# Student Research Article - Nestor Sanchez

PhD Student Nestor Sanchez has written the following article as part of our series of Student Research Articles!

Power blackouts and shortfalls can occur for many reasons and originate at different components of the power grid. My work focusses on measuring the risk of having too little generation capacity to cover a country's power demand at any time, which can occur, for example, when there is a particularly cold winter in which power demand becomes very large, or when generators fail unexpectedly. In Great Britain, capacity auctions take place yearly to ensure enough generation is available for future years; these and other measures have to be based on sound statistical models that output good risk estimates. The models I am working on incorporate the existence of interconnectors to other power systems, such as the Irish one, and the gradual replacement of conventional generators by renewable energy, which is intermittent and could increase the variability of system reserves.

Risk of insufficient power generation comes almost entirely from the tails of the conventional generation and net demand distributions, which means that at least one among abnormally high demand and abnormally low available generation (due to unexpected generator failures or low renewable output) is to blame. Data from the tails are rare by definition, but extreme value theory offers powerful closed-form asymptotic results that allows extrapolation of distribution beyond the data range under very mild conditions. These results are like a central limit theorem for sample maxima instead of sample averages, and allow us to calculate probability mass and other metrics in the regions of interest into the tails.

By taking into account interconnectors to other systems this becomes a problem in multivariate extreme value theory, as the extent to which interconnectors help offset risk strongly depends on the statistical dependence structure between extreme values at both systems. If extremes are highly dependent at both areas (say, if the same weather system affects both countries, driving demand up or renewable generation down at the same time) then interconnectors will be less useful than expected, as neither country will have much spare power to export when needed. Modelling the dependence structure is a subtle problem: statistical dependence between two variables at extreme levels is not necessarily the same as at lower levels, and sparsity of data in the relevant regions makes it hard to clearly see which dependence model is best.

Another issue is how countries share power in such events: do they export only spare available power? Can they over-export so that they share the shortfalls, effectively acting like a large single system? There is a range of possible policies that countries can follow. These policies distort the regions of space that map to shortfall events in relatively complicated ways, so usually Monte Carlo estimation is the most practical way to quantify risk for extreme value models. This makes it important to be able to sample rare events efficiently from them.