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## Wind forecast map Statistical approaches for wind forecasting

In the statistical approach, a vast amount of data is analyzed and meteorological processes are not explicitly represented. The link between historical power production and weather is determine and then use to forecast the future power output wind forecast map.

Unlike physical methods, statistical methods involve only one-step to convert the input variables into power output. Hence, the methods used are describe as ‘black box’.

Generally, a statistical relationship is develope between the weather forecast or prediction and the potential power output from the wind farm. Statistical approaches perform better in shorter horizons in which current conditions strongly determine the future state of the wind.

However, as prediction horizons are larger, the mesoscale atmospheric conditions must be evaluate and, in this case, NWP data become more important.

### Statistical approaches:

There are myriads of articles focused on statistical approaches for wind forecasting. In this section, a review of models for short-term forecasting that have been publish in the international literature is presented.

It has been limiting only to publish works where the models use are base on statistical methods, machine-learning approaches, and/or hybrid methods.

The objective of this review is not to make a thorough compilation of all the published works in this area, but to provide a general overview of the different approaches that are being apply in statistical wind power prediction.

We have tried to select works that used persistence as a reference model, allowing a comparison among approaches.

### The first models:

The first models used in wind speed or wind power forecasting were based on Box–Jenkins methodology (also known as ARIMA models). These models are still being use nowadays as prediction models or reference models in many cases, though limited to a horizon prediction a few hours. Thus, Torres et al. have adjusted several ARMA models to predict the hourly average wind speed up to 10 h in advance in five locations with different topographic characteristics of Navarra (Spain), and obtaining a prediction error decrease of up 20% compared to persistence model.

The classical time-series analysis is not the only way to model the statistical relationships among data. The main machine learning approaches used, so-called soft computing models, are artificial neural networks (ANN) and fuzzy systems. These methods are often refer to as artificial intelligence methods and are know as learning approaches because the relationship between inputs and the expected output is learn by using historical time series. These methods, unlike physical methods, involve only a step to convert the input variables and output, so are often describe as black boxes.

Cadenas and Rivera conducted a study on the prediction of the hourly average wind speed in the region of La Venta (Oaxaca, Mexico) using diverse configurations of ANN and comparing the results based on two forecast error measures: the mean absolute error (MAE) and the mean square error (MSE). Gong Li and Jing Shi also made predicting the hourly average wind speed at two locations of North Dakota (USA) using three architectures of ANN, namely, backpropagation, radial basis function, and adaptive linear, and comparing them.

#### According to three performance measures:

MAE, root mean square error (RMSE), and mean absolute percentage error (MAPE). The same procedure as described is apply by Gong Li et al. to predict the hourly average wind speed up to 48 h, but this time including a technique called Bayesian Model Averaging (BMA) based on an expectation-maximum algorithm, used to select the weights of the model, and the Box-Cox transformation to convert time series in normal distributions.

Many wind speed measurements in different locations allow studying the correlation between the mean values of wind speed in different weather stations. To this end, Alexiadis et al. propose a system based on a neural network for predicting the wind speed in Thessaloniki Bay (Greece) with a forecast horizon of up 2 h with which obtained an improvement of up to 27% compared to the persistence model.

### The first major work:

The first major work where a broad comparison is make among different models was perform by Sfetsos. It provides a prediction of the hourly average wind speed on the island of Crete (Greece) using the following models: persistence, ARMA, five architectures of ANN (adaptive linear, backpropagation, radial basis function, Elman recurrent and neuronal logic), and models based on adaptive network-based fuzzy inference system (ANFIS). The objective was to obtain the best model with respect to the persistence model. The RMSE performance function is use in this study. The best result was obtain by one of the ANN-base models, achieving an improvement of 4.89% over the persistence is obtain for 1-h ahead wind speed prediction. Haque et al. also carry out a performance analysis of short-term wind speed prediction techniques based on ANN (backpropagation and radial basis function) and ANFIS, and comparing them according to three error rates:

MAE, MAPE, and RMSE. Furthermore, the forecasting performance of the models used in this study is improved by similar days method, which considers similar historical weather information corresponding to the forecasting day in order to determine similar wind speed days for processing. Research conducted by Sfetsos provided a novel method for the forecasting of mean hourly wind speed data using two time-series approaches (iterative and simultaneous procedures) wind forecast map. Specifically, the proposed methodology is based on the multistep forecasting of 10 min averaged data and the subsequent averaging to generate mean hourly predictions. Datasets from two different locations (zone 1: Monastery of Odigitria, Crete (Greece), zone 2: Rutherford Appleton Laboratory, Oxfordshire (United Kingdom)) have been used, thus obtaining consistent improvements by means of the iterative method (zone 1 – 19.17%) and simultaneous method (zone 2 – 10.09%) with respect to persistence wind forecast map model.

Campbell and Adamson performed the average wind speed forecasting in different prediction horizons (10 min, 1 h, 2 h, 5 h, and 12 h) on a wind farm located in County Donegal (Ireland), by applying the following models: persistence, ARIMA, Moving Average (MA) and ANN and comparing them based on the RMSE index. Bivona et al. conducted a study for hourly average wind speed forecasting in two areas of Sicily (Italy), using the Seasonal ARIMA and ANN models and comparing them in the function of the following indicators of accuracy.

#### Following indicators of accuracy:

MAE, RMSE, MAPE, and mean absolute scaled error (MASE). On the other hand, Qing Cao et al. provide a comparative analysis of the wind speed forecasting accuracy of univariate and multivariate ARIMA models with their recurrent neural network counterparts for a predicting horizon of 15 min.

The data employed in the study were obtain on the same weather station in five different heights and have been use as multivariate inputs to the building of the assess models.

#### Where the latter was analyze and compare in the function of the following error metrics:

Mean square percentage error (MSPE), MAE, MAPE, and correlation coefficient. The findings indicate that multivariate models perform better than univariate models and that the recurrent ANN models outperform the ARIMA models.

Hybrid forecasting of time-series data is consider to be a potentially viable alternative compare with the conventional single forecasting modeling approaches such as ARIMA and ANN. Cadenas and Rivera conducted a study on the prediction of the hourly average wind speed in three different regions of Mexico using ARIMA, ANN, and Hybrid models (ARIMA-ANN), comparing the results based on mean error (ME), MAE, and MSE, and concluding that the Hybrid models predict the wind speed with higher accuracy than the ARIMA and ANN models in the three examined sites. In addition, Cadenas et al. also made mean wind speed forecasting for the shorter prediction horizon (10 min) using the single exponential smoothing method (SES) and ANN models, comparing the results based on MSE, MAE, mean percentage error (MPE) and MAPE, and concluding that SES method showed the former better results wind forecast map.

Hui Liu et al. propose two ARIMA-ANN and ARIMA-Kalman hybrid models to predict the hourly average wind speed up to 3 h in advance, and they are compared with each other and with the ARIMA model through performance indices MSE, MAE, and MAPE, showing that the ARIMA-Kalman hybrid model has the better results. Another study by Hui Liu et al. also make mean wind speed forecasting up to 3 h in advance using another hybrid model name EMD-ANN that is based on the empirical mode decomposition (EMD) and ANN. This model is compare to persistence, ARIMA, and ANN models through the measurements of performance MSE, MAE, and MAPE, obtaining that the EMD-ANN hybrid model provides the better results wind forecast map.

#### Another powerful technique:

Another powerful technique called support vector machine (SVM) and belonging to soft computing that is widely apply in a variety of classification and function estimation problems carries great potential for the application of short-term wind speed forecasting. Zhou et al. present a systematic study on fine-tuning of SVM model parameters for one-step-ahead wind speed forecasting and these different configurations were compare with the persistence approach according to the RMSE parameter.
##### The SVM parameters

The SVM parameters consider include the training sample, SVM order, regularization parameter, and Kernel parameters (three SVM Kernels, namely linear, Gaussian and polynomial), and it is find that the SVM models can outperform the persistence model in the majority of cases.

Shi et al. investigate two ARIMA-ANN and ARIMA-SVM hybrid models to predict the wind speed and wind power generation for the following prediction horizons: 1, 3, 5, 7, and 9 h.

These hybrid models are compare with ARIMA, ANN, and SVM models base on two metrics of forecasting accuracy (MAE and RMSE), concluding the study that the hybrid approaches are viable options for forecasting both wind speed and wind power generation time series, but they do not always produce superior forecasting performance for all the forecasting time horizons examine wind forecast map.

Forecasting models currently employed can be a divide into two groups: a first group that only employ time-series data and predict future values taking into account past history; and a second group that uses forecasted values from an NWP model. Nowadays, prediction models use the values forecasted by an NWP model and current or historic measures of wind speed and/or wind power generation for its construction.

#### For example

Salcedo-Sanz et al. make the hybridization of the fifth-generation mesoscale model (MM5) with ANN for mean hourly wind speed forecast at specific points of a wind park, obtaining the best model configuration based on MAE and MSE. Ramirez et al wind forecast map. propose two new wind-power forecasting systems up to 72 h in advance where the input variables use in both systems were the same: forecast meteorological variable values obtain from an NWP (MM5) and electric power-generation registers of the wind farm.

The first forecasting system is call FORECAST and combines inputs to predict the wind power production through a power curve model represent by a multilayer perceptron ANN. The other model used, namely the SGP system, uses a combination of the Kalman filter, ARMA model, and several ANN models, selecting the best combination of the models in a fuzzy inference system.

Both the FORECAS and the SGP systems obtained good results and improved very significantly the persistence model forecasts. Khalid and Savkin present a method to improve the short-term wind power prediction (10 min) at a given turbine using information from NWP and from multiple observation points, comparing the results with the persistence and Grey predictor model in terms of MAE and RMSE.