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The smart electric power grid will evolve into a very complex adaptive system under semi-autonomous distributed control. Its spatial and temporal complexity, non-convexity, non-linearity, non-stationarity, variability and uncertainties exceed the characteristics found in today's traditional power system. The distributed integration of intermittent sources of energy and plug-in electric vehicles to a smart grid further adds complexity and challenges to its modeling, control and optimization. Innovative technologies are needed to handle the growing complexity of the smart grid and stochastic bidirectional optimal power flows, to maximize the penetration of renewable energy, and to provide maximum utilization of available energy storage, especially plug-in electric vehicles.