  Harmonic instability occurs frequently in the power electronic converter
system. This paper leverages multi-resolution dynamic mode decomposition
(MR-DMD) as a data-driven diagnostic tool for the system stability of power
electronic converters, not requiring complex modeling and detailed control
information. By combining dynamic mode decomposition (DMD) with the
multi-resolution analysis used in wavelet theory, dynamic modes and eigenvalues
can be identified at different decomposition levels and time scales with the
MR-DMD algorithm, thereby allowing for handling datasets with transient time
behaviors, which is not achievable using conventional DMD. Further, the
selection criteria for important parameters in MR-DMD are clearly defined
through derivation, elucidating the reason for enabling it to extract
eigenvalues within different frequency ranges. Finally, the analysis results
are verified using the dataset collected from the experimental platform of a
low-frequency oscillation scenario in electrified railways featuring a
single-phase converter.
