# Analisis of the power flow in Low Voltage DC grids

## TL;DR

This paper proves that power flow solutions in low voltage DC grids are unique and convergent, providing a rigorous analysis that applies universally regardless of grid size, topology, or load conditions, supported by simulations.

## Contribution

It offers the first non-linear algebraic analysis guaranteeing convergence and uniqueness of power flow solutions in LVDC grids, unlike previous linearized approaches.

## Key findings

- Convergence and uniqueness are guaranteed for any LVDC grid.
- The analysis applies regardless of grid size, topology, or load.
- Simulations confirm the theoretical results.

## Abstract

Power flow in a low voltage direct current grid (LVDC) is a non-linear problem just as its counterpart ac. This paper demonstrates that, unlike in ac grids, convergence and uniqueness of the solution can be guaranteed in this type of grids. The result is not a linearization nor an approximation, but an analysis of the set of non-linear algebraic equations, which is valid for any LVDC grid regardless its size, topology or load condition. Computer simulation corroborate the theoretical analysis.