I. Introduction
In modern power systems, sub-synchronous oscillations (SSO) or sub-synchronous resonance (SSR) are mainly caused by resonances between power electronic devices and compensators [1]–[3] or weak transmission lines [4], [5]. Compared with the SSOs caused by the torsional vibration of traditional steam turbine shaft systems, the resonance mechanism of SSO caused by power electronic devices is more complicated, and the oscillation characteristics are more variable, which in turn has a severe impact on power systems. These SSOs will significantly limit the power generation of renewable energy or even cause system instability. Therefore, it is necessary to accurately identify the parameters of the voltage and current instantaneous signals during SSOs to monitor the occurrence and spreading of SSOs effectively [6], thereby mitigating SSOs [7]–[9]. Early studies have shown that SSOs can be monitored based on synchrophasors, and the frequency of sub-synchronous oscillations can be identified [10], [11]. However, since synchrophasors can only provide synchronized fundamental phasors rather than instantaneous signals, it is difficult to identify other sub-synchronous parameters based on synchrophasors, e.g., the amplitudes and phases [10], [12], [13].