weibull {bReeze}R Documentation

Calculation of Weibull parameters

Description

Calculates the shape parameters (k) and scale parameters (A) of the Weibull distribution per direction sector.

Usage

weibull(mast, v.set, dir.set, num.sectors=12, 
  subset, digits=3, print=TRUE)
wb(mast, v.set, dir.set, num.sectors=12, 
  subset, digits=3, print=TRUE)

## S3 method for class 'weibull'
plot(x, type=c("hist", "dir"), show.ak=FALSE, ...)

Arguments

mast

Met mast object created by mast.

v.set

Set used for wind speed, specified as set number or set name (optional, if dir.set is given).

dir.set

Set used for wind direction, specified as set number or set name (optional, if v.set is given).

num.sectors

Number of wind direction sectors as integer value greater 1. Default is 12.

subset

Optional start and end time stamp for a data subset, as string vector c(start, end). The time stamps format shall follow the rules of ISO 8601 international standard, e.g. "2012-08-08 22:55:00".

digits

Number of decimal places to be used for results as numeric value. Default is 3.

print

If TRUE, results are printed directly.

x

Weibull object, created by weibull.

type

Plot type - one of "hist" (histogram plot) or "dir" (directional plot).

show.ak

If TRUE (the default), the Weibull parameters A and k are added to the legend.

...

Arguments to be passed to methods. For optional graphical parameters see below.

Details

To evaluate the potential energy production of a site the observed data of a particular measurement period must be generalized to a wind speed distribution. This is commonly done by fitting the Weibull function to the data. The two-parametered Weibull distribution is expressed mathematically as:

f(v) = \frac{k}{A} \left({\frac{v}{A}} \right)^{k-1} e^{-\left({\frac{v}{A}} \right)^k}

where f(v) is the frequency of occurence of wind speed v, A is the scale parameter (measure for the wind speed) and k is the shape parameter (description of the shape of the distribution).

The resulting Weibull distribution characterizes the wind regime on the site and can directly be used for the calculation of the potential energy production of a wind turbine (see aep).

Value

Returns a data frame containing:

k

Shape parameter of the Weibull distribution for each direction sector.

A

scale parameter of the Weibull distribution for each direction sector.

wind.speed

Mean wind speed of the Weibull distribution for each direction sector.

frequency

Frequency of the Weibull distribution for each direction sector.

Optional graphical parameters

Graphical parameters to customize the histogram plot:

Graphical parameters to customize the directional plot:

Author(s)

Christian Graul

References

Brower, M., Marcus, M., Taylor, M., Bernadett, D., Filippelli, M., Beaucage, P., Hale, E., Elsholz, K., Doane, J., Eberhard, M., Tensen, J., Ryan, D. (2010) Wind Resource Assessment Handbook. http://www.renewablenrgsystems.com/TechSupport/~/media/Files/PDFs/wind_resource_handbook.ashx

Langreder, W. (2010) Wind Resource and Site Assessment. In: Wei Tong (Ed.), Wind Power Generation and Wind Turbine Design, Chapter 2, p. 49–87, Southampton: WIT Press

Weibull, W. (1951) A Statistical Distribution Function of Wide Applicability. Journal of Applied Mechanics – Trans. ASME 18(3), 293–297

See Also

mast

Examples

## Not run: 
## load and prepare data
data("winddata", package="bReeze")
set40 <- set(height=40, v.avg=winddata[,2], dir.avg=winddata[,14])
set30 <- set(height=30, v.avg=winddata[,6], dir.avg=winddata[,16])
set20 <- set(height=20, v.avg=winddata[,10])
ts <- timestamp(timestamp=winddata[,1])
neubuerg <- mast(timestamp=ts, set40, set30, set20)
neubuerg <- clean(mast=neubuerg)


## calculate Weibull parameters
weibull(mast=neubuerg, v.set=1)  # default

# if only one of v.set and dir.set is given, 
# the dataset is assigned to both
weibull(mast=neubuerg, v.set=1)
weibull(mast=neubuerg, dir.set=1)
weibull(mast=neubuerg, dir.set="set1")

# change number of direction sectors
weibull(mast=neubuerg, v.set=1, num.sectors=16)

# data subsets
weibull(mast=neubuerg, v.set=1, 
  subset=c("2009-12-01 00:00:00", "2009-12-31 23:50:00"))
weibull(mast=neubuerg, v.set=1, 
  subset=c("2010-01-01 00:00:00", NA)) # just 'start' time stamp
weibull(mast=neubuerg, v.set=1, 
  subset=c(NA, "2009-12-31 23:50:00")) # just 'end' time stamp

# change number of digits and hide results
neubuerg.wb <- weibull(mast=neubuerg, v.set=1, digits=2, print=FALSE)


## plot weibull objects - histogram plot
plot(neubuerg.wb)  # default
plot(neubuerg.wb, type="dir")  # same as above
plot(neubuerg.wb, show.ak=TRUE)  # show parameters in legend

# customize plot
plot(neubuerg.wb, bty="l", bty.leg="l", cex.axis=1.2, cex.lab=1.4, cex.leg=0.9, 
  col.axis="darkgray", col.box="darkgray", col.lab="darkgray", col.leg="darkgray", 
  col.ticks="darkgray", las=0, leg.text=c("measured", "calculated"), 
  mar=c(3,3,0.5,0.5), mgp=c(1.8,0.5,0), pos.leg="right", xlab="velocity [m/s]", 
  ylab="frequency [%]", xlim=c(0,20), ylim=c(0,15), x.intersp=1, y.intersp=1)

# customize bars
plot(neubuerg.wb, border="darkgray", breaks=seq(0,21,0.5), 
  col="lightgray")

# customize line
plot(neubuerg.wb, line="black", lty="dotdash", lwd=2)


## plot weibull objects - directional plot
plot(neubuerg.wb, type="dir")

# show parameters in legend
plot(neubuerg.wb, type="dir", show.ak=TRUE)

# customize plot
plot(neubuerg.wb, type="dir", bty="l", bty.leg="o", cex.axis=0.8, cex.lab=0.9, 
  cex.leg=0.7, col=c(rainbow(12), gray(0.4)), col.axis=gray(0.2), col.box=gray(0.4), 
  col.lab=gray(0.2), col.leg=gray(0.2), col.ticks=gray(0.2), las=0, 
  lty=c(rep(3, 12), 1), lwd=c(rep(1, 12), 2), mar=c(3,3,0.5,0.5), mgp=c(1.5,0.5,0), 
  pos.leg="right", xlab="velocity [m/s]", ylab="frequency [m/s]", xlim=c(0,15), 
  ylim=c(0,25), x.intersp=1, y.intersp=1)

## End(Not run)
[Package bReeze version 0.4-4 Index]