The Kirchhoff-Braess Paradox and Its Implications for Smart Microgrids
This work highlights a fundamental challenge for operators of smart microgrids, particularly as small-scale distributed generation becomes more prevalent.
The paper identifies the Kirchhoff-Braess paradox in electric power distribution networks, where adding a conductive line can increase congestion due to Kirchhoff's laws, and argues this phenomenon poses challenges for microgrids with increasing distributed generation.
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.