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Power grids are operated in an increasingly complicated environment. However, operators lack effective and accurate tools for real-time monitoring and control of power systems. The U.S. Department of Energy, along with several utilities and system operators, is making a major $108 million investment in the Western Interconnection for phasor measurement unit (PMU) installation and phasor application development. This phasor measurement network opens up many opportunities for the estimation and prediction of power system states in real time, which enable operators to evaluate the system dynamic security in advance and allow them more time to respond to disturbances. Kalman filter based dynamic state estimation offers a solution suitable for this purpose. Our work indicates that the performance of Kalman filters in dynamic state estimation would degrade if PMU measurements cannot adequately capture the system dynamics. This paper develops a framework to identify how to place PMUs to improve dynamic observability of the power grid. Simulation results validate the concept, and the guidelines for PMU placement are derived.