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 distribution systems nowadays. In this work, 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, i.e., without overloading. The perturbations we consider are the evolution of the connecting topology, the decentralization of hub sources or sinks, and the intermittence of supplier and consumer characteristics. We analyze these conditions and the impact of our results, both on the current United Kingdom power-grid structure and on numerically generated evolving archetypal network topologies.
Highlights
Networks are ubiquitous in nature and in manmade systems
The perturbations we consider are the evolution of the connecting topology, the decentralization of hub sources or sinks, and the intermittence of supplier and consumer characteristics
Power and gas networks bring light and heat to our homes, telecommunication networks allow us to be entertained and to browse for information, and distribution networks allow manufacturers to supply foodstock and other products to the demand chain. In all of these cases, a basic problem needs to be addressed: how to create a network that transports the maximum load that can be moved from one point in the network to another by following optimal paths, without surpassing any edge or node capacity, and generates a steady stable flow
Summary
Networks are ubiquitous in nature and in manmade systems. Power and gas networks bring light and heat to our homes, telecommunication networks allow us to be entertained and to browse for information, and distribution networks allow manufacturers to supply foodstock and other products to the demand chain. We provide analytical expressions for the edge capacities that a steady optimal supply-demand network should have to operate stably under perturbations by using Kirchhoff’s flow network model.
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