In recent years, the application of smart grid system [1] ~ [5] in our lives is becoming more and more extensive. To a certain extent, the smart grid system has changed our way of life. Generally, the smart grid systems depend on two main networks: grid network (conventional power grid) and communication network (providing control function and communication function). In the work-in-progress, smart grid systems need power generation[6] using different kinds of energy sources e.g., fossil-fuels, solar, wind, geothermal, transmission of energy from source to destination, intelligent distribution by monitoring the demand of power in different regions, monitoring the power usage by customers using smart meters, and integrating other facilities e.g., plugged-in-electrical vehicles[7] . In this way, the smart grid systems change significantly and improve the energy usage efficiency in the last few years. In smart grid systems[3] ~ [5], communication network needs grid network to support power energy, while power stations are controlled by communication network. Thus, the two networks are connected and mutually interdependent. Then smart grid systems can be regarded as interdependent systems [8]~[9] . However, for interdependent system architecture, the failures in one network can lead to the cascading risk in another. For example, the breakdown of a power station network [10] could lead the corresponding cascading failure of some nodes in communication network, while in reverse faults in communication network might cause failures of the power station network. Especially, the cascading failures may even occur recursively between the two interdependent grid network and communication network. We call it cascade of failures. Cascading failures are big issues in such coupled networks. Understanding the underlying cascading failures patterns to protect interdependent smart grid systems is quite necessary. In order to improve the reliability of the smart grid systems, it is necessary to explore the cascading failures in interdependent smart gird systems. Recently many researchers have paid more attentions in this research field. Currents research [11]~[14] in smart gird systems mainly focuses on failures about load balancing and load distribution. Most of these techniques rely on methods commonly used in distributed systems. An architecture for distributed generation way, which can help prevent cascading failures, is described in Ref.[15].