In this project, the primary aim is to produce optimum parameters for electric power generation via renewable sea wave energy for the Turkish sea coastlines. The modular system is composed of wave actuation mechanism, hydraulic system and generator. This system is used to model and compute the optimal parameters but also monitor the Turkish coastline characteristics. A hydrodynamic model based optimum PTO drives the generator that are further connected to other similar units to construct a wave energy farm. A testbench is created to mimic the operation of wave actuation in lab environment. This unit drives hydraulic system that can generate mechanical power to excite a generator shaft. Optimal wave actuation mechanism parameters suitable to our coastlines have been calculated. With these aims, the system designed on the basis of the mechanism that based on point absorber buoy. Initial design and hydrodynamic simulations in MATLAB/Simulink is given.

1. Designing and Modelling of a Point Absorber Wave
Energy Converter with Hydraulic Power Take-off
Unit
Celalettin Doğukan Engin
Yıldız Technical University
Department of Mechatronics Engineering
Istanbul, Turkey
dogukan.engin@gmail.com
Aydın Yeşildirek,Ph.D
Yıldız Technical University
Department of Mechatronics Engineering
Istanbul, Turkey
aydin.yesildirek@gmail.com
Abstract— In this project, the primary aim is to produce
optimum parameters for electric power generation via renewable
sea wave energy for the Turkish sea coastlines. The modular
system is composed of wave actuation mechanism, hydraulic
system and generator. This system is used to model and compute
the optimal parameters but also monitor the Turkish coastline
characteristics. A hydrodynamic model based optimum PTO
drives the generator that are further connected to other similar
units to construct a wave energy farm. A testbench is created to
mimic the operation of wave actuation in lab environment. This
unit drives hydraulic system that can generate mechanical power
to excite a generator shaft. Optimal wave actuation mechanism
parameters suitable to our coastlines have been calculated. With
these aims, the system designed on the basis of the mechanism
that based on point absorber buoy. Initial design and
hydrodynamic simulations in MATLAB/Simulink is given.
Keywords - wave energy, renewable, Turkish coastlines,
offshore, point absorber, energy converter, hydraulic, simulation,
design.
I. INTRODUCTION
There are various renewable sources in use such as wind,
solar, geothermal, bioenergetics etc. Beside these sources,
wave is also an important renewable source which has been
investigating for over forty years. First attempt was made by
Japanese in 1965 who built lighthouses that operated on wave
energy [1]. So far lots of methods have been proposed for
absorbing and converting the wave energy. Various offshore
wave energy conversion systems such as PowerBuoy by
Ocean Power Technologies (OPT), Oscillating Water Column
(OWC), the Archimedes Wave Swing (AWS) and Pelamis
wave energy converter are considered as successful examples
which work by the changes in the wave amplitude. Figure 1
shows a sample of point-absorber wave energy converter by
OPT. Recently, a 40 MW wave farm have been approved by
Scotland as a successful commercial deployment plan [9].
Point absorber systems are consists of a float, spar and
heave plate as shown in Figure 1. The float moves up and
down the spar in response to the motion of the waves. The
Figure 1. Point absorber wave energy converter by OPT [2]
heave plate maintains the spar in a relatively stationary
position. The relative motion of the float with respect to the
spar drives a hydraulic cylinder which converts the heave
motion into a hydraulic flow. The produced hydraulic flow is
converted into rotary motion by a hydraulic motor. The rotary
motion drives electrical generators that produce electricity for
the payload or for export to nearby marine applications using a
submarine electrical cable.
Figure 2. Overall power conversion of the system
Wave energy projects start with the characterization of the
wave climate and the wave energy potential. Waves are
generated by the effect of wind and gale on the sea surface.
Wave parameters such as height, wavelength, period etc. are
functions of wind speed and fetch. In order to select favorable
sites and to design wave energy converters, it is crucial to
know the resource availability, its monthly distribution and its
composition in terms of sea states [3].
The main motivation source in this project is the energy
requirement which has foreseen to rise exponentially in the
future by World Energy Council 2014 report. Report shows
that the consumption of energy will rise over 70% and reach
This project is sponsored by Turkish Scientific and Technical Research
Institute, TÜBİTAK BİDEB 2209-B Program.

2. the value of 32.000 TW/h until the year 2035. Thus, because
of the increase in energy demand and the decrease in the fossil
fuel reserves, the raise in the fossil fuel prices can only be
balanced by breakthroughs in renewable energy systems [4].
As known Turkey is surrounded by seas on three sides. This
property of Turkey is a source of motivation in this project.
The researches which have been made to characterize the
wave specifications of different regions, shows that there can
be differences in wave energy potential between the close
coastal lines. That’s why it is crucial to make the wave
measurements with respect to the coordinates before having
any investment in wave energy farms. According to the
predictions from wind measurements which were provided by
the thirty-one meteorological stations around Turkey, indicates
that it can be convenient to make an investment in wave
energy converter systems for Istanbul (Kilyos) and Antalya
(Kalkan) coasts [5]. The investigations to reveal the wave
potential of these regions, shows that the peak wave amplitude
is 1.5 meters and the period of waves can reach to 6 seconds.
The purpose in this work is designing, modelling a point
absorber buoy and simulating via MATLAB/Simulink to
characterize the wave energy potentials of specific locations
off the Turkish coast where the wave energy converter is
supposed to be deployed. The extreme wave data that has been
provided by the researches, determines the main specifications
of the wave energy converter design in this project.
II. DESIGNING, MODELING AND SIMULATING
All companies in this field, regardless of device type, face
the same main engineering problems when designing and
building these devices. The challenges with the wave resource
that condition the development of wave energy converters [6]:
 The irregularity of a sea state in terms of amplitude,
phase and direction.
 Efficient power conversion of variable power levels.
 The conversion of slow (approximately 0.1 Hz)
irregular and oscillatory motion into useful motion to
drive an electrical generator with a grid connection
frequency of 50 Hz.
 Necessity to predict and survive storms and other
extreme conditions when wave power levels can
exceed 2000 kW/m2
.
 More attractive resource is located offshore which
provides maintenance problems.
 The requirement to be highly reliable and have
maintenance intervals of several years to be
commercially viable.
 The lack of robustness in rough seas has often
prevented long term sea trial measurements to be
made.
A. Design of the Point Absorber Wave Energy Converter
Beside the main challenges that are mentioned at the top,
the design should be able to meet some additional
specifications, such as:
 Being convenient to Turkish sea-wave states,
 Minimizing the fabrication and cost
 Manufacturing the first prototype which will be
deployed in sea as an measuring and testing device
 Can be deployed easily in the seas that have various
depth
 The fabricated prototype would be carried by a
personal car and be deployed easily into sea by some
boats. So the weight and the shape should meet these
specifications.
In Figure 3, computer aided design of the system can be
seen. The goal in this design, is to have a system that can only
measure the wave in the region and test the electricity
producibility of the power take-off unit. That’s why the power
take-off unit is on the top of buoy. There are two separate
electrical circuits in this water-isolated box, with the primary
circuit consisting of the power generation components and the
secondary circuit consisting of the telemetry instruments and
acquisition device. The power generation circuit is wired
series to a single resistor. By measuring the voltage and
current of the power generation circuit, it will be available to
calculate the instantaneous power for the system. To measure
the instantaneous power output, a second circuit was designed
with both a voltage and current sensor wired to a
microcontroller and SD data logger shield. There should be an
additional battery for the telemetry system which can be
charged by the produced energy. This system can send
information to the shoreline instantaneously.
Figure 3. Computer-aided design of the system

3. Polyurethane or polyethylene foam would be a good
choice for the buoy. Hydraulic cylinder is connected to the
buoy by the spar section. Heave plate is on the seabed and
works as an anchor and remains stationary while the heaving
motion of the buoy. Heave plate is connected to the spar by
steel cables. This gives an advantage to be deployed easily
into the seas with various depth by adjusting length of cables.
The piston of hydraulic cylinder is directly connected to
heave plate through springs. Thus, when the buoy moves
upwards due to heaving motion, the hydraulic cylinder which
is connected to the buoy, will extend and this move causes
springs to compress. On the other hand, when buoy moves
down with motion of wave, hydraulic cylinder will be
compressed and springs will push back on hydraulic cylinder.
B. Modelling of the Point Absorber Wave Energy Converter
In order to identify the design parameters of the system
such as shape, dimensions, weight, etc; the governing
equations were determined and applied forces on the buoy
were calculated based on the heave motion of the waves.
The system has six degree of freedoms but in this project
we will consider the heave motion of the system as shown in
Figure 4. Other degree of freedoms should be considered in
extreme conditions such as storms, swirls, tsunamis etc.
Figure 4. Representation of 6 degree of freedoms [7]
Regular waves, as shown in Figure 5, can be modeled using
linear wave theory, where it is assumed the wave heights are
small compared to the wave length and the fluid is inviscid,
irrotational and incompressible. Irregular waves on the other
hand, are constracted from a wave frequency spectrum using
the addition of several sinusoids chosen from the spectrum,
such as Bretschneider- Mitsuyasu Spectrum[7].
Figure 5. Regular wave model
The surface displacement of a monochromatic, progressive
wave can be expressed as,
(1)
(2)
(3)
where ‘ ’ is the position of the wave with the respect to time,
‘H’ is the wave length, L is the wavelength, T is the period, k is
the spatial frequency and ‘ ’ is the temporal frequency.
The hydrodynamic system modelling will be constructed
according to the heave motion of the system. The purpose of
this analysis is to determine the maximum power take-off force
that the system can absorb from the heave motion of sea.
Figure 6 shows the forces on the system [8].
Figure 6. Forces on the heave axis
According to the Newton’s second law the dynamics of the
system is,
= Fwave + F pto (4)
In (4) ‘m’ is the mass of the buoy, ‘ ’ is the acceleration in
heave motion, ‘Fpto’ is the power take off unit that is produced
by the system itself and ‘Fwave’ is the total wave force which is
being acted on the system.
Fwave = Fe + Fr + Fb (5)
In (5) ‘Fe’ is the excitation force that is provided by the wave
move on the buoy, ‘Fr’ is the radiation damping force that is
acting on the body opposite to heaving move and ‘Fb’ is the
hydrostatics buoyant force.
Fe (6)
Fb= -Kz = - ρg (7)
Fr = -A – B (8)
where ‘A’ is the added mass, ‘B’ is the radiation damping
coefficient, ‘ρ’ is the density of water, ‘r’ is the diameter of
buoy. Substituting the equations at the top, the state equation of
the buoy is obtained as,
Fpto +Fe) (9)
The hydraulic circuit of the system is given in Figure 7. The
purpose of this circuit is to convert the heaving motion into
rotary motion through hydraulic flow. The crucial point in this
design, is to rotate the hydraulic motor just in one direction.
Rectification with four check valves are used to do that.
When the buoy moves downward, hydraulic cylinder will
pump fluid into the hydraulic circuit and pass through check

4. valves. The fluid will enter into hydraulic motor through Port
A. In other scenario, when the buoy moves upward, hydraulic
cylinder will pump fluid into the circuit through other port.
Thus, the hydro-motor will be excited from the same port.
This flow will rotate hydro-motor in same direction. The
hydraulic flow will be smoothed by pre-charged accumulators.
Figure 7. Hydraulic circuit of the system
The pressure of the port A and B of hydraulic cylinder can
be expressed as,
(10)
(11)
where, ‘βe’ is the effective bulk modulus of the hydraulic
fluid, V0 is the initial volume of the cylinder, ‘Ap’ is the area
of piston. , , and are the volumetric flows of the
numbered check valves that can be seen in Figure 6. The
volumetric flows in high and low pressurized accumulators are
expressed as,
+ (12)
(13)
where, is the swash-plate angle ratio(which is equal to 1 in
our case) , D is the nominal displacement of the motor and w
is the rotational speed of the generator. The instantaneous
pressure of high and low pressurized accumulators are
expressed as,
(14)
(15)
where, and are the pre-charged pressure levels of the
accumulators. and are the total volume of
accumulators. The torque that can be produced by the hydro-
motor can be formulized by,
Tm = D ( pH - pL ) 0.9 (16)
The equation between the hydro-motor and permanent
magnet DC generator is,
] (17)
where, ‘ ’ represents the generator torque, ‘ ’ represents
frictional torque and ‘JT’ is the total moment of inertia in the
coupling between hydro-motor and DC generator. Before you
begin to format your paper, first write and save the content as a
separate text file. Keep your text and graphic files separate
until after the text has been formatted and styled. The power
take-off force which has been mentioned in (1) can be
formulized by,
Fpto = ( pA - pB ) Ap (18)
C. Simulation of the Point Absorber Wave Energy Converter
By using the libraries of SimHydraulics, SimMechanics
and SimPowerSystems, the mechanical, hydraulic and
electrical analysis of the system are tackled all together while
constructing the Simulink model, Figure 8. While analyzing
the system, ‘ode15s’ analyzer was used. The excitation force
which is obtained before from the results of the hydrostatic
analysis, will excite the hydraulic system. In this model, the
dynamic features of the system were settled by determining
the spring and damping coefficients from hydrodynamic
analysis.
Figure 8. Simulink model of the system
In order to provide an access to the system for force, it is
constituted a sine wave model by means of ‘Signal Generator’.
In the previous dynamic analyses, it has been calculated that
the maximum force in the vertical direction can be 100kN. The
system starts to oscillate with 100kN force in the vertical
direction. This oscillation was converted into a hydraulic fluid
over the double-acting hydraulic cylinder. In virtue of the
check valves, the hydraulic engine which is stimulated on the
same direction with the up-and-down motion of the buoy was
coupled up with a permanent magnet DC generator.
The instantaneous input data is shown in Figure 9. In that
figure from top to bottom the input force, the velocity of piston
and the stroke displacement can be seen with the respect to
time. By the sinusoid that has 10 seconds period and 100kN

5. peak amplitude, it becomes convenient to test the system with
2 meter amplitude of regular wave. As a result of this input to
the system, it can be seen that the stroke velocity reaches 1
m/sec.
Figure 9. Instantaneous input data of the system
Figure 10. Instantaneous output data of the system
The instantaneous output data is shown in Figure 10. In that
figure from top to bottom the armature current, the armature
voltage and the output power of the DC generator can be seen
with the respect to time. It can be understood that by the
rectification in the hydraulic flow via check valves, the
sinusoid input becomes in to the curve which is the sum of the
positive side of the sinusoid and symmetrical version of the
sinusoid’s negative side with respect to the x axis.
D. Design and Simulation of the Miniature Testbench
In this design, it was accepted that there is not loss of
synchronization between wave and the buoy and the heaving
motion was sent directly to the cylinder of the power take-off
unit. As it is seen in Figure 11, dynamics of the real system and
the motion damping which occurs on the bottom and the
surface of the sea were ignored in the testing apparatus. It is
endeavored to determine the performance of the power take-off
unit by conveying the motion to the hydraulic cylinder which is
bound to the power take-off unit.
Figure 11. Dynamics of real system vs. test bench
The computer-aided design of the test bench is shown in the
Figure 12. This design which has been minimized by 1/100,
contains two different hydraulic cylinder which have been
connected each other. That’s why the system have two
separated hydraulic circuits. The mission of the driving
cylinder is to act as a wave generator and excite the power take
off unit with various wavelengths and forces.
Figure 12. Computer-aided design of test bench
The design has been modelled in Simulink to investigate
the performance of the driving cylinder and the power take-off
unit as a result of the move of driving cylinder, in Figure 14. In
this simulation it was crucial to produce a curve which is
similar to a sinusoid with the period of 8 seconds and the peak
value of 20 cm, which shown in Figure 13.
Figure 13. Driving cylinder stroke move

6. Figure 14. Simulink model of the test bench
The instantaneous simulation results of the test bench
model is shown in Figure 15. The system was minimized by
1/100 so in that figure the output power of the permanent
magnet DC generator can be seen as 1/100 minimized
according to the output power level of the actual sized point
absorber wave energy converter.
Figure 15. Instantaneous output power of the test bench
III. CONCLUSIONS
Firstly the actual sized point absorber buoy mechanism has
been designed with the respect to the specifications that are
mentioned in the previous sections. According to the design,
the dynamic model and the Simulink model of the system has
been constructed. The simulation results reveals a 70% of
efficiency in power take-off unit of the system. The
investigations points that the most power loss is caused by the
hydraulic motor.
By the experience in the design phase of the actual sized
point absorber buoy, the project aimed to design a test bench
and investigate the features and the performance of the power
take of unit with minimal size. In the 1/100 minimized size
design, the efficiency of power take-off unit has been remained
stationary.
Further researches should be made on the shape and the
functionality of the point absorber buoy to increase the wave
absorption and reduce the radiation damping force between the
waves and buoy. And it is crucial to design a control system for
the variable displacement hydraulic motor to increase the
efficiency of power take-off unit.
ACKNOWLEDGMENT
This work was funded by TÜBİTAK BİDEB 2209-B
Industry-Oriented Undergraduate Thesis Support Program and
carried out under Yıldız Technical University. These supports
and consultations are gratefully acknowledged.
REFERENCES
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Point Absorber Wave Energy Converter for Assulayeh Port,Iranica
Journal of Energy & Environment 4 (2), pp. 130-135, February 2013.
[2] www.oceanpowertechnologies.com
[3] S. Bozzi, A.M. Miquel, A. Antonini, G. Passoni and R. Archetti,
Modelling of a Point Absorber for Energy Conversion in Italian Seas,
energies, 6, 3033-3051; doi: 10.3390/en6063033, June 2013
[4] World Energy Council, Energy Report, 2014
[5] M. Sağlam, E. Sulukan and T. S. Uyar, Wave Energy and Technical
Potential of Turkey, Journal of Naval Science and Engineering, Vol. 6,
No. 2, pp. 34-50,
[6] J. Twidell amd T. Weir, Renewable Energy Resources, Taylor and
Francis, London, UK, second edition, 2006
[7] S. Casey, Modeling, Simulation and Analysis of Two Hydraulic Power
Take-off Systems for Wave Energy Conversion, Oregon State
University, USA, June 2013.
[8] C. Cargo, Design and Control of Hydraulic Power Take-Offs for Wave
Energy Converters, University of Bath, UK, December 2012.
[9] Scottland Business (2013, May 22). Ministers Approve Plans for
World's Biggest Wave Farm in Western Isles [Online]. Available
http://www.bbc.com/news/uk-scotland-scotland-business-2261131