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Synchronized phasor measurements can potentially track the system dynamics between two classical state estimations. However, in the PMU configurations available nowadays and in the near future, those measurements are too scarce for the whole system state to be estimated. Therefore, we investigate the possibility to reconstruct coherent, time-synchronized system states from the available PMU data. State reconstruction is formulated as an optimization problem. The objective is to minimize, in the space of bus powers, the distance between the reconstructed state and the last state estimate provided by a standard state estimator. PMU data are imposed as equality constraints. Furthermore, the placement of PMUs near generators is advocated for higher accuracy of state reconstruction. The performance and potential benefits of the approach are illustrated by processing snapshots obtained from detailed time simulation of a test system subject to a disturbance and corrective actions.