NREL is a national laboratory of the U.S. Department of Energy, Office of Energy 

Efficiency & Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Contract No. DE-AC36-08GO28308

Numerical Prediction of 

Experimentally Observed 

Behavior of a Scale Model of an 

Offshore Wind Turbine 

Supported by a Tension-Leg 

Platform

Preprint

I. Prowell

MMI Engineering

A. Robertson and J. Jonkman

National Renewable Energy Laboratory

G. M. Stewart

University of Massachusetts

A. J. Goupee

University of Maine

To be presented at the 2013 Offshore Technology Conference

Houston, Texas

May 6-9, 2013

Conference Paper

NREL/CP-5000-57615

January 2013
NOTICE

The submitted manuscript has been offered by an employee of the Alliance for Sustainable Energy, LLC 

(Alliance), a contractor of the US Government under Contract No. DE-AC36-08GO28308. Accordingly, the US 

Government and Alliance retain a nonexclusive royalty-free license to publish or reproduce the published form of 

this contribution, or allow others to do so, for US Government purposes.

This report was prepared as an account of work sponsored by an agency of the United States government. 

Neither the United States government nor any agency thereof, nor any of their employees, makes any warranty, 

express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of 

any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately 

owned rights. Reference herein to any specific commercial product, process, or service by trade name, 

trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, 

or favoring by the United States government or any agency thereof. The views and opinions of authors 

expressed herein do not necessarily state or reflect those of the United States government or any agency thereof.

Available electronically at http://www.osti.gov/bridge

Available for a processing fee to U.S. Department of Energy

and its contractors, in paper, from:

U.S. Department of Energy

Office of Scientific and Technical Information

P.O. Box 62

Oak Ridge, TN 37831-0062

phone: 865.576.8401

fax: 865.576.5728

email: mailto:reports@adonis.osti.gov

Available for sale to the public, in paper, from:

U.S. Department of Commerce

National Technical Information Service

5285 Port Royal Road

Springfield, VA 22161

phone: 800.553.6847

fax: 703.605.6900

email: orders@ntis.fedworld.gov

online ordering: http://www.ntis.gov/help/ordermethods.aspx

Cover Photos: (left to right) PIX 16416, PIX 17423, PIX 16560, PIX 17613, PIX 17436, PIX 17721

Printed on paper containing at least 50% wastepaper, including 10% post consumer waste.
1 

Numerical Prediction of Experimentally Observed Behavior of a ScaleModel of an Offshore Wind Turbine Supported by a Tension-Leg Platform

I. Prowell, MMI Engineering; A. Robertson, J. Jonkman, National Renewable Energy Laboratory; G.M. Stewart, 

University of Massachusetts; A.J. Goupee, University of Maine

Abstract

Realizing the critical importance the role physical experimental tests play in understanding the dynamics of floating offshore 

wind turbines, the DeepCwind consortium conducted a one-fiftieth-scale model test program where several floating wind 

platforms were subjected to a variety of wind and wave loading conditions at the Maritime Research Institute Netherlands 

(MARIN) wave basin. This paper describes the observed behavior of a tension-leg support platform (TLP), one of three 

platforms tested, and the systematic effort to predict the measured response with the FAST simulation tool using a model 

primarily based on consensus geometric and mass properties of the test specimen. The initial model was tuned through 

adjusting damping and stiffness of the platform and tower using free-response test results.

Simulation results showed reasonable agreement with the experimental data for most quantities, including platform surge, 

tower-base bending moment, and tendon tension across a broad range of tests. Of particular note was the under prediction of 

platform-pitch acceleration for most scenarios investigated. In light of past findings for TLP pitch behavior, it was 

hypothesized that second-order sum-frequencies present in the experiment and not considered numerically were at least 

partially responsible for this error. For experimental conditions that led to slack-line events in the wave basin, FAST 

simulations sometimes predicted corresponding events. The prediction of the slack-line events and numerical stability of the 

following dynamic response was encouraging. However, multiple experimental tests showed slack-line events that were not 

predicted numerically. In particular, the FAST simulations failed to predict slack-line events that occurred while the rotor 

was stationary. It is believed that under prediction of wind drag on the tower, the exposed portion of the platform, and 

possibly the rotor was the primary cause for this modeling error. Increasing the accuracy for the pitch response would 

improve prediction of slack-line events. 

It is suggested that the following efforts be made to improve FAST’s predictive capabilities for turbines supported on 

floating platforms: 1) Allow specification of platform geometries other than a constant diameter cylinder for the computation 

of hydrodynamic forces. The need for adjustments to damping would likely decrease if the geometry of the TLP were

modeled explicitly (e.g. the larger diameter portion near the bottom of the platform and the platform legs); 2) Implement a 

dynamic model of the platform tendons so that contributions beyond cable tension are more explicitly considered; 

3) Consider second-order hydrodynamics that are believed to be a source of error in the prediction of the platform pitch; and

4) Develop wave loading routines for FAST that more readily allow for reproduction of the experimentally observed wave 

time history instead of only matching the wave spectrum, similar to how a variable wind time history can be explicitly 

defined. 

Further, future wave tank tests for a TLP supported floating turbine should consider: 1) additional instrumentation to 

ascertain tower mode shapes to assist in classification of resonant frequencies as specific mode types; 2) the importance of 

the pitch response of a TLP and how to accurately quantify the pitch response experimentally; 3) higher sampling rates to 

better capture the response of the tower-bending behavior that, for the tested TLP, appears to be highly coupled with platform 

dynamics; and 4) better scaling of rotor aerodynamics. 
2 

In light of potential improvements, results based on current simulation capabilities showed that a calibrated FAST model 

was, within a reasonable level of accuracy, able to predict many dynamic response quantities of a TLP-supported floating 

turbine under numerous loading scenarios.

Introduction 

Under the direction of the University of Maine, an experimental test was performed on a one-fiftieth-scale floating wind 

turbine model to investigate the behavior of three different floating platform concepts at the Maritime Research Institute 

Netherlands (MARIN). The one-fiftieth-scale turbine design was based on the National Renewable Energy Laboratory’s

(NREL) 5-MW reference turbine (Jonkman et al. 2009) with modifications required to accommodate construction at test 

scale. Detailed information regarding the model scale turbine is documented by Martin (2011). The turbine was placed on 

three different support platforms: a spar buoy, a semisubmersible, and a tension-leg platform (TLP). Summaries of 

experimental results from all three support platforms are available in Goupee et al. (2012) and Koo et al. (2012). Of the three 

platforms tested, the TLP was considerably lighterweight and would likely be more economical in terms of material costs, 

but not necessarily in anchoring costs. This manuscript details the test results for the TLP and does not address the results 

from the spar buoy or the semisubmersible. Figure 1 illustrates the turbine test configuration. The paper presents a more 

in-depth analysis of the preliminary TLP results published by Stewart et al. (2012). Specifically, the model developed by 

Stewart is further refined, scenarios for more simulations are presented, and quantities predicted numerically by the FAST 

tool (Jonkman and Buhl 2005) and those observed experimentally are compared. 

Experimental Setup and Conventions

The test turbine represents turbines under consideration for near-term deployment to deepwater sites where a floating 

platform is required. Pertinent details of the model scale turbine are presented in Table 1. In many respects the scaled 

properties of the tested turbine departs significantly from the 5-MW NREL reference turbine. Though tested at one-fiftieth 

scale, all results presented here are translated to full scale using similitude laws (Jain et al. 2012) for ease of interpretation. A 

summary of the platform parameters is shown in Table 2. 

For reference, the coordinate convention used herein is illustrated in Figure 2. Translation of the platform is referred to as 

surge, sway, and heave, which are in the X, Y, and Z directions, respectively. For platform rotation, the terms roll, pitch, and 

yaw are used to represent positive right-handed rotation about each of the X, Y, and Z axes, respectively.

Dynamic Properties of Physical Turbine Model

Impulse-response experiments were performed on the turbine by hitting the structure with a hammer, both while connected to 

a very rigid base (mimicking a land-based support) and also while supported by each of the three floating platforms. The 

turbine was struck in both the X and Y directions at the water level, 25 m above the water level, and 92.5 m above the water 

level. An additional strike was performed in the vertical (Z) direction at 25 m above water level. The hammer used in the 

tests was not instrumented and, as a result, only output quantities are available for analysis. Analyses of hammer tests are 

presented by Martin (2011) and de Ridder et al. (2011b; 2011a). For the rigid-base tests, Martin found a natural frequency of 

0.29 Hertz (Hz) for the tower’s primary bending mode in the fore-aft and side-to-side directions. The second fore-aft natural 

frequency identified by Martin on the rigid platform is 1.24 Hz. When placed on the TLP, little change was observed by 

Martin in the frequency of the tower’s primary fore-aft (0.28 Hz) and side-to-side modes (0.29 Hz). The second fore-aft 

frequency was reported as 1.16 Hz. De Ridder et al. (de Ridder et al. 2011b) only reported the first fore-aft natural frequency 

with a slightly lower value of 0.274 Hz when on the rigid support and 0.267 Hz when supported by the TLP. Full plots of the 

TLP hammer tests that showed results beyond the primary bending mode of the tower were presented by de Ridder et al. (de 

Ridder et al. 2011a), but no interpretation was provided. It appears that peak picking from the power spectrum was used by 

both Martin and de Ridder et al. to develop reported results.

To gain further insight from the hammer tests, the frequency-domain-decomposition (FDD) algorithm (Brincker et al. 

2000) was used to clarify modes that may not have been identified by peak picking. For the hammer tests, the 

instrumentation used was a limited subset of that used in the other tests and was recorded at 141.4 Hz instead of 14.14 Hz. 

For consistency between instruments, only translational accelerometers placed along the tower were used in the analysis 

presented here. Three channels for the low and mid accelerometers (Figure 3) were recorded and available for the tests, 

which results in a total of six channels. The limited number of channels, in particular only one accelerometer on the flexible 

portion of the tower, presents a challenge in identifying the modes of the turbine when supported on the TLP. It is typical 

that the number of modes capable of being identified is limited to the number of channels. Using insight gained from the 

FAST model of the TLP supported turbine, additional modes were inferred. Results are summarized in Table 3 with data 

processing such that the minimum frequency step resolved was 0.004 Hz. Differences between the results reported here and 

those in the past will be addressed later in this manuscript. 
3 

Calibration of the FAST Model 

As reported and clearly demonstrated in Stewart et al. (2012), a FAST model of the TLP-supported turbine simply based on 

scaled-design specifications for the model of the rotor, nacelle, tower, and platform (Martin 2011; de Ridder et al. 2011b; de 

Ridder et al. 2011a) produces results that diverge significantly from those observed in the wave tank. This divergence was 

also present in the spar and semisubmersible results. To reduce the discrepancies and gain more in-depth insight from the 

experimental results, investigations using the DeepCwind data have adopted the approach of adjusting the numerical model 

to more accurately recreate observed test results for a small subset of the tests. This tuning was justified as a preliminary way 

to account for unknown data and to include the effects of physics, such as the viscous drag on the platform legs, that are not 

explicitly modeled numerically. In this investigation two main properties, damping and stiffness, for the platform degrees of 

freedom (DOFs) were adjusted to approximate the influence of unmodeled physics and possibly account for other modeling 

limitations, such as material properties. In addition, component mass, stiffness, and aerodynamic properties were adjusted as 

deemed appropriate (Martin 2011, Stewart et al. 2012).

Because the tendons are critically important to the response of a TLP, it was decided to first determine the appropriate 

platform displacement that best recreated the experimentally reported tendon tension. For the DeepCwind TLP, MARIN 

reports a displacement of 2,840 metric tons (de Ridder et al. 2011b), which for an assumed water density of 1,025 kilograms 

per meter cubed (kg/m3

), is equivalent to a displaced volume of 2,770 m3. In processing the experimental data, tendon 

tension for each test was zeroed to remove sensor drift, and a static value was added from an early calibration test (de Ridder 

et al. 2011b). The static values vary from a minimum of 4,697.6 kilonewtons (kN) for tendon 1 (downwind, positive X), 

4,754.9 kN for tendon 2 (upwind, positive Y), and a maximum of 4,813.3 kN for tendon 3 (upwind, negative Y). However, 

due to the symmetry of the numerical model when simulated in the FAST tool, tendons 2 and 3 show identical tensions when 

the turbine is at rest. Due to this discrepancy between the numerical and experimental results, instead of trying to match the 

individual tendon tension, the average tension was matched. To accomplish this, platform displacement was iteratively 

altered so that the average line tension matched the average line tension observed experimentally. The resulting value of 

displaced volume of 2748.8 m3 was adopted. This change represents less than a 1% reduction in the displaced volume. This 

small discrepancy is possibly due to measurement error or other discrepancies between the idealized configuration and the 

actual test configuration.

Free-decay tests were conducted that focused on identifying the frequencies and decay rates of the six DOFs: surge, sway, 

heave, roll, pitch, and yaw. By applying additional damping and stiffness to each of the six platform DOFs, these test results 

provided the body of information used to calibrate the FAST turbine model. Past efforts to calibrate the TLP model focused 

on adding damping that was linearly proportional to the velocity for each DOF (Stewart et al. 2012). More detailed 

investigation of the damping for each platform DOF, however, showed amplitude dependence. The upper portion of Figure 4

shows the time trace of the experimentally recorded platform-surge displacement in blue for a surge free-decay test. In the 

lower portion, the log-decrement method is used to estimate the approximate damping ratio for each successive cycle. The 

experimental results clearly show amplitude dependence for the damping. Similar to that assumed in the Morison Equation, a 

drag term that is proportional to the velocity squared was added for each of the platform DOFs to approximate the drag 

behavior observed in the test data. 

The platform-heave natural frequency was used to calibrate the tendon axial stiffness. Initial models used a value of 

7,500 meganewtons (MN) for the cross-sectional stiffness of each tendon (de Ridder et al. 2011b). However with the fixed 

system mass and displacement specified above and the specified stiffness, the resulting heave frequency was approximately 1 

Hz (Stewart et al. 2012). Experimental results showed a heave frequency closer to 0.86 Hz (Table 3). The discrepancy is 

possibly caused by compliance introduced by the force gauges used to measure tendon tension. To match the observed 

frequency, the tendon stiffness was reduced to 6,118 MN. Additionally, to reduce initial heave transients, the unstretched 

tendon length was slightly modified from the specified value of 171.4 m to 171.36 m. After adjusting the tendon stiffness 

and unstretched length, the added damping was iteratively adjusted. In the final model, a value of 0 was used for additional 

linear damping and a value of 2.5 MNs2

/m2 was used for quadratic damping. This additional quadratic damping likely 

represents energy dissipation of the unmodeled viscous drag from the platform legs and larger diameter portion of the 

platform moving vertically in the water.

Following calibration of the platform tendons for tension and heave vibration characteristics, the other platform DOFs 

were calibrated in a similar manner to match experimentally recorded free-response tests. A summary of the required 

adjustments are presented in Table 4. An example of the resulting match for the free-decay surge test is provided in Figure 4. 

Visual inspection of the recreated time history (red) shows it is almost identical to that recorded in the wave tank (blue). The 

damping estimates from the model and the experiment differ more significantly than the time histories, but recreate the 

approximate damping levels across a range of displacements with results diverging slightly for large amplitudes.
4 

The tower mode shapes required by FAST were generated in BModes (Bir 2005) using the properties derived for the 

calibrated platform mass and stiffness characteristics, hydrodynamic added mass and hydrostatic restoring properties from a 

WAMIT model (WAMIT Inc. 2006), and mass and stiffness properties of the turbine tower and mooring system. After 

removing the translation and rotation at the tower base as required by FAST (Figure 5), the mode shapes predicted by 

BModes were able to be accurately approximated as a 6th-order polynomial for direct use in the FAST model. Table 3

presents a summary of the modal frequencies predicted by the calibrated model and those observed experimentally. 

For illustrative purposes, the mode shapes predicted at 0.267 Hz and 1.30 Hz are presented in Figure 6 and Figure 7. 

These two frequencies both contain tower fore-aft bending and platform-pitch contributions. In past publications, these two 

modes have been interpreted in various combinations as tower 1st fore-aft bending, platform pitch, and tower 2nd fore-aft 

bending. The figures clearly illustrate the high degree of coupling between tower bending and platform rotation in the overall 

turbine dynamics that has made interpretation of these modes difficult. Investigation of the mode shape at 1.30 Hz (Figure 7) 

shows that the tower is in single curvature, which supports the interpretation of a beam 1st bending mode in which the 

boundary conditions resemble a free-free condition instead of a fixed-free condition. Based on the extremely low frequencies 

for surge and sway, it is clear that translation of the tower base more closely resembles a free condition, but conclusions 

about the rotational fixity are not as clear and have contributed to variations in classification of modes (Koo et al. 2012). 

Because the mode shape at 1.30 Hz shows single curvature and is at a higher frequency than the fixed-base 1st fore-aft 

bending frequency (Martin 2011; de Ridder et al. 2011b), it is interpreted as the 1st fore-aft tower-bending frequency. The 

presence of a higher mode (3.236 Hz) that clearly shows double curvature in the tower (Figure 8) further supports this 

interpretation. Subsequently, the mode at 0.267 Hz is interpreted as platform pitch. Similar logic was employed in 

classification of the tower side-to-side and platform-roll modes.

Simple Loading 

Following hammer and free-response testing, the turbine was subjected to a number of loading scenarios. Initial scenarios 

focused on single-source loading from either wind or waves. A summary of the tests conducted for the wind-only load cases 

is reported in Table 5. Simulations in FAST were conducted that corresponded to the experimental test conditions for these 

tests, but wind speeds were altered slightly from those reported by de Ridder et al. (2011b) to more accurately simulate the 

measured experimental conditions. For each simulation, a total of approximately 43 minutes was simulated, but only the 

final 10-minute period was analyzed to ensure that transient behavior did not influence the reported results. The lengths of 

experimental tests varied, but for consistency in the results reported here, a 10-minute period was selected and used. For the 

wind-only tests, the primary quantity of interest was the force exerted on the system by the wind. Mean platform surge

(Figure 9) and tower-bending moment (Figure 10) were the main measured quantities impacted by static wind forces. The 

MARIN and FAST data show a horizontal offset for display purposes and the FAST simulations occurred at the same wind 

speeds as the MARIN tests. Due to past efforts to calibrate airfoil properties for the tested turbine, simulation results showed

good agreement with those observed experimentally (Martin 2011, Coulling et al. 2013a). Aerodynamic characteristics of 

the scaled model’s rotor were one of the areas that differed most significantly from the 5-MW NREL reference turbine and 

the resulting rated wind speed was approximately 21 m/s instead of 12 m/s. This difference in aerodynamics resulted in 

higher wind speeds for specific rotor speeds than would be expected for the 5-MW reference turbine. It was noted that for 

the high wind condition (30.5 m/s)—when the blades were feathered and the rotor was not spinning—there was a more 

significant under prediction in terms of percentage of platform surge. The primary source of this discrepancy was likely due 

to the wind drag on the tower and exposed portion of the platform not being calculated in the FAST model. When the rotor 

was stationary and feathered, these forces contribute a larger fraction of the overall wind force on the turbine system. The 

trends observed for the wind-only simulations suggest that the wind force should be reasonably predicted for situations where 

the rotor was spinning but may be underestimated when the rotor was stationary.

A complementary set of tests were conducted in which loading consisted of only regular waves at a fixed period and 

magnitude. The parameters of the waves imparted are summarized in Table 6. As with the wind-only tests, a set of 

43-minute simulations were run with corresponding load conditions. Reported results only contain information for the final 

10-minute portion of the simulations after all initial transients had dissipated. As before, only a 10-minute portion of the 

experimental results were considered for comparison. Similar to the wind-only tests, the platform-surge statistics showed

reasonable results (Figure 11). For the smaller sea states (1.92 m and 7.58 m), the predictions were of high quality but 

deteriorated as wave amplitude increased and the period elongated. The largest error, an approximately 25% under

prediction, occurred for waves with a period of 20 s and a height of 11.12 m. However, platform-pitch acceleration, reported 

in Figure 12, was significantly under predicted by as much as a factor of 10 in many cases. Clearly, an underlying 

mechanism exciting pitch of the platform—likely second-order hydrodynamics—was not well captured in the FAST model

(Coulling et al. 2013b). Other investigated parameters, including tendon tension, tower-bending moment, and platform 

heave, showed significantly better agreement. 
5 

An illustrative reproduction of representative platform-response plots is shown in Figure 13 and Figure 14. In the left 

portion of Figure 14, the differences in platform-pitch acceleration are shown. Though the experimental measurement visibly

shows a noise floor that impedes a clear picture of the pitch response in comparison to the simulations, peaks are visible at 

two frequencies, the wave frequency (0.13 Hz) and the platform-pitch frequency (0.268 Hz). The predicted response shows 

reasonable correlation in amplitude at the wave frequency but underestimates the response at the platform-pitch frequency. 

This discrepancy can be partially explained by the presence of harmonics in the experimentally realized regular waves that 

were not present in the simulated waves, which leads to unsimulated excitation at the platform-pitch frequency. It was 

believed that, more generally, the under prediction of platform pitch can be attributed to second-order sum-frequency 

excitation. Past investigations have shown this phenomenon to be important in understanding the pitch response of a TLP 

(Naess and Ness 1992; Kim 1991). This is particularly true because typical pitch and roll frequencies of TLPs reside outside 

of the range of significant wave energy and are not directly excited. Second-order hydrodynamics may also contribute to the 

under prediction of platform surge for long period waves.

These simple load cases suggest that the turbine dynamics are reasonably recreated across many different independent 

wind and wave conditions, but appear to systematically underestimate extremes for investigated response quantities. 

Combined Loading for Normal Conditions 

Of more interest than isolated wind or wave loading is combined wind and wave loading scenarios. Numerous wind and 

wave loading scenarios were conducted in the experiment as identified in Table 7. Here the results where the turbine was 

excited by a JONSWAP (Joint North Sea Wave Observation Project) spectrum while simultaneously being subjected to 

steady winds of different levels are presented. As before, numerical simulations were conducted for a total of approximately 

43 minutes with the last 10-minute portion of the simulation used for the reported results to ensure transient behavior did not 

influence results. Similarly, the last 10-minute portion of the experimental response was selected by visual inspection for 

reported results. In addition, for these simulations, a user-defined wave spectrum was introduced in FAST to match the wave 

spectrum recorded experimentally. Though the realized wave time histories do not coincide, the difference between the wave 

power spectra was minimized through this approach. Figure 15 shows a comparison of the waves recorded in the tank as 

compared to those simulated for the test with 11.4-m/s winds and JONSWAP waves with a peak-spectral wave period (Tp) of 

12.1 s and significant wave height (Hs) of 7.1 m. Both the time history and power spectra show good qualitative correlation. 

A summary of the quantitative statistics of the waves, presented in Figure 15, also shows reasonable agreement. Results for 

the presented cases should be viewed with consideration that differences in wave statistics will likely propagate to the 

turbine-response parameters. This was particularly true for the final scenario presented where the wave basin showed wave 

heights varying from -6.8 m to 7.8 m, but the FAST simulation only had waves varying from -6.2 m to 4.9 m.

For a TLP, tendon tension is of particular importance for design. Figure 16 presents a summary of the tension statistics 

for tendon 1 (the downwind tendon), which exhibited the largest variation among the tendons. Due to direct calibration of 

mean tendon tension and the dominance of the mean component in the magnitude, relatively good agreement was observed 

across most of the tests presented. However, the experimental tendon tension showed a negative value for the test with 

21-m/s winds and a 7.1-m significant wave height, meaning that the tendon had gone slack. It is essential that slack-line 

events do not occur for a deployed system because the following force from the snap-back of the tendon will likely exceed 

the tendon, anchor, or fairlead capacity and create an impulse that will be propagated through the structure, exciting all of its 

Eigen frequencies. For a TLP with 3 legs like the one investigated here (which has no redundancy), such an event could 

cause complete loss of a realistic full-scale system. The FAST simulation for the corresponding scenario does not predict this 

negative tendon tension and the subsequent significant peak in tension. 

Inspection of the slack-line event in the experimental time history clearly showed that it was in direct response to a 

significant wave. The specific wave sequence was a trough elevation of -6.8 m followed by a crest of 7.3 m and another 

subsequent trough of -6.1 m. Though the FAST wave power spectra showed a good match with the experimental power 

spectra, the most extreme comparable wave was a -6.1 m trough followed by a 4.8 m crest and a trough of -4.7 m. It is likely 

that if FAST were capable of directly recreating the large wave, the slack-line event would have been numerically predicted. 

For this reason, it is suggested that efforts be made to enable more direct simulation of an observed wave time history in 

FAST instead of simply matching the wave spectrum.

Again, platform-pitch acceleration (Figure 17) is significantly underestimated. The extent of underestimation is more 

significant than that for the regular wave tests. Figure 18 shows a typical comparison of the wave time history and power 

spectra from the wave tank and the simulation. Unlike the regular wave tests, where harmonics that were present in the wave 

tank were not recreated numerically, the power spectra showed good agreement across all platform frequencies. This 

suggests that some excitation mechanism was not being modeled numerically. Based on past findings (Naess and Ness 1992; 

Kim 1991) showing that second-order sum-frequency wave loads contribute significantly to the pitch response of a TLP, it 

was hypothesized that this was at least partially attributable to their omission in the simulation.
6 

Despite the under prediction of platform-pitch acceleration across all tests and the lack of predicting the observed 

slack-line event in 21-m/s winds with 7.1-m waves, the FAST model did a good job predicting the character of the turbine 

response for many of the investigated parameters. Figure 19 and Figure 20 show the time histories and power spectra for 

some quantities of interest for the test with an 11.4-m/s wind speed and a 7.1-m significant wave height. These figures 

clearly show similar response characteristics for all time histories other than platform-pitch acceleration. Further, with 

consideration of the noise floor of the experimental instrumentation, which is clearly evident in the platform surge above 

0.3 Hz, the power spectra match well. For frequencies above 0.4 Hz, results diverge more significantly than at lower 

frequencies.

Combined Wind and Wave Loading for Extreme Conditions 

Beyond normal operational scenarios, it is vital to be able to predict the extreme response of a structure. Table 8 presents 

parameters for what are considered survival conditions for the turbine. One scenario has the turbine operating in an extreme 

sea state and the other has the turbine rotor stationary in winds beyond the turbine cut-out wind speed. Statistics for the 

simulated wave conditions show better agreement with the experimental conditions (Figure 21) than those for the calmer sea 

states discussed above. Tendon 1 results for the wave tank clearly show slack-line events for both conditions (Figure 22). In 

the numerically simulated results, it was observed that a slack-line event was only predicted for the operational scenario. 

This lack of prediction of a slack-line event when the rotor was stationary can be partially justified by the under prediction of 

wind forces in such a scenario (Figure 9), which would cause the downwind tendon (tendon 1) tension to be overestimated. 

It is possible that improvements in prediction of wind forces for the stationary rotor condition would improve prediction of a 

slack-line event. 

A qualitative comparison of the time histories and power spectra for the operational extreme test shows a better degree of 

correlation between the experimental results and numerical simulations (Figure 23 and Figure 24) than in calmer sea states. 

The time history of tendon 1 in the right portion of Figure 23 shows the slack-line event around 250 seconds. This event was

responsible for both extremes seen in the experiment and the simulation in Figure 22. FAST showed reasonable correlation 

with the minima, but under predicts the snap-back of the line. The source of under prediction of the snap-back was unclear, 

but may be attributable to the lack of a dynamic model for the tendon, or possibly, the selected quadratic damping model over 

estimates the damping for platform pitch in such an extreme event. The power spectrum of the tension for tendon 1 showed

that most of the contributing frequencies to the tendon tension were well modeled. Specifically, the wave excitation centered 

around 0.09 Hz, platform pitch at 0.268 Hz, and platform heave at 0.863 Hz. However, the contribution from tower first 

bending at 1.3 Hz was significantly underestimated by FAST. It is possible that the tower damping value selected, 2.1% for 

the first mode, was too high. However, significantly reducing the value to 0.5% made little difference.

It is interesting to observe the platform-pitch acceleration for the extreme sea scenarios (Figure 25). For the test with the 

stationary rotor, where a slack-line event occurred but was not predicted, the platform-pitch acceleration was severely under 

predicted, as before. However, when a slack-line occurred both in the wave tank and in the numerical simulation, results for 

platform-pitch acceleration showed considerably better agreement. This supports the suggestion that the physical mechanism 

exciting the platform in pitch was not captured in the FAST model for most events, but when the excitation mechanism was 

captured, results for platform response were well predicted. This could, as suggested earlier, be due to the lack of 

second-order sum-frequency excitation in FAST.

Conclusions 

Results presented here confirm that FAST produces meaningful results for simulation of a TLP when a model is carefully 

calibrated. Considering the current capabilities and observed accuracy presented here for FAST simulations, there is a

possibility for large errors in an uncalibrated model, and design of a reliable TLP-supported floating turbine may be more 

challenging than other concepts currently under consideration. Of particular importance is addressing the challenges in 

accurately predicting the pitch response of the platform. It is possible that inclusion of second-order hydrodynamics and a 

dynamic mooring line model will contribute to improving simulation accuracy. This challenge is somewhat unique to the 

TLP concept, where platform roll, pitch, and heave reside outside of frequencies directly excited by the waves. A better 

understanding of interaction between tower bending and platform roll/pitch is also likely to improve simulation accuracy. To 

accomplish this, it is suggested that future tests focus more effort on identifying tower-bending characteristics, improve 

accuracy of platform-pitch measurements to capture the small pitch values associated with a TLP, and capture data at a 

higher rate to better resolve behavior of the tower. The need to simulate additional damping in the platform response will 

likely be reduced if the platform geometry, such as changes in diameter and platform legs, and associated viscous drag are 

explicitly modeled in all directions. Finally, efforts to compare experimental results to simulations would benefit from a 

method that is able to directly simulate the experimentally realized wave time history. The lack of this ability is likely a key 

contributor to the failure to numerically predict some of the slack-line events that occurred experimentally. Overall, the 
7 

results are encouraging and show that, even for a relatively light platform subjected to extreme sea states, many design 

parameters are reasonably predicted by FAST. 

Acknowledgements

The authors thankfully acknowledge the financial support from the U.S. Department of Energy through contract number 

DE-AC36-08GO28308, DeepCwind Grants DE-EE0002981 and DE-EE0003728, the National Science Foundation through 

Grant IIP-0917974; and the University of Maine. In addition, the expertise and support of MARIN in conducting the model 

test is greatly appreciated.

References

Bir, G. S. (2005). User’s Guide to BModes; Software for Computing Rotating Beam Coupled Modes. NREL TP-500-38976, 

National Renewable Energy Laboratory, Golden, Colorado, USA.

Brincker, R., Zhang, L., and Andersen, P. (2000). "Modal Identification from Ambient Responses Using Frequency Domain 

Decomposition." Proceedings of the 18th international modal analysis conference, Society for Experimental Mechanics Inc., 

Bethel, Connecticut, USA, 625-630.

Coulling, A.J., Goupee, A.J., Robertson, A.N., Jonkman, J.M. and Dagher, H.J. (2013a). "Validation of a FAST Semisubmersible Floating Wind Turbine Model with DeepCwind Test Data." Journal of Renewable and Sustainable Energy, in 

review.

Coulling, A.J., Goupee, A.J., Robertson, A.N., and Jonkman, J.M. (2013b). "Importance of Second-Order 

Difference-Frequency Wave-Diffraction Forcing in the Validation of a FAST Semi-Submersible Floating Wind Turbine 

Model. " Proceedings of the 32nd International Conference on Ocean, Offshore and Arctic Engineering, American Society 

of Mechanical Engineers, New York, New York, USA. 1-10

de Ridder, E. J., Koop, A., and van Doeveren, B. (2011a). DeepCwind Floating Wind Turbine Model Tests: Volume 3a: Test 

Data Results – TLP in Mooring System – Draft 30 m. 24602-1-OB, Maritime Research Institute Netherlands, Wageningen, 

The Netherlands. 

de Ridder, E. J., Koop, A., and van Doeveren, B. (2011b).DeepCwind Floating Wind Turbine Model Tests: Volume I: Final 

Text Report. 24602-1-0B, Maritime Research Institute Netherlands, Wageningen, The Netherlands.

Goupee, A. J., Koo, B. J., Lambrakos, K. F., and Kimball, R. W. (2012). "Model Tests for Three Floating Wind Turbine 

Concepts." Offshore Technology Conference, OTC, Richardson, Texas, USA, 1-16.

Jain, A., Robertson, A. N., Jonkman, J. M., Goupee, A. J., Kimball, R. W., and Swift, A. H. P. (2012). "FAST Code 

Verification of Scaling Laws for DeepCwind Floating Wind System Tests." NREL/CP-5000-54221, National Renewable 

Energy Laboratory, Golden, Colorado, USA.

Jonkman, J. M. and Buhl, M. L.,Jr. (2005). FAST User's Guide. NREL/EL-500-38230, National Renewable Energy 

Laboratory, Golden, Colorado, USA.

Jonkman, J., Butterfield, S., Musial, W., and Scott, G. (2009). Definition of a 5-MW Reference Wind Turbine for Offshore 

System Development. NREL/TP-500-38060, National Renewable Energy Laboratory, Golden, Colorado, USA.

Kim, M. (1991). "Second-Order Sum-Frequency Wave Loads on Large-Volume Structures." Appl.Ocean Res., 13(6), 287-

296.

Koo, B., Goupee, A. J., Lambrakos, K., and Kimball, R. W. (2012). "Model Tests for a Floating Windturbine on Three

Different Floaters." Proceedings of the 31st International Conference on Ocean, Offshore and Artic Engineering, American 

Society of Mechanical Engineers, New York, New York, USA, 1-11.

Martin, H. R. (2011). Development of a Scale Model Wind Turbine for Testing of Offshore Floating Wind Turbine Systems. 

Masters of Science thesis, The University of Maine, Orono, Maine, USA.

Naess, A., and Ness, G. (1992). "Second-Order, Sum-Frequency Response Statistics of Tethered Platforms in Random 

Waves." Appl.Ocean Res., 14(1), 23-32.
8 

Stewart, G., Lackner, M., Robertson, A., Jonkman, J., and Goupee, A. (2012). "Calibration and Validation of a FAST 

Floating Wind Turbine Model of the DeepCwind Scaled Tension-Leg Platfrom." NREL/CP-500-54822, National Renewable 

Energy Laboratory, Golden, Colorado, USA.

WAMIT Inc. (2006). WAMIT User Manual. WAMIT, Inc., Chestnut Hill, Massachusetts, USA.
9 

Tables 

Table 1 – Properties of the Tested Turbine

Property Value

Rotor Orientation, Configuration Upwind, 3 Blades

Control Variable Speed and Pitch

Rotor, Hub Diameter 126 m, 3 m

Hub Height 90 m

Freeboard to Tower Base 10 m

Overhang, Shaft Tilt, Precone 10.58 m, 0°, 0°

Rotor Mass 122,220 kg

Nacelle Mass 274,940 kg

Tower Mass 302,240 kg

Table 2 – Platform Properties

Property Value

Legs Configuration 3 radially at 120°

Radius to Fairlead 30 m

Draft of Fairlead 28.5 m

Mass 661,600 kg

Displacement 2,840,000 kg

Platform Draft 30 m

Water Depth 200 m

Radius to Anchor 30 m

Table 3 – Modal Frequencies as Identified and Predicted for the Tuned FAST Model

Mode Description

Orientation Experimental 

Frequency

Model Frequency

(-) (Hz) (Hz)

Platform Surge Fore-Aft 0.0259 0.0267

Platform Sway Side-to-Side 0.0259 0.0267

Platform Yaw Yaw - 0.0548

Platform Pitch Pitch 0.268 0.267

Platform Roll Roll 0.276 0.279

Platform Heave Vertical 0.863 0.864

Tower 1st Bending Fore-Aft 1.631 1.300

Tower 1st Bending Side-to-Side 1.511 1.318

Tower 2nd Bending Side-to-Side 3.328 3.118

Tower 2nd Bending Fore-Aft 3.535 3.236
10

Table 4 – Adjustments for Platform DOFs

DOF Damping Stiffness

Linear Quadratic (Linear)

Surge 7 x104 Ns/m 2.7x105 Ns2/m2 8.5x103 N/m

Sway 2x103 Ns/m 8.0x105 Ns2/m2 8.5x103 N/m

Heave 0 Ns/m 2.5x106 Ns2/m2 0 N/m

Roll 4x108 Ns/rad 9.0 x1010 Ns2/rad2 0 N/rad

Pitch 4x108 Ns/rad 9.0 x1010 Ns2/rad2 0 N/rad

Yaw 4.5x108 Ns/rad 3.6 x109 Ns2/rad2 -1.3x107 N/rad

Table 5 – Summary of Regular Wind Tests

Wind Speed 

Reported by 

MARIN

Wind Speed 

in FAST 

Simulation

Blade Pitch Rotor Speed

(m/s) (m/s) (deg) (RPM)

7.0 6.97 6.4 4.95

9.0 8.51 6.4 5.66

11.4 10.69 6.4 7.78

16.0 15.34 6.4 9.19

21.0 20.75 6.4 12.73

30.5 29.04 85 0.0

Table 6 – Summary of Regular Wave Sea States

Wave Period Wave

Height

(s) (m)

7.5 1.92

12.1 7.58

14.3 7.14

20.0 7.57

12.1 10.30

14.3 10.74

20.0 11.12

Table 7 – Summary of Combined Wave and Wind Tests for Normal Conditions

Wind Speed Blade Pitch Rotor Speed Hs Tp γ*

(m/s) (deg) (RPM) (m) (s) (-)

7.0 6.4 4.95 2.0 7.5 2.0

9.0 6.4 5.66 2.0 7.5 2.0

11.4 6.4 7.78 2.0 7.5 2.0

11.4 6.4 7.78 7.1 12.1 2.2

16.0 6.4 9.19 7.1 12.1 2.2

21.0 6.4 12.73 7.1 12.1 2.2 *

γ is the JONSWAP peak-shape parameter
11

Table 8 – Summary of Combined Wave and Wind Tests for Extreme Conditions

Wind Speed Blade Pitch Rotor Speed Hs Tp γ

(m/s) (deg) (RPM) (m) (s) (-)

21.0 6.4 12.73 10.5 14.3 3.0

30.5 85 0.0 10.5 14.3 3.0
12

Figures 

Figure 1 – Experimental Test Configuration. Photo by Andrew Goupee, University of Maine

Figure 2 – Definition of Axes
13

Figure 3 – Location of Instrumentation (de Ridder et al. 2011a)

Figure 4 – Comparison of Experimental and Numerical Surge Response After FAST Calibration
14

Figure 5 – Conceptual Adaption of Mode Shape

Physical Mode Specified Mode

Figure 6 – Turbine Pitch Mode Shape Predicted by FAST at 0.267 Hz

Front Side

Bending

Rocking

Translation

Bending
15

Figure 7 – Turbine 1st Tower Fore-Aft Bending Mode Shape Predicted by FAST at 1.300 Hz

Front Side

Figure 8 – Turbine 2nd Tower Fore-Aft Bending Mode Shape Predicted by FAST at 3.236 Hz

Front Side
16

Figure 9 – Platform-Surge Response for Regular Wind Tests

Figure 10 – Tower-Base Bending Moment Response for Regular Wind Tests 

0

1

2

3

4

5

6

7

8

9

10

Surge (m)

MARIN

FAST

7 m/s 9 m/s 11.4 m/s 16 m/s 21 m/s 30.5 m/s

0

10000

20000

30000

40000

50000

60000

70000

Tower Base Bending Moment (kN-m)

MARIN

FAST

7 m/s 9 m/s 11.4 m/s 16 m/s 21 m/s 30.5 m/s
17

Figure 11 – Platform-Surge Statistics for Regular Wave Tests

Figure 12 – Platform-Pitch Acceleration for Regular Wave Tests

-10

-8

-6

-4

-2

0

2

4

6

8

10

Surge (m)

MARIN Range

MARIN Std. Dev.

FAST Range

FAST Std. Dev.

7.5 s /

1.92 m

12.1 s /

7.58 m

14.3 s /

7.14 m

20.0 s /

7.57 m

12.1 s /

10.3 m

14.3 s /

10.74 m

20.0 s /

11.12 m

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Pitch Acceleration (deg/s2)

MARIN Range

MARIN Std. Dev.

FAST Range

FAST Std. Dev.

7.5 s /

1.92 m

12.1 s /

7.58 m

14.3 s /

7.14 m

20.0 s /

7.57 m

12.1 s /

10.3 m

14.3 s /

10.74 m

20.0 s /

11.12 m
18

Figure 13 – Illustrative Results for 7.5-s Period, 1.92-m Height Regular Waves

Figure 14 – Illustrative Results for 7.5-s Period, 1.92-m Height Regular Waves
19

Figure 15 – Summary of Realized Wave Statistics for Combined Wave and Wind Tests 

Figure 16 – Tendon 1 Tension Statistics for Combined Wave and Wind Tests

-8

-6

-4

-2

0

2

4

6

8

Wave Elevation (m)

MARIN Range

MARIN Std. Dev.

FAST Range

FAST Std. Dev.

7 m/s /

2 m

9 m/s /

2 m

11.4 m/s /

2 m

11.4 m/s /

7.1 m

16 m/s /

7.1 m

21 m/s /

7.1 m

-1000

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

Tendon Tenson (kN)

MARIN Mean and Range FAST Mean and Range

MARIN Std. Dev. FAST Std. Dev.

7 m/s /

2 m

9 m/s /

2 m

11.4 m/s /

2 m

11.4 m/s /

7.1 m

16 m/s /

7.1 m

21 m/s /

7.1 m
20

Figure 17 – Platform-Pitch Acceleration Statistics for Combined Wave and Wind Tests

Figure 18 – Comparison of Waves for Wind Speed of 11.4 m/s and JONSWAP Waves (Tp = 12.1 s / Hs = 7.1 m)

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

Platform Pitch Acceleration (deg/s2)

MARIN Range

MARIN Std. Dev.

FAST Range

FAST Std. Dev.

7 m/s /

2 m

9 m/s /

2 m

11.4 m/s /

2 m

11.4 m/s /

7.1 m

16 m/s /

7.1 m

21 m/s /

7.1 m
21

Figure 19 – Illustrative Results for Operating in 11.4-m/s Wind with 7.1-m Significant Wave Height JONSWAP Waves

Figure 20 – Illustrative Results for Operating in 11.4-m/s Wind with 7.1-m Significant Wave Height JONSWAP Waves
22

Figure 21 – Summary of Realized Wave Statistics for Combined Wave and Wind Tests for Extreme Conditions

Figure 22 – Tendon 1 Tension Statistics for Combined Wave and Wind Tests for Extreme Conditions

-10

-8

-6

-4

-2

0

2

4

6

8

10Wave Elevation (m)

MARIN Range

MARIN Std. Dev.

FAST Range

FAST Std. Dev.

21 m/s /

10.5 m

30.5 m/s /

10.5 m

-1000

1000

3000

5000

7000

9000

11000

Tendon Tenson (kN)

MARIN Mean and

Range

FAST Mean and

Range

MARIN Std. Dev.

FAST Std. Dev.

21 m/s /

10.5 m

30.5 m/s /

10.5 m
23

Figure 23 – Illustrative Results for Slack-Line Event While Operating in Extreme Conditions

Figure 24 – Illustrative Results for Slack-Line Event While Operating in Extreme Condition
24

Figure 25 – Platform-Pitch Acceleration Statistics for Combined Wave and Wind Tests for Extreme Conditions

-3.5

-2.5

-1.5

-0.5

0.5

1.5

2.5

3.5

Platform Pitch Acceleration (deg/s2)

MARIN Range

MARIN Std. Dev.

FAST Range

FAST Std. Dev.

21 m/s /

10.5 m

30.5 m/s /

10.5 m