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The objective of this paper is to theoretically investigate the application of superconducting magnetic energy storage (SMES) system in damping power system low-frequency electromechanical oscillations. In the paper, the SMES system is studied in the context of a single-machine infinite-bus (SMIB) power system. The mathematical model of the SMIB power system including a SMES unit is established, and the Phillips-Heffron control structure of the power system is described. Based on the principle of the complex torque coefficient (CTC) method, the expression of the complex electromagnetic torque of the entire power system including the SMES unit is derived. A nonlinear proportion-integral-differential (PID) control strategy is proposed for the SMES system to enhance the power system damping. Simulation results demonstrate that the SMES is effective in damping the power system low-frequency oscillations and the proposed nonlinear PID controller is robust to regulate the SMES unit.