Simulation of correlated wind speed and power variates in wind parks

In this paper, we develop a simulation procedure to generate realistic, synthetic wind speed variates for wind parks. These wind variates are defined by their marginal Weibull distributions and their auto- and cross-correlations only. In order to deal with these two types of correlation simultaneously, a vector auto-regressive (VAR) model is used. Power output variates are obtained by applying the nonlinear turbine power curves to the correlated wind speed samples. The complete procedure is illustrated through a numerical example with a few turbines. A comparison is established between real wind time series from a wind park and synthetic wind variates simulated with similar, estimated underlying parameters.

[1]  W. Root,et al.  An introduction to the theory of random signals and noise , 1958 .

[2]  J.B. Theocharis,et al.  A fuzzy model for wind speed prediction and power generation in wind parks using spatial correlation , 2004, IEEE Transactions on Energy Conversion.

[3]  Jr . L. James Marier,et al.  Correlated K-distributed clutter generation for radar detection and track , 1995 .

[4]  Radhakrishnan Nagarajan,et al.  Evidence of crossover phenomena in wind-speed data , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[5]  Eugene P. Wigner,et al.  Formulas and Theorems for the Special Functions of Mathematical Physics , 1966 .

[6]  James D. Hamilton.  Time Series Analysis , 1994 .

[7]  Wheyming Tina Song,et al.  Generation of autocorrelated random variables with a specified marginal distribution , 1993, WSC '93.

[8]  Norman C. Beaulieu,et al.  The generation of correlated Rayleigh random variates by inverse discrete Fourier transform , 2000, IEEE Trans. Commun..

[9]  Ana Estanqueiro,et al.  How to prepare a power system for 15% wind energy penetration: the Portuguese case study , 2006 .

[10]  Mukund Patel,et al.  Wind and Solar Power Systems , 1999 .

[11]  A. H. Murphy,et al.  Time Series Models to Simulate and Forecast Wind Speed and Wind Power , 1984 .

[12]  G. E. Johnson.  Constructions of particular random processes , 1994, Proc. IEEE.

[13]  W. Szajnowski.  The Generation of Correlated Weibull Clutter for Signal Detection Problems , 1977, IEEE Transactions on Aerospace and Electronic Systems.