vietnam is a country with a coastline stretching over 3260 km, a
marine space of over 1 million km2, accounting for 29% of the area
of the East Sea, with nearly 3000 large and small islands, it indicates
that the energy source from the sea is huge. From the monitoring and
survey data show that the average sea wave height at the near coast
is about 0.5÷1.2 m with the wave period from 2÷8 seconds, offshore
wave height is about 1.2÷2 m with a wave period from 6÷8 seconds.
Especially, when the rough sea, the coastal wave height reaches
about 3.5÷5 m, offshore reaches about 6÷9 m [34-37]. This is an
abundant energy source, which is very suitable for the electrical
generator devices from sea wave energy to be with small and
medium power.
Moreover, the demand for electricity to provide for the marine
economics, electricity for national security in the protection of sea
and island sovereignty is an urgent task, while Vietnam’s National
electricity Network can not reach. Therefore, the research and
fabrication of the electrical generator devices for sea wave energy to
meet the actual needs is necessary.
Research orientation of the thesis:
The purpose of the thesis is research, calculate and design a
device to generate electricity from sea wave energy. The device is
6
efficient operation, and suitable for processing ability in Vietnam.
The power source of device generates at two voltage levels are 12
VDC and 220 VAC frequency 50 Hz, with voltage quality is pure
sine wave and according to Vietnam’s National grid Standard.
Especially, the electrical generator can be used for signal buoys of
seaway and can supply the electrical power for lighthouses.
Conclusions of chapter 1
Chapter 1 presents an overview of the electrical generators in the
world, especially, the models mounted on the seabed and vertical
direction operation. Having pointed out that domestic units have
been realizing research and fabrication of the electrical generator
with detailed analysises for each type of device model. The
characteristics of sea wave energy have been collected and analyzed,
with data on wave energy flux, wave height and wave period to
along the Vietnam coast stretching over 3260 km. In which, the
average sea wave height at the near coast is about 0.5÷1.2 m with the
wave period from 2÷8 seconds, offshore wave height is about 1.2÷2
m with a wave period from 6 ÷ 8 seconds. Especially, when the
rough sea, the coastal wave height reaches about 3.5÷5 m, offshore
reaches about 6÷9 m.
Having indicated that the necessity and application capability of
device model in Vietnam. Having shown out the structure of the
electrical generator model for sea wave energy, and orient the
research contents of the thesis, the device operates effectively and
suitable to the actual conditions of Vietnam sea.
7
CHAPTER 2. RESEARCH ON THE MECHANICAL MODEL
AND OPTIMIZATION OF THE ELECTRICAL GENERATOR
FOR SEA WAVE ENERGY
2.1. Building a model of the electrical generator for sea wave
energy
The electrical generator device is fabricated for converting sea
wave energy into electrical energy. This requires a system that can
convert the vertical slow motion of buoy to a high speed rotating
motion at the input of generating motor. The main structures of
device include a circular cylinder-shaped buoy, a rope, a piston-rack,
a gearbox, a generating motor, a block of 12 VDC voltage stabilizer,
a DC-AC inverter and a protection system with the generating
voltage being 220 VAC frequency 50 Hz and pure sine wave, as
shown in Fig. 2.1.
a. Illustration of device model [33]
Figure 2.1. The schematic illustration of an electrical generator
for sea wave energy
z(t)
zS(t)
γ k
m
b. Mechanical model
8
The governing equation of buoy associated with piston-rack, as
shown in Fig. 2.1, can be written as follows:
,)()()( 3002
2
zzkzzk
dt
dz
mgzzgS
dt
zd
m NLemsb
(2.7)
where m is total mass of the buoy and the piston-rack, z= z(t) is the
vertical coordinate describing the position of the buoy at time t; ρ is
the water density, g is the acceleration of gravity, Sb is the bottom
area of the buoy, zs is the vertical coordinate describing the height of
sea wave from the seabed; the damping constant γ = γf +γem , in
which the damping coefficient of fluid, γf, is assumed to be very
small in comparison with the damping coefficient of generating
motor γem [44,45], and can be neglected; kL is the linear spring
coefficient, kN is the nonlinear spring coefficient, z0 is the rest
position.
The average of the power Pgm extracted from the wave by the
converter taken over the time interval [0,τ] is given by [15,20,38-41]:
.)(
1
0
2
dttzgmP em (2.8)
2.2. Oscillating survey in nonlinear case
From the motion equation (2.7), performing the variable
transformation z – z0 = x, the equation (2.7) is rewritten as:
.)(
3
02
2
xkxk
dt
dx
mgxzzgS
dt
xd
m NLems b (2.22)
The wave equation used here is .)cos( 0ztAzs
Use symbols c,,2 and B. In case of near resonance
22 , performing the calculation, the author gets equation:
9
),,,(
2
2
2
txxfx
dt
xd (2.25)
with: .)cos(),,( 3 gtBxx
dt
dx
ctxxf
Use transformation: .)cos(
0
xtax (2.26)
From the characteristics of the model, the thesis considers the
case of weak nonlinear system. Applying the average method of
nonlinear mechanics, to calculate at 0a and ,0 the author
receives the relative formula between the amplitude and frequency as
follows:
.22
2
0
2
2
0
2
0
22 3
4
3 c
a
B
xa (2.39)
Figure 2.2 shows the relationship between the amplitude function
a0 versus frequency Ω2 with the coefficients taken as follows: m = 25
kg; a = 0.35 m; g = 9.81 m/s2; x0 = 0.4 m; kL = 1900 N/m and kN =
700 N/m3. The results showed that, in the case of the amplitude-
frequency curve with the damping coefficient γem = 40, the oscillation
of system is stable in the frequency range from point (1) to (2) and
point (5 ) to (6). In the frequency range is increasing from point (2)
to (3) and decreasing from point (5) to (4), the oscillation of system
is unstable. On the other hand, if there is enough data of the actual
sea wave conditions in sea areas with large wave amplitude, we can
exploit the operating device in the the nonlinear region, and the
received oscillating amplitude of device is the largest.
10
Figure 2.2. Graph of amplitude resonance curves versus frequency
2.3. Optimization of the electrical generator for sea wave energy
With researching orientation for fabrication of the electrical
generator to operate the near coast. From the assumption in sea wave
height is below 1 m, the effect of nonlinear component in the model
is negligible. The model parameters are determined according to a
linear calculation, the equation (2.7) is considered with kN = 0 and
changed the variable .0 xzz Sea wave function acting on the
model is considered by linear wave, and motion in the vertical
direction z has the form:
.)sin( 0ztAzs (2.41)
The motion equation of model received as follows:
).sin(2
2
t
m
AgS
gx
m
kgS
dt
dx
mdt
xd bLbem
(2.42)
Root of the equation (2.42) is found as follows:
),sin(
t
gSk
mg
x
bL
(2.53)
with χ is the oscillating amplitude of the system received as follows:
11
.
2222
embL
b
gSkm
AgS
The mechanical power of the device received from the sea wave
energy in a period is determined:
.
)(
2
1
2222
2
embL
bem
gm
mgSk
AgS
P
(2.56)
The maximum spring force is determined: FL_max = kLHmax. (2.57)
The maximum Acsimet force of buoy: FAcs_max = ρgπa2h. (2.58)
The device model is researched and fabricated with the selection
of Hon Dau - Hai Phong sea to test and exploit in the actual
operation. At Hon Dau sea, the sea wave conditions have a period to
change in the range of 3.5÷4.5 seconds and the wave height of
0.5÷1.4 m [36], so the moving velocity in the vertical direction
reaches from 0.29÷0.62 m/s. In the thesis, the model is determined
with the smallest mechanical power level of device to reach 270 W,
the oscillating range of the model is 0.45 m. From the expressions
(2.57), (2.58) combining the wave data in Hon Dau sea, the model
parameters are determined kL = 2100 N/m, the buoy is circular
cylinder-shaped with a height of 0.42 m and radius of 0.4 m. Figure
2.4 shows the graph of the mechanical power levels of the device
according to the damping coefficient γem at the wave wave periods
3.5 seconds, 4.0 seconds, 4.26 seconds, 4.5 seconds in a wave
amplitude of 0.5 m. In the thesis, the selected generating motor has a
damping coefficient of 3400 Ns/m, corresponding to the mechanical
power of the device is obtained maximum.
12
Survey of the mechanical power according to the buoy size:
In survey calculation, the buoy radius varies from 0.35÷0.55 m.
Calculation results given a comprehensive picture of the mechanical
power levels of device received from sea wave energy. In figure 2.8
is a graph of the mechanical power of the device received from sea
wave energy according to the buoy radii at sea wave periods.
2.4. Building a numerical simulation program and survey the
operation of device to converte from sea wave energy to
mechanical energy
Building a numerical simulation program:
The motion equation (2.7) is solved by the fourth-order Runge -
Kutta method, applying the Simpson method to calculate the
numerical integral and determine the mechanical power level of the
device. The numerical simulation program is programmed on Matlab
software, to investigate the operation of the device with the effect of
the nonlinear spring when the device operates at 1 m wave height or
higher.
Figure 2.8. The power versus
radius of buoy
Figure 2.4. The power versus
damping coefficient
13
Algorithm flowchart of numerical simulation program:
Figure 2.9. Flowchart of the numerical simulation program
In the survey calculation, the author has performed in two cases
that is the first-order wave (linear wave) in the expression (2.41) and
Stockes's second-order wave is given by [38,51,52]:
.00
0
3
0
2
)2sin()]2cosh(2[
)(sinh4
)cosh(
)sin( ztkz
kz
kzkA
tAsz (2.59)
End
Integral (2.8) by Simpson method:
1
,...3,1
)(
2 ),(41
n
j
s
j pZQkq
2
,...4,2
)(
2 ),(22
n
j
s
j pZQkq
321
),)(2(),
)0(
2( t
kqkq
sp
nZQspZQ
gm
P
Yes
Output results
2
)(
2;1
)(
1 Z
j
ZZ
j
Z
ti:= ti+1
ti+1:= ti + Δt
6/)432221(
)()1( tkkkkiZiZ
No
ti+1≥ tmax
k4 = f(ti+Δt, Z(i) + Δtk3, ps)
k3 = f(ti+
2
t
, Z(i) +
2
t
k2, ps)
Calculation:
k1 = f(ti, Zi, ps)
k2 = f(ti+
2
t
, Z(i) +
2
t
k1, ps)
Inputs
t0, Z0, Δt, tmax, ps
Bigin
14
Numerical simulation calculation of the device's operation:
From the calculating results are shown that the operation of the
device depends on both the amplitude and frequency of the sea
waves. In the case, with the first-order wave, the oscillating buoy is
delayed in phase compared with the sea wave about 33.60 (Fig. 2.11).
The Figure 2.16 illustrates the relationship between velocity and
displacement of the buoy motion in the case of the second-order
wave. It shows that the phase orbit of buoy motion is stable and
varies in the frequency and amplitude components of the second-
order sea wave.
0 2 4 6 8 10 12
5
5.2
5.4
5.6
5.8
6
6.2
Am
pl
itu
de
(m
)
Time (s)
Buoy displacement
Sea wave displacement
5.2 5.3 5.4 5.5 5.6 5.7
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
Ve
lo
ci
ty
(m
/s
)
Displacement (m)
Figure 2.20 shows the characteristic curves of mechanical power
according to the sea wave amplitudes, at the wave frequency appears
continuous when testing the device in sea that received 1.47 rad/s.
Figure 2.21 is the motion of the buoy according to the sea wave
amplitude with Stockes's second-order wave function. The results are
calculated at wave amplitude A = 0.5 m, the difference of power
between the two cases when considering linear system (kN = 0) and
nonlinear (with kN = 1680 N/m3) is 4.4%. For wave amplitude A =
1.5 m, the difference is 17.1%, respectively.
Figure 2.11. The displacement
of buoy and t