Solving the Yule-Walker equations to generate synthetic, correlated wind speed variates

The work in this paper continues and improves on the research that has been carried out on the generation of synthetic, correlated wind speed variates that are defined by marginal Weibull distributions and auto- and cross-correlations. Previously, in order to establish the matrix of auto-regressive coefficients for a small number of wind variates, a simple recursive method had been used. However, attempts to apply the model, using simple numerical approaches, to an increasing number of wind turbines or locations, proved useless. Therefore, a direct solution of the Yule-Walker equations is proposed here. These equations, originally in matrix form and of size N-2 for N wind variates, are put in symbolic notation and then broken down for numerical solution using the traditional Newton's method. The complete procedure is explained through a symbolic example and illustrated with two very different numerical cases: with the first, wind in very close locations: with the second, wind in dispersed locations of a region. (C) 2012 Elsevier B.V. All rights reserved.