# Predict Wind Power Output by Using a Multivariate Power Curve Takes multiple environmental variable inputs measured on an operating wind farm and predicts the wind power output under the given environmental condition. ```r kp.pwcurv(y, x, x.new = x, id.spd = 1, id.dir = NA) ``` ## Arguments - `y`: An $n$-dimensional vector or a matrix of size $n$ by 1 containing wind power output data. This along with x trains the multidimensional power curve model. - `x`: An $n$ by $p$ matrix or a data frame containing the input data for $p$ predictor variables (wind and weather variables). This `x` must have the same number of rows as `y`, i.e., $n$. - `x.new`: A matrix or a data frame containing new input conditions of the $p$ predictor variables for which a prediction of wind power output will be made. This is an optional parameter and will be set to `x` by default, if it is not supplied. - `id.spd`: The column number of `x` (and of `x.new`, if supplied) indicating wind speed data . Default to `1`. - `id.dir`: The column number of `x` (and of `x.new`, if supplied) indicating wind direction data. Default to `NA`, but this parameter needs to be set if `x` includes wind direction data. ## Returns A vector representing the predicted power output for the new wind/weather condition specified in `x.new`. If `x.new` is not supplied, this function returns the fitted power output for the given `x`. ## Note * This function is developed for wind power prediction. As such, the response `y` represents wind power output and the covariates `x` include multiple wind and weather variables that potentially affect the power output. * The data matrix `x` is expected to include at least wind speed and wind direction data. As measurements of other environmental variables become available, they can be added to the `x`. Typically, the first column of `x` corresponds to wind speed data and the second column to wind direction data and, as such, `id.spd = 1` and `id.dir = 2`. * If `x` has a single variable of wind speed, i.e., $p = 1$ and `id.spd = 1`, this function returns an estimate (or prediction) of the Nadaraya-Watson estimator with a Gaussian kernel by using the `ksmooth` function in the `stats` package. ## Examples ```r head(windpw) ### Power curve estimation. # By using a single input of wind speed. pwcurv.est <- kp.pwcurv(windpw$y, windpw$V) # By using wind speed and direction: id.dir needs to be set. pwcurv.est <- kp.pwcurv(windpw$y, windpw[, c('V', 'D')], id.dir = 2) # By using full covariates: confirm whether id.spd and id.dir are correctly specified. pwcurv.est <- kp.pwcurv(windpw$y, windpw[, c('V', 'D', 'rho', 'I', 'Sb')], id.spd = 1, id.dir = 2) ### Wind power prediction. # Suppose only 90% of data are available and use the rest 10% for prediction. df.tr <- windpw[1:900, ] df.ts <- windpw[901:1000, ] id.cov <- c('V', 'D', 'rho', 'I', 'Sb') pred <- kp.pwcurv(df.tr$y, df.tr[, id.cov], df.ts[, id.cov], id.dir = 2) ### Evaluation of wind power prediction based on 10-fold cross validation. # Partition the given dataset into 10 folds. index <- sample(1:nrow(windpw), nrow(windpw)) n.fold <- round(nrow(windpw) / 10) ls.fold <- rep(list(c()), 10) for(fold in 1:9) { ls.fold[[fold]] <- index[((fold-1)*n.fold+1):(fold*n.fold)] } ls.fold[[10]] <- index[(9*n.fold+1):nrow(windpw)] # Predict wind power output. pred.res <- rep(list(c()), 10) id.cov <- c('V', 'D', 'rho', 'I', 'Sb') for(k in 1:10) { id.fold <- ls.fold[[k]] df.tr <- windpw[-id.fold, ] df.ts <- windpw[id.fold, ] pred <- kp.pwcurv(df.tr$y, df.tr[, id.cov], df.ts[, id.cov], id.dir = 2) pred.res[[k]] <- list(obs = df.ts$y, pred) } # Calculate rmse and its mean and standard deviation. rmse <- sapply(pred.res, function(res) with(res, sqrt(mean((obs - pred)^2)))) mean(rmse) sd(rmse) ``` ## References Lee, G., Ding, Y., Genton, M.G., and Xie, L. (2015) Power Curve Estimation with Multivariate Environmental Factors for Inland and Offshore Wind Farms, **Journal of the American Statistical Association** 110(509):56-67. ## See Also `windpw`, `ksmooth`

kp.pwcurv function