Elsevier

Solar Energy

Volume 79, Issue 1, July 2005, Pages 65-77
Solar Energy

Forecast of hourly average wind speed with ARMA models in Navarre (Spain)

https://doi.org/10.1016/j.solener.2004.09.013Get rights and content

Abstract

In this article we have used the ARMA (autoregressive moving average process) and persistence models to predict the hourly average wind speed up to 10 h in advance. In order to adjust the time series to the ARMA models, it has been necessary to carry out their transformation and standardization, given the non-Gaussian nature of the hourly wind speed distribution and the non-stationary nature of its daily evolution. In order to avoid seasonality problems we have adjusted a different model to each calendar month. The study expands to five locations with different topographic characteristics and to nine years. It has been proven that the transformation and standardization of the original series allow the use of ARMA models and these behave significantly better in the forecast than the persistence model, especially in the longer-term forecasts. When the acceptable RMSE (root mean square error) in the forecast is limited to 1.5 m/s, the models are only valid in the short term.

Introduction

The forecast of hourly average wind speed 1–10 h in advance, and thereby the power output of wind farm, is of interest for the operation of conventional electric power plants that are connected to the same power grid as those conversion systems (Geerts, 1984, Sfestos, 2000). This is particularly important in weak grids. The modeling and prediction of time series of hourly average wind speed has been a subject of attention to a large number of researchers. The initial studies carried out used a Monte Carlo method to generate simulations when the parameters of the wind speed distribution were known. The series obtained using this method presented the weakness of not considering the autocorrelation of the hourly average wind velocities. Later, Chou and Corotis (1981) included the effect of autocorrelation, but they did not consider the non-Gaussian nature of the wind speed distribution. Brown et al. (1984) proposed a method that took into account the autocorrelated nature, the daytime non-seasonality, and the non-Gaussian shape of the wind speed distribution, applying a pure autoregressive model (AR) to a series of data observed in one month. They pointed out that it would be more appropriate to use wind speed data from several years for each given month, despite the fact that the process would become more cumbersome and the formulas used would have to be modified. Geerts (1984) used an ARMA model for a single series one year long with the same goal of forecasting wind speed values in a relatively short term. The author compared the results with those obtained using a persistence model, concluding that for longer-term predictions than 1 h ARMA worked better than the persistence model. Notwithstanding, the RMSE for 10 h in advance exceeded in both cases the limit of 1.5 m/s that he established as acceptable. Balouktsis et al. (1986) applied the ARMA models to the wind speed time series from three locations with one- and two-year long records, but the prior transformation of the observed data was different from the one proposed by Brown, pointing out that the results were satisfactory. Daniel and Chen (1991) applied the ARMA model to three year long time series, and specifically for three months. For doing so, they admitted that the model used to generate time series of hourly average wind speed based on data from several years could provide future wind velocities more representative than those from the model based on one month data. Cited authors did forecasts 1–6 h in advance and they observed the deterioration of the results when the forecast was predicted more than 2 h in advance. Following the same procedure, Nfaoui et al. (1996) concluded that an AR (2) model is capable of simulating well the wind speed series recorded, that in this case were referred to only one location and had a time span of 12 years, and Kamal and Jafri (1997) confirmed that such procedure is useful to predict past values as well as the forecasted wind data of Quetta (Pakistan).

The aim of this work is to evaluate the applicability of the ARMA models (see Appendix A) to the time series of hourly average wind speed, and assess the predictive behaviour of the models obtained. The application of ARMA models requires time series to be stationary, i.e. the method assumes that the process remains in equilibrium about a constant mean level. The analysis was done from data collected in five weather stations located in two distinct areas of Navarre, one with smooth topography and the other in a mountainous region.

Section snippets

Materials and methods

We collected data from fourteen automated weather stations distributed across the entire territory of the Regional Community of Navarre (Spain) that had long enough data series without gaps. Among other meteorological variables, these stations record wind speed at a height of 10 m every ten minutes with cup anemometers. The value of the hourly average wind speed was obtained averaging the six values measured within each hour.

Given the fact that nine out of the fourteen stations showed average

Results

The last four columns of Table 2 show the indices of the ARMA models identified in each case, and the values of the computed coefficients for each one of them. In six of the sixty series analyzed it was impossible to find an ARMA model that represented them and satisfied the Box–Pierce criterion at a level of significance of 0.1, as recommended by Box and Jenkins (1976).

There are up to ten different ARMA models among those identified, being the most frequent: (1, 2) in 37% of the cases; (1, 1) in

Conclusions

The process of transformation and standardization of the hourly wind speed time series used provide the necessary conditions to represent them using ARMA models, as can be proved by the fact that in most cases it was possible to identify and validate the appropriate model.

The behaviour of the forecasts in the transformed series is similar to that of the actual velocities, so we can conclude that the use of the hourly mean and standard deviation values used on a monthly basis for the

Acknowledgments

The present study was carried out under a research project supported by the Department of Culture and Education, Government of Navarre, Spain. Authors would like to thank Eloisa Izco for her help with tables and figures.

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