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This paper puts forward a framework for estimating transmission line parameters (including series resistance, reactance and shunt susceptance), line temperature and sag utilizing synchronous voltage and current phasors measured by the phasor measurement unit (PMU) in real time. Transmission line parameters are essential inputs to various power system analyses and applications such as power flow analyses and protective relaying applications. The estimated line temperature and sag can be utilized in dynamic thermal rating applications for increased power transfer. Different types of transmission line topology are classified and modeled to facilitate the development of corresponding algorithms. The proposed least square algorithms harness the nonlinear optimal estimation theory, and are capable of detecting and identifying bad measurement data, minimizing the impact of measurement errors and thus significantly improving the estimation accuracy. In addition, this paper studies an optimal approach for placing PMUs in order to determine the line parameters, temperature and sag. Numerical examples and preliminary results are presented.