  Because of the non-uniformity of the electric power CPS network and the
dynamic nature of the risk propagation process, it is difficult to quantify the
critical point of a cyber risk explosion. From the perspective of the
dependency network, this paper proposes a method for quantitative evaluation of
the risk propagation threshold of power CPS networks based on the percolation
theory. First, the power CPS network is abstracted as a dual-layered
network-directed unweighted graph according to topology correlation and
coupling logic, and the asymmetrical balls-into-bins allocation method is used
to establish a "one-to-many" and "partially coupled" non-uniform power CPS
characterization model. Then, considering the directionality between the cyber
layer and the physical layer link, the probability of percolation flow is
introduced to establish the propagation dynamic equations for the internal
coupling relationship of each layer. Finally, the risk propagation threshold is
numerically quantified by defining the survival function of power CPS network
nodes, and the validity of the proposed method is verified by the IEEE 30-bus
system and 150-node Barabsi-Albert model.
