Dual theory of transmission line outages

TL;DR

This paper introduces a dual graph formalism for analyzing transmission line outages, offering a faster computation method for LODFs and new physical insights into outage effects in power networks.

Contribution

The paper presents a novel dual graph approach that simplifies and accelerates the calculation of line outage distribution factors and enhances understanding of outage propagation.

Findings

New formula for LODFs that is faster and more general

Single line outages induce flow changes similar to electrostatic dipoles in planar networks

Dual formalism provides physical insights into outage effects

Abstract

A new graph dual formalism is presented for the analysis of line outages in electricity networks. The dual formalism is based on a consideration of the flows around closed cycles in the network. After some exposition of the theory is presented, a new formula for the computation of Line Outage Distribution Factors (LODFs) is derived, which is not only computationally faster than existing methods, but also generalizes easily for multiple line outages and arbitrary changes to line series reactance. In addition, the dual formalism provides new physical insight for how the effects of line outages propagate through the network. For example, in a planar network a single line outage can be shown to induce monotonically decreasing flow changes, which are mathematically equivalent to an electrostatic dipole field.