An Algorithm for Correlation Halving Distance Analysis of Renewable Energy Resources

Abstract

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.