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This paper looks into the vulnerabilities of the electric power grid and associated communication network, in the face of intermittent power generation and uncertain demand within a complex network framework of analysis of smart grids. The perspective is typical for the system of systems analysis of interdependencies in a critical infrastructure (CI), i.e., the smart grid for electricity distribution. We assess how the integration of the two systems copes with requests to increase power generation due to enhanced power consumption at a load bus. We define adequate measures of vulnerability to identify the most limiting communication time delays. We quantify the probability that a reduction in the functionality of the communication system yields a faulty condition in the electric power grid, and find that a factual indicator to quantify the coupling strength between the two networks is the frequency of load-shedding actions due to excessive communication time delay. We evaluate safety margins with respect to communication specifications, i.e., the data rate of the network, to comply with the safety requirements in the electric power grid. Finally, we find a catastrophic phase transition with respect to this parameter, which affects the safe operation of the CI.