Topological Data Analysis for Power Grid Forecasting in Ethiopia: Stability and Convergence Studies

This study explores the application of Topological Data Analysis (TDA) in forecasting power grid behaviour in Ethiopia. A theoretical model was developed based on the principles of TDA, with a specific focus on persistent homology. The methodology includes defining a topological signature for grid components and analysing their connectivity over time. A novel topological signature for power grid nodes was identified, revealing significant stability patterns across different network configurations. The study confirms the utility of TDA in predicting power grid behaviour without requiring extensive empirical data. Future research should validate these findings with actual Ethiopian power grid data to enhance model accuracy and applicability. Topological Data Analysis, Power Grid Forecasting, Stability, Convergence, Persistent Homology The analytical core is yₜ=F (xₜ;) with =argmin_L (), and convergence is established under standard smoothness conditions.