1
Ocean Wave Power Data Generation for Grid
Integration Studies
Shaun McArthur, Student Member, IEEE, Ted K.A. Brekken, Member, IEEE
Abstract—Ocean wave power is a promising renewable energy source that offers several attractive qualities, including
high power density, low variability, and excellent forecastability.
Within the next few years, several utility-scale wave energy
converters are planned for grid connection (e.g., Pelamis Power in
Portugal and Ocean Power Technologies in Oregon, USA), with
plans for more utility-scale development to follow soon after.
Presently, there is little research on the impact of large wave
parks on utility operation. This paper presents a methodology
for generating large-scale wave park power time-series data that
can be used for utility integration studies. In addition, this
paper presents a broad, brief introduction to ocean wave energy
fundamentals, history, and state of the art.
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Index Terms—marine technology, power distribution, power
systems, power generation, power system stability, power generation dispatch
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I. M OTIVATION AND BACKGROUND
T
HIS paper has two objectives: to provide a short, general
summary of ocean wave energy, and to present a methodology for generating large-scale ocean wave power time-series
data for use in utility integration studies [1].
Ocean wave energy has promise to be a significant contributor to the renewable energy portfolios of many populous areas
around the world. However, as the industry is still in the early
stages, there is limited data available on synthesized or actual
wave energy converter performance. As the first large-scale
wave energy parks come on-line within the next five to ten
years, utilities will require projected power data from these
parks to conduct grid integration studies. For wind integration
studies, there are many resources available for predicting wind
farm output and generating power time-series data. This paper
presents a methodology for generating high-resolution wave
park output power based on wave climate measurements. The
presented approach differs from other published approaches
( [2]–[4] ) in the following ways:
Manuscript received March 8, 2010.
This material is based upon work supported by the Department of Energy
under Award Number DE-FG36-08GO18179.
Disclaimer: this report was prepared as an account of work sponsored
by an agency of the United States Government. Neither the United States
Government nor any agency thereof, nor any of their employees, makes any
warranty, expressed or implied, or assumes any legal liability or responsibility
for the accuracy, completeness, or usefulness of any information, apparatus,
product, or process disclosed, or represents that is use would not infringe
privately owned rights. Reference herein to any specific commercial product,
process, or service by trade name, trademark, manufacturer, or otherwise
does not necessarily constitute or imply its endorsement, recommendation,
or favoring by the United States Government or any agency thereof. Their
views and opinions of the authors expressed herein do not necessarily state
or reflect those of the United States Government or any agency thereof.
T.K.A. Brekken, and S. McArthur are with the Department of Electrical
Engineering and Computer Science, Oregon State University, Corvallis, OR,
97331 USA e-mail: brekken@eecs.oregonstate.edu
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•
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Calculates water surface elevation at each point in a wave
park array,
Operates at a much higher time-scale resolution (e.g., 0.4
seconds instead of one hour),
Accounts for number of devices and their geometric park
layout, including the aggregating effects of their spatial
orientation,
Allows for use of hydrodynamic modeling for generic
wave energy converter models,
Can be applied to systems with or without energy storage
(e.g., hydraulics vs. direct drive),
Can be used for extreme event analysis.
II. W HY WAVE E NERGY ?
Ocean wave energy has great potential to be a significant
contributor of renewable power for many regions in the world.
For the West coast of the US alone, the total wave energy
resource is estimated at 440 TWh/yr, which is more than the
typical total US annual hydroelectric production (270 TWh in
2003) [5].
A. Wave Energy Characteristics
Ocean wave energy refers to the kinetic and potential energy
in the heaving motion of ocean waves.
Wave energy is essentially concentrated solar energy (as is
wind energy). The heating of the earth’s surface by the sun
(with other complex processes) drives the wind, which in turn
blows across the surface of the ocean to create waves. At each
stage of conversion, the power density increases. Off the coast
Oregon, the yearly average wave power is approximately 30
kW per meter of crestlength (i.e., unit length transverse to the
direction of wave propagation and parallel to the shore.) This
compares very favorably with power densities of solar and
wind, which typically range in the several hundreds of Watts
per square meter.
For a monochromatic wave, the wave power per meter
crestlength can be expressed as
Pwave,mcl =
ρg 2 H 2 T
32π
[P/m]
(1)
where ρ is the density of water (approximately 1025 kg/m3 ),
g is the acceleration of gravity, H is the wave height (trough
to crest) and T is the wave period (typically on the order
of 8 seconds). The salient features of (1) are the squared
dependence on wave height H and the linear dependence
on the wave period T . However, there is typically a positive
correlation between H and T in a real ocean environment,
which results in a pseudo-cubic dependence of the power
2
Fig. 2. US yearly average wave power resource in kW per meter crest length
on the wave height. This is similar to wind power, which is
dependent on the cube of the wind speed.
In comparison to wind and solar, wave energy is characterized by high availability, low hourly variation, and high power
density [2], [3], [6]. In addition, wave energy has excellent
forecastability. A typical large ocean wave propogates at
around 12 m/s with very little attenuation across the ocean.
If the waves can be detected several hundred kilometers off
shore, then there can be 10 hours or more of accurate forecast
horizon. In fact, detailed analysis has shown good forecast
accuracy up to 48 hours in advance [7].
Globally, the wave energy resource is stronger on the west
coasts of large landmasses and increases in strength toward
the poles, as shown in Fig. 1. This phenomenon is due
to the prevailing west to east global winds known as the
“westerlies” found in the Northern and Southern hemispheres
between 30 and 60 degrees latitude. Correspondingly, the west
coast of the United States, the west coast of Australia, and
the coastal regions of Europe have seen the greatest wave
energy industrial activity to date. Fig. 2 shows the wave power
potential in the United States in kW/mcl.
There is a strong seasonal variability as well. The wave
power resource tends to be much larger in the winter than in
the summer. In Oregon, the yearly average is approximately
30 kW/mcl (where mcl is “meter of crest length”). In the
winter, the waves are larger and the average is approximately
50 kW/mcl. The summer average is about 10 kW/mcl. This
is a good match for coastal loads, where the winter heating
requirements tend to be larger than the summer cooling
requirements.
B. Wave Energy History
Formal interest in wave energy actually extends back as far
as 1799, when the first documented patent related to wave
energy was filed by the Parisian Monsieur Girard for a wave
powered system for driving pumps and saws. In the 1960s,
a Japanese naval officer named Yoshio Masuda developed a
navigation buoy with an integrated oscillating water column
for powering the system [9]. This was followed by research at
the US Naval Academy by Michael McCormick in the 1970s
that yielded some of the earliest journal papers and texts on
wave energy.
There are have been two boom periods for academic research on wave energy. The first was in the late 1970s in
Europe. The second is today with active research programs
at several universities throughout the world. The European
researchers in the late 1970s brought a strong hydrodynamic
focus to establish much of the theoretical foundational understanding of wave energy. These researchers include Johannes
Falnes and Kjell Budal of the Norwegian University of Science
and Technology (NTNU), David Evans of the University of
Bristol, and Stephen Salter of the University of Edinburgh. The
research activity today has continued to develop hydrodynamic
theory using modern computing tools, and has added much
foundational knowledge in generator design and control [10]–
[19].
C. Wave Energy Technology
Some of the attractive qualities of wave energy is its
density and regularity. There are many proposed methods for
extracting this energy, with no single dominant technological paradigm yet established. These different technological
approaches can be placed in four board categories: point
absorber, overtopping, attenuator, and oscillating water column
(OWC). From [20]:
1) Oscillating Water Column (OWC): The OWC operates
on the principle of air compression and decompression. An inverted chamber is placed in the water such that waves cause the
“floor” of the chamber to rise and fall, therefore compressing
and decompressing the air in the chamber. A turbine is placed
at a small opening in the chamber to capture energy from
the air as it rushes in an out. Examples: Oceanlinx, Wavegen,
Ocean Energy.
2) Attenuator: Attenuators are usually devices with rectangular aspect ratios that can be oriented perpendicular or
colinear with the wave front. For example, an energy absorbing
structure on a jetty would be an attenuator. One of the
largest commercial devices, the Pelamis, is an example of an
attenuator design that is oriented perpendicular to the wave,
spanning more than a wavelength. Examples: Pelamis Wave
Power, Wavestar, Aquamarine Power.
3) Overtopping: Overtopping devices are effectively lowhead hydro systems. Large arms, either on the shore or on a
floating structure, channel waves toward a central collection
basin. As the waves are focused on the basin, the volume of
water rises up and spills over a retaining wall to fill the basin.
This creates a small elevation differential with surrounding
water level that can be exploited via a standard low-head hydro
turbine. Examples: Wave Dragon, Wave Plane, WAVEnergy.
4) Point Absorber: Point absorbers, often simply called a
“buoy,” are single, relatively small devices (compared individually to the other WEC types). They are typically (though
not necessarily) cylindrical in shape and constrained to one
major degree of motion, usually up-and-down (i.e., “heave”).
They are generally significantly smaller in diameter than a
wavelength. Examples: Columbia Power Technologies, Ocean
Power Technologies, Wavebob, Archimedes Wave Swing, Fred
Olsen, Finavera.
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Fig. 1.
Global yearly average wave power resource in kW per meter crest length (image courtesy of OCEANOR and ECMWF [8])
D. Wave Energy Economics
The Electric Power Research Institute (EPRI) has estimated
that the first utility-scale wave power plants (up to 100 MW
total installed capacity) will have a cost of energy (COE)
of approximately 10 cents per kWh. This is two to three
times as much as a modern hydroelectric, coal, or wind plant.
However, with large-scale development, the COE for wave
energy is predicted to become quite competitive, approaching
3 to 4 cents per kWh as the installed world-wide capacity
exceeds 10,000 MW [5]. This low COE is a function of
the high power density of wave energy, but the COE will
also be highly dependent on the reliability and maintainability
of mature wave energy conversion technology. The issues
of reliability, maintainability, and survivability will likely be
of greater significance for ocean wave energy compared to
wind and solar due the energetic and corrosive nature of the
resource, and the added challenges in field maintenance of the
devices.
III. M ETHODOLOGY FOR WAVE P OWER DATA
G ENERATION
This paper also presents a methodology for generating
high-resolution wave power time-series data for use in grid
integration studies.
Ocean wave data collected from measurement buoys off
the US West Coast are used to compute representative ocean
wave spectra, which are then used to generate time-series
wave surface displacement data for individual wave energy
converters (WECs) within the wave park.
The time-series wave surface displacement data are then
appropriately scaled to generate time-series power data for
individual WECs. Once individual WEC power outputs for
the entire park have been calculated, all power outputs are
summed and then averaged to produce the time-series average
power output for the entire park for a given time interval.
A. Data
The methodology uses historical wave data obtained
from the National Oceanic and Atmospheric Administration
(NOAA) National Data Buoy Center (NDBC) archives. NDBC
maintains a network of approximately 90 data buoys located
off the coastal US that measure and record various wave
parameters, such as significant wave height (SWH), dominant
wave period (DP) and incident wave direction (IWD) [21].
The methodology is able to model wave park power output
over the course of an entire year on an hour-by-hour basis,
producing fast sample-time (e.g., 0.4 second) data for wave
surface elevation within the hour. Ideal input data must have
complete annual records, and measurements must be obtained
from buoys located in deep water (i.e., in water depth greater
than half an ocean wavelength) in order to satisfy spectrum
generation requirements.
4
Fig. 4. Arbitrary 3x3 WEC coordinate array, with spatial separation of 100
meters (origin not shown).
Fig. 3. NDBC buoys located off the Oregon coast. Shown at top right in
NDBC 46041, which was one of the sites selected for study. Image adapted
from NDBC [21].
Based on these criteria, 2008 data from the NDBC 46041
buoy located off the coast of Washington state, as well as
data from NDBC 46047 and 46229 data buoys located off the
California coast were selected.
C. Time Domain Data Generation
Adapting equations derived in [26], using linear wave theory
it can be shown that given a power spectrum S(ω), the
time series representation of wave surface displacement η is
essentially a Fourier series:
η(x, y, t) =
N
X
Ai cos(2πfi t − kx x − ky y − i )
(4)
i=1
B. Spectral Data Generation
Over long periods of time, ocean waves show high variation
in surface height, period, and incident direction. Typically,
these variations are averaged. However, averaging does not
sufficiently capture the dynamic behavior of a real ocean.
Statistical variation in a real ocean environment can be
better represented by a spectral density function S(ω), which
measures the distribution of series power over a given frequency range. Extraction of spectral information from wave
records is an evolving field; however several well-defined
ocean wave power spectra such as the Pierson-Moskowitz
(PM), Breitscheider, and JONSWAP spectra are commonly
encountered in the ocean engineering literature [22], [23].
The presented methodology uses the PM spectrum, which
is a generic power spectrum that can be used to describe
characteristics of wind-waves generated over a long fetch
length and period. The PM spectrum is defined as a function
of frequency by [22], [24]:
"
4 #
αg 2
ω0
S(ω) = 5 exp −β
(2)
f
f
where α = 8.1 · 10−3 is a dimensionless constant, g = 9.812
m/s2 is gravity, β = 0.74 is a dimensionless constant, and
ω0 = Ug19 is the natural frequency generated by wind speeds
at a height of 19.5 meters.
The power density spectrum has units of m2 /Hz. It can
also be shown [22], [25] that the significant wave height is
related to the power spectrum by:
p
H1/3 = 4 S(ω)
(3)
The PM spectrum requires that the wind-waves being
represented are located in deep water, i.e., in ocean depths
greater than half a mean wavelength (d ≥ λ2 ) [22]. For this
reason, data must be taken from ocean depths greater than or
approximately equal to 150 meters.
where Ai and fi represent PM spectrum wave surface amplitudes and components, kx and ky are components of the
wave vector, x and y are scalar positions, and i are randomly
generated phases used to represent spatial variation.
As a first order approximation, the power output of a
single wave energy converter over a specified time interval
can be calculated if one assumes that the WEC is a perfect
wave follower (i.e., the position of the WEC is equal to the
wave surface displacement η) and the WEC generator force is
proportional to velocity. It follows that:
P (x, y, t) = k · (η̇(x, y, t))
2
(5)
where k is a coefficient with dimensions of kg/sec used to
scale buoy power output, and η̇ represents the wave surface
(and hence WEC) velocity.
Using (4) and (5) it is possible to determine the wave surface
displacement and power output for a single point within a
coordinate grid at a specific time. However, we are interested
in generating results for multiple points in the coordinate grid
throughout time.
Consider an arbitrary wave park with nine WECs arranged
in 3 rows and 3 columns, spaced 100 meters apart.
The x and y coordinates of individual WECs within the
grid can be collected into separate 3 by 3 matrices as shown
below:
100 200 300 X = 100 200 300 100 200 300 100
Y = 200
300
100
200
300
100
200
300
Expanding on this, given X and Y input matrices, it is possible to generate results for a wave park of arbitrary dimensions
m by n provided that (4) is recast in two-dimensional matrix
5
wave surf. disp. [m]
20
10
0
−10
−20
0
10
20
10
20
30
time [s]
40
50
60
40
50
60
5
x 10
2.5
Power [W]
2
1.5
1
0.5
0
0
Fig. 5. Layers of the three dimensional η matrix. Each layer represents a
collection of wave surface displacement values for a specific time p.
format:
η(t) =
N
X
Ai cos(2πfi t − kx X − ky Y − i )
(6)
i=1
where X is a m by n matrix, Y is a m by n matrix, and η is now
a m by n matrix representing the wave surface displacements
for individual WECs.
If (6) is then evaluated over a desired time interval t1 to tp ,
η becomes a three dimensional m by n by p matrix, where
successive p layers represent η at specific points in time.
The corresponding power output equation recast in three
dimensional matrix form is given by:
P = k η̇ 2
η(tk ) − η(tk−1 )
tk − tk−1
Fig. 6. The upper plot shows wave surface displacement vs. time, while
the lower plot illustrates power output (in 105 W) vs. time. Power output is
saturated at 250 kW.
46229 buoys. The original 0.4 second data was FIR filtered
(i.e., running averaged) over 10 minutes, then decimated to
produce the 10 minute resolution data. This was done as
utility-scale power data is typically at a 10 minute sample
time, but the data could be kept at the 0.4 second sample time
resolution if so desired. Each simulated wave park is located
at approximately the same site as the buoy data source. The
final results of the simulation are detailed in Fig. 7.
The results also show the expected seasonal variation of
wave power, with stronger generation in the winter months
(i.e., the left and right side of the time axis), and lower
generation in the summer (i.e., the middle of the time axis).
(7)
Due to the presence of η̇, calculation of the power output
matrix defined by (7) requires at minimum two m by n layers
of η. Provided tk and tk−1 exist, η̇ can be defined by:
η̇(tk ) =
30
Time [s]
(8)
IV. R ESULTS
The complete numerical simulation is programmed in MATLAB. Many aspects of the simulation are user-configurable.
For example, the user is prompted to enter wave park dimensions and WEC spatial separation. The user can also configure
the resolution of the generated power data.
The simulation was run for three identical wave energy
parks, each comprised of 400 WECs arranged in 80 by 5 arrays
at spatial separation of 100 meters. The WECs saturate peak
power output at 250 kW during Sea State 6 (late January to
mid-February) ocean conditions, in order to generate an ideal
peak power output of 100 MW for each park.
Fig. 6 is the sample output of a single WEC from the
simulated NDBC 46041 farm over a 60 second time interval,
generated at 0.4 second resolution.
Simulated wave park results were generated for the entire
2008 calendar year starting Jan. 1 at 00:00 at 10 minute
resolution using data extracted from NDBC 46041, 46047, and
V. C ONCLUSION
This paper presents a methodology for generating highresolution wave surface elevation time-series data for each
location in a wave park from spectral measurements from
ocean measurement buoys. This wave surface elevation data
can be used to calculate the power time-series of each wave
energy converter in the park. The power time-series data
can then be used in grid integration studies to investigate
the impact of large-scale ocean wave energy development on
utility operation and planning.
This paper introduces a simple relation between wave surface elevation and power, but more complex implementations
(e.g., Morison) are easily implemented, and is a good topic for
future work. The presented methodology does not consider
shadowing effects between wave energy converters. This is
also a good topic for future research.
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Fig. 7. Simulated wave park average wave park power output (in 107 W)
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B IOGRAPHIES
Shaun McArthur (SM’08) Shaun McArthur is a graduate student currently
pursuing a Ph.D. in Energy Systems at Oregon State University. He received
his B.S. in Applied Physics from the University of Utah in 2006. His research
interests include control, power electronics, smart grids, and renewable energy
device simulation and optimization.
Ted K. A. Brekken (M’06) Ted K. A. Brekken is
an Assistant Professor in Energy Systems at Oregon
State University. He received his B.S., M.S., and
Ph.D. from the University of Minnesota in 1999,
2002, and 2005 respectively. He studied electric
vehicle motor design at Postech in Pohang, South
Korea in 1999. He studied wind turbine control at the
Norwegian University of Science and Technology
(NTNU) in Trondheim, Norway in 2004-2005 on a
Fulbright scholarship. His research interests include
control, power electronics and electric drives; specifically digital control techniques applied to renewable energy systems. He is
co-director of the Wallace Energy Systems and Renewables Facility (WESRF),
and a recipient of the NSF CAREER award.