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The collection and prompt analysis of synchrophasor measurements is a key step towards enabling the future smart power grid, in which grid management applications would be deployed to monitor and react intelligently to changing conditions. The potential exists to slash inefficiencies and to adaptively reconfigure the grid to take better advantage of renewables, coordinate and share reactive power, and to reduce the risk of catastrophic large-scale outages. However, to realize this potential, a number of technical challenges must be overcome. We describe a continuously active, timely monitoring framework that we have created, architected to support a wide range of grid-control applications in a standard manner designed to leverage cloud computing. Cloud computing systems bring significant advantages, including an elastic, highly available and cost-effective compute infrastructure well-suited for this application. We believe that by showing how challenges of reliability, timeliness, and security can be addressed while leveraging cloud standards, our work opens the door for wider exploitation of the cloud by the smart grid community. This paper characterizes a PMU-based state-estimation application, explains how the desired system maps to a cloud architecture, identifies limitations in the standard cloud infrastructure relative to the needs of this use-case, and then shows how we adapt the basic cloud platform options with sophisticated technologies of our own to achieve the required levels of usability, fault tolerance, and parallelism.