1066-033X/14©2014IEEE
30 IEEE CONTROL SYSTEMS MAGAZINE » OCTOBER 2014
Digital Object Identifier 10.1109/MCS.2014.2333253
ith the recent sharp increases in the price of oil, issues of security of
supply, and pressure to honor greenhouse gas emission limits (e.g.,
the Kyoto protocol), much attention has turned to renewable energy
sources to fulfill future increasing energy needs. Wind energy, now
a mature technology, has had considerable proliferation, with other
sources, such as biomass, solar, and tidal, enjoying somewhat less deployment.
Waves provide previously untapped energy potential, and wave energy has been
shown to have some favorable variability properties (a perennial issue with many
renewables, especially wind), especially when combined with wind energy [1].
Date of publication: 16 September 2014
ThE dEvELOpMENT
Of CONTROL SYSTEM
TEChNOLOGY TO OpTIMIZE
ThEIR OpERATION
JOHN V. RINGWOOD,
GIORGIO BACELLI, and
FRANCESCO FUSCO
Energy-Maximizing
Control of Wave-Energy
Converters
W
OCTOBER 2014 « IEEE CONTROL SYSTEMS MAGAZINE 31
The main reason for the lack of proliferation of wave en-
ergy is that harnessing the irregular reciprocating motion
of the sea is not as straightforward as, for example, extract-
ing energy from the wind. Wind-energy turbine design
has mostly converged on a generic device form—the three-
bladed horizontal axis turbine—and turbine technology
and its associated control systems are well developed.
It is interesting that as solar energy is subsequently con-
verted into wind and then waves, the power density
increases. For example, at a latitude of 15
° N (northeast
trades), the solar insolation is 0.17 kW/m
2
. However, the
average wind generated by this solar radiation is about 20
kn (10 m/s), giving a power intensity of 0.58 kW/m
2
that, in
turn, has the capability to generate waves with a power
intensity of 8.42 kW/m
2
[2]. This progressive increase in
energy intensity can be attributed to the time integration of
the primary driving resource. In particular, a significant
amount (intensity and duration) of surface heating must
occur before wind is generated, while consistent wind is
required to generate waves. In fully developed seas, wind is
assumed to have been in steady state for a sufficient dura-
tion to generate the maximum wave amplitude attributable
to a particular wind velocity. The time integration phenom-
enon also results in a slowing of the dynamical response to
the stimulus. For example, wind velocity slowly diminishes
after the solar heating stimulus is removed, while the same
is true for wave motion with respect to the wind stimulus.
The distribution of wave energy worldwide is depicted in
Figure 1. An interesting characteristic of the wave-energy dis-
tribution is that some countries with a relatively high depen-
dence on imported fossil fuels for electricity production (for
example, Ireland was at 88% in 2008) have access to significant
wave-energy resources (70 kW/m of wave crest). As a case in
point, Ireland has the potential to capture 14 TWh of wave
energy per year, which is more than half of its annual energy
consumption of about 26 TWh. However, a complicating
factor is that wave-energy resources are frequently located a
significant distance from consumption centers, which is also
an issue for other renewable resources [3].
The current poor state of wave-energy technology devel-
opment is highlighted by the availability of just a few com-
mercially available wave-energy converters (WECs), includ-
ing the Wave Dragon [5], Pelamis [6], Oyster [7], and
Wavestar [8]. The stark contrast in the operational principles
of these four devices, as well as the diversity in appearance
and operation of the 147 prototypes listed in [9], provides
further evidence of the relative immaturity of wave-energy
technology. A useful overview of wave-energy devices and
technology classification is provided in [10]; see also
“Diverse Operating Principles of Wave-Energy Converters.”
In addition to the relative lack of progress in basic WEC
design, there is, understandably, a corresponding “fertile
field” in the development of control system technology to op-
timize the operation of wave-energy devices. This article will
attempt to show that the availability of such control technolo-
gy is vitally important if WECs are to be serious contenders in
the renewable energy arena. Ultimately, energy conversion
must be performed as economically as possible to minimize
the delivered energy cost, while also maintaining the struc-
tural integrity of the device, minimizing wear on WEC com-
ponents, and operating across a wide range of sea conditions.
Dynamic analysis and control system technology can
impact many aspects of WEC design and operation, including
device sizing and configuration, maximizing energy extrac-
tion from waves, and optimizing energy conversion in the
power take-off (PTO) system. Ultimately, commissioned
wave-energy devices or “farms” must provide energy at prices
competitive with other renewable sources. In the short term, a
number of state agencies, including in Portugal and Ireland,
have provided guaranteed feed-in tariffs to stimulate the
development and proliferation of wave-energy devices, at
€0.23/kWh and €0.22/kWh, respectively. As a benchmark for
comparison, the cost of domestic electricity in Ireland is cur-
rently €0.17/kWh. Some recent analysis suggests that current
costs for wave energy are in the region of €1/kWh [11].
60
40
20
10
40
70
40
50
60
70
100
40
40
40
30
20
20
20
20
20
20
20
15
20
30
30
30
10
20
20
50
70
30
30
30
Figure 1 An outline global wave map [4]. In general, the latitudes
40–60°, north and south, contain high energy waves. However,
proximity to population centers is a major determinant in the utility of
wave energy.
There are many new promising areas where control can make further
contributions in wave-energy applications, including cooperative
control of arrays of wave-energy devices.
32 IEEE CONTROL SYSTEMS MAGAZINE » OCTOBER 2014
As a measure of the challenge, since energy density in-
creases by a factor of almost 15 in the conversion from wind
to wave, wave devices might be expected to be 15 times
smaller than their wind counterparts, for a comparable
power output. However, a typical conventional 850-kW
horizontal axis wind turbine, such as the Vestas V52–850
kW, has a tower height of 60 m and a rotor diameter of 52 m,
whereas the Pelamis WEC rated at 750 kW has a length of
150 m and a diameter of 3.5 m. This rough comparison sug-
gests that considerable improvements to the mechanical
design of WECs could still be made. However, since raw
renewable resources (such as wind, wave, and tidal) are
free, the predominant performance metric [12] for wave
energy is the cost of energy delivered to the grid, rather
than a pure efficiency measure.
The control community has a significant role to play in
making wave-energy extraction economical. While much
work remains to be done on optimizing the basic geometry
of WECs and the development of efficient PTO systems, it is
already clear that appropriate control technology has the ca-
pability to double the energy taken from WECs [13]. How-
ever, the control problem does not fit neatly into a traditional
Diverse Operating Principles of Wave-Energy Converters
D
espite the fact that the earliest wave-energy devices were
suggested in the 19th century, the development of wave-
energy technology has been slow, and little convergence on an
optimum shape, or even operating principle, has been achieved.
Figures S1–S3 show a variety of devices, each of which essen-
tially harness wave energy through a different mechanism.
However, apart from the device shown in FigureS4, each of the
devices harnesses ocean energy through an oscillating motion,
and therefore relate directly to the control issues described in
this article. Though the device of FigureS4 has natural rectifica-
tion of wave motion, some interesting control problems are still
associated with such devices [S1].
This sidebar is not intended to be a comprehensive over-
view of the diversity or range of wave-energy devices, nor is
the intention to provide a set of classes under which all WECs
can be placed. Rather, the intention is to show some of the
diversity in operating principles and the lack of convergence
in the development of WEC prototypes. For a more compre-
hensive treatment, the interested reader is referred to [S2]
and [S3].
OSCILLATING WATER COLUMNS
The device shown in Figure S1 is an oscillating water column
(OWC), where vertical (heave) motion in the column of water
drives air through a turbine. Often, Wells or impulse turbines
are used, which provide unidirectional torque to the turbine
despite the bidirectional air flow. Both land-based and floating
OWC devices have been proposed. Land-based OWCs can be
sensitive to tidal height variations.
pOINT ABSORBERS
Point absorbers usually harness the heaving motion of the
device for conversion to useful energy. Point absorbers have
the advantage of being insensitive to wave direction and can
be bottom referenced, where motion relative to the seabed is
Generator
Turbine
Chamber
Sea Bed
Incoming Wave
Figure S1 A land-based oscillating water column device.
Power
Take-Off
Torus
Tank
Mooring
Power Control
and Grid
P
ower
T
ake-
O
f
f
Toru
s
Tank
M
oor
i
n
g
P
ower Control
and Grid
Figure S2 The Wavebob device concept is an example of a
heaving buoy. Energy is harnessed from the relative motion of
the torus and tank.
OCTOBER 2014 « IEEE CONTROL SYSTEMS MAGAZINE 33
form such as setpoint tracking, although more traditional
regulation loops are required for some special cases such as
potable water production [14]. In addition, servo loops are
often required in hierarchical WEC control (see the section
“Wave-Energy Control Fundamentals”).
This article articulates the control problem associated
with WECs, examines the structure of a typical WEC
model, and provides some examples of how control and
associated technologies can be applied to WECs and WEC
arrays. An overview of the forecasting problem associated
with noncausal control strategies is also given, along with
some sample forecasting results, while a comprehensive
overview of the general research literature relating to the
control of wave-energy devices is contained in the section
“Overview of the WEC Control Literature.”
QUANTIfYING ThE WAvE RESOURCE
The two measurable properties of waves are height and
period. Researchers and mariners usually characterize wave
heights by the average of the highest one-third of the observed
wave heights. This statistically averaged measure is termed
the significant wave height and usually denoted as
H
/
13
or
H
s
.
captured or can be used to also harness the relative motion
between two device components. Figure S2 shows the Wave-
bob device concept, where the bottom section remains rela-
tively motionless, while the top part (the torus) is sensitive to
incident wave motion. The Wavebob device, as shown in Fig-
ureS2 employs a hydraulic PTO [S4]. An example of a bottom-
referenced point absorber is the Seabased device [S5], which
employs a direct electrical PTO.
CONNECTEd STRUCTURES
A variety of devices fall into the class of connected structures,
including the commercial Pelamis device [S6] and the McCabe
wave pump (MWP), shown in Figure S3. Useful power is captured
from the relative motion of the device sections. For the Pelamis
device, both yaw and pitch motion between sections are accom-
modated, while the MWP device permits only relative pitch motion.
OvERTOppING dEvICES
Overtopping devices use a ramp in the incident wave direction
to create a forward motion of breaking waves, somewhat like the
action of waves on a beach. However, unlike a beach, the forward-
progressing waves are captured in a reservoir, which has a mean
water height above the mean sea level, as shown in FigureS4.
This potential head is then harnessed in a manner similar to a
conventional hydroelectric system. Both land-based and floating
overtopping devices have been proposed, although land-based
schemes can be sensitive to tidal height variations. Ballast control
is an important feature of floating overtopping devices [S1].
REfERENCES
[S1] J. Tedd, J. Kofoed, M. Jasinski, A. Morris, E. Friis-Madsen, R.
Wisniewski, and J. Bendtsen, “Advanced control techniques for WEC
wave dragon,” in Proc. 7th European Wave Tidal Energy Conf., Porto,
Portugal, 2007.
[S2] B. Drew, A. Plummer, and M. Sahinaya, “A review of wave en-
ergy converter technology,” in Proc. IMechE Part A: Power and Energy,
2009, vol. 223, pp. 887–902.
[S3] K. Koca, A. Kortenhaus, H. Oumeraci, B. Zanuttigh, E. Angelelli,
M. Cantu, R. Suffredini, and G. Franceschi, “Recent advances in the
development of wave energy converters,” in Proc. 9th European Wave
Tidal Energy Conf., Uppsala, Sweden, 2013.
[S4] K. Schlemmer, F. Fuchshumer, N. Bohmer, R. Costello, and C.
Villegas, “Design and control of a hydraulic power take-off for an axi-
symmetric heaving point absorber,” in Proc. 9th European Wave Tidal
Energy Conf., 2011.
[S5] M. Leijon, O. Danielsson, M. Eriksson, K. Thorburn, H. Bernhoff, J.
Isberg, J. Sundberg, I. Ivanova, E. Sj
östedt, O. Ågren, K. E. Karlsson,
and A. Wolfbrandt, “An electrical approach to wave energy conversion,”
Renewable Energy, vol. 31, no. 9, pp. 1309–1319, 2006.
[S6] R. Yemm, D. Pizer, C. Retzler, and R. Henderson, “Pelamis: Expe-
rience from concept to connection,” Philos. Trans. Roy. Soc. A: Math.
Phys. Eng. Sci., vol. 370, no. 1959, pp. 365–380, 2012.
Reservoir
Overtopping
Turbine Outlet
Figure S4 Overtopping devices provide natural rectification of
the hydraulic power flow and employ a low-head power take-off
not dissimilar to conventional hydroelectric systems.
Figure S3 The McCabe wave pump harnesses relative pitch
motion between sections. An underwater horizontal damper
plate is attached to the central section to reduce heave motion.
34 IEEE CONTROL SYSTEMS MAGAZINE » OCTOBER 2014
In addition, real ocean waves do not generally occur at a single
frequency. Rather, a distributed amplitude spectrum is used
to model ocean waves, with random phases. Energy spectra
are widely used to represent sea states [15]–[18]. The wave spec-
tral density (or wave spectrum) has the form
() ,ST AT e
T
BT3
4
=
-
(1)
with the coefficients
A
and
B
, for example, given for the
Pierson-Moskowitz model by [16]
.
()
,A
g
81010
2
3
4
2
#
r
=
-
(2)
.,
B
V
g
074
2
4
r
=
cm
(3)
where
V
is the wind velocity measured
19.5 m above the still-water level (SWL),
g
is the acceleration due to gravity, and
T
is
the wave period in seconds. Some typical
wave spectra generated from this model
are shown in Figure 2. Note that the avail-
able wave energy increases (approximately)
exponentially with wave period
.T
Not all waves are well represented by
the spectral models of the type shown in
(1). In some cases, where swell and local
wind conditions are relatively uncorrelated
(which can often be the case, for example,
on the west coast of Ireland [19]), “split
spectra,” consisting of spectra containing
two distinct peaks, can occur. The variety
of spectral shapes, illustrated in Figure 3,
presents a significant challenge to both the
WEC designer and control engineer.
All of the aforementioned wave spec-
tral models are for fully developed waves; in
other words, the fetch (the distance over
which the waves develop) and the duration for which the
wind blows are sufficient for the waves to achieve their
maximum energy for the given wind speed. In addition,
linear wave theory is assumed, meaning that waves are
well represented by a sinusoidal form, which relies on
assuming that there are no energy losses due to friction,
turbulence, or other factors and that the wave height
H
is
much smaller than the wavelength
m
.
However, not only is the “wind-wave” component in
Figure 3 for set
G
3
at odds with the spectrum shown in
Figure 2, there are three distinct low-frequency compo-
nents in set
G
1
. Directional wave analysis [20] can be used
0 1234
0
0.5
1
~ (rad/s) ~ (rad/s) ~ (rad/s)
(a) (b) (c)
S(~) (m
2
s/rad)
S(~) (m
2
s/rad)
Set G
1
H
s
. 2.31 m
Wide Banded
0 1234
0
0.05
01234
0
0.05
Set G
2
H
s
. 0.31 m
Narrow Banded
Set G
3
H
s
. 0.34 m
Predominant Wind Waves
S(~) (m
2
s/rad)
Figure 3 Real wave spectra recorded at Galway Bay in Ireland. In general, low-frequency waves have the highest power. Narrow-banded
seas make wave forecasting and wave-energy converter control more straightforward, allowing a focus on a predominant single frequency.
0 2 4 6 8 10 12 14 16 18 20
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
S
T
(T) (m
2
/s)
T (s)
V = 10 kn
V = 15 kn
V = 20 kn
V = 25 kn
V = 30 kn
S
T
(T
Max
)
Figure 2 A typical Pierson-Moskowitz wave spectra, from (1), for different steady-state
wind velocities. Both the wave amplitude and period increase with an increase in the
driving wind speed.
![Figure 1 An outline global wave map [4]. in general, the latitudes 40–60°, north and south, contain high energy waves. However, proximity to population centers is a major determinant in the utility of wave energy.](/figures/figure-1-an-outline-global-wave-map-4-in-general-the-35dvv8lw.webp)
