This paper systematically analyzes the relationships among the $dq$-domain, $αβ$-domain, and sequence-domain representations used in small-signal impedance modeling of voltage-source converters (VSCs). It is shown that the AC impedance matrix expressed with $dq$-complex and $αβ$-complex variables leads to different formulations in the sequence domain. The study demonstrates that asymmetric systems exhibit different physical phenomena in the rotating and stationary reference frames; therefore, the transformations between these frames are not physically consistent in such cases. It is also demonstrated that the so-called modified sequence-domain impedance is equivalent to the universal impedance model in the frequency domain. The analysis clarifies several notational inconsistencies found in the literature. Finally, a physical interpretation is presented highlighting the implications of using stationary and rotating reference frames for stability analysis of power converters.
The whole-system impedance model has proven a powerful tool for assessing the small-signal stability of multi-inverter power systems; however, its application is limited to a small range around a steady-state operating point due to the inherent assumptions of time invariance and…
Large-scale power networks are often organized by geography, ownership, or control authority, making stability certificates that require a fully assembled global model challenging. This paper develops a time-domain small-signal stability certification framework for grid-forming i…
We present a swing-equation model with generalized and equilibria-dependent inertia, damping, and synchronization constants for energy conversion interfaces with second-order active-power versus voltage-phasor-angle dynamics connected to an infinite bus. The model is unified in t…
Dynamic grid stability is traditionally ensured with synchronous generators. Modern grids rely substantially more on inverter-based resources, which require grid-forming control to guarantee adequate system-wide synchronization and stability. Small-signal stability has granted va…
Small-signal instabilities, such as unforced sub-synchronous oscillations (SSOs), are increasingly observed in inverter-based resource (IBR) dominated grids. While decentralized stability certificates offer a scalable means to avoid instability onset, they are typically derived u…
Electrical railway harmonic instability issues are common in the high-frequency range. The effective frequency of the traditional converter's small-signal averaging model is below 1/2 switching frequency since the pulse width modulation (PWM) sideband harmonic components are igno…