Modeling and Stability Analysis of Grid-Following Voltage-Source Converters Utilizing Individual Channel Design Method

Current controllers of three-phase grid-following voltage source converters (VSCs) are usually designed without considering dynamics of phase-locked loop (PLL) or frequency-locked loop (FLL). However, neglecting the impact of these synchronization units can lead to inaccurate robustness and stability assessment results. This paper proposes a general framework for the modeling and stability analysis of grid-following VSCs. It is applicable to combinations of different current controllers and synchronization techniques. Firstly, the system is described in the complex domain and linearized by using Wirtinger calculus. The obtained small-signal multiple-input multiple-output (MIMO) model reveals that the synchronization unit causes coupling between the original and complex conjugate systems. Then, by using individual channel design (ICD) approach, the cross-coupling effects are evaluated, and an equivalent single-input single-output (SISO) description of the MIMO model is established. Next, stability analysis procedure, applying Nyquist criterion to the equivalent SISO model, is proposed. Simulation results are provided to validate the effectiveness of the proposed methodology.