Stability enhancement against fluctuations in complex networks by optimal bandwidth allocation

Abstract

Fluctuations of resources in complex networks such as power grids are common and may cause current flows to exceed the capacity limit of the transmission links, resulting in failures. Such a failure can easily trigger cascading failures in the network. This problem can occur in power grids especially when renewable energy sources with large fluctuations such as solar and wind energy are increasingly deployed in power supply. In this work, we introduce the discrete Green’s function formulation to elucidate how resource fluctuations determine flow fluctuations in links of a network with a quadratic cost function. Furthermore, we develop an optimized bandwidth allocation scheme so as to minimize the number of failed links or the amount of excess flows in networks under fluctuations, given that the total bandwidth of the network is fixed. Compared with the conventional approach of proportionate bandwidth assignment, it is found that the optimized bandwidth allocation can highly enhance the stability of the networks against fluctuations.