Type: Package
Title: Functions for Wind Resource Assessment
Version: 0.4-4
Date: 2024-02-05
Author: Christian Graul and Carsten Poppinga
Maintainer: Christian Graul <christian.graul@gmail.com>
Description: A collection of functions to analyse, visualize and interpret wind data and to calculate the potential energy production of wind turbines.
License: MIT + file LICENSE
URL: https://github.com/chgrl/bReeze
Depends: R (≥ 2.14.2)
Imports: graphics, grDevices, lubridate, stats, utils
Suggests: RColorBrewer, RgoogleMaps, XML
NeedsCompilation: no
Packaged: 2024-02-05 20:04:50 UTC; SauerGraul
Repository: CRAN
Date/Publication: 2024-02-05 20:40:09 UTC

Functions for Wind Resource Assessment

Description

A collection of functions to analyse, visualize and interpret wind data and to calculate the potential energy production of wind turbines.

Details

Wind power is a global source of energy which attracts a large share of investments in renewables. Project sites with high wind potential do not only minimise the financial risk but increase the efficiency in carbon footprint reduction. Hence a thorough productivity analysis of a wind project is essential, regarding both economic and environmental aspects. The evaluation of the potential of a site requires a wind resource assessment, which is best based on data gained by a local measurement campaign. A methodology of processing the measured data has been established, resulting in a better understanding of the wind conditions of a site and therefore a more reliable estimation of energy production.

bReeze is a collection of widely used methods to analyse, visualise and interpret wind data. Wind resource analyses can subsequently be combined with characteristics of wind turbines to estimate the potential energy production on the investigated site.

Usually the data to be analysed are collected by meteorological masts (met masts) and averaged over ten minutes, but other time intervals are also processable.

bReeze suggests three packages, written by other developers: RColorBrewer (by Erich Neuwirth) provides nice colours for the graphics, XML (by Duncan Temple Lang) provides xml parsing for power curve import and RgoogleMaps (by Markus Loecher) provides simple site maps.

Try the examples below to check if bReeze has been correctly installed. Any question and feedback is welcome via email to <christian.graul@gmail.com> or on GitHub.

Author(s)

Christian Graul and Carsten Poppinga

Maintainer: Christian Graul <christian.graul@gmail.com>

References

The following handbook gives a detailed thematic overview and is available online:

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

Further references are given under the specific functions of the package.

Examples

## Not run: 
# load example data
data("winddata", package="bReeze")

# create two datasets
set40 <- set(height=40, v.avg=winddata[,2], v.std=winddata[,5],
  dir.avg=winddata[,14])
set30 <- set(height=30, v.avg=winddata[,6], v.std=winddata[,9],
  dir.avg=winddata[,16])

# format time stamp
ts <- timestamp(timestamp=winddata[,1])

# create met mast object
metmast <- mast(timestamp=ts, set40=set40, set30=set30)

# plot time series of met mast signals
plot(metmast)

# calculate frequency and mean wind speed per wind direction sector
freq <- frequency(mast=metmast, v.set=1)

# plot frequency
plot(freq)

# calculate availability of pairs of wind speed and direction
availability(mast=metmast)

# calculate monthly means of wind speed
month.stats(mast=metmast)

# calculate turbulence intensity
turbulence(mast=metmast, turb.set=1)

# calculate weibull parameters
wb <- weibull(mast=metmast, v.set=1)

# calculate total wind energy content
energy(wb=wb)

# calculate wind profile
pf <- windprofile(mast=metmast, v.set=c(1,2), dir.set=1)

# import power curve
pc <- pc("Enercon_E126_7.5MW.pow")

# calculate annual energy production
aep <- aep(profile=pf, pc=pc, hub.h=135)

# plot AEP
plot(aep)

## End(Not run)

Calculation of annual energy production

Description

Calculates annual energy production (AEP) from a site's wind profile and wind turbine characteristics.

Usage

aep(profile, pc, hub.h, rho=1.225, avail=1, bins=c(5,10,15,20), 
  sectoral=FALSE, digits=c(3,0,0,3), print=TRUE)

## S3 method for class 'aep'
plot(x, show.total=TRUE, ...)

Arguments

profile

Wind profile object created by profile.

pc

Power curve object created by pc.

hub.h

Hub heigth of wind turbine as numeric value.

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.

avail

Availability of turbine as numeric value between 0 (not available at all) and 1 (100% available).

bins

Edges of wind speed bins as numeric vector or NULL if only total AEP is desired. Default values are c(5, 10, 15, 20).

sectoral

If TRUE, wind speeds are extrapolated to hub height using the wind profiles of each direction sector. Otherwise the general profile ("all") is used for extrapolation (default).

digits

Number of decimal places to be used for results as numeric vector. The first value is used for wind.speed, the second for operation, the third for aep and the fourth for capacity results. Default is c(3,0,0,3).

print

If TRUE, results are printed directly.

x

AEP object, created by aep.

show.total

If TRUE (the default) the total AEP is added to the plot.

...

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

Details

For a wind turbine the mean energy production can be expressed by

E = T \, \int_{v_{in}}^{v_{out}} \! f(v) \, p(v)

where f(v) is the probability density function of the wind speed v, p(v) is the power curve of the turbine and T is the production time period. Energy production starts at the turbine's cut-in wind speed v_{in} and stops at cut-out wind speed v_{out}.

Based on this fundamental expression, aep calculates the annual energy production as follows:

AEP = A_{turb} \, \frac{\rho}{\rho_{pc}} \, H \, \sum_{b=1}^{n} \! W(v_b) \, P(v_b)

where A_{turb} is the average availability of the turbine, \rho is the air density of the site and \rho_{pc} is the air density, the power curve is defined for. W(v_b) is the probability of the wind speed bin v_b, estimated by the Weibull distribution and P(v_b) is the power output for that wind speed bin. H is the number of operational hours – the production time period of the AEP is per definition 8760 hours.

The wind speed v_h at hub height h of the turbine is extrapolated from the measured wind speed v_{ref} at reference height h_{ref} using the Hellman exponential law (see profile):

v_h = v_{ref} \, \left(\frac{h}{h_{ref}} \right)^\alpha

The productive suitability of a wind turbine for a site can be evaluated by the capacity factor CF. This factor is defined as the ratio of average power output of a turbine to the theoretical maximum power output. Using the AEP as the average power output, the rated power P_{rated} of a turbine and the maximum operational hours of a year we get:

CF = \frac{AEP}{P_{rated} \, 8760}

Value

Returns a list containing:

wind.speed

Mean wind speed for each direction sector.

operation

Operational hours per year for each direction sector.

total

Total annual energy production for each direction sector.

...

Annual energy production per wind speed bin for each direction sector.

capacity

Capacity factor of the wind turbine.

Optional graphical parameters

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

Note

Sectoral extrapolation should be used carefully. Some sector's profile might be abnormal – particularly in case of short measurement periods (<= one year) and/or few samples per sector – causing biased results. Always check the profiles and set sectoral to FALSE to get more robust results.

Author(s)

Christian Graul

References

Burton, T., Sharpe, D., Jenkins, N., Bossanyi, E. (2001) Wind Energy Handbook. New York: Wiley

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

Jangamshetti, S.H., Rau, V.G. (1999) Site Matching of Wind Turbine Generators: A Case Study. IEEE Transaction on Energy Conversion 14(4), 1537–1543

See Also

windprofile

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])
ts <- timestamp(timestamp=winddata[,1])
neubuerg <- mast(timestamp=ts, set1, set2)
neubuerg <- clean(mast=neubuerg)


## calculate AEP
# calculate wind profile
neubuerg.wp <- profile(mast=neubuerg, v.set=c(1,2), dir.set=1, 
  print=FALSE)

# load power curve
pw.56 <- pc("PowerWind_56_900kW.wtg")

# calculate AEP
aep(profile=neubuerg.wp, pc=pw.56, hub.h=71)

# calculate AEP with site specific air density and availability of 97
aep(profile=neubuerg.wp, pc=pw.56, hub.h=71, rho=1.195, avail=0.97)

# calculate total AEP using sectoral profiles
aep(profile=neubuerg.wp, pc=pw.56, hub.h=71, sectoral=TRUE)

# calculate AEP for 1 m/s speed bins and without binning
aep(profile=neubuerg.wp, pc=pw.56, hub.h=71, bins=seq(0,25))
aep(profile=neubuerg.wp, pc=pw.56, hub.h=71, bins=NULL)

# change number of digits and hide results
aep(profile=neubuerg.wp, pc=pw.56, hub.h=71, digits=c(1,1,1,1))
neubuerg.aep <- aep(profile=neubuerg.wp, pc=pw.56, hub.h=71, print=FALSE)
neubuerg.aep


## plot AEP objects
# default
plot(neubuerg.aep)

# omit total AEP
plot(neubuerg.aep, show.total=FALSE)

# change colours and text sizes
plot(neubuerg.aep, col=gray(5:0 / 5), cex=0.8)

# manual definition of circles
plot(neubuerg.aep, circles=c(250, 750, 250))

# plot sectors in foreground
plot(neubuerg.aep, fg=TRUE)

# change position of axis labels
plot(neubuerg.aep, pos.axis=135)

# no legend
plot(neubuerg.aep, width.leg=0)

# freaky
plot(neubuerg.aep, 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="12345678", lty.cross="87654321", 
  sec.space=0.6, title.leg="* WiNd SpEeD *", x.intersp=2, y.intersp=5)

## End(Not run)

Internal function for aep

Description

Internal function for aep

Arguments

wb.par

Weibull parameters A and k.

lim

Lower and upper calculation limit (wind speed) as numeric vector.

pc

Power curve object

rho.pc

Air desity the power curve is defined for.

op

Operational hours

rho

Air density

avail

Availability of turbine

Value

Returns annual energy production as numeric value.

Author(s)

Christian Graul

See Also

aep

Calculate availability for pairs of wind speed and direction

Description

Calculates the availability for pairs of wind speed and wind direction of a met mast.

Usage

availability(mast, v.set, dir.set, subset, digits=1, print=TRUE)
avail(mast, v.set, dir.set, subset, digits=1, print=TRUE)

## S3 method for class 'availability'
plot(x, set, ...)

Arguments

mast

Met mast object created by mast.

v.set

Set(s) to be used for wind speed, specified as set number(s) or set name(s). Argument is optional – if missing, all sets containing wind speed and wind direction data are used.

dir.set

Set(s) to be used for wind direction, specified as set number(s) or set name(s). Argument is optional – if missing, the set(s) used for wind speed data will also be used for wind direction.

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 1.

print

If TRUE (the default), results are printed directly.

x

Availability object created by availability.

set

Number of dataset to be plotted, specified as set number or set name (optional).

...

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

Details

The availability is the number of pairs of valid wind speed and valid wind direction data samples as a percentage of the total possible for the measurement period, i.e.:

Availability = \frac{N(v_{valid} \wedge dir_{valid})}{N}

where N is the total possible number of samples and v_{valid} \wedge dir_{valid} is a pair of valid wind speed and direction data.

Causes of invalid or missing data are manifold. Typical causes are icing and defects of sensors or other measurement equipment.

Value

Returns a list of sub lists for each pair of v.set/dir.set containing:

total

Total availability (%), effective period (days) and total period (days) of a set/pair of wind speed and direction.

daily

Availability per day, i.e. number of samples per day.

Optional graphical parameters

The following graphical parameters can optionally be added to customize the 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

See Also

mast, clean

Examples

## Not run: 
## load and prepare data
data("winddata", package="bReeze")
set40 <- set(height=40, v.avg=winddata[,2], v.std=winddata[,5],
  dir.avg=winddata[,14])
set30 <- set(height=30, v.avg=winddata[,6], v.std=winddata[,9],
  dir.avg=winddata[,16])
set20 <- set(height=20, v.avg=winddata[,10], v.std=winddata[,13])
ts <- timestamp(timestamp=winddata[,1])
neubuerg <- mast(timestamp=ts, set40=set40, set30=set30, 
  set20=set20)
neubuerg <- clean(mast=neubuerg)


## calculate availability
neubuerg.avail <- availability(mast=neubuerg)

# compare the total availability of 'set40' and 'set30'
neubuerg.avail$set40$total
neubuerg.avail$set30$total

# check the daily availability of 'set40'
neubuerg.avail$set40$daily

# note: availability for 'set20' is missing - its availability is NULL,
# since it does not contain wind direction data

# calculate availability for 'set20' using wind direction data from 'set40'
set20.avail <- availability(mast=neubuerg, v.set=3, dir.set=1)
# same as above
set20.avail <- availability(mast=neubuerg, v.set="set20", dir.set="set40")

# calculate availability for all sets using wind direction data from 'set40'
neubuerg.avail <- availability(mast=neubuerg, v.set=c(1,2,3), dir.set=1)

# data subsets
availability(mast=neubuerg, v.set=1, 
  subset=c("2009-12-01 00:10:00", "2009-12-31 23:50:00"))
availability(mast=neubuerg, v.set=1, 
  subset=c("2010-01-01 00:10:00", NA)) # just 'start' time stamp
availability(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.avail <- availability(mast=neubuerg, digits=0)
neubuerg.avail <- availability(mast=neubuerg, print=FALSE)
neubuerg.avail


## plot availability objects
plot(neubuerg.avail)  # default
plot(neubuerg.avail, set=2)	 # one dataset
plot(neubuerg.avail, set="set30")  # same as above
plot(neubuerg.avail, set=c(1,2))  # several datasets

# customize plot
plot(neubuerg.avail, border="darkgray", cex.axis=0.7, 
  cex.lab=0.9, col=c("darkgreen", "orange", "red4"), col.axis="blue", 
  col.lab="blue", fill=c("lightgreen", "yellow", "red"), lwd=0.5, 
  mar=c(1,1,1,1), plot.names=FALSE, xlab="jour", ylab="mois")

## End(Not run)

Internal function for availability

Description

Internal function for availability

Arguments

v.avg

Average wind speed.

dir.avg

Average wind direction.

ts

Time stamp

start.year

First year of measurement period.

start.month

First month of measurement period.

num.months

Number of months.

period.days

Days of measurement period.

digits

Number of digits.

Value

Returns a list of:

total

Total availability

daily

Daily availability

Author(s)

Christian Graul

See Also

availability

Show the NEWS file

Description

Show the NEWS file of the bReeze package.

Usage

changes(pkg="bReeze")

Arguments

pkg

"bReeze"

Value

NULL

Clean faulty values

Description

Cleans faulty values of a met mast object, set or specified set of a met mast. Faulty values are replaced by NA.

Usage

clean(mast, set, v.avg.min=0.4, v.avg.max=50, dir.clean=TRUE, 
	turb.clean=4, icing=FALSE, rep=NULL, n.rep=5, ts=FALSE)
cln(mast, set, v.avg.min=0.4, v.avg.max=50, dir.clean=TRUE, 
	turb.clean=4, icing=FALSE, rep=NULL, n.rep=5, ts=FALSE)

Arguments

mast

Met mast object created by mast. To be ignored, if a single dataset shall be cleaned.

set

Set object created by set (if no mast is given) or set of met mast specified as set number or set name. To be ignored, if all datasets of mast shall be cleaned.

v.avg.min

Lower limit for wind speeds as numeric value. Default is 0.4 m/s. Set to NULL to omit minimum wind speed.

v.avg.max

Upper limit for wind speeds as numeric value. Default is 50 m/s. Set to NULL to omit maximum wind speed.

dir.clean

If TRUE (default), faulty wind direction values are excluded. Faulty values are dir.avg<0, dir.avg>360 and dir.avg, where the wind speed is lower than the v.avg.min specified.

turb.clean

Wind speed limit for turbulence intensity as numeric value. Turbulence intesity values are excluded for wind speeds lower then this limit. Default is 4 m/s.

icing

If TRUE, wind direction values are excluded, where standard deviation of wind direction is 0, assuming icing. Default is FALSE.

rep

Signal (or a vector of signals), for which repetitions shall be cleaned – default is NULL.

n.rep

Minimum number of repetitions that shall be cleaned, as integer value – default is 5. Only used if rep is not NULL.

ts

If TRUE, uneven time intervals are corrected. Can only be used with mast objects. Default is FALSE.

Details

Turbulence can be ignored for low wind speeds. Use turb.clean to clean the respective turbulence intensity values. See turbulence for more details.

If icing is detected using icing, the time stamp should be checked to exclude implausible assumptions, e.g. in summer.

Repetitions are often generated by a corrupted data stream between sensor and data logger. Some sensors also repeat their last captured value during calm conditions. Although they are unlikely for averaged time intervals, repetitions are no faulty values by default. Do only clean repetitions if you know your data. Note: the number of repetitions n.rep means n.rep+1 consecutive values in a dataset are identical. The default of 5 repetitions corresponds to one hour in case of a ten minutes interval.

Uneven time intervals might come up due to rounding errors. ts corrects them to the median time interval.

Value

Returns the input met mast or dataset object with cleaned data.

Author(s)

Christian Graul

See Also

mast, set

Examples

## Not run: 
# load and prepare data
data("winddata", package="bReeze")
set40 <- set(height=40, v.avg=winddata[,2], v.std=winddata[,5],
  dir.avg=winddata[,14])
set30 <- set(height=30, v.avg=winddata[,6], v.std=winddata[,9],
  dir.avg=winddata[,16])
set20 <- set(height=20, v.avg=winddata[,10], v.std=winddata[,13])
ts <- timestamp(timestamp=winddata[,1])
neubuerg <- mast(timestamp=ts, set40=set40, set30=set30, 
  set20=set20)

# clean faulty values of a met mast
neubuerg.clean <- clean(mast=neubuerg)

# compare a subset of the original and cleaned data
neubuerg$sets$set40$data$v.avg[660:670]
neubuerg.clean$sets$set40$data$v.avg[660:670]


# clean faulty values of a dataset
set40.clean <- clean(set=set40)
  
# clean just one dataset of a met mast
neubuerg.clean.2 <- clean(mast=neubuerg, set=1)
neubuerg.clean.2 <- clean(mast=neubuerg, set="set40")	# same as above

# change lower wind speed limit 
neubuerg.clean.3 <- clean(mast=neubuerg, v.avg.min=0.3)

# compare number of samples set to 'NA', due to lowered limit
length(which(is.na(neubuerg.clean$sets$set40$data$v.avg)==TRUE))
length(which(is.na(neubuerg.clean.3$sets$set40$data$v.avg)==TRUE))


# change wind speed limit for cleaning of turbulence intensity
neubuerg.clean.4 <- clean(mast=neubuerg, turb.clean=3)

# compare number of samples set to 'NA', due to turb.clean
neubuerg.clean$sets$set40$data$turb.int[75:100]
neubuerg.clean.4$sets$set40$data$turb.int[75:100]


# check whether icing is assumed for any samples
neubuerg.clean.5 <- clean(mast=neubuerg, set=1, v.avg.min=0, 
  v.avg.max=100, dir.clean=FALSE, turb.clean=0, icing=TRUE)
not.cleaned <- which(is.na(neubuerg$sets$set40$data$dir.avg)==TRUE)
cleaned <- which(is.na(neubuerg.clean.5$sets$set40$data$dir.avg)==TRUE)
length(cleaned)-length(cleaned)	# no icing here

# checked time stamp to exclude implausible icing assumptions (e.g. in summer)
# (which makes no sense here, since cleaned is empty)
neubuerg.clean.5$timestamp[cleaned]


# clean repetitions
neubuerg.clean.6 <- clean(mast=neubuerg, rep=c("v.avg", "dir.avg"))
neubuerg.clean.7 <- clean(mast=neubuerg, rep="v.avg", n.rep=3)

## End(Not run)

Internal function for clean

Description

Internal function for clean

Arguments

dat

Dataset to be cleaned.

v.avg.min

Lower limit for wind speeds as numeric value. Default is 0.4 m/s.

v.avg.max

Upper limit for wind speeds as numeric value. Default is 50 m/s.

dir.clean

If TRUE, faulty wind direction values are excluded. Faulty values are dir.avg<0, dir.avg>360 and dir.avg, where the wind speed is lower than the v.avg.min specified. Default is TRUE.

turb.clean

Wind speed limit for turbulence intensity. Turbulence intesity values are excluded for wind speeds lower then this limit. Default is 4 m/s.

icing

If TRUE, wind direction values are excluded, where standard deviation of wind direction is 0, assuming icing. Default is FALSE.

rep

Signal (or a vector of signals), for which repetitions shall be cleaned.

n.rep

Number of repetitions that shall be cleaned, as integer value – default is 5.

Value

Returns cleaned dataset.

Author(s)

Christian Graul

See Also

clean

Plot diurnal wind speed

Description

Plots the diurnal variation of wind speed or wind direction.

Usage

day.plot(mast, set, dir.set=set, signal, num.sectors=NULL, subset, ...)
day(mast, set, dir.set=set, signal, num.sectors=NULL, subset, ...)

Arguments

mast

Met mast object created by mast.

set

Set used for plotting, specified as set number or set name. Argument is optional – if missing, all sets containing the choosen signal are used.

dir.set

Direction set used for sectoral splitting of the data, specified as set number or set name. Argument is used for sectoral plotting only (see num.sectors).

signal

Signal to be plotted as string.

num.sectors

Number of wind direction sectors as integer value greater 1. Argument is optional – if not NULL, data is splitted into directional sectors for plotting. Sectoral plots are available only for single sets.

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".

...

Optional graphical parameters, see below for details.

Details

plotDay reveals diurnal variations of a signal. The plot may show outliers that indicate data inconsistancy.

Optional graphical parameters

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

Author(s)

Christian Graul

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)

# plot all datasets
day.plot(mast=neubuerg, signal="v.avg")
day.plot(mast=neubuerg, signal="dir.avg")

# plot one dataset
day.plot(mast=neubuerg, set=1, signal="v.avg")
day.plot(mast=neubuerg, set="set1", signal="v.avg")	# same as above
day.plot(mast=neubuerg, set=2, signal="dir.avg")

# sectoral plot
day.plot(mast=neubuerg, set=1, signal="v.avg", num.sectors=8)

# data subsets
day.plot(mast=neubuerg, signal="v.avg", 
  subset=c("2009-12-01 00:00:00", "2009-12-31 23:50:00"))
day.plot(mast=neubuerg, signal="v.avg",  
  subset=c("2010-01-01 00:00:00", NA)) # just 'start' time stamp
day.plot(mast=neubuerg, set=1, signal="v.avg", num.sectors=4, 
  subset=c(NA, "2009-12-31 23:50:00")) # just 'end' time stamp

# customize plot
day.plot(mast=neubuerg, signal="v.avg", 
  bty="l", cex.axis=0.8, cex.lab=0.9, cex.leg=0.7, 
  col=c("darkgreen", "royalblue", "purple"), col.axis="darkgray", 
  col.box="darkgray", col.lab="darkgray", col.leg="darkgray", 
  col.ticks="darkgray", las=2, lty=c(2,3,4), lwd=1.5, mar=c(3, 3, 0.5, 0.5), 
  mgp=c(1.5, 0.5, 0), pos.leg="topleft", xlab="hour", ylab="velocity", 
  ylim=c(3.5,6), x.intersp=1, y.intersp=1)

## End(Not run)

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:

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)

Internal function for energy

Description

Internal function for energy

Arguments

lim

Lower and upper calculation limit (wind speed) as numeric vector.

k

Shape parameter of the weibull distribution.

A

Scale parameter of the weibull distribution.

rho

Air density

Value

Returns energy as numeric value.

Author(s)

Christian Graul

See Also

energy

Calculation of frequency and mean wind speed

Description

Calculates the frequency of occurrence and mean wind speed per wind direction sector.

Usage

frequency(mast, v.set, dir.set, num.sectors=12, 
  bins=c(5, 10, 15, 20), subset, digits=3, print=TRUE)
freq(mast, v.set, dir.set, num.sectors=12, 
  bins=c(5, 10, 15, 20), subset, digits=3, print=TRUE)

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.

bins

Wind speed bins as numeric vector or NULL if no classification is desired. Default is c(5, 10, 15, 20).

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 (the default), results are printed directly.

Details

The directional frequency of occurrence is an important factor for the design of a wind project. The influence is clear for the arrangement of turbines in a wind farm, that should be perpendicular to the most frequent wind direction. But also single turbines are affected, e.g. by fatigue tower loads in most frequent directions or in directions with highest wind speeds.

Value

Returns a data frame containing:

wind.speed

Mean wind speed per direction sector.

total

Frequency per direction sector.

...

Frequencies per direction sector, for each given wind speed bin.

Optional graphical parameters for plotting

The following graphical parameters can optionally be added to customize the 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

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 frequency
frequency(mast=neubuerg, v.set=1)

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

# use different datasets for wind speed and direction
frequency(mast=neubuerg, v.set=3)	# no direction in dataset
frequency(mast=neubuerg, v.set=3, dir.set=2)
frequency(mast=neubuerg, v.set="set3", dir.set="set2")	# same as above

# change number of direction sectors 
frequency(mast=neubuerg, v.set=1, num.sectors=4)
frequency(mast=neubuerg, v.set=1, num.sectors=16)

# calculate frequency for 1 m/s speed bins and without binning
frequency(mast=neubuerg, v.set=1, bins=1:25)
frequency(mast=neubuerg, v.set=1, bins=0:25)	# same as above
frequency(mast=neubuerg, v.set=1, bins=NULL)

# data subsets
frequency(mast=neubuerg, v.set=1, 
  subset=c("2009-12-01 00:00:00", "2009-12-31 23:50:00"))
frequency(mast=neubuerg, v.set=1, 
  subset=c("2010-01-01 00:00:00", NA)) # just 'start' time stamp
frequency(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
frequency(mast=neubuerg, v.set=1, digits=2)
neubuerg.freq <- frequency(mast=neubuerg, v.set=1, print=FALSE)
neubuerg.freq

## plot frequency objects
plot(neubuerg.freq)  # default
plot(neubuerg.freq, col=gray(5:0 / 5.5), cex=0.8)  # change colours/text sizes
plot(neubuerg.freq, circles=c(10, 30, 10))  # manual definition of circles
plot(neubuerg.freq, fg=TRUE)  # plot sectors in foreground
plot(neubuerg.freq, pos.axis=135) # change axis label position
plot(neubuerg.freq, width.leg=0)  # no legend

# freaky
plot(neubuerg.freq, border.leg=heat.colors(5), bty.leg="o", 
  cex.axis=0.5, cex.lab=2, cex.leg=0.5, circles=c(5, 30, 5), 
  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=3, 
  lty.circle="12345678", lty.cross="87654321", sec.space=0.6, 
  title.leg="* WiNd SpEeD *", x.intersp=2, y.intersp=5)

## End(Not run)

Plot map or satellite image

Description

Plots a map or satellite image of the met mast location.

Usage

map.plot(mast, type=c("satellite", "terrain", "hybrid", "roadmap"), 
  zoom, label, ...)
map(mast, type=c("satellite", "terrain", "hybrid", "roadmap"), 
  zoom, label, ...)

Arguments

mast

Met mast object created by mast.

type

Type of the map as string. One of "satellite" (satellite image), "terrain" (map with terrain information), "hybrid" (satellite image with map overlay) or "roadmap" (map).

zoom

Zoom level as integer from 1 (small scale) up to 18 (large scale) – default is 15.

label

Label to be placed next to the location symbol as string. Set to NA to leave the label blank. If ignored, the location coordinates are used as label default.

...

Optional graphical parameters, see below for details.

Details

This function is based on the RgoogleMaps package by Markus Loecher, which uses the Google Static Maps API.

Optional graphical parameters

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

Author(s)

Christian Graul

See Also

mast

Examples

## Not run: 
# load and prepare data
data("winddata", package="bReeze")
set1 <- set(height=40, v.avg=winddata[,2])
ts <- timestamp(winddata[,1])
neubuerg <- mast(timestamp=ts, set1, loc=c(49.8909,11.4017))

# plot satellite image
map.plot(neubuerg)

# plot terrain map
map.plot(neubuerg, type="terrain")

# change zoom level
map.plot(neubuerg, zoom=1)
map.plot(neubuerg, zoom=18)

# change symbol (and label) 
map.plot(neubuerg, col="white", pch="+", cex=2)

# change label
map.plot(neubuerg, col.lab=3, cex.lab=1.5)
map.plot(neubuerg, pos.lab=1)
map.plot(neubuerg, label="Site #247 - Neubuerg")  # custom label
map.plot(neubuerg, label=NA)  # no label

## End(Not run)

Creation of met mast objects

Description

Creates met mast objects from one or more datasets (measurement heights). All datasets are sorted by height in descending order.

Usage

mast(timestamp, ..., loc=NULL, desc=NULL)

## S3 method for class 'mast'
plot(x, set, signal=c("v.avg", "dir.avg", "turb.int"), subset, ...)

Arguments

timestamp

Time stamp as POSIXlt vector, e.g. created by timestamp.

...

At least one dataset created by set. For plotting function: optional graphical parameters (see below).

loc

Lat/lon coordinates of the site in decimal degrees as vector of two numeric values (optional).

desc

Plain text information about the site, measurement, met mast condition, etc. as string (optional).

x

Met mast object, created by mast.

set

Set used for plotting specified as set number or set name. Argument is optional – if missing, all sets containing the given signal(s) are used.

signal

Signal(s) to be plotted as vector of strings giving the signal names.

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".

Details

Valuable information about a met mast is usually provided by an installation protocol.

Measurements of wind speed in several heights is required for the computation of the site's wind profile. Met masts might have mounted more than one sensor of the same type at the same height. Thus, the data of a broken sensor can later be substituted by the 'backup-sensor'.

Value

Returns a met mast object, which is necessary for all data analyses. A met mast object is a list of:

timestamp

Time stamp of the observations.

location

Lat/lon coordinates of the site (optional).

description

Mast information (optional).

sets

List of one or more datasets (measurement heights) consisting of height information and the data.

Optional graphical parameters

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

Author(s)

Christian Graul

See Also

POSIXlt, set, timestamp

Examples

## Not run: 
## load data, prepare sets and time stamp
data("winddata", package="bReeze")
set40 <- set(height=40, v.avg=winddata[,2], v.std=winddata[,5],
  dir.avg=winddata[,14])
set30 <- set(height=30, v.avg=winddata[,6], v.std=winddata[,9],
  dir.avg=winddata[,16])
set20 <- set(height=20, v.avg=winddata[,10], v.std=winddata[,13])
ts <- timestamp(timestamp=winddata[,1])

## create met mast object
neubuerg <- mast(timestamp=ts, set40, set30, set20)  # default

# add location and description
neubuerg.2 <- mast(timestamp=ts, set40, set30, set20, 
  loc=c(49.8909,11.4017), desc="Site #247 - Neubuerg")

# name sets
neubuerg.3 <- mast(timestamp=ts, C1.A1=set40, C2.A2=set30, 
  C3=set20, loc=c(49.8909,11.4017), desc="Site #247 - Neubuerg")


## plot met mast (time series)
plot(neubuerg)  # default
plot(neubuerg, set=1, legend=FALSE)  # only one set
plot(neubuerg, set="set1", legend=FALSE)  # same as above 
plot(neubuerg, signal=c("v.avg", "dir.avg"))  # change signals

# change time scale
plot(neubuerg, subset=c("2010-01-01 00:10:00", NA))
plot(neubuerg, subset=c("2009-10-11 00:10:00", "2009-10-11 23:50:00"))
plot(neubuerg, set=1, signal="dir.avg", subset=c(NA, "2009-12-27 18:30:00"))

# customize plot
plot(neubuerg, bty="n", bty.leg="o", cex.axis=1.2, cex.lab=1.4, cex.leg=1.2, 
  col=c("darkblue", "red2", "darkgreen"), col.axis="darkgray", 
  col.lab="darkgray", col.leg="darkgray", col.ticks="darkgray", 
  las=0, lty=rep(1.5,3), mar=c(0.5,4,0,0.5), mgp=c(2,0.5,0), 
  ylab=c("v [m/s]","dir [deg]","ti [-]"), x.intersp=1)

## End(Not run)

Calculation of monthly statistics

Description

Calculates monthly statistics.

Usage

month.stats(mast, set, signal="v.avg", 
  fun=c("mean", "median", "min", "max", "sd"), subset, 
  digits=3, print=TRUE)
ms(mast, set, signal="v.avg", 
  fun=c("mean", "median", "min", "max", "sd"), subset, 
  digits=3, print=TRUE)

## S3 method for class 'month.stats'
plot(x, set, ...)

Arguments

mast

Met mast object created by mast.

set

Set used for calculation or plotting specified as set number or set name. If missing, the calculation or plotting is carried out for all datasets that contain the specified signal.

signal

The signal to be used, as string value. Default is "v.avg".

fun

Statistical function, as string value – one of "mean" (arithmetic mean), "median", "min" (minimum), "max" (maximum) or "sd" (standard deviation).

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 (the default), results are printed directly.

x

Monthly statistics object created by month.stats.

...

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

Details

month.stats calculates statistics of valid data for each month and year in the measurement period. Usually this function is used for the calculation of average wind speeds. Means strongly depend on the measurement period and the number of samples. One important requirement for a reliable wind assessment is a measurement period covering the full seasonal cycle of variations. A typical bias is a measurement limited to winter months, which usually results in overestimated wind speeds.

Value

Returns a list of data frames (one for each dataset) containing monthly, annual and total statistics of the specified signal.

Optional graphical parameters

The following graphical parameters can optionally be added to customize the 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

See Also

mast

Examples

## Not run: 
## load and prepare data
data("winddata", package="bReeze")
set40 <- set(height=40, v.avg=winddata[,2], v.max=winddata[,3])
set30 <- set(height=30, v.avg=winddata[,6], v.max=winddata[,7])
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 monthly means
neubuerg.stats <- month.stats(mast=neubuerg)  # default
month.stats(mast=neubuerg, set=1)  # one dataset
month.stats(mast=neubuerg, set="set1")  # same as above
month.stats(mast=neubuerg, signal="v.max")  # change signal

# calculate monthly median, min, max and standard deviation
month.stats(mast=neubuerg, fun="median")
month.stats(mast=neubuerg, fun="min")
month.stats(mast=neubuerg, fun="max")
month.stats(mast=neubuerg, fun="sd")

# data subsets
month.stats(mast=neubuerg, 
  subset=c("2009-12-01 00:10:00", "2009-12-31 23:50:00"))
month.stats(mast=neubuerg, 
  subset=c("2010-01-01 00:10:00", NA)) # just 'start' time stamp
month.stats(mast=neubuerg, 
  subset=c(NA, "2009-12-31 23:50:00")) # just 'end' time stamp

month.stats(mast=neubuerg, digits=2)  # change number of digits
neubuerg.ms <- month.stats(mast=neubuerg, print=FALSE)  # hide results
neubuerg.ms


## plot month stats object
plot(neubuerg.ms)  # default
plot(neubuerg.ms, set=1)  # one dataset
plot(neubuerg.ms, set="set1")  # same as above

# customize plot
plot(neubuerg.ms, border="darkgray", bty="l", cex.axis=0.7, 
  cex.lab=0.9, col=c(gray(0.3), gray(0.7)), col.axis="darkgray", 
  col.box="darkgray", col.lab="darkgray", col.ticks="darkgray", las=0, 
  legend=FALSE, mgp=c(2, 0.7, 0), plot.names=FALSE, ylim=c(0,7), 
  ylab="Wind speed [m/s]")

## End(Not run)

Internal function for month.stats

Description

Internal function for month.stats

Arguments

data

Data vector

fun

Function

ts

Time stamp

years

Vector of measurement period

digits

Number of decimal places.

Value

Returns data frame with monthly statistics.

Author(s)

Christian Graul

See Also

month.stats

Import power curve from file

Description

Imports a power curve from a WAsP 'wgt' file or a WindPower program 'pow' file.

Usage

pc(pc, ...)

## Default S3 method:
pc(pc, rho=1.225, rated.p, desc, ...)
## S3 method for class 'read'
pc(pc, ...)
## S3 method for class 'pc'
plot(x, cp=TRUE, ct=TRUE, ...)

Arguments

pc

list or data.frame of power curve variables – v (wind speed in m/s), p (corresponding power output in kW), cp (power coefficient, optional), ct (thrust coefficient, optional), all as numeric vectors of same length. Or the name of, or the path to a 'wgt' or 'pow' file containing power curve data.

rho

Air density as numeric value. Default is 1.225 kg/m3 according to the International Standard Atmosphere (ISA) at sea level and 15 degrees Celsius.

rated.p

Rated power of wind turbine in kW as numeric value. If not given, the rated power is set to the maximum value of p.

desc

Plain text information about the wind turbine as string (optional).

x

Power curve object created by pc.

cp

If TRUE (the default), the power coefficient (cp) is added to the plot (if available).

ct

If TRUE (the default), the thrust coefficient (ct) is added to the plot (if available).

...

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

Details

Power curve

A power curve characterizes the power production of a wind turbine and gives the amount of generated electrical power output as a function of wind speed. The theoretical power curve of a turbine is defined as:

P \propto v^3 \mbox{for} \ v<v_{rated}
P = P_{rated} \mbox{for} \ v>v_{rated}

Hence the generated power is proportional to the wind speed cubed, for wind speeds lower than rated wind speed. For higher wind speeds the generated power is equal to the rated power of the turbine.

Conventionally a power curve consists of pairs of wind speed and power in 0.5 or 1 m/s wind speed bins, starting at 0 m/s or the cut-in wind speed of the turbine and ending with the cut-out wind speed, e.g. at about 25 m/s.

Coefficients

The power coefficient c_p is defined as:

c_p = \frac{P_t}{P}

where P_t is the ratio of the electrical power extracted by the wind turbine and P is the energy available in the wind stream. According to Betz's law, the theoretically achievable power coefficient is approximately 0.59. However, no wind turbine will obtain this value, due to inefficiencies and various losses of the machine.

The thrust coefficient is a turbine specific characteristic and used for the modelling of wake effects. Therefore it is an important parameter for wind farm configuration.

bReeze provides several power curves of common manufacturers, that can be read from the package directory. See examples for usage.

Available 'wtg' files

Nordex_N80_2.5MW Nordex_N90_2.5MW_HS Nordex_N90_2.5MW_LS
Nordex_N100_2.5MW PowerWind_56_900kW PowerWind_90_2.5MW
Vestas_V52_850kW Vestas_V60_850kW Vestas_V80_2.0MW_os
Vestas_V80_2.0MW Vestas_V82_1650kW Vestas_V90_1.8MW
Vestas_V90_2.0MW Vestas_V90_3.0MW Vestas_V100_1.8MW_50Hz
Vestas_V100_1.8MW_60Hz Vestas_V112_3.0MW

Available 'pow' files

Bonus_82.4m_2.3MW Bonus_MKIV_600kW Clipper_LibertyC89_2.5MW
Clipper_LibertyC93_2.5MW Clipper_LibertyC96_2.5MW Clipper_LibertyC100_2.5MW
Enercon_E33_330kW Enercon_E40_500kW Enercon_E44_900kW
Enercon_E48_800kW Enercon_E53_800kW Enercon_E66_1870kW
Enercon_E66_2000kW Enercon_E70_2.3MW Enercon_E82_2.0MW
Enercon_E82_2.3MW Enercon_E82_3.0MW Enercon_E101_3.0MW
Enercon_E126_7.5MW EWT_DW52_500kW EWT_DW54_500kW
EWT_DW90_2MW EWT_DW96_2MW Gamesa_G52_850kW
Gamesa_G58_850kW Gamesa_G80_2.0MW Gamesa_G83_2.0MW
Gamesa_G87_2.0MW Gamesa_G90_2.0MW GE_1.5sl_1.5MW
GE_1.5sle_1.5MW GE_1.5xle_1.5MW GE_1.6MW
GE_2.5xl_2.5MW GE_3.6sl_3.6MW Leitwind_LTW70_1.7MW
Leitwind_LTW70_2.0MW Leitwind_LTW77_1.5MW Leitwind_LTW80_1.5MW
Leitwind_LTW80_1.8MW Leitwind_LTW101_3.0MW Nordex_N60_1.3MW
Nordex_N70_1.5MW Nordex_N90_2.5MW Nordex_N100_2.5MW
Nordex_S70_1.5MW Nordex_S77_1.5MW Nordic_1000_1.0MW
PowerWind_56_500kW Repower_5M_5.0MW Repower_MM82_2.0MW
Repower_MM92_2.0MW Siemens_SWT-2.3MW-93m Siemens_SWT-2.3MW-101m
Siemens_SWT-3.6MW-107m Siemens_SWT-3.6MW-120m Suzlon_S64_1.25MW
Suzlon_S64_950kW Suzlon_S66_1.25MW Suzlon_S88_2.1MW
VensysEnergy_77_1.5MW Vensys_82_1.5MW Vensys_100_2.5MW
Vensys_109_2.5MW Vensys_112_2.5MW Vestas_V27_225kW
Vestas_V39_500kW Vestas_V52_850kW Vestas_V80_2.0MW_os
Vestas_V80_2.0MW Vestas_V82_1.65MW Vestas_V90_2.0MW
Vestas_V90_3.0MW Vestas_V112_3MW Vestas_V164_7.0MW_os

Value

Returns a data frame binding the given data

Optional graphical parameters

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

Note

All power curves are provided without any warranty of accuracy and timeliness. Reliable data can only be received from the respective manufacturer directly.

Author(s)

Christian Graul

Source

Wind turbine generator files (*.wtg) were collected from the WAsP website:

http://www.wasp.dk/Download/PowerCurves.aspx

Power curve files (*.pow) were collected from the WindPower Program website:

http://www.wind-power-program.com/download.htm

Both links are not active anymore and the turbine list is now a bit outdated.

References

Betz, A. (1966) Introduction to the Theory of Flow Machines. Oxford: Pergamon Press

Burton, T., Sharpe, D., Jenkins, N., Bossanyi, E. (2001) Wind Energy Handbook. New York: Wiley

International Electrotechnical Commission (2005) IEC 61400-12 Wind Turbines – Part 12-1: Power Performance Measurements of Electricity Producing Wind Turbines. IEC Standard

Milan, P., Wächter, M., Barth, S., Peinke, J. (2010) Power Curves for Wind Turbines. In: Wei Tong (Ed.), Wind Power Generation and Wind Turbine Design, Chapter 18, p. 595–612, Southampton: WIT Press

Ragheb, M., Ragheb, A.M. (2011) Wind Turbines Theory – The Betz Equation and Optimal Rotor Tip Speed Ratio. In: Rupp Carriveau (Ed.), Fundamental and Advanced Topics in Wind Power, Chapter 2, p. 19–38, InTech

Examples

## Not run: 
## create power curve
# minimal theoretic power curve
pc.1 <- pc(list(1:25, c(0, 0, seq(0,1000,length.out=8), rep(1000,15))))
pc.1
	
# detailed power curve
v <- seq(3, 25, 0.5)
p <- c(5, 15.5, 32, 52, 71, 98, 136, 182, 230, 285, 345, 419, 497, 594, 
  687, 760, 815, 860, 886, rep(900, 26))	
cp <- c(0.263, NA, 0.352, NA, 0.423, NA, 0.453, NA, 0.470, NA, 0.478, 
  NA, 0.480, NA, 0.483, NA, 0.470, NA, 0.429, NA, 0.381, NA, 0.329, 
  NA, 0.281, NA, 0.236, NA, 0.199, NA, 0.168, NA, 0.142, NA, 0.122, 
  NA, 0.105, NA, 0.092, NA, 0.080, NA, 0.071, NA, 0.063)
ct <- c(0.653, NA, 0.698, NA, 0.705, NA, 0.713, NA, 0.720, NA, 0.723, NA, 
  0.724, NA, 0.727, NA, 0.730, NA, 0.732, NA, 0.385, NA, 0.301, NA, 0.242, 
  NA, 0.199, NA, 0.168, NA, 0.146, NA, 0.128, NA, 0.115, NA, 0.103, NA, 
  0.094, NA, 0.086, NA, 0.079, NA, 0.073)	

# variables as list
pc.2 <- pc(list(v=v, p=p, cp=cp, ct=ct), 
  rho=1.195, rated.p=900, desc="PowerWind 56")
pc.2

# variables as data frame
pc.3 <- pc(data.frame(v=v, p=p, cp=cp, ct=ct), 
  rho=1.195, rated.p=900, desc="PowerWind 56")
pc.3

## import power curve
## note: XML package required for WAsP .wtg files
vestas.v90 <- pc("Vestas_V90_2.0MW.wtg")  # bReeze wtg file
repower.mm92 <- pc("Repower_MM92_2.0MW.pow")  # bReeze pow file
#my.pc <- pc("~/Projects/bReeze/Sandbox/myPC.wtg")  # user file


## plot power curve
plot(pc.2)  # default
plot(pc.2, cp=FALSE, ct=FALSE)  # drop coefficients

# customize plot
plot(pc.2, bty="u", bty.leg="o", cex.axis=0.8, cex.lab=0.9, 
  cex.leg=0.7, col=c("red", gray(0.4), gray(0.4)), col.axis=gray(0.2), 
  col.box=gray(0.5), col.lab=gray(0.2), col.leg=gray(0.2), 
  col.ticks=gray(0.5), las=2, leg.text=c("electric Power", 
  "power coefficient", "thrust coefficient"), lty=2:4, lwd=c(2,1,1), 
  mar=c(3.5,3.5,0.5,3.5), mgp=c(1.8,0.6,0), pos.leg="top", 
  xlab="velocity [m/s]", ylab=c("electric power", "coefficients"), 
  ylim=c(0,1100), x.intersp=1, y.intersp=1)

## End(Not run)

Plot wind speed vs. direction

Description

Plots wind speeds against directions in a polar plot.

Usage

polar.plot(mast, v.set=1, dir.set=1, subset, ...)
pol(mast, v.set=1, dir.set=1, subset, ...)

Arguments

mast

Met mast object created by mast.

v.set

Set used for wind speed values, specified as set number or set name.

dir.set

Set used for wind direction values, specified as set number or set name.

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".

...

Optional graphical parameters, see below for details.

Optional graphical parameters

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

Author(s)

Christian Graul

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)

# plot v vs. dir
polar.plot(mast=neubuerg)
polar.plot(mast=neubuerg, v.set=3, dir.set=2)
polar.plot(mast=neubuerg, v.set="set3", dir.set="set2")	# same as above

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

# customize plot
polar.plot(mast=neubuerg, cex.axis=1.2, cex.lab=1.5, cex.pts=0.8, 
  circles=c(10,20,5), col="red3", col.axis=gray(0.2), col.circle=gray(0.3), 
  col.cross=gray(0.3), col.lab=gray(0.2), fg=TRUE, lty.circle="dotted", 
  lty.cross="longdash", lwd.circle=1.2, lwd.cross=1.2, pch=1, pos.axis=135)

## End(Not run)

Creation of datasets

Description

Creates a dataset object, by combining all signals of one height of measurement.

Usage

set(height, desc, v.avg, v.max, v.min, v.std, 
  dir.avg, dir.std, tmp, ...)

Arguments

height

Height of measurement in m as numeric value.

desc

Plain text information about the set, signals, instruments, etc. as string (optional).

v.avg

Average of wind speed within interval in m/s as numeric vector (optional, if at least one other signal is given).

v.max

Maximum of wind speed within interval in m/s as numeric vector (optional, if at least one other signal is given).

v.min

Minimum of wind speed within interval in m/s as numeric vector (optional, if at least one other signal is given).

v.std

Standard deviation of wind speed within interval in m/s as numeric vector (optional, if at least one other signal is given).

dir.avg

Average of wind direction within interval in degrees from north as numeric vector (optional, if at least one other signal is given).

dir.std

Standard deviation of wind direction within interval in degrees from north as numeric vector (optional, if at least one other signal is given).

tmp

Temperature in °C as numeric vector (optional, if at least one other signal is given).

...

Further signals, e.g. air pressure, humidity, etc. as numeric vector (optional).

Details

Anemometer and wind vanes are usually mounted as pairs at same or similar heights of the met mast. Signals with marginal differences in height, about 1 or 2 m, may or may not be combined to one dataset. In case of a combination of two heights the height of the anemometer should be used for the whole dataset, as in subsequent analyses wind speed might be extrapolated to other heights. A dataset shall not contain data from more than one sensor of the same type, say data of two anemometers.

A typical interval of wind measurments is 10 minutes, but also other intervals are applicable.

For datasets containing mean wind speed v.avg and its standard deviation within the time interval v.std, the turbulence intensity is calculated and added to the data, named turb.int. See turbulence for more details about turbulence intensity.

Value

Returns a dataset object which is a list of:

height

Height of measurement.

data

Data of measured signals.

Author(s)

Christian Graul

See Also

mast

Examples

## Not run: 
# load data
data("winddata", package="bReeze")

# minimal dataset
s <- set(height=40, v.avg=winddata[,2])

# detailed dataset
s2 <- set(height=40, desc=
  "C1: cup anemometer (SN: 4.3250.128), A1: wind vane (SN: 4.2800.205)", 
  v.avg=winddata[,2], v.max=winddata[,3], v.min=winddata[,4], 
  v.std=winddata[,5], dir.avg=winddata[,14], dir.std=winddata[,15])

## End(Not run)

Internal function data subsets

Description

Internal function for data subsets

Arguments

timestamp

Time stamp

subset

Subset, containing start and end time stamp.

Value

Returns index of start and end time stamp.

Author(s)

Christian Graul

See Also

aep, availability, energy, frequency, month.stats, day.plot, polar.plot, turb.iec.plot, profile, turbulence, weibull

Format time stamps

Description

Converts time stamps from string to POSIXlt. The conversion specification (pattern) is looked up if not given as argument.

Usage

timestamp(timestamp, pattern, tz)
ts(timestamp, pattern, tz)

Arguments

timestamp

Time stamp as string vector.

pattern

Conversion specification of time stamp as string (optional). See Details for usage.

tz

Optional character string specifying the time zone to be used for the conversion. System-specific (see as.POSIXlt), but "" is the current time zone (used as default). Use "?" to check timestamp for time zone abbreviation.

Details

If the time stamp is already formatted as POSIXlt, the usage of timestamp is not necessary. strptime can also be used to create an applicable time stamp. Usage of timestamp is recommeded, since it checks the created time stamp, thus faulty time stamps are avoided.

Pattern

A conversion specification is introduced by "%", usually followed by a single letter. Any character in the format string not part of a conversion specification is interpreted literally. Widely implemented conversion specifications include:

For details see strptime.

Value

Returns a POSIXlt vector.

Author(s)

Christian Graul

See Also

POSIXlt, strptime, mast

Examples

## Not run: 
# load and prepare data
data("winddata", package="bReeze")

# format time stamp
timestamp <- timestamp(timestamp=winddata[,1])

# format time stamp with given pattern
timestamp.2 <- timestamp(timestamp=winddata[,1], "%d.%m.%Y %H:%M")

# wrong pattern (
timestamp.2 <- timestamp(timestamp=winddata[,1], "%d.%m.%y %H:%M")

# strange time stamp pattern
ts <- c("TS 08/2012-10 8h10m30s", "TS 08/2012-10 8h20m30s", 
  "TS 08/2012-10 8h30m30s")
timestamp.3 <- timestamp(timestamp=ts)	# pattern not found
timestamp.3 <- timestamp(timestamp=ts, "TS %m/%Y-%d %Hh%Mm%Ss")

# time zones
# manually define time zone
timestamp.4 <- timestamp(timestamp=winddata[,1], tz="CET")

# get time zone from timestamp
timestamp.5 <- timestamp(timestamp="2012-08-08 22:55 GMT", tz="?")

## End(Not run)

Plot turbulence intensity site classification

Description

Plots the turbulence intensity and site classification after IEC.

Usage

turb.iec.plot(mast, set, subset, ...)
iec(mast, set, subset, ...)

Arguments

mast

Met mast object created by mast.

set

Set used for plotting specified as set number or set name.

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".

...

Optional graphical parameters, see below for details.

Details

The IEC defines wind turbine classes by wind speed and turbulence characteristics. In terms of turbulence intensity three reference values (at 15 m/s) are defined:

Turbulence class Reference value
A 0.16
B 0.14
C 0.12

plotTurbIEC plots these IEC references together with the sites values to allow for a classification.

See turbulence for a definition of turbulence intensity.

Optional graphical parameters

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

Author(s)

Christian Graul

References

International Electrotechnical Commission (2005) IEC 61400-1 Wind Turbines – Part 1: Design Requirements. IEC Standard

See Also

mast

Examples

## Not run: 
# load and prepare data
data("winddata", package="bReeze")
set40 <- set(height=40, v.avg=winddata[,2], v.std=winddata[,5])
set30 <- set(height=30, v.avg=winddata[,6], v.std=winddata[,9])
set20 <- set(height=20, v.avg=winddata[,10], v.std=winddata[,13])
ts <- timestamp(timestamp=winddata[,1])
neubuerg <- mast(timestamp=ts, set40, set30, set20)
neubuerg <- clean(mast=neubuerg)

# plot
turb.iec.plot(mast=neubuerg, set=1)
turb.iec.plot(mast=neubuerg, set="set1")	# same as above

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

# customize plot
turb.iec.plot(mast=neubuerg, set=1, bty="l", cex.axis=0.8, cex.lab=0.9, 
  cex.leg=0.7, col.axis="darkblue", col.box="lightblue", col.lab=
  "darkblue", col.leg="darkblue", col.ticks="darkblue", las=0, 
  leg.text=c("IEC class A", "IEC class B", "IEC class C", "measured"), 
  mar=c(3,3,0.5,0.5), mgp=c(1.8,0.5,0), pos.leg="top", xlab="v [m/s]", 
  ylab="ti [-]", xlim=c(0,25), ylim=c(0,0.5), x.intersp=1, y.intersp=1)

# customize bars
turb.iec.plot(mast=neubuerg, set=1, col="gray", border="black", space=0.6)

# customize lines
turb.iec.plot(mast=neubuerg, set=1, line=gray(1:3 / 10), lty=2:4, 
  lwd=0.5:2.5)

## End(Not run)

Calculation of turbulence intensity

Description

Calculates turbulence intensity and mean wind speed for each given direction sector.

Usage

turbulence(mast, turb.set, dir.set, num.sectors=12, 
  bins=c(5, 10, 15, 20), subset, digits=3, print=TRUE)
turb(mast, turb.set, dir.set, num.sectors=12, 
  bins=c(5, 10, 15, 20), subset, digits=3, print=TRUE)

Arguments

mast

Met mast object created by mast.

turb.set

Set used for turbulence intensity, 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 turb.set is given).

num.sectors

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

bins

Wind speed bins as numeric vector or NULL if no classification is desired. Default is c(5, 10, 15, 20).

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 (the default), results are printed directly.

Details

Turbulence can be perceived as wind speed fluctuations on a relatively short time scale and it strongly depends on surface roughness, terrain features, as well as thermal effects. High turbulence should be avoided, since it is a main driver of fatigue loads and might decrease energy output. A measure of the overall level of turbulence, is the turbulence intensity I, which is defined as:

I = \frac{\sigma}{\bar v}

where \sigma is the standard deviation of wind speed – usually measured over a 10-minutes period – and \bar v is the mean wind speed over this period.

Value

Returns a data frame containing:

wind.speed

Mean wind speed for each direction sector.

total

Total turbulence intensity for each direction sector.

...

Turbulence intensities per direction sector for each given wind speed bin.

Optional graphical parameters for plotting

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

Author(s)

Christian Graul

References

Albers, A. (2010) Turbulence and Shear Normalisation of Wind Turbine Power Curve. Proceedings of the EWEC 2010, Warsaw, Poland

Burton, T., Sharpe, D., Jenkins, N., Bossanyi, E. (2001) Wind Energy Handbook. New York: Wiley

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

See Also

mast

Examples

## Not run: 
## load and prepare data
data("winddata", package="bReeze")
set40 <- set(height=40, v.avg=winddata[,2], v.std=winddata[,5],
  dir.avg=winddata[,14])
set30 <- set(height=30, v.avg=winddata[,6], v.std=winddata[,9],
  dir.avg=winddata[,16])
set20 <- set(height=20, v.avg=winddata[,10], v.std=winddata[,13])
ts <- timestamp(timestamp=winddata[,1])
neubuerg <- mast(timestamp=ts, set40, set30, set20)
neubuerg <- clean(mast=neubuerg)


## calculate turbulence intensity
turbulence(mast=neubuerg, turb.set=1)  # default
turbulence(mast=neubuerg, turb.set=1, dir.set=2)  # use different datasets
turbulence(mast=neubuerg, turb.set="set1", dir.set="set2")  # same as above
turbulence(mast=neubuerg, turb.set=1, num.sectors=4)  # change sector number

# calculate turbulence intensity for 1 m/s speed bins and without binning
turbulence(mast=neubuerg, turb.set=1, bins=1:25)
turbulence(mast=neubuerg, turb.set=1, bins=NULL)

# data subset
turbulence(mast=neubuerg, turb.set=1, 
  subset=c(NA, "2010-01-01 00:00:00"))

# change number of digits and hide results
turbulence(mast=neubuerg, turb.set=1, digits=2)
neubuerg.ti <- turbulence(mast=neubuerg, turb.set=1, print=FALSE)
neubuerg.ti


## plot turbulence intensity object
plot(neubuerg.ti)  # default

# change colour, text size etc.
plot(neubuerg.ti, cex.axis=0.7, cex.lab=0.9, circles=c(0.05,0.20,0.05), 
  col="lightgray", col.axis="darkgray", col.border="gray", col.circle="darkgray", 
  col.cross="darkgray", col.lab="darkgray", fg=TRUE, lty.circle="dotdash", 
  lty.cross="longdash", lwd.border=1.2, lwd.circle=1.2, lwd.cross=1.2, 
  pos.axis=135, sec.space=0.6)

## End(Not run)

Uncertainty assessment

Description

Calculates probability of exceedance based of AEP data and given uncertainties of applied methods.

Usage

uncertainty(aep, uc.values, uc.names, prob=seq(5,95,5), 
  digits=c(0,0), print=TRUE)
uc(aep, uc.values, uc.names, prob=seq(5,95,5), 
  digits=c(0,0), print=TRUE)

## S3 method for class 'uncertainty'
plot(x, type=c("prob", "uncert"), p.values=c(50,75,90), ...)

Arguments

aep

AEP object created by aep.

uc.values

Uncertainty values (in percent) for applied methods as numeric vector.

uc.names

Names of the uncertainty components. Normally a string vector of the same length as uc.values. If uc.names is a string vector with the length of uc.values + 1, the calculated total uncertainty is named after the additional name (default is "total"). If uc.names is NULL, the methods are numbered consecutively.

prob

Probability values used for the probability of exceedance analysis. Default is seq(5,95,5).

digits

Number of decimal places to be used for results as numeric vector. The first value is used for uncertainties of applied methods, the second for probability of exceedance results. Default is c(0,0).

print

If TRUE, results are printed directly.

x

Uncertainty object created by uncertainty.

type

Type of plot as string. One of "prob" (probability of exceedance plot) or "uncert" (uncertainties overview plot).

p.values

The P-values highlighted in the plot as numeric vector – default is P50, P75 and P90.

...

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

Details

A wind resource assessment, like every statistical analysis, is only complete with an accompanying uncertainty assessment. uncertainty provides a simple tool to arrange uncertainties of the methods applied and analyse their approximate effects to the energy output of a turbine. The total uncertainty arises from many uncertainty components of different type and impact. Common components are wind measurement (sensor quality/calibration, mast influences, etc.), data analysis (missing data, data selection, simplifications/assumptions etc.), long term data (reference data, length of measuring period, etc.), flow modelling (horizontal and vertical extrapolations, etc.) or power curve (measurement quality, assumptions, etc.).

Assuming all uncertainty components to be independent from each other, the combined standard uncertainty is calculated as follows:

U = \sqrt{u_1 + u_2 + ... + u_n}

where U is the total uncertainty and u_1 untill u_n are the uncertainty components.

Value

Returns a list containing:

uncertainty.meth

Table of uncertainty components and their uncertainty value.

prob.exceedance

Table of probability values and the related annual energy production.

Optional graphical parameters

The following graphical parameters can optionally be added to customize the probability of exceedance plot (type="prob"):

Optional graphical parameters for the uncertainty overview plot (type="uncert"):

Author(s)

Christian Graul

References

Measnet (2009) MEASNET Procedure: Evaluation of Site Specific Wind Conditions, Version 1

See Also

aep

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])
ts <- timestamp(timestamp=winddata[,1])
neubuerg <- mast(timestamp=ts, set1, set2)
neubuerg <- clean(mast=neubuerg)


## calculate uncertainty
# calculate AEP
nb.wp <- profile(mast=neubuerg, v.set=c(1,2), dir.set=1, 
  print=FALSE)
pw.56 <- pc("PowerWind_56_900kW.wtg")
nb.aep <- aep(profile=nb.wp, pc=pw.56, hub.h=71, print=FALSE)

# calculate uncertainty
uncertainty(nb.aep, uc.values=c(5,10,5,5), 
  uc.names=c("Wind Measurement Mast", "Long Term Correlation", 
  "Flow Model", "Power Curve"))

# unnamed uncertainty components
uncertainty(nb.aep, uc.values=c(5,10,5,5), 
  uc.names=NULL)

# new name for combined uncertainty
uncertainty(nb.aep, uc.values=c(5,10,5,5), 
  uc.names=c("Wind Measurement Mast", "Long Term Correlation", 
  "Flow Model", "Power Curve", "Total Uncertainty"))

# changed probability values
uncertainty(nb.aep, uc.values=c(5,10,5,5), 
  uc.names=c("Wind Measurement Mast", "Long Term Correlation", 
  "Flow Model", "Power Curve"), prob=seq(50,90,10))

# change number of digits and hide results
neubuerg.uc <- uncertainty(nb.aep, uc.values=c(5,10,5,5), 
  uc.names=c("Wind Measurement Mast", "Long Term Correlation", 
  "Flow Model", "Power Curve"), digits=c(1,2), print=FALSE)
neubuerg.uc


## plot uncertainty objects - probability of exceedance plot 
plot(neubuerg.uc)  # default
plot(neubuerg.uc, p.values=c(50, 95))  # change highlighted P-values

# change colours, line types, line width and text size
plot(neubuerg.uc, col="blue", lty=c(1, 2, 3, 4), lwd=2, cex=1.2)

# freaky
plot(neubuerg.uc, bty="l", bty.leg="o", cex.axis=2, 
  cex.lab=0.5, cex.leg=0.8, col=c(5, 10, 15, 20), col.axis="sienna", 
  col.box="purple", col.lab="plum", col.leg="orchid", col.ticks="gold", 
  las=0, lty=c(8, 7, 6, 5), lwd=c(5, 3, 1, 0.5), mar=c(6, 5, 4, 3), 
  mgp=c(4, 2, 1), pos.leg="bottomleft", xlim=c(0.1, 0.9), ylim=c(1000, 2000), 
  x.intersp=2, y.intersp=1.5)


## plot uncertainty objects - uncertainty overview plot
plot(neubuerg.uc, type="uncert")  # default

# change colours and border
plot(neubuerg.uc, type="uncert", col="red", border="red4")
plot(neubuerg.uc, type="uncert", col=c(gray(0.7), gray(0.5)), 
  border=c(gray(0.6), gray(0.4)))
plot(neubuerg.uc, type="uncert", col=c(5:1), border=c(1:5))

# change text size, space and margin
plot(neubuerg.uc, type="uncert", cex=1.5, space=0.1, mar=c(1, 13, 1, 1))

# freaky
plot(neubuerg.uc, type="uncert", border=c(11, 22, 33, 44, 55), cex.axis=0.7, 
  cex.text=2, col=c("maroon", "navy", "thistle", "rosybrown", "papayawhip"), 
  col.axis="pink3", col.text="seagreen", mar=c(3, 8, 2, 1), mgp=c(0, 1, 2), space=1)

## End(Not run)

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)

Internal function for weibull

Description

Internal function for weibull

Arguments

v.dat

Vector of wind speed data.

msg

If TRUE, messages are printed.

Value

Returns the shape parameter k and scale parameter A of the weibull distribution.

Author(s)

Christian Graul

See Also

weibull

Example data for bReeze

Description

This dataset is provided as part of the bReeze package for use with the examples in the documantation. It contains measured wind speed and wind direction in a 10 minute interval, collected by a meteorological mast.

Format

Data frame with 36548 observations on the following 17 variables:

date_time

Date and time of observation as character vector.

v1_40m_avg

Average wind speed in m/s at a height of 40 m as numeric vector.

v1_40m_max

Maximum wind speed in m/s at a height of 40 m as numeric vector.

v1_40m_min

Minimum wind speed in m/s at a height of 40 m as numeric vector.

v1_40m_std

Standard deviation of wind speed in m/s at a height of 40 m as numeric vector.

v2_30m_avg

Average wind speed in m/s at a height of 30 m as numeric vector.

v2_30m_max

Maximum wind speed in m/s at a height of 30 m as numeric vector.

v2_30m_min

Minimum wind speed in m/s at a height of 30 m as numeric vector.

v2_30m_std

Standard deviation of wind speed in m/s at a height of 30 m as numeric vector.

v3_20m_avg

Average wind speed in m/s at a height of 20 m as numeric vector.

v3_20m_max

Maximum wind speed in m/s at a height of 20 m as numeric vector.

v3_20m_min

Minimum wind speed in m/s at a height of 20 m as numeric vector.

v3_20m_std

Standard deviation of wind speed in m/s at a height of 20 m as numeric vector.

dir1_40m_avg

Average wind direction in degrees from north at a height of 40 m as numeric vector.

dir1_40m_std

Standard deviation of wind direction in degrees from north at a height of 40 m as numeric vector.

dir2_30m_avg

Average wind direction in degrees from north at a height of 30 m as numeric vector.

dir2_30m_std

Standard deviation of wind direction in degrees from north at a height of 30 m as numeric vector.

Examples

## Not run: 
# load example data
data("winddata", package="bReeze")

# display the structure of the data
str(winddata)

## End(Not run)

Calculate wind profile

Description

Calculates a wind profile, using on the Hellman exponential law.

Usage

windprofile(mast, v.set, dir.set, num.sectors=12, 
  method=c("hellman", "loglm", "fixed"), alpha=NULL, 
  subset, digits=3, print=TRUE)
pro(mast, v.set, dir.set, num.sectors=12, 
  method=c("hellman", "loglm", "fixed"), alpha=NULL, 
  subset, digits=3, print=TRUE)

## S3 method for class 'windprofile'
plot(x, sector, measured=TRUE, ...)

Arguments

mast

Met mast object created by mast.

v.set

Set(s) to be used for wind speed, specified as set number or set name. The first given dataset is used as reference height. If one single dataset is given, the same Hellman exponent is assumed for each sector and can be specified using alpha (see Details for empirical values). If two or more datasets are given, the Hellman exponent is calculated for each sector. If more than two datasets are given, currently only the first two datasets are used.

dir.set

Set to be used for wind direction, specified as set number or set name.

num.sectors

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

method

Method to be used for the calculation. One of "hellman", "loglm" or "fixed" (see Details section). Optional argument: "fixed" is used if v.set is a single dataset, "hellman" is used if v.set specifies two, "loglm" if v.set specifies three datasets.

alpha

Hellman exponent – one general exponent or a vector of exponents (one per sector). Optional and only used if the choosen method is "fixed". If alpha is NULL (the default), 0.2 is used as default.

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 (the default), results are printed directly.

x

Wind profile object created by profile.

sector

Direction sector as integer (sector number) or string (sector code). If missing or NULL, all sectors are plotted. For plotting the general profile only use "all".

measured

If TRUE (the default), measured sector mean wind speeds are added to the plot.

...

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

Details

The average wind speed as a function of height above ground gives a site's wind profile. For reasons of cost-efficiency met mast heights are usually below hub heights of modern wind turbines, thus measured wind speeds must be extrapolated by based wind profile. A common method is the Hellman exponential law or power law ("hellman"), defined as:

\frac{v_2}{v_1} = \left(\frac{h_2}{h_1} \right)^\alpha

where v_2 is the wind speed at height h_2, v_1 is the wind speed at height h_1 and \alpha is the Hellman exponent (also power law exponent or shear exponent).

To calculate \alpha, profile uses the inverted equation as:

\alpha = \frac{\log \left(\frac{v_2}{v_1} \right)}{\log \left(\frac{h_2}{h_1} \right)}

If data is available for two or more heights, a log-linear model fit can be used for the computation of \alpha. In this case the data is logarithmized to allow for fitting a linear model. The models slope is then used as \alpha. Please note: depending on the data this method might result in negative \alpha.

If the wind speed is only known for one height, \alpha must be estimated. \alpha depends on various issues, including roughness and terrain of the site. Some empirical values for temperate climates are:

Site conditions \alpha
Open water 0.08--0.15
Flat terrain, open land cover 0.16--0.22
Complex terrain with mixed or continuous forest 0.25--0.40
Exposed ridgetops, open land cover 0.10--0.14
Sloping terrain with drainage flows 0.10--0.15

Value

Returns a list of:

profile

Data frame containing alpha and reference wind speed for each direction sector.

h.ref

Reference height of the profile (the height of the first given dataset in v.set).

Optional graphical parameters

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

Author(s)

Christian Graul

References

Bañuelos-Ruedas, F., Camacho, C.A., Rios-Marcuello, S. (2011) Methodologies Used in the Extrapolation of Wind Speed Data at Different Heights and Its Impact in the Wind Energy Resource Assessment in a Region. In: Gastón O. Suvire (Ed.), Wind Farm – Technical Regulations, Potential Estimation and Siting Assessment, Chapter 4, p. 97–114, InTech

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

International Electrotechnical Commission (2005) IEC 61400-12 Wind Turbines – Part 12-1: Power Performance Measurements of Electricity Producing Wind Turbines. IEC Standard

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], v.std=winddata[,13])
ts <- timestamp(timestamp=winddata[,1])
neubuerg <- mast(timestamp=ts, set40, set30, set20)
neubuerg <- clean(mast=neubuerg)


## calculate profile
# create profile based on one height
windprofile(mast=neubuerg, v.set=1, dir.set=1)	# default alpha=0.2
windprofile(mast=neubuerg, v.set=1, dir.set=1, alpha=0.15)

# calculate profile based on two heights
windprofile(mast=neubuerg, v.set=c(1,2), dir.set=1)
windprofile(mast=neubuerg, v.set=c(1,3), dir.set=1)
# same as above
windprofile(mast=neubuerg, v.set=c("set1", "set3"), dir.set="set1")

# calculate profile based on three heights
windprofile(mast=neubuerg, v.set=c(1,2,3), dir.set=1)

# change the method used for computation
# note: negative alphas!
windprofile(mast=neubuerg, v.set=c(1,2), dir.set=1, method="loglm")

# change number of direction sectors
windprofile(mast=neubuerg, v.set=c(1,2), dir.set=1, num.sectors=8)

# data subsets
windprofile(mast=neubuerg, v.set=1, dir.set=1, 
  subset=c("2009-12-01 00:00:00", "2009-12-31 23:50:00"))
windprofile(mast=neubuerg, v.set=c(1,2), dir.set=1, 
  subset=c("2010-01-01 00:00:00", NA)) # just 'start' time stamp
windprofile(mast=neubuerg, v.set=c(1:3), dir.set=1, 
  subset=c(NA, "2009-12-31 23:50:00")) # just 'end' time stamp

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


## plot profile objects
plot(neubuerg.wp)  # default
plot(neubuerg.wp, measured=FALSE)  # omit 'measured' points

# plot only one sector
plot(neubuerg.wp, sector=3)	# ENE by sector number
plot(neubuerg.wp, sector="ene")	# ENE by sector code
plot(neubuerg.wp, sector="all")	# general profile

# customize plot
plot(neubuerg.wp, bty="l", bty.leg="o", cex.axis=0.8, 
  cex.lab=0.9, cex.leg=0.7, col=rainbow(13), col.axis=gray(0.2), 
  col.box=gray(0.2), 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(1.2,12), 1.7), mar=c(3,3,0.5,0.5), mgp=c(2,0.7,0), 
  pos.leg="right", xlab="velocity [m/s]", ylab="height [m]", 
  xlim=c(0,11), ylim=c(0,150), x.intersp=1, y.intersp=1.2)

## End(Not run)