The Kirchhoff-Braess Paradox and Its Implications for Smart Microgrids

TL;DR

This paper explores the Kirchhoff-Braess paradox in electrical grids, showing how adding lines can unexpectedly increase congestion, especially relevant for the future of smart microgrids with distributed generation.

Contribution

It introduces the Kirchhoff-Braess paradox in power networks, highlighting nonlinear congestion phenomena and implications for microgrid operation with distributed energy sources.

Findings

Adding a conductive line can cause nonlinear congestion increases.

The paradox can occur in any looped grid with distributed generation.

Implications for microgrid management and stability.

Abstract

Well known in the theory of network flows, Braess paradox states that in a congested network, it may happen that adding a new path between destinations can increase the level of congestion. In transportation networks the phenomenon results from the decisions of network participants who selfishly seek to optimize their own performance metrics. In an electric power distribution network, an analogous increase in congestion can arise as a consequence Kirchhoff's laws. Even for the simplest linear network of resistors and voltage sources, the sudden appearance of congestion due to an additional conductive line is a nonlinear phenomenon that results in a discontinuous change in the network state. It is argued that the phenomenon can occur in almost any grid in which they are loops, and with the increasing penetration of small-scale distributed generation it suggests challenges ahead in the operation of microgrids.