JensenFactor: For a given distance 'x', computes the penalty factor for a...

In wflo: Data Set and Helper Functions for Wind Farm Layout Optimization Problems

For a given distance x, computes the penalty factor for a turbine's wake.

Description

In Jensen's wake model, a wake cone is generated by a turbine based on the turbine's hub height z, its rotor radius r_0, the terrain's roughness length z_0 and the distance x between the turbine under investigation and a certain second point. z, r_0 and z_0 are taken from the FarmVars settings object, while x is to be provided.

Usage

JensenFactor(x)

Arguments

x	must be a single value. Provide distance in meters.

Details

If a second turbine (B) is in a first turbine (A)'s wake, turbine B's power output must be penalized due to turbulence. This function computes the penalty factor for that wake.

Value

JensenFactor returns the a single number between 0 and 1, which can immediately be used a a penalty factor.

Note

Note that for Jensen's multiple wake model, wake penalties from several potentially influencing upwind turbines must be computed. As the factors are between 0 and 1, they can conveniently multiplied by each other afterward. If there are four turbines (A, B, C, D) inside a wind farm, you are investigating turbine D and it turns out that D is in the wake of B and C, but not A, then compute penalty for B (assume 0.7) and C (assume 0.8). Now, the penalty factors for A, B and C are 1, 0.7 and 0.8, so 1 * 0.7 * 0.8 = 0.56 is the penalty for turbine D.

Author(s)

Carsten Croonenbroeck

References

Jensen, N. O. (1983). A note on wind generator interaction. Roskilde: Risø National Laboratory. Risø-M, No. 2411

See Also

Use JensenAngle to compute the wake cone and with it, use JensenTrapezoid to see if another turbine B is in turbine A's wake. Apply JensenFactor only if this is the case.

Examples

JensenFactor(500)
## Provided that turbine B is in turbine A's wake and that the two turbines are 500 meters apart,
## turbine B must be penalized by a factor of 0.7952.

wflo documentation built on Jan. 15, 2023, 5:10 p.m.