Geometry of power flow in negatively curved power grid

Motivated by the concept of the smart power grid, reliability of a power network is investigated from a topological viewpoint. Inspired from Riemannian geometry of manifolds, it is claimed that extreme load at specific parts of a large power grid can occur as a consequence of the local negative curvature in its hidden metric space. This paper contributes to four areas: (1) It draws a new course in the topological study of a power grid, which is, unlike most previous studies, in accordance with the electrical characteristic, not the topographical structure, of the power grid. (2) It extends the Riemannian geometry metaphor developed for data communication networks to the power grid, an area it has never pervaded. (3) It develops a unifying approach to deal with power and data networks, precisely at a juncture where the smart grid is bringing the two networks together. (4) It provides an analytical measure for the criticality of lines and stations in a bulk transmission system, which can find a place in reliability assessment and centralized flow control in the future smart grid.