Prediction intervals for power generation from multiple wind farms

New Zealand has several existing or proposed wind farms to generate electric power. Small variations in wind speed can cause large variations in power output, due to a nonlinear relationship between wind speed and power. These variations may be correlated across different wind farms. There is interest in finding prediction intervals to quantify the risk of extreme changes in total wind power generation. At the individual wind farm level, an ad hoc method is proposed for modelling the probability distribution for wind some minutes in the future. This is used to estimate the conditional cumulative distribution function for future power output at each farm, given the regression model. A discrete approximation is used for the power output random variable, which reduces the problem to a set of conditional probabilities that can be calculated. A recursive algorithm is used to combine the discrete cumulative distribution functions to find the conditional distribution of total power across all the wind farms given the most recent winds, and hence to find a prediction interval. References B. Whiten, B. McDonald and R. Bedford. Modelling power output from correlated wind farms. ANZIAM J. (MISG2011), 53:M104–M141, 2013. http://journal.austms.org.au/ojs/index.php/ANZIAMJ/ article/view/5194/1759. Electricity Authority. Wind integration analysis. Technical Report, 2010. ftp://ftp.emi.ea.govt.nz/Datasets/Supplementary_information/Archive/20101109_Wind_integration_analysis/ The WindAction Group. Wind turbine explodes. February, 2008. http://youtu.be/u14tBwO5QV