Previous studies have demonstrated that disharmony among voltage-source-controlled units may occur on an AC transmission or distribution line under steady-state operating conditions or quasi-static operating conditions. To prevent disharmony oscillations from threatening the secure and stable operation of power grids, two novel disharmony oscillation suppression (DOS) methods are proposed in this paper. First, the oscillation characteristics of single-phase instantaneous current and power under disharmony operating conditions are investigated. The key parameters and typical indicators for monitoring disharmony oscillations, such as disharmony frequency and average power, are listed. Second, two DOS strategies are designed based on directly monitoring the frequency difference and indirectly monitoring line power, respectively. Finally, the characteristics of disharmony oscillations are thoroughly analyzed through a case study, and the proposed DOS strategies are validated in simulations using MATLAB/Simulink.