Admittance-based Ollivier-Ricci curvature for power grid structural robustness analysis

• An Ollivier-Ricci curvature using admittance matrix to analyze the structural robustness of power grids to cascading failures. • A curvature-based method for adding new transmission lines to improve the structural robustness of power grids. This paper investigates the structural robustness of power grids against cascading failures from a geometric perspective based on the Ollivier-Ricci curvature. A curvature metric based on the grid’s admittance matrix is proposed, based on which structurally fragile sub-networks, transmission lines, or buses can be identified without relying on power flow calculations. Then a method is proposed to strengthen the structural robustness of the grid by adding new transmission lines in order to increase the values of the most negative curvatures. Furthermore, the connection between the proposed admittance-based Ollivier-Ricci curvature and edge betweenness centrality index is shown. Experimental results for benchmark power grids including IEEE 118- and 145-bus systems demonstrate the effective performance of the proposed curvature metric and the grid hardening method in capturing and enhancing the structural robustness of power grids.