Dynamic response and power

Renewable Energy 50 (2013) 47e57
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Renewable Energy
journal homepage: www.elsevier.com/locate/renene
Dynamic response and power performance of a combined Spar-type floating wind
turbine and coaxial floating wave energy converter
Made Jaya Muliawan a, *, Madjid Karimirad a, b, Torgeir Moan a, b
a
b
Centre for Ship and Ocean Structures (CeSOS), Norwegian University of Science and Technology, Otto Nielsens vei 10, NO-7491 Trondheim, Norway
Norwegian Research Centre for Offshore Wind Technology (Nowitech), Norwegian University of Science and Technology, Otto Nielsens vei 10, NO-7491, Trondheim, Norway
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 16 January 2012
Accepted 30 May 2012
Available online 17 July 2012
Wind turbines need to be spaced at a distance of the order of 1 km apart to reduce the effect of aerodynamic wakes. To increase the density of the power production in the farm, the deployment of wave
energy converters (WECs) in the spaces between FWTs could be considered. However, the cost of energy
from WECs is still very large. Therefore, the deployments of the WECs will reduce the economic value of
the total project. In the present paper, a combined concept involving a combination of Spar-type FWTs
and an axi-symmetric two-body WECs is considered. Compared with segregated deployments of FWTs
and WECs, this combined concept would imply reduced capital costs of the total project because it will
reduce the number of power cables, mooring line and the structural mass of the WECs. However, the
effect of the addition of a Torus (donut-shape heaving buoy) on the FWT’s motions as well as the power
production should first be investigated. In the present study, coupled (wave- and wind-induced
response-mooring) analysis is performed using SIMO/TDHMILL3D in the time domain to study the
motion behaviour of the combined concept and to estimate the power production from both FWT and
WEC under operational conditions. Mooring tension in the combined concept is also compared with the
mooring tension in the Spar-type FWT alone. Hydrodynamic loads are determined using HydroD. The
validated simplified method called TDHMILL is implemented to calculate the aerodynamic forces as
a function of the relative wind velocity. The analysis is performed for several operational conditions
according to metocean data taken in the Statfjord field in the North Sea. Finally, the behaviour of the
combined concept under operational conditions is assessed, and it is shown to result in a positive
synergy between wind and wave energy generation in terms of both capital investment and power
production.
Ó 2012 Elsevier Ltd. All rights reserved.
Keywords:
Combined wind and wave powers
Floating wind turbine
Wave energy converter
Dynamic response
Power performance
1. Introduction
The increase in energy demand and concerns about global
warming have, among other things, led to a focus on renewable
energy resources. Among the available renewable energy
resources, wind is considered the one that has grown rapidly in
the last decade. It is reported in [1] that wind energy production
has increased at an annual rate of 25e30%. The large number of
wind turbine deployments has increased the technological readiness as well as reduced the cost of energy produced by wind
turbines. However, most of the installed wind turbines are based
onshore. By the end of 2009, just 1.3% of the global installed wind
power capacity was installed offshore [2] in water depths of less
* Corresponding author.
E-mail addresses: made.muliawan@ntnu.no (M.J. Muliawan), madjid.karimirad@
ntnu.no (M. Karimirad), torgeir.moan@ntnu.no (T. Moan).
0960-1481/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.renene.2012.05.025
than 20 m and with a distance to shore most often below 20 km.
Fixed support wind turbines, such as the ones with a mono-pile or
a jacket foundation, are the most common and suitable technology
used for this purpose. Motivated by the need to access to additional and higher-quality wind resources, deeper water offshore
areas are now being considered. In deep water, wind turbines that
are supported by a floating platform are expected to be attractive
from a cost-benefit point of view. Several floating platform types
have been proposed to support offshore wind turbines. They
include Spar, tension-leg platform, barge and semi-submersible
types, which are similar to the proven offshore floating platforms used by the oil and gas industry. However, no floating wind
turbine (FWT) technology has yet reached the stage of commercial
deployment.
Offshore wind turbines in a plant/farm need to be spaced at
a certain distance to account aerodynamic wake effect. Hence there
will be enough space between the FWTs that can be used for others
purposes, especially to achieve synergy for overall energy
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M.J. Muliawan et al. / Renewable Energy 50 (2013) 47e57
production infrastructure and integration. Placing wave energy
converters (WECs) in the spaces of a wind farm for instance make it
possible to utilize the same power cables or others used by the
wind turbines could possibly help WEC projects reduce the high
cost of energy and therefore make them more economical. The
more infrastructures that can be used for more than one purpose,
the lower the cost of the resulting energy. Therefore, the possible
combination of FWT and WEC on one floating platform should be
explored. Some studies regarding combination of FWT and WEC
have been performed and reported by previous researchers. As
reported in [3,4], both numerical and laboratory models have been
developed to study the integration of an oscillating water column
type WEC and a point-absorber-type WEC into semi-submersible
type FWT ‘WindFloat’ [5] hull. In the present study, a combined
concept involving a combination of a Spar-type FWT and a floating
point-absorber-type WEC is considered. Additional details about
the concept are described in Section 2. The application of this
concept is expected to result in a higher energy production density
and a lower cost of energy compared with segregated applications
of FWTs and WECs. However, the addition of WEC will change the
behaviour of the FWT due to mechanical and hydrodynamic
couplings between the floating bodies. A decrease in the power
produced by the FWT is not desirable but could occur as the result
of adding WEC. The purpose of the present study is therefore to
investigate the effect of the integrating a WEC with a Spar-type
FWT, in term of motions, mooring load and power under operational conditions. The investigation is conducted by comparing the
motions, mooring load and power production of the Spar-type FWT
with the motions, mooring load and power production of the FWT
in the combined concept. Additionally, the power absorbed by the
WEC will be estimated. Finally, the feasibility of the specified
combined concept to produce more energy at lower costs is
discussed.
2. The combined concept (SpareTorus Combination)
The combined concept considered in this study, that is referred
as the ‘SpareTorus Combination’ (STC) herein, is inspired by the
Spar-type FWT ‘Hywind’ [6] and the two-body floating WEC
‘Wavebob’ [7] shown in Fig. 1(a) and (b), respectively. These two
concepts are briefly described as follows:
Hywind is a concept that was developed by Statoil in Norway.
The prototype test structure (2.3 MW) of this concept has
been installed off the south-west coast of Norway. It uses
a Spar buoy tower in which the wind turbine tower is
extended to 100 m below sea level. Heavy ballast is put at the
bottom of the tower, bringing the centre of gravity below the
centre of buoyancy. This gives the Spar tower sufficient
stability to carry a 2.3 MW wind turbine on top. Three
mooring lines have been used for maintaining the position of
the station. Based on this concept, others Spar-type floating
wind turbine platforms such as OC3-Hywind [9] and catenary
moored Spar (CMS) [10] have been introduced to make the
concept suitable for supporting 5 MW machinery and appropriate for public dissemination.
Wavebob is an axi-symmetric WEC, a self-reacting point
absorber that primarily operates in the heave mode [7]. It
consists of two concentric bodies with different heave
frequencies, which are called Torus for the shallower body
and Float for the deeper body, as illustrated in Fig. 1(b). The
hydraulic power take-off (PTO) system is driven by the
relative motion of the Torus as it slides along the Float.
The present STC concept is illustrated in Fig. 2. In this concept,
the Float in the WEC system is replaced by a Spar-type FWT. The
PTO system and the connection between the Torus and the Spar
in the concept are described more detail in [11]; therefore, the
Torus will slide along the Spar to extract energy from waves
while the wind turbine generates power from the wind. In this
way, the structural cost of the WEC project will be reduced
because the Float, which is actually the main structure of the
Wavebob-type WEC with a displacement of approximately
4700 m3 and a draft of 50 m, is not needed anymore. The WEC
also benefits from using the FWT’s mooring system as well as the
power cable.
Fig. 1. (a) Hywind [6] and (b) Wavebob [8] concepts.
M.J. Muliawan et al. / Renewable Energy 50 (2013) 47e57
49
Fig. 2. Conceptual sketch of the combined concept ‘STC’ considered in the present study.
The present STC has been based on the Spar-type FWT with
a 5 MW wind turbine used in [10] and the Torus properties used in
[12]. They are illustrated in Fig. 2 and the main characteristic are
summarised in Table 1. It should be noted that Fig. 2 is only
a conceptual drawing and that the properties listed in Table 1 are
directly adopted from the properties of the existing Spar-type FWT
and WEC publicly available. Therefore, no detail engineering and
optimisation has been carried out for this specific combined
concept. The PTO system has been simplified by introduction of
a linear PTO stiffness (Kpto) and a linear PTO damper (Bpto), as
discussed in [12]. The mooring system configuration and properties
used in [10] that are shown in Fig. 3 and summarised in Table 2 are
adopted.
3. Modelling and analysis of the STC
3.1. General
The STC in the present study is modelled as two rigid bodies
which are a Spar FWT and a Torus, connected by mechanical and
hydrodynamic couplings between their interfaces. Mooring system
shown in Fig. 3 is added to be the station-keeping of the STC. Fig. 4
shows the illustration of the present model in general that is mainly
developed using features available in SIMO [13]. SIMO is
a computer program that was developed by Marintek for simulating the motions and station-keeping behaviour of complex
systems of floating vessels and suspended loads. SIMO’s essential
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M.J. Muliawan et al. / Renewable Energy 50 (2013) 47e57
Table 1
Parameters of the combined concept system used in the present analysis.
Property
TORUS
Outer diameter
Inner diameter
Draft
Height
Displacement
Mass
Centre of mass
Moment of inertia Ixx
Moment of inertia Izz
Stroke length
Stiffness upper end stop spring
Stiffness lower end stop spring
SPAR
Diameter at water level
Diameter at bottom
Draft
Displacement
Mass (total)
Centre of mass
Moment of inertia Ixx
Moment of inertia Izz
Fairlead elevation
OTHERS
Wind turbine
PTO damper
PTO stiffness
Water depth
Table 2
The properties of mooring system components (see Fig. 3) from [10].
Value
Unit
Property
Delta line Upper line Lower line Clump
(DL)
(UL)
(LL)
mass
End line (EL)
20
8
2
8
408
418
0.9
10,760
20,560
6
106
106
m
m
m
m
m3
tones
m below the free surface
t.m2
t.m2
m
kN/m
kN/m
Length (m)
Diameter (m)
Mass/length (kg/m)
Axial stiffness
(EA) (kN)
50
0.09
42.5
384,243
370
0.09
42.5
384,243
6.5
9.4
120
8016
8216
78.5
69,840,000
167,800
70
m
m
m
m3
Tons
m below the free surface
t.m2
t.m2
m
5
8000
50
320
MW
kN.s/m
kN/m
m
250
0.09
42.5
384,243
600
0.09
42.5
384,243
2
1.67
17,253
384,243
Additionally, the viscous forces have been included and
modelled by the Morison equation given as:
!
!
! !
! 1
F viscous ¼ rCd Að V G V 0 Þ V G V 0 2
(1)
where:
!
V 0 is the undisturbed flow velocity taken at the instantaneous
position of the gravity centre.
!
V G is the velocity of the body.
Cd is the viscous coefficient on the specific direction that has
projection area A.
r is the density of sea water.
feature for the present analysis is its flexible modelling of multibody systems that can accommodate the introduction of both
mechanical and hydrodynamic couplings between the Spar and the
Torus. Additionally, HydroD [15] and TDHMILL [16] are used to
estimate hydrodynamic properties and aerodynamic load,
respectively.
3.2. Hydrodynamics
Hydrodynamic properties of two rigid bodies involved in the
STC, including its interactions, are calculated in the frequency
domain using HydroD and then applied in SIMO/TDHMILL to carry
out the coupled motion (wave- and wind-induced responses)mooring analysis of two bodies in given environmental conditions
in the time domain through retardation functions. Fig. 5 shows the
panel model that was developed for the two-body hydrodynamic
analysis in the present study.
Fig. 3. Schematic layout of the mooring system adopted in the present study from [10].
The Torus is not shown in the figure.
Fig. 4. Simple sketch of the two-body system model that is developed to study the STC
in the present paper.
M.J. Muliawan et al. / Renewable Energy 50 (2013) 47e57
51
Fig. 5. Panel models applied in the hydrodynamic analysis.
Viscous on the Torus; the viscous forces are applied at centre of
gravity for each direction. The viscous coefficients for each direction are estimated according to the Keulegan-Carpenter (KC) and
Reynold (Re) numbers. In this study, Cdx ¼ Cdz ¼ 1 are applied as
nominal viscous coefficients for Torus.
Viscous on the Spar; due to long structure, one cannot neglect the
variation of the velocity along the Spar. Hence, the viscous force on
the Spar is estimated by a sum of discrete contribution of the Spar
section. In the present model, 34 discrete sections are used to
estimate viscous force along submerged part of the Spar. The
nominal viscous coefficient of 0.6 has been applied in the transversal direction.
3.3. Aerodynamics
Aerodynamic force at the wind turbine; we are borrowing
Statoil’s informal implementation of a simplified method called
TDHMILL (Thrust-Dynamic-Horizontal-Mill) [17] to calculate
the aerodynamic forces as a function of the relative wind
velocity. It simplifies the aerodynamics of the turbine system to
be represented as a thrust force at the top of the tower that is
calculated using the relative wind speed at each time step as
given by:
1
2
TH ðtÞ ¼ :p:ra :R2 :CT ðUrel ðtÞÞ:Urel
ðtÞ
2
(2)
where:
ra is the mass density of air.
R is the radius of the rotor.
CT is a thrust coefficient given as a function of Urel(t) is
the relative velocity between the wind and the rotor hub at
time t.
To remove the negative damping introduced by the application
of the thrust force, a filter representing the controller has been
implemented for high wind speeds. This simplified approach was
validated in [16]. The approach has been compared with the
comprehensive aero-hydro-servo-elastic analysis, and it has been
shown that the response differ by approximately 10% for a Spartype FWT.
Aerodynamic force at the tower; is simplified as a lumped force
and moment that act at the centre of resulting wind load of the
Spar. The lumped force is given as:
FH ðtÞ ¼
1
2
:p:ra :CD :A:Urelðz
* Þ ðtÞ
2
(3)
where:
CD is a drag coefficient at the Spar surface. (CD ¼ 0.6 has been
applied in the present model).
Urel(z*)(t) is the relative velocity between the wind and the
tower measured at elevation z* at time t.
A is the Spar’s tower projected area above mean water level.
z* is estimated therefore the integration of distributed wind
force on the tower could be represented as in Eq. (3) as follows:
zZ¼ 90
dFðzÞ:dz ¼
z¼0
1
:p:ra :CD
2
1
2
:p:ra :CD :A:Urelðz
*Þ
2
(4)
zZ¼ 90
2
DðzÞ:Urel
ðzÞ:dz ¼
z¼0
1
2
:p:ra :CD :A:Urelðz
*Þ
2
where: D(z) is a distribution of the Spar’s diameter as illustrated in
Fig. 6.
Knowing that D(z ¼ 0) ¼ 6 m and D(z ¼ 90) ¼ 3.8 m then Spar’s
diameter distribution can be written as:
DðzÞ ¼ 6 2:2
z
90
(5)
For simplification, it is assumed that the Spar’s motion is small.
Therefore, Urel ðzÞzUðzÞ ¼ Ur ðz=zr Þa
Here, a ¼ 0.11 is referred as used in ISO and API, then z* ¼ 33 m
above mean water level has been estimated.
3.4. Mechanical connection between Spar and Torus
The connection between the Spar and the Torus should
accommodate the system to freely move in heave but the two
bodies move together in surge, sway, roll, pitch and yaw. It should
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M.J. Muliawan et al. / Renewable Energy 50 (2013) 47e57
Table 3
The load cases for the operational conditions from [10]. Turbine status is in operation
for all cases.
Case no.
Vmeana (m/s)
Hs (m)
Tp (s)
1
2
3
4
8
11.2
14
17
2.5
3
3.6
4.2
9.8
10
10.2
10.5
a
Fig. 6. Sketch of wind speed distribution around the tower.
at least include two main connections systems. They are the main
bearing and the end stop systems [11].
Those connections are modelled using features available in
SIMO. Docking cone feature is applied to model the main bearing
and fender feature is used for the end stop. Fig. 7(a) and (b) illustrates the mechanical coupling using SIMO’s features to model the
Spar-plus-Torus system. The responses of the system due to the
introduction of these mechanical coupling have been discussed
in [12].
3.5. WEC power take-off (PTO)
As in the Wavebob-type WEC, the PTO of the combined concept
is derived from the relative motion between the Spar and the Torus.
The 10-min averaged wind speed at the nacelle.
In the present study, the PTO system is modelled as an ideal linear
damper with coefficient Bpto and linear stiffness coefficient Kpto
connecting the Spar and Torus. This model will result in the internal
forces in the system where the force related to Bpto is proportional
to the relative velocity and the force related to Kpto is proportional
to the relative motion between the two involved bodies. For a given
sea state, the relative motion and the relative velocity between the
Spar and the Torus will depend on the values of Bpto and Kpto
(together with end stops setting). This system implies that the
power that is captured by the WEC can simply be estimated using
the total force associated with these two terms and the relative
velocity between the two bodies. PTO parameters, which are
Bpto ¼ 8000 kN s/m and Kpto ¼ 50 kN/m, as listed in Table 1, are
introduced in the present model. As indicated in [12] using these
PTO parameters yield an absorbed power for the Wavebob-type
WEC that is in good agreement with the estimated power from
the application of the optimised PTO parameter in [14].
3.6. Mooring system modelling
In the present study, we introduce simple mooring model in
SIMO that works like nonlinear springs but neglects drag and
inertia forces due to line motion. As described in [12], the effect of
the drag and inertia forces on the lines is negligible for power
estimation, but they are important for the mooring system design.
The maximum tension estimated by neglecting the drag and inertia
forces on the lines is a slight underestimate of the tension that is
estimated by including the drag and inertia forces on the lines.
Because the present study is limited to investigating the effect of
the addition of a Torus on the mooring load under operational
Fig. 7. Introductions of (a) mechanical coupling to let the two bodies move together in sway, surge, roll and pitch yet move freely in heave; (b) end stops to limit the relative heave
motion.
M.J. Muliawan et al. / Renewable Energy 50 (2013) 47e57
53
conditions, a simplified mooring model is considered to be
sufficient.
4. Simulation setting and results
4.1. General
The main objective of the present study is to investigate the
effect of the addition of a Torus on a Spar-type FWT’s motions and
power production under operational conditions. The operational
conditions from the relevant metocean data taken in the Statfjord
at the North Sea used in [10] are referred to for the present simulations. Those operational environmental conditions are listed in
Table 3 below. V is the 10-min averaged wind speed at the nacelle.
The JONSWAP spectrum with a default peak parameter g value of
3.3 is used to represent the wave condition for all cases. Only first
order wave forces and a steady wind force are considered as
external forces for the simulations. A water depth of 320 m is used.
4.2. Spar motion comparison for waves-only
The effect of the addition of a Torus on the Spar’s motion in
waves only (without application of a wind force) is determined by
comparing the Spar’s motion both for the specified Spar-type FWT
(‘Spar alone’) and in the specified STC for the four sea states listed in
Table 3. Fig. 8 shows one of the comparisons of the motion spectra
that resulted from the present simulation for case no. 4, which
applies Hs ¼ 4.2 m and Tp ¼ 10.5 s. The present simulation results
for the four considered cases are summarised in Fig. 9. The mean
displacement for all motion modes of the Spar for both in ‘Spar
alone’ and STC for all four cases are very close to zero, therefore not
presented as a figure. From those results, we see that the mean
displacement of the Spar is not affected by the addition of a Torus.
However, the standard deviation (STD) of the Spar’s motion in the
combined concept ‘STC’ is higher than the STD of the Spar’s motion
in the ‘Spar alone’, especially for heave. This is because the addition
of a Torus adds wave forces on the Spar structure through their
mechanical connection. In heave mode, the Torus will move
following the water level, and it will carry the Spar. This behaviour
occurs because the Spar has a small heave stiffness and the Torus is
exposed to large wave forces. It has been presented in [12] that the
amplitude heave motion for both bodies will depend on the set PTO
Fig. 8. Comparisons of the smoothed spectra between the Spar’s motions in the
specified Spar-type FWT (‘Spar alone’) and in the present combined concept (STC) for
Hs ¼ 4.2 m and Tp ¼ 10.5 s based on 1-h simulations (a) for surge at mean water level,
(b) for heave and (c) for pitch modes.
Fig. 9. Comparison of the standard deviation (STD) of the Spar’s motions in the
specified Spar-type FWT (‘Spar alone’) and in the combined concept (STC) for the
waves-only cases. (Surge at mean water level is referred).
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M.J. Muliawan et al. / Renewable Energy 50 (2013) 47e57
Fig. 10. Comparisons of the smoothed Spar’s motions spectra and estimated wind power production in the specified Spar-type FWT (‘Spar alone’) and in the specified combined
concept (STC) for Hs ¼ 2.5 m, Tp ¼ 9.8 s and V ¼ 8 m/s, based on 1-h simulations for (a) surge at mean water level, (b) heave and (c) pitch modes and (d) wind power production.
Fig. 11. Comparison of the responses in the two Spar concepts: (a) surge at mean water level, (b) heave, (c) pitch, and (d) wind power production in the specified Spar-type FWT
(‘Spar alone’) and in the specified combined concept (STC)for the waves-and-steady-wind cases.
M.J. Muliawan et al. / Renewable Energy 50 (2013) 47e57
55
Table 4
Power estimation from the specified Spar-type FWT (Spar FWT alone) and the present combined concept (STC).
Power (kW)
Case no.
Vmean (m/s)
Hs (m)
Tp (s)
a
b
a
b
8
11.2
14
17
2.5
3
3.6
4.2
9.8
10
10.2
10.5
Wind powera
Wave power
Wind power
1
2
3
4
Combined concept ‘STC’
Spar FWT alone
Wave powerb
Mean
STD
Mean
STD
Mean
STD
Mean
STD
1727.1
4573.0
4937.6
4929.5
244.3
327.9
12.4
8.17
e
e
e
e
e
e
e
e
1820.1
4875.0
4947.0
4939.5
233.2
296.5
13.1
8.7
275.4
420.9
622.6
883.4
379.9
576.2
852.8
1211
The power production.
The absorbed power.
parameter that connects the two bodies to absorb the wave power.
It can be simply understood that if no PTO connection is set, then
the Torus and the Spar will move independently of each other. In
contrast, if a very stiff PTO connection is applied, they will move
together. Overall, the addition of a Torus for the simulated wavesonly cases has a small effect on the surge and pitch modes of the
Spar. And since heave motion of the Spar will not provide significant effect to power production from the wind turbine, therefore
the introduction of a WEC makes it possible to absorb and utilise
this wave power.
located 78.5 m below the mean water level. Therefore, additional
damping at the mean water level due to additional WEC system will
create a significant damping for the pitch because the moment arm
is large. As a consequence of more stable pitch motion, the WT in
the STC concept will get better exposure to the incoming wind,
therefore experience higher aerodynamic load to be converted
become electrical power compared with the one in the specified
Spar-type FWT alone (‘Spar alone’), as shown in Fig. 11(d) for a case
with wind speed lower than the rated speed of the wind turbine.
However, due to the application of control, the power production of
4.3. Spar motions and power production for waves and steady wind
The effect of the addition of a Torus on the Spar’s motion and
wind power production are also investigated by comparing the
Spar’s motion and wind power production both for the specified
Spar-type FWT (‘Spar only’) and for the specified combined concept
for the four waves-plus-steady-wind cases listed in Table 3. Fig. 10
shows one of the comparisons of the motion spectra and wind
power production estimated from the present simulation for case
no. 1, which applies Hs ¼ 2.5 m, Tp ¼ 9.8 s and V ¼ 8 m/s. The present
simulation results for the four considered cases are summarised in
Fig. 11. From these comparisons, we can observe that the addition of
a Torus increases the mean displacement of the Spar, but by an
insignificant amount. The standard deviation of the surge and pitch
motions of the Spar were actually reduced by the addition of
a Torus. This means that the specified Torus damps the Spar’s surge
and pitch motions; therefore, the amplitude of these motions
decreases. This occurs because the centre of gravity of the Spar is
Fig. 12. Percentage of the wind power production and the absorbed wave power by
the STC concept compared with the wind power production of the Spar-type FWT
alone for the waves-and-steady-wind cases.
Fig. 13. Time series of (a) heave motions of two bodies in the combined concept and
(b) the absorbed wave power by the concept for Hs ¼ 4.2 m, Tp ¼ 10.5 s and V ¼ 17 m/s.
56
M.J. Muliawan et al. / Renewable Energy 50 (2013) 47e57
referred as ‘SpareTorus Combination (STC)’ has been introduced.
This STC concept is considered to reduce the total capital cost
compared with segregated deployment of a Spar-type FWT and
a Wavebob-type WEC. The specified STC concept has been
modelled, and analysed coupled in the time domain to study the
motions, power production and mooring load of the combined
concept under operational conditions. The dimensions and
parameters of the present STC are directly adopted from the
properties of existing Spar-type FWT and WEC publicly available.
No dimensional or parameter optimisations have been carried out
during this study. Based on this study, the following conclusions
can be made:
Fig. 14. Maximum tension on lower line 2 (LL2) shown in Fig. 3, both in the specified
Spar-type FWT (‘Spar alone’) and in the STC concept under operational conditions for
the waves-and-steady-wind cases listed in Table 3.
WT will stay constant at wind speed between rated and cut-out
speeds. In the present study, a 5 MW rated WT with rated wind
speed of 11e13 m/s has been considered.
The estimated wind power production and the absorbed wave
power for the considered operational conditions are summarised in
Table 4 both for the ‘Spar alone’ condition and for the STC concept.
Comparisons of the power obtained are presented in Fig. 12. At
wind speed lower than the rated speed of the turbine, the wind
power production by the STC concept is 6e6.6% higher than the
wind power production by the ‘Spar alone’. At wind speed higher
than the rated one, the control system will pitch the blade to reduce
the load while the turbine keeps spinning at the same rotational
speed to produce some power as the rated power. Additionally, the
combined concept absorbs the power from the waves, which is
approximately 9e18% of the power production of the ‘Spar alone’.
Fig. 13(a) and (b) show the time series of heave motions of two
bodies and the absorbed wave power by the combined concept for
case no. 4, respectively. If 50% efficiency is introduced to represent
energy losses for other components such as PTO and electrical, we
could estimate that the wave power production by the STC is
approximately 4.5e9% of the power production of the Spar FWT
alone. Therefore, the total power production from the STC concept
is about 10e15% higher than from the Spar FWT alone.
4.4. Mooring tension
The effect of the addition of a Torus on the mooring line tension
under operational conditions is investigated. The maximum
tension on the lower line 2 (see Fig. 3), the most loaded line, both in
the Spar-type FWT (‘Spar alone’) and in the specified STC under the
operational cases listed in Table 3 are presented in Fig. 14. The figure
shows that the addition of a Torus increases the line tension
insignificantly. However, further mooring analyses needs to be
performed to compare the mooring dimensions needed to survive
during extreme conditions for the Spar-type FWT and the
combined concept. This analysis is not included in the present
study.
5. Conclusions
In the present study, a combined concept involving the
combination of a Spar-type FWT and a Wavebob-type WEC
By combining a Torus (donut-shape heaving buoy) with a Spartype FWT increases the wave induced motions of the Spar due
to increased wave forces on the system. In the heave mode, the
Torus moves to follow the water level, and it carries the Spar.
This occurs because the Spar has a small heave hydrostatic
stiffness and the Torus is exposed to large wave forces. It has
been presented in [12] that the amplitude of the heave motion
for both bodies will depend on the PTO parameter that
connects the two bodies to absorb the wave’s power. However,
only an insignificant effect due to the addition of a Torus is
observed for the surge and pitch motions of the Spar when
considering wave load cases only.
The addition of a Torus on the Spar-type FWT for wave-andsteady-wind cases increases the mean displacement of the
Spar slightly but decreases the standard deviation of the Spar’s
motion, especially for surge and pitch. This is because this
specific Torus damps the Spar’s motions. This occurs because
the centre of gravity of the Spar is located 78.5 m below the
mean water level. Therefore, additional damping at the mean
water level due to additional WEC system will create a significant damping for the pitch because the moment arm is large,
therefore the amplitude decreases. As a consequence of more
stable pitch motion, the WT in the STC concept will get better
exposure to the incoming wind, therefore experience higher
aerodynamic load to be converted become electrical power
compared with the one in the specified Spar-type FWT alone,
especially at wind speed lower than the rated speed of the
wind turbine.
At wind speed lower than the rated speed of the turbine, the
wind power production by the STC concept is about 6% higher
than the wind power production by the Spar-type FWT alone.
Combined with the WEC power production, the estimated
total power production by the combined concept is 10e15%
higher than the one produced by the specified Spar-type
FWT alone.
By combining the Torus WEC with the Spar-type FWT under
operational conditions (for wave-and-steady-wind cases)
causes only a slight increase the mooring tension.
All of the results mentioned above indicate that the presented
combined concept not only reduces the total capital cost but
also increases the total power production compared to those
for a segregated FWT and WEC concept.
6. Future work
The present study focuses on the feasibility of a novel concept by
combining a Spar-type FWT and a Wavebob-type WEC to produce
power under operational conditions. Further work is needed to
optimise the power production of the concept by optimising the
structure and PTO properties. Further analyses are also necessary to
investigate the structural integrity of the concept under survival
conditions.
M.J. Muliawan et al. / Renewable Energy 50 (2013) 47e57
Acknowledgements
We thank the Research Council of Norway (RCN) for their
financial support through the Centre for Ship and Ocean Structures.
We also would like to thank the offshore wind department of Statoil
for access to TDHMILL.
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