## An Algorithm for Correlation Halving Distance Analysis of Renewable Energy Resources

##### Summary

Europe’s transition from fossil fuel energy to renewable energy sources requires
expensive changes to the continent’s electricity grid that should hold
up for decades. As renewable energy generation methods such as solar and
wind are heavily dependent on changes in the weather, there will be increased
variability in the power supply. To reduce this energy-meteorological variability,
areas of Europe’s grid that have low renewable energy generation correlation
must be discovered. By using conversion models on climate model
output to get relevant energy variables, there is hourly data available for solar
and wind energy capacity factors for each grid cell in Europe. Due to the
sheer number of grid cells in the data (21,019), calculating correlation between
all pairs of grid cells is not feasible without algorithm optimisation.
We introduce a novel metric called the "Correlation Halving Distance", which
gives the distance value that indicates at what distance the wind and/or
solar time series yield 0.5 correlation for any given grid cell. We also explore
optimised approaches to calculate the metric efficiently. Here we show
that one algorithm based on Active Learning, called Uncertainty Sampling,
performed the best on synthetic data and was chosen to be tested on real-world
data. In validation, Uncertainty Sampling yields a correlation value
of [0.5±0.05] in 87 out of a 100 experiments with random starting grid cells.
Additionally, each run calculated only 62 correlations on average, greatly
saving on computation cost compared to the brute force approach. We found
that the correlation halving distance values varied greatly by geography.
Grid cells in land-locked and mountainous eastern Switzerland and western
Austria show Correlation Halving Distance values of 105-110 km, while
grid cells in the North Sea area show values in the order of 435-440 km. The
metric could assist in future-proofing changes to Europe’s energy grid as it
transitions to renewable energy, given that many types of renewable energy
sources rely on specific weather conditions. Additionally, spatial interpolation
techniques could be utilised to estimate the Correlation Halving Distance
for cells to further reduce the number of computations.