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.Wind power; Vine copula; Optimal turbine allocation

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. (C) 2011 Elsevier Ltd. All rights reserved

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.Wind power Vine copula Optimal turbine allocation

Measuring association and dependence between random vectors

Measures of association are suggested between two random vectors. The measures are copula-based and therefore invariant with respect to the univariate marginal distributions. The measures are able to capture positive as well as negative association. In case the random vectors are just random variables, the measures reduce to Kendall’s tau or Spearman’s rho. Nonparametric estimators, based on ranks, for the measures are derived. Their large-sample asymptotics are derived and their small-sample behavior is investigated by simulation. The measures are applied to characterize strength and direction of association of northern and southern European bond markets during the recent Euro crisis as well as association of stock markets with bond markets