Sequence Domain SISO Equivalent Models of a Grid-Tied Voltage Source Converter System for Small-Signal Stability Analysis

This paper presents a generalized method for converting multi-input and multi-output (MIMO) dq impedance model of a grid-tied voltage source converter system into its sequence domain single-input and single-output (SISO) equivalents. As a result, two types of SISO impedance models were derived, one of which was derived from relatively strong and dq symmetric grid assumption (reduced SISO model) and the other was based on closed-loop equivalent (accurate SISO model). It was proven that the accurate SISO model has the same marginal stability condition as the MIMO model. Accuracy of these models is assessed with respect to the measured impedances in PSCAD/EMTDC simulations, their effects on stability are analyzed as well. Findings show that the accurate SISO model presents identical stability conclusions as the MIMO model. However, the reduced SISO model may lead to inaccurate results if the system is highly dq asymmetric, e.g., VSC with fast phase-locked loop or an actively controlled grid.