Frequency-domain coupling in two-level VSC small-signal dynamics

Sequence impedance is a new tool for small-signal analysis and design of three-phase converters and systems, and has been proven effective especially for studying system resonance involving wind turbines, PV inverters and/or HVDC converters. As a small-signal characterization method, sequence impedance measures the response of current to a voltage perturbation at the same frequency. Under certain conditions, the current response at a frequency different from the frequency of the voltage perturbation may be significant and this has raised questions about whether sequence impedance analysis should be expanded to include such frequency-domain coupling in general. This paper is part of the effort to provide a practical answer to the question. A systematic method called multi-harmonic linearization is used to model small-signal responses of two-level voltage source converters (VSC) in a vector form that allows all possible coupling effects to be captured. Fast phase locked loop (PLL) design, and high dc bus impedance are identified as two common causes for possible coupling. A general small-signal model that takes into account both factors is developed and used to study the characteristics of coupling. Simplified models are then presented for two special cases each considering one of the factors to provide insights into how the degree of coupling depends on converter and circuit design. The coupled response is shown to be at a frequency which is apart from the injected perturbation by two times the fundamental frequency and is found to be most noticeable near the fundamental. The modeling and analysis results are validated by detailed circuit simulation.