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Electric power transmission lines face increased threats from malicious attacks and natural disasters. This underscores the need to develop new techniques to ensure safe and reliable transmission of electric power. This paper deals with the development of an online monitoring technique based on mechanical state estimation to determine the sag levels of overhead transmission lines in real time and hence determine if these lines are in normal physical condition or have been damaged or downed. A computational algorithm based on least squares state estimation is applied to the physical transmission line equations to determine the conductor sag levels from measurements of tension, temperature, and other transmission line conductor parameters. The estimated conductor sag levels are used to generate warning signals of vertical clearance violations in the energy management system. These warning signals are displayed to the operator to make appropriate decisions to maintain the line within the prescribed clearance limits and prevent potential cascading failures.