ArticlePDF Available

Control Strategies Applied to Wave Energy Converters: State of the Art

Authors:

Abstract and Figures

Wave energy's path towards commercialization requires maximizing reliability, survivability, an improvement in energy harvested from the wave and efficiency of the wave to wire conversion. In this sense, control strategies directly impact the survivability and safe operation of the device, as well as the ability to harness the energy from the wave. For example, tuning the device's natural frequency to the incoming wave allows resonance mode operation and amplifies the velocity, which has a quadratic proportionality to the extracted energy. In this article, a review of the main control strategies applied in wave energy conversion is presented along their corresponding power takeoff (PTO) systems.
Content may be subject to copyright.
energies
Review
Control Strategies Applied to Wave Energy
Converters: State of the Art
Aleix Maria-Arenas 1, * , Aitor J. Garrido 2, Eugen Rusu 3and Izaskun Garrido 2
1Department of Engineering, Wedge Global S.L., 35017 Las palmas de Gran Canaria, Spain
2Automatic Control Group—ACG, Department of Automatic Control and Systems Engineering,
Engineering School of Bilbao, University of the Basque Country (UPV/EHU), 48012 Bilbao, Spain
3Department of Applied Mechanics, University Dunarea de Jos of Galati, Galati 800008, Romania
*Correspondence: aarenas@wedgeglobal.com
Received: 29 June 2019; Accepted: 6 August 2019; Published: 14 August 2019


Abstract:
Wave energy’s path towards commercialization requires maximizing reliability, survivability,
an improvement in energy harvested from the wave and eciency of the wave to wire conversion.
In this sense, control strategies directly impact the survivability and safe operation of the device, as well
as the ability to harness the energy from the wave. For example, tuning the device’s natural frequency
to the incoming wave allows resonance mode operation and amplifies the velocity, which has
a quadratic proportionality to the extracted energy. In this article, a review of the main control
strategies applied in wave energy conversion is presented along their corresponding power take-o
(PTO) systems.
Keywords:
ocean energy; marine energy; wave energy; renewable energy; wave energy converter;
control system
1. Introduction
Marine Renewable Energy (MRE) is one of the least tapped renewable energy resources. Despite
decades of development eorts, more than 90% of the 529 MW of the MRE operating capacity at the
end of 2017 was represented mainly by two tidal barrage facilities: 254 MW from Sihwa plant in
the Republic of Korea (completed in 2011) and the 240 MW La Rance tidal power station in France
(built in 1966) [
1
]. Main barriers for MRE causing this slow development are analyzed in [
2
] with
special interest in the Mediterranean Sea (MS), although the results can be applied to a great extent for
any other geographical areas. Remarkable conclusions about MRE barriers include:
Bathymetry and distance to shore: Near-shore facilities can have a direct aection on nearby coastal
areas, maritime routes, fishing areas or visual impacts. Narrow and step near-shore continental
shelfs can also have a negative impact for economic reasons, mainly installation (including grid
connectivity) and maintenance.
Electricity infrastructure: On the contrary, if we move large distances from the shore to minimize
the previously cited negative impacts over coastal areas, it can significantly increase the relevant
cost of cabling and substations, especially for areas with large depths.
Potential environmental impacts: Underwater noise, sediment dispersal, increased turbidity,
electromagnetic field eects (EMF), wave radiation and diraction alteration can lead to significant
changes to coastal morphology; fixed structures can also generate artificial reef eect. It is
concluded that environmental impacts for MRE are hardly clear and not suciently quantified,
hence, more research is necessary about this topic.
Energies 2019,12, 3115; doi:10.3390/en12163115 www.mdpi.com/journal/energies
Energies 2019,12, 3115 2 of 19
Economics: The great diversity of MRE technologies and the early development status result
in a wide range of levelized cost of energy (LCOE) [
3
], in the particular case of wave energy
ranging from 108
/MWh to 530
/MWh. This level of economic uncertainty creates a less favorable
environment for investments.
Legal and regulatory framework: There is a lot of uncertainty in this regard for MRE, and it is
not adequately addressed by the relevant national/international entities. Many key parameters
aecting directly any MRE installation are interrelated with several other aspects such as the
environmental impact assessment, rights and ownership, international law, management of ocean
space, etc.
Geographical or energy islands remain as the most interesting technological enablers for MRE
research and deployment, as highlighted in [
4
]. For remote areas or small islands, the electrical energy
production is still based on outdated, polluting and expensive technologies, powered by fossil fuels.
Many islands around the world are working on important projects in order to achieve energetic
independence based on MRE. Hybrid solutions such as solar-wave [
5
] or wind-wave [
6
] can also favor
the development of MRE, combining more stablished technologies such as oshore wind and PV in
the same oshore device (e.g., spar sharing) or energy farm.
MRE technologies have seen new capacity come online over the recent years; in particular,
wave energy development in Spain [
7
] holds some notorious projects, such as the so called
MARMOK-A-5 being the first operational point absorber connected to the grid in Spain, developed by
OCEANTEC (acquired by IDOM in September 2018), installed at BIMEP test site in 2016. Mutriku Wave
Power Plant, operates since July 2011 connected to the grid, being the first oscillating water column
(OWC) multi-turbine facility acting as a test rig for dierent technology developers; the Portuguese
company Kymaner finished testing of its bi-radial air turbine last August 2018. WEP+demonstration
project, based on the industrial scale W1 point absorber developed by Wedge Global, accumulated
roughly 5 years of testing at PLOCAN test site on the Canary Islands. LifeDemoWave demonstration
project deployed a 25-kW prototype in June 2018 in the Galician coast for a no grid connected test.
European highlights from 2018 resulted from H2020 funded projects, including the fabrication of the
second Penguin Wave Energy Converter (WEC) at EMEC as part of the CEFOW project, the deployment
of the Corpower WEC at EMEC, the installation of the new turbine on the Marmok wave device and
the deployment of Minesto’s Deepgreen500 device.
The wave energy sector is still in a very early development stage when compared to other
renewable energies, especially wind or solar PV. There is a low level of consensus among the WEC
technology developers that are still, at best, in a prototype demonstration phase, and there is a lot of
discussion among said developers about the best WEC topology and/or PTO configurations. It is not so
common to discuss at this level about control strategies given the diculties in eectively implementing
most of the control strategies listed in Section 3of this review. Most of the existing industry scale
prototypes in the water have the simplest control strategy resulting in low energy absorption.
The main purpose of this article is to establish a framework for the control strategies being
discussed over the recent years (2017–2019) for WECs. References older than 2017 will not be discussed
(unless for introductory purposes) to avoid redundancies with older reviews with a similar approach.
A brief review will be provided about the analytical formulation of the mean power absorption and
optimal control [
8
] particularized for heaving WECs, which is the most extended WEC technology in the
form of floating point absorbers [
9
]; however, the same approach is extensible to any other oscillatory
mode (sway, surge, pitch, roll or yaw). A point absorber is a floating buoy moored (2 bodies) or fixed
(1 body) to the seabed. The incoming waves induce into the floating body a synchronous oscillation
mainly in heave motion. It is this movement that is converted into an energy vector (e.g., hydrogen [
10
],
desalination [11] or electricity) through a power take-olocated inside the buoy.
Great eort has been made in the last decades about control strategies for WEC, as we can see from
older state-of-the-art reviews such as [
12
14
]. The main objective in wave energy conversion for control
is the maximization of power absorption, aiming for resonance operation. The best control approach
Energies 2019,12, 3115 3 of 19
to achieve said resonance is known as complex-conjugate control, based on solving the impedance
matching problem. As we will explain later, this control always achieves optimal power absorption
since it regulates the system reactance and resistance simultaneously. However, this control strategy is
not practical for real world applications because of large motions and loads. Hence, under-optimal
control solutions, it needs to be analyzed and implemented considering physical constrains in motion,
force and power rating of the WEC.
In Section 2a brief introduction about wave energy technology is presented with the purpose
of helping the uninitiated reader understand the dierent technologies and parts (oscillator body,
PTO) of WECs. In Section 3, we will start with a comprehensive introduction for WEC modelling
and optimal control, as originally introduced in [
15
], to establish a reference framework, continuing
with classification, introduction and discussion for each control strategy found in recent WEC control
publications. Finally, conclusion and further research end the article in Section 4.
2. Wave Energy Technology
In the same way that a wind turbine transforms the kinetic energy of the wind into mechanical
energy of rotation through the blades, and this one into electrical energy through the electrical generator,
a WEC transforms the energy from the waves into mechanical energy through the oscillating body and
this one into an energy vector through the PTO.
In the wind energy sector, there is a predominant type over the rest, the three-bladed horizontal axis
turbine; it is not so for wave energy, where there is a wide spectrum of options for both oscillator body
and PTO without a clear predominant type. Over 1000 dierent wave energy conversion techniques
were patented in Japan, North America and Europe [
16
] just in 2004, and it is expected this number has
greatly increased since 2004 based on the general renewables energies patent numbers shared recently
by EMW Law [17].
2.1. Wave Energy Converters
Despite the great number of dierent technologies for harvesting wave energy, all of them can
generally be categorized on the basis of three criteria [1821].
2.1.1. Location
This classification is according to the relative distance between the device, coast and seabed depth.
This classification is somehow qualitative because of the many dierences between continental shelfs
around the world. Nevertheless, this classification is not used in practical discussions and remains as
a first qualitative approach to WEC technologies.
Onshore: Located in coast proximity, commonly aected by swallow waters (h/
λ
<1/25), where h is
the water depth and
λ
is the wavelength. These converters are usually integrated in a breakwater,
dam, fixed to a clior rest on the seabed. The distinctive characteristics for these converters are
easy maintenance and installation. The drawbacks are that coastline waves have less energy than
deep-water waves along with a potential coastline reshape.
Nearshore: They are installed close to the shore, commonly aected by swallow or intermediate
waters (1/25 <h/
λ
<1/2). Their deployment and maintenance expenses are limited since they do
not need mooring systems as they are usually fixed or rest on the seabed.
Oshore: They are placed in deep waters (h/
λ
>1/2), far from the shore. They are able to harvest
energy from the most energetic places, but installation and maintenance can be much more
expensive because of the required mooring systems (high depth), long underwater cabling,
underwater substations and oshore maintenance.
Energies 2019,12, 3115 4 of 19
2.1.2. Dimensions of the Prime Mover and Orientation with Respect to the Wave
This classification is according to the orientation of the wave energy device with respect to the
wave propagation front (Figure 1). This classification along with the working principle are used to
clearly dierentiate any WEC.
Attenuators: The length of the device is of the same order of magnitude (or larger) than the
wavelength; these devices are oriented in such a way that they are parallel to the incident wave.
Terminators: Similar in dimensions to attenuators but placed perpendicular to the incident wave.
Point Absorbers: Axisymmetric devices capable of harvesting waves from any direction, known
as antenna eect, their dimensions are usually an order of magnitude lower than the wavelength.
Energies 2018, 11, x FOR PEER REVIEW 4 of 19
Attenuators: The length of the device is of the same order of magnitude (or larger) than the
wavelength; these devices are oriented in such a way that they are parallel to the incident wave.
Terminators: Similar in dimensions to attenuators but placed perpendicular to the incident wave.
Point Absorbers: Axisymmetric devices capable of harvesting waves from any direction, known
as antenna effect, their dimensions are usually an order of magnitude lower than the wavelength.
Figure 1. Classification according to device dimensions and orientation.
2.1.3. Working Principle
Oscillating water column: This type of technology builds, among its main elements, an air
chamber. It is this air, subjected to oscillating pressure by the action of the waves, which ascends or
descends moving a conventional air turbine linked to an electrical generator (Figure 2). Hence, the
air turbine can take advantage of the complete oscillation cycle of the wave. It is generally installed
in a breakwater, but there are shore-based and floating models. The main benefits for oscillating
water column concept commonly accepted are its simplicity and robustness [22]. Common examples
are Oceanlinx device deployed in 2005 designed to sit in shallow water, approximately 21 meters
wide and 24 meters long, and Mutriku wave energy plant, located in the Bay of Biscay and
commissioned in July 2011, which is one of the few wave energy plants still in operation.
Figure 2. Oscillating water column working mode of operation [22].
Floating structures: Unibody or multibody structures moving in heave, pitch, roll or in any
combination of the three (Figure 3) when affected by a wave. The relative movement between
different parts of the device allows converting it into electricity. These kinds of devices are rarely
named as floating structures but using the dimensions with respect to the wave: attenuators or
floating-point absorbers. Multiple examples can be found for this kind of technology. Pelamis was an
attenuator floating structure deployed during 2007. The machine is composed by a number of semi-
submerged, linked sections. These sections move relatively when the waves pass along the length of
the machine. W1 is a point absorber floating technology deployed in 2014. The machine has two main
bodies linked without restrictions in heave motion, which allows the relative movement between
them.
Figure 1. Classification according to device dimensions and orientation.
2.1.3. Working Principle
Oscillating water column: This type of technology builds, among its main elements, an air
chamber. It is this air, subjected to oscillating pressure by the action of the waves, which ascends or
descends moving a conventional air turbine linked to an electrical generator (Figure 2). Hence, the air
turbine can take advantage of the complete oscillation cycle of the wave. It is generally installed in
a breakwater, but there are shore-based and floating models. The main benefits for oscillating water
column concept commonly accepted are its simplicity and robustness [
22
]. Common examples are
Oceanlinx device deployed in 2005 designed to sit in shallow water, approximately 21 m wide and
24 m long, and Mutriku wave energy plant, located in the Bay of Biscay and commissioned in July
2011, which is one of the few wave energy plants still in operation.
Energies 2018, 11, x FOR PEER REVIEW 4 of 19
Attenuators: The length of the device is of the same order of magnitude (or larger) than the
wavelength; these devices are oriented in such a way that they are parallel to the incident wave.
Terminators: Similar in dimensions to attenuators but placed perpendicular to the incident wave.
Point Absorbers: Axisymmetric devices capable of harvesting waves from any direction, known
as antenna effect, their dimensions are usually an order of magnitude lower than the wavelength.
Figure 1. Classification according to device dimensions and orientation.
2.1.3. Working Principle
Oscillating water column: This type of technology builds, among its main elements, an air
chamber. It is this air, subjected to oscillating pressure by the action of the waves, which ascends or
descends moving a conventional air turbine linked to an electrical generator (Figure 2). Hence, the
air turbine can take advantage of the complete oscillation cycle of the wave. It is generally installed
in a breakwater, but there are shore-based and floating models. The main benefits for oscillating
water column concept commonly accepted are its simplicity and robustness [22]. Common examples
are Oceanlinx device deployed in 2005 designed to sit in shallow water, approximately 21 meters
wide and 24 meters long, and Mutriku wave energy plant, located in the Bay of Biscay and
commissioned in July 2011, which is one of the few wave energy plants still in operation.
Figure 2. Oscillating water column working mode of operation [22].
Floating structures: Unibody or multibody structures moving in heave, pitch, roll or in any
combination of the three (Figure 3) when affected by a wave. The relative movement between
different parts of the device allows converting it into electricity. These kinds of devices are rarely
named as floating structures but using the dimensions with respect to the wave: attenuators or
floating-point absorbers. Multiple examples can be found for this kind of technology. Pelamis was an
attenuator floating structure deployed during 2007. The machine is composed by a number of semi-
submerged, linked sections. These sections move relatively when the waves pass along the length of
the machine. W1 is a point absorber floating technology deployed in 2014. The machine has two main
bodies linked without restrictions in heave motion, which allows the relative movement between
them.
Figure 2. Oscillating water column working mode of operation [22].
Floating structures: Unibody or multibody structures moving in heave, pitch, roll or in any
combination of the three (Figure 3) when aected by a wave. The relative movement between dierent
parts of the device allows converting it into electricity. These kinds of devices are rarely named as
floating structures but using the dimensions with respect to the wave: attenuators or floating-point
Energies 2019,12, 3115 5 of 19
absorbers. Multiple examples can be found for this kind of technology. Pelamis was an attenuator
floating structure deployed during 2007. The machine is composed by a number of semi-submerged,
linked sections. These sections move relatively when the waves pass along the length of the machine.
W1 is a point absorber floating technology deployed in 2014. The machine has two main bodies linked
without restrictions in heave motion, which allows the relative movement between them.
Energies 2018, 11, x FOR PEER REVIEW 5 of 19
Figure 3. Floating structure with multiples bodies mode of operation. Reprinted from [22].
Pressure differential: Typically located nearshore, this kind of technology can be explained as a
combination of two technologies working together—oscillating water column and floating point-
absorbers. This is because it uses the working principle for both: difference of pressure and relative
heave/pitch/roll displacement between parts, the fixed air chamber in the seabed and the moveable
upper body (Figure 4). When a wave crest passes over the device, the water pressure above the device
compresses the air within the cylinder, moving the upper cylinder down creating a relative
movement in the same way as in punctual absorbers, this happens in the opposite way when a trough
passes over. Potential advantages of these devices include: Better survivability, they are not exposed
to splash zone corrosion nor the various hazards that could take effect when floating on surface and
reduced/negligible visual impact. A major drawback for pressure differential technology is the
required underwater maintenance. A good example of evolution with pressure differential
technology is Carnegie Clean Energy device (CETO). Deployed in 2015, CETO 5 served the purpose
of delivering pressured water for reverse osmosis membranes in the desalination plant, but CETO 6
(still in development) will include electrical generation onboard.
Figure 4. Pressure differential mode of operation.
Overtopping devices: These devices collect the water from the incident waves into a reservoir in
order to move one or more reduced jump hydraulic turbines, usually Kaplan turbines. They take
advantage of the potential energy of the waves to convert it, through synchronous generators, into
electrical energy (Figure 5). Within this type of device, we can distinguish between converters with a
fixed structure located on the coast (onshore) and those with a floating structure far away from it
(nearshore–offshore). A common example of these kind of devices is the Wave Dragon [23], which is
characterized by having a reflector that directs the incident waves towards a ramp to the reservoir
above sea level.
Figure 3. Floating structure with multiples bodies mode of operation. Reprinted from [22].
Pressure dierential: Typically located nearshore, this kind of technology can be explained
as a combination of two technologies working together—oscillating water column and floating
point-absorbers. This is because it uses the working principle for both: dierence of pressure and
relative heave/pitch/roll displacement between parts, the fixed air chamber in the seabed and the
moveable upper body (Figure 4). When a wave crest passes over the device, the water pressure
above the device compresses the air within the cylinder, moving the upper cylinder down creating
a relative movement in the same way as in punctual absorbers, this happens in the opposite way when
a trough passes over. Potential advantages of these devices include: Better survivability, they are
not exposed to splash zone corrosion nor the various hazards that could take eect when floating on
surface and reduced/negligible visual impact. A major drawback for pressure dierential technology
is the required underwater maintenance. A good example of evolution with pressure dierential
technology is Carnegie Clean Energy device (CETO). Deployed in 2015, CETO 5 served the purpose
of delivering pressured water for reverse osmosis membranes in the desalination plant, but CETO 6
(still in development) will include electrical generation onboard.
Energies 2018, 11, x FOR PEER REVIEW 5 of 19
Figure 3. Floating structure with multiples bodies mode of operation. Reprinted from [22].
Pressure differential: Typically located nearshore, this kind of technology can be explained as a
combination of two technologies working together—oscillating water column and floating point-
absorbers. This is because it uses the working principle for both: difference of pressure and relative
heave/pitch/roll displacement between parts, the fixed air chamber in the seabed and the moveable
upper body (Figure 4). When a wave crest passes over the device, the water pressure above the device
compresses the air within the cylinder, moving the upper cylinder down creating a relative
movement in the same way as in punctual absorbers, this happens in the opposite way when a trough
passes over. Potential advantages of these devices include: Better survivability, they are not exposed
to splash zone corrosion nor the various hazards that could take effect when floating on surface and
reduced/negligible visual impact. A major drawback for pressure differential technology is the
required underwater maintenance. A good example of evolution with pressure differential
technology is Carnegie Clean Energy device (CETO). Deployed in 2015, CETO 5 served the purpose
of delivering pressured water for reverse osmosis membranes in the desalination plant, but CETO 6
(still in development) will include electrical generation onboard.
Figure 4. Pressure differential mode of operation.
Overtopping devices: These devices collect the water from the incident waves into a reservoir in
order to move one or more reduced jump hydraulic turbines, usually Kaplan turbines. They take
advantage of the potential energy of the waves to convert it, through synchronous generators, into
electrical energy (Figure 5). Within this type of device, we can distinguish between converters with a
fixed structure located on the coast (onshore) and those with a floating structure far away from it
(nearshore–offshore). A common example of these kind of devices is the Wave Dragon [23], which is
characterized by having a reflector that directs the incident waves towards a ramp to the reservoir
above sea level.
Figure 4. Pressure dierential mode of operation.
Overtopping devices: These devices collect the water from the incident waves into a reservoir
in order to move one or more reduced jump hydraulic turbines, usually Kaplan turbines. They take
Energies 2019,12, 3115 6 of 19
advantage of the potential energy of the waves to convert it, through synchronous generators,
into electrical energy (Figure 5). Within this type of device, we can distinguish between converters
with a fixed structure located on the coast (onshore) and those with a floating structure far away from
it (nearshore–oshore). A common example of these kind of devices is the Wave Dragon [
23
], which is
characterized by having a reflector that directs the incident waves towards a ramp to the reservoir
above sea level.
Figure 5. Overtopping mode of operation [22].
Oscillating wave surge: These devices typically have one end attached to a fixed structure or
the bottom of the sea while the other end is free to move. A hinged deflector, this part is positioned
perpendicular to the wave direction, terminator (Figure 6). The axis of the deflector (or paddle) oscillates
like a pendulum mounted on a pivoting joint in response to the impact of the horizontal movement of
the wave particle. They often come in the form of floats, fins or membranes. This working principle
could be associated to the unique Japanese ‘Pendulor’ system [
24
]; but these devices do not take
advantage of any harbor resonance. An example for this kind of technology is the Aquamarine Power
Oyster, a nearshore device, where the top of the deflector is above the water surface and is hinged from
the sea bed.
Energies 2018, 11, x FOR PEER REVIEW 6 of 19
Figure 5. Overtopping mode of operation [22].
Oscillating wave surge: These devices typically have one end attached to a fixed structure or the
bottom of the sea while the other end is free to move. A hinged deflector, this part is positioned
perpendicular to the wave direction, terminator (Figure 6). The axis of the deflector (or paddle)
oscillates like a pendulum mounted on a pivoting joint in response to the impact of the horizontal
movement of the wave particle. They often come in the form of floats, fins or membranes. This
working principle could be associated to the unique Japanese 'Pendulor' system [24]; but these
devices do not take advantage of any harbor resonance. An example for this kind of technology is the
Aquamarine Power Oyster, a nearshore device, where the top of the deflector is above the water
surface and is hinged from the sea bed.
Figure 6. Oscillating wave surge mode of operation [22].
2.2. Power Take-Off Systems
In this section, a brief introduction for each of the different PTO technologies, as presented in
[18,25–27], is given. Three main technology paths can be applied to obtain electricity from the wave
power conversion chain (PCC), converting the energy being carried by the wave into fluid capture,
linear motion or rotary motion. Many different rotary electrical solutions can be applied, but these
technologies imply a lot of intermediate steps: Pistons, accumulators, air chambers or mechanical
gear systems [25]. The number of intermediate steps is critical for the wave energy conversion
efficiency and reliability:
Efficiency: The larger the number of intermediate steps, the greater are the mechanical and
transformation losses that we obtain as a result of the PCC. This causes a reduction in the annual
energy production (AEP), which in turn affects the levelized cost of the electricity (LCOE),
increasing it.
Reliability: The offshore equipment undergoes an accelerated degradation in comparison with
the same equipment implemented within a ground installation due to the high salinity of the
maritime environment where it is implemented. This fact makes it desirable to minimize the
amount of equipment to monitor and maintain while the equipment is in operation.
2.2.1. Air Turbines
Commonly used in OWC devices, air turbines require an air chamber to convert wave energy
into mechanical power (Section 2.1.3). The basic principle is to drive the air turbine with the
oscillating air pressure in the air chamber as a consequence of the oscillating water level. As a result,
this PTO solution presents a challenge coming from the bidirectional nature of the flow. A possible
solution for this challenge includes non-returning valves combined with a conventional turbine.
However, due to complexity, size and high maintenance costs, this configuration is not considered
Figure 6. Oscillating wave surge mode of operation [22].
2.2. Power Take-OSystems
In this section, a brief introduction for each of the dierent PTO technologies, as presented
in [
18
,
25
27
], is given. Three main technology paths can be applied to obtain electricity from the wave
power conversion chain (PCC), converting the energy being carried by the wave into fluid capture,
linear motion or rotary motion. Many dierent rotary electrical solutions can be applied, but these
technologies imply a lot of intermediate steps: Pistons, accumulators, air chambers or mechanical gear
systems [
25
]. The number of intermediate steps is critical for the wave energy conversion eciency
and reliability:
Eciency: The larger the number of intermediate steps, the greater are the mechanical and
transformation losses that we obtain as a result of the PCC. This causes a reduction in the
annual energy production (AEP), which in turn aects the levelized cost of the electricity (LCOE),
increasing it.
Reliability: The oshore equipment undergoes an accelerated degradation in comparison with
the same equipment implemented within a ground installation due to the high salinity of the
maritime environment where it is implemented. This fact makes it desirable to minimize the
amount of equipment to monitor and maintain while the equipment is in operation.
Energies 2019,12, 3115 7 of 19
2.2.1. Air Turbines
Commonly used in OWC devices, air turbines require an air chamber to convert wave energy into
mechanical power (Section 2.1.3). The basic principle is to drive the air turbine with the oscillating
air pressure in the air chamber as a consequence of the oscillating water level. As a result, this PTO
solution presents a challenge coming from the bidirectional nature of the flow. A possible solution
for this challenge includes non-returning valves combined with a conventional turbine. However,
due to complexity, size and high maintenance costs, this configuration is not considered as a viable
option [
25
]. A better solution involves a self-rectifying air turbine that converts an alternating air flow
into a unidirectional rotation.
2.2.2. Hydraulic Systems
These are typically used in attenuators, point absorbers and wave surge devices (Section 2.1.3),
in which the energy conversion system is based on taking advantage of the linear movement generated
by the interaction of the body (or bodies) with the waves. Conventional rotary electrical solutions
may not be directly compatible [
25
]. Therefore, a suitable conversion interface is required between
the linear energy capture and the electrical generator, capable of operating with high forces at
low frequencies, such as hydraulic systems that operate reversed with respect to their traditional
counterpart, that is, the movement of the body feeds the energy of the hydraulic motor which in turn
feeds an electric generator.
2.2.3. Hydro Turbines
Used for overtopping devices [
25
], hydraulic turbines [
28
] take advantage of the potential energy
of the water stored in the accumulation chamber of the device, which is converted to mechanical power
using low-head turbines and rotary electrical generators.
2.2.4. Direct Mechanical Drive Systems
This form of PTO solution requires additional mechanical systems driving a rotary electrical
generator [
25
]. It can comprise pulleys, cables, gear boxes or energy storage systems, such as Flywheels
(for rotation-based systems) in order to accumulate and release energy, if needed, for reactive operation
or to smooth any power variation.
2.2.5. Direct Electrical Drive Systems
Direct electrical drive PTO directly couples the moving part of the electrical generator with
the moving body of the WEC [
25
]. A direct electrical drive PTO system presents two main parts:
(i) a translator coupled to the moving body of the WEC, which can be equipped with permanent
magnets (conventional solution) or magnetic steel (switched reluctance) and (ii) the stator equipped
with coils. The waves induce a heave motion in the moving body coupled with the translator, generating
a relative displacement of the translator within the stator, inducing electrical current.
Critical added value of direct linear drive systems is the ability to move instantly in any of the
4-quadrant modes of operation, commonly called 4-quadrant control, allowing instant swap from
motor to generator mode at any given moment of the wave oscillation cycle (upwards or downwards)
to handle the required reactive power for some of the control strategies we will list in Section 3.
In the first (I) and third (III) quadrants, the electric machine delivers positive power, clockwise
or counterclockwise, supplying mechanical energy (motor). On the other hand, in the second (II)
and fourth (IV) quadrants, the electric machine delivers negative power, supplying electrical power
(generator). Applying a single cycle of regular waves to a WEC, for example, the period between
two consecutive wave peaks, the required operation for each quadrant will be as follows: During the
downward movement the electric machine will work in downward generator mode (quadrant II) once
it reaches the valley, and the consequent upward movement the electric machine will start working in
Energies 2019,12, 3115 8 of 19
upward generator mode (quadrant IV). If the WEC is operating with a control strategy that requires to
brake or accelerate the machine within the same cycle to achieve resonance, as we will see in the next
section, the instantaneous swap between the quadrants II-I-III or IV-I-III will be required.
Additionally, direct drive electrical systems have less components to maintain, avoiding
intermediate steps while providing simpler/cheaper construction and better reliability. Thus, direct
drive is the preferable technology for WECs and oshore facilities where reliability and eciency are
key parameters.
3. Control Strategies
The control problem for the wave energy sector does not fit the classic description of control
for other industries where control strategies involve the use of feedback (open loop, closed loop and
set-point tracking) and forcing the system variables to a constant value. Instead, WEC control aims for
maximization of captured energy while relying on feedforward control to generate optimal device
velocity or PTO force setpoints (Figure 7).
Energies 2018, 11, x FOR PEER REVIEW 8 of 19
3. Control Strategies
The control problem for the wave energy sector does not fit the classic description of control for
other industries where control strategies involve the use of feedback (open loop, closed loop and set-
point tracking) and forcing the system variables to a constant value. Instead, WEC control aims for
maximization of captured energy while relying on feedforward control to generate optimal device
velocity or PTO force setpoints (Figure 7).
Figure 7. Hierarchical control structure. Manipulated variable depends on the PTO: Bypass
valves, swashplate angle, excitation current or conduction angle. Optimal force/velocity
calculated as setpoint for the feedforward control.
Optimal calculation involves the performance function of the form:
𝐽=𝑣(𝑡)
𝑓
(𝑡)𝑑𝑡
(1)
where 𝑣(𝑡) is the device velocity, and 𝑓(𝑡) is the exerted PTO force. To ease the understanding
of how control maximizes this captured energy, we will start this section in 3.1 with a simple
analytical revision of the mean absorbed power and optimal control as originally defined in [15] and
further discussed in [8], concluding with a discussion of why suboptimal control approaches are
required before starting with the main topic for this paper, recent studies about different control
strategies for wave energy converters.
A good qualitative first approach to understand how to maximize the absorbed power is the
concept of resonance. A system being excited at its natural frequency is described as resonant. When
operating in resonance, the response amplitude is highest. Resonance does not usually occur
naturally for wave energy converters that have a natural frequency higher (Figure 8) than the power-
rich frequency components of a typical wave spectrum, so we have to trick the system into resonance
tuning the PTO damping and stiffness as needed, solving the impedance matching problem as we
will explain later.
Figure 8. Variation of WEC oscillator velocity (no PTO) for a set of regular wave frequencies
with Reference Model 3 [29] geometry with minor variations; simulations performed in
WECSIM [30]. Natural resonance operation found for periods of 3.8 s and 16.4 s.
Figure 7.
Hierarchical control structure. Manipulated variable depends on the PTO: Bypass valves,
swashplate angle, excitation current or conduction angle. Optimal force/velocity calculated as setpoint
for the feedforward control.
Optimal calculation involves the performance function of the form:
J=ZT
0
v(t)fPTO(t)dt (1)
where
v(t)
is the device velocity, and
fPTO(t)
is the exerted PTO force. To ease the understanding
of how control maximizes this captured energy, we will start in Section 3.1 with a simple analytical
revision of the mean absorbed power and optimal control as originally defined in [
15
] and further
discussed in [
8
], concluding with a discussion of why suboptimal control approaches are required
before starting with the main topic for this paper, recent studies about dierent control strategies for
wave energy converters.
A good qualitative first approach to understand how to maximize the absorbed power is the concept
of resonance. A system being excited at its natural frequency is described as resonant. When operating
in resonance, the response amplitude is highest. Resonance does not usually occur naturally for wave
energy converters that have a natural frequency higher (Figure 8) than the power-rich frequency
components of a typical wave spectrum, so we have to trick the system into resonance tuning the PTO
damping and stiness as needed, solving the impedance matching problem as we will explain later.
Energies 2019,12, 3115 9 of 19
Energies 2018, 11, x FOR PEER REVIEW 8 of 19
3. Control Strategies
The control problem for the wave energy sector does not fit the classic description of control for
other industries where control strategies involve the use of feedback (open loop, closed loop and set-
point tracking) and forcing the system variables to a constant value. Instead, WEC control aims for
maximization of captured energy while relying on feedforward control to generate optimal device
velocity or PTO force setpoints (Figure 7).
Figure 7. Hierarchical control structure. Manipulated variable depends on the PTO: Bypass
valves, swashplate angle, excitation current or conduction angle. Optimal force/velocity
calculated as setpoint for the feedforward control.
Optimal calculation involves the performance function of the form:
𝐽=𝑣(𝑡)
𝑓
(𝑡)𝑑𝑡
(1)
where 𝑣(𝑡) is the device velocity, and 𝑓(𝑡) is the exerted PTO force. To ease the understanding
of how control maximizes this captured energy, we will start this section in 3.1 with a simple
analytical revision of the mean absorbed power and optimal control as originally defined in [15] and
further discussed in [8], concluding with a discussion of why suboptimal control approaches are
required before starting with the main topic for this paper, recent studies about different control
strategies for wave energy converters.
A good qualitative first approach to understand how to maximize the absorbed power is the
concept of resonance. A system being excited at its natural frequency is described as resonant. When
operating in resonance, the response amplitude is highest. Resonance does not usually occur
naturally for wave energy converters that have a natural frequency higher (Figure 8) than the power-
rich frequency components of a typical wave spectrum, so we have to trick the system into resonance
tuning the PTO damping and stiffness as needed, solving the impedance matching problem as we
will explain later.
Figure 8. Variation of WEC oscillator velocity (no PTO) for a set of regular wave frequencies
with Reference Model 3 [29] geometry with minor variations; simulations performed in
WECSIM [30]. Natural resonance operation found for periods of 3.8 s and 16.4 s.
Figure 8.
Variation of WEC oscillator velocity (no PTO) for a set of regular wave frequencies with
Reference Model 3 [
29
] geometry with minor variations; simulations performed in WECSIM [
30
].
Natural resonance operation found for periods of 3.8 s and 16.4 s.
3.1. Numerical Modeling
For any WEC, the inertial force is balanced by the whole forces acting on the WEC. These forces
are usually split into external loads, WEC-wave interaction (hydrostatic force, excitation load and
radiation force) and reaction forces (caused by PTO, mooring or end-stop mechanism). Interaction
between WECs (i.e., floater) and ocean waves is a high-order nonlinear process that can be simplified
to linear equations for waves and small-amplitude device oscillation motions, which is acceptable
throughout the device’s operational regime. This means that the superposition principle applies [31].
The PTO system results in a complex nonlinear dynamic behavior. To keep the superposition
principle valid, the PTO forces must be linearized. In this linear form, the PTO force is composed
of two contributions [
32
]: A force proportional to velocity (damper) and a force proportional to the
displacement (spring). Mooring systems are often represented by a linear function of the captor
displacement and the mooring spring stiness. End-stop mechanism and other constrains (velocity or
PTO force operational limits) are abrupt nonlinear forces which are usually not considered, given the
complexity of a nonlinear approach for wave energy conversion. Instead, the optimum method of
achieving an acceptable displacement amplitude is to increase the PTO damping until the body has the
maximum allowance displacement [33].
In [
8
], M. Alves obtains the mean absorbed power assuming linearity and sinusoidal waves for
a heave motion wave energy converter as:
Pa=1
2
Bptoω2ˆ
Fe
2
hω2(m+A)+G+Kpto +Kmi2
ω2R+Bpto2=1
2
Bptoω2ˆ
Fe
2
Zi+Zpto
2(2)
where
ω
is the wave frequency,
ˆ
Fe
is the excitation force, m is the total inertia of the captor, A is the
added mass,
G
is the hydrostatic spring stiness,
Kpto
is the PTO mechanical spring,
Km
is the mooring
spring stiness, Ris the radiation damping,
Bpto
is the PTO damping,
Zi
is the intrinsic impedance and
Zpto is the PTO impedance.
An alternative, yet equivalent, formulation considers the force-to-velocity model of a WEC in the
frequency domain [15] as,
V(ω)
Fex(ω)+Fu(ω)=1
Zi(ω)(3)
where
V(ω)
,
Fex(ω)
, and
Fu(ω)
represent the Fourier transform of the velocity v(t), excitation force
f
ex
(t) and control force f
pto
(t), respectively.
Zi(ω)
is the intrinsic impedance in the frequency domain of
the system as
Zi(ω)=Br(ω)+ω[M+Ma(ω)Kb
ω2](4)
Energies 2019,12, 3115 10 of 19
where
Br(ω)
is the radiation damping (real and even) and
Ma(ω)
is the frequency-dependent added
mass, often replaced by its high-frequency asymptote m.
The model in (4) allows the derivation of conditions for optimal energy absorption assuming
a linear approach, and the intuitive design of the energy-maximizing controller in the frequency
domain [15] as
ZPTO(ω)=Z
i(ω)(5)
The choice of Z
PTO
as in (5) is referred to as optimal, reactive or complex conjugate control which
is the solution to the so-called impedance-matching problem. Technically, reactive control refers only
to the fact that the PTO reactance must cancel the inherent reactance. However, the PTO resistance and
the hydrodynamic resistance must also be equal. Thus, complex-conjugate control is a more accurate
description since it refers to the fact that the optimum PTO impedance equals the complex conjugate of
the intrinsic impedance.
The result in (5) has a number of relevant implications [34]:
The result is frequency dependent, implying a great optimization diculty for irregular seas
containing a mixture of frequencies.
Future knowledge of the excitation force may be required. While this knowledge is straightforward
for regular waves, it is more complex for irregular seas.
Since force and velocity can have opposite signs, the PTO may need to supply power for some
parts of the sinusoidal cycle.
The optimal control takes no constrains into consideration; it is more than likely a real system will
have velocity and displacement constrains.
Nevertheless, delivering optimal control may be infeasible due to the associated excessive motions
and loads in extreme waves. Hence, alternative suboptimal control schemes have been implemented,
which include physical constraints on the motions, forces and power rating of the device. While a lot
of discussion and dierent approaches can be found over the recent years for sub-optimal control
solutions, we have classified most of them according to the nomenclature that most commonly
appears—damping, reactive, latching and model predictive control.
3.2. Damping Control
A widely studied approach to avoid the diculties in the implementation of the feedback control
of the WECs is known in the literature as linear damping of the PTO, also called passive loading [
35
]
or resistive [
36
], a suboptimal approach where the instantaneous value of the PTO force is linearly
proportional to the oscillating body speed, that is to say
fpto(t)=Bpto v(t)(6)
where B
pto
>0 is the PTO damping coecient. This methodology does not require a prediction of
the excitation force, thus making it a simple strategy to implement. In fact, it is the one we can
usually find in the demonstrators or pre-commercial devices currently deployed around the world.
Conventionally, it only requires knowing the instantaneous value of the PTO velocity, for which
measurement instruments are usually available in the market.
Figure 9shows a simulation example in WECSIM [
30
] for Reference Model 3 using damping
control; the electric power (Pe) is always negative, Pe <0, so the machine does not need to return
energy at any point of the oscillating cycle to maximize the energy output in resonance operation.
Energies 2019,12, 3115 11 of 19
Energies 2018, 11, x FOR PEER REVIEW 10 of 19
accurate description since it refers to the fact that the optimum PTO impedance equals the complex
conjugate of the intrinsic impedance.
The result in (5) has a number of relevant implications [34]:
The result is frequency dependent, implying a great optimization difficulty for
irregular seas containing a mixture of frequencies.
Future knowledge of the excitation force may be required. While this knowledge is
straightforward for regular waves, it is more complex for irregular seas.
Since force and velocity can have opposite signs, the PTO may need to supply power
for some parts of the sinusoidal cycle.
The optimal control takes no constrains into consideration; it is more than likely a
real system will have velocity and displacement constrains.
Nevertheless, delivering optimal control may be infeasible due to the associated excessive
motions and loads in extreme waves. Hence, alternative suboptimal control schemes have been
implemented, which include physical constraints on the motions, forces and power rating of the
device. While a lot of discussion and different approaches can be found over the recent years for sub-
optimal control solutions, we have classified most of them according to the nomenclature that most
commonly appears—damping, reactive, latching and model predictive control.
3.2. Damping Control
A widely studied approach to avoid the difficulties in the implementation of the feedback
control of the WECs is known in the literature as linear damping of the PTO, also called passive
loading [35] or resistive [36], a suboptimal approach where the instantaneous value of the PTO force
is linearly proportional to the oscillating body speed, that is to say
𝑓
(𝑡)=−𝐵
𝑣(𝑡) (6)
where B𝑝𝑡𝑜 > 0 is the PTO damping coefficient. This methodology does not require a prediction of
the excitation force, thus making it a simple strategy to implement. In fact, it is the one we can usually
find in the demonstrators or pre-commercial devices currently deployed around the world.
Conventionally, it only requires knowing the instantaneous value of the PTO velocity, for which
measurement instruments are usually available in the market.
Figure 9. Linear damping–WEC simulation for regular waves. In the upper graphic PTO
force (blue) is compared with PTO velocity (red). The lower graphic represents ideal power
Figure 9.
Linear damping–WEC simulation for regular waves. In the upper graphic PTO force (blue) is
compared with PTO velocity (red). The lower graphic represents ideal power output (blue) and power
output considering electrical losses (red); negative values for power means the WEC is delivering
energy to the grid.
Damping control, however, provides a much smaller amount of power absorbed when compared
to other strategies such as reactive control [
37
], as we will see in the next section, and the linear
relationship between the speed and the force of the PTO, when it is a straightforward relation, may not
be easy to implement without using any feedback control. In addition, the optimal value of the PTO
damping, which is the value of B
pto
that maximizes the instantaneous power absorbed, can be easily
calculated for regular waves. However, in practice, where the incident wave is irregular (defined by the
wave spectrum), B
pto
is more dicult to calculate because of the changes in the spectral components of
the incident wave which are not constant over time, so a real time feedback control for a time-varying
damping value is required.
Therefore, we can distinguish between a real time-varying damping control and a constant
(or passive) damping control. First generation WEC control is based on damping strategies with
constant values for B
pto
. This particular strategy is still very common in recent WEC prototypes by
technology developers (given the simplicity of implementation).
3.2.1. Constant Damping Control
The work [
38
] presents a PTO force via constant damping coecient applied to compare the
power conversion performances of three WEC devices modelled in a computational fluid dynamic
software (CFD) model based on a 1/50 scale heaving point absorber WEC. Results from this article
quantify crucial hydrodynamic parameters for the three devices, revealing a prominent aection of
the device amplitude response in free motion without PTO. When PTO is included under eect of
regular and irregular waves, the joint eects of geometry and PTO damping on the power absorption
are very significant.
Experimental evidence with CECO device (a floating point absorber) with dierent linear damping
coecients is shown in [
39
] with the following conclusions: (a) optimal PTO damping coecients for
low-energy irregular waves are higher than for high-energy regular waves, and (b) wave conditions
aect significantly the optimal damping coecients.
Energies 2019,12, 3115 12 of 19
3.2.2. Time-Varying Damping Control
Passive damping control is analyzed and compared in [
35
] with a real-time passive control (PC)
based on the Hilbert–Huang transform (HHT). For this solution the damping coecient is time-varying
and tuned instantaneously, based on the frequency of the excitation force. This solution adds a grade
of complexity to damping control, since it is required that excitation force be known. The results of this
study prove that the proposed solution with real-time calibration of the damping coecient improves
from 21% to 65% the results that a conventional damping control strategy can obtain.
An experimental solution to calibrate the optimum damping coecients has been presented
in [
40
], based on tank testing experiments on the power performance of a bottom hinged oscillating
wave surge converter (OWSC) for regular and irregular waves with damping control, testing dierent
damping coecients for dierent wave conditions. The best damping coecient based on performance
was obtained. In this study it is concluded that there are no dierences between linear or non-linear
strategies in relation to the amount of energy absorbed, but nonlinear strategies have better stability
and a broader damping range.
Damping control is electronically implemented in a solid-state relay (SSR) with pulse-width
modulation (PWM) in [
38
]. The objective for this analysis is to mimic analog current flow and compare
it with a nonlinear model predictive control (NMPC). It is concluded that peak values of absorbed
power and the capture width greatly improve, compared with passive damping strategy.
3.3. Reactive Control
Reactive control is often misleading in the literature and can be confused with complex conjugate
control. As the dierences between these definitions were already explained in Section 3.1, for clarity
reasons, we will keep “reactive control” as it can be usually found in the literature, but a new term
such as “sub-optimal reactive control” should be used, as it is done in [
41
]. These control strategies
usually involve the tuning of both PTO resistance and reactance (B
pto
and K
pto
), taking into account
constrains such as PTO power rating or displacement limits, adjusting the resistance of the PTO to
avoid non-linear approaches [
33
]. Therefore, we will need to consider the generic approach to a PTO
characterization as explained in Section 3.1.
fpto(t)=Bpto v(t)Kptox(t)(7)
where
Kpto
is the stiness coecient, and x(t) is the displacement in the PTO. This kind of control when
implemented in demo prototypes usually employs a tabular approach to alleviate the computational
constrains required to calculate optimum values in real time. Hence, sub-optimal values for damping
and stiness coecients are pre-calculated with an optimization algorithm to be stored in tables.
For this reason, this particular technique is prone to modelling errors requiring a reanalysis of the
constant values after a certain testing period.
Figure 10 shows a simulation in WECSIM for Reference Model 3 [
29
] using reactive control.
The electric power (Pe) varies between positive and negative values, so the PTO needs to switch
from motor to generator mode and vice versa at least two times for every oscillation cycle. This kind
of mode switching is commonly called “4-quadrant control” and is not obtainable within the time
constrains for all of the available typologies of PTOs in the market. Reactive power is a back and forth
exchange between the PTO and the oscillating body and does not contribute to the facility energy
production. This energy may be supplied by any hydraulic, compressed-air, thermal, chemical, kinetic,
electrostatic, electromagnetic storage source [
42
] or the electrical grid. The biggest disadvantage of
reactive strategies comes from the reactive energy exchange process. This process does not suppose an
electrical energy gain, but it is subject to dissipative energy loss processes. The magnitude of these
losses can negatively aect the overall eciency of the device.
Energies 2019,12, 3115 13 of 19
Energies 2018, 11, x FOR PEER REVIEW 12 of 19
compare it with a nonlinear model predictive control (NMPC). It is concluded that peak values of
absorbed power and the capture width greatly improve, compared with passive damping strategy.
3.3. Reactive Control
Reactive control is often misleading in the literature and can be confused with complex conjugate
control. As the differences between these definitions were already explained in section 3.1, for clarity
reasons, we will keep “reactive control” as it can be usually found in the literature, but a new term
such as “sub-optimal reactive control” should be used, as it is done in [41]. These control strategies
usually involve the tuning of both PTO resistance and reactance (Bpto and Kpto), taking into account
constrains such as PTO power rating or displacement limits, adjusting the resistance of the PTO to
avoid non-linear approaches [33]. Therefore, we will need to consider the generic approach to a PTO
characterization as explained in 3.1.
𝑓
(𝑡)=−𝐵
𝑣(𝑡)−𝐾
𝑥(𝑡) (7)
Where 𝐾 is the stiffness coefficient, and x(t) is the displacement in the PTO. This kind of control
when implemented in demo prototypes usually employs a tabular approach to alleviate the
computational constrains required to calculate optimum values in real time. Hence, sub-optimal
values for damping and stiffness coefficients are pre-calculated with an optimization algorithm to be
stored in tables. For this reason, this particular technique is prone to modelling errors requiring a
reanalysis of the constant values after a certain testing period.
Figure 10. Reactive control–WEC simulation for regular waves.
Figure 10 shows a simulation in WECSIM for Reference Model 3 [29] using reactive control. The
electric power (Pe) varies between positive and negative values, so the PTO needs to switch from
motor to generator mode and vice versa at least two times for every oscillation cycle. This kind of
mode switching is commonly called “4-quadrant control” and is not obtainable within the time
constrains for all of the available typologies of PTOs in the market. Reactive power is a back and forth
exchange between the PTO and the oscillating body and does not contribute to the facility energy
production. This energy may be supplied by any hydraulic, compressed-air, thermal, chemical,
kinetic, electrostatic, electromagnetic storage source [42] or the electrical grid. The biggest
disadvantage of reactive strategies comes from the reactive energy exchange process. This process
does not suppose an electrical energy gain, but it is subject to dissipative energy loss processes. The
magnitude of these losses can negatively affect the overall efficiency of the device.
Figure 10. Reactive control–WEC simulation for regular waves.
Energy storage requirements for the reactive power are analyzed in [
41
] based on a time-domain
approach. These storage systems facilitate the exchange of reactive energy and can help to decrease
the associated losses, so they are a critical element of the system to maximize the power absorption.
The performance of a floating heaving-only point absorber is analyzed in [
43
]. The objective is to
maximize the wave energy absorption by actively controlling damping and stiness parameters on the
basis of a linear model in the frequency domain. The study concludes with a comparison of the results
with similarly validated studies.
Reinforcement learning methodologies are studied in [
44
]. Calculating the optimum reactive
control variables by means of a Q-learning algorithm, the model is able to maximize the energy
absorbed for each sea state.
3.4. Latching/Unlatching
Firstly suggested in [
45
], the latching control is based on achieving the resonance of the WEC
through a clamping system, fixing the device during a certain part of the wave oscillation cycle [
46
].
When the device is released, the control of the device is usually governed by a linear damping as in
Section 3.2. This way, the device presents resonance operation without need of reactive power control.
However, some energy needs to be drawn from an external source in order to activate the clamping
system when the device velocity is null. The critical point for this control strategy is the calculation of
the latching-unlatching time periods. Latching control avoids the two-way energy transfer and the
associated energy dissipation that characterize reactive control, so a wider spectrum of PTO systems
operating only in generator mode can be used under this control strategy.
Setting as base case scenario the passive damping control strategy in [
47
], the performance
improvement when latching control strategy is applied was quantified. The results show that the
capture width increases by 70% and the optimal damping coecient decreases by 60%.
An economic approach was made with dierent latching control strategies assessed for the
WEC in [
48
], including an interesting comparison with passive damping control. Results are based
on the simulated performance of the WEC using regular monochromatic waves, revealing similar
annual energy production for constant damping when compared with suboptimal latching, 201 and
197 MWh/yr, respectively. Optimal latching shows the best results with a 45% increase over the annual
energy production, 286 MWh/yr.
Energies 2019,12, 3115 14 of 19
3.5. Model Predictive Control
Due to its ability to deal with linear and non-linear models, together with the system constrains and
real time evaluation of future behavior, model predictive control (MPC) is a widely used and analyzed
strategy in the industry [
49
], and it should not be dierent for WECs. MPC solutions can handle the
physical constraints present for any WEC technology and the non-causal optimal control solution.
However, the problem of maximizing WEC energy requires an important modification over
the regular approach in the objective function of the MPC, resulting in a potentially non-convex
optimization problem. Given the benefits and growing understanding of these algorithms, this strategy
has become the most common control research topic in recent years. MPC maximizes the energy
absorption, applying at each time step the optimum force to achieve resonance over a future time
horizon, as firstly defined in [50].
As a starting point, [
51
] presents results of a comparison between MPC control and classical
(complex-conjugate control) methods for a Linear Permanent Magnet (LPMG) PTO controlled by
a machine side back-to-back actuator. It is concluded that complex-conjugate control when applied to
real world solutions shows to be inecient in maximizing the power absorption from the ocean waves.
Presented as an improvement to reactive control, a predictive strategy is analyzed in [
52
]
where a neural network trained with machine learning is used to predict future waves (height and
period), aecting the WEC and optimizing in real time the relevant parameters for the wave energy
absorption (PTO stiness coecient and PTO damping coecient). The algorithm does not present
any improvements over similar state-of-the-art reactive control solutions in relation with the absorbed
power, but it solves associated control inaccuracies from laboratory calibration and enables the
controller to be adaptative to variations in the machine response caused by ageing.
In a similar way for a heaving point-absorber, a neural network is employed to forecast the
short-term wave height and period in [
53
] to implement real-time adaptative latching control. This work
presents some results comparing the dierences of absorbed power for a particular wave scenario with
and without control.
An innovative MPC solution is proposed in [
54
]. Named as robust model predictive control
(R-MPC), it combines a predictive controller considering PTO constrains, ensuring maximum power
absorption while being realistic, and an innovative model to solve some parametric uncertainties and
model mismatches.
An interesting approach to control strategies for 3-degree of freedom WECs is presented in [
55
] and
compared with classical heave-only WECs. Presenting a parametric MPC, it optimizes independently
the pitch-surge and heave motion. Numerical algorithms are employed to find the optimal conditions
and results. In this work, several numerical tests are conducted for regular and irregular waves.
The presented results reveal a great improvement in absorbed power over heavy-only WECs. Contrary
to these results, in [
56
] A. Korde states that near-optimal control for pitch-surge motions are not
significant for wave energy absorption when compared to heave motion which is presented as the
dominant contributor to power absorption.
A hybrid MPC strategy is presented in [
57
], constrains are applied to PTO damping and damping
force for a two-body WEC. A Mixed-integer Quadratic Programming (MIQP) problem is proposed to
obtain the maximum power absorption. Results from this problem are compared with other MPC
solutions and classical models for an irregular wave scenario.
Future wave frequency prediction is used in [
58
] using a Fuzzy Logic controller to determine the
optimum PTO damping and stiness coecients in real time. The proposed solution combines some
regular tuning techniques with an innovative slow tuning methodology.
Fatigue, reliability and survivability controlled by MPC are analyzed in [
36
]. The results show
a trade-obetween maximized electrical power and the necessary dimensions for the WEC to resist
large loads and fatigue periods. These results are also compared with conventional reactive control,
where MPC improves the average annual energy production by 29%.
Energies 2019,12, 3115 15 of 19
3.6. Others
This category includes any mixed or innovative control strategies that do not clearly fit into any
of the categories presented above.
A genetic algorithm is used to optimize truncated power series along with the geometry for
nonlinear WECs in [
59
]. It enables higher energy harvesting without large motions and less dependence
of reactive power as a result.
A so-called Adaptive Parameter Estimation (APE) is proposed in [
60
]. The algorithm updates
in real time several WEC model parameters such as the radiation and excitation force coecients,
combining the benefits associated with optimal control (maximum energy output) and APE dealing
with any of the model parameter variation.
In [
61
] a new power take-otechnique is proposed for oscillating wave surge WECs. The main
innovation is to avoid any kind of braking system while keeping the amplitude within the specified
range. Then, the results are compared with constant damping control, showing the benefits of the new
proposed control system.
A new controller which is a variation for the complex conjugate through impedance matching
in the time-domain is proposed in [
62
,
63
]. The main benefit for the proposed control lies in that it
does not need a wave prediction or measurement. It is novel in that it is a feedback strategy with
a multi-resonant generator strategy, decomposing the control problem into multiple sub-problems
with independent single-frequency controllers. The solution is based on the spectral decomposition of
the measurement signal which is employed to construct the optimal solution.
Stochastic control derived from optimal control for heave-only point absorbers considering
force constrains is analyzed in [
64
]. Results indicate performance close to optimal in terms of mean
absorbed power.
A crosscutting solution can be found for a cabin-suspended catamaran with a motion control
system in [
65
]. The main objective is to minimize the heave velocity in the cabin, but a secondary
measured result of interest for this review is the power absorption from incoming waves which can
then be used as an energy vector for dierent applications, such as feeding auxiliary systems or driving
the main engines.
4. Conclusions and Further Research
Since the mean absorbed power for any WEC is frequency dependent, maximum power absorption
is achieved in resonance operation when the natural frequency of the WEC matches the wave frequency,
causing the excitation force. We can force the WEC into resonance with dierent control strategies
tuning the PTO damping and stiens constants (B
pto
and K
pto
). In this article, we have classified
dierent wave energy technologies based on dierent criteria commonly used in the literature. Optimal
control strategy (complex conjugate control) based on solving the impedance matching problem is
impractical for implementation, given the need for future knowledge of the excitation force in irregular
waves and the absence of constrains in force and speed for the PTO. Hence, suboptimal control
techniques are required, such as damping, reactive (misleading definition which should be revised to
suboptimal reactive), latching, MPC and other novelty control ideas.
Wave Energy Technologies are still far from the commercialization point. Only a few successful
demonstration projects can be found all over the world and even less when we try to find grid connected
projects. Several regulatory, social, economic, environmental and technological barriers need to be
addressed from dierent stakeholders at the same time to perceive an eective pulling action. Control
strategies is one of the main technological topics to be discussed. Great eorts have been made over
the years in developing eective suboptimal solutions for WECs.
Damping control, usually constant damping control, has been (and still is) the best approach
for technology developers willing to test an industrial scale WEC device, given the simplicity of
implementation and the safety of operation. Safety is not a minor issue for industrial scale marine
devices. Large forces and motions provided by optimal control and top suboptimal approaches could
Energies 2019,12, 3115 16 of 19
exceed the operational limits of prototype devices fabricated by shipyards and/or associated industries
still unfamiliar with WEC technology.
Reactive control is the natural evolution from damping control, presenting an aordable tabular
approach for any WEC prototype being deployed for a demonstration phase. Calibration of PTO
constants based on simulations or previous experiences do not represent a challenge to the current
state of art, although this kind of control strategy requires a PTO capable of switching from motor to
generator mode multiple times in a single wave oscillation.
Latching control solves the PTO limitation of reactive control, but it requires an additional
clamping mechanism to be installed and energized in the WEC, generating extra costs while also
lowering the reliability. Oshore equipment, especially mechanical pieces, are prone to failure because
of the extreme salinity ambient. Even well protected (marinization) pieces require a yearly basis
maintenance to avoid failures.
MPC solutions represent the best approach to optimal control. Enabling excitation force prediction
applies at each time step the optimum PTO force for maximum energy absorption while still considering
constrains (non-linear models). MPC has been found to be the most interesting topic among the scientific
community (Figure 11) over the recent years, given the good results presented in dierent articles.
This is due to the growing experience in simulated and tank-testing environments, the incremental
available advances in computational capacity and the improved expertise with environments based
on neural networks. Nevertheless, the complexity of implementation and absence of industry scale
demonstration projects disfavored MPC solutions for WEC technology developers. MPC strategies
can become a WEC technology enabler in the near future. Maximizing the energy reliability while
maintaining equipment costs will result in overall reduction of LCOE, along with the support from
dierent stakeholders. Caring about the other WEC barriers previously presented will result in a market
competitive renewable energy technology.
Energies 2018, 11, x FOR PEER REVIEW 15 of 19
Stochastic control derived from optimal control for heave-only point absorbers considering force
constrains is analyzed in [64]. Results indicate performance close to optimal in terms of mean
absorbed power.
A crosscutting solution can be found for a cabin-suspended catamaran with a motion control
system in [65]. The main objective is to minimize the heave velocity in the cabin, but a secondary
measured result of interest for this review is the power absorption from incoming waves which can
then be used as an energy vector for different applications, such as feeding auxiliary systems or
driving the main engines.
4. Conclusion and Further Research
Since the mean absorbed power for any WEC is frequency dependent, maximum power
absorption is achieved in resonance operation when the natural frequency of the WEC matches the
wave frequency, causing the excitation force. We can force the WEC into resonance with different
control strategies tuning the PTO damping and stiffens constants (Bpto and Kpto). In this article, we
have classified different wave energy technologies based on different criteria commonly used in the
literature. Optimal control strategy (complex conjugate control) based on solving the impedance
matching problem is impractical for implementation, given the need for future knowledge of the
excitation force in irregular waves and the absence of constrains in force and speed for the PTO.
Hence, suboptimal control techniques are required, such as damping, reactive (misleading definition
which should be revised to suboptimal reactive), latching, MPC and other novelty control ideas.
Figure 11. Recent studies for different WEC control strategies, 2017–2019.
Wave Energy Technologies are still far from the commercialization point. Only a few successful
demonstration projects can be found all over the world and even less when we try to find grid
connected projects. Several regulatory, social, economic, environmental and technological barriers
need to be addressed from different stakeholders at the same time to perceive an effective pulling
action. Control strategies is one of the main technological topics to be discussed. Great efforts have
been made over the years in developing effective suboptimal solutions for WECs.
Damping control, usually constant damping control, has been (and still is) the best approach for
technology developers willing to test an industrial scale WEC device, given the simplicity of
implementation and the safety of operation. Safety is not a minor issue for industrial scale marine
devices. Large forces and motions provided by optimal control and top suboptimal approaches could
Figure 11. Recent studies for dierent WEC control strategies, 2017–2019.
Author Contributions:
A.M.-A. conceived of the presented idea and took the lead in writing the manuscript.
A.J.G., E.R. and I.G. reviewed and supervised the manuscript. All authors discussed the results and contributed to
the final manuscript.
Funding:
This work was supported in part by the Basque Government through project IT1207-19 and by the
MCIU through the Research Project RTI2018-094902-B-C22 (MCIU/AEI/FEDER, UE).
Acknowledgments: The authors gratefully acknowledge Wedge Global for the helpful discussion and support.
Conflicts of Interest: The authors declare no conflict of interest.
Energies 2019,12, 3115 17 of 19
References
1. REN21. Renewables 2018 Global Status Report; REN21: Paris, France, 2018.
2.
Soukissian, T.H.; Denaxa, D.; Karathanasi, F.; Prospathopoulos, A.; Sarantakos, K.; Iona, A.; Georgantas, K.;
Mavrakos, S. Marine Renewable Energy in the Mediterranean Sea: Status and Perspectives. Energies
2017
,
10, 1512. [CrossRef]
3.
Doe Oce of Indian Energy. US Department of Energy. Available online: https://www.energy.gov/sites/
prod/files/2015/08/f25/LCOE.pdf (accessed on 14 July 2019).
4.
Franzitta, V.; Curto, D.; Rao, D. Energetic Sustainability Using Renewable Energies in the Mediterranean Sea.
Sustainability 2016,8, 1164. [CrossRef]
5. Franzitta, V.; Catrini, P.; Curto, D. Wave Energy Assessment along Sicilian Coastline, Based on DEIM Point
Absorber. Energies 2017,10, 376. [CrossRef]
6.
Karimirad, M.; Koushan, K. WindWEC: Combining wind and wave energy inspired by hywind and wavestar.
In Proceedings of the 2016 IEEE International Conference on Renewable Energy Research and Applications
(ICRERA), Birmingham, UK, 20–23 November 2016.
7. OES. Ocean Energy Systems. IEA. Available online: https://www.ocean-energy-systems.org/ocean-energy-
in-the-world/(accessed on 12 July 2019).
8.
Alves, M.; Causon, D.; Child, B.; Davidson, J.; Elsaßer, B.; Ferreira, C.; Fitzgerald, C.; Folley, M.; Forehand, D.;
Giorgi, S.; et al. Numerical Modelling of Wave Energy Converters; Elsevier: London, UK, 2016.
9.
Magagna, D.; Monfardini, R.; Uihlein, A. JRC Ocean Energy Status Report; European Commission: Brussels,
Belgium, 2016.
10. Orecchini, F. The era of energy vectors. Int. J. Hydrogen Energy 2006,31, 1951–1954. [CrossRef]
11.
Franzitta, V.; Curto, D.; Milone, D.; Viola, A. The Desalination Process Driven by Wave Energy: A Challenge
for the Future. Energies 2016,9, 1032. [CrossRef]
12.
Wilson, D.; Bacelli, G.; Coe, R.G.; Bull, D.L.; Abdelkhalik, O.; Korde, U.A.; Robinett, R.D., III. A Comparison of
WEC Control Strategies; Sandia National Laboratories: Albuquerque, NM, USA, 2015.
13.
Ozkop, E.; Altas, I.H. Control, power and electrical components in wave energy conversion systems: A review
of the technologies. Renew. Sustain. Energy Rev. 2017,67, 106–115. [CrossRef]
14.
Wang, L.; Isberg, J.; Tedeschi, E. Review of control strategies for wave energy conversion systems and their
validation: The wave-to-wire approach. Renew. Sustain. Energy Rev. 2018,81, 366–379. [CrossRef]
15. Falnes, J. Ocean Waves and Oscillating Systems; Cambridge University Press: Trondheim, Norway, 2002.
16.
Duckers, L. Wave energy. In Renewable Energy, 2nd ed.; Boyle, G., Ed.; Oxford University Press: Oxford, UK,
2004; p. 8.
17.
Bioenergy International. Global Green Energy Patent Filings 2017 Jump 43% Compared to 2016. Available
online: https://bioenergyinternational.com/research-development/global-green-energy-patent-filings-2017-
jump-43-compared-to-2016 (accessed on 13 July 2019).
18.
Ochs, M.E.; Bull, D.L.; Laird, D.L.; Jepsen, R.A.; Boren, B. Technological Cost-Reduction Pathways for Point
Absorber Wave Energy Converters in the Marine Hydrokinetic Environment; Sandia Report 7204; Sandia National
Laboratories: Albuquerque, NM, USA, 2013.
19.
Drew, B.; Plummer, A.R.; Sahinkaya, M.N. A review of wave energy converter technology. Proc. Inst. Mech.
Eng. Part A J. Power Energy 2009,223, 887–902. [CrossRef]
20.
Cl
é
ment, A.; McCullen, P.; Falc
ã
o, A.; Fiorentino, A.; Gardner, F.; Hammarlund, K.; Lemonis, G.; Lewis, T.;
Nielsen, K.; Petroncini, S.; et al. Wave energy in Europe: Current status and perspectives. Renew. Sustain.
Energy Rev. 2002,6, 405–431. [CrossRef]
21.
O’Sullivan, D.; Blavette, A.; Mollaghan, D.; Alcorn, R. Dynamic Characteristics of Wave and Tidal Energy
Converters and a Recommended Structure for Development of a Generic Model for Grid Connection; A Report
Prepared by HMRC-UCC for OES-IA under ANNEX III, Document No. T0321. Cork, Ireland, 2010. Available
online: https://hal.archives-ouvertes.fr/hal-01265981/document (accessed on 14 August 2019).
22.
Laboratory, N.R.E. Marine and Hydrokinetic Technology Glossary. Available online: https://openei.org/wiki/
Marine_and_Hydrokinetic_Technology_Glossary (accessed on 22 May 2019).
23. Wave Dragon. Available online: http://www.wavedragon.net/(accessed on 22 May 2019).
24.
Matt, F.; Trevor, W.; Max, O. The Oscillating Wave Surge Converter. In Proceedings of the International
Oshore and Polar Engineering Conference, Toulon, France, 23–28 May 2004.
Energies 2019,12, 3115 18 of 19
25.
Pecher, A.; Kofoed, J.P. Handbook of Ocean Wave Energy. Ocean Engineering & Oceanography; No. Power
Take-OSystems for WECs; Springer: Berlin/Heidelberg, Germany, 2017; Volume 7.
26.
Schwartz, D.; Mentzer, A. Feasibility of Linear Induction Wave Power Generation. Available online: https:
//linearinductionwavepower.weebly.com/(accessed on 22 May 2019).
27.
So, R.; Casey, S.; Kanner, S.; Simmons, T.K.A.B.A. PTO-Sim: Development of a Power Take OModeling
Tool for Ocean Wave Energy Conversion. 06 2014. Available online: https://energy.sandia.gov/wp-content/
uploads/2014/06/2015-IEEE-PES_PTO-Sim_Nak.pdf (accessed on 22 May 2019).
28.
Basic Principles of Turbomachines. IIT 2016. Available online: http://nptel.ac.in/courses/112104117/chapter_7/
(accessed on 19 July 2019).
29.
Sandia. Reference Model Project. Available online: https://energy.sandia.gov/energy/renewable-energy/
water-power/technology-development/reference-model-project-rmp/(accessed on 21 June 2019).
30.
NREL&Sandia. WECSIM. Available online: https://wec- sim.github.io/WEC-Sim/(accessed on 22 May 2019).
31.
Denis, M.S. Some Cautions on the Employment of the Spectral Technique to Describe the Waves of the
Sea and the Response Thereto of Oceanic Systems. In Proceedings of the Oshore Technology Conference,
Houston, TX, USA, 29 April–2 May 1973.
32.
Xuereb, A.; Spiteri Staines, C.; Sant, T.; Mule Stagno, L. Design of a Linear Electrical Machine for a Wave
Generation System in the Maltese Waters; Sayigh, A., Ed.; Renewable Energy in the Service of Mankind; Springer
International Publishing: New York, NY, USA, 2015; Volume I.
33.
Evans, D. Maximum wave-power absorption under motion constraints. Appl. Ocean Res.
1981
,3, 200–203.
[CrossRef]
34.
Ringwood, J.V.; Bacelli, G.; Fusco, F. Energy-Maximizing Control of Wave-Energy Converters. IEEE Control
Syst. Mag. 2014,34, 30–55.
35.
Garcia-Rosa, P.B.; Kulia, G.; Ringwood, J.V.; Molinas, M. Real-Time Passive Control of Wave Energy
Converters Using the Hilbert-Huang Transform. IFAC-PapersOnLine 2017,50, 14705–14710. [CrossRef]
36.
Nielsen, K.M.; Pedersen, T.S.; Andersen, P.; Ambühl, S. Optimizing Control of Wave Energy Converter with
Losses and Fatigue in Power Take o.IFAC-PapersOnLine 2017,50, 14680–14685. [CrossRef]
37.
Son, D.; Yeung, R.W. Real-time implementation and validation of optimal damping control for
a permanent-magnet linear generator in wave energy extraction. Appl. Energy
2017
,208, 571–579. [CrossRef]
38.
Jin, S.; Patton, R.J.; Guo, B. Enhancement of wave energy absorption eciency via geometry and power
take-odamping tuning. Energy 2019,169, 819–832. [CrossRef]
39.
Rodr
í
guez, C.A.; Rosa-Santos, P.; Taveira-Pinto, F. Assessment of damping coecients of power take-o
systems of wave energy converters: A hybrid approach. Energy 2019,169, 1022–1038. [CrossRef]
40.
Jiang, X.; Day, S.; Clelland, D. Hydrodynamic responses and power eciency analyses of an oscillating wave
surge converter under dierent simulated PTO strategies. Ocean Eng. 2018,170, 286–297. [CrossRef]
41.
Korde, U.A. Preliminary consideration of energy storage requirements for sub-optimal reactive control of
axisymmetric wave energy devices. Annu. Rev. Control 2015,40, 93–101. [CrossRef]
42.
Robyns, B.; François, B.; Delille, G.; Saudemont, C. Energy Storage in Electric Power Grids; Wiley-ISTE: Lille,
France, 2015.
43.
Jin, P.; Zhou, B.; Göteman, M.; Chen, Z.; Zhang, L. Performance optimization of a coaxial-cylinder wave
energy converter. Energy 2019,174, 450–459. [CrossRef]
44.
Anderlini, E.; Forehand, D.; Bannon, E.; Xiao, Q.; Abusara, M. Reactive control of a two-body point absorber
using reinforcement learning. Ocean Eng. 2018,148, 650–658. [CrossRef]
45. Budal, K.; Falnes, J. Optimum operation of wave power converter. Mar. Sci. Commun. 1977,3, 133–150.
46.
Babarit, A.; Duclos, G.; Cl
é
ment, A. Comparison of latching control strategies for a heaving wave energy
device in random sea. Appl. Ocean Res. 2004,26, 227–238. [CrossRef]
47.
Wu, J.; Yao, Y.; Zhou, L.; Göteman, M. Real-time latching control strategies for the solo Duck wave energy
converter in irregular waves. Appl. Energy 2018,222, 717–728. [CrossRef]
48.
Temiz, I.; Leijon, J.; Ekergard, B.; Bostrom, C. Economic aspects of latching control for a wave energy converter
with a direct drive linear generator power take-o.Renew. Energy 2018,128, 57–67. [CrossRef]
49.
Faedo, N.; Olaya, S.; Ringwood, J.V. Optimal control, MPC and MPC-like algorithms for wave energy
systems: An overview. IFAC J. Syst. Control 2017,1, 37–56. [CrossRef]
50.
Hals, J.; Falnes, J.; Moan, T. Constrained Optimal Control of a Heaving Buoy Wave-Energy Converter.
J. Oshore Mech. Arct. Eng. 2010,133, 011401. [CrossRef]
Energies 2019,12, 3115 19 of 19
51.
O’Sullivan, A.C.; Lightbody, G. Co-design of a wave energy converter using constrained predictive control.
Renew. Energy 2017,102, 142–156. [CrossRef]
52.
Anderlini, E.; Forehand, D.; Bannon, E.; Abusara, M. Reactive control of a wave energy converter using
artificial neural networks. Int. J. Mar. Energy 2017,19, 207–220. [CrossRef]
53.
Li, L.; Yuan, Z.; Gao, Y. Maximization of energy absorption for a wave energy converter using the deep
machine learning. Energy 2018,165, 340–349. [CrossRef]
54.
Jama, M.; Wahyudie, A.; Noura, H. Robust predictive control for heaving wave energy converters. Control Eng.
Pract. 2018,77, 138–149. [CrossRef]
55.
Zou, S.; Abdelkhalik, O.; Robinett, R.; Korde, U.; Bacelli, G.; Wilson, D.; Coe, R. Model Predictive Control
of parametric excited pitch-surge modes in wave energy converters. Int. J. Mar. Energy
2017
,19, 32–46.
[CrossRef]
56.
Korde, U.A.; Lyu, J.; Robinett, R.D.; Wilson, D.G.; Bacelli, G.; Abdelkhalik, O.O. Constrained near-optimal
control of a wave energy converter in three oscillation modes. Appl. Ocean Res.
2017
,69, 126–137. [CrossRef]
57.
Xiong, Q.; Li, X.; Martin, D.; Guo, S.; Zuo, L. Semi-Active Control for Two-Body Ocean Wave Energy
Converter by Using Hybrid Model Predictive Control. In Proceedings of the ASME Dynamic Systems and
Control Conference, Atlanta, GA, USA, 30 September–3 October 2018.
58.
Burgaç, A.; Yavuz, H. Fuzzy Logic based hybrid type control implementation of a heaving wave energy
converter. Energy 2019,170, 1202–1214. [CrossRef]
59.
Abdelkhalik, O.; Darani, S. Optimization of nonlinear wave energy converters. Ocean Eng.
2018
,162, 187–195.
[CrossRef]
60.
Zhan, S.; Wang, B.; Na, J.; Li, G. Adaptive Optimal Control of Wave Energy Converters. IFAC-PapersOnLine
2018,51, 38–43. [CrossRef]
61.
Senol, K.; Raessi, M. Enhancing power extraction in bottom-hinged flap-type wave energy converters through
advanced power take-otechniques. Ocean Eng. 2019,182, 248–258. [CrossRef]
62.
Song, J.; Abdelkhalik, O.; Robinett, R.; Bacelli, G.; Wilson, D.; Korde, U. Multi-resonant feedback control of
heave wave energy converters. Ocean Eng. 2016,127, 269–278. [CrossRef]
63.
Lekube, J.; Garrido, A.J.; Garrido, I. Rotational Speed Optimization in Oscillating Water Column Wave Power
Plants Based on Maximum Power Point Tracking. IEEE Trans. Autom. Sci. Eng.
2017
,14, 681–691. [CrossRef]
64.
Sun, T.; Nielsen, S.R. Stochastic control of wave energy converters for optimal power absorption with
constrained control force. Appl. Ocean Res. 2019,87, 130–141. [CrossRef]
65.
Han, J.; Kitazawa, D.; Kinoshita, T.; Maeda, T.; Itakura, H. Experimental investigation on a cabin-suspended
catamaran in terms of motion reduction and wave energy harvesting by means of a semi-active motion
control system. Appl. Ocean Res. 2019,83, 88–102. [CrossRef]
©
2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access
article distributed under the terms and conditions of the Creative Commons Attribution
(CC BY) license (http://creativecommons.org/licenses/by/4.0/).
... Indeed, the main contribution of the paper is the experimentation and validation of MF surrogate models to WEC control design. We will adopt a very simple control approach, essentially based on reactive control (Maria-Arenas et al., 2019;Ringwood et al., 2014), taking the specific sea-state occurrence into account. ...
... In the PeWEC application case, even if some initial attempts have been performed to move towards an optimizationbased solution of the OCP (Pasta et al., 2021b), the current control strategy is the so-called reactive control (Maria-Arenas et al., 2019;Ringwood et al., 2014). The law adopted in this type of configuration is a feedback control law, in which the control action is a linear combination of velocity and position on the conversion axis. ...
Article
Full-text available
The energy coming from the motion of the waves of seas and oceans could be an important component in the solution of the energy problem related to the pursuit of alternatives to fossil fuels. However, wave energy is still technologically immature and it has not reached the economic feasibility required for economy of scale. One of the major technological challenges for the achievement of this goal is the development of control strategies capable of maximizing the extracted energy, adapting to the conditions of the seas and oceans that surround the Wave Energy Converter (WEC) devices. To perform this task, control systems often adopt explicitly control-oriented models, that are by nature affected by uncertainties. On the contrary, to address the problem a data-driven solution is proposed here. The presented strategy applies an optimization approach based on a Gaussian Process Regression (GPR) metamodel to learn the control strategy to be applied. In order to accelerate the learning process, we present a novel method that exploits in the initial phase a previous knowledge given by simulations with the system model and based on the co-kriging concept. To test this approach the Pendulum Wave Energy Converter has been adopted as a case study. To differentiate the previous knowledge and the real system behaviour, a simplified linear model is used to obtain the prior knowledge, while a complex nonlinear one acts as the environment in which simulate the behaviour of the real system. A month-long simulation is used to validate the effectiveness of the proposed strategy, showing the ability of adapting to a real system different from the simplified model on the basis only of data, and overcoming the model-based strategy in terms of performance.
... 2018). 2 Considering the orientation or position relative to the wavefront Totalizers or terminators: small structures compared to the incident waves. Generally, several devices are grouped following a line. ...
... Some of the first works to use neural networks in wave energy systems were [67,793], and machine learning methods have since been used in a variety of different control and optimisation works [17,19,496,442]. Recently these AI approaches have also been employed for the optimisation of wave farms [770,771,627]. ...
... In order to overcome these drawbacks, various ideas and solutions have been proposed and investigated in the open literature. Amongst them, different active control strategies were proposed to create and maintain resonance [7][8][9]. Although the robustness of such active control schemes has been highlighted in many studies, there are still some limitations that stand against their practicality. ...
Article
Full-text available
Because of their wide resonant frequency bandwidth which extends to the lower range of wave frequencies, the research community has recently paid significant attention to the design and performance analysis of bi-stable point wave energy absorbers (PWAs). Along this line, we dedicate this study to shed more light onto the behavior of bi-stable PWAs under random wave excitations. We use Monte Carlo simulations to study the effect of the wave spectral content on the statistical response of the absorber; mainly the average output power and the average capture width ratio (CWR), for different shapes of the potential energy function of the absorber. We show that there is a direct correlation between the stochastic response of the absorber and its steady-state behavior under harmonic wave excitations. In particular, we show that the PWA exhibits its best performance when the peak frequency of the waves’ spectral density function is tuned to the center of the steady-state effective bandwidth of the absorber, where large-amplitude inter-well oscillations of the buoy are uniquely realized. We develop design maps to demonstrate how the CWR of the bi-stable PWA varies with the peak frequency and significant height of the waves. We use those maps to demonstrate how to design the shape of the potential energy function of the absorber to maximize the CWR for waves of known spectral content. We believe that such understanding is vital to design effective bi-stable PWAs.
... In the PeWEC application case, even if some initial attempts have been performed to move towards an optimizationbased solution of the OCP (Pasta et al., 2021b), the current control strategy is the so-called reactive control (Maria-Arenas et al., 2019;Ringwood et al., 2014). The law adopted in this type of configuration is a feedback control law, in which the control action is a linear combination of velocity and position on the conversion axis. ...
Preprint
Full-text available
The energy coming from the motion of the waves of seas and oceans could be an important component in the solution of the energy problem related to the pursuit of alternatives to fossil fuels. However, wave energy is still technologically immature and it has not reached the economic feasibility required for economy of scale. One of the major technological challenges for the achievement of this goal is the development of control strategies capable of maximizing the extracted energy, adapting to the conditions of the seas and oceans that surround the Wave Energy Converter (WEC) devices. To perform this task, control systems often adopt explicitly control-oriented models, that are by nature affected by uncertainties. On the contrary, to address the problem a data-driven solution is proposed here. The presented strategy applies an optimization approach based on a Gaussian Process Regression (GPR) metamodel to learn the control strategy to be applied. In order to accelerate the learning process, we present a novel method that exploits in the initial phase a previous knowledge given by simulations with the system model and based on the co-kriging concept. To test this approach the Pendulum Wave Energy Converter has been adopted as a case study. To differentiate the previous knowledge and the real system behaviour, a simplified linear model is used to obtain the prior knowledge, while a complex nonlinear one acts as the environment in which simulate the behaviour of the real system. A month-long simulation is used to validate the effectiveness of the proposed strategy, showing the ability of adapting to a real system different from the simplified model on the basis only of data, and overcoming the model-based strategy in terms of performance.
... An offshore floating device known as the Mighty Whale was installed in Japan, with a rated capacity of 110 kW. These devices convert the up-and-down wave oscillation into pressurized air to drive the air turbine in order to generate electrical energy [174][175][176]. This is an oscillating water column plant that features a unidirectional impulse turbine. ...
Article
Full-text available
As the global interest in renewable energy generation continues, the need to develop new and innovative solutions is being explored every day throughout the world by researchers and innovators. Hybrid renewable energy innovations are gaining progressive interest not only because of the threat of climate change but also due to the technological advancements seen in renewables. Ocean waves have immense potential as a renewable energy source, and related technologies have advanced continuously over the past few decades. In response, this paper extensively studies wave energy converters (WECs) based on the power take-off (PTO) technique, and presents a novel hybrid wave-plus-photon energy (HWPE) harvester called Wavevoltaics, based on wave and solar energy capture systems for coastal communities’ power needs, in line with decarbonization measures. The HWPE harvester uses a simple rack-and-pinion mechanism in combination with solar cell technology to convert the wave energy into usable electrical energy in a water column structural design. This novel HWPE device can be used to provide power for lighting and gadgets for coastal communities that rely heavily on fossil fuels for their lighting and electrical needs. Later in the paper, the challenges faced in hybrid wave energy development are presented.
Article
The ocean is a huge energy conversion field, and ocean renewable energy (ORE) can provide us with a constant source of energy. Research on ORE collection and utilization has been emerging in recent years, and the number of ORE research results has been increasing. This paper visualizes the trends and current research status of ORE by performing bibliometric analysis using VOSviewer and CiteSpace. The results are analyzed in terms of annual publications, countries, institutions, authors, journals, keywords, topics, and references. The results indicate that current research hotspots include (1) theoretical calculations and simulation modeling, (2) design of ocean renewable energy devices (OREDs), (3) deployment of OREDs and optimization improvements, and (4) evaluation of ORE projects. Wave energy harvesting applications, offshore wind energy harvesting applications, design and improvement of triboelectric nanogenerator, and artificial reefs or islands are the frontiers of research in the field of ORE. With the development of energy conversion technologies, the future of ocean power generation will have a promising and attractive prospect. The results of the study provide a comprehensive overview of the evolution of research hotspots in this field and can help those researchers willing to work in this research area to quickly understand the research frontiers and the general situation.
Article
Harnessing energy from ocean waves, although not a new concept, is beginning to gain traction in the renewable energy research community. This largely untapped energy resource has considerable potential; however, researchers are still seeking to understand how to make it economically viable. This paper presents an overview of wave energy conversion as follows. It identifies various advantages of wave energy conversion as well as challenges that researchers and industry developers must overcome before large-scale installations can be fully realized. This paper also reviews the devices that have been designed to achieve efficient energy conversion. Multiple studies concerning wave energy converters placed in an array are reviewed and discussed, focusing specifically on consistent trends concerning array performance. The paper also reviews recent control methods for wave energy conversion.
Article
Full-text available
This work proposes an approach for the optimal sizing of a cylindrical heaving wave energy converter (WEC). The approach is based on maximising the absorbed power density (APD) of the buoy, with the diameter being the decision variable. Furthermore, two types of buoy shapes were compared to get the best option. The two buoy shapes are the cone cylinder buoy (CCB) and the hemisphere cylinder buoy (HCB). The aim was therefore to determine the best shape and as well as the optimal size of the cylindrical point absorber. To validate the approach, the simulation was performed under Durban (South Africa) sea characteristics of 3.6 m wave significant height and 8.5 s peak period, using the openWEC simulator. The buoy diameter range considered was from 0.5 m to 10 m for both shapes. Simulation results revealed that a diameter of 1 m was the optimal solution for both buoy shapes. Furthermore, the APD method revealed that the HCB was more efficient than the CCB. The power density of the HCB was 1070 W/m2, which was almost double the power density of the CCB, while the two shapes present almost the same absorbed power.
Article
Full-text available
In this work a three dimensional computational fluid dynamic (CFD) model has been constructed based on a 1/50 scale heaving point absorber wave energy converter (PAWEC). The CFD model is validated first via wave tank tests and then is applied in this study to investigate the joint effects of device geometry and power take-off (PTO) damping on wave energy absorption. Three PAWEC devices are studied with the following geometrical designs: a cylindrical flat-bottom device (CL); a hemispherical streamlined bottom design (CH) and a 90°-conical streamlined bottom structure (CC). A PTO force via varying damping coefficient is applied to compare the power conversion performances of the aforementioned devices. Free decay, wave-PAWEC interaction and power absorption tests are conducted via the CFD model. The results show that for CH and CC designs the added mass and hydrodynamic damping decrease by up to 60% compared with the CL device. Moreover, the CC design is the best of the three structures since its amplitude response increases by up to 100% compared with the CL. Applying an appropriate PTO damping to the CC device prominently increases the achievable optimal power by up to 70% under both regular and irregular waves (compared with the CL device).
Article
Full-text available
The damping coefficient of the power take-off (PTO) system is a key parameter in the performance assessment of a wave energy converter (WEC). However, since in most WEC studies the focus is mainly on the absorbed power, damping estimation is generally overlooked on the assumption that a single constant coefficient can properly characterize the WEC's damping of a given configuration for all wave conditions. Recently, while analyzing the experimental tests of CECO, a floating-point absorber WEC, significant discrepancies were found among their experimental responses under different incident waves. Instead of attributing those differences to nonlinear hydrostatic or Froude-Krylov effects, it was hypothesized that variations in the PTO damping associated to incident waves was the main cause. This study presents the experimental evidences of that behavior for regular and irregular waves. Furthermore, a hybrid approach for the assessment of damping coefficients is proposed and applied to CECO's experimental responses. The results demonstrated that: a) damping coefficients were significantly affected by wave conditions; b) higher PTO damping coefficients were obtained for milder irregular waves than for rougher regular waves; c) the hybrid approach reliably and efficiently estimated the WEC power in regular and irregular waves.
Article
The linear and non-linear dynamics of a bottom-hinged, flap-type wave energy converter in response to regular waves were studied through computational simulations to assess the performance of power takeoff techniques and enhance the power extraction. The computational model was developed in Comsol Multiphysics using its Multibody Dynamics Module and was carefully validated. The hydrodynamic coefficients are from the linear wave theory. To avoid damages to the device, especially in extreme sea conditions, a brake mechanism is used to limit the amplitude of flap oscillations. With that limit imposed, we show that the optimum damping coefficient proposed in the literature for power takeoff does not actually lead to an optimum power extraction for a range of wave frequencies. Over that range, the brake mechanism becomes engaged, leading to a significant energy loss. We propose new power takeoff techniques that avoid the engagement of the brake, yet keep the amplitude within the specified range. They are proposed for both the linear and non-linear flap dynamics, and their efficacy is demonstrated for several flap geometries. The proposed techniques enhance the power extraction by as high as 600% (linear) and 19% (non-linear), in the latter case by minimizing the energy loss due to brake.
Article
This paper presents an analytical solution derived for optimal control of the power take-off of a single-degree of freedom heave point absorber with constraints on the control force. The optimal control law turns out to be noncausal with a functional dependence on future velocities. To handle this problem, an algorithm for predicting future velocities is derived. Based on the solution the mean (time-averaged) absorbed power in a given sea-state is calculated. The performance of the indicated controller in terms of the mean absorbed power is close to the optimal value obtained by nonlinear programming and better than a controller with feedback from the present displacement, velocity and acceleration, and with optimized gain factors.
Article
To achieve a wider frequency range where the device has a larger capture width ratio, the performance of a heaving coaxial-cylinder wave energy converter is optimized through actively controlled generator damping and stiffness using a linear frequency domain model. The generator power take-off system is modeled as a damping-spring system, and the numerical model is validated against published results. The coupled dynamics of a two-body model is analyzed to search for the optimal generator damping and stiffness leading to maximal capture width ratio. The optimization process, which can be decoupled into two independent steps, leads to an improved performance of the device, with increased frequency bandwidth and better capture width ratio. The effects of water depth, mooring stiffness, and the dimensions of the WEC on the capture width ratio are also studied, and parameter values are identified which correspond to optimal performance of the device.
Article
A novel concept catamaran equipped with a suspended cabin, named Wave Harmonizer Type 4 (WHzer-4), is proposed and evaluated. The mass-spring-mass system is constructed by mounting four sets of suspensions in-between the cabin and the twin-hull. Two sets of dual motor/generators (M/Gs) are attached on the center beam of the cabin's deck fore and aft. Each shaft-end of the dual M/Gs is connected to the twin-hull through a rack-pinion gear unit. In this way the vertical relative motion between the cabin and the twin-hull can be transferred into the rotational motion of the M/Gs, and vice versa. A semi-active motion control system, which contains a proportional-integral (PI) controller, is designed and applied to each of the dual M/Gs for the aim of absorbing wave energy under the condition of suppressing the local vertical velocity of the cabin as much as possible. A 1/5 scale model ship with a length of 1.6 m is built, and a forced-oscillation bench test is implemented to validate the performance of the control system. Then, a series of towing tank tests is carried out in regular head waves. The heave and pitch responses of the cabin, those of the twin-hull and the corresponding wave energy capture width ratio (CWR) at five control scenarios and two reference scenarios are investigated. Discussion on the results of the tank test shows that the motion reduction of the cabin and the wave energy harvesting can be achieved simultaneously at a few wave conditions. However, at other conditions, although noticeable amount of wave energy is harvested, motion reduction of the heave and pitch of the cabin could not be obtained at the same time. It is suggested that varying the gain settings of the PI controllers according to the location of the controllers may improve the effectiveness of the proposed control system.
Article
This study presents the results of the Fuzzy Logic based control application for a heaving wave energyconverter operating in realistic sea-state conditions. It has been shown in literature that the powercapture performance of a heaving wave energy converter depends on meeting the resonance conditionwith the incident wave frequency. In regular sea wave conditions, the task of setting the control pa-rameters is a well-known easy task where the wave frequency is known. However, in irregular seaconditions, the wave frequency needed for control settings is not clearly defined. One of the approachesproposed in literature is to use of the dominant wave frequency that can be estimated by a model usingthe Discrete Fourier Transform approach. The presented model utilises the estimated wave frequency inFuzzy Logic controller for determination of Power Take-Off control settings. This approach combineswidely used fast tuning technique with a new slow tuning method. As a part of the study, the developedrealistic simulation model and proposed Fuzzy Logic based controller are used to combine the fast andslow tuning techniques to form a novel hybrid control technique. The simulation results for this newcontrol technique in realistic sea conditions are presented.
Conference Paper
Model predictive control (MPC) has been considered as one important feed-forward optimal control strategy for ocean wave energy converter (WEC) targeted on power maximization. The capability of MPC to handle system constraints (ex. stroke, velocity, actuator limitations), and the availability to provide optimal solution for linear system provide potential for the implementation of such algorithm in the WEC control. However, currently, only active MPC control has been introduced for single and two-body WECs. Such control strategy may introduce negative power during the optimization process, since the power take-off (PTO) damping has no constraint. In this paper, we proposed a hybrid MPC strategy in limiting both the PTO damping force and PTO damping to avoid negative power generation during cost function minimization (negative power minimization) for the two-body WEC. The problem is formulated into a quadratic programming (QP) problem targeted at power maximization. However, the standard QP problem formulation cannot be directly applied to the semi-active control problem due to the PTO damping constraints. Therefore, the problem is reformulated as a Mixed-integer Quadratic Programming (MIQP) problem, which contains logical switch to select constraint matrices based on the sign of the relative velocity between the buoy and submerged body. The optimal solution is compared with those of the active MPC control strategy and the passive model with the same irregular wave input.
Article
Experimental investigation on the power performance of a bottom hinged oscillating wave surge converters (OWSC) with different power take-off (PTO) damping strategies (provided by a generic PTO simulation platform) are conducted in regular and irregular waves. The hydrodynamic performance of the OWSC under different damping modes, in regular waves and irregular waves, is observed. For regular waves, the effects of the main influential parameters (including the incident wave height, wave frequency, phase difference between the buoy velocity and wave elevation) on the output power were quantitatively studied. Six damping coefficients of the linear PTO damping is examined under constant incident wave height, and increasing wave frequencies and an output power curve along wave frequency are presented for each input gain of the PTO simulation platform in both linear damping mode and nonlinear damping mode. Additionally, the best coefficient or input gain is obtained for both linear or nonlinear PTO damping mode in different wave conditions. The phase difference between the buoy velocity and wave elevation of the OWSC model in irregular waves has the same trend as that in regular waves. The output electricity in the JONSWAP spectrum is found to be (approximately 300%) higher than that in a user-defined spectrum for the same wave parameters. However, nonlinear PTO strategies have no distinct advantage in the amount of electricity output but have better stability and broader damping range.