The most severe failures in power grids are often characterized as cascading failures where an initial event triggers consequent failures all along the grid often leading to blackouts. Upon identifying a failure and its cascade potential, timely control actions should be performed by the grid operators to mitigate the effect of the cascade. These actions have to be delivered to one or more control devices, creating a dependency between the power grid and its control network. This paper examines the dependency of the operation of the power grid on the control network. Different from literature studies on failure control, our dependency model captures the impact of networking parameters. We formulate an algorithmic model that describes the impact of this dependency on cascade control. Based on this model, we propose an efficient cascade control algorithm using load shedding with consideration of delays in the communication network for power grids. Finally, we evaluate the impact of the power-communication network dependency with uncontrolled grids, ideal/simple control grids and our proposed control scheme. The results demonstrate that the proposed algorithm can significantly reduce the failure of power lines while sustaining larger power demand for users.