Wind Tunnel Testing on Negative-damped Responses of a
7MW Floating Offshore Wind Turbine
KARIKOMI Kai, KOYANAGI Takuya, OHTA Makoto, NAKAMURA Akihiro,
IWASAKI Satoshi, HAYASHI Yoshiyuki and HONDA Akihiro
Nagasaki Research & Development Center, Mitsubishi Heavy Industries, Ltd.
5-717-1, Fukahori-machi, Nagasaki, 851-0392, Japan
E-mail: kai karikomi@mhi.co.jp Phone: +81-95-834-2385

Abstract
For pitch-controlled Floating Offshore Wind Turbines (FOWTs), the instability problem might occur
by coupling of the floater pitch motion and the rotor speed control regulated by the blade pitch, whichleads to adverse effect on the loads on the FOWTs. Some experiments related to scaled tank tests for
FOWTs have been performed in recent years. To the best knowledge of the authors, however, there arefew experimental studies where the unstable motion of FOWT due to the negative damping is clearly
demonstrated by a tank or wind tunnel testing using a scaled FOWT model. On the other hand, there
exist a number of papers which deal with the instability problem by using aeroelastic codes for FOWTs.
In this paper, we demonstrated experimentally the unstable motion of FOWT caused by the pitch
control, and investigated effects of the gain parameters of the blade-pitch control on the behaviour of thefloater pitch motion. Furthermore we validated an enhanced control method to suppress the negative
damped response of the platform. The instability of the FOWT response in pitch motion depends
on controller bandwidth. The negative damped response appeared in the cases with high controller
bandwidth. Even for the controller bandwidth as high as the conventional fixed bottom turbines, wevalidated the enhanced control method to suppress the negative damped response of the platform.

1 INTRODUCTION
For pitch-controlled Floating Offshore Wind Turbines (FOWTs), the instability problem might occur by
the coupling of the floater pitch motion and the rotor speed control regulated by the blade pitch [1]. Thisinstability, which is well known as the negative damping, is caused by the fact that a thrust force loadedon the turbine rotor shows a negative slope against variations of wind speeds in rated power region. For
a bottom-fixed wind turbine, the negative damping in the direction of fore-aft cannot appear because thetower natural frequency is an order of magnitude higher than the blade-pitch control bandwidth then the
aerodynamic damping due to thrust shows positive most of the operation time. On the other hand, thenegative damping can be problematic for a FOWT whose floater has a natural frequency almost equal toor lower than the blade-pitch control bandwidth and has very low hydrodynamic damping. The negative
damping leads to large fluctuation of the floater pitch motion and then it has an adverse influence on
integrity of the FOWT and fatigue loads on support structures. It is of great significance to assess thepossibility of negative damping during the design process of FOWTs.
In this study, we performed wind tunnel testing on the negative damping responses and demonstrated
experimentally the unstable motion of FOWT. In addition, the effect of the controller bandwidth on the
behaviour of the floater pitch motion was investigated. Finally we validated an enhanced control method
to suppress the negative damping.

2 WIND TUNNEL TESTING
2.1 Overview of wind tunnel testing
The objectives of this work are: 1) to realize the negative damping by wind tunnel testing, 2) to figureout effects of the control parameters on the stability of a FOWT, and 3) to validate an enhanced control

Table 1: Properties of wind tunnel test modelSpecification

Controller
Floater
Fluid dynamic
condition

Rated power
Rated rotational
speed
Rotor diameter
Hub height
Froude No.
Reynolds No.
(blade)Figure 1: Wind tunnel test section

Prototype7,000 kW10.3 rpm

Wind tunnel model
3.3 W
82.4 rpm

167 m
2.61 m105.3 m1.65 mVariable-speed pitch regulated
Advanced-spar-buoy typeequal
5 – 9 x 106
1 – 2 x 104

Figure 2: Schematic view of the wind tunnel and thewater wankmethod to suppress the negative damped response of the platform.
We conducted a series of wind tunnel tests at the Mitsubishi Heavy Industries, Ltd. wind tunnel
facility, using a 1/64 scale 7MW FOWT model equipped with the blade pitch actuator to control therotational speed of the rotor during the full load operation, as shown Tab.1. The floating platform used iscategorized into the spar-buoy type. The wind tunnel is equipped with a small water tank, which enables
wind and wave combined conditions.

2.2 Wind tunnel setup
Figure 1 shows the wind tunnel test section. The dimensions of the wind tunnel test section are thelength of 30 m, width of 6 m and height of 5 m. This wind tunnel, utilized conventionally in the windengineering field, can simulate the atmospheric turbulent boundary layer with the use of devices suchas roughness blocks and spires. In order to perform scaled FOWT model testing, a water tank has been
newly built on the floor of test section, as shown schematically in Fig.2. This square shaped water tankhas dimensions of 4.5m width and 2.2 m depth. Regular waves can be generated by a wave-making
device driven by a motor. It should be noted, however, that this paper presents only experimental results
which were measured under conditions of no turbulence and no waves, due to limitations of space.

2.3 Aerodynamic problem due to Froude similitude
Scale model tests of FOWTs often raises the difficulty to properly scale hydrodynamic forces and aerodynamic forces simultaneously.
In this study on the negative damping, we focused on the pitch motion of FOWT as depicted in Fig.3.
The simplified equation of motion for this case is described as Eq.1.
(I + Aradiation )θ̈ + (Cradiation + Cviscous )θ̇ + Khydro θ = FX H

(1)Terms in the left hand side (LHS) are the mass inertia and added mass, the radiation damping andviscous damping, the restoring moment. The right hand side (RHS) is a aerodynamic moment causedby the rotor thrust. It is clear that the LHS is dominated by the Froude similitude whereas the RHS isFigure 3: Illustration of 1 DOF pitch motion of FOWT
governed by the Reynolds similitude. Conventionally, model tests for FOWTs focuses on the motions offloating platform and the Froude similitude should be employed in order to properly scale the gravitationaland hydrodynamic properties. However, as pointed out by [2], the Froude and Reynolds scaling cannot
be satisfied simultaneously as described below, then the dominant equation of motion Eq.1 in scaletesting with the use of a strictly-geometry scaled model might not be appropriately scaled relative to thereal prototype scale.
When the Froude similarity rule is applied for this test, the Reynolds number is scaled to 1/512
compared to the real turbine, because the wind speed is proportional to square root of the dimension
scale ratio according to the Froude similitude, and because the kinetic viscosity√ is constant for the real
scale and model scale, then the Reynolds number should be proportional to 1/64 × 1/64 = 1/512. As
a result, the Reynolds number of 5 − 9 × 106 in real scale decreases to 1 − 2 × 104 in test scale.
This very low Reynolds number causes serious aerodynamic problems; the Reynolds number withthe order of 104 , because of the laminar separation and the increased drag on aerofoils, results indefinitely poor rotor performance and loads compared to the real turbine. In this study, to ensure thesimilarity of the test model’s power and thrust with the real turbine, rotor blades were re-designed using
thinner aerofoil and wider blades than the full scale prototype rotor.

2.4 Scale model
The scale model of wind turbine part is based on the MHI 7MW wind turbine whose properties are described in [6]. The floater part is modelled on the advanced-spar type floater designed by Japan Marine
United [4]. The advanced spar is a axisymmetric floater composed of a column and hulls. Unfortunately,
detailed information about this floater cannot be described here due to confidentiality. One of features ofthis floating structure is that although the shape is similar to a conventional spar-buoy typed floater, thedraft is lower than the spar-buoy then easier to manufacture and install.
The dimensions of turbine and floater are on a scale of 1/64 to the prototype FOWT, except for therotor blade dimensions such as the blade thickness, chord length and twist angle, as mentioned above.
For model testing of the floater motion of FOWT, it is of significance that masses of the model parts
are manufactured so that they are proportional to the third power of the scale ratio. It is, however,
not easy task because the scale model incorporates many sensing devices and cables connecting thesensors to data loggers, and their masses are comparable to the order of wind turbine parts. For
example, a sensor with the weight of 100 g in wind tunnel becomes a 26 ton device in real scale. In thisstudy, the tower top mass of model is 134% of the scaled mass of prototype FOWT, although many efforts
were done such as the use of light-weight materials of carbon and aluminium, and the optimization of
structure by using FEM. The difference of tower top mass can cause the difference of the natural periodof floater motion. In order to practically equalize the FOWT model’s the natural period of floater pitch
motion to that of the prototype, the mass distribution of floater was tuned a little by adding small ballast.
Regarding vibration characteristics of the FOWT model, the structural properties of stiffness anddamping of the rotor blades and tower were not scaled because this study only focuses on the unstablefloater behaviour exerted by the turbine control.
2.4.1 Nacelle
Figure 5 shows the nacelle inside. The turbine model was designed to implement the variable-speed
pitch regulated control in the same way as the prototype turbine. The nacelle incorporates a bladeFigure 4: FOWT model

Figure 5: Nacelle inside

Rotor speed control+

Floating
Offshore Wind
Turbine+-Limiter

FilterEnhanced control
Figure 6: Schematic block diagram of enhanced control to suppress the negative damping
pitch actuator that can actuate the three blade pitch angles collectively according to control signals froma external controller unit. For use as a generator, an AC servo motor is implemented whose torquedemand can also be variably set by the external controlling unit.
2.4.2 Baseline controller
The baseline control system has two conventional PI-regulators: the blade-pitch controller and the generator torque controller. In the full-load operation where the negative damping is expected to occur, thiscontrol system regulates the rotor speed and the generator torque to constant values. In this experiment,in order to investigate the influence of blade-pitch controller on the stability of floater motion, parametricstudy was performed varying the proportional gain Kp and integral gain Ki .
2.4.3 Enhanced control to suppress the negative damping
In order to avoid the negative damping, we have developed an enhanced controller as shown in Fig.6,
inspired by the NMPZ(Non-Minimum Phase Zeros) compensation method [5]. Our design of the gain
Kdamp , filters and limiters are elaborately optimized to maximize the suppressing effect.
As derived by Fischer [5], the transfer function from the blade pitch angle to the rotor speed includes
the aerodynamic term which is composed of the derivatives of thrust force and rotor torque with respect
to the relative wind speed at the rotor. When this aerodynamic term has the negative sign and theabsolute value of it is smaller than the hydrodynamic damping of the floater pitch, the floater pitch
motion becomes unstable, resulting in the negative damping.
The enhanced controller suppress the unstable floater pitch motion by adding damping to the aerodynamic term in the transfer function. This damping term is provided by the feedback of the floater
angular velocity to the generator torque demand. From the point of view of the control engineering,
this additional damping corresponds to compensation of the non-minimum phase zeros of the transfer
function expressing the rotor speed control loop.

2.5 Test cases
Test cases are divided into preliminary tests and main tests. In the preliminary tests, without the watertank, the scale model except the floater part is fixed on the wind tunnel floor likewise a onshore wind turbine, in order to figure out the steady performance of the re-designed rotor and the blade-pitch controller
to regulate the rotor speed. Next, as the main tests, putting the scale model of FOWT including thefloater on the water tank in the wind tunnel, the FOWT behaviour was measured to investigate effects ofthe various parameters of blade-pitch controller and to validate the enhanced controller.
Throughout all the test cases shown in this paper, the wind condition was set to quasi-uniform flow;
the quasi-uniform flow here means the airflow generated over smooth surface without any roughness
devices in the wind tunnel. Figure 7 shows longitudinal wind speed profiles of the wind tunnel speed of
1.5 m/s and 3 m/s, which covers wind speeds for the full load operation in the testing. The wind speeds
are normalized by the wind speed at 1m height. There exists the wind speed deficit region below 0.5
m which can be regarded as the maximum height of the internal boundary layer generated on the floor.
Above this height, the wind speeds are kept almost constant with the difference within 3%. Since thereis the wind speed reduction in the region between the 0.5 m height and the lower rotor tip height of 0.34m, it cannot be said that the inflow wind profile is strictly uniform. However, since the estimated area of
the wind speed deficit part in the rotor plane is 0.6% compared with the entire rotor area of 5.35[m2 ], thewind speed profile can be regards as the quasi-uniform in terms of the performance measurement. The
turbulence intensity is below 0.5%.

3 RESULTS AND DISCUSSIONS
3.1 Rotor performance
In order to evaluate the aerodynamic rotor power and thrust force of the re-designed rotor blades, thesteady rotor performance was measured in the condition where the wind turbine part of the FOWT
model, that is except for the floater, was fixed on the wind tunnel floor, as shown in Fig.8.
The reference wind speed was measured at a upstream position from the model to avoid the influenceof rotor; the distance of the position is 5 times the rotor diameter.
The blockage of the rotor is not negligible because the rotor area and the test section area are
5.35[m2 ] and 30[m2 ] then the blockage ratio is 18%. The blockage effects on the performance and thrustcoefficient were corrected according to Mikkelsen & Sørensen method [7].
The blade-pitch controller was not activated and the pitch angles were fixed during measurement
runs. The rotor speed was also fixed to 82.4 rpm. Tip speed ratios were set to from 3 to 14 by changing
the wind speed from 0.8 to 4 m/s.
The rotor performance and thrust coefficient are shown in Fig.9 and Fig.10. The power coefficient
CP varies with the change in pitch angles and reaches the maximum value of 0.32 at the tip speed ratioof 8.5 and the pitch angle of 0 deg. At this point, the thrust coefficient CT is 0.88. This thrust coefficientvalue is almost same as the CT = 8/9 = 0.889 obtained from the general momentum theory at a optimum
rotor. Therefore the aerodynamic performance of the model rotor is found to be properly designed inspite of the low Reynolds number.

3.2 Steady power and thrust with the blade-pitch controller
Following the rotor performance testing, the steady operational power and thrust forces were obtained
against various mean wind speeds. The model setup is the same as the previous rotor performance
test except for the controller; the blade-pitch controller was activated for this case. The fine pitch angle
was set to 0 deg. The reference rotation speed and rated torque were set to 82.4 rpm and 0.387 Nm,
respectively.
Figure 11-13 show the measurement results of power, thrust force and pitch angle. These figures
present scatter plots of time-averaged values. The rated wind speed at which the power reaches the
rated power of 3.3 W is 1.5 m/s, which corresponds to 12 m/s in the real scale. Above the rated windspeed, the power is kept constant with the increase of pitch angles, which proves that the blade-pitch
controller responds appropriately to the wind speed changes.

3

1.5 m/s
3 m/s

2.5

Height [m]

2
1.5
1
0.5
0
0.6
0.8
1
1.2
Normalized wind speed [−]Figure 8: Setup for steady performance testing

Figure 7: Vertical profile of longitudinal wind speed
at the position of model

0.35

CP, aero

0.3
0.25
0.2

1.4

−2 deg
0 deg
2 deg
5 deg
10 deg15 deg

1
0.8
0.6

0.15
0.1

0.4

0.05

0.2

0
0

−2 deg
0 deg
2 deg
5 deg
10 deg15 deg

1.2

CT

0.4

2

4

6
8
10
Tip speed ratio

12

0
0

14

Figure 9: Aerodynamic power coefficient

2

4

6
8
10
Tip speed ratio

12

14

Figure 10: Thrust coefficient

In the full load operation region, the thrust force is decreased with the increase of wind speed; thisnegative slope of thrust is essential for occurrence of the negative damping of FOWT.
6

25
Blade pitch angle [deg]4

5
Thrust [N]Power [W]

3

2

4
3
2

1
1
0
0

1
2
Wind speed [m/s]3

Figure 11: Power curve

0
0

1
2
Wind speed [m/s]

Figure 12: Thrust curve

3

20
15
10
5
0
0

1
2
Wind speed [m/s]3

Figure 13: Pitch angle

3.3 Floating model tests
Next, putting the entire FOWT model including the floater on the water tank, the FOWT behaviour wasinvestigated both for various gain parameters of the blade-pitch controller and for the enhanced controller
to avoid the negative damping.
The set of gain parameters of the blade-pitch controller to be tested were determined by the following
way. First, a baseline set of the proportional gain Kp and integral gain Ki of the controller were defined

(1)

(2)

(3)

(4)

Figure 14: Snapshots of the negative damped floater pitch motion
by tuning these gains so that the response of the closed loop system were identical to that of theconventional bottom-fixed wind turbine in the real scale. Next, utilizing the model matching method,
seven sets of the control gains were determined in order for their controller bandwidths fcb to cover therange from the frequency of floater pitch motion fFloater to higher frequencies than the frequency of floater
pitch motion. The non-dimensional controller bandwidths of the seven sets, which are normalized by the
fFloater , range from 0.95 to 2.24.
The common test conditions for the floating model tests are the following: the wind speed of 1.8 m/s,
in the still water (no wave), the fine pitch angle of 0°, the reference rotor speed of 82.4 rpm, the rated
torque of 0.387 Nm, the rated power of 3.34 W.
3.3.1 Negative damping of FOWT
Without the enhanced controller, the negative damped responses were observed for five cases of theparametric study in terms of the controller gains for the blade-pitch controller. The highest controller
bandwidth case showed significantly unstable motion of the FOWT; this case corresponds to the conventional settings for a bottom-fixed WT.
Figure14 shows the snapshots of the negative damped floater pitch motion for the highest controllercase. The stop motions of the pitch oscillation presents that: (1)the floater pitch remained stationary with
2.5° at the measurement start; (2)(3)the FOWT began oscillation of pitch motion; (4)the amplitude ofpitch motion was increasing with lapse of time and reached the limit cycle oscillation where the negative
aerodynamic damping is considered to be balanced with the hydrodynamic damping of floater.
As shown in Fig.15 Case A, where the rotor speed controller gains are identical to the above case,the time series clarifies the signals of FOWT responses during the negative damping.
3.3.2 Controller bandwidth effect
In order to investigate the influence of the controller bandwidth on the stability of FOWT, the parametricstudy was performed changing the gains of blade-pitch controller. The FOWT responses observed inthree representative cases are shown in Fig.15, where these three cases are set for the non-dimensional
controller bandwidth of fcb / fFloater equal to: 2.24 (Case A, high case), 1.68 (Case B, medium case) and1.44 (Case C, low case). Here the controller bandwidth fcb is normalized by the natural frequency of thefloater pitch motion fFloater . The time axis is also non-dimensionalized by measurement periods. It should
be noted that Case A can be regarded as the conventional setting for the bottom-fixed wind turbine; thisCase A is identical to that shown in Section 3.3.1.

86

86

86

84

84

84

82

82

82

80

80

80

78

78

78

10
8
6
4
2
0

10
8
6
4
2
0

10
8
6
4
2
0

0.5

0.5

0.5

0.4

0.4

0.4

0.3

0.3

0.3

0.2

0.2

0.2

0.1

0.1

0.1

8
6
4
2
0
−2
−4
0

8
6
4
2
0
−2
−4
0

8
6
4
2
0
−2
−4
0

Floater pitch [deg]Torque [Nm]Wind speed [m/s]Case C
2.4
2.2
2
1.8
1.6
1.4
1.2
1

Rotor speed [rpm]Case B
2.4
2.2
2
1.8
1.6
1.4
1.2
1

Blade pitch [deg]Case A
2.4
2.2
2
1.8
1.6
1.4
1.2
1

0.2

0.4
0.6
t/T0 [−]

0.8

1

0.2

0.4
0.6
t/T0 [−]

0.8

1

0.2

0.4
0.6
t/T0 [−]

0.8

1

Figure 15: FOWT responses for the selected three cases of controller bandwidth fcb / fFloater = 2.24 (left:
Case A), 1.68 (center: Case B), 1.44 (right: Case C)
The stability of FOWT is apparently affected by the controller bandwidth. For the highest bandwidth
Case A, the amplitude of floater pitch motion rapidly increased and converged to the limit cycle, whereas
for the middle bandwidth Case B the amplitude growth rate of the pitch motion is slower then Case A.
Only for the lowest bandwidth Case C, at the start of measurement, the initial floater pitch angle of 6°
was given by pulling a string connected to the tower top, and subsequently releasing it in order to obtain
the decay response of floater. This is because, with this controller bandwidth, the response of pitch
regulation against fluctuations of the relative inflow speed to the rotor is slow enough to give positive
aerodynamic damping to the FOWT.
0.25

Log. decrement of Floater Pitch δ

0.2
0.15
0.1

C

0.05
0

B
−0.05
−0.1

A

−0.15
−0.2
−0.25
0.8

1
1.2
1.4
1.6
1.8
2
2.2
Non−dimensional Controller Bandwidth fcb/fFloater

2.4

Figure 16: Effect of the blade-pitch controller bandwidth on the stability of floater pitch response
To quantitatively figure out the controller bandwidth effect on the floater motion, as index of thestability, the values of logarithmic decrement were estimated from envelopes fitted to the time series offloater pitch fluctuations for each measurement case. The logarithmic decrement δ with negative sign

Wind speed [m/s]Case A with the enhanced controller
2.4
2.2
2
1.8
1.6
1.4
1.2
1

Rotor speed [rpm]

86
84
82
80
78
Blade pitch [deg]

10
8
6
4
2
0

Torque [Nm]

0.5
0.4
0.3
0.2
0.1
Floater pitch [deg]

8
6
4
2
0
−2
−4
0

0.05

0.1

0.15

0.2

0.25
t/T0 [−]

0.3

0.35

0.4

0.45

0.5

Figure 17: Effect of the enhanced controller on the FOWT response; with the enhanced controller added
to the conventional blade-pitch controller gains Case A
represents the negative damping like Case A and B; the positive δ means that the FOWT is positively
damped and stable like Case C.
Figure 16 clearly explains the influence of the controller bandwidth, where the logarithmic decrements
are plotted against the normalized controller bandwidth. The aforementioned three cases A, B and C
are marked with the case names in this plot.
The higher bandwidth than around 1.5 causes the unstable motion of the FOWT, whereas the lower
bandwidth stabilizes the floater motion. Although decreasing the blade-pitch controller bandwidth to thenatural period of floater has positive effect on the stability, it could increase the rotor speed fluctuation asa trade-off [5]. Hence reduction of the blade-pitch control gains could not be practical in terms of actual
control for a real turbine.
3.3.3 Validation of the enhanced controller
The enhanced controller that we have developed can suppress the negative damped response of thefloater, instead of decreasing the gains of blade-pitch controller.
The observed response of FOWT is shown in Fig.17 where the enhanced controller was applied
together with the blade-pitch controller gains of Case A. In this case, the measurement started onlywith the blade-pitch controller gain Case A and without the enhanced controller. That is why, during theinitial stage of the measurement, the floater pitch motion shows the limit cycle oscillation resulted fromthe negative damping. It is clear that after the enhanced controller was switched on at t/T0 = 0.12, thefloater pitch motion was rapidly stabilized.
The enhanced controller absorbs the fluctuation of the energy flux of inflow into the rotor by use of thetorque control which provides feedback of the floater angular velocity to the generator torque demand;
that fluctuation of the energy flux of inflow is exerted by the conventional pitch-regulated rotor speed
control. According to the above mechanism, immediately after the activation of enhanced controller,
the torque began to fluctuate and the floater pitch motion became positively damped together with therotor speed and blade pitch. Finally, after t/T0 = 0.45, the fluctuating torque and floater pitch almost
converged with the steady state.
The logarithmic decrement estimated for this case is δ = 0.18 with the non-dimensionalized bladepitch control bandwidth of 2.24 being the same as Case A. This fact confirms that FOWTs can operate
without the occurrence of negative damping in spite of the similar bandwidth of the blade-pitch controller
to the fixed-bottom wind turbine, if the enhanced controller to suppress the negative damping is applied.
It should be also noted that, in actual situations for the real turbine, if this enhanced controller was
activated all the time, there would be no occurrence of such large fluctuations of the torque, the rotor
speed and the floater pitch motion that were observed in the experimental demonstration case as shown
above.

4 CONCLUSIONS
We investigated effects of the gain parameters of the blade-pitch controller on the behaviour of thefloater pitch motion. It was demonstrated that the instability of the FOWT response in pitch motion wasdependent on controller bandwidth and the negative damped response appeared in the test cases withhigh controller bandwidth.
Even for the controller bandwidth as high as the conventional fixed bottom turbines, we validated theenhanced control method to suppress the negative damped response of the floating platform.

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[2] Martin, H.R., ”Development of a Scale Model Wind Turbine for Testing of Offshore Floating Wind
Turbine Systems,” Electronic Theses and Dissertations. Paper1578, The University of Maine, 2011.
[3] William E-J.R et al., ”State of the Art Model Testing Techniques for Floating Wind Turbines,” EWEA
Offshore 2013.
[4] Yoshimoto, H. et al., ”Development of floating offshore substation and wind turbine for Fukushima
FORWARD,” Proc. International Symposium on Marine and Offshore Renewable Energy, 2013,
Tokyo, Japan.
[5] Fischer, B., ”Reducing rotor speed variations of floating wind turbines by compensation of nonminimum phase zeros,” EWEA 2012.
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