Energy and Power Engineering, 2013, 5, 72-77
doi:10.4236/epe.2013.54B014 Published Online July 2013 (
Hydraulic Power Take-off and Buoy Geometries
Characterisation for a Wave Energy Converter
Pedro Beirão, Cândida Malça
Mechanical Engineering Department, Coimbra Polytechnic Engineering Institute, Coimbra, Portugal
Received April, 2013
In the past few decades, world energy consumption grew considerably. Regarding this fact, wave energy should not be
discarded as a valid alternative for the production of electricity. Devices suitable to harness this kind of renewable en-
ergy source and turn it into electricity are not yet commercially competitive. The work described in this paper aims to
contribute to this field of research. It is focused on the design and construction of robust, simple and affordable hydrau-
lic Power Take-Off using hydraulic commercial components.
Keywords: Hydraulic Power Take-off; wave Energy Converter; Simulation; Structural Analysis; Buoy Geometries
1. Introduction
In the past few decades, world energy consumption grew
consider ably and th e tenden cy is to incr ease ev en furthe r.
Regarding this fact, wave energy should not be discarded
as a valid alternative for the production of electricity.
Different countries with exploitable wave power re-
sources are considering wave energy as a viable source
of power supply. Governments introduced several meas-
ures to help researchers and the industry towards the de-
velopment of technically feasible wave power conversion
technologies in the medium and long term.
Devices suitable to harness this kind of renewable en-
ergy source and turn it into electricity, called Wave En-
ergy Converters (WECs) are not yet commercially com-
petitive when compared with more mature renewable
technologies, such as wind and solar energy. There are
several concepts being tested and some of them have
already reached full scale.
In order to convert wave energy into electricity WECs
must have some kind of Power Take-Off (PTO). PTO
systems should include, among others, the ability to cre-
ate high thrust because sea waves produce low velocity
movement of floating bodies; high efficiency which is
related from the economical point of view with the price
of electricity; low maintenance requirements due to the
obvious WEC inaccessibility during large periods of time
The WEC and its hydraulic PTO components are illus-
trated in Figure 1.
This system should provide a reaction force at the hy-
draulic cylinder in order to harness energy from the floa-
ter motion. As a matter of fact the force developed by the
buoy is transmitted through the PTO system.
As a consequence the hydraulic cylinder pumps oil
from the tank to the accumulator and the fluid returns to
the tank trough the hydraulic motor. The floater has a
mass and a vertical stiffness associated with the buoy-
ancy force and the PTO behaves as a viscous damper
with non-linear features due to the valves opening and
closing. Being a near shore WEC, the hydraulic PTO
components (rectangle of Figure 1) should be enclosed
in a sealed waterproof platform placed at the seabed and
the foundations should provide the reaction force [1].
The hydraulic PTO converts the reciprocating motion of
the hydraulic cylind er into a rotary motion of th e hydrau-
lic motor coupled to an electrical generator. It is well
known that particles near the sea surface move in circles
Figure 1. WEC with hydraulic PTO [1].
Copyright © 2013 SciRes. EPE
but as the depth increases, the radius of the circular mo-
tion decreases. The whole system containing the hydrau-
lic PTO is assumed to be at that depth, not being affected
by the wave motion.
The paper describes several stages concerning the de-
sign, development and construction of a robust, simple
and affordable hydraulic PTO prototype using hydraulic
commercial components for a floating point absorber
WEC. It includes a section describing the initial virtual
simulation and the subsequ ent construction and testing of
didactic hydraulic PTO using hydraulic didactic compo-
nents. The following section describes the development
and building of the prototype using hydraulic commercial
components. Results are presented in an independent
2. Characterisation of the Hydraulic PTO
The partially submerged WEC considered belongs to the
point absorber category [2], since its characteristic di-
mension has a negligible size when compared to the wa-
velength. The two main components are a floating buoy
which is connected to a hydraulic cylinder. The working
principle is quite simple – the buoy is submitted to the
sea waves. As a result the buoy moves upwards under the
influence of a wave crest and moves downwards under
the effect of a wave trough. There will be a reaction force
applied by the hydraulic cylinder to the buoy. The rela-
tive heave motion between the two main components is
converted into electrical energy by means of a hydraulic
PTO [3]. Although six modes of motion are possible [2],
the WEC is assumed to oscillate only in heave.
The PTO design is based in a hydraulic circuit, sche-
matised in Figure 2, since this kind of system has several
favourable characteristics. Many WECs have incorpo-
rated hydraulic PTOs in their design [4] as this is an af-
fordable, robust, well proven technology [5].
The hydraulic design also produces a smooth output
power and is dimensionally compact [2]. Additionally,
oil protects the sensitive sliding surfaces from corrosion
and lubricates the seals.
Figure 2. Hydraulic PTO (based on [5]).
Nevertheless there are some disadvantages, since this
kind of system includes oil which is a potential sea pol-
lutant. Also the finite life of seals due to friction and fa-
tigue loading of main components should be taken into
account [2].
For a detailed description of a hydraulic PTO see [1]
and [3].
The main hydraulic components are a double effect
hydraulic cylinder, non-returnable valves, an oil tank, an
accumulator and a hydraulic motor. The hydraulic cylin-
der will be responsible by the relative motion between
the buoy and the mooring platform, but only when the
force applied to the buoy surpasses the hydraulic force
corresponding to the pressure difference between the
accumulator and the tank.
The maximum allowed velocity for hydraulic cylin-
ders is 0.5 m/s, however a velocity of 0.1 m/s should be
used to extend the life of the hydraulic cylinder seals [1].
The successive wave crests and troughs cause a heave
motion to the buoy. As a consequence there is an alter-
nating oil flow which is rectified by the non-returnable
valves. The flow is smoothed by the accumulator [3]
which could also be used as energy storage [1].
Since sea waves are irregular significant variations that
can occur. Therefore the accumulator should have
enough capacity to accommodate the fluid flow for two
or three wave cycles [1]. The goal is to deliver a reason-
able smooth electrical outpu t. The continuous f low of the
oil through the hydr aulic motor is converted in rotational
motion [5] and will drive an electric g enerator, turning at
typically 1000 or 1500 rpm [2], which will be responsi-
ble to convert the wave energy into electricity [3].
There are several options to maintain a continuous ro-
tation of the electrical generator [1]. One is to use a fixed
displacement hydraulic motor to drive a variable speed
electrical generator. Another possibility is using a hy-
draulic motor with variable displacement [3] which al-
lows a flow rate adjustment according to the average
power del ivered by sea w aves.
3. Hydraulic PTO
3.1. Didactic Hydraulic PTO
A virtual simulation of the hydraulic circuit (excluding
the electric generator) of the hydraulic PTO prototype
was made resorting to a specific software.
Figure 3 schematizes the full assembly of the circuit,
which is divided in three parts: the hydraulic circuit of
the hydraulic PTO prototype based on Figure 2; the hy-
draulic part of the electrohydraulic test circuit and the
electric part of the electrohydraulic test circuit.
Being a passive system without auxiliary power sup-
plies, the aim of the electrohydraulic test circuit was to
impose external forces with different signs and magni-
Copyright © 2013 SciRes. EPE
tudes to the hydraulic cylinder of the hydraulic PTO
prototype in order to simulate different wave crests and
troughs the floating buoy will be exposed to.
Prior to the construction of the hydraulic PTO proto-
type, a didactic hydraulic PTO and the corresponding
electrohydraulic test circuit, depicted in Figure 4, were
built in laboratory using didactic hydraulic components.
Figure 3. Full assembly of the simulation.
Figure 4. Assembly of the didact ic hydraulic PTO.
These two circuits were mechanically coupled by their
hydraulic cylinders, that is, the cylinder of the PTO hy-
draulic circuit was coupled to the cylinder of the elec-
trohydraulic test circuit. As a result a heave motion was
imposed to the former one. The two cylinders move to-
gether but in opposite directions. The goal was to simu-
late wave crest and troughs. When the test cylinder
moves backwards it pushes up the PTO hydraulic cylin-
der simulating a wave crest. A wave trough is simulated
when the test cylinder moves downwards pulling down
the PTO hydraulic cylinder.
3.2. Hydraulic PTO Prototype
After the didactic hydraulic PTO has been tested and its
feasibility proven the next stage comprises the assembly
of the hydraulic PTO prototype using commercial hy-
draulic components. Final result is shown in Figure 5.
4. Buoys
4.1. Geometries
Three different buoy geometries, spherical, cylindrical
and tulip, this later being a combination between a cone
and a cylinder [6], were analysed using a finite element
code, in order to conclude which one would have the best
behavior when submitted to hydrodynamic forces.
It was necessary to make an approximate drawing of
the three buoy geometries with the required characteris-
tics, as seen in Figure 6. Among these, the most impor-
tant is the volume since it is related with the buoyancy
Most of the commercial buoys have a polyurethane
core and a high density polyethylene shell. Based on this
information, buoys studied and analysed were assumed
to be made of these two materials. Their relevant proper-
ties are listed on Table 1.
Figure 5. Hydraulic PTO prototype mounted on the support
Copyright © 2013 SciRes. EPE
Figure 6. Buoy geometries (spherical, cylindrical and tulip).
Table 1. Mechanical properties.
Polyethylene Polyurethane
Young’s modulus 1860×106 N/m2 2410×106 N/m2
Poisson coefficient 0.39 0.39
Yield stress 30×106 N/m2 40×106 N/m2
Density 940 kg/m3 45 kg/m3
As stated before, the interior and exterior of the buoys
are made of different materials. This will increase the
difficulty of the structural analysis due to the relationship
definitions that would have to be made. Therefore only
the outer shell of the buoys was consid ered.
4.2. Calculations
Computations for the three buoys were based on the Ar-
chimedes principle. It is known that a buoy immersed in
water is submitted to an upward buoyancy force Fb
which should be greater than or equal to the gravity force
Fg [6], as in (1)
F (1)
For the gr avity for ce Fg it should be taken into account
the sum of the weights of submerged movable compo-
nents and also the forces responsible by the upward and
downward movements of the hydraulic cylinder piston.
For the spherical buoy, the volume of the displaced
water is equal to the volume of the buoy Vb, given by (2)
where rb is the buoy radius. As a result there will be a
buoyancy force Fb given by (3)
 (3)
where b is the polyethylene density and g is the accel-
eration due to gravity.
For the other two buoys geometries the computation
procedure is analogous.
The computations of the forces applied on the buoys
are based on [6].
Equation (4) was used to calculate the drag force Fdrag
0.5 C
drag b
 (4)
The drag coefficient C can be easily obtained from ta-
bles available in the literature according with the object
geometry. The fluid velocity v can be calculated by (5)
 (5)
where h is the maximum height. In this particular situa-
tion it matches the cylinder piston length. This will be the
worst-case scenario since it is the maximum height re-
lated with the buoy motion.
Forces applied on buoys must also take into account
both slamming [6] and hydrostatic pressures. The slam-
ming pressure is the pressure to which a body close to the
water surface is exposed to, namely is the force caused
by the bursting of the wave that hits the body. The hy-
drostatic pressure is the force exerted by the water in the
submerged body. In this situation the body will be the
submerged buoy, which is the worst case scenario.
Equation (6) was used for the calculation of the slam-
ming pressure pslam
slamb slam
  (6)
where Cslam is the slamming pressure coefficient. For flat
surfaces it must not be less than 2, which is the worst
case scenario [7]. Equation (7) should be used for com-
pute Cslam for wedged surfaces with an angle greater
than 15 degrees [7]
2.5/ tan.
None of the buoys used has a flat surface. Neverthe-
less, due to its shape it is impossible to identify the value
of the angle for the spherical and cylindrical buoys.
Due to this reason it was considered the worst case sce-
nario. Therefore it was used a coefficient Cslam with the
value of 2.
Equation (8) was used for the calculation of the hydro-
static pressure
 (8)
where w is the seawater density and
h is the height
5. Results and Discussion
5.1. Didactic Hydraulic PTO
Results of the simulations performed were as expected,
that is, the rotational velocity of the hydraulic motor var-
ies with the force applied on the hydraulic cylinder.
Some of the experimental results obtained during the
tests of the PTO hydraulic circuit, built with didactic
components, are presented in Table 2.
A flow control valve was used to adjust the velocity of
the hydraulic cylinder piston of the test circuit to ap-
proximately 0.1 m/s.
Table 2 shows three different values for the pump
Copyright © 2013 SciRes. EPE
pressure. However the remaining values are quite the
same. This is due to the effect of the flow control valve.
The differences of the values registered in the forward
and backward strokes arise from the fact that both cylin-
ders are asymmetrical.
The rotational velocity of the hydraulic motor of the
didactic hydraulic PTO was measured using a portable
The role of the accumulator was also tested by chang-
ing the adjustment of its pressure relief valve. When ad-
justed to a lower value the oil flowed to the low pressure
reservoir. When increasing the opening value of the
pressure relief valve the oil was kept inside the accumu-
During the tests performed it was found that the low
pressure reservoir should be pressurized (2 bar) with
compressed air. This led to an improvement of the oil
flow inside the PTO hydraulic circuit and also to an in-
crease of the rotational velocity of the hydraulic motor.
Additionally it would prevent the presence of cavitation
in the hydraulic circuit [3].
5.2. Buoys
From Figure 7 it is seen that values are bounded and
none inconsistency was noticed, both at the places of
greater displacement, either at the points where are ap-
plied the maximum stresses and forces. It was found that
maximum stress (15.5 N/mm2) never exceeded the mate-
rial stress. A maximum displacement of 32.61 mm is
located at the top of the buoy. A safety factor of 1.90 was
obtained in the docking of the buoy.
According with Figure 8 it is seen that this geometry
would be subject to a minor stress, since maximum stress
(15.14 N/mm2) is lower than the obtained with the
spherical buoy. A maximum displacement of 20.51 mm
is located at the top of the buoy. A safety factor of 1.95
was obtained in the docking of the buoy.
Concerning the tulip buoy geometry shown in Figure
9 it can be observed that this buoy geometry is the best
one regarding the request that is submitted to. The max-
imum stress (13.37 N/mm2) is the lowest of the three
buoys. It was obtained a maximum displacement of
33.51 mm, located on top of the buoy. A safety factor of
2.21 was obtained in the docking of the buoy.
Table 2. Test results.
PTO hydraulic cylinder
forward backward PTO hydraulic motor
20 N/m2 0.073 m/s 0.14 m/s 110 rpm
25 N/m2 0.081 m/s 0.13 m/s 110 rpm
30 N/m2 0.078 m/s 0.15 m/s 110 rpm
Figure 7. Spherical buoy structural analysis.
Figure 8. Cylindrical buoy structural analysis.
Figure 9. Tulip buoy structural analysis.
Copyright © 2013 SciRes. EPE
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6. Conclusions
Results were obtained by means of simulation of the
PTO hydraulic circuit using specific software and a di-
dactic hydraulic PTO specially built for this purpose. It
was possible to demonstrate the working principle of the
hydraulic PTO using didactic components. A hydraulic
PTO prototype was built using commercial hydraulic
components mounted on a steel support structure.
In order to understand the WEC behavior when sub-
mitted to simulated wave forces, structural calculations
were done resorting to a finite element code.
Until attaining the final stage there are yet many prob-
lems to surpass and some aspects to develop and improve,
namely the coupling between the buoy and the hydraulic
cylinder piston using a kinetic joint; the pressurization of
the oil reservoir through a compressor powered by the
system; the sizing of the rotary electric generator that
should be coupled to the hydraulic motor; the sealing of
the hydraulic PTO by means of a enclosure that should
also serve as a mooring base put at the sea bottom near
shore and the test of the whole system performed in a
wave tank or at real sea conditions.
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