WindCurves: A Tool to Fit Wind Turbine Power Curves
In WindCurves: Tool to Fit Wind Turbine Power Curves

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
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Introduction:

This is a Vignettes of R package, WindCurves. The package WindCurves is a tool used to fit the wind turbine power curves. It can be useful for researchers, data analysts/scientist, practitioners, statistians and students working on wind turbine power curves. The salient features of WindCurves package are:

Fit the power curve with Weibull CDF, Logistic [1] and user defined techniques.
Comparison and visualization of the performance of curve fitting techniques.
Utilise as a Testbench to compare performace of user defined curve fitting techniques with user defined error measures.
Availability of Dataset [2] on the power curves of wind turbine from four major manufacturers: Siemens, Vestas, REpower and Nordex.
Feature to extract/capture Speed Vs Power discrete points from power curve image

Instructions to Use:

A power curve can be fitted with the WindCurves package from a discrete samples of wind turbine power curves provided by turbine manufacurers as:

library(WindCurves)
data(pcurves)
s <- pcurves$Speed
p <- pcurves$`Nordex N90`
da <- data.frame(s,p)
x <- fitcurve(da)
x
validate.curve(x)
plot(x)

User can utilize WindCurves package as a testbench so that a new curve fitting technique can be compared with above mentioned existing environment.
- The user defined function (similar to random()) should be saved in .R format and it should return the fitted values in terms of "Power values". The random() function used in this example is stored as .R file with dump() function and made available in the WindCurves package and written as:

random <- function(x)
{
  data_y <- sort(sample(1:1500, size = 25, replace = TRUE))
  d <- data.frame(data_y)
  return(d)
}
dump("random")
rm(random)

A random() function is attached in the comparison the parameters MethodPath and MethodName as shown below, where MethodPath is a location of the function proposed by the user and MethodName is a name given to the function.

library(WindCurves)
data(pcurves)
s <- pcurves$Speed
p <- pcurves$`Nordex N90`
da <- data.frame(s,p)
x <- fitcurve(data = da, MethodPath = "source('dumpdata.R')", MethodName = "Random values")

## The user can specify .R files from other locations as:
# x <- fitcurve(data = da, MethodPath = "source('~/WindCurves/R/random.R')", MethodName = "Random values")
validate.curve(x)
plot(x)

Also, WindCurves allows user to add more error measures with validate.curve() function as explained below:

Consider error() is a function which uses two vectors as input and returns a error value with a specific error measure, such as RMSE or MAPE as shown below:

# PCV as an error metric
error <- function(a,b)
{
d <- (var(a) - var(b)) * 100/ var(a)
d <- as.numeric(d)
return(d)
}
dump("error")
rm(error)

The effect of this function can be seen in the results obtained with Validate.curve() function as:

library(WindCurves)
data(pcurves)
s <- pcurves$Speed
p <- pcurves$`Nordex N90`
da <- data.frame(s,p)
x <- fitcurve(da)
validate.curve(x = x, MethodPath = "source('dumpdata.R')", MethodName = "New Error")
plot(x)

Similarly, user can compare various techniques used for wind turbine power curve fitting.

Dataset [2] on the power curves of wind turbine from four major manufacturers: Siemens, Vestas, REpower and Nordex. These datsset represent wind turbine power output in 'kW' against wind speed in 'metres per second' as shown below:

data(pcurves)
pcurves

Further, WindCurves package provides feature to extract/capture Speed Vs Power discrete points from power curve image. This can be achieved with the following simple instruction:

#img2points("image.jpeg")

where, image.jpeg is the name of power curve image from which discrete points are to extracted. The procedure of extraction is as follows:

With the command img2points("image.jpeg"), an image will get appeared in the Viewer.
Click on leftmost point of the X-axis of the curve image and assign the respective appropriate value.
click on rightmost point on X-axix, downmost point of Y-axis and topmost point of Y-axis, and assign their values, respectively.
click of the points on the curve image. By default, 15 points can be captured from the curve image, but user can set the desired number of points with n parameter in img2points() function.
This function returns a data.frame with two columns, i.e., wind speed and wind power, which can be used as input data for fitcurve() function.

References

[1] D. Villanueva and A. E. Feij´oo, “Reformulation of parameters of the logistic function applied to power curves of wind turbines,” Electric Power Systems Research, vol. 137, pp. 51–58, 2016.(via)

[2] Iain Staffell, “Wind turbine power curves, 2012” (via)