Power loss with yaw misalignment

Dear community,

I have a doubt that I would like to share with you.

I am trying to perform some simulations using FAST.Farm that include yaw misalignment.

I have read from literature that the power loss introduced by misaligning the rotor relatively to the inflow with an angle gamma follows the following relation
The values of the exponent Pp that I found in literature always lie between 1.8 and 3 (for instance, in the default FLORIS .json input file for the NREL 5MW this value is 1.88).

When trying to estimate this coefficient using FAST.Farm, I always obtain the value 3 (with steady inflow conditions and the Pitt/Peters skewed inflow model). As I understood, this is the value to be expected from a standard BEM code.

The relatively high value for the exponent Pp is giving me a hard time to apply wake steering for power maximization in FAST.Farm, since the power losses introduced by yawing a turbine are quite high.

I am not sure whether the value of Pp=3 is realistic. Could maybe things be improved by tuning the input files, such as Aerodyn?

Thanks for the attention.

Kind regards,
Simone Tamaro

Dear Simone,

Good question. We’ve been looking into this topic recently as well. The blade-element/momentum (BEM) solution of OpenFAST will use an exponent of Pp = 3 because it uses the flow normal to the disk and neglects the flow tangent to the disk in its aerodynamic calculations. With the velocity cubed in the equation for power, this results in COS(yaw)^3. We’ve recently heard about the lower exponent in FLORIS, which presumably was calibrated against HFM simulations. We are currently studying which is more correct and will propose a change based on that. The way to address this would be a source code change, not an input file change.

Do you have specific literature that you feel provide a good physical understanding of this issue? If so, can you share?

Best regards,

Dear Dr. Jonkman,

Thank you for the interesting reply. I have a list of references that could be a good starting point.

  • Helge Madsen, Niels N. Sørensen and Scott Schreck. “Yaw Aerodynamics Analyzed with Three Codes in Comparison with Experiment,” AIAA 2003-519. 41st Aerospace Sciences Meeting and Exhibit. January 2003.

  • J.G. Schepers, S. Schreck, “The importance of aerodynamics and the role of aerodynamic measurements”, Torque 2012, 9-11 October 2012, Oldenburg, Germany

  • Micallef, Daniel and Tonio Sant. “A Review of Wind Turbine Yaw Aerodynamics.” (2016).

Kind regards,
Simone Tamaro

Hi Simone and Jason,

Just to jump in with some additional data points. Identifying these exponents in SOWFA for different turbines we’ve found best fit values ranging from 1.4 up to 2.2 or so. We also have made a few attempts at fitting the exponent to field data. In this paper:

Fleming, Paul, et al. “Full-scale field test of wake steering.” Journal of Physics: Conference Series. Vol. 854. No. 1. IOP Publishing, 2017.

Trying to read these in the field is tough because it can be tricky both to measure the yaw offset (the vane isn’t typically very good at it) and also because knowing what the power would’ve been when aligned isn’t always obvious. Then there’s just a ton of noise and lots of things “fit”. We took a shot though in the first attached paper and found 1.8 was reasonably for the GE at the wind site.

More recently though is Eric’s paper:


where he digs a bit deeper and finds that this fit exponent also shows a dependence on wind speed (second attachment, Fig 16) you’ll see the best fit exponent start at 2.22 at low wind speeds and drop from there.

Mike Howland considered the exponent also in this paper:

Michael F. Howland, Carlos Moral González, Juan José Pena Martínez, Jesús Bas Quesada, Felipe Palou Larrañaga, Neeraj K. Yadav, Jasvipul S. Chawla, and John O. Dabiri , “Influence of atmospheric conditions on the power production of utility-scale wind turbines in yaw misalignment”, Journal of Renewable and Sustainable Energy 12, 063307

Then there is also this paper:

Pedersen, Troels Friis. “On wind turbine power performance measurements at inclined airflow.” Wind Energy: An International Journal for Progress and Applications in Wind Power Conversion Technology 7.3 (2004): 163-176. which includes a figure (Fig 1) showing a good fit of experimental data to cos^2 and add an explanatory paragraph:

The cos2 relationship might be explained by the fact that not only the projected swept area is reduced with the cosine, but also the flow component perpendicular to the rotor.

Hope this is helpful!


Hi all,

Thank you for the useful references and interesting discussion.

As a check, we have used SOWFA to simulate the same turbine model for which I had obtained a coefficient 3 with OpenFAST. From a preliminary look at the results, I can confirm that - with uniform inflow, a wind speed just below rated, and in absence of tower/nacelle - SOWFA predicts a coefficient that is close to 1.8 .

Kind regards,
Simone Tamaro

Dear Paul,

Recently, I have been studying the yaw offset for power and load, and I have studied your paper"Simulation comparison of wake mitigation control strategies for a two-turbine case". I would like to repeat your simulation with Openfast. I wonder these simulation parameters: a) turbulence density? b) the wind shear ? c) Is there a tilt during yaw, and if so, what is the value of the tilt Angle.

Thank you very much!
Best regards,
Liye Zhao