Curvature, Entropy, Congestion Management and the Power Grid

Abstract

This work develops a congestion management method for the power grid utilizing the notion of curvature. It initially uses the curvature concept to detect areas prompt to congestion (negative curvature areas) and it subsequently applies load balancing techniques (through FACTS devices) and load (storage devices) deployment to maximize curvature (grid decongestion) and cost-effectively minimize the generated energy throughout the grid, while at the same time guaranteeing stability under phase angle and voltage constraints. Two different curvature definitions are compared (Ollivier-Ricci Curvature and Effective Resistance Curvature), and an entropy concept suitable to power grid is introduced as a new measure to analyze grid congestion.