# Import power curve from file Imports a power curve from a WAsP 'wgt' file or a WindPower program 'pow' file. UTF-8 ```r 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: |||| |:--|:--|:--| ||$P ~ v^3$|$for vv_rated$| 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 $cp$ is defined as: $$ c_p = \frac{P_t}{P}cp = Pt/P $$ where $Pt$ 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| ## Optional graphical parameters The following graphical parameters can optionally be added to customize the plot: * `bty`: Type of box to be drawn around the plot region. Allowed values are `"o"` (the default), `"l"`, `"7"`, `"c"`, `"u"`, or `"]"`. The resulting box resembles the corresponding upper case letter. A value of `"n"` suppresses the box. * `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. * `col`: Vector of colours. The first colour is used for the power curve. If only one coefficient is available, the second colour is used for this coefficient, if both coefficients are available, the second colour is used for `pc` and the third for `ct`. * `col.axis`: Colour to be used for axis annotations -- default is `"black"`. * `col.box`: Colour to be used for the box around the plot region (if `bty`) -- default is `"black"`. * `col.lab`: Colour to be used for axis labels -- default is `"black"`. * `col.leg`: Colour to be used for legend text -- default is `"black"`. * `col.ticks`: Colours for the axis line and the tick marks respectively -- default is `"black"`. * `las`: Style of axis labels. One of `0` (always parallel to the axis, default), `1` (always horizontal), `2` (always perpendicular to the axis), `3` (always vertical). * `legend`: If `TRUE` (the default) a legend is drawn. * `leg.text`: A character or `expression` vector to appear in the legend. * `lty`: Vector of line types, assigned like `col`. See `par` for available line types. * `lwd`: Vector of line widths, assigned like `col`. See `par` for usage. * `mar`: A numerical vector of the form c(bottom, left, top, right) which gives the number of lines of margin to be specified on the four sides of the plot -- default is `c(5, 5, 1, 5)` for one y axis and `c(5, 5, 1, 1)` for two y axes. * `mgp`: A numerical vector of the form c(label, annotation, line), which gives the margin line for the axis label, axis annotation and axis line. The default is `c(3, 1, 0)`. * `pos.leg`: Position of legend -- one of `"bottomright"`, `"bottom"`, `"bottomleft"`, `"left"`, `"topleft"`, `"top"`, `"topright"`, `"right"` or `"center"`. Use `NULL` to hide the legend. * `xlab`: Alternative label for the x axis. * `ylab`: Alternative labels for the y axis, as vector of the form c(left axis label, right axis label). * `ylim`: Limits of the y axis, as vector of two values. * `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`. ## Returns Returns a data frame binding the given data ## 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 ## Author(s) Christian Graul ## Note All power curves are provided without any warranty of accuracy and timeliness. Reliable data can only be received from the respective manufacturer directly. ## Examples ```r ## 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) ```

pc function