Question about calculating power deficit

[labbatessa]

How does FLORIS calculate power deficit (e.g. theta)? To provide some context, there have been papers in the literature that have calculated reference power as: Reference Power = Pₘₑₐₛᵤᵣₑ / cos²(θ), and I'm curious how FLORIS calculates θ. Thank you!

[misi9170]

Hi @labbatessa ,

Yes, this "cosine loss" is the standard loss model in FLORIS when there is a yaw misalignment (when the turbine is not directly aligned with the flow). Here is the FLORIS documentation that describes that. Note that $p_P$ is the cosine exponent, which is 2 in your question, but there is some debate in the literature about what the appropriate value for this should be, and FLORIS defaults to $p_P = 1.88$. However, you can change this by modifying the cosine_loss_exponent_yaw key on your turbine model (here is the line to change on the NREL 5MW model).

For a brief discussion on why $p_P$ defaults to 1.88 in FLORIS, you could look at Section 2.3 of Annoni et al. (2018).

In all of these contexts, $\gamma$ (which is the same as your $\theta$) is the "error" between the turbine's absolute yaw position ($\text{AYP}$) and the wind direction ($\text{WD}$). That is, $\gamma = \theta = \text{AYP} - \text{WD}$. Note that the sign of $\gamma$ is not important for calculating the effect on turbine power due to the symmetry of the cosine about zero (however, it will affect the direction a wake deflects). In FLORIS, $\gamma$ ($\theta$) is set using the yaw_angles keyword argument to fmodel.set(). Here, you should think of yaw_angles as being the relative yaw angle (so that 0 represents the turbine pointing directly into the wind, whatever the wind direction may be).

You can also see the effects of yawing in examples/examples_control_types as well as examples/examples_turbine/001_check_turbine.py.

Cheers,
Misha

[labbatessa]

Thank you @misi9170!