Bayesian estimation of copula parameters for wind speed models of dependence

Abstract

Modelling the uncertainty of wind speed is essential in power flow analysis. Having abundant knowledge of the wind speed in an area is critical. A low volume of data can increase uncertainty in wind speed analysis. Spatial dependencies are often modelled before running probabilistic power flow and load flow analysis. Copulas are a popular way of capturing spatial dependence between multiple wind farms. Using NREL data from seven Northeastern United States wind farm sites, Bayesian inference will be used to determine the copula parameter uncertainty between weekly, daily, and hourly wind speed observations. This approach will be used on elliptical and single parameter Archimedean copulas. For each possible wind farm pair, an uninformative prior will be placed on the copula parameter. The resulting posterior will contain a distribution of copula parameter values based on the prior and the observed wind speed data. The posterior's credible interval is reviewed to determine the uncertainty in parameter estimation. The results show that using a data volume considerably more petite than 8760 hourly data points will result in more uncertainty in parameter estimation and inaccuracies in wind speed forecasting if using non-Bayesian methods for copula parameter estimation.