Spatial dependence in wind and optimal wind power allocation: A copula-based analysis

The investment decision on the placement of wind turbines is, neglecting legal formalities, mainly driven by the aim to maximize the expected annual energy production of single turbines. The result is a concentration of wind farms at locations with high average wind speed. While this strategy may be optimal for single investors maximizing their own return on investment, the resulting overall allocation of wind turbines may be unfavorable for energy suppliers and the economy because of large fluctuations in the overall wind power output. This paper investigates to what extent optimal allocation of wind farms in Germany can reduce these fluctuations. We analyze stochastic dependencies of wind speed for a large data set of German on- and offshore weather stations and find that these dependencies turn out to be highly nonlinear but constant over time. Using copula theory we determine the value at risk of energy production for given allocation sets of wind farms and derive optimal allocation plans. We find that the optimized allocation of wind farms may substantially stabilize the overall wind energy supply on daily as well as hourly frequency.

[1]  Mark Z. Jacobson,et al.  Supplying Baseload Power and Reducing Transmission Requirements by Interconnecting Wind Farms , 2007 .

[2]  T. Bedford,et al.  Vines: A new graphical model for dependent random variables , 2002 .

[3]  Edward Kahn,et al.  The reliability of distributed wind generators , 1979 .

[4]  D. Clayton.  A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence , 1978 .

[5]  H. Joe.  Families of $m$-variate distributions with given margins and $m(m-1)/2$ bivariate dependence parameters , 1996 .

[6]  Fred Espen Benth,et al.  Analysis and modelling of wind speed in New York , 2010 .

[7]  D. Cox,et al.  An Analysis of Transformations , 1964 .

[8]  C. Genest,et al.  Statistical Inference Procedures for Bivariate Archimedean Copulas , 1993 .

[9]  J. Seinfeld,et al.  Atmospheric Chemistry and Physics: From Air Pollution to Climate Change , 1997 .

[10]  H. Joe.  Asymptotic efficiency of the two-stage estimation method for copula-based models , 2005 .

[11]  E. Luciano,et al.  Copula methods in finance , 2004 .

[12]  J. Seinfeld.  Atmospheric Chemistry and Physics of Air Pollution , 1986 .

[13]  A. Frigessi,et al.  Pair-copula constructions of multiple dependence , 2009 .

[14]  R. Nelsen.  An Introduction to Copulas , 1998 .

[15]  Matthias Fischer,et al.  An empirical analysis of multivariate copula models , 2009 .

[16]  Michael Milligan,et al.  Determining the Capacity Value of Wind: A Survey of Methods and Implementation; Preprint , 2005 .

[17]  Klaus Hubacek,et al.  What to expect from a greater geographic dispersion of wind farms? A risk portfolio approach , 2007 .

[18]  K. Aas,et al.  Models for construction of multivariate dependence – a comparison study , 2009 .

[19]  Roger M. Cooke,et al.  Probability Density Decomposition for Conditionally Dependent Random Variables Modeled by Vines , 2001, Annals of Mathematics and Artificial Intelligence.

[20]  Bruno Rémillard,et al.  Goodness‐of‐fit Procedures for Copula Models Based on the Probability Integral Transformation , 2006 .

[21]  Jay Apt,et al.  The variability of interconnected wind plants , 2010 .

[22]  Gregor Czisch,et al.  High wind power penetration by the systematic use of smoothing effects within huge catchment areas shown in a European example , .

[23]  B. Rémillard,et al.  Goodness-of-fit tests for copulas: A review and a power study , 2006 .

[24]  H. Joe.  Multivariate models and dependence concepts , 1998 .

[25]  Monique Bernier,et al.  Synthetic aperture radar satellite data for offshore wind assessment: A strategic sampling approach , 2011 .