Statistical modelling of dependence between net demands and deficits in two area power systems

Power system resource adequacy risks is dominated by the extremes of the relevant distributions or processes: the upper tail of demand and the lower tail of available generation. Because of this, relevant data in the historic record are sparse. Moreover, for interconnected systems, the degree of statistical dependence in these extremes between systems can also have a sizeable impact on the level of risk in each system. This paper uses results from statistical extreme value theory (EVT) to fit smoothed joint distributions for the values of (demand minus available renewables) and of surplus/deficit dependencein a two-area system, using data from the Irish and Great Britain power system for examples.
As well as the statistical smoothing mitigating the consequences of limited volumes of data, the concept of asymptotic dependence provides a useful explanation of the strength of dependence. There is strong evidence that the deficits in the GB and Ireland systems are asymptotically independent, whereas there is evidence for asymptotic dependence in the distributions of (demand minus available wind capacity). This is consistent with the intuition that, when independent distributions of conventional capacity are convoluted with those of demand and wind, the dependence is weakened. The consequent use of a Gaussian copula to describe the dependence of deficits provides a convenient means of carrying out sensitivity analysis to the strength of relationship.