Kuramoto-like model is adopted to model a power grid reasonably. And critical synchronization coupling strength and average synchronization error are used to describe synchronization ability and robustness of a power grid, respectively. It is found that power distribution of generators has a great influence on transmission power of lines, and the more high-load lines in power grid, the more difficult the network synchronization. Based on the discovery, we calculate transmission power of each line under uniform power distribution method of generators (EG mode). Then, based on a power flow tracking algorithm, an non-uniform power distribution method (TG mode) of the generators is further proposed. With this method, as the total amount of power generated is given, power of the hub generator node is increased and power of the edge generator node is reduced. It shows that the new power distribution strategy reduces effectively critical synchronization coupling strength and average synchronization error. Thus the method improves synchronization performance and robustness of a power grid.

We use Kuramoto-like model as node model of power grids, and use local order parameters to describe local synchroniz ability. It shows that nodes with high power are difficult to locally synchronize to their direct neighbors. We propose a heterogeneous distribution method for network coupling strength. Keeping the total coupling strength, we increase coupling strength of links between high power nodes and their direct neighbor nodes, as well as links between other related nodes, and reduce coupling strength of links between the rest nodes. It shows that the method reduces critical synchronous coupling strength and improve synchronization performance in a certain range. As heterogeneity of the coupling strength is too great, synchronization performance of the network begins to deteriorate.

In order to identify key nodes in network effectively, a comprehensive index of node importance recognition which considers local and global characteristics of network is proposed. Nodes in weighted standard test system IEEE39 and IEEE118 are sorted according to importance based on this index. Ranking results are compared with those based on betweenness centrality method and point weight method. Meanwhile these important methods of node recognition are compared using structure-based network efficiency analysis and dynamics-based loss-of-synchronization diffusion time and synchronization capability. It shows that ranking of node importance based on comprehensive index is more reasonable, which is superior to node recognition method based on betweenness centrality and point weight.

We present a cluster immunization strategy and study its immune effect on scale-free network with tunable clustering in a modified classic rumor propagation model. Study shows that effect of cluster immunization becomes better with increasing of network clustering coefficient. Several immunization strategies including target immunization, betweenness immunization, closeness immunization and cluster immunization are compared. It shows that betweenness immunization is always the best regardless of network clustering. As a network clustering coefficient is relatively great,effect of cluster immunization is better than that of closeness immunization and close to target immunization. With further increasing network clustering coefficient,cluster immunization exceeds target immunization and approaches to betweenness immunization.

We study cascading failures of the western United States power grid under three attack strategies,Initial load of an edge ij is defined as(k_ik_j)^θ with k_iand k_j the degrees of nodes connected with the edge,where θ is a tunable parameter.Three attack strategies are LL(attack on edges with the lowest load),SPC(attack on edges with the smallest proportion between total capacities of neighboring edges and capacity of the attacked edge)and HL(attack on edges with the highest load).It is observed that cascading failure scales are quite different under three attack strategies with different θ.Analyzing topology of the power grid in detail,we study otherness of cascading failures under three attack strategies.It shows that select ranges of attacked edges are not varied with θ under strategies of HL and LL.Attack effect of HL is enhanced with increasing θ,however,attack effect of LL is weaken with increasing θ. Select ranges of attacked edges of SPC varies with θ.At a small θ,attacked edges of SPC are belong to LL with a special topology,As θ increased,attacked edges of SPC tend to those edges with relatively high loads.Consequently,attacked effect of SPC is close to that of LL with a small θ and it is close to that of HL with a great θ.