aep {bReeze} | R Documentation |
Calculates annual energy production (AEP) from a site's wind profile and wind turbine characteristics.
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, ...)
profile |
Wind profile object created by |
pc |
Power curve object created by |
hub.h |
Hub heigth of wind turbine as numeric value. |
rho |
Air density as numeric value. Default is |
avail |
Availability of turbine as numeric value between |
bins |
Edges of wind speed bins as numeric vector or |
sectoral |
If |
digits |
Number of decimal places to be used for results as numeric vector. The first value is used for |
print |
If |
x |
AEP object, created by |
show.total |
If |
... |
Arguments to be passed to methods. For optional graphical parameters see below. |
For a wind turbine the mean energy production can be expressed by
E = T*integral(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*rho/rho_pc*H*sum(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*(h/h_ref)^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 = AEP/(P_rated*8760)
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. |
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 aep
only contains the total AEP.
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.
type
: If "n"
nothing is plotted.
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
.
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.
Christian Graul
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
## 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)