diff --git a/vignettes/EnergyIndicators.Rmd b/vignettes/EnergyIndicators.Rmd index f4a1a04b722a6b250efadc015808dc5691811969..5a65c4759ee4932b76b791e1f3787fa6dcafaf25 100644 --- a/vignettes/EnergyIndicators.Rmd +++ b/vignettes/EnergyIndicators.Rmd @@ -30,24 +30,38 @@ Although wind turbines cannot extract all of the kinetic energy in the wind, and As an example, we simulate a time series of 1000 wind speed values from a Weibull distribution with scale factor of 6 and a shape factor of 2, which represent a sample of wind speed values obtained at a single location. The Weibull distribution is often assumed to fit observed wind speed values to a probability distribution function. Then, each instantaneous wind speed value is converted to its equivalent WPD. The `mean` and `sd` of the WPD can be employed to summarize the wind resource in that location. Otherwise, we can plot the histograms to see the full distribution of values: -```{r, fig.width=7} +``` library(CSIndicators) set.seed(1) -oldpar <- par(no.readonly = TRUE) wind <- rweibull(n = 1000, shape = 2, scale = 6) WPD <- WindPowerDensity(wind) mean(WPD) +``` + +``` +## [1] 170.6205 +``` + +``` sd(WPD) +``` + +``` +## [1] 251.1349 +``` + +``` par(mfrow = c(1, 2)) hist(wind, breaks = seq(0, 20)) hist(WPD, breaks = seq(0, 4000, 200)) ``` +![WPD](./Figures/WPD_histogram.png) As you can see the histogram of the WPD is highly skewed, even if the wind speed was only a little skewed! If not specified, an air density of 1.225 kg/m^3 is assumed. Otherwise, the parameter `ro` can be set to a fixed value (for instance the mean air density at the site elevation could be used), or a timeseries of density values measured at each time stamp can be used to obtain more accurate results. -```{r} +``` WPD <- WindPowerDensity(wind, ro = 1.15) ``` @@ -61,16 +75,16 @@ Notice that power curves are intended to be used with 10-minutal steady wind spe Following on the previous example, we will compute now the CF that would be obtained from our sample of 1000 wind speed values when using a turbine of class IEC I, and compare it to the CF values for a class III: -```{r, fig.width=7} +``` WCFI <- WindCapacityFactor(wind, IEC_class = "I") WCFIII <- WindCapacityFactor(wind, IEC_class = "III") par(mfrow = c(1, 3)) hist(wind, breaks = seq(0, 20)) hist(WCFI, breaks = seq(0, 1, 0.05), ylim = c(0, 500)) hist(WCFIII, breaks = seq(0, 1, 0.05), ylim = c(0, 500)) -par(oldpar) ``` +![WCF](./Figures/WCF_histogram.png) From the CF histograms we can see that, for this particular wind speed distribution, the IEC I turbine (designed for high winds) producess less energy than the IEC III turbine, which is more suitable for this range of wind speed values.