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The synchronized phasor measurement unit (PMU), developed in the 1980s, is considered to be one of the most important devices in the future of power systems. The recent development of PMU technology provides high-speed, precisely synchronized sensor data, which has been found to be useful for dynamic state estimation of the power grid. While PMU measurements currently cover fewer than 1% of the nodes in the U.S. power grid, the power industry has gained the momentum to advance the technology and install more units. However, with limited resources, the installation must be selective. Previous PMU placement research has focused primarily on network topology, with the goal of finding configurations that achieve full network observability with a minimum number of PMUs. Recently we introduced an approach that utilizes stochastic models of the signals and measurements, to characterize the observability and corresponding uncertainty of power system static states (bus voltage magnitudes and phase angles), for any given configuration of PMUs. Here we present a new approach to designing optimal PMU placement according to estimation uncertainties of the dynamic states. We hope the approach can provide planning engineers with a new tool to help in choosing between PMU placement alternatives.