OC3-Hywind RAOs

I am planning to compute RAOs for OC3-Hywind by coupling Sesam and FAST following the same method introduced in the paper “Investigation of Response Amplitude Operators for Floating Offshore Wind Turbines” by Ramachandran and Jonkman.

I used Sesam to build a freely floating panel model to compute the hydrodynamic quantities(added mass,damping and wave excitation forces) and hydrostatic restoring forces by assuming the center of gravity position is at the intersection of the still water level and the centerline of the platform which is also the reference point. Moreover, I compared the hydrodynamic quantities from Sesam with that from the paper “Definition of the Floating System for Phase IV of OC3” and agreed very well.

I then added some additional matrices according to the paper “Definition of the Floating System for Phase IV of OC3”,including the additional linear damping matrix for surge and sway, heave and yaw motions, the mooring stiffness matrix, the additional yaw stiffness matrix.

Mass matrix is the last I need, and I used FAST linearization to get it,the followings are my steps:
(1)Download the FAST OC3-Hywind model from “Index of /public/jjonkman/NRELOffshrBsline5MW/NRELOffshrBsline5MW_OC3Hywind.zip”
(2)Redefine the added mass and damping as zero in the file named “spar.1”
(3)Disable all DOFs except the six platform DOFs
(4)Set WaveMod,CurrMod and PtfmCD and all the initial platform displacement to zero in the platform file
(5)Set a wind file with zero wind speed and activate the feature flag-CompAero
(6)Set CalcStdy to false in the linearization file
(7)Shut all controllers down and set all the initial conditions(including Azimuth and RotSpeed) to zero, and set AnalMode to 2
(8)linearize it and got the mass matrix

I got my RAOs for surge,heave and pitch(rigid wind turbine with no wind) :

And they differed in some way from that RAOs in the paper by Ramachandran and Jonkman under the same condition(rigid wind turbine with no wind):My RAOs are less in amplitude but have similar shape.
Why they are different?I would really appreciate it if anyone could offer me some suggestions!

Dear Minxi,

For some reason I am not able to see your images, but from your message your process sounds correct. You can double-check the mass matrix by comparing the mass, CG, and inertias with those report for the OC3-Hywind system in my Nov 16, 2012 post in the following forum topic: http://forums.nrel.gov/t/inertial-moments-of-oc3-hywind-components/610/1.

Best regards,

Dear Jason
Thank you for your immediate reply. The mass and inertia quantities are what I exactly need.

I used the mass and inertia quantities from that forum topic to compute RAOs once again, but doesn’t work. The RAOs remain still,which may suggest my initial guess of the mass matrix has a good accuracy.

I also updated the pictures, they should be available now.

Best regards.

Dear Minxi,

I can now see your images; like you said, it looks like the overall form of your ROA is similar to ours, including the frequencies where there are peaks, but the amplitudes of your peaks are not always the same as ours. It is difficult for me to guess the exact cause, but my guess is the differences are related to damping.

Best regards,

Dear Jason

Thank you again for your reply,I will keep working on it.

I would post the cause in the forum if find the key in case it might be helpful to anyone who are interested.


Hi guys,
I am also trying to reproduce the results in the ISOPE paper: Investigation of Response Amplitude Operators for Floating Offshore Wind Turbines. But I encountered a problem with the FAST running. Could anyone help me out?
I am using the OC3-Hywind model coming with the FAST V8. I added the extra damping and stiffness as suggested in the OC3 definition pdf file. Since my OS is win7 64 bit, I released the 64bit OC3 controller .dll file using Visual Studio.

The error message is :

Message from MAP_Init:
MSQS_Init not available using dummy MAP dll.

MSQS_End not available using dummy MAP dll.
FAST encountered an error at initialization.

Does anyone know what may cause this?

Thanks in advance!


Dear Jinsong,

The extra damping and stiffness in the OC3-Hywind model are included in the HydroDyn input file in the model provided in the FAST v8 archive – see NRELOffshrBsline5MW_OC3Hywind_HydroDyn.dat.

At this time, MAP cannot only be run in 32 bits. The provided 64-bit FAST executable can run all cases except those that call MAP. The 64-bit version of MAP provided in the FAST archive is nothing but a dummy version that enables the rest of the 64-bit FAST executable to run. We provided a 64-bit version of the standard DISCON.dll for the NREL 5-MW turbine; we didn’t provide 64-bit versions of the DLL for the floating versions of the NREL 5-MW turbine, because these models require MAP, which doesn’t yet work in 64 bits anyway. See the ReadMe file provided in the FAST v8 archive for more information.

We are working on a new version of MAP that will be able to compile in 64 bits, but this has not yet been released.

Best regards,

Dear Jingson,

I’m interested to know that you are also reproducing the results in the ISOPE paper mentioned.

Mat I ask if you are planning to reproduced the RAOs by FAST or linear frequency domain simulation?

Dear all,
I am also trying to reproduce RAOs for OC3 Hywind by using commercial software ANSYS – AQWA as a first step for future analysis in frequency and time domains.
I am making reference to the papers: “Definition of the floating system for phase IV of OC3” (Jonkman, 2010) and the already mentioned in the previous posts “Investigation of Response Amplitude Operators for Floating Offshore Wind Turbines” (Ramachandran, Robertson, Jonkman, and Masciola, 2013).

Since my RAOs were different from those of the second paper in all the degrees of freedom, I compared added mass, radiation damping and hydrodynamic forces with those of the first paper. While doing that I noticed significant differences in pitch/roll DOFs, while the same quantities in translational DOFs are almost identical. I think that this difference is due to a different reference system. Can you tell me:

• what axis are used to rotate the body when solving the radiation potential?
• which integration point has been used to integrate the hydrodynamic and hydrostatic force?
• if it has been used the drag linearization when solving the first order motion?

At last, Hydrostatic restoring in pitch and roll in the first paper is about - 5.0 E9 Nm/rad and I assume that this negative value takes into account only the position of center of buoyancy while the position of center of gravity is taken into account elsewhere. Am I right?

Thank you in advance for your kind answers.
Best regards,

Dear Carlo,

The reference point for the rotations and integration of the hydrodynamic moments in those papers is the intersection of the undisplaced spar centerline and the still water level (SWL).

Viscous drag on the spar was neglected in the paper by Ramachandran et al, but the ROAs presented do include the so-called “additional linear damping” in surge, sway, heave, and yaw mentioned in the first paragraph of the “CASE STUDY” section on page 3.

Yes, the "-5.E9 Nm/rad only includes the effects of the hydrostatic pressure; the restoring effect from the center of gravity is taken into account elsewhere.

Best regards,

Dear Jason,

thank you very much for your reply.

I will keep working on it.

Best regards,

Dear all,

I have built my model in AQWA, using data found in the papers mentioned above. All the hydrodynamic quantities (added mass, damping and wave excitation forces) agree very well.

Similarly to Minxi, I added linear additional matrices and I got my RAOs but these were different from those in the paper of Ramachandran and Jonkman (rigid wind turbine with no wind).

Here are my RAOs (including linearized mooring line effect) in surge, heave and pitch (reference system centered in s.w.l.). As it can be seen, heave RAO is OK both in frequency and amplitude, while pitch RAO is completely wrong and affects also surge RAO in the second peak frequency.

I tried also to run analysis in AQWA’s reference system (centered in C.o.G.) where pitch is different in definition. I obtained a very similar (correct) RAO in heave, while RAO in pitch was equal to the one of the paper in peak frequency (about 0.034 Hz) but showed again very large amplitude. In surge I had correct frequencies too but wrong amplitude of the surge peak (I expected this RAO to be equal to the one of the first analysis but it was not so).

Can anyone help me in understanding why such differences (between my two models and the one of the paper mentioned) arise?
I have also a couple of specific questions that may be very useful for me:

• Is there any procedure to compare directly RAOs from different reference systems?
• Can I find in literature RAOs without mooring line effect, i.e. for the free floating body? (before using mooring linearization pitch amplitude seems to be good)

I would really appreciate it if anyone could help me!
Thank you in advance for your kind answers,

Dear Carlo,

I don’t recall seeing a publication where the OC3-Hywind spar ROAs are reported without moorings present.

Changing the origin of the platform will change the interpretation of the translational DOFs (not the rotational DOFs) and change the magnitude of the moments. For example, consider the linear system:

(M_swl + A_swl)qdd_swl + B_swlqd_swl + C_swl*q_swl = F_swl

where q_swl = [ surge, sway, heave, roll, pitch, yaw ]^T are the platform displacements, and F_swl are the platform loads, relative to the platform centerline at still water level (SWL) (0,0,0). The same equations can be written in terms of displacements and loads about the center of gravity located at (x_cg, y_cg, z_cg) using the following transformation:

q_cg = TransMatq_swl
F_cg = TransMat^T

TransMat =
[ [ 1 0 0 0 -z_cg y_cg ];
[ 0 1 0 z_cg 0 -x_cg ];
[ 0 0 1 -y_cg x_cg 0 ];
[ 0 0 0 1 0 0 ];
[ 0 0 0 0 1 0 ];
[ 0 0 0 0 0 1 ] ]

TransMat^T =
[ [ 1 0 0 0 0 0 ];
[ 0 1 0 0 0 0 ];
[ 0 0 1 0 0 0 ];
[ 0 z_cg -y_cg 1 0 0 ];
[ -z_cg 0 x_cg 0 1 0 ];
[ y_cg -x_cg 0 0 0 0 1 ] ]

Thus, the transformed system is:

(M_cg + A_cg)qdd_cg + B_cgqd_cg + C_cg*q_cg = F_cg

M_cg = TransMat^TM_swlTransMat
A_cg = TransMat^TA_swlTransMat
B_cg = TransMat^TB_swlTransMat
C_cg = TransMat^TC_swlTransMat

Are these the transformations you’ve applied between the two systems?

Best regards,

Dear Jason,

I am very grateful for your immediate reply.

If I understand correctly, the mass matrix I should use in my reference system is:

M_cg [kg; kg*m2] =
[ [8066048, 0, 0, 0, 629151756 , 0];
[0, 8066048, 0, -629151756, 0, 0];
[0, 0, 8066048, 0, 0, 0];
[0, -629151756, 0, 117099814443, 9913521, -8687816];
[629151756, 0, 0, 9913521, 117096372256, 6965877];
[0, 0, 0, -8687816, 6965877, 191573001] ]

Similarly, I transform Additional Linear Damping, while Additional Stiffness remains the same. Before your reply I missed transformational of Additional Damping Matrix.

Then, once I obtain RAOs in my reference system, if I understand correctly, I should have:

SurgeRAO_swl = SurgeRAO_cg + zG * RollRAO_cg - yG * YawRAO_cg

At last I can compare my transformed RAOs with those of the paper.

Am I right?

Best regards,
Carlo Ruzzo

Dear Carlo,

I don’t believe your M_cg is correct. The mass matrix about the cg should be basically a diagonal matrix (with maybe some small nonzero off-diagonal terms in the lower-right inertia quadrant). The mass matrix of the OC3-Hywind spar system about the SWL is given in my Nov 16, 2012 post in the following forum topic: http://forums.nrel.gov/t/inertial-moments-of-oc3-hywind-components/610/1.

I’m not sure what you mean when you say the “additional stiffness remains the same”, but as my prior post explains, the mass (M), added mass (A), damping (B), stiffness (C), force (F), and displacement (q) all get transformed between SWL and CG.

To convert RAOs from the CG to the SWL, you could write:

q_swl = TransMat^-1*q_cg

TransMat^-1 =
[ [ 1 0 0 0 z_cg -y_cg ];
[ 0 1 0 -z_cg 0 x_cg ];
[ 0 0 1 y_cg -x_cg 0 ];
[ 0 0 0 1 0 0 ];
[ 0 0 0 0 1 0 ];
[ 0 0 0 0 0 1 ] ]

Your equation is almost correct, except that “roll” should be changed to “pitch”.

Best regards,

Dear Jason,

thank you for your reply. I’ve spent some time working on it and I concluded that the best thing to do for me, in order to reproduce your results, is to work in your reference system.

Indeed, if I transform the mass matrix given in the link you suggested me (it was the one I was already using, thank you for sharing with us), I don’t achieve a diagonal matrix, neither using your transformation [M_cg = TransMat^T * M_swl * TransMat], nor using mine [M_cg = TransMat^T * M_swl * TransMat^-1].
Taking into account also that additional damping and stiffness have been evaluated empirically, I think it is formally better to work in the original reference system instead of using transformations.

I will keep working on it and I will let you know as soon as I have some interesting result to share.
Thank you very much,

Dear all,

I hope that it’s not a problem that I post in this old topic, but since I have a similar problem, and most of the relevant information is within this topic I took the liberty of posting here.

I’m also trying to recreate the OC3-Hywind within (Ansys) AQWA. I found the information about the mass/inertia of the total system in this old forum post: http://forums.nrel.gov/t/inertial-moments-of-oc3-hywind-components/610/1

I’m also trying to transform the mass matrix and I’m also fail to achieve a diagonal matrix. But maybe I’m doing something wrong?

If I do the transformation as mentioned in the topic (M_cg = TransMat^TM_swlTransMat) I get the following mass matrix:

1.0e+10 *

0.000806604815450 0 0 0 0.062916225372230 0.000008979927815
0 0.000806604815450 0 -0.062916225372230 0 0.000011226426962
0 0 0.000806604815450 -0.000008979927815 -0.000011226426962 0
0 -0.062916225372230 -0.000008979927815 5.587772915049737 0.000991477122271 -0.001744457491839
0.062916225372230 0 -0.000011226426962 0.000991477122271 5.587772971327059 0.001397033728988
0.000008979927815 0.000011226426962 0 -0.001744457491839 0.001397033728988 0.019157556316314

My second question is a question regarding the provided moments of inertia. I found a paper called ‘Wave- and Wind-Induced Dynamic Response of a Spar-Type Offshore Wind Turbine’ by Madjid Karimirad and Torgeir Moan in which they used the NREL 5mw wind turbine mounted on a spar platform, similar to the hywind platform. Although their platform looks similar, for some reason it is slightly heavier. These are the properties they described in their paper:

Total draft 120 m
Diameter above taper 6.5 m
Diameter below taper 9.4 m
Spar mass including ballast 7,593,000 kg
Total mass 8,329,230 kg
Center of gravity -78.61 m
Pitch inertia about the center of gravity 2:20E + 10 kg·m2
Yaw inertia about the centerline 1:68E + 08 kg·m2
Rating 5 MW
Rotor configuration 3 blades
Rotor and hub diameter 126 and 3 m
Hub height 90 m
Cut-in, rated, and cut-out wind speed 3, 11.4, and 25 m/s
Rotor mass 110,000 kg
Nacelle mass 240,000 kg
Tower mass 347,460 kg

The first thing I noticed is their Pitch inertia about the CM, which is way lower than yours? When I transform the values you provided I have a pitch about the cm of 5.58E + 10 , but if I just make a quick hand calculation where I take the moment of inertia of the floater about the cm and see the tower and nacelle+ rotor as 2 point masses and add them times the length between the cm and the points squared . I 'm also in the region of 2.0E + 10. As you may understand I’m somewhat confused and I hope that someone may have an answer.

With regards,

Dear Joeri,

Your 6x6 mass matrix, M_cg, includes large off-diagonal terms. Using values from your matrix, I see that your matrix is not about the cg, but includes a large 78-m offset in the z-direction i.e.

z_cg = 0.062916225372230/0.000806604815450 = 78

This will of course also impact the inertia quadrant of the matrix. Are you sure you’ve applied the transformation correctly?

I agree that a full-system pitch inertia about the full-system cg for the OC3-Hywind floating wind system should be closer to 2E10 kgm^2.

Best regards,

Dear Jason,

Thank you for answering to my post, no I don’t think transformation is correct, but for some reason it is not working. I’ll try the find a solution.

Best regards,

Dear Jason,
Using the transformations you indicated in this topic I tried to obtain the mass matrix in the center of mass (Figure 1). To obtain this matrix, I started from the SWL mass matrix you suggested in the topic Inertial Moments of OC3-Hywind Components, applying the necessary transformations.
Does it seem right to you? Above all, I am uncertain about the inertia.
Best regards,