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energies
Article
Simplified Floating Wind Turbine for Real-Time Simulation of
Large-Scale Floating Offshore Wind Farms
Thanh-Dam Pham 1,2,† , Minh-Chau Dinh 3,† , Hak-Man Kim 4,† and Thai-Thanh Nguyen 5,*
Citation: Pham, T.-D.; Dinh, M.-C.;
Kim, H.-M.; Nguyen, T.-T. Simplified
Floating Wind Turbine for Real-Time
Modeling of Large-Scale Floating
Offshore Wind Farms. Energies 2021,
14, 4571. https://doi.org/
10.3390/en14154571
Academic Editor: Andrzej Bielecki
Received: 24 June 2021
Accepted: 19 July 2021
Published: 28 July 2021
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1Institute of Theoretical and Applied Research, Duy Tan University, Hanoi 100000, Vietnam;
phtdam@gmail.com
2Faculty of Natural Sciences, Duy Tan University, Da Nang 550000, Vietnam
3Center for Advanced Power Technologies Application, Research Institute of Mechatronics,
Changwon National University, Changwon 51140, Korea; thanchau7787@gmail.com
4Department of Electrical Engineering, Incheon National University, Songdo-dong, 119 Academy-ro,
Yeonsu-gu, Incheon 22012, Korea; hmkim@inu.ac.kr
5Department of Electrical and Computer Engineering, Clarkson University, Potsdam, NY 13699, USA
*Correspondence: tnguyen@clarkson.edu; Tel.: +1-315-268-6511
† These authors contributed equally to this work.
Abstract:
Floating offshore wind has received more attention due to its advantage of access to
incredible wind resources over deep waters. Modeling of floating offshore wind farms is essential
to evaluate their impacts on the electric power system, in which the floating offshore wind turbine
should be adequately modeled for real-time simulation studies. This study proposes a simplified
floating offshore wind turbine model, which is applicable for the real-time simulation of large-scale
floating offshore wind farms. Two types of floating wind turbines are evaluated in this paper: the
semi-submersible and spar-buoy floating wind turbines. The effectiveness of the simplified turbine
models is shown by a comparison study with the detailed FAST (Fatigue, Aerodynamics, Structures,
and Turbulence) floating turbine model. A large-scale floating offshore wind farm including eighty
units of simplified turbines is tested in parallel simulation and real-time software (OPAL-RT). The
wake effects among turbines and the effect of wind speeds on ocean waves are also taken into account
in the modeling of offshore wind farms. Validation results show sufficient accuracy of the simplified
models compared to detailed FAST models. The real-time results of offshore wind farms show the
feasibility of the proposed turbine models for the real-time model of large-scale offshore wind farms.
Keywords: wind turbine modeling; floating offshore wind turbine; offshore wind farm
1. Introduction
Renewable energy is being considered as the best solution to replace fossil energy and
reduce carbon dioxide emissions. All types of renewable generations keep growing in the
last decade, and wind energy has accounted for about 50 percent of renewable generations
by 2018 [
1
]. Offshore wind energy has recently shown greater interest in research and
development as well as in investment rather than onshore wind energy. It is reported that
the year 2019 was remarkable in the history of the global offshore wind industry with
6.1 GW of the new installation [
2
]. The total global floating wind reaches up to 65.7 MW
by 2019. Among 65.7 MW floating wind [
3
], 32 MW is located in the UK [
4
], 19 MW in
Japan [4], 10.4 MW in Portugal [4], 2.3 MW in Norway [4], and 2 MW in France [2].
Hywind is known as the first floating offshore wind farm (FOWF) in the world with a
30 MW capacity. It is located in the UK, known as the most established design of floating
turbine today, verified through eight years of successful operation [
5
]. In this project,
the floating foundation is a spar-buoy and anchored to the seabed. WindFloat 1 project
implemented a demonstration unit using a 2MW turbine and semi-submersible floating
foundation in Portugal in 2011. After succeeding in the demonstration phase, the next
Energies 2021,14, 4571. https://doi.org/10.3390/en14154571 https://www.mdpi.com/journal/energies
Energies 2021,14, 4571 2 of 18
step would be the pre-commercial phase. So, WindFloat Atlantic was commissioned in
January 2020, well known as the first floating wind farm in continental Europe [
6
]. In
Japan, two pioneering floating offshore wind turbines (FOWT), using Hitachi turbines
of 5 MW and 2 MW units, have been installed and investigated their performance at a
test site off the coast of Fukushima, Japan [
7
,
8
]. The 2 MW Floatgen is the only floating
wind turbine in France. Floatgen is comprised of a Vestas V80 turbine and damping pool
foundation [
9
]. So far, the practical FOWF projects are only being tested on a small scale.
In the future, when the FOWFs are scaled up to several hundred MWs or GW-class, the
integration of FOWFs to the utility becomes a critical issue. Because the output power
of FOWF will fluctuate depending not only on the wind variation but also on the ocean
wave. So, the complicated variation of FOWF will threaten the stability of the power
network such as voltage stability, frequency stability, power quality, etc. For a future study
of grid-connection of the large-scale FOWF, a high fidelity FOWF modeling that can run in
a real-time simulation environment is essential.
From the design stage, detailed mathematical models of floating offshore wind tur-
bines (FOWTs) have been made to analyze the performance in terms of system dynam-
ics, turbine loads, fatigue damage, cost assessment, etc. The detailed models of FOWT
developed using the FAST (Fatigue, Aerodynamics, Structures, and Turbulence) simula-
tion tool are well used not only for on-land but also for floating offshore wind turbine
designs [
10
–
12
]. In [
13
] a linear, frequency-domain model with four planar degrees of
freedom (DoFs): floater surge, heave, pitch and first tower modal deflection for quick load
analysis of floating offshore wind turbines has been introduced. A simplified, control-
oriented mathematical model of an offshore variable speed turbine with a tension leg
platform has been introduced in [
14
]. In [
15
], a simplified, control-oriented mathematical
model of an offshore wind turbine with a spar buoy platform was developed for analysis
and control purposes. A nonlinear model with 6 DoFs has been developed for the 5 MW
FOWT with a semi-submersible platform [
16
]. In [
17
], the authors presented a development
of a simplified FOWT model for time-domain simulation. The model was validated by
comparing it with the FAST model in several test cases.
Full detailed models [
10
–
12
] representing all physical features of floating offshore
wind turbines, which is suitable for dynamic studies of offshore wind turbines. The electric
power produced by the FOWT is the main focus of electrical power system research.
As a result, the comprehensive FOWT models can be represented in a simplified model
while maintaining sufficient accuracy in the electric power responses. The simplified
models should be efficient for real-time studies of large-scale offshore wind farms. The
existing models are still complicated to model in real-time simulation and they have not
been validated in real-time simulations. Efficient computation is an important factor for
simplified models as complicated models might pose a computational burden on real-time
simulators. Consequently, a limited number of turbines can be run in real-time simulations.
For the real-time model of large-scale offshore wind farms, it is interesting to develop
simpler, accurate physical turbine models that can represent the main dynamic of the
overall system and suitable for real-time simulation programs such as real-time digital
simulator (RTDS) or parallel simulation and real-time software (OPAL-RT).
We put effort into developing a simplified, linear, grid integration analysis-oriented
FOWT model that is applicable for the real-time simulations of large-scale offshore wind
farms. The proposed FOWT only considers three movements of the floating platform
(surge, heave, and pitch) as they have the most impact on output electric power. Compared
to existing models, the floater responses in this paper are estimated by the transfer functions,
which are efficient and suitable for real-time simulations of large-scale offshore wind farms.
The response of the proposed models and the FAST models to the same environment
conditions was presented and compared to evaluate the accuracy of the developed models.
Two FOWT models with different types of floating foundations: spar-buoy and semi-
submersible platform were evaluated. The main contributions of this paper are listed
as follows.
Energies 2021,14, 4571 3 of 18
•
A simplified FOWT model which is applicable for the real-time simulation of large-
scale offshore wind farms is proposed. The simplified model is validated against the
detailed FAST model.
•
A simplified offshore wind farm model is developed with the consideration of wake
effects and ocean waves throughout the offshore wind farms.
•
A real-time modeling of the simplified floating offshore wind farm is developed
and tested in Opal-RT real-time simulator to show the feasibility of the proposed
FOWT models.
The rest of this paper is organized as follows. Section 2presents the structure of FOWT
with the spar-buoy and semi-submersible floaters. Section 3describes the simplification
of FOWT for power system studies. The validation of the simplified models and the
performance of the large-scale offshore wind farms are presented in Section 4. Finally, the
main findings of this paper are summarized in Section 5.
2. Floating Platforms for Offshore Wind Turbines
2.1. Floating Offshore Wind Turbines
This paper considers two typical floating platforms to support the NREL 5 MW
reference offshore wind turbine [
18
], as shown in Figure 1. The first model is the OC4
DeepCwind semi-submersible [19], which is stabilized by the restoring moment obtained
by a sufficiently large spacing and diameter of columns. The second model is the OC3
Hywind spar-buoy [
20
], which is stabilized by the lower center of gravity compared to
the center of buoyancy of the system. Table 1describes the main properties of the semi-
submersible platform and spar platform. The detailed specification of mooring systems for
the semi-submersible and the spar-buoy models are given in Table 2.
Offshore wind turbines including floating platforms and wind turbines freely move
in three-dimensional space, which is referred to as six degrees of freedom (DoFs). A rigid
body of offshore wind turbine freely changes position in three perpendicular axes: surge
motion in normal axis (backward/forward), heave motion in transverse axis (down/up),
and sway motion in longitudinal axis (right/left); combining three rotational changes about
three axes, namely, yaw, pitch, and roll, respectively.
Figure 1. Overall configuration of the semi-submersible and spar-buoy offshore wind turbines.
Energies 2021,14, 4571 4 of 18
Table 1.
Physical properties of the OC4 DeepCwind semi-submersible and the OC3 Hywind spar-
buoy floating platforms [19,20].
Description Unit Semi-
Submersible
Spar-
Buoy
Volume displacement m313,917 8029
Center of buoyancy below still water level
(SWL) m 13.15 62.1
Platform mass ton 13,473.00 7466.33
Center of mass (CM) of platform below SWL m 13.46 89.916
Platform roll inertia about CM
kg
·
m
26.827 ×109
4.229
×
10
9
Platform pitch inertia about CM
kg
·
m
26.827 ×109
4.229
×
10
9
Platform yaw inertia about CM
kg
·
m
21.226 ×1010
1.642
×
10
8
Table 2. Specification of mooring systems [19,20].
Description Unit Semi-
Submersible Spar-Buoy
Water depth m 200 320
Number of mooring line - 3 3
Mooring diameter mm 76.6 90
Mooring line mass density (air)
kg/m
113.35 77.7066
Axial stiffness (EA) MN 753.6 384.24
Unstretched mooring line length m 835.5 902.2
Depth to fairleads below SWL m 14 70
Radius to fairlead m 40.868 5.2
Radius to anchor m 837.6 853.87
2.2. FAST Wind Turbine Model
FAST is a publically accessible FOWT modeling program from NREL [REF], which
predicts the coupled aero-hydroservo-elastic responses in the time domain, taking into
consideration aerodynamics, control logic, structural elasticity, and first-order hydrody-
namics plus viscous effects [
12
]. Wind-inflow data is used in the aerodynamic models,
which solve for rotor-wake effects and blade-element aerodynamic stresses, including
dynamic stall. Both regular and irregular waves can be simulated by the hydrodynamic
models. The control and electrical system models simulate the turbine and generator
controllers, including blade-pitch, generator-torque, nacelle-yaw, and other control de-
vices. The structural-dynamics models take into account the control and electrical system
responses, as well as aerodynamic and hydrodynamic loads, gravity loads, and the rotor,
drivetrain, and support structure’s elasticity. A modular interface and coupler are used
to connect all of the models. An executable version of FAST can be implemented in Mat-
lab/Simulink environment. FAST_SFunc is a level-2 Matlab S-function that implements the
FAST interface to Simulink, which is built in C, and it calls a DLL of FAST routines that are
written in Fortran [
21
]. The complexity of the FAST interface poses a challenge to compile
and run FAST models in real-time simulators such as OPAL-RT or RTDS.
3. Simplification of Floating Offshore Wind Turbine
Floating offshore wind turbine includes mainly two components, which are a wind
turbine generator and floating platform. The overall configuration of the simplified FOWT
model is shown in Figure 2.
Energies 2021,14, 4571 5 of 18
Figure 2. Overall configuration of simplified FOWT model.
3.1. Wind Turbine Modeling
As shown in Figure 2, the wind turbine model consists of an aerodynamics model,
driver-train, generator, and power converter, and turbine control system including con-
verter and pitch controls. In general, the wind turbine captures wind energy and produces
electric power. Power captured by the turbine rotor is expressed as (1).
Pt=1
2ρπR2v3
inCp(λ,β)(1)
where
ρ
is the air density,
R
is the rotor blade radius,
β
is the blade pitch angle,
vin
represents the wind speed perceived by the blade in m/s.
Cp
is the power coefficient which
is a function of pitch angle (
β
) and tip speed ratio (
λ
). The tip speed ratio is the ratio
between tip speed of ωRand the blades pitch angle (β).
A table data of
Cp
with two different indexes
β
and
λ
was derived from the FAST
model of the 5 MW model, in which
β
is selected from 0
◦
to 90
◦
and
λ
is selected from 0.25
to 25. The mechanical torque (Tm) of the wind turbine is expressed as (2)
Tm=Pt
ωR
, (2)
Equations (1) and (2) are used to represent the aerodynamic model of the FOWT.
The turbine rotor includes blades, hub, shaft, gearbox-if presented and generator is often
represented as a single mass model, which is expressed in (3).
Tm−Te =JR
dωR
dt , (3)
where
Tm
is the mechanical torque,
Te
is the electrical torque, and
JR
is the inertia constant
of the turbine rotor.
The turbine generator is simplified by a first-order function. Because the main focus
of this study is on the active power management of floating offshore wind, the power
converter system is excluded from the proposed modeling for additional simplification.
Detailed modeling of turbine generators and power converter systems could be modeled
in the same way as conventional turbine modeling. The difference between the FOWT and
fixed wind turbine is the wave and hydrodynamic models, which will be explained in the
next section.
The turbine control system includes two main controllers, which are the torque and
pitch controls. Under these controllers, the turbine can operate under four regions depend-
ing on wind speeds, as shown in Figure 3. In region 2, the MPPT control algorithm based
on the torque controller is implemented to capture the maximum power from the wind.
The maximum power of the wind turbine is expressed as (4) [22].
PMPPT =0.5ρπR5Cmax
p(λ,β)ωopt
λopt 3(4)
Energies 2021,14, 4571 6 of 18
where
Cmax
p
is the maximum power coefficient of the turbine,
λopt
is the optimal tip speed
ratio,
ωopt
is the optimal mechanical angular velocity of the rotor. In region 3, the pitch
controller is activated to limit the power of the turbine at the rated value. The wind
generator is shut down in regions 1 and 4 where the wind speed is smaller than the cut-in
speed and larger than the cut-out speed.
Figure 3. The output power versus wind speed.
3.2. Simplified Modeling of Floating Platforms
Unlike the conventional fixed wind turbine, total FOWT output power is affected by
not only winds but also ocean waves. As FOWT is free to change position in six DoFs, the
use of full six DoFs could increase the complexity of the turbine modeling, which would
pose a significant impact on the computational burden. Thus, the 6 DoFs representation of
FOWT is reduced to three DoFs that have the most significant impacts on the total output
power, which are surge, heave, and pitch. The following assumptions are considered in
this paper for simplification of the floating wind turbines:
• The aero-elastic effects are neglected.
• The wind turbine is always supposed to be aligned with the wind.
• The floating system is assumed to be aligned with the coming way.
The coordinate system that describes the wind turbine movements is depicted in
Figure 4. The x-axis is aligned with the water surface and its direction is the same as the
wind speed direction. The z-axis points upward. The y-axis is perpendicular to the x-axis
and z-axis as shown in Figure 4. The origin is placed in the static equilibrium position.
As shown in Figure 4, positive surge (
ξ1
) coincides with the x-axis direction, positive
heave(
ξ2
) coincides with the z-axis direction, and positive pitch (
ξ3
) is clockwise. The
motion equation of the FOWT is expressed in (5) [23].
ξω=Fω
−(M+Aω)ω2+i(B+Bω)ω+K(5)
where
M
is the structure mass and inertia matrix of whole FOWT systems, except for
mooring systems;
ω
is angular frequency;
Aω
is hydrodynamic added mass and inertia
matrix;
B
is hydrodynamic linear damping matrix;
Bω
is a damping matrix;
K
is restoring
matrix;
ξ(ω)
is the response for the three DoFs;
Fω
is a vector of excitation forces and
moments in the frequency domain.
Energies 2021,14, 4571 7 of 18
Figure 4.
Movement of floating wind turbines under wind and wave conditions: (
a
) Semi-
submersible; (b) Spar-buoy.
All data of matrices
M,A,B,K
, and
F
are derived from the FAST code for the 5 MW
turbine model, as presented in [
19
,
20
]. By solving Equation (5), the response amplitude
operators (RAOs) were obtained in the frequency domain, as given by a vector form in (6).
ξ(ω) = [ξ1(ω),ξ2(ω),ξ3(ω)]T(6)
where ξ1(ω) is the floater surge, ξ2(ω) is the floater heave, ξ3(ω) is the floater pitch.
The transfer functions are estimated based on the frequency response of RAOs by
using tfest function that is provided by the system identification toolbox in Matlab. Based
on the estimated transfer functions, RAOs can be represented in the time domain, which
can be used for time-domain simulation such as Matlab/Simulink or PSCAD/EMTDC.
An overall diagram of the simplified floater response is depicted in Figure 5. It
should be noted that only surge and pitch movements are considered as they introduced
a significant impact on the total output power. RAOs movements in the time domain (
ξ1
and
ξ3
) are affected by both wind (
vw
) and ocean waves (
a(t)
). By multiplying the specific
time series of free surface elevation
a(t)
with the transfer functions of response amplitude
operators (RAOs) including surge and pitch, the dynamic response of surge (
ξ1
) and pitch
(
ξ3
) in time series can be obtained. Since the floating structure can move, the effective wind
speed (vin ) is different from the absolute wind velocity (vw), as given by (7).
vin =vw−∆v=vw−d(ξ1+hTtan(ξ3))
dt (7)
where
∆v
is the variation of wind speed at the rotor hub due to the structure movement,
hTis the turbine hub height, ξ1is a sum of dynamic ξdyn.
1, and static ¯
ξ1, and ξ3is a sum of
dynamic
ξdyn.
3
, and static
¯
ξ3
. The static values of the surge and pitch are extracted from the
FAST model for each mean wind speed. Within this paper, we considered only the surge
and pitch response because they affect directly the relative wind speed seen by blades.
Energies 2021,14, 4571 8 of 18
3.3. Ocean Wave Modeling for Offshore Wind Farms
The ocean wave is generated by JONSWAP Spectrum, which is produced by the wind
at each turbine, as given by (8). Thus, the ocean waves are simply modeled throughout
offshore wind farms considering the effect of wind speeds.
Si=αg2
ω5
i
exp"−5
4ωp
ωi4#γr, (8)
r=exp"−(ωi−ωp)2
2σ2ω2
p#, (9)
σ=(0.07 ωi≤ωp
0.09 ωi>ωp
, (10)
γ=2.2, (11)
where
ωi=
2
πfi
;
fi
is the wave frequency;
Si
is the surface elevation spectrum at frequency
ωi
;
g=
0.9806 m/s
2
;
α=
8.1
×
10
−3
;
ωp=
0.877
g/U19.5
;
U19.5
is the wind speed measured
at a height of 19.5 m above the sea surface, which is calculated based on wind power profile
law relationship (12).
U19.5 =Unac (19.5/hT)ζ, (12)
where
Unac
is the wind speed measured at the nacelle of the wind turbine;
hT
is the turbine
hub height in meter;
ζ
is the constant coefficient. Recommended value of
ζ
for the offshore
wind farm application is 0.11 [24].
Wave amplitude at frequency
ωi
is calculated by (13) then it is converted to the time
domain by (14). Wave amplitude in time domain
a(t)
is used as input of the simplified
turbine models. The wave spectra under different wind speeds shown in Figure 6indicates
that a stronger wind speed results in a stronger ocean wave.
Ai=p2Si∆ω, (13)
a(t) =
n
∑
i=1
Aicos(ωit). (14)
Figure 5. Overall configuration of simplified FOWT model.
Energies 2021,14, 4571 9 of 18
Figure 6.
JOHNSWAP wave spectra under different wind speeds: (
a
) Surface elevation spectrum;
(b) Amplitude of ocean wave.
4. Simulation Results
4.1. Validation of Simplified Models
4.1.1. System Parameters
The transfer functions of motion RAOs is converted from continuous domain to the
discrete domain with the sample time of 0.0125 s. The discrete transfer functions of motion
RAOs for the semi-submersible and spar-buoy platforms are given by (15) to (18).
ξsemi
1(z) = 7.86 ×10−8z−1+2.35 ×10−7z−2−2.354 ×10−7z−3−7.821 ×10−8z−4
1−3.99z−1+5.97z−2−3.971z−3+0.9902z−4, (15)
ξsemi
3(z) = z−503 −2.999 ×10−8−9.461 ×10−8z−1+1.081 ×10−7z−2+1.322 ×10−8z−3
1−2.998z−1+2.995z−2−0.9977z−3, (16)
ξspar
1(z) = 0.003736z−1−0.003729z−2
1−1.998z−1+0.998z−2, (17)
ξspar
3(z) = 0.001905z−1−0.001899z−2
1−1.996z−1+0.9962z−2. (18)
Variation of static motion RAOs (
¯
ξ1
and
¯
ξ3
) under different wind speeds is shown in
Figure 7, which is used as lookup tables for the simplified turbine models. Smaller mean
values of motion RAOs of the semi-submersible platform indicate that the semi-submersible
platform is more stable than the spar-buoy platform.
4.1.2. Validation Results
The accuracy of the simplified models is validated against the FAST models in this sec-
tion. Two types of floating wind turbines are investigated in this paper: semi-submersible
and spar-buoy floating wind turbines, in which the rating of turbine generators is 5 MW.
The motion RAOs and output turbine power under both regular and irregular wave
conditions are calculated to validate the proposed models.
The validation results of RAO motions in the frequency domain for the simplified semi-
submersible floating wind turbine are shown in Figure 8. It can be seen that the simplified
model successfully captures the dynamic response of RAO motions at a frequency above
0.45 rad/s. There is a slight difference in pitch motion at a frequency below 0.45 rad/s.
The RAO responses under a regular wave in the time domain are shown in Figure 9and
output power in this condition is shown in Figure 10. With the wind speed of 8 m/s, the
turbine tower inclines with the mean pitch angle of 1.79
◦
and oscillates around that mean
Energies 2021,14, 4571 10 of 18
value due to the regular wave effect. The output power oscillates around the mean value
of 1.75 MW. Figures 11 and 12 show the response of RAO motions and output power under
the irregular wave condition. The comparison in form of mean and standard deviation
(STD) of RAO motions and output power is shown in Table 3.
Figure 7. Mean of motion RAOs under different wind speeds: (a) Surge; (b) Pitch.
Similarly, the validation results for the spar-buoy floating wind turbine model are
shown in Figures 13–17. Compared results in Table 4show that the simplified models show
sufficient accuracy compared to the detailed FAST models.
The differences between FAST and proposed models are caused by the reduction of
floating dynamic models. Although the FAST model is available in the simulation package,
however, it is computationally intensive and unsuitable for real-time simulation of large-
scale offshore wind farms with many turbines. The proposed turbine model overcomes
the limitation as it is sufficient for real-time simulation while retaining acceptable accuracy.
The real-time simulation of a large-scale offshore wind farm with eighty turbines was
conducted in the next section to verify the effectiveness of the proposed turbine models.
Figure 8.
Frequency response of motion RAO for semi-submersible floater: (
a
) Surge; (
b
) Heave;
(c) Pitch.
Energies 2021,14, 4571 11 of 18
Figure 9.
Time response of motion RAO for semi-submersible floater under regular wave: (
a
) Surge;
(b) Pitch.
Figure 10.
Output power of the semi-submersible floating turbine under regular wave and wind
speed of 8 m/s.
Figure 11.
Time response of motion RAO for semi-submersible floater under irregular wave: (
a
) Surge;
(b) Pitch.
Energies 2021,14, 4571 12 of 18
Figure 12.
Output power of the semi-submersible floating turbine under an irregular wave and wind
speeds of 8 m/s.
Table 3.
Mean and standard deviation of RAO motions and output power for the semi-submersible
turbine model.
Model RAOs Mean STD
FAST model
Surge (m) 4.921 0.085
Pitch (deg) 1.787 0.087
Power (MW) 1.754 0.0076
Simplified model
Surge (m) 4.92 0.133
Pitch (deg) 1.79 0.087
Power (MW) 1.75 0.0059
Figure 13. Frequency response of motion RAO for spar-buoy floater: (a) Surge; (b) Heave; (c) Pitch.
Energies 2021,14, 4571 13 of 18
Figure 14.
Time response of motion RAO for spar-buoy floater under regular waves: (
a
) Surge;
(b) Pitch.
Figure 15.
Output power of the spar-buoy floating turbine under regular wave and wind speeds
of 8 m/s.
Figure 16.
Time response of motion RAO for the spar-buoy floater under irregular waves: (
a
) Surge;
(b) Pitch.
Energies 2021,14, 4571 14 of 18
Figure 17.
Output power of the spar-buoy floating turbine under irregular wave and wind speeds
of 8 m/s.
Table 4.
Mean and standard deviation of RAO motions and output power for the spar-buoy turbine
model.
Model RAOs Mean STD
FAST
Surge 9.51 0.2489
Pitch 2.61 0.0962
Power 1.746 0.0076
Simplified
Surge 9.5 0.2339
Pitch 2.6 0.1072
Power 1.74 0.0073
4.2. Floating Offshore Wind Farm Using Simplified Models
The offshore wind farm system including 80 turbines is used to evaluate the per-
formance of the simplified turbine models. The power rating of each turbine is 5 MW,
resulting in a total of 400 MW capability of the offshore wind farm system. Eighty turbines
are grouped into 10 clusters, in which each cluster consists of 8 turbines, as shown in
Figure 18.
This figure also shows the wake effects in the tested offshore wind farm system.
It can be seen that the wind speeds of the downstream turbines are lower than the upstream
turbines due to the wake effects. The wind field of the tested system considering wake
effects is generated by using the SimWindFarm toolbox [25].
The offshore wind farm system is managed by the central windplant level controller
(WF control), as shown in Figure 19. The main objective of the central wind controller is
to regulate the total power of offshore wind systems following the required power (
P∗
WF
)
from the transmission system operator (TSO). As the output power of each turbine is
different due to the wake effects, the power command to each turbine (
P∗
TBi
) should be
chosen regarding its available power (
Pavli
), as given by (19). The tested wind farm system
is simulated in the OP5600 real-time simulator to evaluate the effectiveness of the proposed
simplified turbine models for real-time application.
P∗
TBi =P∗
WF
Pavli
∑N
i=1Pavli
, (19)
where Nis the number of turbines in the offshore wind farm system.
Energies 2021,14, 4571 15 of 18
Figure 18. Wind field throughout offshore wind farm.
Figure 19. Offshore wind farm controller.
Two offshore wind farm systems are evaluated, one uses the semi-submersible turbine
model and the other uses the spar-buoy turbine model. It is assumed that the power
command from TSO is 300 MW and it is reduced to 240 MW at 1500 s. The central wind-
plant level controller generated power set-points to each turbine based on its available
power to meet the required power from TSO. The performance of two wind farms is shown
in Figure 20, which includes the power output of semi-based and spar-based offshore wind
farms. Due to the wake effect, the available power of the wind farm can be smaller than the
required power of 300 MW. In this condition, all wind turbines operate under maximum
power mode to produce maximum power. When the available power is larger than the
required power, the pitch angle of the turbine is adjusted to regulate output turbine power
following the set-point power from the central wind-plant level controller. It can be seen
that the total output power of offshore wind farms tracks closely to the power reference of
240 MW. It is observed that the power fluctuation in the semi-based wind farm is smaller
Energies 2021,14, 4571 16 of 18
than the spar-based wind farm system as the semi-submersible floater is more stable than
the spar-buoy floater, which is also indicated by a smaller value of standard deviation
shown in Table 5.
Figure 20. Total output power of offshore wind farms.
Table 5. Mean and standard deviation of output wind farm power (MW).
Model Mean STD
Semi-based WF 259.05 22.25
Spar-based WF 259.15 27.40
Offshore wind farms can operate under deloaded conditions to participate in the
primary frequency control. In this paper, two offshore wind farms are tested with the
deloaded mode with 5% reserved power. Real-time simulation result in this condition is
shown in Figure 21. It can be observed that wind farm output power is always lower than
available wind power, which allows the wind farm to respond to frequency changes as
necessary. It is also observed that the semi-based offshore wind farm is more stable than
that of the spar-based offshore wind farm.
Figure 21.
Total output power of offshore wind farms under deloaded operation: (
a
) Semi-based
wind farm; (b) Spar-based wind farm.
5. Conclusions
This paper has proposed a simplified floating wind turbine model that can be eas-
ily modeled in the real-time electromagnetic transient environments such as RT-LAB or
RSCAD. As the effect of an ocean wave on the floater is simplified as transfer functions,
the proposed simplified models bring significant benefits of computations compared to
the detailed FAST model, especially for the case of a wind farm system consisting a large
number of turbines. Two types of floating wind turbines were conducted in this paper,
Energies 2021,14, 4571 17 of 18
which are the semi-submersible and spar-buoy turbines. The performance of the simplified
models was evaluated in conditions of regular and irregular waves. The validation of
the simplified models against detailed FAST models showed sufficient accuracy of the
proposed model. Advantage of proposed models over existing detailed models is the
computational efficiency, which allows real-time simulation of the large-scale offshore wind
farm systems. Two offshore wind farm systems including eighty units of the 5-MW turbine
were developed based on both types of floating turbines to show the effectiveness of the
simplified turbine models for the large-scale wind farm studies. The wake effects among
turbines and the effect of wind speeds on ocean waves were involved in the offshore wind
farm simulation. Real-time simulation studies on Opal-RT real-time simulator showed
the promising application of the simplified models for the large-scale offshore wind farm
system. The real-time model of floating offshore wind farm based on proposed FOWT
models will be used to develop the offshore wind farm controllers and reveal its impact on
the interconnected power system.
Author Contributions:
Conceptualization, T.-D.P. and M.-C.D.; validation, M.-C.D. and T.-T.N.;
writing—original draft preparation, T.-D.P.; writing—review and editing, M.-C.D., H.-M.K. and T.-
T.N.; supervision, T.-T.N.; All authors have read and agreed to the published version of the manuscript.
Funding: This research received no external funding.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Conflicts of Interest: The authors declare no conflict of interest.
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