Resiliently evolving supply-demand networks

TL;DR

This paper derives exact edge capacity conditions for supply-demand networks to maintain stability amid topology changes, decentralization, and intermittency, with applications to power grids and evolving network models.

Contribution

It introduces a method using Kirchhoff's laws to determine capacities ensuring network stability under various perturbations, advancing the design of resilient supply-demand systems.

Findings

Derived explicit capacity formulas for stable operation.

Analyzed impact on UK power-grid structure.

Validated results on simulated evolving networks.

Abstract

The ability to design a transport network such that commodities are brought from suppliers to consumers in a steady, optimal, and stable way is of great importance for nowadays distribution systems. In this Letter, by using the circuit laws of Kirchhoff and Ohm, we provide the exact capacities of the edges that an optimal supply-demand network should have to operate stably under perturbations. The perturbations we consider are the evolution of the connecting topology, the decentralisation of hub sources or sinks, and the intermittence of suppliers/consumers characteristics. We analyse these conditions and the impact of our results, both on the current UK power-grid structure and on numerically generated evolving archetypal network topologies.