Influence models of cascading failure and frequency oscillation in the power grid

Power grid is a complex network of connected components interacting with each other. In this paper we focus on the random dynamics of both load cascading failure and the propagation of frequency oscillation in power grids. We effectively identify the vulnerable nodes by the steady state probabilities of influence model. Influence model is a type of inter-connected Markov chains that could efficiently model the interactive dynamic processes of networked components. We present the procedure to construct both homogenous and heterogeneous influence models using realtime frequency measurements. A low-complexity algorithm is proposed to compute the steady state probability of the Influence model. The computational complexity is dropped from O(N
⁶
) FLOPS to O(N
⁴
) for N-node networks. The computational memory space is reduced by 68%.