# On the Network Topology Dependent Solution Count of the Algebraic Load Flow Equations

arXiv: https://arxiv.org/abs/1512.04987 · HTML: https://mlsanity.com/paper/1512.04987/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Dec 2015.

## Built on by (most cited first, 1 of 1)

- [Understanding the Behavior of Belief Propagation](https://mlsanity.com/paper/2209.05464/) (2022)

## Abstract (arXiv)

A large amount of research activity in power systems areas has focused on developing computational methods to solve load flow equations where a key question is the maximum number of isolated solutions.Though several concrete upper bounds exist, recent studies have hinted that much sharper upper bounds that depend the topology of underlying power networks may exist. This paper establishes such a topology dependent solution bound which is actually the best possible bound in the sense that it is always attainable. We also develop a geometric construction called adjacency polytope which accurately captures the topology of the underlying power network and is immensely useful in the computation of the solution bound. Finally we highlight the significant implications of the development of such solution bound in solving load flow equations.