Fluctuations of resources in complex networks such as power grids are common and it may cause the current flows to exceed the capacity limit of the transmission links and cause them to fail. The failure or breakdown of a transmission line can easily trigger cascading failures in the network. This problem receives renewed attention especially in power grids when renewable energy sources with large fluctuations such as solar and wind energy are increasingly deployed in power supply.

In this thesis, we introduce the message passing algorithm and discrete Green's function to elucidate how resource fluctuations determine flow fluctuations in links of a network with quadratic cost functions. The methods are also generalized to networks using general cost functions and our n...[ Read more ]

Fluctuations of resources in complex networks such as power grids are common and it may cause the current flows to exceed the capacity limit of the transmission links and cause them to fail. The failure or breakdown of a transmission line can easily trigger cascading failures in the network. This problem receives renewed attention especially in power grids when renewable energy sources with large fluctuations such as solar and wind energy are increasingly deployed in power supply.

In this thesis, we introduce the message passing algorithm and discrete Green's function to elucidate how resource fluctuations determine flow fluctuations in links of a network with quadratic cost functions. The methods are also generalized to networks using general cost functions and our numerical simulations show that the methods yield excellent agreement with simulation results when the fluctuations are not too high. 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.