energy: Calculation of total wind energy content

Description

Calculates the total wind energy content per direction sector from Weibull data.

Usage

energy(wb, rho=1.225, bins=c(5, 10, 15, 20), 
  digits=0, print=TRUE)
en(wb, rho=1.225, bins=c(5, 10, 15, 20), 
  digits=0, print=TRUE)
# S3 method for energy
plot(x, show.total=TRUE, ...)

Value

Returns a data frame containing:

total: Total wind energy content per direction sector.
...: Wind energy content per direction sector for each given wind speed bin.

Arguments

wb: Weibull object created by weibull.
rho: Air density as numeric value. Default is 1.225 kg/m3 according to the International Standard Atmosphere (ISA) at sea level and 15°C.
bins: Wind speed bins as numeric vector or NULL if no classification is desired. Default is c(5, 10, 15, 20).
digits: Number of decimal places to be used for results as numeric value. Default is 0.
print: If TRUE (the default), results are printed directly.
x: Energy object created by energy.
show.total: If TRUE (the default), the total amount of wind energy per square meter is shown.
...: Arguments to be passed to methods. For optional graphical parameters see below.

Optional graphical parameters

The following graphical parameters can optionally be added to customize the plot:

border.leg: Border colour(s) for the legend. One colour for each wind speed bin or a single colour -- default is same as col.
bty.leg: Type of box to be drawn around the legend. Allowed values are "n" (no box, the default) and "o".
cex: Amount by which text on the plot should be scaled relative to the default (which is 1), as numeric. To be used for scaling of all texts at once.
cex.axis: Amount by which axis annotations should be scaled, as numeric value.
cex.lab: Amount by which axis labels should be scaled, as numeric value.
cex.leg: Amount by which legend text should be scaled, as numeric value.
circles: Manual definition of circles to be drawn, as numeric vector of the form c(inner circle, outer circle, interval between the circles).
col: Vector of colours -- one colour for each wind speed bin or a single colour if energy only contains the total energy per direction sector.
col.axis: Colour to be used for axis annotations -- default is "gray45".
col.border: Colour to be used for sector borders -- default is NULL (no border is drawn).
col.circle: Colour to be used for circles -- default is "gray45".
col.cross: Colour to be used for axis lines -- default is "gray45".
col.lab: Colour to be used for axis labels -- default is "black".
col.leg: Colour to be used for legend text -- default is "black".
fg: If TRUE, sectors are plotted in foreground (on top of axis lines and circles) -- default is FALSE.
lty.circle: Line type of circles -- default is "dashed". See par for available line types.
lty.cross: Line type of axis lines -- default is "solid". See par for available line types.
lwd.border: Line width of the sector borders -- default is 0.5. Only used if col.border is set.
lwd.circle: Line width of circles, as numeric value -- default is 0.7.
lwd.cross: Line width of axis lines, as numeric value -- default is 0.7.
pos.axis: Position of axis labels in degree, as numeric value -- default is 60.
sec.space: Space between plotted sectors, as numeric value between 0 and 1 -- default is 0.2.
title.leg: Alternative legend title, as string.
width.leg: Widths of legend space relative to plot space, as numeric value between 0 and 1. If 0, the legend is omitted, default value is 0.2.
x.intersp: Horizontal interspacing factor for legend text, as numeric -- default is 0.4.
y.intersp: Vertical line distance for legend text, as numeric -- default is 0.4.

Author

Christian Graul

Details

The total wind energy content can be perceived as the theoretic energy potential of a particular site. Therefore it is usefull for a resource assessment, independent of the wind turbine.

The power density function $$E(v) = \frac{1}{2} \, \rho \, v^3 \, f(v)$$ where $\rho$ is the air density, $v$ is the wind speed and $f(v)$ is its probability density function, leads to an analytical solution using wind speed bins as: $$E(v) = \frac{1}{2} \, \rho \, H \, \sum_{b=1}^{n} \! v_b^3 \, W(v_b)$$ where $H$ is the number of hours of the desired period, $v_b$ is the wind speed bin and $W(v_b)$ is the probability of that bin estimated by the Weibull distribution. The result for $H=8760$ is the available wind energy per square meter and year.

References

Fördergesellschaft Windenergie e.V. (2007) Technical Guidelines for Wind Turbines, Part 6: Determination of Wind Potential and Energy Yields, Revision 7

International Organisation for Standardization (1975) ISO 2533:1975 Standard Atmosphere. ISO Standard

Troen, I., Petersen, E.L. (1989) European Wind Atlas. Tønder: Laursen

Examples

Run this code

if (FALSE) {
## load and prepare data
data("winddata", package="bReeze")
set1 <- set(height=40, v.avg=winddata[,2], v.std=winddata[,5],
  dir.avg=winddata[,14])
set2 <- set(height=30, v.avg=winddata[,6], v.std=winddata[,9],
  dir.avg=winddata[,16])
set3 <- set(height=20, v.avg=winddata[,10], v.std=winddata[,13])
ts <- timestamp(timestamp=winddata[,1])
neubuerg <- mast(timestamp=ts, set1, set2, set3)
neubuerg <- clean(mast=neubuerg)


## calculate Energy object
# calculate Weibull object
neubuerg.wb <- weibull(mast=neubuerg, v.set=1, print=FALSE)

# calculate energy
neubuerg.e <- energy(wb=neubuerg.wb)

# calculate energy for 1 m/s speed bins and without binning
energy(wb=neubuerg.wb, bins=0:25)
energy(wb=neubuerg.wb, bins=NULL)

# calculate energy with site specific air density
energy(wb=neubuerg.wb, rho=1.115, bins=NULL)

# change number of digits and hide results
energy(wb=neubuerg.wb, digits=2)
energy(wb=neubuerg.wb, print=FALSE)


## plot energy objects
plot(neubuerg.e)  # default
plot(neubuerg.e, show.total=FALSE)  # omit total amount
plot(neubuerg.e, col=gray(5:0/5.5), cex=0.8)  # change colours/text sizes
plot(neubuerg.e, circles=c(100, 500, 100))  # manual definition of circles
plot(neubuerg.e, fg=TRUE)  # plot sectors in foreground
plot(neubuerg.e, pos.axis=135)  # change axis label position
plot(neubuerg.e, width.leg=0)  # no legend

# freaky
plot(neubuerg.e, border.leg=heat.colors(5), bty.leg="o", 
  cex.axis=0.5, cex.lab=2, cex.leg=0.5, circles=c(80, 800, 80), 
  col=rainbow(5), col.axis="green", col.border="orange", 
  col.circle="purple", col.cross="yellow", col.lab="pink", 
  col.leg="lightblue", fg=TRUE, lwd.border=2, lwd.circle=3, lwd.cross=4, 
  lty.circle="52168319", lty.cross="12223242", sec.space=0.6, 
  title.leg="* WiNd SpEeD *", x.intersp=2, y.intersp=5)
}

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