Energy and Power Engineering, 2013, 5, 70-91
http://dx.doi.org/10.4236/epe.2013.51009 Published Online January 2013 (http://www.scirp.org/journal/epe)
Copyright © 2013 Sci Res. EPE
Time Series-, Time-Frequency- and Spectral Analyses of
Sensor Measurements in an Offshore Wave Energy
Converter Based on Linear Generator Technology
Erland Strömstedt, Andrej Savin, Olle Svensson, Mats Leijon
The Swedish Centre for Renewable Electric Energy Conversion, Division for Electricity,
Department of Engineering Sciences, Uppsala University, Uppsala, Sweden
Email: erland.stromstedt@angstrom.uu.se
Received August 20, 2012; revised September 24, 2012; accepted October 10, 2012
ABSTRACT
Inside the second experimental wave energy converter (WEC) launched at the Lysekil research site on the Swedish west
coast in March 2009 a number of sensor systems were installed for measuring the mechanical performance of the WEC
and its mechanical subsystems. One of the measurement systems was a set-up of 7 laser triangulation sensors for meas-
uring relative displacement of the piston rod mechanical lead-through transmission in the direct drive. Two measure-
ment periods, separated by 2.5 month, are presented in this paper. One measurement is made two weeks after launch
and another 3 months after launch. Comparisons and correlations are made between different sensors measuring simul-
taneously. Noise levels are investigated. Filtering is discussed for further refinement of the laser triangulation sensor
signals in order to separate noise from actual physical displacement and vibration. Measurements are presented from the
relative displacement of the piston rod mechanical lead-through, from magnetic flux in the air gap, mechanical strain in
the WEC structure, translator position and piston rod axial displacement and active AC power. Investigation into the
measurements in the time domain with close-ups, in the frequency domain with Fast Fourier transform (FFT) and with
time-frequency analysis with short time Fourier transform (STFT) is carried out to map the spectral content in the
measurements. End stop impact is clearly visible in the time-frequency analysis. The FFT magnitude spectra are inves-
tigated for identifying the cogging bandwidth among other vibrations. Generator cogging, fluctuations in the damping
force and in the Lorenz forces in the stator are distinguished and varies depending on translator speed. Vibrations from
cogging seem to be present in the early measurement period while not so prominent in the late measurement period.
Vibration frequencies due to wear are recognized by comparing with the noise at generator standstill and the vibration
sources in the generator. It is concluded that a moving average is a sufficient filter in the time domain for further analy-
sis of the relative displacement of the piston rod mechanical lead-through transmission.
Keywords: Wave Power; Wave Energy Converter; Linear Generator; Sensor Measurements; Spectral Analysis;
Cogging; Filtering; Laser Triangulation Sensor; Draw-Wire Sensor; Force Transducer; Strain Gauges;
Search Coil; Power Generation
1. Introduction
For the past decade, the Swedish Centre for Renewable
Electric Energy Conversion at Uppsala University, Swe-
den, has been working on wave energy system, consist-
ing of a point absorber with a surface-floating buoy and
an encapsulated permanent magnet linear generator on
the seabed. The Uppsala project is one of many past and
present wave energy projects around the world, with very
different technical approaches. A few of the other pro-
jects and technologies are described in [1-5].
During operation an offshore WEC has to sustain mil-
lions of cyclical sequences of varying static, dynamic and
potentially very high mechanical loads at sea. For a com-
plete understanding of a wave energy converter device it
is important to know how the device operates in the wa-
ter, how the motion of the waves affects the electrical
and mechanical subsystems, how this motion can be
measured and how to interpret the information in the
measured data. Only a few full scale experimental studies
have been presented so far with sensor measurements
inside WECs in operation at sea, summarized in Lindroth
et al. [6]. The magnitude and character of the motion has
impact on engineering issues and optimization of control
parameters, as well as theoretical understanding of the
system in order to come up with durable designs for long
term sustainability.
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71
In this paper experimental data from different meas-
urement systems in the second WEC prototype at the
Lysekil Research Site (LRS) are studied and compared in
the time and frequency domain. A post-measurement
time -frequency analysis based on STFT and frequency
analysis based on FFT is carried out to map the spectral
content in the measurements inside the WEC during in-
tervals with two narrow sea states with 2.5 month separa-
tion.
The purpose of the work is to 1) present the spectral
content of the laser sensor measuring systems inside the
WEC, 2) to make comparisons in both the time and fre-
quency domain with output from other sensors to identify
typical vibrations, mainly cogging and end stop impact,
and 3) reflections on finding a suitable filter for refining
the laser sensor measurements in the time domai n.
In Section 2, the background of the Lysekil project
is presented and described along with the WEC in focus
for the study. Section 3 deals with the theoretical model
used for the spectral analysis and sources of vibration
along with assumptions made. The experimental set-up
of the sensor measuring systems and details of the meas-
urements are then presented in Section 4. Finally, in Sec-
tions 5 and 6 the measurement data and achieved results
are put forward and discussed.
2. Background
The experimental work presented in this paper was per-
formed at the Lysekil Research Site (LRS) off the Swed-
ish west coast. LRS is located about 10 km south-
southwest of the town of Lysekil, between a northern
(58˚11'850N 11˚22'460E) and a southern marker
(58˚11'630N 11˚22'460E); see Figure 1. The LRS was
established in 2004 for the purpose of studying full-scale
devices of the selected wave energy conversion system
under development at Uppsala University. The wave
climate is moderate with a typical average energy flux of
3.4 kW/m. From an evaluation point of view the LRS
serves the purpose with regard to wave height of an oth-
erwise scalable WEC system [7,8]. The site has a water
depth of about 25 m and a flat sandy bottom. It is con-
nected electrically to the small island of Gullholmen
through a 3 km long sea cable. More details about the
LRS can be found in [7].
Three different complete wave energy converter pro-
totypes, named L1, L2 and L3, an underwater substation
[9], an observation tower [10], a wave measurement
buoy [11] and around 8 biology buoys, for environmental
studies [12,13], were operating in the LRS at the time of
the experiment. The data in this paper comes from meas-
urements on L2 during the first wave power park ex-
periments in during the period from the 15th of May until
the 23rd of September. Figure 2(b) shows a photo of
Figure 1. The Lysekil research site during the experiments
in 2009.
Figure 2. (a) The buoy attached to L2 after launch; (b)
WEC L2 on cay before launch; (c) CAD assembly of L2 to
scale at 25 m depth.
WEC L2 before deployment and Figur e 2(a) of the buoy
at the LRS just after launch. Figure 2(c) shows a CAD
assembly image to scale of the WEC deployed at 25 me-
ters depth with the buoy at the surface. The force trans-
ducer measuring system is indicated.
The internal layout of the WEC is shown in Figure 3.
As a wave passes, the buoy is lifted, and this motion is
transferred to the generator. 37 rows of permanent Neo-
dymium Iron Boron (Nd2Fe14B) magnets with the pole
width of 50 mm are mounted on the translator and the
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Figure 3. Cross-sectional view of a CAD assembly of L2
with functional parts indicated.
relative motion between these and the stator induces
voltage in the stator windings. At a translator speed of
0.67 m/s the generator produces 10 kW at a line-to-line
voltage of 200 V when connected to a nominal load of 4
Ω and an air gap of approx. 2.5 mm. The efficiency of
the generator in this case is 86% [7]. Further generator
parameters are described in [14,15].
There are 8 tensile springs mounted between the bot-
tom of L2 and high up inside the translator framework.
The springs pull down the translator when the buoy is in
a wave trough. There are also end stops with compres-
sion springs to prevent the translator from slamming into
the capsule bottom and top plate. The free stroke length
is 1.79 m. It can then move another additional 0.243 m at
the top and 0.200 m at the bottom. While compressing
the end stop springs, making the full possible stroke
length 2.21 m.
The buoy line is guided by a funnel at the top of a
flooded superstructure. A piston rod transfers the me-
chanical force from the guided buoy line in to the gen-
erator through a seal housing in a mechanical lead-
through device; see Figu re 4. The seal housing is mounted
on a C-shaped rubber gasket at the centre opening in the
capsule top plate. The seal housing flange is clamped
around the gasket by two large hook nuts screwed on to
the outside of the seal housing inside the capsule; see
Figure 4. A dynamic sealing system inside the seal hous-
ing keeps the capsule watertight as the piston rod recip-
rocates with the translator without rotating.
A double hinged link between the piston rod and trans-
lator enables the lower rod end to move sideways. The
Figure 4. Piston Rod Laser Sensors (PRLS) 1 - 3 and Seal
Housing Laser Sensor (SHLS) 1 - 4 with rigid sensor set-up
rig attached to the capsule top plate.
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73
centre of rotation for the tilting of the piston rod and seal
housing is thereby maintained inside the seal housing at
level with the top plate middle layer. The capsule is
pressurized with nitrogen gas to equal the pressure of the
outside seawater at the level of the capsule bottom plate.
Several papers have been published on the Lysekil pro-
ject, e.g. regarding energy potential [16], force measure-
ments [17-19], power absorption [20-22], farm layout
[23], electrical control [24].
The subject of studying WECs in the frequency do-
main is not uncommon. Earlier research has for example
investigated numerical and experimental modelling as-
pects [25], wave spectra for performance assessment [26]
and assessing dynamic effects relevant for wear in hy-
draulic direct drives [27]. A study of the spectral content
in the measurements from inside L2 at the LRS may add
to the understanding of the mechanical performance in
the WEC and how the measured data is to be interpreted
for further analysis of the piston rod mechanical lead-
through transmission.
3. Experimental Set-Up
3.1. Sensors and Measurements on L2
The sensors inside WEC L2 measure: translator position
and piston rod outside length, air temperature, humidity,
water leakage, water level, stator temperature, magnetic
flux in the air-gap between stator and translator, relative
sideway displacement (i.e. lateral movements) of the
piston rod and its matching seal housing in the mechani-
cal lead-through transmission, strain in the inner me-
chanical framework and bending strain in the generator
capsule [28].
This paper focuses on sensors in L2 which measure the
relative displacement in of the piston rod mechanical
lead-through transmission and which may be influenced
by mechanical vibrations. Temperature, humidity, water
detection and water level are therefore excluded. The
laser triangulation sensor measurements on the piston rod
and seal housing are compared within the time and fre-
quency domain with added measurements of cogging
frequency, active AC power, magnetic flux in the air gap,
mechanical strain in the WEC structure and measure-
ments of piston rod axial displacement and translator
position. The force transducer measuring axial force in
the buoy line from underneath the buoy is also included,
even though it measures with 16 Hz and uses another
data acquisition system communicating through the GSM
network.
The analogue output from the sensors inside the WEC
was signal-conditioned in the WEC and sent through a 70
m twisted pair cable to the substation where it was si-
multaneously sampled by a programmable automation
controller (PAC) on all channels at 256 Hz with a com-
pactRio system from National instruments [29]. The
digitized data was then transferred 3 km with a point-
to-point copper link from the substation to the onshore
measuring station, where it was stored on a hard disk
drive. All the measuring systems, excluding the force
transducer, communicate through the data acquisition
system in the sea cables described in [29,30]; see Fig-
ures 1 and 2.
A brief description will now follow of the individual
sensor measuring systems involved in the study.
A. Laser triangulation sensors. A set-up of 7 laser
triangulation sensors from Micro Epsilon, model op-
toNCDT 1700-20, have been installed to measure the
relative sideway displacements of the piston rod and seal
housing in the piston rod mechanical lead-through trans-
mission in WEC L2; see Figures 4 and 5.
The laser sensors are rigidly mounted onto a rigid
sensor set-up rig surrounding the mechanical lead-through
underneath the capsule top plate. Each stationary sensor
measures linear displacement with a diode laser beaming
a spot onto the moving target surface and detecting dif-
fuse reflection with optics and a CCD array. The sensors
are mounted with fixed angular, radial and vertical posi-
tions relative to each other. The laser sensor measure-
ment system has been system calibrated (end-to-end-
calibrated) for good accuracy.
Each sensor measures relative displacement within a
measuring range of ±10 mm at a working distance of 50
mm. with an accuracy estimated to be in the order of the
sensor non-linearity of due to the very accurate system
calibration method and relative aspect of measuring, as
presented in Strömstedt et al. [30].
Piston Rod Laser Sensors (PRLS) 1 - 3 measures the
relative displacement of the piston rod by beaming hori-
zontally and radially in towards the moving target sur-
face of the piston rod with a 120 degree angular separa-
tion. Seal Housing Laser Sensors (SHLS) 1 - 3 measures
the same way towards the moving target surface of the
seal housing and are mounted 96 mm higher up. SHLS 4
measures the vertical motion of the seal housing by
beaming a laser toward the bottom target surface of a
seawater collector plate used for detecting if any leakage
occurs through the rubber gasket. The seawater collector
Figure 5. The laser triangulation sensor set-up rig sur-
rounding the piston rod mechanical lead-through in L2.
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74
is rigidly mounted to the outside of the seal housing
above rigid the laser sensor set-up rig.
The sensor output is amplified by a factor of 2.8 inside
the WEC and damped by a factor of 0.5 in the substation
to fit the input swing of the sampling PAC in the data
acquisition system. An in-depth presentation of the entire
laser triangulation sensor measuring system, choice of
sensor, geometrical set-up of sensors, sensor adaptation,
configuration, mounting, system calibration and accuracy,
noise analysis, among other things, is described in Ström-
stedt et al. [30]
B. Draw-wire sensor. A draw-wire sensor has been
installed to measure the vertical translator position and
the axial displacement and position of the piston rod. The
draw -wire sensor is a standard wire sensor from Micro
Epsilon, WDS-3000-P115-SA-P-E. The sensor is at-
tached to the top side of the upper end stop plate of the
inner mechanical framework; see Figur es 2, 6 and 7. A
hole is drilled through the upper end stop for the wire
which is fastened to the top of the translator; see Figure
6. The sensor is protected from large vibrations by the
use of a rubber damper. An in-depth presentation of the
entire draw-wire sensor measuring system including cali-
bration, accuracy and noise analysis was presented in
Strömstedt et al. [30].
C. Strain gauges. WEC L2 was provided with strain
Figure 6. The draw-wire sensor on top of the upper end
stop and the attachment of the wire to the top of the trans-
lator.
Figure 7. The positions of the draw-wire sensor, the strain
gauges SG3 and SG13, and other important parts close by
the upper end stop and at the top of the translator in L2.
gauge circuits for measuring bending strain on the cap-
sule wall and for measuring uni-axial strain in the inner
framework structure. In this paper two of the eleven
strain gauge circuits (SG) are singled out to represent the
typical strain gauge signal content in the inner and outer
WEC structure.
SG 13 is a 2-active-gauge system for bending strain
measurement with two resistive strain gauges from
Kyowa, KFN-5-350-C9-16, mounted inside the capsule
on opposite sides with a separation of 180˚; see F igur es
7 and 8. SG 3 is a strain gauge circuit of an active-
dummy 2-gauge system mounted on the corner pillar of
the inner framework close to the upper end stop; see
Figures 7 and 8.
When the WEC is under working load and the transla-
tor moves up and down stress occurs in the capsule and
inner framework structure. The strain gage amplifying
electronics has two major design parts. The first one is
the discrete amplifier placed close to the strain element
amplifying the differential signal from the measurement
bridge.
This signal was sent to an instrument amplifier inside
the WEC that increased the gain even more before the
signal was transmitted to the substation and sampled by
the PAC together with all other measurements.
The set-up of strain gauges in L2, calibration, accuracy,
formulas for calculating the strain and measurements
have been presented in-depth in Savin et al. [18,19].
D. Search coils. The magnetic flux in the air-gap be-
tween stator and translator is measured with a so-called
search coil (SC) [31]. A SC is a passive inductive sensor
composed of a single coil. It measures the induced elec-
tromotive force (EMF) in a closed loop equal to the neg-
ative time derivate of the enclosed magnetic flux (Ф).
The SCs used in L2 is designed on a two layer printed
circuit board (PCB) with ten turns on every side. 8 SCs
were installed in L2. SC 5 was selected to represent the
typical signal measured by the SCs as the translator re-
ciprocates in the generator; see Figure 9. The SC signal
is amplified with a factor 20.8 in the WEC and transmit-
ted through the data acquisition system.
SC 5 is positioned in the vertical middle position and
closed by the horizontal edge of one of the 4 stator sec-
tions; see Fig ure 9. The search coil design, calibration,
set-up in L2, accuracy and time domain measurements
Figure 8. The position and mounting of SG 3 and SG 13 in
L2.
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Figure 9. The position of SC 5 in the air gap of one of the 4
stator sections in L2.
are further described in [28].
E. Force transducer. A force transducer from HBM,
U2B 200 kN, is used for measuring the axial force in the
buoy line with a frequency of 16 Hz; see Figure 10.
The cylindrical buoy attached to L2, weighing 2 tons,
with a diameter of 3 m and a height of 1.2 m has the
force transducer mounted underneath the buoy, between
a couple of chain links and the buoy line; see Figure 10.
The battery powered transducer is protected by a casing
and embedded in a polymer resin for protection. The
cables enter the buoy through a watertight rubber hose.
The signal is transmitted from an antenna on the buoy
through the GSM network with the use of a Mitec-Sate-
Lite60 data logger system and stored at the measuring
station. Since the buoy is moving relative to the ocean
floor, it is difficult to make a cable connection to the
substation. The communication of the axial force meas-
urements from underneath the buoy is made through the
GSM network and described in [32].
The force transducer measuring system has been de-
scribed including calibration and accuracy in Savin et al.
[18]. The axial force measurements indicate if an end
stop impact has occurred. Changes in the axial force may
affect the bending of the steel structures in the WEC and
cause possible vibrations.
F. Voltage and current measurements. The 3-phase
AC voltages from the WEC are measured in the substa-
tion, where also the currents are measured with hall cur-
rent transducers. Active AC power is studied in order to
draw conclusions on cogging frequencies. The WEC was
connected to 14.1 Ω air cooled DC loads onshore in the
May measurements and delta-connected to 12 Ω water
cooled dump loads close by the WEC in the August
measurements presented in this paper. The loads are per
phase. The sampling frequency for the power measure-
ments is 256 Hz for both measurements periods, which is
the same as the sampling frequency for the sensor meas-
urements inside the WEC. The voltage and current meas-
urements are presented in detail in Boström et al. [24,
33].
4. Theory
4.1. Signal Content and Noise
Inside the WEC the generator is running with a varying
Figure 10. (Left) The force transducer; (Right) The connec-
tion underneath the buoy with the force transducer encased
and sealed off in a soft polymer resin.
speed following the waves at the surface. In theory the
signals from the laser triangulation sensors and the other
sensors will be of a non-stationary continuous character:
Sine components with changing amplitudes and/or
changing frequencies, such as the signal content asso-
ciated with the ripples of cogging and the oscillating
motion of the translator following the varying ampli-
tudes and/or frequencies of the waves.
Random signals with statistical properties changing
with time, such as noise and disturbances within the
measuring environment and within the measuring
system.
Transients appearing with varying intervals and with
varying characteristics in time and frequency, such as
the signal content associated with the end stop im-
pacts.
The RMS noise and the signal-to-noise ratio (SNR) for
the laser triangulation sensors and the draw wire sensor
measurements have been investigated for a typical meas-
urement period in May and August without end stop im-
pact in [30]. A reference case from measurements with
the generator at a standstill on the 14th of October is pre-
sented in this paper for further information about the
noise characteristics.
4.2. Vibrations from Cogging
Mechanical vibrations in the WEC may influence sensor
output, especially for sensors measuring mechanical enti-
ties, such as the laser triangulation sensors measuring the
relative motion of the piston rod and the seal housing.
Cogging is a source of vibration in the generator. The
vibrations may influence the motion of the objects and/or
the sensors.
Cogging is the result of fluctuations in the electro-
magnetic force between the translator magnets and the
stator armature in the generator. It has been extensively
investigated in linear generators and motors; for example
in [34-40]. In conventional rotating permanent magnet
generators cogging is mostly referred to the interaction
between the edges of the magnets and the stator teeth at
the winding slots. At high speed the moment of inertia
will however filters out most of the effect of cogging
torque in conventional generators. In power production
with slow moving permanent magnet linear generators
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76
many poles are needed to compensate for the lack in ro-
tational speed. The translator moves in and out of the
stator instead of rotating inside it. This causes another
specific effect relating to cogging.
The most prominent cogging effect occurs when the
permanent magnets pass the longitudinal stator outlet
ends [40]. At the longitudinal ends of the stator the mag-
netic field density increase in the stator armature as the
magnets starts to slip out of the stator and the magnetic
circuit. A field concentration occurs at the edge causing a
pulsating attraction force in the air gap with every mag-
net that passes by. The pulsating force can be separated
into a normal and a tangential component. The long itu-
dinal end effect also propagates inwards in the stator af-
fecting the other magnetic circuits and cause electrome -
chanical force ripples throughout the machine. The nor-
mal force component attracts the translator towards the
translator and has been investigated at no load by Nilsson
et al. [39]. The tangential component counteracts the
axial force in the buoy line which emanates from the
waves pulling the buoy and the translator in the generator.
This pulsating cogging force results in vibration. The
magnitude of the cogging mainly depends on the geome-
try and strength of the magnets, the armature geometry
and the air gap width [34].
In L2 the translator is 1867 mm long. The stator is
1264 mm long. This means that the magnets will always
be moving past one of the stator outlet ends during op-
eration. In other words, as long as the translator is mov-
ing cogging will occur, however with low frequency to-
wards the end stops and no frequency at end stop stand-
still. The cogging frequency will vary with the speed of
the reciprocating translator as it moves with the varying
amplitude and frequency of the ocean waves. The char-
acteristic frequency (fcogging) is set by the magnetic pole
width (wpole) and varies with the speed of the translator
(vtranslator) according to Equation (1),
translator
cogging
pole
v
fw
=
(1)
Vibrations from cogging may propagate through the
WEC structure and the frequencies may be detected in
the different sensor measurements. The spectral content
from cogging will have a continuous distribution over a
certain bandwidth and be repeated over different har-
monics. With Equ a tion (1) it is possible to calculate the
instantaneous cogging base frequency in the generator
and compare it with the spectral content found in the
sensor measurements in a time-frequency analysis.
4.3. Vibrations from a Fluctuating Damping
Force
The interaction between the magnetic flux from the per-
manent magnets and the counteracting induced flux in
the armature from the currents in the winding cables re-
sult in a damping force in the air gap [21]. The force
counteracts the pulling force from the waves. Generally
when more power is generated with a certain load a
higher damping force affects the WEC. As a con se-
quence the translator speed is reduced and the system is
balanced.
In an ordinary 3-phase generator the phase voltages
balance each other, causing an even power output. In a
1-phase generator the power output will fluctuate with
the only phase present and consequently so will the
damping force. In a 1-phase generator the power and
damping force fluctuations inevitable cause vibrations.
The damping force can fluctuate if the voltages in a
3-phase generator are not balanced. In L2 the windings
were connected in an unintentional order with one phase
being phase-shifted 180 degrees creating what could be
called a 3-wire single phase or a quasi-one-phase gen-
erator. The unbalanced currents cause increased fluctua-
tions in the power and damping force which can be seen
in the power output fluctuations of L2.
The fluctuations in power and damping force shift
with the amplitude of the currents at the same pace as the
magnets pass by the windings. The base frequency for
the damping force fluctuations therefore has the same
frequency as the cogging, which is not so strange since
the two forces depend on the same magnetic flux from
the reciprocating translator magnets. The magnitude of
the damping force fluctuations depends on translator
speed, the electric load and how far out of the stator the
translator has moved. In the May measurements the gen-
erator was connected to a rectifier bridge, a capacitive
filter and resistive DC loads at 14.1 Ω. In the August
measurements the generator was delta-connected to a
purely resistive water cooled AC dump load nearby the
WEC with phase resistances of 12 Ω. These describe two
different load cases, a linear load case and a non-linear
load case, as described respectively in Waters et al. [20]
and Boström et al. [14].
Cogging and fluctuations in the damping force both
lead to vibrations which cause an unstable translator
motion. This and can potentially destroy the air gap by
causing wear on the mechanical parts [35]. Vibrations
may also increase wear on the sealing system in the pis-
ton rod mechanical lead-through transmission [27].
4.4. Vibrations from Interacting Lorenz Forces
Another frequency of vibration in the generator may
come from the Lorenz force interactions between the
cables inside the stator. These fluctuate with the fre-
quency of the electric circuit, which is half the cogging
frequency given in Equation (1). Thus two frequencies
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77
co-exist separated by a factor of 2. The vibrations from
the Lorenz forces come from inside the stator and may
propagate through the WEC structure and may be seen in
the sensor measurements.
4.5. Vibrations from End Stop Impact
End stop impact obviously happens less frequent and
may produce transients with a lot higher frequencies than
cogging, fluctuations in damping and Lorenz force inter-
actions. In higher sea states end stop impact may occur in
every wave period, while in smaller sea states it does not
have to occur at all.
The appearance of end stop impact in the laser sensor
measurements is investigated in the time domain and in
the frequency domain with short time Fourier transforms
(STFT) plotting the spectral content with a spectrogram.
4.6. Spectral Analysis with FFT
The spectral content in the laser triangulation sensor
measurements are investigated in the frequency domain
with Fast Fourier transform (FFT) and compared with the
spectral content in simultaneous measurements with other
sensors in the WEC and the measured active AC power.
The purpose is to try to separate vibrations in the sensor
signals from noise and to draw conclusions from com-
parison with the other sensors on the possible source of
the vibrations in the frequency domain and if and what
filtering is needed.
Frequency analysis using FFT is the most commonly
used method for constant bandwidth analysis [41]. The
FFT algorithm in Matlab calculates the discrete Fourier
transform (DFT) described in [42]. The FFT algorithm in
Matlab is used to find the spectral content in the sensor
measurements within a selected measurement period.
The methods for obtaining the spectral content are
well known and explained in [42]. In this paper the spec-
tral intensity is given as log of FFT magnitude. The re-
sulting decibel level in a power spectrum is exactly the
same. The interest lies in the comparison between fre-
quencies and relative amplitudes, not absolute amplitudes.
Reference levels for the spectra are therefore not neces-
sary. The FFT of the measured data is carried out with
the parameters given in Table 1.
The frequency spacing (or resolution) in the FFT de-
pends on the sample size N and the sampling period, Ts.
Ts is determined by the sampling frequency of 256 Hz
and N by the selected measuring period of 8.5 s.
The force transducer output is not suitable for spectral
analysis since it is sampling with such a low frequency.
In fact it is under sampling with regard to the cogging
frequency, and show a lot of aliasing, which can be spot-
ted in the time domain comparisons.
Table 1. FFT parameters used in the spectral analysis of the
measurements in May and August (excl. the force trans-
ducer).
Parameter Notation Value
Time domain
Sample interval Ts 3.90625 μs
Sample size N 2177
Sample length (N 1)∙Ts 8.5 s
Frequency domain
Frequency spacing fs = 1/NTs 0.1176 Hz
Spectrum size N components 2177
Max. frequency (N/2)∙fs = Fmax 128 Hz
Frequency period Fp = Nfs 256 Hz
4.7. Time-Frequency Analysis with STFT
Spectrograms are plotted of the laser triangulation sensor
measurements to measure the frequency information over
time, using the joint time-frequency functions in the
Matlab STFT algorithm. The Hamming window is used
in Matlab. The spectrograms are mainly presented to
display the changes in spectral content and the differ-
ences between normal operation and what happens at end
stop impact. The laser triangulation sensor measurements
are analyzed with STFT and correlated with the instan-
taneous cogging frequency calculated with the speed of
the translator as measured by the draw-wire sensor in the
time domain.
5. Results
5.1. Sea States during Measurements
The wave height at the LRS is measured by a non-direc-
tional Datawell Waverider buoy. The buoy measures the
vertical surface displacement and sends the information
through radio link to the Sven Lovén Centre for Marine
Studies in Fiskebäckskil. The measurement frequency is
2.56 Hz. Spectral analysis is carried out onshore. The
overall accuracy of the buoy is 3.5% of the measured
value and the measuring system is presented in [11]. A
significant wave height (HS), a mean energy period (TE)
and a wave power density (J) are calculated as half-
hourly averages. In this paper, the first measurement pe-
riod is taken from measurements logged on the 28th of
May with a sea state characterized by HS = 1.6 m, TE =
5.7 s and J = 7.2 kW/m. The second measurement period
was logged on the 15th of August with a sea state of HS =
1.8 m, TE = 6.0 s and J = 9.5 kW /m.
5.2. Reference Signal and Estimation of Noise at
Standstill
The laser triangulation sensor measurements with the
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WEC at standstill separated from the buoy in October
after the experiment are shown in Figure 11. The laser
triangulation sensors show a rms noise level, i.e. ±1
standard deviation, between 0.0003 - 0.0008 mm, and a
peak-to-peak noise, representing 6 standard deviations of
0.002 - 0.004 mm. The measured objects still seem to os-
cillate slightly from the waves. This is possibly due to
wear on the sealing system.
5.3. Measurements in the Time Domain
The measurements in the time domain for 8.5 s from the
28th of May between 13:00:20-13:00:28.5 are shown in
Figure 12. 8.5 s represents a little more than a wave pe-
riod to show the typical sensor amplitudes at the given
sea state during a wave on the 28th of May without the
translator impacting on the upper or lower end stop. The
overall signal characteristics on the scale of a wave pe-
riod can thus be studied.
Close-ups of 1 second at a specific point in time be-
tween 22.5 - 23.5 s when the translator is ascending with
a constant speed of approx. 0.6 m/s, are shown in Figure
13. On the smaller time scale of a second the particular
relations in signal content, like frequencies and noise,
can be distinguished and correlated.
Output is presented from the laser triangulation sen-
sors, the draw-wire sensor measuring piston rod outside
length, SC 5, SG 3, SG 13, the force transducer and the
active AC power. The translator is in the middle position
when the piston is 1185 mm outside the seal housing (in
the water). The upper end stop compression spring does
not contact the translator until the piston has moved 2092
mm outside the seal housing and into the water. The
lower end stop compression spring contacts the translator
when the piston rod outside length is 295 mm. These
impacts are not happening during the wave period in
Figures 12 and 13. Figure 14 displays the sensor meas-
urements for an equally long time period of 8.5 s on the
15th of August. The Strain gauges did not function at this
moment in time and cannot be displayed for this time
period. The elevated noise levels in PRLS 1 - 3 and the
draw -wire sensor has already been explained in [30]. A
faulty ground in the underwater substation may be the
reason. It was corrected after the underwater substation
was picked up in June, fixed and re-launched a week
later.
The close-ups of 1 second in Figure 15 are taken from
Figure 14 between 20.7 - 21.7 s. It is important to point
out that the two measurement periods are taken with the
WEC connected to two different load cases described in
Section 4.3. This is the reason for the different generated
power visible in the active AC power output plots from
the WEC. However, the axial force in the buoy line is
Figure 11. Output and spectrum with FFT for the draw-wire sensor, PRLS 1 and SHLS 1 at generator stand still in October.
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Figure 12. Measurements from one wave period in the WEC in May 28, 13:00:20-13:00:28.5 from PRLS 1 - 3, SHLS 1 - 4, the
draw wire sensor, the force transducer, SG3, active AC power, SC5, and SG13.
comparable in magnitude and fluctuates similarly in both
cases. The average translator speed in Figure 13 is 0.6
m/s, while it is 0.7 m/s in Figu re 15. The higher transla-
tor speed consequently results in a higher average fre-
quency of 14 Hz for the cogging and fluctuations in
damping force as presented in Figure 15, compared to 12
Hz in Fig ure 13. The electric frequency of the currents in
both the May and the August measurements oscillate
with half the cogging frequency, which can be seen in the
output of the SC 5.
The search coils measure the passage of each perma-
nent magnet in the air gap. The magnetic field from the
strong magnets completely dominate the visible output in
the time domain. The force transducer is visibly under
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Figure 13. Measurements from 1 s in May 28, 13:00:22.5-13:00:23.5 from PRLS 1 - 3. SHLS 1 - 4, the draw wire sensor, the
force transducer, SG 3, active AC power, SC 5, and SG 13.
sampling and show aliases at 4 Hz in the May and 6 Hz
in the August measurements. The PRLS 1 - 3 have a visi-
bly lower noise level in August.
5.4. Measurements in the Frequency Domain
FFT calculations are performed in Matlab on the data
from both 8.5 s measurements in May and August to en-
able spectral analysis. Log of FFT magnitude in dB is
presented in order to display the relative intensities of the
different frequencies adding information to the time do-
main studied above. The results are presented in two
graphs with selected offset decibel values added to each
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Figure 14. Measurements from one wave period in August 15, 00:00:20-00:00:28.5 from PRLS 1 - 3, SHLS 1 - 4, the draw
wire sensor, SC 5, active AC power, and the force transducer.
curve for the purpose of not concealing each other. Cen-
tred moving averages with a sliding window of 9 fre-
quency spacings are superimposed on the spectra to clar-
ify the peaks. The spectra for the May measurements
are displayed in Figure 16 and for the August meas-
urements in Figu re 17. The Nyquist frequency is 128 Hz
for both cases. The data and the original units of meas-
urement for the different curves are found in Figures 12
and 14.
5.5. Measurements in the T ime-Frequency
Domain
Figure 18 presents time-frequency analysis on PRLS 3
and SHLS 3 for the measurements on the 28th of May
between 13:16:00-13:17:00 hours, incl. end stop impact.
Figure 19 presents the same analysis performed on data
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Figure 15. Measurements from 1 s in August 15, 00:00:20.7-00:00:21.7 from PRLS 1 - 3, SHLS 1 - 4, the draw wire sensor, SC
5, active AC power, and the force transducer.
from the 15th of August between 00:00:00-00:01:00
hours for PRLS 1 and SHLS 1, with two end stop im-
pacts. The sensor output and spectral content in Figu res
12-17 show that PRLS 1 - 3 and SHLS 1 - 4, respectively,
contain more or less the same signal and noise character-
istics. In the continued time-frequency analysis with
STFT only one sensor from each group needs to be used
for calculating the representative power spectral density
for the sensor groups. The selected sensors measure in
the directions of the incoming waves at the particular
times in question and will therefore be the sensors with
the largest output within each group of sensors.
The sensor output is first presented in the time domain
over one minute of sampling for both May and August. A
centred moving average (CMA) with a window of 51
samples is applied to the May measurement with PRLS 3;
see superimposed red line in Figure 18. Two graphs
showing the power spectral density is then plotted
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Figure 16. Magnitude spectra for PRLS 1 - 3. SHLS 1 - 4,
SG 3, SG 13, SC 5, the draw-wire sensor, and measured
active AC power for a measurement period of 8.5 s on May
the 28th between 13:00:20-13:00:28.5 hours.
underneath. The first covers up to the Nyquist frequency
of 128 Hz. Below that a close-up displays the power spec-
tral densities within the cogging bandwidth in greater
detail. The same is performed for SHLS 3 in May and
SHLS 1 in August and presented PRLS 3 and 1 in Fig-
ures 18 and 19 respectiv e ly.
Figure 17. Magnitude spectra for PRLS 1 - 3, SHLS 1 - 4,
SC 5, the draw-wire sensor and measured active AC power
for a measurement period of 8.5 s on August the 15th be-
tween 00:00:20-00:00:28.5 hours.
STFT in Matlab is used with a Hamming window with
NFFT length of 145 for the PRLSs and 250 for the
SHLSs. NFFT is a value for setting the spectral reso lu-
tion. A higher value has a smoothing effect on the output
due to increased window overlaps.
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Figure 18. Measurements on May 28th between 13:16:00-13:17:00 hours. PRLS 3 for 60 s in the time domain. Power spectral
densities for PRLS 3 up to the Nyquist frequency followed by a close-up of the cogging bandwidth. SHLS 3 for 60 s in the
time domain followed by power spectral densities for SHLS 3 up to Nyquist frequency and a close-up of the cogging band-
width. The instantaneous cogging frequency and piston rod outside length measured by the draw-wire sensor. End stop im-
pact occurs after 46 s.
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Figure 19. Measurements on August 15th between 00:00:00-00:00:01 hours. PRLS 1 for 60 s in the time domain. Power spec-
tral densities for PRLS 1 up to the Nyquist frequency followed by a close-up of the cogging bandwidth. SHLS 1 for 60 s in the
time domain followed by power spectral densities up to the Nyquist frequency and a close-up of the cogging bandwidth. The
instantaneous cogging frequency and piston rod outside length measured by the draw-wire sensor. End stop impact occurs
after 17 s and 31 s.
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Piston rod axial displacement, which with and offset
correlates to translator position, is presented at the bot-
tom of Figures 18 and 19. In this section the position is
foremost used to display the end stop impacts, but also to
give information about the position of the transmission
and translator during operation. When the piston rod out-
side length is 1185 mm the translator is in its vertical
middle position with the centre in the middle of the stator.
When the translator hits the upper end stop the piston rod
outside length is 2335 mm. The lower end stop is im-
pacted on when the piston rod has a 125 mm outside
length. The sampled measurements include one upper
end stop impact in May at 46 s and two end stop impacts
in August at 17 s and 31 s.
The power spectral densities for the different frequ en-
cies may be compared with the instantaneous cogging
frequencies, based on the translator speed and the mag-
netic pole width; see Equation (1) in Section 4.2. The
translator speed is calculated by Newton’s difference
quotient to find the derivatives of the axial piston rod
displacement. A least squares method with a linear fit
and a window of 51 samples sweeping the measurements
of the piston rod outside length is applied. In May the
piston rod outside length is represented by a CMA cal-
culated with a sweeping window of 101 samples, due the
increased noise level.
The next step is to calculate the instantaneous cogging
frequency by dividing the translator speed with the mag-
netic pole width of 50 mm and turning the amplitudes
into magnitude by using the absolute value. The resulting
instantaneous cogging frequency is displayed in the sec-
ond graph from the bottom in both Figures 18 and 19.
The peaks in cogging frequency do not seem to be af-
fected by the selected windows sizes, just the overall
smoothness is visibly affected.
5.6. Close Up of End Stop Impact in the Time
Domain
In order to suggest a suitable filter for further studies
with calculations of the macro displacements in the me-
chanical lead-through transmission a comparison be-
tween 5 filters is presented in Fig ur e 20. The inverse
FFT is a mathematical filter with an ideal response func-
tion separating all frequencies above the cut-off fre-
quency, which is useful to investigate what signal may
contain in the time domain with a limited number of ac-
cepted frequencies. In post-measurement signal process-
ing it is possible to use the ideal inverse FFT (IFFT)
low-pass filter with a chosen cut-off frequency. The
CMA filters with a window of 51 samples have been pro-
posed and motivated in [30].
The results in Figure 20 show that continued use of
the CMA filter is adequate for evaluating the larger mo-
tions without excluding too much information or cutting
Figure 20. Close-up of output from PRLS 3 at end stop impact with different IFFT filters and a CMA filter applied on the
May measurements.
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of peaks too much, even though vibrations should be
further investigated by other means and treated sepa-
rately if those were in focus for the study. Figure 21 in-
dicates that a smaller CMA window of 21 samples would
follow the steepest gradients more precisely. However,
with more noise it is not necessarily better for the inves-
tigation. The smoothing aspect is important in order to
give a meaningful content to the measurements when
they are combined to calculate the tilt angles and azimuth
angles of the measured objects. The results from Figures
18 and 19 suggest that an ideal low-pass filter would not
be able to include all vibrations and separate the noise at
the same time for a more meaningful study of the relative
displacements since the vibrations are spread out over
such a wide band at end stop impact. However, the CMA
filter responds well to the shifting magnitudes. It is thus
concluded that a CMA filter suits the data from the laser
triangulation sensors for further investigations into the
results with regard to performance of the mechanical
device.
6. Discussion
The aim of the paper is to investigate the signal and
spectral content in the time and frequency domain, to
investigate vibrations and noise, and to find a suitable
filter for further refinement of the signal to separate noise
from actual physical displacement.
Normally the currents, voltages and flux waves in a
3-phase generator balance each other and superimpose to
create a smooth resulting armature flux with a smooth
damping force. However, in WEC L2 one of the phases
were unintentionally phase shifted 180 degrees creating a
combined unbalanced quasi 1-phase voltage. The result
Figure 21. Close up of two CMA filters with different win-
dow size at end stop impact in the August measurement.
was a generator with increased fluctuating damping force
at the same frequency as the cogging, resembling that of
a 1-phase generator.
If we have the generator connected to a purely delta-
connected resistive load the cogging is more pronounced,
than if it is connected to a non-linear load case with a
rectifier, capacitive filter and a DC load, as described in
[14]. The damping force is affected by the smoothing
from the capacitive filter. The capacitors discharge main-
taining the power for short time intervals when the WEC
is connected to the DC load like a pressure accumulator
in a hydraulic system. It evens out the fluctuations in the
damping load as the WEC is disconnected from the load
by the rectifiers at lower production levels.
Theoretically the cogging bandwidth starts at very low
frequencies from translator standstill and increase up to
approximately 20 Hz. However, the cogging is most
pronounced between 5 and 20 Hz. which has to do with
the translator quickly picking up speed and maintaining it
rather constant throughout each half cycle between the
turning points. The reason for this has to do with the
non-linear loading case. The electrical frequency of the
generator is directly proportional to the speed of the
translator. Maximum power is achieved during minimum
and maximum line force assumed with generator stroke
length. When the translator changes its direction it
changes the phase order of the 3-phase voltage. With the
generator connected to a non-linear load case the control-
ling DC-level, after the diode rectifiers, limits the trans-
lator speed to some extent and makes it more constant. If
the translator speed is low, inducing a no-load voltage
below the DC-voltage level, no power is extracted and
the speed of the translator is allowed to increase without
damping. This explains the form of the power curves in
May and the reason for the appearance of the cogging
plateau.
The amplitude of the fluctuating damping force de-
pends on the number of poles activated inside the stator,
which in turn depends on how far out of the stator the
translator has moved. The cogging force at the longitu-
dinal outlet ends of the stator will mainly be affected if
the translator leaves one of the outlet ends of the stator.
The speed of the translator varies and the number of
poles inside the stator decrease towards the end stops.
Both frequency and amplitude of the vibrations from
cogging and fluctuating damping force decrease towards
the end stops. This can be seen in the time domain in
Figures 12 and 14 and is also visible in the spectrograms
of Figures 18 and 19.
Increased induction occurs at elevated translator speed.
At 26 s, in the May measurements of Figure 12, the
translator drops down as the axial buoy line force reaches
almost 0 kN. Overall increased mechanical vibrations
can be seen in the measurements from PRLS 1 - 3, SHLS
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88
1 - 4, SG 3 and SG 13 at this point in time. At a constant
translator speed of 0.6 m/s the damping fluctuations and
cogging coexist at 12 Hz; see Figure 13. The same fre-
quency can also be seen in the active AC power.
The overall cogging bandwidth can be seen in the ac-
tive AC power in Figure 16. It can be compared with the
peaks in the laser triangulation sensor output. The cog-
ging frequencies are apparent there, specifically at 18 Hz
corresponding with the largest peak in the power curve.
18 Hz corresponds to a translator speed of 0.9 m/s.
Cogging occurs over a bandwidth, during measure-
ments for more than a second, and in the spectral analysis.
The peak at 18 Hz and the multiple harmonics thereof are
clearly seen in the laser triangulation sensor measure-
ments. In the time domain, in Figu res 13 and 15, the
cogging frequency can be seen in the laser triangular-
tion sensor measurements at 12 and 14 Hz, respectively,
for the two cases presented. These values correspond to a
translator speed of 0.6 and 0.7 m/s and correlate well
with the oscillations in the active AC power with the
peaks between 5 - 20 Hz in Figures 16 and 17. In Figu re
17 for the August measurements the frequencies are there
but not at all as apparent as in May. However the fluctua-
tions can be seen in Figure 15 .
The results in Figure 13 show that SG 3 and SG 13
oscillate at half the cogging frequency, i.e. 6 Hz at a con-
stant translator speed of 0.6 m/s. This is the frequency of
the electrical circuits and the magnetic circuit at this par-
ticular translator speed. It can be concluded that the
source is the Lorenz forces between the cables in the
stator. Peaks are seen in Figure 16 at the bandwidth of
the SC 5 measurements. SC 5 keeps absolute track of the
magnets passing by the sensor. The signal oscillates at 6
Hz. The cogging frequency, which is twice the frequency
of the Lorenz forces can thereby be verified at this speed.
The Lorenz forces spread to all sensors, but the cogging
do not seem to reach the inner frame work or the capsule.
The Lorenz forces in the stator are possible to detect
with SG 3 and SG 13. The vibrations propagate through
the inner framework and over to the capsule. The inner
framework is almost completely separated from the cap-
sule apart from four horizontal and rectangular plates
nearby the upper end stop. These plates are mainly in-
tended for internal support when the WEC is lying down
during transportation. They do not carry any mechanical
load during operation apart from when bending of the
capsule and superstructure might subject them to buck-
ling as large waves pull the buoy line hard towards the
guiding funnel. Nevertheless, vibrations are apparently
transmitted through them from the stator through the
inner framework to the capsule.
The oscillations in the PRLS 1 - 3 measurements in
May indicate that the vibrations in the moving translator
from cogging and fluctuating damping force propagate
through the piston rod and into the seal housing via the
sealing components. The vibrations may be transmitted
through the double hinged link and up through the piston
rod, but the rubber gasket suspending the seal housing
isolates the top plate from the vibrations, since the cap-
sule strain gauge do not pick up the cogging frequency.
The Lorenz forces in the stator also seem to reach the
laser triangulation sensor measurements somewhat.
The vibrations from cogging and fluctuation in the
damping force seem to be generally higher in August.
The cogging was most pronounced within the bandwidth
of 5 to 20 Hz. This can be seen in the spectrograms
comparing Figures 18 and 19. The frequencies with high
relative spectral density seem to coincide rather well with
the cogging frequencies. The laser triangulation sensor
output in the time domain show such a large increase in
relative displacements in August compared to May, that
the vibrations do not seem larger in August. However,
since the amplitudes of the signal are so much higher the
impression is false. They do show larger vibration am-
plitudes in August. Looking at the displacement scale
and comparing with the spectral densities displayed in
Figures 18 and 19 it becomes evident. It is possible to
see that the PRLSs vary most in amplitude in the time
domain in Figure 15 compared to the SHLSs. The dis-
tance scales along the Y-axes are the same. The reason
for this may be that speckle occur more on the more pol-
ished surface of the piston rod.
In August the generator is directly delta-connected to a
water-cooled resistive dump load close by the WEC. This
results in more cogging which can be seen in the time
domain. The frequencies in August are more arbitrary
than in the May measurements. It may be increased wear
that explains it. This is supported by the spectral analysis
in Figure 17, showing smaller peaks for the cogging and
electrical circuit frequencies in August and smeared out
and elevated relative intensity levels across the board in
lower regions compared to the left image for May. In
Figures 12 and 14 the WEC is affected by a similar wave
with a similar axial force in the buoy line. The power
level in August is the same as in May on the upstroke,
but much lower compared to May on the down stroke,
which should result in less vibration magnitudes in the
WEC overall in August, when comparing Figure 16 with
17. The sensors do however detect more vibrant motion
in the mechanical lead-through in August, which may be
connected to wear. The vibrations themselves do have a
detrimental effect on the sealing system and result in
more wear. The time-frequency analyses shows more
cogging and more vibrations in August, which probably
comes from wear on the mechanical parts and in the me-
chanical-lead -through transmission.
A slight outstretched plateau is identified within the
cogging bandwidth for the seal housing in the late meas-
E. STRÖMSTEDT ET AL.
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89
urements in August. The explanation is suggested to be
attributed to the friction between the piston rod and the
seal housing in combination with an increased play be-
tween the seal housing and piston rod. Post-experimental
inspection of the sealing system in L2 indicates general
wear in all direction but most prominently in the direc-
tion of the predominant incoming waves.
The PRLS and SHLS measurements support the state-
ment that the laser sensor set-up rig is adequately stabile
for measuring the relative displacement of the piston rod
and seal housing. The sensors do not seem to move with
the cogging frequency or the frequency would not be
picked up by the sensors. There does not seem to any
other common frequency for the PRLSs and SHLSs that
could be attributed to an Eigen-frequency (or resonance
frequency) of the set-up rig. The source of vibrations
from cogging is quite far away from the location of the
laser sensor set-up rig. The path is long and the possible
attenuation of vibrations along the way is good enough to
suggest a negligible influence on the laser sensor set-up
rig. The seal housing is isolated from the capsule top
plate by a rubber gasket. Any vibration transmitted from
the piston rod to the seal housing would be attenuated by
the dampening rubber gasket. The cogging frequencies
are not transmitted through the rubber gasket and into the
top plate, which can be verified but checking the data for
SG 13. If for instance the sensors were to vibrate in uni-
son with the measured objects they would have problems
detecting cogging, which was not the case. The results in
Figures 12-19 support the notion that the sensor set-up
rig has a structural integrity with regard to the vibrations
in the WEC.
Other sources of vibrations in the WEC are the fric-
tional interface between the buoy line and the funnel at
the top of the super structure and between the yoke type
track rollers on the translator and inner framework. These
are difficult to detect since the characteristic base fre-
quency is unknown and might be changing all the time
with translator position and speed. The rubber gasket
isolates the seal housing and piston rod from being af-
fected by vibrations emanating from the outer WEC
structure, such as the funnel. The slamming of the trans-
lator against the end stops will of course generate mas-
sive vibrations but only as occasional transients. This
may have implications on the choice of filter.
7. Conclusions
The time and frequency analysis for the different sensors
show variations in content relating to the position where
they are mounted. The laser triangulation sensors detect
cogging frequencies and the frequency from the Lorenz
forces in the stator. The strain gauges only detect the
Lorenz forces.
The cogging frequencies appear within the bandwidth
from 5 to 20 Hz, varying with translator speed. The cog-
ging is most apparent in the active AC power spectral
content, as expected. The search coil sensors measuring
the air gap detects the magnetic circuit frequency, which
coincides with the frequency of the Lorenz forces within
the stator. The vibrations from the Lorenz forces propa-
gate through the inner framework and out through the
capsule.
The spectral peaks are most prominent in May for the
laser triangulation sensors. A slight plateau can be dis-
tinguished in August but the signals are contaminated by
wear oriented frequencies with arbitrary spectral distri-
bution.
The seal housing is isolated from the outer WEC struc-
ture by a rubber gasket. The vibrations from the outer
structures do not propagate to the seal housing and vice
ver sa.
The conclusion from analysis with different filters is
that a moving average with a window of 21 to 51 may
very well be adequate for the continued analysis of tilt
angles and azimuth angles when combining the meas-
urements from the different laser triangulation sensors.
The structural integrity of the sensor set-up has been
verified on a micro measurement level and vibrations do
not seem to be a problem for evaluating the performance
of the piston rod mechanical lead-through.
8. Acknowledgements
This paper is the product of research carried out within
the Lysekil project. The authors are affiliated with the
Swedish Centre for Renewable Electric Energy Conver-
sion at Uppsala University in Uppsala, Sweden. The re-
search is supported by The Swedish Energy Agency.
VINNOVA, Statkraft AS, Vattenfall AB, Fortum OY,
Falkenberg Energy AB, Helukabel, Draka Cable AB, Pro
Enviro, Seabased AB, The Gothenburg Energy Research
Foundation, The Göran Gustavsson Research Foundation,
Ångpanneföreningen’s Foundation for Research and De-
velopment, The Olle Engkvist Foundation, The J. Gust.
Richert Foundation, CF Environmental Fund, Vargöns
Research Foundation, The Swedish Research Council
grant No. 621-2009 -3417 and the Wallenius Foundation.
Fredrik Bülow, Kalle Haikonen and Venugoplan Kuru-
path are thanked for their knowledge in Matlab and for
fruitful discussions.
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 Time Series-, Time-Frequency- and Spectral Analyses of Sensor Measurements in an Offshore Wave Energy Converter Based on Linear Generator Technology
Energy and Power Engineering, 2013, 5, 70-91
http://dx.doi.org/10.4236/epe.2013.51009 Published Online January 2013 (http://www.scirp.org/journal/epe)
Copyright © 2013 Sci Res. EPE
Time Series-, Time-Frequency- and Spectral Analyses of
Sensor Measurements in an Offshore Wave Energy
Converter Based on Linear Generator Technology
Erland Strömstedt, Andrej Savin, Olle Svensson, Mats Leijon
The Swedish Centre for Renewable Electric Energy Conversion, Division for Electricity,
Department of Engineering Sciences, Uppsala University, Uppsala, Sweden
Email: erland.stromstedt@angstrom.uu.se
Received August 20, 2012; revised September 24, 2012; accepted October 10, 2012
ABSTRACT
Inside the second experimental wave energy converter (WEC) launched at the Lysekil research site on the Swedish west
coast in March 2009 a number of sensor systems were installed for measuring the mechanical performance of the WEC
and its mechanical subsystems. One of the measurement systems was a set-up of 7 laser triangulation sensors for meas-
uring relative displacement of the piston rod mechanical lead-through transmission in the direct drive. Two measure-
ment periods, separated by 2.5 month, are presented in this paper. One measurement is made two weeks after launch
and another 3 months after launch. Comparisons and correlations are made between different sensors measuring simul-
taneously. Noise levels are investigated. Filtering is discussed for further refinement of the laser triangulation sensor
signals in order to separate noise from actual physical displacement and vibration. Measurements are presented from the
relative displacement of the piston rod mechanical lead-through, from magnetic flux in the air gap, mechanical strain in
the WEC structure, translator position and piston rod axial displacement and active AC power. Investigation into the
measurements in the time domain with close-ups, in the frequency domain with Fast Fourier transform (FFT) and with
time-frequency analysis with short time Fourier transform (STFT) is carried out to map the spectral content in the
measurements. End stop impact is clearly visible in the time-frequency analysis. The FFT magnitude spectra are inves-
tigated for identifying the cogging bandwidth among other vibrations. Generator cogging, fluctuations in the damping
force and in the Lorenz forces in the stator are distinguished and varies depending on translator speed. Vibrations from
cogging seem to be present in the early measurement period while not so prominent in the late measurement period.
Vibration frequencies due to wear are recognized by comparing with the noise at generator standstill and the vibration
sources in the generator. It is concluded that a moving average is a sufficient filter in the time domain for further analy-
sis of the relative displacement of the piston rod mechanical lead-through transmission.
Keywords: Wave Power; Wave Energy Converter; Linear Generator; Sensor Measurements; Spectral Analysis;
Cogging; Filtering; Laser Triangulation Sensor; Draw-Wire Sensor; Force Transducer; Strain Gauges;
Search Coil; Power Generation
1. Introduction
For the past decade, the Swedish Centre for Renewable
Electric Energy Conversion at Uppsala University, Swe-
den, has been working on wave energy system, consist-
ing of a point absorber with a surface-floating buoy and
an encapsulated permanent magnet linear generator on
the seabed. The Uppsala project is one of many past and
present wave energy projects around the world, with very
different technical approaches. A few of the other pro-
jects and technologies are described in [1-5].
During operation an offshore WEC has to sustain mil-
lions of cyclical sequences of varying static, dynamic and
potentially very high mechanical loads at sea. For a com-
plete understanding of a wave energy converter device it
is important to know how the device operates in the wa-
ter, how the motion of the waves affects the electrical
and mechanical subsystems, how this motion can be
measured and how to interpret the information in the
measured data. Only a few full scale experimental studies
have been presented so far with sensor measurements
inside WECs in operation at sea, summarized in Lindroth
et al. [6]. The magnitude and character of the motion has
impact on engineering issues and optimization of control
parameters, as well as theoretical understanding of the
system in order to come up with durable designs for long
term sustainability.
E. STRÖMSTEDT ET AL.
Copyright © 2013 Sci Res. EPE
71
In this paper experimental data from different meas-
urement systems in the second WEC prototype at the
Lysekil Research Site (LRS) are studied and compared in
the time and frequency domain. A post-measurement
time -frequency analysis based on STFT and frequency
analysis based on FFT is carried out to map the spectral
content in the measurements inside the WEC during in-
tervals with two narrow sea states with 2.5 month separa-
tion.
The purpose of the work is to 1) present the spectral
content of the laser sensor measuring systems inside the
WEC, 2) to make comparisons in both the time and fre-
quency domain with output from other sensors to identify
typical vibrations, mainly cogging and end stop impact,
and 3) reflections on finding a suitable filter for refining
the laser sensor measurements in the time domai n.
In Section 2, the background of the Lysekil project
is presented and described along with the WEC in focus
for the study. Section 3 deals with the theoretical model
used for the spectral analysis and sources of vibration
along with assumptions made. The experimental set-up
of the sensor measuring systems and details of the meas-
urements are then presented in Section 4. Finally, in Sec-
tions 5 and 6 the measurement data and achieved results
are put forward and discussed.
2. Background
The experimental work presented in this paper was per-
formed at the Lysekil Research Site (LRS) off the Swed-
ish west coast. LRS is located about 10 km south-
southwest of the town of Lysekil, between a northern
(58˚11'850N 11˚22'460E) and a southern marker
(58˚11'630N 11˚22'460E); see Figure 1. The LRS was
established in 2004 for the purpose of studying full-scale
devices of the selected wave energy conversion system
under development at Uppsala University. The wave
climate is moderate with a typical average energy flux of
3.4 kW/m. From an evaluation point of view the LRS
serves the purpose with regard to wave height of an oth-
erwise scalable WEC system [7,8]. The site has a water
depth of about 25 m and a flat sandy bottom. It is con-
nected electrically to the small island of Gullholmen
through a 3 km long sea cable. More details about the
LRS can be found in [7].
Three different complete wave energy converter pro-
totypes, named L1, L2 and L3, an underwater substation
[9], an observation tower [10], a wave measurement
buoy [11] and around 8 biology buoys, for environmental
studies [12,13], were operating in the LRS at the time of
the experiment. The data in this paper comes from meas-
urements on L2 during the first wave power park ex-
periments in during the period from the 15th of May until
the 23rd of September. Figure 2(b) shows a photo of
Figure 1. The Lysekil research site during the experiments
in 2009.
Figure 2. (a) The buoy attached to L2 after launch; (b)
WEC L2 on cay before launch; (c) CAD assembly of L2 to
scale at 25 m depth.
WEC L2 before deployment and Figur e 2(a) of the buoy
at the LRS just after launch. Figure 2(c) shows a CAD
assembly image to scale of the WEC deployed at 25 me-
ters depth with the buoy at the surface. The force trans-
ducer measuring system is indicated.
The internal layout of the WEC is shown in Figure 3.
As a wave passes, the buoy is lifted, and this motion is
transferred to the generator. 37 rows of permanent Neo-
dymium Iron Boron (Nd2Fe14B) magnets with the pole
width of 50 mm are mounted on the translator and the
E. STRÖMSTEDT ET AL.
Copyright © 2013 Sci Res. EPE
72
Figure 3. Cross-sectional view of a CAD assembly of L2
with functional parts indicated.
relative motion between these and the stator induces
voltage in the stator windings. At a translator speed of
0.67 m/s the generator produces 10 kW at a line-to-line
voltage of 200 V when connected to a nominal load of 4
Ω and an air gap of approx. 2.5 mm. The efficiency of
the generator in this case is 86% [7]. Further generator
parameters are described in [14,15].
There are 8 tensile springs mounted between the bot-
tom of L2 and high up inside the translator framework.
The springs pull down the translator when the buoy is in
a wave trough. There are also end stops with compres-
sion springs to prevent the translator from slamming into
the capsule bottom and top plate. The free stroke length
is 1.79 m. It can then move another additional 0.243 m at
the top and 0.200 m at the bottom. While compressing
the end stop springs, making the full possible stroke
length 2.21 m.
The buoy line is guided by a funnel at the top of a
flooded superstructure. A piston rod transfers the me-
chanical force from the guided buoy line in to the gen-
erator through a seal housing in a mechanical lead-
through device; see Figu re 4. The seal housing is mounted
on a C-shaped rubber gasket at the centre opening in the
capsule top plate. The seal housing flange is clamped
around the gasket by two large hook nuts screwed on to
the outside of the seal housing inside the capsule; see
Figure 4. A dynamic sealing system inside the seal hous-
ing keeps the capsule watertight as the piston rod recip-
rocates with the translator without rotating.
A double hinged link between the piston rod and trans-
lator enables the lower rod end to move sideways. The
Figure 4. Piston Rod Laser Sensors (PRLS) 1 - 3 and Seal
Housing Laser Sensor (SHLS) 1 - 4 with rigid sensor set-up
rig attached to the capsule top plate.
E. STRÖMSTEDT ET AL.
Copyright © 2013 Sci Res. EPE
73
centre of rotation for the tilting of the piston rod and seal
housing is thereby maintained inside the seal housing at
level with the top plate middle layer. The capsule is
pressurized with nitrogen gas to equal the pressure of the
outside seawater at the level of the capsule bottom plate.
Several papers have been published on the Lysekil pro-
ject, e.g. regarding energy potential [16], force measure-
ments [17-19], power absorption [20-22], farm layout
[23], electrical control [24].
The subject of studying WECs in the frequency do-
main is not uncommon. Earlier research has for example
investigated numerical and experimental modelling as-
pects [25], wave spectra for performance assessment [26]
and assessing dynamic effects relevant for wear in hy-
draulic direct drives [27]. A study of the spectral content
in the measurements from inside L2 at the LRS may add
to the understanding of the mechanical performance in
the WEC and how the measured data is to be interpreted
for further analysis of the piston rod mechanical lead-
through transmission.
3. Experimental Set-Up
3.1. Sensors and Measurements on L2
The sensors inside WEC L2 measure: translator position
and piston rod outside length, air temperature, humidity,
water leakage, water level, stator temperature, magnetic
flux in the air-gap between stator and translator, relative
sideway displacement (i.e. lateral movements) of the
piston rod and its matching seal housing in the mechani-
cal lead-through transmission, strain in the inner me-
chanical framework and bending strain in the generator
capsule [28].
This paper focuses on sensors in L2 which measure the
relative displacement in of the piston rod mechanical
lead-through transmission and which may be influenced
by mechanical vibrations. Temperature, humidity, water
detection and water level are therefore excluded. The
laser triangulation sensor measurements on the piston rod
and seal housing are compared within the time and fre-
quency domain with added measurements of cogging
frequency, active AC power, magnetic flux in the air gap,
mechanical strain in the WEC structure and measure-
ments of piston rod axial displacement and translator
position. The force transducer measuring axial force in
the buoy line from underneath the buoy is also included,
even though it measures with 16 Hz and uses another
data acquisition system communicating through the GSM
network.
The analogue output from the sensors inside the WEC
was signal-conditioned in the WEC and sent through a 70
m twisted pair cable to the substation where it was si-
multaneously sampled by a programmable automation
controller (PAC) on all channels at 256 Hz with a com-
pactRio system from National instruments [29]. The
digitized data was then transferred 3 km with a point-
to-point copper link from the substation to the onshore
measuring station, where it was stored on a hard disk
drive. All the measuring systems, excluding the force
transducer, communicate through the data acquisition
system in the sea cables described in [29,30]; see Fig-
ures 1 and 2.
A brief description will now follow of the individual
sensor measuring systems involved in the study.
A. Laser triangulation sensors. A set-up of 7 laser
triangulation sensors from Micro Epsilon, model op-
toNCDT 1700-20, have been installed to measure the
relative sideway displacements of the piston rod and seal
housing in the piston rod mechanical lead-through trans-
mission in WEC L2; see Figures 4 and 5.
The laser sensors are rigidly mounted onto a rigid
sensor set-up rig surrounding the mechanical lead-through
underneath the capsule top plate. Each stationary sensor
measures linear displacement with a diode laser beaming
a spot onto the moving target surface and detecting dif-
fuse reflection with optics and a CCD array. The sensors
are mounted with fixed angular, radial and vertical posi-
tions relative to each other. The laser sensor measure-
ment system has been system calibrated (end-to-end-
calibrated) for good accuracy.
Each sensor measures relative displacement within a
measuring range of ±10 mm at a working distance of 50
mm. with an accuracy estimated to be in the order of the
sensor non-linearity of due to the very accurate system
calibration method and relative aspect of measuring, as
presented in Strömstedt et al. [30].
Piston Rod Laser Sensors (PRLS) 1 - 3 measures the
relative displacement of the piston rod by beaming hori-
zontally and radially in towards the moving target sur-
face of the piston rod with a 120 degree angular separa-
tion. Seal Housing Laser Sensors (SHLS) 1 - 3 measures
the same way towards the moving target surface of the
seal housing and are mounted 96 mm higher up. SHLS 4
measures the vertical motion of the seal housing by
beaming a laser toward the bottom target surface of a
seawater collector plate used for detecting if any leakage
occurs through the rubber gasket. The seawater collector
Figure 5. The laser triangulation sensor set-up rig sur-
rounding the piston rod mechanical lead-through in L2.
E. STRÖMSTEDT ET AL.
Copyright © 2013 Sci Res. EPE
74
is rigidly mounted to the outside of the seal housing
above rigid the laser sensor set-up rig.
The sensor output is amplified by a factor of 2.8 inside
the WEC and damped by a factor of 0.5 in the substation
to fit the input swing of the sampling PAC in the data
acquisition system. An in-depth presentation of the entire
laser triangulation sensor measuring system, choice of
sensor, geometrical set-up of sensors, sensor adaptation,
configuration, mounting, system calibration and accuracy,
noise analysis, among other things, is described in Ström-
stedt et al. [30]
B. Draw-wire sensor. A draw-wire sensor has been
installed to measure the vertical translator position and
the axial displacement and position of the piston rod. The
draw -wire sensor is a standard wire sensor from Micro
Epsilon, WDS-3000-P115-SA-P-E. The sensor is at-
tached to the top side of the upper end stop plate of the
inner mechanical framework; see Figur es 2, 6 and 7. A
hole is drilled through the upper end stop for the wire
which is fastened to the top of the translator; see Figure
6. The sensor is protected from large vibrations by the
use of a rubber damper. An in-depth presentation of the
entire draw-wire sensor measuring system including cali-
bration, accuracy and noise analysis was presented in
Strömstedt et al. [30].
C. Strain gauges. WEC L2 was provided with strain
Figure 6. The draw-wire sensor on top of the upper end
stop and the attachment of the wire to the top of the trans-
lator.
Figure 7. The positions of the draw-wire sensor, the strain
gauges SG3 and SG13, and other important parts close by
the upper end stop and at the top of the translator in L2.
gauge circuits for measuring bending strain on the cap-
sule wall and for measuring uni-axial strain in the inner
framework structure. In this paper two of the eleven
strain gauge circuits (SG) are singled out to represent the
typical strain gauge signal content in the inner and outer
WEC structure.
SG 13 is a 2-active-gauge system for bending strain
measurement with two resistive strain gauges from
Kyowa, KFN-5-350-C9-16, mounted inside the capsule
on opposite sides with a separation of 180˚; see F igur es
7 and 8. SG 3 is a strain gauge circuit of an active-
dummy 2-gauge system mounted on the corner pillar of
the inner framework close to the upper end stop; see
Figures 7 and 8.
When the WEC is under working load and the transla-
tor moves up and down stress occurs in the capsule and
inner framework structure. The strain gage amplifying
electronics has two major design parts. The first one is
the discrete amplifier placed close to the strain element
amplifying the differential signal from the measurement
bridge.
This signal was sent to an instrument amplifier inside
the WEC that increased the gain even more before the
signal was transmitted to the substation and sampled by
the PAC together with all other measurements.
The set-up of strain gauges in L2, calibration, accuracy,
formulas for calculating the strain and measurements
have been presented in-depth in Savin et al. [18,19].
D. Search coils. The magnetic flux in the air-gap be-
tween stator and translator is measured with a so-called
search coil (SC) [31]. A SC is a passive inductive sensor
composed of a single coil. It measures the induced elec-
tromotive force (EMF) in a closed loop equal to the neg-
ative time derivate of the enclosed magnetic flux (Ф).
The SCs used in L2 is designed on a two layer printed
circuit board (PCB) with ten turns on every side. 8 SCs
were installed in L2. SC 5 was selected to represent the
typical signal measured by the SCs as the translator re-
ciprocates in the generator; see Figure 9. The SC signal
is amplified with a factor 20.8 in the WEC and transmit-
ted through the data acquisition system.
SC 5 is positioned in the vertical middle position and
closed by the horizontal edge of one of the 4 stator sec-
tions; see Fig ure 9. The search coil design, calibration,
set-up in L2, accuracy and time domain measurements
Figure 8. The position and mounting of SG 3 and SG 13 in
L2.
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Figure 9. The position of SC 5 in the air gap of one of the 4
stator sections in L2.
are further described in [28].
E. Force transducer. A force transducer from HBM,
U2B 200 kN, is used for measuring the axial force in the
buoy line with a frequency of 16 Hz; see Figure 10.
The cylindrical buoy attached to L2, weighing 2 tons,
with a diameter of 3 m and a height of 1.2 m has the
force transducer mounted underneath the buoy, between
a couple of chain links and the buoy line; see Figure 10.
The battery powered transducer is protected by a casing
and embedded in a polymer resin for protection. The
cables enter the buoy through a watertight rubber hose.
The signal is transmitted from an antenna on the buoy
through the GSM network with the use of a Mitec-Sate-
Lite60 data logger system and stored at the measuring
station. Since the buoy is moving relative to the ocean
floor, it is difficult to make a cable connection to the
substation. The communication of the axial force meas-
urements from underneath the buoy is made through the
GSM network and described in [32].
The force transducer measuring system has been de-
scribed including calibration and accuracy in Savin et al.
[18]. The axial force measurements indicate if an end
stop impact has occurred. Changes in the axial force may
affect the bending of the steel structures in the WEC and
cause possible vibrations.
F. Voltage and current measurements. The 3-phase
AC voltages from the WEC are measured in the substa-
tion, where also the currents are measured with hall cur-
rent transducers. Active AC power is studied in order to
draw conclusions on cogging frequencies. The WEC was
connected to 14.1 Ω air cooled DC loads onshore in the
May measurements and delta-connected to 12 Ω water
cooled dump loads close by the WEC in the August
measurements presented in this paper. The loads are per
phase. The sampling frequency for the power measure-
ments is 256 Hz for both measurements periods, which is
the same as the sampling frequency for the sensor meas-
urements inside the WEC. The voltage and current meas-
urements are presented in detail in Boström et al. [24,
33].
4. Theory
4.1. Signal Content and Noise
Inside the WEC the generator is running with a varying
Figure 10. (Left) The force transducer; (Right) The connec-
tion underneath the buoy with the force transducer encased
and sealed off in a soft polymer resin.
speed following the waves at the surface. In theory the
signals from the laser triangulation sensors and the other
sensors will be of a non-stationary continuous character:
Sine components with changing amplitudes and/or
changing frequencies, such as the signal content asso-
ciated with the ripples of cogging and the oscillating
motion of the translator following the varying ampli-
tudes and/or frequencies of the waves.
Random signals with statistical properties changing
with time, such as noise and disturbances within the
measuring environment and within the measuring
system.
Transients appearing with varying intervals and with
varying characteristics in time and frequency, such as
the signal content associated with the end stop im-
pacts.
The RMS noise and the signal-to-noise ratio (SNR) for
the laser triangulation sensors and the draw wire sensor
measurements have been investigated for a typical meas-
urement period in May and August without end stop im-
pact in [30]. A reference case from measurements with
the generator at a standstill on the 14th of October is pre-
sented in this paper for further information about the
noise characteristics.
4.2. Vibrations from Cogging
Mechanical vibrations in the WEC may influence sensor
output, especially for sensors measuring mechanical enti-
ties, such as the laser triangulation sensors measuring the
relative motion of the piston rod and the seal housing.
Cogging is a source of vibration in the generator. The
vibrations may influence the motion of the objects and/or
the sensors.
Cogging is the result of fluctuations in the electro-
magnetic force between the translator magnets and the
stator armature in the generator. It has been extensively
investigated in linear generators and motors; for example
in [34-40]. In conventional rotating permanent magnet
generators cogging is mostly referred to the interaction
between the edges of the magnets and the stator teeth at
the winding slots. At high speed the moment of inertia
will however filters out most of the effect of cogging
torque in conventional generators. In power production
with slow moving permanent magnet linear generators
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many poles are needed to compensate for the lack in ro-
tational speed. The translator moves in and out of the
stator instead of rotating inside it. This causes another
specific effect relating to cogging.
The most prominent cogging effect occurs when the
permanent magnets pass the longitudinal stator outlet
ends [40]. At the longitudinal ends of the stator the mag-
netic field density increase in the stator armature as the
magnets starts to slip out of the stator and the magnetic
circuit. A field concentration occurs at the edge causing a
pulsating attraction force in the air gap with every mag-
net that passes by. The pulsating force can be separated
into a normal and a tangential component. The long itu-
dinal end effect also propagates inwards in the stator af-
fecting the other magnetic circuits and cause electrome -
chanical force ripples throughout the machine. The nor-
mal force component attracts the translator towards the
translator and has been investigated at no load by Nilsson
et al. [39]. The tangential component counteracts the
axial force in the buoy line which emanates from the
waves pulling the buoy and the translator in the generator.
This pulsating cogging force results in vibration. The
magnitude of the cogging mainly depends on the geome-
try and strength of the magnets, the armature geometry
and the air gap width [34].
In L2 the translator is 1867 mm long. The stator is
1264 mm long. This means that the magnets will always
be moving past one of the stator outlet ends during op-
eration. In other words, as long as the translator is mov-
ing cogging will occur, however with low frequency to-
wards the end stops and no frequency at end stop stand-
still. The cogging frequency will vary with the speed of
the reciprocating translator as it moves with the varying
amplitude and frequency of the ocean waves. The char-
acteristic frequency (fcogging) is set by the magnetic pole
width (wpole) and varies with the speed of the translator
(vtranslator) according to Equation (1),
translator
cogging
pole
v
fw
=
(1)
Vibrations from cogging may propagate through the
WEC structure and the frequencies may be detected in
the different sensor measurements. The spectral content
from cogging will have a continuous distribution over a
certain bandwidth and be repeated over different har-
monics. With Equ a tion (1) it is possible to calculate the
instantaneous cogging base frequency in the generator
and compare it with the spectral content found in the
sensor measurements in a time-frequency analysis.
4.3. Vibrations from a Fluctuating Damping
Force
The interaction between the magnetic flux from the per-
manent magnets and the counteracting induced flux in
the armature from the currents in the winding cables re-
sult in a damping force in the air gap [21]. The force
counteracts the pulling force from the waves. Generally
when more power is generated with a certain load a
higher damping force affects the WEC. As a con se-
quence the translator speed is reduced and the system is
balanced.
In an ordinary 3-phase generator the phase voltages
balance each other, causing an even power output. In a
1-phase generator the power output will fluctuate with
the only phase present and consequently so will the
damping force. In a 1-phase generator the power and
damping force fluctuations inevitable cause vibrations.
The damping force can fluctuate if the voltages in a
3-phase generator are not balanced. In L2 the windings
were connected in an unintentional order with one phase
being phase-shifted 180 degrees creating what could be
called a 3-wire single phase or a quasi-one-phase gen-
erator. The unbalanced currents cause increased fluctua-
tions in the power and damping force which can be seen
in the power output fluctuations of L2.
The fluctuations in power and damping force shift
with the amplitude of the currents at the same pace as the
magnets pass by the windings. The base frequency for
the damping force fluctuations therefore has the same
frequency as the cogging, which is not so strange since
the two forces depend on the same magnetic flux from
the reciprocating translator magnets. The magnitude of
the damping force fluctuations depends on translator
speed, the electric load and how far out of the stator the
translator has moved. In the May measurements the gen-
erator was connected to a rectifier bridge, a capacitive
filter and resistive DC loads at 14.1 Ω. In the August
measurements the generator was delta-connected to a
purely resistive water cooled AC dump load nearby the
WEC with phase resistances of 12 Ω. These describe two
different load cases, a linear load case and a non-linear
load case, as described respectively in Waters et al. [20]
and Boström et al. [14].
Cogging and fluctuations in the damping force both
lead to vibrations which cause an unstable translator
motion. This and can potentially destroy the air gap by
causing wear on the mechanical parts [35]. Vibrations
may also increase wear on the sealing system in the pis-
ton rod mechanical lead-through transmission [27].
4.4. Vibrations from Interacting Lorenz Forces
Another frequency of vibration in the generator may
come from the Lorenz force interactions between the
cables inside the stator. These fluctuate with the fre-
quency of the electric circuit, which is half the cogging
frequency given in Equation (1). Thus two frequencies
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co-exist separated by a factor of 2. The vibrations from
the Lorenz forces come from inside the stator and may
propagate through the WEC structure and may be seen in
the sensor measurements.
4.5. Vibrations from End Stop Impact
End stop impact obviously happens less frequent and
may produce transients with a lot higher frequencies than
cogging, fluctuations in damping and Lorenz force inter-
actions. In higher sea states end stop impact may occur in
every wave period, while in smaller sea states it does not
have to occur at all.
The appearance of end stop impact in the laser sensor
measurements is investigated in the time domain and in
the frequency domain with short time Fourier transforms
(STFT) plotting the spectral content with a spectrogram.
4.6. Spectral Analysis with FFT
The spectral content in the laser triangulation sensor
measurements are investigated in the frequency domain
with Fast Fourier transform (FFT) and compared with the
spectral content in simultaneous measurements with other
sensors in the WEC and the measured active AC power.
The purpose is to try to separate vibrations in the sensor
signals from noise and to draw conclusions from com-
parison with the other sensors on the possible source of
the vibrations in the frequency domain and if and what
filtering is needed.
Frequency analysis using FFT is the most commonly
used method for constant bandwidth analysis [41]. The
FFT algorithm in Matlab calculates the discrete Fourier
transform (DFT) described in [42]. The FFT algorithm in
Matlab is used to find the spectral content in the sensor
measurements within a selected measurement period.
The methods for obtaining the spectral content are
well known and explained in [42]. In this paper the spec-
tral intensity is given as log of FFT magnitude. The re-
sulting decibel level in a power spectrum is exactly the
same. The interest lies in the comparison between fre-
quencies and relative amplitudes, not absolute amplitudes.
Reference levels for the spectra are therefore not neces-
sary. The FFT of the measured data is carried out with
the parameters given in Table 1.
The frequency spacing (or resolution) in the FFT de-
pends on the sample size N and the sampling period, Ts.
Ts is determined by the sampling frequency of 256 Hz
and N by the selected measuring period of 8.5 s.
The force transducer output is not suitable for spectral
analysis since it is sampling with such a low frequency.
In fact it is under sampling with regard to the cogging
frequency, and show a lot of aliasing, which can be spot-
ted in the time domain comparisons.
Table 1. FFT parameters used in the spectral analysis of the
measurements in May and August (excl. the force trans-
ducer).
Parameter Notation Value
Time domain
Sample interval Ts 3.90625 μs
Sample size N 2177
Sample length (N 1)∙Ts 8.5 s
Frequency domain
Frequency spacing fs = 1/NTs 0.1176 Hz
Spectrum size N components 2177
Max. frequency (N/2)∙fs = Fmax 128 Hz
Frequency period Fp = Nfs 256 Hz
4.7. Time-Frequency Analysis with STFT
Spectrograms are plotted of the laser triangulation sensor
measurements to measure the frequency information over
time, using the joint time-frequency functions in the
Matlab STFT algorithm. The Hamming window is used
in Matlab. The spectrograms are mainly presented to
display the changes in spectral content and the differ-
ences between normal operation and what happens at end
stop impact. The laser triangulation sensor measurements
are analyzed with STFT and correlated with the instan-
taneous cogging frequency calculated with the speed of
the translator as measured by the draw-wire sensor in the
time domain.
5. Results
5.1. Sea States during Measurements
The wave height at the LRS is measured by a non-direc-
tional Datawell Waverider buoy. The buoy measures the
vertical surface displacement and sends the information
through radio link to the Sven Lovén Centre for Marine
Studies in Fiskebäckskil. The measurement frequency is
2.56 Hz. Spectral analysis is carried out onshore. The
overall accuracy of the buoy is 3.5% of the measured
value and the measuring system is presented in [11]. A
significant wave height (HS), a mean energy period (TE)
and a wave power density (J) are calculated as half-
hourly averages. In this paper, the first measurement pe-
riod is taken from measurements logged on the 28th of
May with a sea state characterized by HS = 1.6 m, TE =
5.7 s and J = 7.2 kW/m. The second measurement period
was logged on the 15th of August with a sea state of HS =
1.8 m, TE = 6.0 s and J = 9.5 kW /m.
5.2. Reference Signal and Estimation of Noise at
Standstill
The laser triangulation sensor measurements with the
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WEC at standstill separated from the buoy in October
after the experiment are shown in Figure 11. The laser
triangulation sensors show a rms noise level, i.e. ±1
standard deviation, between 0.0003 - 0.0008 mm, and a
peak-to-peak noise, representing 6 standard deviations of
0.002 - 0.004 mm. The measured objects still seem to os-
cillate slightly from the waves. This is possibly due to
wear on the sealing system.
5.3. Measurements in the Time Domain
The measurements in the time domain for 8.5 s from the
28th of May between 13:00:20-13:00:28.5 are shown in
Figure 12. 8.5 s represents a little more than a wave pe-
riod to show the typical sensor amplitudes at the given
sea state during a wave on the 28th of May without the
translator impacting on the upper or lower end stop. The
overall signal characteristics on the scale of a wave pe-
riod can thus be studied.
Close-ups of 1 second at a specific point in time be-
tween 22.5 - 23.5 s when the translator is ascending with
a constant speed of approx. 0.6 m/s, are shown in Figure
13. On the smaller time scale of a second the particular
relations in signal content, like frequencies and noise,
can be distinguished and correlated.
Output is presented from the laser triangulation sen-
sors, the draw-wire sensor measuring piston rod outside
length, SC 5, SG 3, SG 13, the force transducer and the
active AC power. The translator is in the middle position
when the piston is 1185 mm outside the seal housing (in
the water). The upper end stop compression spring does
not contact the translator until the piston has moved 2092
mm outside the seal housing and into the water. The
lower end stop compression spring contacts the translator
when the piston rod outside length is 295 mm. These
impacts are not happening during the wave period in
Figures 12 and 13. Figure 14 displays the sensor meas-
urements for an equally long time period of 8.5 s on the
15th of August. The Strain gauges did not function at this
moment in time and cannot be displayed for this time
period. The elevated noise levels in PRLS 1 - 3 and the
draw -wire sensor has already been explained in [30]. A
faulty ground in the underwater substation may be the
reason. It was corrected after the underwater substation
was picked up in June, fixed and re-launched a week
later.
The close-ups of 1 second in Figure 15 are taken from
Figure 14 between 20.7 - 21.7 s. It is important to point
out that the two measurement periods are taken with the
WEC connected to two different load cases described in
Section 4.3. This is the reason for the different generated
power visible in the active AC power output plots from
the WEC. However, the axial force in the buoy line is
Figure 11. Output and spectrum with FFT for the draw-wire sensor, PRLS 1 and SHLS 1 at generator stand still in October.
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Figure 12. Measurements from one wave period in the WEC in May 28, 13:00:20-13:00:28.5 from PRLS 1 - 3, SHLS 1 - 4, the
draw wire sensor, the force transducer, SG3, active AC power, SC5, and SG13.
comparable in magnitude and fluctuates similarly in both
cases. The average translator speed in Figure 13 is 0.6
m/s, while it is 0.7 m/s in Figu re 15. The higher transla-
tor speed consequently results in a higher average fre-
quency of 14 Hz for the cogging and fluctuations in
damping force as presented in Figure 15, compared to 12
Hz in Fig ure 13. The electric frequency of the currents in
both the May and the August measurements oscillate
with half the cogging frequency, which can be seen in the
output of the SC 5.
The search coils measure the passage of each perma-
nent magnet in the air gap. The magnetic field from the
strong magnets completely dominate the visible output in
the time domain. The force transducer is visibly under
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Figure 13. Measurements from 1 s in May 28, 13:00:22.5-13:00:23.5 from PRLS 1 - 3. SHLS 1 - 4, the draw wire sensor, the
force transducer, SG 3, active AC power, SC 5, and SG 13.
sampling and show aliases at 4 Hz in the May and 6 Hz
in the August measurements. The PRLS 1 - 3 have a visi-
bly lower noise level in August.
5.4. Measurements in the Frequency Domain
FFT calculations are performed in Matlab on the data
from both 8.5 s measurements in May and August to en-
able spectral analysis. Log of FFT magnitude in dB is
presented in order to display the relative intensities of the
different frequencies adding information to the time do-
main studied above. The results are presented in two
graphs with selected offset decibel values added to each
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Figure 14. Measurements from one wave period in August 15, 00:00:20-00:00:28.5 from PRLS 1 - 3, SHLS 1 - 4, the draw
wire sensor, SC 5, active AC power, and the force transducer.
curve for the purpose of not concealing each other. Cen-
tred moving averages with a sliding window of 9 fre-
quency spacings are superimposed on the spectra to clar-
ify the peaks. The spectra for the May measurements
are displayed in Figure 16 and for the August meas-
urements in Figu re 17. The Nyquist frequency is 128 Hz
for both cases. The data and the original units of meas-
urement for the different curves are found in Figures 12
and 14.
5.5. Measurements in the T ime-Frequency
Domain
Figure 18 presents time-frequency analysis on PRLS 3
and SHLS 3 for the measurements on the 28th of May
between 13:16:00-13:17:00 hours, incl. end stop impact.
Figure 19 presents the same analysis performed on data
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Figure 15. Measurements from 1 s in August 15, 00:00:20.7-00:00:21.7 from PRLS 1 - 3, SHLS 1 - 4, the draw wire sensor, SC
5, active AC power, and the force transducer.
from the 15th of August between 00:00:00-00:01:00
hours for PRLS 1 and SHLS 1, with two end stop im-
pacts. The sensor output and spectral content in Figu res
12-17 show that PRLS 1 - 3 and SHLS 1 - 4, respectively,
contain more or less the same signal and noise character-
istics. In the continued time-frequency analysis with
STFT only one sensor from each group needs to be used
for calculating the representative power spectral density
for the sensor groups. The selected sensors measure in
the directions of the incoming waves at the particular
times in question and will therefore be the sensors with
the largest output within each group of sensors.
The sensor output is first presented in the time domain
over one minute of sampling for both May and August. A
centred moving average (CMA) with a window of 51
samples is applied to the May measurement with PRLS 3;
see superimposed red line in Figure 18. Two graphs
showing the power spectral density is then plotted
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Figure 16. Magnitude spectra for PRLS 1 - 3. SHLS 1 - 4,
SG 3, SG 13, SC 5, the draw-wire sensor, and measured
active AC power for a measurement period of 8.5 s on May
the 28th between 13:00:20-13:00:28.5 hours.
underneath. The first covers up to the Nyquist frequency
of 128 Hz. Below that a close-up displays the power spec-
tral densities within the cogging bandwidth in greater
detail. The same is performed for SHLS 3 in May and
SHLS 1 in August and presented PRLS 3 and 1 in Fig-
ures 18 and 19 respectiv e ly.
Figure 17. Magnitude spectra for PRLS 1 - 3, SHLS 1 - 4,
SC 5, the draw-wire sensor and measured active AC power
for a measurement period of 8.5 s on August the 15th be-
tween 00:00:20-00:00:28.5 hours.
STFT in Matlab is used with a Hamming window with
NFFT length of 145 for the PRLSs and 250 for the
SHLSs. NFFT is a value for setting the spectral reso lu-
tion. A higher value has a smoothing effect on the output
due to increased window overlaps.
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Figure 18. Measurements on May 28th between 13:16:00-13:17:00 hours. PRLS 3 for 60 s in the time domain. Power spectral
densities for PRLS 3 up to the Nyquist frequency followed by a close-up of the cogging bandwidth. SHLS 3 for 60 s in the
time domain followed by power spectral densities for SHLS 3 up to Nyquist frequency and a close-up of the cogging band-
width. The instantaneous cogging frequency and piston rod outside length measured by the draw-wire sensor. End stop im-
pact occurs after 46 s.
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Figure 19. Measurements on August 15th between 00:00:00-00:00:01 hours. PRLS 1 for 60 s in the time domain. Power spec-
tral densities for PRLS 1 up to the Nyquist frequency followed by a close-up of the cogging bandwidth. SHLS 1 for 60 s in the
time domain followed by power spectral densities up to the Nyquist frequency and a close-up of the cogging bandwidth. The
instantaneous cogging frequency and piston rod outside length measured by the draw-wire sensor. End stop impact occurs
after 17 s and 31 s.
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Piston rod axial displacement, which with and offset
correlates to translator position, is presented at the bot-
tom of Figures 18 and 19. In this section the position is
foremost used to display the end stop impacts, but also to
give information about the position of the transmission
and translator during operation. When the piston rod out-
side length is 1185 mm the translator is in its vertical
middle position with the centre in the middle of the stator.
When the translator hits the upper end stop the piston rod
outside length is 2335 mm. The lower end stop is im-
pacted on when the piston rod has a 125 mm outside
length. The sampled measurements include one upper
end stop impact in May at 46 s and two end stop impacts
in August at 17 s and 31 s.
The power spectral densities for the different frequ en-
cies may be compared with the instantaneous cogging
frequencies, based on the translator speed and the mag-
netic pole width; see Equation (1) in Section 4.2. The
translator speed is calculated by Newton’s difference
quotient to find the derivatives of the axial piston rod
displacement. A least squares method with a linear fit
and a window of 51 samples sweeping the measurements
of the piston rod outside length is applied. In May the
piston rod outside length is represented by a CMA cal-
culated with a sweeping window of 101 samples, due the
increased noise level.
The next step is to calculate the instantaneous cogging
frequency by dividing the translator speed with the mag-
netic pole width of 50 mm and turning the amplitudes
into magnitude by using the absolute value. The resulting
instantaneous cogging frequency is displayed in the sec-
ond graph from the bottom in both Figures 18 and 19.
The peaks in cogging frequency do not seem to be af-
fected by the selected windows sizes, just the overall
smoothness is visibly affected.
5.6. Close Up of End Stop Impact in the Time
Domain
In order to suggest a suitable filter for further studies
with calculations of the macro displacements in the me-
chanical lead-through transmission a comparison be-
tween 5 filters is presented in Fig ur e 20. The inverse
FFT is a mathematical filter with an ideal response func-
tion separating all frequencies above the cut-off fre-
quency, which is useful to investigate what signal may
contain in the time domain with a limited number of ac-
cepted frequencies. In post-measurement signal process-
ing it is possible to use the ideal inverse FFT (IFFT)
low-pass filter with a chosen cut-off frequency. The
CMA filters with a window of 51 samples have been pro-
posed and motivated in [30].
The results in Figure 20 show that continued use of
the CMA filter is adequate for evaluating the larger mo-
tions without excluding too much information or cutting
Figure 20. Close-up of output from PRLS 3 at end stop impact with different IFFT filters and a CMA filter applied on the
May measurements.
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of peaks too much, even though vibrations should be
further investigated by other means and treated sepa-
rately if those were in focus for the study. Figure 21 in-
dicates that a smaller CMA window of 21 samples would
follow the steepest gradients more precisely. However,
with more noise it is not necessarily better for the inves-
tigation. The smoothing aspect is important in order to
give a meaningful content to the measurements when
they are combined to calculate the tilt angles and azimuth
angles of the measured objects. The results from Figures
18 and 19 suggest that an ideal low-pass filter would not
be able to include all vibrations and separate the noise at
the same time for a more meaningful study of the relative
displacements since the vibrations are spread out over
such a wide band at end stop impact. However, the CMA
filter responds well to the shifting magnitudes. It is thus
concluded that a CMA filter suits the data from the laser
triangulation sensors for further investigations into the
results with regard to performance of the mechanical
device.
6. Discussion
The aim of the paper is to investigate the signal and
spectral content in the time and frequency domain, to
investigate vibrations and noise, and to find a suitable
filter for further refinement of the signal to separate noise
from actual physical displacement.
Normally the currents, voltages and flux waves in a
3-phase generator balance each other and superimpose to
create a smooth resulting armature flux with a smooth
damping force. However, in WEC L2 one of the phases
were unintentionally phase shifted 180 degrees creating a
combined unbalanced quasi 1-phase voltage. The result
Figure 21. Close up of two CMA filters with different win-
dow size at end stop impact in the August measurement.
was a generator with increased fluctuating damping force
at the same frequency as the cogging, resembling that of
a 1-phase generator.
If we have the generator connected to a purely delta-
connected resistive load the cogging is more pronounced,
than if it is connected to a non-linear load case with a
rectifier, capacitive filter and a DC load, as described in
[14]. The damping force is affected by the smoothing
from the capacitive filter. The capacitors discharge main-
taining the power for short time intervals when the WEC
is connected to the DC load like a pressure accumulator
in a hydraulic system. It evens out the fluctuations in the
damping load as the WEC is disconnected from the load
by the rectifiers at lower production levels.
Theoretically the cogging bandwidth starts at very low
frequencies from translator standstill and increase up to
approximately 20 Hz. However, the cogging is most
pronounced between 5 and 20 Hz. which has to do with
the translator quickly picking up speed and maintaining it
rather constant throughout each half cycle between the
turning points. The reason for this has to do with the
non-linear loading case. The electrical frequency of the
generator is directly proportional to the speed of the
translator. Maximum power is achieved during minimum
and maximum line force assumed with generator stroke
length. When the translator changes its direction it
changes the phase order of the 3-phase voltage. With the
generator connected to a non-linear load case the control-
ling DC-level, after the diode rectifiers, limits the trans-
lator speed to some extent and makes it more constant. If
the translator speed is low, inducing a no-load voltage
below the DC-voltage level, no power is extracted and
the speed of the translator is allowed to increase without
damping. This explains the form of the power curves in
May and the reason for the appearance of the cogging
plateau.
The amplitude of the fluctuating damping force de-
pends on the number of poles activated inside the stator,
which in turn depends on how far out of the stator the
translator has moved. The cogging force at the longitu-
dinal outlet ends of the stator will mainly be affected if
the translator leaves one of the outlet ends of the stator.
The speed of the translator varies and the number of
poles inside the stator decrease towards the end stops.
Both frequency and amplitude of the vibrations from
cogging and fluctuating damping force decrease towards
the end stops. This can be seen in the time domain in
Figures 12 and 14 and is also visible in the spectrograms
of Figures 18 and 19.
Increased induction occurs at elevated translator speed.
At 26 s, in the May measurements of Figure 12, the
translator drops down as the axial buoy line force reaches
almost 0 kN. Overall increased mechanical vibrations
can be seen in the measurements from PRLS 1 - 3, SHLS
E. STRÖMSTEDT ET AL.
Copyright © 2013 Sci Res. EPE
88
1 - 4, SG 3 and SG 13 at this point in time. At a constant
translator speed of 0.6 m/s the damping fluctuations and
cogging coexist at 12 Hz; see Figure 13. The same fre-
quency can also be seen in the active AC power.
The overall cogging bandwidth can be seen in the ac-
tive AC power in Figure 16. It can be compared with the
peaks in the laser triangulation sensor output. The cog-
ging frequencies are apparent there, specifically at 18 Hz
corresponding with the largest peak in the power curve.
18 Hz corresponds to a translator speed of 0.9 m/s.
Cogging occurs over a bandwidth, during measure-
ments for more than a second, and in the spectral analysis.
The peak at 18 Hz and the multiple harmonics thereof are
clearly seen in the laser triangulation sensor measure-
ments. In the time domain, in Figu res 13 and 15, the
cogging frequency can be seen in the laser triangular-
tion sensor measurements at 12 and 14 Hz, respectively,
for the two cases presented. These values correspond to a
translator speed of 0.6 and 0.7 m/s and correlate well
with the oscillations in the active AC power with the
peaks between 5 - 20 Hz in Figures 16 and 17. In Figu re
17 for the August measurements the frequencies are there
but not at all as apparent as in May. However the fluctua-
tions can be seen in Figure 15 .
The results in Figure 13 show that SG 3 and SG 13
oscillate at half the cogging frequency, i.e. 6 Hz at a con-
stant translator speed of 0.6 m/s. This is the frequency of
the electrical circuits and the magnetic circuit at this par-
ticular translator speed. It can be concluded that the
source is the Lorenz forces between the cables in the
stator. Peaks are seen in Figure 16 at the bandwidth of
the SC 5 measurements. SC 5 keeps absolute track of the
magnets passing by the sensor. The signal oscillates at 6
Hz. The cogging frequency, which is twice the frequency
of the Lorenz forces can thereby be verified at this speed.
The Lorenz forces spread to all sensors, but the cogging
do not seem to reach the inner frame work or the capsule.
The Lorenz forces in the stator are possible to detect
with SG 3 and SG 13. The vibrations propagate through
the inner framework and over to the capsule. The inner
framework is almost completely separated from the cap-
sule apart from four horizontal and rectangular plates
nearby the upper end stop. These plates are mainly in-
tended for internal support when the WEC is lying down
during transportation. They do not carry any mechanical
load during operation apart from when bending of the
capsule and superstructure might subject them to buck-
ling as large waves pull the buoy line hard towards the
guiding funnel. Nevertheless, vibrations are apparently
transmitted through them from the stator through the
inner framework to the capsule.
The oscillations in the PRLS 1 - 3 measurements in
May indicate that the vibrations in the moving translator
from cogging and fluctuating damping force propagate
through the piston rod and into the seal housing via the
sealing components. The vibrations may be transmitted
through the double hinged link and up through the piston
rod, but the rubber gasket suspending the seal housing
isolates the top plate from the vibrations, since the cap-
sule strain gauge do not pick up the cogging frequency.
The Lorenz forces in the stator also seem to reach the
laser triangulation sensor measurements somewhat.
The vibrations from cogging and fluctuation in the
damping force seem to be generally higher in August.
The cogging was most pronounced within the bandwidth
of 5 to 20 Hz. This can be seen in the spectrograms
comparing Figures 18 and 19. The frequencies with high
relative spectral density seem to coincide rather well with
the cogging frequencies. The laser triangulation sensor
output in the time domain show such a large increase in
relative displacements in August compared to May, that
the vibrations do not seem larger in August. However,
since the amplitudes of the signal are so much higher the
impression is false. They do show larger vibration am-
plitudes in August. Looking at the displacement scale
and comparing with the spectral densities displayed in
Figures 18 and 19 it becomes evident. It is possible to
see that the PRLSs vary most in amplitude in the time
domain in Figure 15 compared to the SHLSs. The dis-
tance scales along the Y-axes are the same. The reason
for this may be that speckle occur more on the more pol-
ished surface of the piston rod.
In August the generator is directly delta-connected to a
water-cooled resistive dump load close by the WEC. This
results in more cogging which can be seen in the time
domain. The frequencies in August are more arbitrary
than in the May measurements. It may be increased wear
that explains it. This is supported by the spectral analysis
in Figure 17, showing smaller peaks for the cogging and
electrical circuit frequencies in August and smeared out
and elevated relative intensity levels across the board in
lower regions compared to the left image for May. In
Figures 12 and 14 the WEC is affected by a similar wave
with a similar axial force in the buoy line. The power
level in August is the same as in May on the upstroke,
but much lower compared to May on the down stroke,
which should result in less vibration magnitudes in the
WEC overall in August, when comparing Figure 16 with
17. The sensors do however detect more vibrant motion
in the mechanical lead-through in August, which may be
connected to wear. The vibrations themselves do have a
detrimental effect on the sealing system and result in
more wear. The time-frequency analyses shows more
cogging and more vibrations in August, which probably
comes from wear on the mechanical parts and in the me-
chanical-lead -through transmission.
A slight outstretched plateau is identified within the
cogging bandwidth for the seal housing in the late meas-
E. STRÖMSTEDT ET AL.
Copyright © 2013 Sci Res. EPE
89
urements in August. The explanation is suggested to be
attributed to the friction between the piston rod and the
seal housing in combination with an increased play be-
tween the seal housing and piston rod. Post-experimental
inspection of the sealing system in L2 indicates general
wear in all direction but most prominently in the direc-
tion of the predominant incoming waves.
The PRLS and SHLS measurements support the state-
ment that the laser sensor set-up rig is adequately stabile
for measuring the relative displacement of the piston rod
and seal housing. The sensors do not seem to move with
the cogging frequency or the frequency would not be
picked up by the sensors. There does not seem to any
other common frequency for the PRLSs and SHLSs that
could be attributed to an Eigen-frequency (or resonance
frequency) of the set-up rig. The source of vibrations
from cogging is quite far away from the location of the
laser sensor set-up rig. The path is long and the possible
attenuation of vibrations along the way is good enough to
suggest a negligible influence on the laser sensor set-up
rig. The seal housing is isolated from the capsule top
plate by a rubber gasket. Any vibration transmitted from
the piston rod to the seal housing would be attenuated by
the dampening rubber gasket. The cogging frequencies
are not transmitted through the rubber gasket and into the
top plate, which can be verified but checking the data for
SG 13. If for instance the sensors were to vibrate in uni-
son with the measured objects they would have problems
detecting cogging, which was not the case. The results in
Figures 12-19 support the notion that the sensor set-up
rig has a structural integrity with regard to the vibrations
in the WEC.
Other sources of vibrations in the WEC are the fric-
tional interface between the buoy line and the funnel at
the top of the super structure and between the yoke type
track rollers on the translator and inner framework. These
are difficult to detect since the characteristic base fre-
quency is unknown and might be changing all the time
with translator position and speed. The rubber gasket
isolates the seal housing and piston rod from being af-
fected by vibrations emanating from the outer WEC
structure, such as the funnel. The slamming of the trans-
lator against the end stops will of course generate mas-
sive vibrations but only as occasional transients. This
may have implications on the choice of filter.
7. Conclusions
The time and frequency analysis for the different sensors
show variations in content relating to the position where
they are mounted. The laser triangulation sensors detect
cogging frequencies and the frequency from the Lorenz
forces in the stator. The strain gauges only detect the
Lorenz forces.
The cogging frequencies appear within the bandwidth
from 5 to 20 Hz, varying with translator speed. The cog-
ging is most apparent in the active AC power spectral
content, as expected. The search coil sensors measuring
the air gap detects the magnetic circuit frequency, which
coincides with the frequency of the Lorenz forces within
the stator. The vibrations from the Lorenz forces propa-
gate through the inner framework and out through the
capsule.
The spectral peaks are most prominent in May for the
laser triangulation sensors. A slight plateau can be dis-
tinguished in August but the signals are contaminated by
wear oriented frequencies with arbitrary spectral distri-
bution.
The seal housing is isolated from the outer WEC struc-
ture by a rubber gasket. The vibrations from the outer
structures do not propagate to the seal housing and vice
ver sa.
The conclusion from analysis with different filters is
that a moving average with a window of 21 to 51 may
very well be adequate for the continued analysis of tilt
angles and azimuth angles when combining the meas-
urements from the different laser triangulation sensors.
The structural integrity of the sensor set-up has been
verified on a micro measurement level and vibrations do
not seem to be a problem for evaluating the performance
of the piston rod mechanical lead-through.
8. Acknowledgements
This paper is the product of research carried out within
the Lysekil project. The authors are affiliated with the
Swedish Centre for Renewable Electric Energy Conver-
sion at Uppsala University in Uppsala, Sweden. The re-
search is supported by The Swedish Energy Agency.
VINNOVA, Statkraft AS, Vattenfall AB, Fortum OY,
Falkenberg Energy AB, Helukabel, Draka Cable AB, Pro
Enviro, Seabased AB, The Gothenburg Energy Research
Foundation, The Göran Gustavsson Research Foundation,
Ångpanneföreningen’s Foundation for Research and De-
velopment, The Olle Engkvist Foundation, The J. Gust.
Richert Foundation, CF Environmental Fund, Vargöns
Research Foundation, The Swedish Research Council
grant No. 621-2009 -3417 and the Wallenius Foundation.
Fredrik Bülow, Kalle Haikonen and Venugoplan Kuru-
path are thanked for their knowledge in Matlab and for
fruitful discussions.
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