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Due to the wide frequency range of sub-synchronous oscillations (SSOs) in converter-tied grids, existing SSO parameter estimators generally use a long window to pre-identify the SSO frequency, and thus generally have slow responses in SSO parameter estimation. To deal with this problem, this paper proposes an online SSO stability analysis-based SSO parameter estimator. The operating condition of the grid is updated online by measuring the fundamental voltage/current phasor. Then the impedance of the converter is updated based on the identified operating condition, and the SSO stability is analyzed online. If an unstable SSO mode is detected, the identified SSO frequency is used to build the imaginary exponential function-based signal model, and the SSO parameters are estimated based on the least square method. Case studies show that the proposed method has a much faster response than the methods recently published in the literature, and can obtain accurate SSO parameter estimates. • A new SSO estimator is shown • SSO analysis results are used • It is fast and accurate [ABSTRACT FROM AUTHOR]