The problem

The end intention is to identify the distribution of contribution of wind power to the flow of electricity from one part of Great Britain to the remainder of Great Britain, i.e. across a transmission boundary, for example from Scotland to England. The 90% or the 95% point of this distribution determines the quantity of transmission boundary capability, that National Grid must build, to comply with the security requirements of its Transmission Licence.

To achieve this, one must identify the joint likelihood that there is a high level of wind output in Scotland and a low level of wind output in England – thus the anti-correlation of these outputs. This may be contrasted with the often-studied problem of Wind contribution to peak generation security, for which one needs to study the correlation of (say) Scottish and English wind outputs.

The Approach

Several strategies were used to try and model the power output of wind farms. These attempts were a process that took place in concert with attempts to understand and to describe the dataset in a way that would illuminate of its essential structure.

The difficulties were mainly in finding a straightforward way to represent the dependencies between wind speeds in different areas of the UK. One strategy, that of conditional distributions, proved reliable but its complexity became overwhelming for more than a few zones. Other usual statistical methods, such as linear regression, were hampered by the nature of the data; distributions of wind power outputs are bimodal and therefore far from normal.

Finally a multivariate Weibull model was developed to represent outputs across geographic zones. In mathematical terms this used a 'Weibull copula', analogous to the well known 'normal copula'. In practical terms, this approach was intuitively appealing because it mapped power outputs onto a distribution known to accurately approximate variations in average wind speed. Thus although the Weibull distributions in the model may not have corresponded directly to actual measured wind speed, they were sufficiently close to for their correlations to behave in an regular way.

Modelling of wind outputs then took place firstly for a subset of the geographic zones in the original data as a trial set, secondly for the complete set of 27 zones across the UK, and thirdly for a modified set of 14 zones which were chosen to reflect projected wind farm installations as well as areas of particular importance for the transmission network.