Empirical orthogonal function analysis of wind farm power output

Abstract

One of the major challenges to supporting, facilitating and developing wind generated power is matching supply and demand. Wind generated power is obviously subject to fluctuations due to variation in the wind. There is also a shutdown mechanism which is employed when the wind becomes very strong which prevents damage to the turbines. Thus, when the wind is light or very strong, there is no power generated. Predicting the output from the turbines is currently an important research topic. In the past, time series analysis and other methods have been employed in order to better understand the nature of the data. These include ARMA and GARCH models as well as relatively new methods of detrended fluctuation analysis, (Ward et al., 2009; Boland et al., 2009; Magnano and Boland, 2007; Kavasseri and Nagarajan, 2004). The behaviour of complex time series, as is the wind farm power output, and as is seen in the financial sector has been and is currently well researched. Some of these time series have been found to be non-linear, stochastic and chaotic, and are notoriously difficult to model. There is evidence however, that there could be some scaling behaviour apparent in these series (Weron and Przybylowicz, 2000). The particular objective of this project is to reduce the error in predicting the power supply generated by wind farms (or the individual turbines) five minutes into the future so that the power company is able to guarantee the promised power. Currently this is not possible due to the financial risks involved in not delivering the guaranteed amount. Apart from climatic research, there is not much in the way of research into spatial correlations where records are available of similar variables at different locations. Since the temporal nature of the time series is currently being thoroughly investigated by many researchers, this study explores the possible spatial correlations between wind farms. This paper describes the investigation into the spatial correlation between five South Australian wind farms using empirical orthogonal function analysis, (EOF). If there is spatial correlation between farms, this can be used to better predict what might happen at one farm based upon what has happened at a different farm at some earlier time. There has also been speculation among experts that power output of sites along a weather front behave in a similar way. One of the main difficulties with determining the power output of wind turbines is that wind speed is not a useful predictor. The wind speed isn't actually measured at the height of the blades and if instruments were installed the to measure the wind speed immediately in front of the turbine blades, then the likelihood of correct measurements would be compromised by their existence. This study has focused on the spatial correlations between farms and the initial results from this study indicate that there is evidence of some spatial correlation between some of the farms.