The future electric power grids with high penetrations of renewables and distributed energy resources will experience significant variations in operating points that are larger in magnitude, faster in timescale, stronger in nonlinearity and in higher-dimensional space. These operating points constitute an non-flat space, or more mathematically, a manifold, that is hard to analyze its global structure. 

Non-Euclidean geometry, discovered independently by Carl Friedrich Gauss, Nikolai Lobachevsky, Janos Bolyai and further developed by Bernhard Riemann into differential geometry, specifically targets on revealing both local and global geometric properties of non-flat space. Hence, it is a very promising mathematical tool to study the global behavior of future power grids in high-variaility.