energy {bReeze}

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 class 'energy'
plot(x, show.total=TRUE, ...)

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.

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.

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.

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(s)

Christian Graul

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

See Also

weibull

Examples

## Not run: 
## 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)

## End(Not run)