To Erik
List of Papers
This thesis is based on the following papers, which are referred to in the text
by their Roman numerals.
I
II
III
IV
V
VI
VII
VIII
Leijon, M., Boström, C., Danielsson, O., Gustafsson, S., Haikonen, K.,
Langhamer, O., Strömstedt, E., Stålberg, M., Sundberg, J., Svensson,
O., Tyrberg, S., and Waters, R., “Wave energy from the North Sea: experiences from the Lysekil research site” Surveys in Geophysics, Springer,
29(3):221–240, 2008.
Leijon, M., Waters, R., Rahm, M., Svensson, O., Boström, C., Strömstedt, E., Engström, J., Tyrberg, S., Savin, A., Gravråkmo, H., Bernhoff,
H., Sundberg, J., Isberg, J., Ågren, O., Danielsson, O., Eriksson, M.,
Lejerskog, E., Bolund, B., Gustafsson, S., and Thorburn, K., “Catch the
wave to electricity: the conversion of wave motions to electricity using
a grid-oriented approach” IEEE Power and Energy Magazine, 7(1):50–
54, 2009.
Waters, R., Rahm, M., Eriksson, M., Svensson, O., Strömstedt, E.,
Boström, C., Sundberg, J., and Leijon, M., “Ocean wave energy
absorption in response to wave frequency and amplitude - offshore
experiments on a wave energy converter” Conditionally accepted for
publication in IET Renewable Power Generation. Revision submitted
in December 2010.
Boström, C., Lejerskog, E., Stålberg, M., Thorburn, K., and Leijon,
M., “Experimental results of rectification and filtration from an offshore
wave energy system” Renewable Energy, 34(5):1381–1387, 2009.
Boström C., Waters, R., Lejerskog, E., Svensson, O., Stålberg, M., and
Leijon, M., “Study of a wave energy converter connected to a nonlinear
load” IEEE Journal of Oceanic Engineering, 34(2):123–127, 2009.
Boström, C., Lejerskog, E., Tyrberg, S., Svensson, O., Waters, R.,
Savin, A., Bolund, B., Eriksson, M., and Leijon, M., “Experimental
results from an offshore wave energy converter” Journal of Offshore
Mechanics and Arctic Engineering, 132(4):041103, 2010.
Boström, C., and Leijon, M., “Operation analysis of a wave energy
converter under different load conditions” Accepted for publication in
IET Renewable Power Generation, December 2010.
Leijon, M., Boström, C., Lejerskog, E., Rahm, M. and Svensson, O.
“A wave power unit”, International patent WO 2010/085188, published
2010-07-29.
IX Boström, C., Svensson, O., Rahm, M., Lejerskog, E., Savin, A., Strömstedt, E., Engström, J., Gravråkmo, H., Haikonen, K., Waters, R., Björklöf, D., Johansson, T., Sundberg, J., and Leijon, M., “Design proposal
of electrical system for linear generator wave power plants” Proceedings of the IEEE Industrial Electronics, IECON2009, Porto, Portugal,
PD-027448:4429–4434, 2009.
X Rahm, M., Boström, C., Svensson, O., Grabbe, M., Bülow, F., and Leijon, M., “Offshore underwater substation for wave energy converter arrays” IET Renewable Power Generation 4(6):602–612, 2010.
XI Svensson, O., Boström, C., Rahm, M., and Leijon, M. “Description
of the control and measurement system used in the low voltage marine
substation at the Lysekil research site” Proceedings of the 8th European
Wave and Tidal Energy Conference, EWTEC2009, Uppsala, Sweden,
pp. 44–50, 2009.
XII Boström, C., Rahm, M., Svensson, O., Strömstedt, E., Savin, A., Waters, R., and Leijon, M. “Temperature measurements in a linear generator and marine substation for wave power” Submitted to Journal of
Offshore Mechanics and Arctic Engineering, June 2010.
XIII Rahm, M., Svensson, O., Boström, C., Waters, R., and Leijon, M. “Experimental results from the operation of aggregated WECs” Submitted
to IET Renewable Power Generation, December 2010.
XIV Boström, C., Ekergård, B., Waters, R., Eriksson, M., and Leijon M.
“Linear generator connected to a resonance circuit” Submitted to Renewable Energy, January 2011.
Patents pending, not official.
XV
Leijon, M., Boström, C., and Eriksson, M., “Resonance circuit” Patent
submitted to PCT/EPO, PCT/SE2010/051356, 2010-12-09.
Other contributions of the author, not included in the thesis.
Lundin, J., Goncalves, J., Boström, C., Yuen, K., Kjellin, J., Rahm, M.,
Bernhoff, H., and Leijon, M., “Dynamic stability of a generation system
based on renewable energy” Submitted to the 21st International Conference and Exhibition on Electricity Distribution, CIRED2011, Frankfurt,
Germany, 6–9 June 2011, January 2011.
XVII Savin, A., Svensson, O., Strömstedt, E., Bolund, B., Boström, C., and
Leijon, M. “Determining the service life of a steel wire under a working load in the wave energy converter (WEC)” Proceedings of the ASME
28th International Conference on Ocean, Offshore and Arctic Engineering, OMAE2009, Honolulu, Hawaii, OMAE2009-79164, 2009.
XVIII Tyrberg, S., Stålberg, M., Boström, C., Waters, R., Svensson, O.,
Strömstedt, E., Savin, A., Engström, J., Langhamer, O., Gravråkmo,
H., Haikonen, K., Tedelid, J., Sundberg, J., and Leijon, M., “The
Lysekil wave power project: Status update” Proceedings of the 10th
XVI
World Renewable Energy Congress (WRECX), Glasgow, UK, pp.
1061–1066, 2008.
XIX Rahm, M., Boström, C., Svensson, O., Grabbe, M., Bülow, F., and Leijon, M., “Laboratory experimental verification of a marine substation”
Proceedings of the 8th European Wave and Tidal Energy Conference,
EWTEC2009, Uppsala, Sweden, pp. 51–58, 2009.
XX Boström, C., Lejerskog, E., Tyrberg, S., Svensson, O., Waters, R.,
Savin, A., Bolund, B., Eriksson, M., and Leijon, M., “Experimental
results from an offshore wave energy converter” Proceedings of the
ASME 27th International Conference on Ocean, Offshore and Arctic
Engineering, OMAE2008, Estoril, Portugal, OMAE2008-57415, 2008.
XXI Boström, C., Rahm, M., Svensson, O., Strömstedt, E., Savin, A., Waters, R., and Leijon, M., “Temperature measurements in a linear generator and marine substation for wave power” Proceedings of the ASME
29th International Conference on Ocean, Offshore and Arctic Engineering, OMAE2010, Shanghai, China, OMAE2010-20881, 2010.
Reprints were made with permission from the publishers.
6
Contents
1
2
3
4
5
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1 Ocean waves – a source of energy . . . . . . . . . . . . . . . . . . . . . .
1.2 Wave energy technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Wave energy system developed at Uppsala University . . . . . . .
1.3.1 Wave energy converter . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.2 Conversion and transmission system . . . . . . . . . . . . . . . .
1.3.3 Generator connected to different loads . . . . . . . . . . . . . . .
1.3.4 Theses published by the wave power group . . . . . . . . . . .
Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1 Waves and wave energy spectrum . . . . . . . . . . . . . . . . . . . . . .
2.2 Generator theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Electromagnetic field theory . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Equivalent circuit model . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Forces acting on the generator and the damping function . . . . .
2.4 Generator connected to different loads . . . . . . . . . . . . . . . . . . .
2.4.1 Resistive load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.2 Diode rectifier, filter and actively controlled DC-voltage
loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.3 Resonance circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The Lysekil research site . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1 Biology buoys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Observation tower . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Wave measuring buoy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Wave energy converters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5 Marine substations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6 Measuring station and grid connection point . . . . . . . . . . . . . .
Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1 Modelling of generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1 Voltage and current measurements . . . . . . . . . . . . . . . . . . . . . .
5.2 Calculation of power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Generator connected to resistive load . . . . . . . . . . . . . . . . . . . .
5.4 Generator connected to diode rectifier and filter . . . . . . . . . . . .
5.4.1 Design of filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5 Generator connected to actively controlled DC-voltage . . . . . .
5.6 Generator connected to resonance circuit . . . . . . . . . . . . . . . . .
17
17
17
20
21
22
23
24
25
25
26
27
28
29
30
30
30
33
39
41
42
43
43
46
47
51
51
53
53
54
55
56
57
58
59
6
Summary of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1 Generator connected to resistive load . . . . . . . . . . . . . . . . . . . .
6.2 Generator connected to diode rectifier and filter . . . . . . . . . . . .
6.3 Generator connected to actively controlled DC-voltage . . . . . .
6.4 Generator connected to resonance circuit . . . . . . . . . . . . . . . . .
7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.1 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2 Generator connected to resistive load and DC-voltage loads . . .
7.3 Limitations in power absorption . . . . . . . . . . . . . . . . . . . . . . . .
7.4 Resonance circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.5 Simulated results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10 Summary of Papers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11 Svensk sammanfattning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
61
61
63
66
68
73
73
74
75
77
77
79
81
83
91
95
97
Nomenclature
A
Aabs
A f ac
B
C, CDC
CC
cg
D
Db
E
Ei , ei , ea , eb , ec
f
Fb
Fem
Fes
Fs
g
H
h
H
Hm0 , HS and H1/3
i
iain , ibin , icin
iDC
J
[m2 ]
[%]
[T]
[F]
[F]
[m/s]
[C/m2 ]
[m]
[V/m]
[V]
[Hz]
[N]
[N]
[N]
[N]
[m/s2 ]
[m]
[m]
[A/m]
[m]
[A]
[A]
[A]
[W/m]
Cross-sectional area
Absorbed power
Active stator area
Magnetic flux density
Capacitance
Sea cable capacitance
Group velocity
Electric displacement field
Diameter of buoy
Electric field
internal EMF or no-load voltage
Frequency
Buoy force
Electromagnetic force
End stop force
Spring force
Acceleration due to gravity
Wave height
Water depth
Magnetizing field
Significant wave height
Current
Incoming current
Current in DC-load
Wavepower level or power density
j
l
LC
LS
m
mn
N
P
Pabs , PG_res , PG_re f
PDC
Pin
PL_res , PL_re f
Ploss
Pmax
Pout
PRC
PRG
Q
r
R0
RC
Ri
RG
RDC , RL
RPE
S( f , θ )
t
t0 , ts
TE , Tm0−1
TZ , T02
Vd
vD
vDC , VDC , vL
vin
vain , vbin , vcin
[A/m2 ]
[m]
[H]
[H]
[kg]
varies
[W]
[W]
[W]
[W]
[W]
[W]
[W]
[W]
[W]
[W]
[m]
[Ω]
[Ω]
[Ω]
[Ω]
[Ω]
[Ω]
[m2 /Hz]
[s]
[s]
[s]
[s]
[V]
[V]
[V]
[V]
[V]
Free current density or electric current density
Length
Sea cable inductance
Generator synchronous inductance
Mass
Spectral moment
Number of turns
Power
Absorbed power
Power in DC-load
Incoming power or power in resistive load
Power in load
Resistive power losses in sea cable and generator
Maximum power
Power out from generator
Resistive power losses in sea cable
Resistive power losses in generator
Quality factor
Radius of buoy
DC-resistance
Sea cable resistance
Internal resistance of switching device
Generator resistance
Load resistance
Power electronic resistance
Directional wave spectra
Time
Time when diodes stop and start conducting
Mean energy period
Zero-upcrossing period
Line-to-line voltage rms
Voltage drop over diode
Voltage over load
Segments of three phase voltages
Incoming voltages
VW EC
wp
x
Zeq
α
γ
λ
ω
ω0
Φ
ρ
ρc
ρr
θ
ξ
[V]
[m]
[m]
[Ω]
[Np/s]
[Ns/m]
[m]
[rad/s]
[rad/s]
[Wb]
[kg/m3 ]
[C/m3 ]
[Ωm]
Degrees
Controlled DC-voltage
Pole width of magnets
Translator position
Equivalent impedance
Damping ratio
Damping function
Wave length
Angular frequency
Resonant frequency
Magnetic flux
Density
Charge density
Resistivity
Direction
Damping factor
Abbreviations
AC
D
DC
EMF
FEM
FPGA
HF
IGBT
KCL
KVL
L1–L9
MOSFET
OWC
PAC
PWM
WEC
WEP
Alternating Current
Diode
Direct Current
Electromotive force
Finite Element Method
Field Programmable Gate Array
High Frequency
Insulated Gate Bipolar Transistor
Kirchhoff’s Current Law
Kirchhoff’s Voltage Law
Refers to WEC 1–9 installed at Lysekil
Metal Oxide Semiconductor Field Effect Transistor
Oscillating Water Column
Programmable Automation Controller
Pulse Width Modulation
Wave Energy Converter
Wave Energy Plant
13
Preface
Converting the energy in ocean waves into usable electric power is not trivial.
At the Division for Electricity, Uppsala University, a team of scientists are
working together in the wave power research field. Today, there are 15 PhD
students working in the team. The main goals with the research are to optimize
and develop the wave energy system further and to study the wave energy
project from an overall perspective, from the waves to the grid connection
point. Beside the main goals, all the PhD students have their own individual
goals with the research.
The aim of the work performed by the author has been to study what impact the electrical system has on the WEC performance and how the electrical
system could be designed. An electrical conversion system is needed between
the WEC and the grid. Depending on how the first conversion step is carried
out, converting a fluctuating AC into DC, the generator will be subjected to
different loads which affect the power production and absorption of the WEC.
Based on the results presented in this thesis, conclusions about system operation characteristics can be drawn and they can act as a foundation for future
system and WEC designs.
The aim of the following chapters is to give the reader a deeper understanding of the research presented in the appended papers and to present some of
the preparatory work made to achieve the results. The author also wishes to
give the reader an overall picture of the project and the work carried out by
the research group.
Previous work by the author was presented in a Licentiate thesis in 2009 [1].
A detailed study of the WEC connected to a diode rectifier and filter was made
in the thesis and the experimental set-up was described in detail.
15
1. Introduction
Since the late 19th century, the Western world’s society has been developed
into an infrastructure highly dependent on electric generation [2,3]. To ensure
the social welfare in the future, a central issue will be to secure a long-term
energy supply and energy production. Therefore, it has been important to find
efficient and environmentally friendly ways to utilize electric energy. This is
one of the reasons for the increasing use of sustainable energy resources for
electricity production [4]. One energy resource that can be seen as a sustainable energy source is the energy from the ocean waves.
1.1
Ocean waves – a source of energy
Ocean waves can be created in several ways. The source creating the waves
could for example be an earthquake, a ship or the tide. However, when studying wave energy, the ocean waves created by the winds, wind waves, are the
most important [5]. When the wind sweeps over the ocean surface some of its
kinetic energy is transferred to the ocean due to the friction between the wind
and the ocean surface. There are also pressure variations in the wind which
force the water particles into motion resulting in waves [6].
The potential of ocean waves for energy utilization is large, it has both a
high utilization factor and a high power density [7]. Fig. 1.1 shows a map
of how the wave-power level is distributed over the globe in kW/m crest
length. On an yearly average, the wave climate is estimated to be better on
the southern hemisphere because of its smaller variations in sea state, but on
a monthly basis, the northern and southern hemisphere can have similar sea
states [8]. The global power potential represented by waves is estimated to be
1–15 TW [9–11].
Technically, the potential available in Sweden is estimated to 5–10 TWh
annually [13] which can be compared to Sweden’s total electric energy consumption during one year, 144 TWh (2008) [14]. Additional reports about the
wave climate in Swedish waters can be found in [15, 16].
1.2
Wave energy technologies
Scientists have struggled for centuries to find a way to utilize the energy in the
oceans, and a series of different concepts have come up over the years. In connection with the oil crisis in the middle of the seventies, the research started
17
Figure 1.1: Estimated average annual power density of ocean waves expressed in
kW/m [12].
to emerge in Europe. However, in the middle of the eighties, several governments, the UK government amongst others, decided to stake only power
utilization projects with constructions rated 2 GW or more [17]. The consequence was that many smaller projects got funding problems and were forced
to phase out their research [8]. About 15 years later, research in the area started
to grow again, and today there are a number of different ongoing wave power
projects with representatives from all over the world [18]. In 2007, there were
approximately 75 different projects and around 16 of them had come to a full
scale prototype that had been tested in real sea conditions [19].
There are different proposals on how a WEC could be designed and which
kind of generator should be used [20]. A WEC could either operate offshore
or be a shoreline device. Today, the offshore market is predicted to have the
largest opportunities for expansion since shoreline devices are limited by the
low number of available sites and high installation costs [6]. Moreover, a WEC
can be grouped in different ways, see for example [11, 21–23]. One classification used is based on how the device utilizes its energy and is as follows:
OWC, overtopping devices and wave activated bodies, see Fig. 1.2.
An OWC consists of a chamber with an open bottom. The incident waves
will force the water in the chamber to rise and fall which compresses and
expands the air in the chamber, Fig. 1.2a. The energy is extracted from the airflow using a unidirectional air turbine. Two devices based on this technology
are further described in [24, 25].
The operation of an overtopping device is similar to the technique used in
a hydropower plant. The devices use a reservoir at a higher level than the
surrounding sea level. The reservoir is filled with water by the waves and the
water is led back to the ocean via a turbine. The principle is illustrated in Fig.
18
a)
Turbine
b)
Reservoir
Air
Turbine
c)
Heaving
Pitching
Surging
Figure 1.2: Schematic of different operating principles divided into a) OWC, b) overtopping devices and c) wave activated bodies.
1.2b. Wave dragon [26] and the Sea-wave Slot-cone Generator (SSG) [27] are
two examples of overtopping devices.
The last group, wave activated bodies or oscillating bodies, use one or several of the oscillating motions in the waves to run a generator. Alternatively,
the energy can be extracted first by using a hydraulic system. The system can
have two moving parts moving relative to each other, or one moving body
that moves relative to a fixed reference. Wave activated bodies are often classified according to how their power take-off moves in the water, i.e. if they
have a pitching, surging or heaving motion, see Fig. 1.2c. One example of a
pitching system is Pelamis1 . The device consists of cylindrical bodies that are
connected by hinged joints. The wave motion will get the joints to pump high
pressure fluid through a hydraulic motor, which in turn drives an electric generator. WaveRoller2 is a device using the surging motion of the oceans. The
power take-off device is a vertical plate placed on the seabed. The plate will
get a surging motion by the waves and the kinetic energy is transferred to a
hydraulic system by a pump.
The WEC treated in this thesis is one example of a device that mainly utilizes its energy from the heaving and surging motion of the waves. Two other
examples of wave activated bodies using the heaving motion are Wave Bob3
and AquaBuOY [28].
Even if two concepts belong to the same group, their systems to convert the
wave energy into electricity can be completely different, see Fig. 1.3 and [29].
1 Pelamis
Wave Power, http://www.pelamiswave.com/ Accessed 2010-12-13
Roller, http://www.aw-energy.com/ Accessed 2010-12-13
3 Wave Bob, http://www.wavebob.com/ Accessed 2010-12-13
2 Waver
19
Fluid power
Mechanical power
Electric power
a)
PM linear generator
Wave
PE conversion
system
Grid
PE conversion
system
Grid
b)
Wave
Hose
pump
Accum- Impulse
turbine
ulator
PM
generator
Figure 1.3: Different conversion schemes for wave activated bodies using the heaving
motion of the waves. a) The conversion principle of the Uppsala University concept.
b) The conversion principle of AquaBuOY.
1.3 Wave energy system developed at Uppsala
University
The technology treated in this thesis is based on a direct driven synchronous
permanent magnet linear generator. Instead of having one large WEC with a
high power rating, several smaller units are interconnected to get the desired
power out of the system, see Fig. 1.4 for an illustration.
Figure 1.4: An illustration of how a wave power system could look in the future.
©Seabased Industry AB
The design should be based on having as many full load hours per year
as possible [7]. Therefore, the generator will have different power ratings depending on the sea state it will operate in. For example, a generator on the
20
Swedish west coast could be designed to have a nominal power of 5–20 kW,
whereas on the coast of Norway, a more appropriate rating could be 50–100
kW.
A direct drive approach is used to eliminate mechanical parts, like gear
boxes, turbines etc., that otherwise are required to connect a conventional high
speed generator to the low speed motion of the waves. Thereby, the maintenance work is believed to decrease. However, a direct drive system tends to
have a somewhat more complicated electrical system since a conversion is
needed before the connection to the grid. Furthermore, a generator moving
with a low speed is larger compared to a 50 Hz generator with the same power
rating [30, 31].
There are several researchers working with linear generators for wave energy conversion, see for example [32–37]. However, to the best of the author’s
knowledge, no results have been published for offshore operation of WECs
using the same electrical system as presented in this thesis.
1.3.1
Wave energy converter
A schematic of the WEC is illustrated in Fig. 1.5. The generator is placed on
the seabed and connected to a point absorbing buoy on the ocean surface. The
WEC acts as a point absorber if the diameter of the buoy is approximately less
than half of the wave length [8].
Figure 1.5: The wave energy converter with its most essential parts marked.
21
The buoy, and thereby the translator with permanent magnets mounted on it,
moves upward with wave crests. At wave troughs, the mass of the system and
possible springs mounted at the bottom of the generator pulls the translator
downwards. When the translator moves in relation to the fixed stator, a voltage
is induced in the stator windings. The voltage will drive a current in the cable
windings if the generator is connected to a load.
A linear generator can be seen as an unrolled rotary generator. Many of the
magnetic and electric properties are similar to a rotary generator, but there
are some essential differences [30]. First, a linear generator has in almost all
applications a varying speed and cannot be connected directly to the grid. Second, a linear generator has open magnetic circuits at both ends of the generator
which influence the magnetic flux in the generator [38, 39].
Simulations, calculations and laboratory experiments on a four-sided linear generator based on Uppsala University’s concept can be found in [40–43]
and an octagonal linear generator based on Uppsala University’s concept is
investigated in [44, 45].
1.3.2
Conversion and transmission system
Since the translator moves with a varying speed, the generator will produce
an irregular voltage and current which needs to be converted before grid connection. The transmission system can be designed in several ways depending
on the size of the wave power plant, the distance to the shore, the need to
reduce losses and costs etc. Transmission schemes for different power plant
cases are presented in [20, 46–48]. Moreover, there exist several studies on
electrical conversion and control schemes for direct driven generators, see for
example [49–55]. An overview diagram indicating how a conversion system
could look is shown in Fig. 1.6.
The conversion strategy shown in Fig. 1.6, is to first rectify the varying
AC into a DC with diode rectifiers [56, 57]. The generators are then interconnected in parallel on the DC-side to achieve power smoothening [58]. After
the interconnection, the DC-voltage is stabilized and inverted back to an AC
with a constant frequency and amplitude. Finally, the AC is transformed one
or two times, depending on distance to shore and the number of generators, to
decrease the transmission losses.
Both generators and substations are placed on the seabed, see Fig. 1.4. In
this way, the cable installation becomes easier and the most expensive parts in
the system are protected against the harsh climate at the ocean surface. There
are also good cooling possibilities for power electronics since the cold surrounding water can be used as cooling element. However, the maintenance
work is more difficult, especially in a research stage. In the future, with a line
production of WECs and marine substations, the strategy is to change a defected part (WEC or substation) with a new one and perform the maintenance
work onshore.
22
WEC
Low Voltage Marine Substaion
Sea Cable
Medium Voltage Marine Substaion
WEC
Sea Cable
Sea Cable
WEC
Sea Cable
Sea Cable
WEC
Low Voltage Marine Substaion
Grid
Sea Cable
WEC
Sea Cable
Sea Cable
WEC
Sea Cable
Figure 1.6: Overview diagram of a conversion and transmission system.
1.3.3
Generator connected to different loads
The conversion system required to connect the generators to the grid has an
impact on the damping of the generator and depending on how the system is
designed, the generator is subjected to different loads. In turn, the damping
has an impact on the power absorption and the power production. The effect
of the damping is shown and discussed in Paper VII and is a key issue for
the thesis. Four different load cases are studied in the appended papers. The
studied cases are a generator connected to:
•
•
•
•
a resistive load (Paper III)
a diode rectifier and filter (Paper IV–VI)
an actively controlled DC-voltage (Paper VII and Paper X)
a resonance circuit (Paper XIV)
A resistive load has been used when designing the generator but it will not
represent a load case for a grid connected generator. To improve the design
of the WEC, it has been important to show the difference between the resistive load case and the case when the generator is connected to an electrical
conversion system.
The study with the generator connected to the diode rectifier and filter was
made to see to which extent the power could be smoothened out from one
WEC and to investigate the non-linear load behaviour which occurs when the
generator is connected to a stable DC-voltage.
By connecting the generators to a stable DC-voltage, a number of generators are controlled by one converter and a power smoothening is achieved at
an early stage in the system. Moreover, the system between the converter and
the grid can be performed in a straightforward way.
23
Initial studies have been done on the WEC connected to a novel resonance
circuit. The purpose with the circuit is to increase the damping of the generator
and at the same time increase the amounts of power produced and increase the
voltage.
As mentioned before, there exist a wide variety of load cases for a grid
connected generator and the studied cases in this thesis are just a few of them.
Other common existing control strategies are to use an active rectifier [32, 53]
or control the motion of the buoy by a latching control, discrete control, or a
reactive control, continuous control [59, 60].
1.3.4
Theses published by the wave power group
So far, the project has resulted in four Licentiate theses and six Doctoral theses. The first PhD thesis [61] was written in 2006. The author of the thesis, Dr.
Thorburn, has done simulations, calculations and suggestions of different designs of the wave energy conversion and transmission systems. An extensive
theoretical study of the electromagnetic properties of the linear synchronous
generator can be found in the PhD thesis written by Dr. Danielsson [62]. A
model including the interaction between wave, buoy and generator was developed and verified with experimental data by Dr. Eriksson [63]. The mechanical design, construction of the first full scale generator and offshore results are
presented by Dr. Waters in [64]. Dr. Waters has also done a study of the wave
climate off the Swedish West coast and made a program that can calculate
the incident power in the waves on the research site using data from the wave
measuring buoy. Dr. Rahm presented in his thesis a detailed description of the
mechanical design of the first marine substation [65]. Dr. Rahm focused on
studying array operation of WECs. The effects of a wave power plant on the
marine environment are studied by Dr. Langhamer in [66].
The Licentiate thesis by Mrs. Ivanova covers a theoretical study of an octagonal permanent magnet generator for wave energy conversion [67]. Mr.
Tyrberg presented an observation system that can be used to study how the
buoys will move in the water and what impact the sea level will have on the
power production in his Licentiate thesis [68]. Mr. Engström has continued
with Dr. Erikssons work and studies the hydrodynamic wave/device interaction [69].
24
2. Theory
This chapter presents basic theory about wave energy, generator modelling
and circuit theory. For the reader who would like more information about the
different areas, there are references in each section that expand on the subject.
2.1
Waves and wave energy spectrum
Physically, a wave can be described by its length, λ , and height, H, see Fig.
2.1. To describe the behaviour of a wave more accurately, different wave theories can be applied depending on the water depth and the steepness of the
waves. For deep water, λ < 0.5h [70], 95% of the energy in the waves is
available between the surface and a depth h = λ /4 [17]. The water particles
are moving in an oscillating pattern and the amplitude of the circles decrease
exponentially with water depth. For waves in deep water, the linear wave theory developed by Airy (1845) can be applied [71]. If the waves become steep,
e.g. the ratio between the wavelength and wave height is small, the linear wave
theory is not valid, and instead, Stokes second order theory is used [72]. The
particles in waves at shallow waters will move in an elliptical pattern and the
theory for solitary waves is preferable to use [72].
l
Crest
H
mean water level
wave direction
Trough
h
Behaviour of particles
beneath the surface (deep
water).
Sea bed
Figure 2.1: Basic characteristics of a wave.
25
To describe the wave energy resource at a site, a spectrum analysis is often
performed [73]. One commonly used spectrum is the directional wave spectrum, S ( f , θ ), [8]. The term describes the distribution of energy density in
frequencies, f , and directions, θ . Some parameters typically used to characterize a sea state are expressed in terms of the spectral moment, mn ,
Z ∞
mn =
f nS ( f ) d f
(2.1)
0
where m0 is the total energy (variance) of the wave system.
The significant wave height, HS , can be expressed in two different ways;
H1/3 or Hm0 [8]. When the term H1/3 is used, the significant wave height is
defined as the average crest-to-trough height of one third of the highest waves
in the spectrum. The other term, Hm0 , represents the spectral expression, see
Eq. 2.2. However, the two terms are approximately equal, 0.9Hm0 < H1/3 <
Hm0 [74].
√
Hm0 = 4 m0
(2.2)
The mean energy period, Tm0−1 , is defined as
Tm0−1 = m−1 /m0 .
(2.3)
Tm0−1 depends on low frequency components and is often denoted as TE .
Another term that is used to express the time period is the zero-upcrossing
period, T02 or TZ
p
(2.4)
T02 = m0 /m2 ,
where TZ depends on high frequency components. TZ is not used as commonly
as TE in ocean wave theory [75].
According to linear wave theory and the deep water condition, the wavepower level or power density [70, 76], can be expressed as
Z ∞
J = ρg
0
cg ( f , h) S ( f , θ ) d f =
ρg2
2
Tm0−1 Hm0
64π
(2.5)
where ρ is the density, g is the acceleration due to gravity and cg is the group
velocity.
2.2
Generator theory
Depending on the purpose of the study, a generator can be modelled differently. In the design process of the generator, it is important to have a model
where the physical dimensions and the electric and magnetic behaviour can
26
be set and studied. A field based model of the generator is often chosen in this
case.
In a power system, the generator is usually represented by its equivalent circuit. In this case, the no-load voltage, power rating and internal inductance and
resistance must be known before the study. With an equivalent circuit, short
circuit analysis as well as system analysis (generator connected to different
loads) can be performed.
2.2.1
Electromagnetic field theory
Field theory is used to explain electric and magnetic phenomena in generators.
Mathematically, there are two different kinds of fields of interest when studying generators, scalar fields and vector fields [77]. A scalar field associates to a
scalar value given for each point in a space and could for example be the field
of temperature or pressure. A vector field has a vector linked to each point in
space and could be an electric field or a magnetic field. The relation between
scalar and vector fields underlies the fundamental laws of electromagnetism
and can be represented by Maxwell’s equations Eq. 2.6–2.9 [78],
∇×E = −
∂B
,
∂t
∇×H = j+
∂D
,
∂t
(2.6)
(2.7)
∇ · D = ρc ,
(2.8)
∇ · B = 0,
(2.9)
where E is the electric field, B is the magnetic flux density, H is the magnetizing field, j represents the electric current density, D is the electric displacement
field and ρc is the charge density.
The first equation, Eq. 2.6, can be seen as a vector formula of Faraday’s
law of induction and states: “An electromotive force is induced in a closed
circuit when the magnetic flux, Φ, linking the circuit changes” [30]. If the
circuit consists of a tightly-wound N-turn coil of wires, the induced voltage,
e, is given by
e = −N
dΦ
.
dt
(2.10)
Where Φ can be expressed in terms of the electric and the magnetic field as
in Eq. 2.11 and Eq. 2.12.
Z
Φ=
Bda
(2.11)
S
27
dΦ
=−
dt
I
Eds
(2.12)
c
A field based model of the generator can be done by using Maxwell’s equations and inserting boundary conditions. To solve the model numerically, a
finite element method (FEM) could be used. The method is described and
used in literature; see for example [79–81].
2.2.2
Equivalent circuit model
Once the electrical characteristics of the generator are well-defined, an equivalent circuit model can be created. The generator can be represented by resistances, inductances and voltage sources.
It should be mentioned that an equivalent circuit is a rough model of a linear
generator and several of the non-linear effects are neglected. An example of
an equivalent circuit representation of a generator can be seen in Fig. 2.2.
i
LS
RG
ei
Generator
Figure 2.2: Equivalent circuit of a generator.
In Fig. 2.2, ei is the internal EMF of the generator, RG is the resistance in
the armature winding and LS is the synchronous inductance. In reality, both
the resistance, RG , and inductance, LS , will vary. The resistance is mainly temperature dependent, but also dependent of the frequency. Since the frequency
is low for the generator considered in this thesis, the DC-resistance, R0 , can
be used to express the resistance in the generator
RG ≈ R0 =
ρr l
A
(2.13)
where ρr is the resistivity of the conductor, l is the length of the conductor and
A is the cross-sectional area of the conductor.
The inductance, Ls , is proportional to the magnetic flux, Φ, and the current,
i, flowing in the circuit.
Ls ∝
28
Φ
i
(2.14)
Since the magnetic flux is not symmetrical as in a round machine, i.e. the
magnetic flux will change with translator position, the synchronous inductance will vary for a linear generator. Other parameters affecting the inductance are saturation, air gap variations and other anomalies.
2.3 Forces acting on the generator and the damping
function
There are a number of different forces acting on the generator. Some of the
forces damp the translator motion and some of them contribute with energy to
the system. The forces acting on the generator can be expressed with Newton’s
second law
mẍ = Fb + Fs + Fes + Fem + mg.
(2.15)
Where m is the mass of the moving parts in the system, i.e. the mass of the
buoy and the translator if the rope does not slacken and ẍ is the acceleration
of the translator. The first force in the equation, Fb , is the lifting force from
the buoy. This is the driving force in the system. Fs is the force from possible
springs mounted at the bottom of the generator. The force pulls the translator
downwards. Fes is the force of the end stop at the top of the generator. The
force Fem is a consequence of the damping from the electrical system. The
term describes how the electrical system affects the translator motion, e.g.
how the generator is electrically damped. Eq. 2.15 is further described and
used in [56, 82].
The electromagnetic force, Fem , has an influence on the WEC’s ability to
absorb energy. Fem is proportional to the damping function, γ, and the translator speed ẋ [82];
Fem = A f ac · γ · ẋ,
(2.16)
where A f ac is the active area of the stator, i.e. the part of the stator that is
covered by the translator.
The damping function can be derived from the statement that the power is
equal to the force multiplied with the velocity;
Pabs = Fem ẋ.
(2.17)
Eq. 2.16 and Eq. 2.17 give the following expression for γ, assuming A f ac
equal to one;
γ=
Pabs
,
ẋ2
(2.18)
where Pabs is the internal power generated in the generator.
29
2.4
Generator connected to different loads
The theory behind the four different studied load cases are presented in this
section.
2.4.1
Resistive load
The simplest load to connect the generator to is a purely resistive load, as in
Fig. 2.3.
i
LS
RG
ei
vL
RL
Load
Generator
Figure 2.3: Generator connected to a resistive load.
The voltage, vL , over the load, RL , can according to KVL be expressed as;
vL (t) = ei (t) − i(t)RG − LS
di
.
dt
(2.19)
The expression of the current, i(t), is derived from Ohm’s law;
i(t) =
vL (t)
.
RL
(2.20)
2.4.2 Diode rectifier, filter and actively controlled DC-voltage
loads
If the generator is connected to a diode rectifier and capacitor as in Fig. 2.4,
the diodes make the circuit non-linear [83, 84]. There are two different cases:
when the diodes are conducting and when they are blocking.
Knowing that only two diodes, one of the positive diodes, D1 , D3 or D5 , and
one of the negative diodes, D2 , D4 or D6 , are conducting at the same time, the
circuit in Fig. 2.4 can be described with the equivalent circuit shown in Fig.
2.5. Where vin (t) is made up of segments of the line-to-line voltages, ea (t),
eb (t) and ec (t) [83].
When the diodes are conducting, the voltage and the current in Fig. 2.5
can according to KVL and KCL be described with Eq. 2.21 and Eq. 2.22
respectively.
30
ea
n
ia
RG
LS
RG
LS
RG
LS
D3
D1
D5
eb
CDC vDC
ec
D4
Generator
D6
RDC
D2
Load
Figure 2.4: Circuit diagram of a generator connected to a diode bridge rectifier and
filter.
i
RG
LS
DP
vin
CDC vDC
RG
LS
RDC
DN
Load
Generator
Figure 2.5: Equivalent circuit of the system shown in Fig. 2.4.
vDC (t) = vin (t) − 2i(t)RG − 2LS
di
− 2vD
dt
(2.21)
where vD is the voltage drop across the diode.
i(t) = CDC
dvDC vDC (t)
+
dt
RDC
(2.22)
When the diodes are blocking, there is no current flowing in the circuit,
i(t) = 0, and the voltage, vDC (t), over the load is expressed as
dvDC
1
=−
vDC (t).
dt
CDC RDC
(2.23)
The solution to Eq. 2.23 is
t −t
− C s R0
DC DC ,
vDC (ts ) = vDC (t0 )e
t0 < t < ts
(2.24)
where t0 is the time when the diodes stop to conduct and ts is the time when
the diodes start to conduct again. The capacitance needed to maintain a stable
DC-voltage can be calculated from Eq. 2.24.
31
If CDC RDC is much larger than ts − t0 , the voltage over the load in Eq. 2.24
can be written as [83]
vDC (ts ) = vDC (t0 ) = VDC
(2.25)
and the capacitance, CDC , and resistance, RDC , can be approximated to a constant voltage source, VDC , and the circuit in Fig. 2.5 can be expressed as in
Fig. 2.6.
i
LS
RG
DP
vin
VDC
LS
RG
DN
Load
Generator
Figure 2.6: Equivalent circuit of the system shown in Fig. 2.4, if CDC and RDC are
assumed to be larger than ts − t0 .
Another way to achieve a constant DC-voltage, without using capacitors
with a high capacitance is to control the current on the DC-side of the rectifier, and thereby controlling the power. By controlling the power on the DCside, the DC-voltage can be set to different values [85–87]. The active device
controlling the power could for example be an IGBT or a MOSFET in a buckboost converter or in an inverter. To be able to maintain a constant DC-voltage,
the load after the active device should have a small impedance value.
A simplified model of the control is shown in Fig. 2.7.
i
RG
LS
vin
RG
LS
Generator
DP
RPE
VWEC
VDC
RDC
DN
Load
Figure 2.7: Generator connected to a load with active power regulation. The resistance, RPE , represents the active device in the circuit.
The active device is represented by a variable resistor in series with the load.
The resistor could be switched to have an average resistance, RPE , between Ri
and infinity. Where Ri is the internal resistance of the switching component.
By decreasing the value of RPE , the current delivered to the load RDC will increase and the controlled DC-voltage, VW EC , decrease, and vice versa, when
32
RPE is increased, VW EC is increased. However, there will be a limit on the maximum power, Pmax , the system can supply to the DC-side without changing the
DC-voltage, VW EC . The limit is given by Eq. 2.26.
Pmax =
VW2 EC
.
Ri + RDC
(2.26)
Fig. 2.7 is a rough model of a circuit with an active control and would in
reality also include other components such as capacitors and inductors for
filtering. However, the aim with the figure is to show the principle of the operation.
2.4.3
Resonance circuit
Resonance is a phenomenon that occurs in electrical circuits when the capacitive reactance is equal to the inductive reactance.
The simplest way to achieve resonance in an inductive circuit is to add a
capacitor to the system as in Fig. 2.8. The circuit in Fig. 2.8 is used to define
some basic expressions used in general to describe resonance circuits.
i
LS
RG
ei
C
Generator
Figure 2.8: Generator connected to a capacitor representing a simple resonance circuit.
Fig. 2.8 can be described by the second order equation
dei
di
d2i 1
= RG + LS 2 + i(t).
dt
dt
dt
C
(2.27)
The characteristic expression for Eq. 2.27 can be written as
s2 +
RG
1
s+
= 0.
LS
LS C
(2.28)
The solution to Eq. 2.28 is given in terms of resonant frequency, ω0 , and
damping ratio, α:
q
(2.29)
s1,2 = −α ± α 2 − ω02
where the resonant frequency is
33
1
ω0 = √
LSC
(2.30)
and the damping attenuation is
α=
RG
.
2LS
(2.31)
The resistance, RG , will give rise to a damping of the oscillations in the
circuit and depending on the relative magnitude of α and ω0 , the system will
behave differently. To describe the behaviour of the system, the damping
factor, ξ = α/ω0 , and the quality factor, Q = 1/(2ξ ), are used [88]. There
are three different cases:
1. If ξ > 1 or Q < 0.5, the system is over-damped.
2. If ξ = 1 or Q = 0.5, the system is critically damped.
3. If ξ < 1 or Q > 0.5, the system is under-damped.
At steady-state, the equivalent impedance of the circuit in Fig. 2.8 can be
written as
Zeq = RG + jωLS +
1
.
jωC
(2.32)
Inserting ω0 in Eq. 2.32, Zeq becomes purely resistive. The small impedance
occurring at resonance will result in high currents and voltages especially if
the resistance in the circuit is small. Therefore, resonance is often something
to avoid in power circuits. However, in some circuits resonance is preferable
as in resonant converters [83,88] and in wireless energy transmission [89]. It is
also common to use a capacitor for decreasing the phase angle if the generator
has a high inductive reactance, but never to reach the resonance mode [90].
If a load is added to the circuit in Fig. 2.8, as in Fig. 2.9.
i
RG
ei
LS
C vL
Generator
RL
Load
Figure 2.9: A load, RL is added to the resonance circuit.
The power delivered to the load, PL_res , in Fig. 2.9 will not be significantly
increased compared to a system without the capacitor, see Fig. 2.10. In the
34
example shown in Fig. 2.10, the resistance RG = 1 Ω, the inductance LS = 20
mH, the voltage ei = 400 V, the load RL = 10 Ω and the capacitance C =
12.665 mF in the resonance case and C is not present in the reference case.
When the frequency is smaller than the resonant frequency, ω/ω0 < 1, the
capacitive reactance is larger compared to the inductive reactance and the voltage over and power delivered to the resistive part of the load, RL is larger. For
frequencies higher than the resonant frequency, ω/ω0 > 1, the inductive reactance is dominating and the voltage drop over the inductor is increasing. The
power delivered and voltage over the resistive part of the load decreases since
the current through the capacitor increases.
PG_res
PL_res
PG_ref
PL_ref
30
P/PL_ref
20
10
0
0
0.5
1
w/w0
1.5
2
Figure 2.10: Power for a generator equivalent circuit with a constant voltage source,
ei , connected to a capacitor and resistive load, the resonance case, and a generator
connected to a purely resistive load, the reference case. PG_res and PG_re f refer to the
power in the generator, the absorbed power. PL_res and PL_re f refer to the power in
load. The average value of PL_re f is used as a reference on the y-axis.
The significant difference in the resonance circuit compared to the circuit
without a capacitor can be observed by studying the generated power in the
generator, PG_res and PG_re f in Fig. 2.10 where PG_res is much larger than
PG_re f resulting in a higher damping function (Eq. 2.18).
Novel resonance circuit
A novel resonance circuit is presented in this thesis and a patent has been
submitted, Paper XV. The basic concept of the circuit is shown in Fig. 2.11. A
single-phase generator is used to describe the theory behind the circuit. For a
35
three-phase generator, the resonance circuit will consist of three single-phase
circuits connected in parallel on the DC-side.
The purpose with the circuit is to have more power delivered to the load at
resonance. The power generated in the generator will not be as large as in the
pure resonance case in Fig. 2.10, but the power supplied to the load can be
much larger compared to a circuit with a single-phase full bridge rectifier, see
Fig. 2.12.
D3
i
RG
LS
C2
D1
vDC
ei
D2 D4
C1
Generator
RDC
Load
Figure 2.11: The generator connected to the novel resonance circuit.
15
PG_res
PL_res
PG_ref
PL_ref
P/PL_ref
10
5
0
0
2
1
3
w/w0
Figure 2.12: The power in the load, PL and the power generated by the generator, PG ,
in two different cases. In one case the generator is connected to the circuit in Fig. 2.11
and in the other case, the reference case, it is connected to a single-phase full bridge
rectifier.
36
In, Fig. 2.12, the same values for the parameters as in Fig. 2.10 are used.
For frequencies larger than ω0 , PG_res is not decreasing as much as for the pure
resonance case in Fig. 2.10.
By assuming that the diodes are ideal, the circuit shown in Fig. 2.11 can be
drawn as in Fig. 2.13.
LS
RG
i
C2
ei
RDC
C1
Figure 2.13: A circuit diagram of the circuit shown in Fig. 2.11 assuming that the
diodes are ideal and conducting.
The circuit in Fig. 2.13 can then be expressed as
dei
di
d2i
1 di
1
= RG + LS 2 +
+ i(t)
dt
dt
dt
RDC dt 2C
(2.33)
with C = C1 = C2
The characteristic expression for Eq. 2.33 can be written as
2
s +
1
RG + RDC
LS
s+
1
= 0.
2LSC
(2.34)
The resonant frequency for the circuit will then be
1
ω0 = √
2LSC
(2.35)
and the damping attenuation is
α=
1
RG + RDC
2LS
.
(2.36)
37
3. The Lysekil research site
A review is done by Ref. [18] of the present research sites and test centres for
testing wave power devices in Europe, see Fig. 3.1. The authors to [18] have
divided the test sites into three different categories: “pre-prototype stage gate
requirements test sites”, “pre-production stage gate requirements test sites”
and “pre-commercial stage gate requirements test sites”.
Figure 3.1: Different test sites in Europe. Test sites marked in green are in the
pre-prototype stage gate requirements stage, those marked in purple are in the preproduction stage gate requirements stage and test sites marked in blue are in the precommercial stage gate requirements stage. [18]
39
To be in the third category, it should be possible to test the following at the
site [18]:
•
•
•
•
•
multiple units performance
device array interactions
power supply interaction
environmental impacts issues
full technical and economic due diligence
There are four test sites in Europe belonging to the third category and one
of them is the Lysekil research site. The other three sites are the Agucadoura
test site in Portugal where Pelamis Wave Power has tested their device1 , the
Santona test site where the Ocean Power Technologies has tested their device
“the Power Buoy”2 and the Mutriku test site in the north of Spain where an
OWC has been tested [91].
The work with the Lysekil research site started during 2003 and in 2004
permissions were granted by the County Administration to set up a research
park consisting of 10 generators and approximately 30 buoys for environmental studies. A site on the Swedish west coast near the town Lysekil was chosen
because of its proximity to field stations and harbours. The location of the site
is shown in Fig. 3.2.
Figure 3.2: A sea chart over the test area with the research site, sea cable and measuring station label.
1 Pelamis Wave Power, http://www.pelamiswave.com/our-projects/agucadoura/ Accessed 2010-
12-13
2 Ocean
Wave Technologies, http://www.oceanpowertechnologies.com/spain.htm/ Accessed
2010-12-13
40
The site has a fairly good sea state (especially during the winter months)
and the distance to shore is about 2 km. The sea state at the site is investigated
in [92], and annually, the wave climate at the site, based on eight years of
satellite data, is estimated to be 2.6±0.3 kW/m.
The seabed conditions at the test site were investigated in May 2006. The
investigation showed that the bottom area consists mainly of a 1 m thick sandy
silt material. The area is fairly level and the water depth varies between 24–25
m. More of the results from the study are presented in [93]. The water level
variations at the site are investigated in [94].
Some of the main components installed at the site can be seen in Fig. 3.3
and are further described in the following subsections.
2 km
150 m
Wave
measuring
Biology
buoy
buoy
12 m
Wave
power
plant
Measuring
station &
dump load
200 m
Observation
tower
2.9 km
25 m
Marine
Substation
Figure 3.3: Overview of the different components installed at the research site.
3.1
Biology buoys
The purpose of having a number of biology buoys at the site is to investigate
what impact a wave power plant will have on the surrounding eco system and
vice versa. One of the purposes is to see what the environmental impact will be
if one places large structures on an otherwise rather empty sandy bottom and
what will be the consequences of having large structures on the ocean surface.
To get prior and after results, the measurements started in 2004 before the
biology buoys were placed in the area. The first buoys were launched in 2005
and some of them can be seen in Fig. 3.4d.
41
Results from measurements can be found in [95,96] where it is investigated
if a wave power plant can act as an artificial reef.
Another important issue is to investigate what effect the environment has
on the WEC. It is especially important to study if the amount of biofouling
that occurs on the generator and buoy has an impact on the energy absorption
and the material of the WEC. This was studied in [97].
Figure 3.4: Photos of installations at the research site. a) Observation tower. b) Wave
measuring buoy. c) Buoy in ice formation. d) Biology buoys.
3.2
Observation tower
An observation tower equipped with a Sony SNC-RX550 remotely controllable network camera is located approximately 150 meters from the WECs. A
photo of the tower is shown in Fig. 3.4a. Images from the network camera will
make it possible to correlate voltage data and line force data with the movement of the buoy in the water. The construction of the tower and some results
are presented in [68].
The tower will be equipped with a weather station to measure temperature, precipitation and barometric pressure. In connection to the tower, a hydrophone system will be installed to measure the underwater noise from the
generators and the substations.
42
3.3
Wave measuring buoy
The first wave measuring buoy was installed at the site in April 2004. The
buoy is a Datawell Waverider buoy3 and is shown in Fig. 3.4b. The sampling
frequency of the wave data is 2.56 Hz and the data are transmitted to shore via
an HF radio link and sampled in 20 minute files. A description of its operation
can be found in [98]. The winter of 2009/2010 was quite cold and the harsh
climate resulted in an ice formation at the site, see Fig. 3.4c. The Datawell
Waverider buoy was not built for such conditions which resulted in a line
breaking of the elastic part of the line and the buoy was drifting away. In May
2010, a new Datawell Waverider buoy was installed at the site with the same
properties as the first buoy.
3.4
Wave energy converters
So far, eight WECs have been installed at the research site. The work with the
first WEC, L1, started in 2005 and the WEC was launched in March 2006.
Some of the design characteristics and physical dimensions of the WEC are
presented in Table 3.1 and a picture of the WEC can be seen in Fig. 3.5a.
Results from L1 are presented in [99, 82, 100, 101] and Paper I–VI.
Main parameters of L1
Nominal power at 0.7 m/s
Voltage, line-to-line, rms at 0.7 m/s, Vd
Generator resistance, RG
Generator inductance, LS
Air gap
Size of magnet block
Pole width, w p
Number of stator sides
Vertical stator length
Vertical translator length
Translator resp. stator width
Translator weight
10 kW
200 V
0.44±1.5% Ω
11.7 mH
3 mm
6.5x35x100 mm3
50 mm
4
1264 mm
1867 mm
400 mm
1000 kg
Table 3.1: Mechanical parameters and electrical design parameters for L1.
The next generators to be installed were L2 and L3, see Fig. 3.5b and c.
They are electrically similar to L1, but some changes in the mechanical construction were done. They were launched in February 2009 and brought to
shore in October the same year since the stator windings were connected in3 Datawell
Waverider, http://www.datawell.nl/ Accessed 2010-12-13
43
Figure 3.5: The WECs that have been installed at the research site, with exception for
L5. In a) L1, b) L2, c) L3, d) L4, L7 and L8 and e) L9.
correct, resulting in a phase shift of one of the phases. Results from L2 and
L3 are presented in Paper VI and Paper VII.
L9 was installed in October 2009 and a photo is shown in Fig. 3.5e. L9
is a second generation WEC with both electrical and mechanical changes.
Electrically, the no-load voltage has been increased and instead of mounting
the stators on an inner frame, they are mounted directly on the hull walls. The
weight has been reduced with approximately 50% compared to L1. Data for
L9 are presented in Table 3.2.
During 2010, four more WECs were installed, L4–L8. Three of the WECs
can be seen in Fig. 3.5d. The WECs L4–L8 have been built by Seabased Industry AB. L4–L6 are three phase generators electrically similar to L1–L3.
44
Main parameters of L9
Nominal power at 0.7 m/s
Voltage, line-to-line, rms at 0.7 m/s, Vd
Generator resistance RG
Generator inductance LS
Air gap
Size of magnet block
Pole width, w p
Number of stator sides 4
Vertical stator length
Vertical translator length
Translator resp. stator width
Translator weight
20 kW
450 V
1±1.5% Ω
20 mH
3 mm
6.5x47x230 mm3
55 mm
2000 mm
2000 mm
230x2 mm
2700 kg
Table 3.2: Mechanical parameters and electrical design parameters for L9.
L7 and L8 are one phase generators but are otherwise similar to L1–L3 with
exception of the size of the magnets.
The magnets used to magnetise the generators are of the N40 NE-Fe-B type
of magnets and have a remanence induction of 1.3 T and a maximum energy
production of 320 kJ/m4 .
The generators have been connected to buoys with different shapes and
weights. Three of the buoys can be seen in Fig. 3.6. The purpose with using
different kinds of buoys is to see what impact the shape and size of the buoy
have on the power absorption.
Figure 3.6: Three different kind of buoys that the generators have been connected to.
4 Sura
Magnets, http://www.suramagnets.se, Accessed 2010-12-13
45
3.5
Marine substations
To be able to interconnect the WECs and transmit the aggregated power to
shore, a substation is needed. A first marine substation was installed in 2009
to interconnect three of the WECs, L1–L3. A circuit diagram of the system
can be seen in Fig. 3.7. Since the generators do not have any “on/off”-switch,
the WECs are connected to dummy loads when they are disconnected from the
system, Paper VIII. The dummy loads are made of delta-connected resistive
loads consisting of immersion heaters.
L1
Marine Substation
Measuring Station
L2
Aux
L3
Figure 3.7: Circuit diagram of the system consisting of three generators, one substation and a measuring station.
The marine substation is placed on the seabed in a similar way to the WECs.
The substation is a 3 bar pressure vessel with a volume of 3 m3 and it was filled
with nitrogen before deployment. The generators are connected to the substation by underwater connectors in the lower dished end, see Fig. 3.8a. Heat
sensitive components, such as power electronics and capacitors, are mounted
on the vessel wall of the substation to take advantage of the cold water on the
outside of the vessel.
The voltage from each WEC is rectified in a six-pulse diode rectifier. After
the rectification, the WECs are interconnected in parallel on a common DCbusbar. The rectified voltage is filtered by electrolytic capacitors connected
in parallel to the DC-busbar to even out the DC-voltage further before it is
inverted to a 50 Hz AC. The capacitors are shown in Fig. 3.8b. A three phase
IGBT bridge with an IR2130 driver circuit is used as an inverter. No filter is
placed after the inverter.
The PWM pulses controlling the inverter are created in LabVIEW and implemented in the control system. In the process of time, the control algorithm can be modified and the operation characteristics of the inverter can be
changed. Finally, a tap-changed Y-Y transformer is placed after the inverter,
Fig. 3.8c. The transformer has five different taps (80-100-125-180-250/1000
V) and is controlled by contactors to maintain the voltage fairly constant out
from the substation.
46
Figure 3.8: The first installed substation. a) The substation casing. b) Picture taken
from the inside of the substation where sets of DC-link capacitors and auxiliary batteries can be seen. c) The transformer with the contactors that are used to switch
between different winding taps.
The substation has an auxiliary system which distributes power to the breakers and the control system. The system is supplied from the main circuit after
the transformer. Thereby, the auxiliary system can be supplied from the generators, and if necessary, from shore.
A control system has been developed in a National Instruments FPGAbased PAC computer for measurement acquisition and control.
Another marine substation is currently under construction. The new substation can handle the power from seven WECs. The substation is larger than the
first one, 5 m3 , and some changes in the mechanical construction have been
made, see Fig. 3.9.
3.6
Measuring station and grid connection point
In connection with the test site, a measuring station has been built on the
nearby island of Hermanö (frequently called Gullholmen). The measuring station is located in a nature reserve and is built to fit in the surrounding environment as much as possible, see Fig. 3.10a.
47
Figure 3.9: a) Substation casing of the new marine substation. b) Capacitors mounted
on a curved disk to achieve better contact with the casing. c) Assembly of contactors.
A sea cable transmits the power from the offshore research site to the measuring station. Data for the sea cable are presented in Table 3.3.
Main parameters of the sea cable
Sea cable resistance RC
Sea cable inductance LC
Sea cable capacitance CC
0.54±1.5% Ω
<0.01 mH
145 µF
Table 3.3: Parameters for the sea cable.
Before the launching of L1, the measuring station was equipped with resistive loads and a control and measurement system that enables data acquisition
and the possibility to control the system remotely from Uppsala.
During the winter of 2006/2007, the system was complemented with a sixpulse diode rectifier and a large power storage packet consisting of ultra capacitors. New resistive loads, DC-loads, were constructed in several steps during
the year. The measurement system was supplemented with current measurements. Hall transducers and resistive shunts were used for the current measurement.
48
In 2010, IGBTs where installed to actively control the DC-voltage and a
resonance circuit was installed. A simplified overview diagram of the measuring station is shown together with the rest of the system in Fig. 3.7.
Figure 3.10: a) The measuring station on Hermanö. b) The transformer station and
grid connection point.
In future, the WEP will be connected to the 11 kV grid on Hermanö and
preparations for the grid connection have been made. A cable and a transformer station transforming 1 kV to 11 kV have been installed, see Fig. 3.10b.
49
4. Simulations
There exist several simulation programs for simulating electrical circuits.
Some widely used programs are presented and described in [102]. The tools
that have been used for simulating electrical systems in the present work
are the commercially available programs PSpice (used in Paper IV) and
MATLAB Simulink (used in Paper VII, X and XIV).
Since circuit oriented simulation tools are used, the modelling of the electrical components as capacitors and diodes can be well defined in the simulations. The critical part of the simulations is to model the generator in an
accurate way.
4.1
Modelling of generator
The modelling of the generator can be done in different ways depending on
the study, i.e. how to choose ea , eb and ec in Fig. 4.1.
Generator
RGa
LSa
RGb
LSb
RGc
LSc
ea
eb
ec
Figure 4.1: Circuit diagram of the model of the generator in the simulations.
When the size of the filter was investigated (Paper IV), it was important to
include the real movement pattern of the translator. To get the shape of the
voltage that was expected during operation in real sea conditions, the variations in frequency and amplitude were applied to the model. A simple way of
doing this in the simulations is to implement a set of experimentally measured
voltage data as voltage sources, ea , eb and ec .
In Paper X, with the substation connected to two experimental generators
running with a constant speed, a good representation of ea , eb and ec could be
51
a constant voltage source corresponding to the no-load voltage of the experimental generator at the operating speed. The inductance and the resistance in
the cable windings are then added to the circuit.
If the no-load voltage and frequency are known for a certain translator
speed, a rough estimation of the produced power and losses can be elicited
from the simulations. The results are approximate since the model is linear
and does not take into account any non-linear effects. However, it can be a
good starting point when evaluating different load cases of the generator.
In Paper VII and XIV, the voltage is assumed to increase linearly with the
translator speed. The assumptions made to simplify the models are:
• The induced voltage is assumed to be proportional to the translator speed.
Iron losses, mechanical and non-linear effects are ignored.
• The stator is assumed to be 100% covered by the translator, A f ac = 1.
• The value of LS will be constant for all x.
The frequency of the voltage from the generator, f , can be expressed as
f=
ẋ
2 · wp
(4.1)
where ẋ is the speed of the translator and w p is the pole width of the magnets.
The no-load voltage is, with the assumptions given above, increasing linearly with translator speed
Ei =
ẋ
·Vd
ẋd
(4.2)
where ẋd and Vd are the design speed and the no-load voltage at design speed
respectively. The different values for Ei and f and the electrical data in Table
3.1–3.3 are used as input parameters for the generator and sea cable modelling
in the simulations.
52
5. Experiments
A summary of the offshore experiments is presented in this chapter. The first
two sections describe the voltage and current measurements and the calculation of power. The following sections describe the experimental set-up for the
different load cases.
5.1
Voltage and current measurements
The voltage and current are measured at two different places in the measuring station, see Fig. 5.1. The current denoted iin is measured with hall current
transducers on the three incoming phases, iain , ibin and icin . The voltage denoted vin in Fig. 5.1, is measured between the three incoming phases and the
neutral conductor and are vain , vbin and vcin . Before the voltage is sampled in
the data acquisition system, it is decreased by voltage division to ±10 V. The
sampling frequency of the measurements carried out on the AC-side is either
50 Hz or 256 Hz.
The DC-current, iDC = iDC+ = −iDC− , is measured with shunt resistors and
hall current transducers. The DC-voltage, denoted vDC = vDC+ − vDC− , where
vDC+ is measured between the positive conductor and neutral conductor and
vDC− is measured between the negative conductor and neutral conductor and
divided in a similar way as the AC-voltage. The sampling frequency on the
DC-side will vary depending on whether the study is carried out over a long
time (hours) or over a shorter time period (seconds).
Measuring Station
vin
Sea cable
Rectifier
vDC
iDC
iin
CDC
RL
RDC
Resonance circuit
Figure 5.1: The electrical system in the measuring station with the measuring points
marked. RL represents the Y-equivalent value of the delta-connected load.
The voltage and current measurements carried out in the substation are performed in a similar way as in the measuring station. The measuring points in
the substation are the same as in the measuring station, at the incoming AC
53
from each WEC, on the DC-side and on the AC-side before and after the transformer. The voltage and current are sampled with 256 Hz before the inverter
and the sampling frequency is 500 Hz after the inverter.
The accuracy of the voltage measurements is after calibration estimated to
±2.2% and the accuracy of the current measurements with hall sensors in the
measuring station is after calibration estimated to ±3.1%. In the substation,
the accuracy of the voltage measurements is estimated to ±1.2% and the accuracy of the current measurements is estimated to ±1.7%, see Paper XII.
5.2
Calculation of power
Mainly three different power calculations are discussed in the papers. First,
the power dissipated in the resistive load, Pin in the purely resistive case, Eq.
5.1, and PDC in the non-linear cases, Eq. 5.2. Second, the power produced
by the generator, Pout , which is calculated as Pin added to the resistive losses
in the sea cable, PRC . Third, the absorbed power by the generator, Pabs , Eq.
5.5. In Paper I, III, V, VI, the absorbed power, Pabs , is calculated as the power
delivered to the measuring station, Pin , with the resistive losses added. In Paper
XIV, the absorbed power is calculated by adding the resistive losses, Ploss to
the power in DC-load, PDC .
Pin = vain iain + vbin ibin + vcin icin
PDC = vDC iDC =
v2DC
RDC
(5.1)
(5.2)
Ploss = (RC + RG ) i2ain + i2bin + i2cin = PRC + PRG
(5.3)
Pout = Pin + PRC
(5.4)
Pabs = Pin + Ploss
(5.5)
The calculated absorbed power, Pabs , is an approximate value since there
exist losses that are not included in the calculations. The losses in the generator are discussed in [62, 64, 65] and can be divided into three different groups:
mechanical losses, iron losses and conductor losses. The mechanical losses
will occur between moving parts in the generator due to friction. Iron losses
are a consequence of the magnetic field in the stator and can be divided into
hysteresis losses, eddy currents and excess losses. Finally, there will be conductor losses. The conductor losses due to the resistance in the generator and
the sea cable can be calculated with Eq. 5.3. In Paper XIV there will also exist
54
losses in the resonance circuit which are not included in the calculations of
Pabs .
An expression for the absorbed power by the buoy in percent of the incident
power can be written as:
Aabs = 100
Pabs
Db · J
(5.6)
where Db is the diameter of the buoy. In the case of a torus shaped buoy, the
diameter of the buoy is calculated as in Eq. 5.7.
q
(5.7)
Db = 2 r22 − r12
where r1 is the inner radius and r2 is the outer radius of the buoy.
The incident power, J, measured in W/m wave crest is calculated with the
help of data collected from the Datawell Waverider buoy described in Section
4.3.
5.3
Generator connected to resistive load
Two different kinds of loads have been used in the experiments; the generator
has either been connected to resistive loads at the measuring station consisting
of a number of aluminium housed resistors, Fig. 5.2a, or it has been connected
to its dump load, Fig. 5.2b.
Figure 5.2: a) Resistive loads mounted on the roof and wall of the measuring station.
The resistive loads are both used on the AC-side, RL , and on the DC-side, RDC . b)
Dump load placed on the seabed.
A number of different values of the resistive load have been tested in the experiments. The resistive values were changed by connecting/disconnecting a
number of resistors. The resistance was measured after installation and the
different values of the delta-connected load were 2.2 Ω, 4.9 Ω and 10 Ω
55
per phase. The dump load consists of immersion heaters with a resistance
of 12±0.6 Ω which also are connected in delta.
Results from when the generators have been connected to different resistive
loads are presented in Paper III, Paper XII and [99, 82, 100].
5.4
Generator connected to diode rectifier and filter
The installed rectifier and capacitors used in the experiment can be seen in Fig.
5.3. Two stacks of ultracapacitors, CDC+ and CDC− , are connected in parallel
after the rectifier, see Fig. 5.3. Ultracapacitors are primarily used in electric,
hybrid and fuel cell vehicles, but in later years there has been an increased use
in renewable energy systems, mainly in wind power systems. The ultracapacitors that can be found on the market today have a capacitance of approximately
5000 F at 2.7 V [103]. A good review of the different types of capacitors can
be found in [104].
Figure 5.3: The installed system including the diode rectifier, ultracapacitors and contactors for switching the resistive part of the load.
The rectifier consists of three passive diode modules from Semikron,
SKKD162. Each diode has an RC-snubber circuit connected in parallel with
the diode. The resistive value of the snubber circuit is 68 Ω and the value of
the capacitance is 1 µF. The diode modules are mounted on an aluminum
heat sink to achieve cooling.
Resistors, RDC+ and RDC− , are placed in parallel with the capacitors. In
the first test presented in Paper IV, the resistive load was measured to RDC+ ,
RDC− = 6.84 Ω. Before the tests made in Paper V and Paper VI, the system
was extended with more resistors. Four different values of the load could be
chosen and were measured after the installation to RDC+ , RDC− = 4.58, 6.88,
9.17 and 13.75 Ω. The circuit used in the experiment can be seen in Fig. 2.4
and in Fig. 5.1 with
56
RDC = RDC+ + RDC−
(5.8)
CDC+CDC−
.
CDC+ +CDC−
(5.9)
and
CDC =
Results from when the generator is connected to the circuit are as presented
primarily in Paper IV–VI.
5.4.1
Design of filter
There are several fluctuations in the voltage out from the generator. One of
the fluctuations occurs due to the speed of the translator in combination with
the size of magnets, see A in Fig. 5.4 and Eq. 4.1. The second variation is
larger and is a result of the shape of the incident wave in combination with
the damping of the system, see B in Fig. 5.4. Finally, there exists a long term
variation in hour timescale due to changes in the sea state.
300
B
Voltage [V]
200
A
100
0
-100
-200
-300
0
1
2
3
4
5
Time [s]
6
7
8
9
Figure 5.4: Three phase voltage out from the generator connected to resistive load.
“A” denotes the frequency variation due to size of magnet and translator speed. “B”
shows the large variation in amplitude due to the shape of the incoming waves.
The filter used in the experiment was designed to smooth out the fluctuations A and B in Fig. 5.4. If the filter was designed to handle the variations
in power over hour timescales, it would have been unreasonably large and
expensive.
One expression for deriving the required capacitance, CDC , was presented
in Chapter 3 (see Eq. 2.24) and can be rewritten as
CDC = −
ts − t0
.
vDC (ts )
ln v (t ) RDC
DC 0
(5.10)
57
Another expression that can be used is derived in Paper IV and shown in
Eq. 5.11.
CDC =
2P∆t
(5.11)
2
2
VDCmax
−VDCmin
In the first expression, Eq. 5.10, ts − t0 was chosen to be 4 s and the voltage
was not allowed to vary more than 5%, vDC (ts )/vDC (t0 ) = 0.95. The most
common sea state at the research site has a wave period of around 4 seconds
and a significant wave height of less than 0.5 meters (Paper I). The value of
the load resistor will vary in the experiments, but to receive a good filtering
for low values of RDC , 8 Ω was chosen as the load resistance in the design
calculations. The calculated value of CDC using Eq. 5.10 was 9.75 F, or 20.5
F on both the positive and negative DC-side, CDC+ and CDC− . If Eq. 5.11 is
used, the required calculated capacitance was 10.25 F, see Paper IV.
The real capacitance ended up to be12.17 F or 24.34 F on both the positive
and negative DC-side (CDC+ and CDC− ). The used ultracapacitors had a rated
voltage of 48.6 V each and a capacitance of 144 F respective 160 F (values
from data sheet). By adding six of those in series on both the positive and
negative DC-side, the total voltage ended up to be ±292 V. The discharge
curve for the capacitor is shown in Fig. 5.5.
200
4.6 Ohm
6.9 Ohm
13.7 Ohm
Voltage [V]
150
100
50
0
0
200
400
600
800
1000
1200
Time [s]
Figure 5.5: Discharge time for the filter with a capacitance of 24.34 F for different
values of RDC+ .
5.5 Generator
DC-voltage
connected
to
actively
controlled
When the generators are connected to the substation it is possible to control
the DC-voltage by controlling the power through the inverter. The different
implemented control algorithms for operating the inverter are presented in
Paper XI and the design of the substation is described in detail in Paper X
58
and in general in Section 4.5. The DC-voltage is controlled by changing the
modulation index. A photo of the inverter is shown in Fig. 5.6 and results from
the operation are presented in Paper X–XII.
Figure 5.6: The inverter installed in the substation.
5.6
Generator connected to resonance circuit
The first experiment on the resonance circuit was done with L9 as shown in
Fig. 5.7. A photo of the experimental set-up is show in Fig. 5.8.
It was not possible to place the resonance circuit directly after the generator in the experiment since the generator and sea cable were already installed.
Moreover, the values of the capacitors are not optimized and a higher capacitive value would be preferable. The purpose of the experiment was to test the
circuit under realistic conditions and to verify the simulations.
The diodes used in the bridge are of the SKKE 600/22 type and the capacitors, C, have a capacitance of 17 mF and a rated voltage of 450 V each. In the
experiments, two different values of the resistive part of the load were used,
RDC = 14.1 Ω and RDC = 27.4 Ω. By using Eq. 2.35, the resonant frequency
was calculated to 6.10 Hz representing a translator speed of 0.67 m/s for L9
without including the sea cable parameters in the calculations. With the sea
cable capacitance included, the resonant frequency was calculated to 6.09 Hz.
59
Resonance circuit
RG
iDC, vDC
Sea cable
Generator
LS
RC
CC/2
ea
C
iin, vin
CC/2
CDC
C
RG
LS
RC
CC/2
eb
C
iin, vin
CC/2
C
RG
ec
LS
RC
CC/2
C
iin, vin
CC/2
C
Figure 5.7: Circuit diagram of the experimental set-up.
Figure 5.8: A picture of the installed resonance circuit.
60
Load
RDC
6. Summary of Results
Results from the different load cases are discussed in this chapter.
6.1
Generator connected to resistive load
When the generator is connected to a resistive load, the voltage and current
have a linear relation and the WEC is subjected to a fairly constant damping. The three phase voltage measured over the resistive load, RL is shown in
Fig. 6.1. The voltage is zero at the translator’s turning points and increases in
amplitude until it reaches its centre position after which it starts to decrease.
200
Voltage [V]
100
0
-100
-200
0
2
4
6
8
10
Time [s]
Figure 6.1: Voltage out from L1 measured over a resistive load.
The power, speed of the translator and the damping are shown in Fig. 6.2.
The damping of L1 is not constant for all translator speeds. However, with
the exception of the transients and the rise times, a stable damping is visible
around 30 kWs/m. The filtering of the speed curve results in the curve being
larger than zero for cases when the power is zero, see Fig. 6.2 between t =
9 − 10 s and t = 41 − 43 s. In turn, this has an impact on the damping curve.
Experimental data from the generator were used to verify the generator
model in the simulations made in Paper VII, and the result can be seen in
Fig. 6.3. The data were sampled with a frequency of 50 Hz and the translator
speed was calculated with the knowledge of the pole width and period time of
the voltage. The match between experimental and simulated data is good, but
the experimental power data is more scattered.
61
Power [kW]
30
15
0
Speed [m/s]
1.5
1
0.5
Damping factor [kNs/m]
0
60
30
0
0
5
10
15
20
25
Time [s]
30
35
40
45
50
55
Figure 6.2: 55 s of measurements from L1 connected to a 4.9 Ω load. a) Power in the
load. b) Translator speed. c) The damping, γ. (Paper III)
a)
Experimental data 2.2 Ohm
Power in load (kW)
12
Simulated data 2.2 Ohm
8
4
0
0
0.2
0.4
Translator speed (m/s)
0.6
0.8
Figure 6.3: Comparison between experimental and simulated data. (Paper VII).
The main purpose with the simulations made in Paper VII was to show
the difference between having the generator connected to a linear load and a
non-linear load. The simulated results of the power in the load and damping
function for the linear case are shown in Fig. 6.4. The lowest resistive value,
RL = 0.5 Ω, results in the highest damping but the lowest amount of delivered
power to the load.
62
The results presented in Paper III indicate that the two lower values of the
load, RL = 2.2 Ω and 4.9 Ω, result in the highest amount of absorbed power.
0.5 Ohm
2.2 Ohm
4.9 Ohm
10 Ohm
80
a)
Damping function (kNs/m)
Power in load (kW)
40
30
20
10
0
0
0.4
0.8
1.2
Translator speed [m/s]
1.6
60
0.5 Ohm b)
2.2 Ohm
4.9 Ohm
10 Ohm
40
20
0
0
0.4
0.8
1.2
Translator speed [m/s]
1.6
Figure 6.4: Simulated results from the generator connected to resistive load. a) Power
measured in the load for different values of RL . b) Damping function for the resistive
case. (Paper VII).
A high damping results in high currents and low voltages which decrease
the efficiency of the generator. A more suitable system would be if a high
power absorption coincides with a high power production. In the simulations,
no consideration has been taken to the current limits of the generator. Moreover, in the simulations, the power production is studied for a certain translator
speed. In reality, the translator will move with an irregular speed resulting in
a spectrum of frequencies, see Fig. 6.2b. The load sets the limits for how high
the translator speed will be for a certain sea state and a higher damping results
in lower translator speeds.
For a certain sea state, a generator connected to a resistive load with a low
value will move slower compared to a generator with a higher value of the
load. There exists a limit for how low the value of the load can be and still get
the translator to move.
6.2
Generator connected to diode rectifier and filter
The purpose to have the generator connected to a diode rectifier and a load
with a high capacitive part was to investigate to which extent the voltage and
power from the generator could be smoothened and to study a non-linear operation of the WEC. The circuit gives the first indications on how the WEC will
operate in a grid connected system with an intermediate link with a constant
DC-voltage. The DC-voltage over the load, RDC = 13.75 Ω, is shown in Fig.
6.5.
The graph shows a 2000 s period of measurements of the DC-voltage which
is fairly constant during the period. The frequency and the amplitude variations due to size of magnets and translator speed and the variations due to the
shape of incoming waves are smoothed out. However, a small variation in the
voltage is still visible when the waves change drastically in height and period.
63
Voltage (V)
50
0
-50
0
500
1500
1000
Time (s)
2000
Voltage (V)
50
0
Current (A)
-50
50
0
-50
120
130
Time (s)
140
150
Figure 6.5: The upper graph shows the voltage measured over RDC during a time
period of 30 minutes. The two lower graphs zoom in 30 seconds of the upper graph
and show the incoming voltage and current, vin and iin from L1. (Paper IX).
During the studied period, the highest DC-voltage was VDC = 92 V at t = 1250
s and the lowest value obtained was VDC = 62 V at t = 0 s. Overall, the filter
operates as expected and keeps the DC-voltage and power in the load stable
during time periods where the sea state is not drastically changing.
The part that is zoomed in Fig. 6.5 shows the incoming voltage and current,
vin and iin , from L1. In this case, compared to the resistive case, there is no
linear relation between the voltage and the current. The capacitor controls the
amplitude of the incoming voltage to some extent. When the AC-voltage is
lower than the DC-voltage, the generator will be undamped and no current is
64
produced since the diodes are not conducting, see Fig. 6.5 between t =132–
135 s. When the AC-voltage reaches the required value to get the diodes to
conduct, the generator is damped and a current is delivered to the load. In the
zoomed part, the variation in DC-voltage is maximum 8 V.
Fig. 6.6 shows what impact the resistive load value has on the power absorption. The power spectrum with a total resistive value of RDC = 27.5 Ω has
less power peaks compared to the case with a resistive value of RDC = 9.2 Ω,
but the power peaks are higher. The two spectrums were sampled at a similar
sea state, HS was about 1.9 m and TE was approximately 5.8 s.
20
a)
Produced power [kW]
I
R = 9.2 Ohm
15
10
5
0
Time [s]
30
b)
I
R = 27.5 Ohm
Produced power [kW]
25
20
15
10
5
Time [s]
Figure 6.6: Incident produced power by the generator, sea cable losses are included.
The time series were sampled at a similar sea state, the significant wave height was
approximately 1.9 m and the wave period was about 5.8 s. a) The resistive part of the
load is 9.2 Ohm. b) The resistive part of the load is 27.5 Ohm. (Paper VI).
A sampling of 713.5 h of measurements is shown in Fig. 6.7. Each data
point represents a 30 minute mean value calculated of data sampled with 50
Hz. The results show that RDC = 9.17 Ω results in the highest amount of absorbed power for sea states higher than 10 kW/m. In two of the load cases,
RDC = 13.75 Ω and RDC = 18.34 Ω, there are no data available for sea states
above 10 kW/m.
The results in Fig. 6.7 show that the value of the load has a higher impact
on the power produced when the sea state increases. For low sea states, J < 5
65
3.0
Absorbed power [kW]
2.5
2.0
1.5
9.17 Ohm
9.17 Ohm trendline
13.75 Ohm
13.75 Ohm trendline
18.34 Ohm
18.34 Ohm trendline
27.50 Ohm
27.50 Ohm trendline
1.0
0.5
0
0
5
10
20
15
25
Sea state [kW/m]
Figure 6.7: 30 minute mean values of the absorbed power, Pabs , when L1 is connected
to the rectifier, capacitors and four different values of the resistive load. The presented
data represents 713.5 h of measurements. (Paper V).
kW/m, it is not obvious which load is the most ideal since the data from the
different load cases are scattered in the same interval.
For the lowest value of the load, RDC = 9.17 Ω, the data are more scattered
compared to the data from the highest value of the load, RDC = 27.5 Ω.
6.3 Generator
DC-voltage
connected
to
actively
controlled
The first figure, Fig. 6.8, shows experimental data from L2 and L3 connected
to the substation. The upper figure shows the incoming voltages from the generators and the DC-voltage. The DC-voltage is controlled by the inverter to
be 80 V but the impedance after the inverter is too high to have a fixed DCvoltage at this voltage level and variations in the DC-voltage are visible. The
lower figure shows the power from the individual WECs and the combined
power delivered to the DC-bus is shown in the green curve in the graph. A
more detailed study of the power smoothening when aggregating the power
from a number of generators is made in Paper XIII.
Simulations were made of the generator connected to a constant
DC-voltage representing a circuit with an active control and a low value of
the load impedance after the control device. Results from the simulations are
shown in Fig. 6.9.
The translator must reach a certain translator speed before the generator
starts to produce power and starts to be damped. This was also noticed in
66
60
40
Voltage [V]
20
0
-20
-40
-60
10
Electrical power [kW]
8
6
4
2
0
0
10
20
30
40
50
Time [s]
Figure 6.8: a) One of the phase voltages, vain , from L2, blue, and L3, red, and the
DC-voltage in black. The voltages are measured in the substation. b) Individual power
from the two generators and the combined power delivered to the DC-bus in green.
(Paper X).
30
50 V
100 V
150 V
200 V
20
10
0
0
0.4
1.2
0.8
Translator speed [m/s]
80
a)
Damping function [kNs/m]
Power in load [kW]
40
1.6
50 V b)
100 V
150 V
200 V
60
40
20
00
1.2
0.4
0.8
Translator speed [m/s]
1.6
Figure 6.9: Simulated results from the generator connected to a constant DC-voltage.
a) Power measured in the load for different values of VDC . b) Damping function for
the non-linear case. (Paper VII).
67
the result shown in Fig. 6.5. Compared to the linear case shown in Fig. 6.4,
the optimal load value will be different for different translator speeds. The
damping function shown in Fig. 6.9b will first increase drastically and then
start to level out. For high translator speeds, the damping function for the
different load cases will not differ significantly.
6.4
Generator connected to resonance circuit
One of the phase voltages, vain , and the currents, iain , from L9 are shown in
Fig. 6.10.
AC voltage [V]
a)
200
0
-200
b)
AC current [A]
50
0
-50
DC voltage [V]
c)
200
0
-200
0
2
4
6
8
10
12
Time [s]
Figure 6.10: Experimental results from L9 connected to a resonance circuit a) Phase
voltage measured before the resonance circuit, vain . b) Current measured before the
resonance circuit, iain . c) DC-voltage measured over the resistive load, RDC . (Paper
XIV).
The voltage and current are unbalanced due to the resonance circuit which
allows the negative side of the AC-voltage to oscillate between the capacitor
68
and the inductor and the current is larger on the positive side. However, the
DC-voltage over the load, RDC , is balanced, see Fig. 6.10c.
A comparison of the absorbed power in percent and in kW, Aabs resp. Pabs ,
for L1 connected to the diode bridge and capacitors as in the results presented
in Section 7.2 and for L9 connected to the resonance circuit is made in Fig.
6.11. The results for L9 show a higher power absorption compared to L1. This
can mainly be explained by the upgrades that have been done on L9, compare
Table 3.1 and Table 3.2.
a)
60
L9 27.4 W
L9 27.4 W trendline
L9 14.1 W
L9 14.1 W trendline
L1 9.2 W
L1 9.2 W trendline
L1 27.5 W
L1 27.5 W trendline
4
Absorbed power [%]
Absorbed power Pabs [kW]
6
2
0
0
2
1
Significant wave height [m]
L9 27.4 W
L9 27.4 W trendline
L9 14.1 W
L9 14.1 W trendline
L1 9.2 W
L1 9.2 W trendline
L1 27.5 W
L1 27.5 W trendline
40
20
0
0
3
b)
2
1.5
0.5
1
Significant wave height [m]
2.5
Figure 6.11: Half-hour mean values of the power, Pabs and Aabs , for different significant wave heights and loads. L9 is connected to the resonance circuit and L1 is
connected to the rectifier and capacitors as in the results in Section 7.2. (Paper XIV).
One of the objectives with the experiment was to verify the simulations
made on the resonance circuit and see if the model could be used for this
kind of study. The results of the comparison can be seen in Fig. 6.12. As in
Fig. 6.3, the simulated and experimental data are in the same region, but the
experimental data are more scattered.
Power [kW]
120
Experiment 27.4 W
Simulation 27.4 W
Experiment 14.1 W
Simulation 14. 1W
80
40
0
0
0.4
1.2
0.8
Translator speed [m/s]
1.6
Figure 6.12: Comparison between simulated and experimental results. (Paper XIV).
69
The results from the simulations of the resonance circuit can be seen in Fig.
6.13 and 6.14. The data for L9 presented in Table 3.2 are used in the simulations and two different circuits are simulated. First, the generator is connected to a six-pulse diode bridge circuit as in Fig. 2.4 with CDC = 9 mF and
RDC = 5 Ω and 20 Ω, i.e. the reference case. In the other circuit, the generator
is connected to the resonance circuit shown in Fig. 5.7, but the sea cable is
not included in the simulations, i.e. the resonance case. In the resonance circuit C = 17 mF, CDC = 9 and RDC = 5 Ω and 20 Ω. In the simulations shown
in Fig. 6.14 the resistive load, RDC is exchanged to a constant DC-voltage,
VDC = 200 V and 400 V.
120
Pabs_ref 5 W
Pabs_ref 20 W
Pabs_res 5 W
Pabs_res 20 W
a)
80
Power [kW]
Power [kW]
160
80
5
20
5
20
W
W
W
W
b)
40
20
40
00
60
PL_ref
PL_ref
PL_res
PL_res
5
10
Frequency [Hz]
15
0
0
5
10
Frequency [Hz]
15
Figure 6.13: Simulations of L9 connected to a resonance circuit and to a diode bridge.
a) Absorbed power, Pabs_re f in the diode bridge case and Pabs_res in the resonance case.
b) Power in the load, PL_re f in the diode bridge case and PL_res in the resonance case.
(Paper XIV).
In the results shown in Fig. 6.13a, the resonance circuit results in the highest
power absorbed (highest damping) for the same value of the resistive load,
RDC. The power in the load studied for RDC = 5 Ω is similar for frequencies
up to about 7 Hz. For higher values, the resonance circuit has a slightly higher
power production. For RDC = 20 Ω, the resonance circuit delivers a higher
amount of power to the load for all frequencies in the studied interval.
With a constant DC-voltage, the resonance circuit results in an even better
power absorption compared to the case with just a diode bridge, see Fig. 6.14a.
For frequencies higher than 7 Hz, both the 200 V and 400 V case results in a
higher damping compared to the reference case. Moreover, in the resonance
case, the system will start to deliver power to the load for lower frequencies,
i.e. lower translator speeds for the same value of the DC-voltage.
While studying the power in the load, the reference case has the highest
produced power between f = 3.6 − 7 Hz. Otherwise, the 400 V resonance
case shows a good power production for frequencies higher than 4 Hz. The
400 V resonance case shows a better power production compared to the 400
V reference case for frequencies lower than 10.5 Hz.
70
200
60
Power [kW]
160
Power [kW]
a)
Pabs_ref 200 V
Pabs_ref 400 V
Pabs_res 200 V
Pabs_res 400 V
120
80
PL_ref 200 V
PL_ref 400 V
PL_res 200 V
PL_res 400 V
b)
40
20
40
0
0
4
8
Frequency [Hz]
12
00
4
8
Frequency [Hz]
12
Figure 6.14: Simulations of L9 connected to a resonance circuit and to a diode bridge
with a constant DC-voltage. a) Absorbed power, Pabs_re f in the diode bridge case and
Pabs_res in the resonance case. b) Power in the load, PL_re f in the diode bridge case and
PL_res in the resonance case. (Paper XIV).
71
7. Discussion
One of the main tasks for the author has been to study how the electrical conversion system between the generator and grid could be designed to both fit
the generator and in the future fit the grid. So far, the author has studied the
generator connected to four different electrical circuits where three of them
can represent two different load cases occurring when the WEC is connected
to the grid. Both experiments and simulations have been carried out and the
results show that the load cases work well and fulfil their purposes. However,
it is hard to draw any conclusions about which load case would be most preferable. The design of the WEC has an impact on the system performance and
vice versa. A change in for example the no-load voltage of the generator, or a
change in buoy shape will affect the operation of the generator and a change in
the electrical system could be needed. Therefore, to make the right optimizations in the design of the WEC as well as in the design of electrical system,
the development of the different parts should be carried out in parallel.
7.1
Experimental results
In all of the experimental results, there are uncertainties in the measurements
that are not included in the result graphs. With exception for Paper XII, the
presentation of the accuracy of the measurements is not described and discussed in detail in the papers. Therefore, another way to present the experimental results is shown in Fig. 7.1.
The accuracy of the voltage and current measurements is given in Section
3.1 and the accuracy of the resistance in the generator and the sea cable is
presented in Table 3.1–3.3. The error of Pin is estimated to ±5.4% and the
error of Ploss is estimated to ±7.8%. These errors represented with error bars
are shown in Fig. 7.1. However, in figures including a lot of data, the error
bars can make the graph difficult to analyze.
Moreover, as mentioned before, when calculating the absorbed power, Pabs ,
only the resistive losses are added to the incoming power or power in the load.
The actual value for Pabs is therefore believed to be higher than the value presented in the results. Losses that should be added to the experimental value of
Pabs are the iron losses, the mechanical losses, losses due to the inductance and
capacitance in the generator respective sea cable, and for L9, the losses in the
resonance bridge. The iron losses can be estimated from the FEM simulation
model of the WEC. The mechanical losses occur due to friction between different parts and can be hard to estimate and are assumed to change over time.
73
4
Absorbed power [kW]
L9 27.4 W
L9 27.4 W trendline
3
2
1
0
0.2
0.6
1
Significant wave height [m]
1.4
Figure 7.1: Example of data representation with error bars. Result data from Paper
XIV are used.
The losses due to the inductive and capacitive reactance could be estimated
but it will not be straightforward since the frequency will vary. A more correct
value of the absorbed power could therefore be estimated by using the force
measurement on the line connecting the buoy to the translator to decide the
force that is transferred to the translator and calculate Fem from Eq. 2.15. By
studying the force measurement data and the electrical power data, an experimental analysis of the mechanical losses and iron losses could be performed.
When the speed of the translator is calculated from experimental data, as
in Paper III, VII and XIV, the speed is calculated by dividing the pole width
with the time between two zero crossings of the voltage, see the black circles
in Fig. 7.2.
At the turning points of the translator, there is some noise in the voltage. An
example of the noise is marked in Fig. 7.2. The noise results in the calculated
speed being much larger than the actual speed. Therefore, the speed curve is
filtered. The filtration of the noise affects the calculation of the speed which
in turn affects the calculation of the damping. Because of the filtration, the
damping function shown in Fig. 6.2, Paper III, is believed to be even more
constant and similar to the simulated result if a more accurate calculation had
been performed.
7.2 Generator connected
DC-voltage loads
to
resistive
load
and
In a system with a constant DC-voltage, several generators can be connected
in parallel before the device controlling the voltage, see the system presented
in Paper IX–XIII. Advantages with this system compared to a system with
74
80
Voltage [V]
40
Zero crossing
Noise
0
-40
-80
0
1
2
Time [s]
3
4
Figure 7.2: Three phase voltage out from the WEC. The black circles show two zero
crossings of the voltage. The black box indicates a disturbance or noise in the voltage
which causes problems when the translator speed is calculated from the voltage.
individual control for each WEC are: a reduction in complexity, an increased
efficiency for the conversion system, saving of space, and reduction in price.
A drawback is that the power production will probably not be as high as for an
individually control system since the generators must reach a certain translator
speed before they start to produce power.
For the resistive case and DC-voltage cases, the results indicate that the generator will absorb more power when the damping increases. This will result
in increased currents and decreased voltages since the increase in damping is
achieved by decreasing the resistive value of the load or decreasing the DCvoltage, see the results in Paper III–VII. A high current in combination with a
low voltage will give higher losses in the generator and sea cable. As a result,
the optimum load for most amount of power delivered to the load and power
absorbed will not coincide.
7.3
Limitations in power absorption
There is a limitation in how much the WEC can be damped and still move.
When the translator is on its way down, roughly, the electromagnetic force,
Fem , must be smaller than mg or (mg + Fs ) if springs are used. When the translator is on its way up, the lifting force of the buoy, Fb , must be larger than Fem ,
mg and Fs , e.g. Fb > Fem + Fs + mg. A stationary condition for Fb is calculated
by using Archimede’s law.
For L9, which has a translator weight of 2700 kg, the largest value of
Pabs_limit1 is given in Fig. 7.3a together with the simulated results. Pabs_limit1 is
calculated as the maximum power that can be absorbed when the translator is
on its way down. Pabs_limit2 and Pabs_limit3 in Fig. 7.3, give the maximum value
75
of Pabs when the translator is on its way up. In the calculation of Pabs_limit2 ,
the whole volume of the buoy is included when the lifting force of the buoy
is calculated. In the calculation of Pabs_limit3 , 50% of the volume is included.
The buoy concerned is a torus shaped buoy with a outer diameter of 6.6 m.
When studying Fig. 7.3a, one realizes that Pabs_limit1 , will limit the WEC’s
ability to both absorb and produce power. Only the 20 Ω reference case is
below the limit during the studied interval and this will also be the load case
with the lowest amount of produced power in the load, see Fig. 6.14.
Pabs_limit1= Maximum allowed value of Pabs when the translator is on its way down.
Pabs_limit2= Maximum allowed value of Pabs when the translator is on its way up. 100%
of the buoy’s volume is used.
Pabs_limit3 = Maximum allowed value of Pabs when the translator is on its way up. 50%
of the buoy’s volume is used.
160
120
80
40
0
0
(0)
Pabs_ref 5 W
Pabs_ref 20 W
Pabs_res 20 W
Pabs_res 20 W
Pabs_limit1
Pabs_limit2
Pabs_limit3
a)
160
Absorbed power [kW]
Absorbed power [kW]
200
15
5
10
(1.65)
(0.55)
(1.1)
Frequency [Hz], (Speed [m/s])
120
80
Pabs_ref 5 W
Pabs_ref 20 W
Pabs_res 20 W
Pabs_res 20 W
Pabs_limit1
Pabs_limit2
Pabs_limit3
b)
40
0
0
(0)
15
5
10
(1.65)
(0.55)
(1.1)
Frequency [Hz], (Speed [m/s])
Figure 7.3: The simulated results of L9 and the limitation in Pabs due to the mass of
the translator. In a) the estimation of Pabs with a translator mass of 2700 kg, and in b),
the estimation of Pabs with a translator mass of 4000 kg.
The limitation of Pabs_limit1 , is a consequence of the mass of the translator
and if the mass of the translator is increased, a higher damping could be applied and thereby a higher power production. An example with a generator
with the same properties as L9 but with a translator mass of 4000 kg is shown
in Fig. 7.3b. This generator can both be subjected to a higher damping and is
also believed to move with a higher speed which also increases the produced
power.
In both of the cases in Fig. 7.3, the lifting force of the buoy is sufficiently
high for almost all of the studied load cases keeping Pabs_limit2 higher than the
simulated cases. There will be an optimum mass of the translator which could
be studied further. This is both a question of cost and power optimization.
Another limitation in how high damping that can be applied to the generator
is given by the current and voltage rating of the generator and sea cable. These
parameters can also be optimized and studied further.
76
7.4
Resonance circuit
The resonance circuit enables a higher damping of the generator, see Paper
XIV. The focus of the experiment with the resonance circuit was to study if
the circuit operated as predicted in the simulations. The simulations made in
Paper XIV show that an increase in power production can be achieved with
the new circuit. However, the performance is strongly dependent on how the
WEC and the rest of the system will be designed. Further experimental studies
are required for evaluating the circuit properly.
There were mainly three parameters responsible for the experiment on the
circuit not working in a satisfactory way. First, the value of the capacitance
was too low, the resonant frequency was about 6.1 Hz, representing a translator speed of 0.67 m/s. Second, the resonance circuit was placed in the measuring station and not directly after the generator. The placement of the resonance circuit decreases the effect of the resonance and there is no possibility
to measure the power between the generator and the sea cable which makes
the analysis of the circuit more difficult. The third parameter is the mass of
the translator of L9. In Fig. 7.3, the limit in Pabs is shown and the mass sets
a clear limit on how high the damping function can be without slowing down
the speed of the translator. In this case, the mass of the translator is too low for
the resonance circuit, and even for other load cases, and will limit the motion
of the translator and thereby limit the power production.
Because of the reasons mentioned, the results from the experiments can
not be used to evaluate the resonance circuit in a suitable way. Moreover, a
reference case with L9 connected to the diode rectifier would be necessary to
make a good evaluation of the circuit. The experimental results are used to
verify the simulations and the simulated and experimental results match quite
well, but because of the scattering of the experimental data, a deeper study
with more experimental data would be preferable. However, the results from
the experiments show that L9 is significantly improved compared to L1 and a
higher energy absorption is achieved.
It should also be mentioned that a one phase generator has primarily been
studied in the development of the resonance circuit and there would be other
connection options for a three phase generator that would be more favourable
than the one used here.
7.5
Simulated results
The simulation model used in Paper VII, X and XIII works well for the initial
study of the system and gives indications on how the load affects the generator
performance. It also gives indications on how well the generator could work
according to the electrical design of the WEC.
When studying the simulated results one should be aware of the fact that
the translator will move with an irregular speed and the speed is strongly connected to the sea state and the damping of the generator. The results from the
77
simulations are therefore rough but seem to agree relatively well with the experimental results, especially for cases when A f ac = 1. For L9 with the translator length equal to the stator length, there could be an option in the future to
study different values of A f ac .
78
8. Conclusions
Conclusions that can be drawn form the present work are:
• All of the studied systems worked well and a good agreement between
the simulations and the experiments was shown. The results from all of
the papers show that the studied technology can convert the energy in the
waves into electric energy.
• The load to which the generator is connected to has an impact on the power
production and power absorption. In the resistive case and in the case with
a stable DC-voltage, a higher absorption was noticed for low values of the
resistive part of the load or for low DC-voltages. (Paper III, Paper V, Paper
VI)
• The DC-capacitors were able to maintain the DC-voltage within the designated limits. (Paper IV)
• The fluctuating power of the waves can be smoothened to a great extent by
using capacitors after the rectifier. (Paper V)
• An absorption of around 5–15 % was obtained for L1 when it was connected to the rectifier and filter and when it was connected to a resistive
load. (Paper III and Paper VI)
• An absorption of around 20–30% was obtained for L9 when it was connected to the resonance circuit. However, this is mainly because of the improvements made on the design of the WEC. (Paper XIV)
• The generators can be connected in parallel to a common DC-bus despite
the fluctuations in amplitude and frequency of the generator voltages. (Paper X)
• Marine substations placed on the seabed can be used for offshore renewable
energy systems. (Paper IX–XIII)
• With the resonance circuit, an increase in damping function and power produced can be achieved for higher DC-voltages and higher resistive loads
compared to a case with a diode bridge. (Paper XIV)
79
9. Future Work
Even if there exists a well functioning wave energy conversion system, there
are a lot of future improvements and studies to be done. On the electrical
system there are six main areas closely connected to the author’s work that
need to be studied further:
• Further improvements and experimental tests on the resonance circuit. An
initial study of the resonance circuit is done in the thesis and the circuit
needs to be improved. Important subjects to study are how to choose an
optimum value of the resonant frequency, if the circuit could be built for a
reasonable price, could there be a benefit to use thyristors instead of diodes
in the bridge, and how should the system after the resonance circuit be
designed. More experiments need to be done on both three phase and one
phase generators to investigate the advantages with the circuit compare to
other systems.
• Study other control options, mainly the option to controlling individual
generators. There could be other control options in addition to having the
generator connected to a constant DC-voltage.
• Connect the system to the grid. Test different inverters such as multilevel
inverters and different control algorithms. Test the transformer with the onload tap changer system.
• Improve the simulation model.
• Evaluate efficiency, costs, maintenance work and complexity for different
load cases based on experimental results and risk analysis.
• Make accurate simulations of the thermal properties in the substation.
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10. Summary of Papers
Paper I
Wave energy from the North Sea: experiences from the Lysekil research
site
The paper gives an overview of the project and includes results from studies
on the generator, L1, connected to a resistive load and non-linear load, as well
as results from environmental studies. One of the objects of the paper was to
present the different research areas in the group within the same paper to give
an overall picture of the project. The launching process of the first generator
is presented in detail.
The author has contributed to the written material, mainly in the section
about the measuring station and in the result section about the electrical system. The author has participated in the work with the experimental set-up at
the Lysekil research site.
Published in Surveys in Geophysics, Springer, 29(3):221–240, 2008, invited
paper.
Paper II
Catch the Wave to Electricity - The Conversion of Wave Motions to
Electricity Using a Grid-Oriented Approach
Paper II focuses on the development and design of the first linear generator.
The paper presents the design process and the challenges when constructing L1. The results show the performance of the generator which has a good
agreement with the numerical models.
The author has contributed to the written material and to the experimental
set-up at the measuring station.
Published in IEEE Power and Energy Magazine 7(1):50–54, 2009.
Paper III
Ocean wave energy absorption in response to wave frequency and
amplitude - offshore experiments on a wave energy converter
83
The WEC’s ability to capture the energy from the ocean is investigated
at different sea states and with the generator connected to different resistive
loads. The result showed a maximum absorption of about 24%.
Results showing the damping function together with the power and translator speed are also presented in the paper.
The author has contributed to the experimental set-up in the measuring station.
Conditionally accepted for publication in IET Renewable Power Generation, July 2010. Revision submitted in December 2010.
Paper IV
Experimental results of rectification and filtration from an offshore wave
energy system
The paper describes the design of the experimental set-up studied in Paper
IV–Paper VI, where the WEC is connected to a diode rectifier and a load
consisting of capacitors and resistors. The paper explains how the value of the
capacitor can be chosen. The focus of the paper is to investigate whether the
DC-voltage after the rectifier can be smoothed to the extent that is expected
from calculations and simulations. Both simulated and experimental results
are presented.
The results of the experiments show that a smooth DC-voltage can
be achieved and there was a good agreement between simulated and
experimental results.
Most parts of the paper were written by the author. The author had a leading
role in the design and installation of the rectifier and load system.
Published in Renewable Energy, 34(15):1381–1387, 2009.
Paper V
Study of a Wave Energy Converter Connected to a Nonlinear Load
The resistive part of the non-linear load in the experiment in Paper IV has
been supplemented with more resistive loads. This makes it possible to load
the generator differently at different sea states. The paper focuses on how the
generator operates, i.e. how it moves and produces power when it is connected
to the rectifier and the filter. The results show that a smooth power can be
achieved with only one direct driven linear generator. The absorbed power
will increase when the resistive value of the load is decreased.
Most parts of the paper were written by the author. The author had a leading role in the design and installation of the rectifier and load system. The
paper has been on the IEEE Journal of Oceanic Engineering “top ten accessed
84
articles”-list from June to October 2009 (except for August) and in January
2010.
Published in IEEE Journal of Oceanic Engineering, 34(2):123–127, 2009.
Paper VI
Experimental Results From an Offshore Wave Energy Converter
In this paper, the performance of the WEC is investigated at different nonlinear loads. The results show what impact the damping of the WEC has on
the power production. The highest absorption reached was about 26% and the
average absorption was 5–10%.
Most parts of the paper were written by the author. The author had a leading
role in the design and installation of the rectifier and load system.
The paper has been presented orally by the author at the 27th International Conference on Offshore Mechanics and Arctic Engineering OMAE
2008, June 15–20, 2008, Estoril, Portugal, OMAE2008-57415 (Paper XX).
The paper was the most downloaded article from JOMAE during October and
November 2010.
Published in Journal of Offshore Mechanics and Arctic Engineering, JOMAE, 132(4):5 pages, 2010.
Paper VII
Operation analysis of a wave energy converter under different load
conditions
The paper analyses the electrical behaviour of the generator when it is subjected to different loads. Two different cases were studied. First, to verify the
generator model, the generator connected to a resistive load, and second, the
generator connected to a rectifier and a controlled DC-voltage. A simulation
model was made in MATLAB Simulink and verified with experimental results. The results show that the power production is strongly dependent on
how the generator is damped. The generator will absorb the most power when
it is damped the hardest. However, with the system presented in the paper, this
will result in a high current which is not optimal for the rest of the system.
The author has written the paper and done the simulations.
Accepted for publication in IET Renewable Power Generation, December
2010.
85
Paper VIII
A wave power unit
The invention presented in the patent gives a solution on how to cope with
the power from the WEC when it becomes higher than the power rating of the
marine substation. The idea is basically to have an additional circuit, a dump
load, which the WEC can be connected to when the power is higher than the
substation limit, or in other cases when the substation can’t handle the power
from the WECs, for example an error in the grid.
The WEC can be connected to the dump load and the substation at the same
time, which enables a power production to the grid at high sea sates.
The author has contributed to the layout and function of the electrical system.
International patent, publication number WO 2010/085188, published
2010-07-29.
Paper IX
Design proposal of electrical system for linear generator wave power
plants
Paper IX presents two different marine substation designs, one built and
developed by Uppsala University and one built and developed by Seabased
Industry AB. Power data from L1 are presented during a three month period
and the difference between a linear load and a non-linear load is discussed.
The paper was presented orally by the author at the IECON 2009 conference
in Porto, Portugal. Most parts of the paper were written by the author. The
author has contributed to the electrical design of the two substations.
Published in the proceedings of IECON 2009, 35th annual conference of
IEEE Industrial Electronics, Porto, Portugal, PD-027448:4429–4434, 2009.
Paper X
Offshore underwater substation for wave energy converter arrays
The construction work and design of the first marine substation are described in detail in the paper. Tests of the rectifiers and filter have been done
with the help of two laboratory generators. The experiment was verified with
simulations done in MATLAB Simulink.
The results show a good agreement between the simulations and experiments and the first part of the system worked as expected. Results from offshore operation are presented showing the power production from two generators connected to the substation.
86
A shorter version of the paper was presented by Dr. Rahm at the 8th European Wave and Tidal Energy Conference, EWTEC, 7–10 September, Uppsala,
Sweden, 2009 (Paper XIX).
The author has done the simulations and contributed to the design of the
electrical system in the marine substation.
Published in IET Renewable Power Generation 4(6):602–612, 2010.
Paper XI
Description of the control and measurement system used in the Low
Voltage Marine Substation at the Lysekil research site
The paper describes how the control and measurement system are constructed. The control system was developed on The National Instrument CompactRIO platform consisting of a real-time controller with real-time operating
software, one FPGA chip and different input and output modules. The result
shows how the control system can manage to control the inverter in a laboratory experiment.
The paper was presented by Mr. Svensson at the 8th European Wave and
Tidal Energy Conference, EWTEC, 7–10 September, Uppsala, Sweden, 2009.
The author was involved in the experiments presented in Fig. 7.
Published in the proceedings of the 8th European Wave and Tidal Energy
Conference, EWTEC, Uppsala, Sweden, pp. 44–50, 2009.
Paper XII
Temperature measurements in a linear generator and marine substation
for wave power
The temperatures in the WEC and in the marine substation are studied in
the paper. Two different experiments are presented. In the first experiment,
the temperature was measured in the WEC during 34 hours. The sea state was
quite good during the experiment, 15 kW/m. In the second experiment the
temperatures were also measured in the substation during 158 minutes. No
drastic temperature increase was found in the two experiments.
The paper was presented orally by the author at the 29th International Conference on Offshore Mechanics and Arctic Engineering OMAE 2010, June
6–11, Shanghai, China, OMAE2010-20881 (Paper XXI).
The author made a significant contribution in writing the paper, especially
to the experiment, result and discussion section. Submitted to Journal of Offshore Mechanics and Arctic Engineering, June 2010.
87
Paper XIII
Experimental results from the operation of aggregated WECs
In Paper XIII, it is studied how the power from a wave power plant can be
smoothened by aggregating the power from several WECs. The paper presents
experimental results from offshore operation of the marine substation. The
results show that the maximum to mean power could be reduced with 48%
and the standard deviation of power was reduced by 28.5% by connecting two
WECs in parallel.
The author has contributed to the design of the electrical system in the marine substation.
Submitted to IET Renewable Power Generation, December 2010.
Paper XIV
Linear generator connected to a resonance circuit
A novel circuit is described in the paper which combines a resonance circuit
with a diode bridge. Both experiments and simulations are presented. In the
experiment, L9 is connected to the resonance circuit. The results shows that
an increase in absorbed power is achieved compared to the results from L1.
However, this is most likely due to the improvements made on L9.
The match between the simulations and experiments show a good agreement. Moreover, the simulated results showed that an increase in damping
and in produced power can be achieved with the resonance circuit. The resonance circuit also showed a better performance at higher DC-voltages and
higher values of the resistive load compared to the case with a diode bridge.
The author has written the paper, done the simulations, contributed to the
experimental set-up in the measuring station and been involved in the design
of the circuit.
Submitted to Renewable Energy, January 2011.
Paper XV
Resonance circuit
The invention in the patent is a novel circuit which enables more power
delivered to an external load compared to a conventional resonance circuit.
The resonance circuit is suitable for the studied wave power system since
it increase the damping of the generator and the optimum load case results
in higher voltages compared to the other electrical systems that have been
studied.
88
The principle of the circuit is to combine capacitors with power electronics
controlling the current flow. The circuit allows parts of the power to oscillate
between the capacitors and the armature winding inductance of the generator
and the remaining parts of the power is delivered to the load trough the power
electronic devises.
The author has contributed to the design and function of the resonance circuit.
International patent submitted to PCT/EPO PCT/SE2010/051356, 201012-09.
89
11. Svensk sammanfattning
Vågkraft är en förnybar energikälla som har en stor potential att bidra till
Världens elenergiförsörjning. Vid Sveriges centrum för förnybar elenergiomvandling, Uppsala universitet, pågår det ett forskningsprojekt om ett vågkraftsystem som består utav direkt drivna linjärgeneratorer. Generatorerna är placerade på havsbotten och kopplade till bojar på havsytan. När bojarna rör sig
med vågorna kommer translatorn i varje generator att få en linjär rörelse och
en spänning kommer att induceras i statorlindningarna.
Då spänningen från generatorerna kommer att variera i frekvens och amplitud måste denna konverteras innan vågkraftverken kan anslutas till nätet. För
att sammankoppla och omvandla effekten från generatorerna används marina
ställverk. Ställverken kommer att placeras på havsbotten och omvandla den
varierande växelspänningen från vågkraftverken till en konstant växelspänning som är möjlig att ansluta till nätet. I stora drag kommer omvandlingen att
gå till så att man först likriktar den varierande växelspänningen från generatorerna och på likspännings sidan kopplar man samman ett antal generatorer och
har en aktivt styrd likspänning. Efter detta steg omvandlar man likspänningen
till en växelspänning med en konstant frekvens och amplitud.
Generatorerna kommer att dimensioneras efter det vågklimat som de ska
installeras i. Märkeffekten av varje generator ska väljas för att få ut så många
fullasttimmar som möjlig från systemet. Antalet aggregat i en park väljs sedan
för att komma upp till den önskade installerade effekten.
För att kunna testa tekniken under så realistiska förhållanden som möjligt
har man ett forskningsområde på den svenska västkusten. Forskningsområdet
är ett av fyra områden i Europa som har klassats som ett område där
det är möjligt att testa de krav som ställs på ett kommersiellt gångbart
vågkraftsystem. I dag är forskningsområdet det enda av de fyra områdena
som har fungerande vågkraftverk i vattnet. Fram tills nu har 8 stycken olika
vågkraftverk och ett bottenställverk installerats i området. Man har även
installerat ett antal biologibojar för att kunna studera de biologiska effekterna
och i anslutning till området finns det även en mast utrustad med en kamera
och en mätstation.
Ett av författarens huvudområde har varit att designa det elektriska systemet mellan generatorn och nätet och undersöka hur utformningen av systemet kommer att påverka vågkraftverkets förmåga att absorbera och producera effekt. Fyra olika lastfall har studerats:
• Generator kopplad mot resistiv last
• Generator kopplad mot likriktare och filter
• Generator kopplad mot aktivt styrd likspänning
91
• Generator kopplad mot resonanskrets
Det första vågkraftverket som sjösattes var till en början kopplad mot en
resistiv last. En resistiv last är även den belastning som har använts i de numeriska simuleringsmodellerna av generatorn. Modellerna har legat till grund
för hur generatorn har konstruerats och dimensionerats. Till en början var det
därför viktigt att visa vilka skillnader som uppstår då vågkraftverket istället
kopplas mot ett nätanslutet system och visa hur ett sådant system ska utformas.
För att enkelt kunna representera det första steget i det elektriska systemet
som innebär att spänningen ut från vågkraftverket ska likriktas till en likspänning och på likspänningssidan ska spänningen kunna hållas på en stabil nivå
gjordes det simuleringar och senare byggdes ett system bestående av en diodlikriktare, kondensatorer och resistiva laster. Kondensatorerna var dimensionerade för att kunna hålla likspänningen stabil under kortare perioder (4–5 s).
Belastningen som generatorerna kommer att utsättas för när de kopplas mot
systemet kan på så sätt ses som ett belastningsfall som uppstår vid en nätanslutning.
Resultatet från experimentet visade att spänningen och effekten ut från ett
vågkraftverk går att stabilisera. Belastningen kommer att skilja sig jämfört
med det resistiva fallet. I det här fallet kommer generatorn att gå obelastad
tills dioderna börjar leda. Belastningen beror sedan på vilket värde den resistiva delen av lasten har, vilket i framtiden är det samma som vilken likspänningsnivå man väljer. I likhet med en rent resistiv last kommer vågkraftverket
att absorbera mer effekt för lägre värden på lasten. Vilket medför en ökad
strömproduktion och minskad spänning.
Nästa steg var att utveckla systemet ytterligare och koppla samman flera
generatorer ute till havs i ett marint ställverk. I ställverket likriktas först spänningen från varje vågkraftverk innan de kopplas samman parallellt på likspänningssidan. På likspänningssidan kontrolleras spänningen genom att man ändrar modulations index i växelriktaren. Efter växelriktaren är en transformator
med fem stycken olika lindningar på primär sidan placerad. Genom att skifta
lindningar för olika vågklimat kan man bibehålla en konstant spänning ut från
ställverket.
Först gjordes en mekanisk och en elektrisk dimensionering av ställverket
och sedan byggdes och testades det. De initiala resultaten visade att växelriktaren kunde till viss mån kontrollera likspänningen mot generatorerna och
omvandla spänningen till en 50 Hz växelspänning. Dock var styrningen av
likspänningen i vissa fall begränsad av impedansen efter växelriktaren. Resultaten visade även till vilken grad effekten ut från vågkraftverken kan jämnas
ut genom att man parallellkopplar spänningen från generatorerna på likspänningssidan.
Det system som har använts i det marina ställverket och i mätstationen innebär att man sänker spänningen och höjer strömmen från generatorerna för
att öka dämpningen och därmed öka absorptionen. Detta sätt att belasta generatorerna medför att man ökar de resistiva förlusterna i systemet och man
92
kommer till en gräns där de resistiva förlusterna är högre än den producerade
effekten.
Det vore önskvärt om man kunde ha ett system där dämpningen ökas samtidigt som man får en spänningsökning och en ökning i producerad effekt. En
ny krets har utvecklats för att komma närmare detta mål. I kretsen strävar man
efter att få resonans vilket kommer att öka den reaktiva effekten i generatorn
och därmed öka dämpningen. Men för att kunna erhålla en högre effekt i lasten har man gjort en kombinerad resonans- och likriktarkrets där en viss del av
effekten oscillerar mellan kondensatorer och generatorns lindningsinduktans
och en viss del av effekten levereras till lasten via dioderna.
Initiala simuleringar och tester har gjorts på kretsen. Simuleringarna visar
att man kan få en effekthöjning i last och en ökad dämpning med resonanskretsen jämfört med om man använder en vanlig likriktarbrygga. I de experiment som har utförts har L9:an varit kopplad mot en resonanskrets installerad i mätstationen. Experimentet gjordes främst för att kunna verifiera
simuleringarna. Vid en jämförelse mellan L9:an ansluten till resonanskretsen
och L1:an ansluten till en likriktarbrygga visade resultaten att L9:an har en
mycket högre effekt absorption och produktion jämfört med L1:an. Detta kan
till största del förklaras med de uppgraderingar som har gjorts på L9:ans design, då resonanskretsen inte är optimalt designad för L9:an.
Framtida studier som är nära sammankopplade till författarens arbete är
främst att göra fler experiment på resonanskretsen, både med trefas- och enfasgeneratorer. Under det kommande året planerar man även att ansluta vågkraftparken till nätet, vilket kommer att bli ännu en stor milstolpe för hela vågkraftgruppen.
93
12. Acknowledgments
Jag skulle vilja börja med att tacka min handledare, Mats Leijon, för
att jag har fått möjligheten att jobba med det här projektet och för
den frihet som du låter oss jobba under. Tack för alla intressant diskussioner och för att du alltid tar dig tid och hjälper till när det dyker upp problem.
Min biträdande handledare, Karin Thorburn, tackar jag för all hjälp som jag
fick för att komma igång med mitt arbete.
Jag skulle vilja tacka alla finansiärer till projektet igen. Min doktorandtjänst
har varit finansierad av Sveriges Centrum för Förnybar Elenergiomvandling
(CFE), där VINNOVA och Energimyndigheten står som huvudfinansiärer.
ÅF och J. Gust. Richters Minnesfond har bidragit med resestipendier till två
av konferenserna som jag har deltagit vid.
Alla på avd. för elektricitetslära, tack för att ni alla bidrar till att ni gör detta
till en så bra arbetsplats!
Jag frågade ett antal personen om hjälp att läsa igenom min avhandling och
jag trodde inte att så många utav er skulle tänka er att hjälpa till och det
värmde verkligen att ni ville ta er tid så nära inpå jul. Janaina, Mårten, Erik,
Magnus, Simon, Olle, Jens, Rafael, Andrej, Halvar, Rickard, Emilia och Boel
tack för alla kommentarer och värdefulla synpunkter.
Till alla i våggruppen, och speciellt till Olle, Magnus, Rickard och Boel som
har jobbat med elsystemet, tack för alla diskussioner och för att ni utför era
jobb på ett så bra sätt. Utan ert bidrag skulle inte jag ha kunnat genomföra de
experiment och studier som har behövts för mitt arbete.
Gunnel och Elin, tack för all hjälp med alla vardagliga bestyr och för ert
tålamod med felaktiga reseräkningar och blanketter mm. Thomas tack för att
du fixar datorn när den krånglar och hjälper till med andra tekniska problem.
Alla kollegor på Seabased, speciellt ni i Elsystemgruppen, jag är tacksam
för att jag har fått möjligheten att jobba tillsammans med er ett par dagar i
veckan. Jag har lärt mig så otroligt mycket utav er!
95
Till min familj och Eriks familj vill jag ge ett stort tack för allt stöd som jag
har fått.
Erik, tack för att du alltid finns där och ställer upp för mig. Du stöttar och
peppar mig när det går motigt och gläds med mig när det går bra, någon bättre
människa än du finns inte.
96
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