Augmented Sequence Impedance Networks of Grid-tied Voltage Source Converter for Stability Analysis

Impedance-based stability analysis normally splits an interconnected system into source and load subsystems and the stability of the closed loop system can be analyzed by the combined input-output gains of source and load. This is an intuitive approach in the case of Single-Input Single-Output (SISO) systems. However, in the case of grid-tied voltage source converter (VSC) systems, dq impedances of source and load (VSC) subsystems are typically Multi-Input Multi-Output (MIMO) systems in which case the Generalized Nyquist Criterion (GNC) is required for analyzing the closed loop stability, which increases the complexity of the analysis. Modeling the impedances in phase domain has been an alternative to remove the coupling due to passive elements e.g. inductance and capacitance. However, recent research has shown that also in the sequence domain there still exist couplings between sequences and they can be important for stability analysis, especially in the low frequency range. Therefore, it seems evident that matrix impedance models are required whenever accuracy is the first priority. This paper explores further the coupling between positive and negative sequence impedances, in particular the dependency and bindings between them. It shows that the couplings in each subsystem can be compounded into two non-coupled sequence impedances if the source and load subsystems are viewed as an integrated system instead of as two separate subsystems. Therefore, in this paper the closed loop gain is used instead of the minor loop gain for stability analysis. Subsequently, the closed loop gain is analytically derived using dq sequence impedances and two decoupled SISO systems are obtained which are defined as Augmented Sequence Impedance Networks (ASIN). From this, the stability analysis of the closed loop system can be performed directly on the loop impedance of ASIN with the principal of Argument. In order to justify the validity and accuracy, both numerical and time domain simulations are presented. In addition, the impact of PLL on sequence couplings and circuit dynamics are elucidated.