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The complexity of power systems continue to increase as load demands grow and new energy technologies emerge. Efficient methodologies and instrumentation are needed for real time monitoring and control of power systems. Accurately tracking the state variables (rotor angle and speed) is necessary for monitoring system stability conditions and assessing the risks of large-scale system collapse. Previous work proposed an extended Kalman filter (EKF) method, which makes use of data from phasor measurement units (PMU) and corrects the estimation predicted by the system model, for real-time tracking of system dynamics. This paper will explore how the number and locations of PMUs installed in the system should be determined to ensure satisfactory performance of the EKF-based tracking. Finding the optimal PMU placement, i.e., attaining whole system observability with the fewest PMUs, is very difficult to solve. In this paper, a novel search algorithm is presented for determining PMU placement (location and quantity). The algorithm determines a placement that gives small tracking error in polynomial time, while the optimal placement would be determined in exponential time. A modified, scalable algorithm is also presented. Observability of grid dynamics is considered in the sense that all the state variables can be tracked dynamically. Furthermore, observability in the presence of faults is considered. Simulation results for a 16-machine system and a 50 machine system are provided.