# Accurate and reduced SISO Sequence Impedance Models of Grid-tied Voltage Source Converter for Small Signal Stability Analysis

## TL;DR

This paper develops accurate and simplified SISO impedance models for grid-tied voltage source converters, enabling easier stability analysis while maintaining precision, and discusses their limitations based on system parameters.

## Contribution

It introduces two types of SISO impedance models derived from MIMO systems, validated against measurements, and analyzes their impact on stability assessment.

## Key findings

- Accurate SISO model matches MIMO impedance in stability analysis.
- Reduced SISO model may produce incorrect results with large PLL bandwidth.
- Models validated through PSCAD/EMTDC measurements.

## Abstract

Impedance models are widely used in assessing small signal stability of grid-tied voltage source converter (VSC) systems. Recent research has proven that impedance models of grid-tied VSC in both dq and sequence domains are generally Multi-Input Multi-Output (MIMO) systems, and the generalized Nyquist criterion has to be applied for stability analysis to these MIMO systems. However, finding Single-Input and Single-Output (SISO) equivalents for this system is always appealing because of the simplicity and the convenience for physical interpretation when assessing the stability, compared to MIMO systems. This paper presents two types of SISO impedance models of grid-tied VSC system, one is derived from the strong grid assumption, and the other is from the closed-loop equivalence. The accuracy of these models is assessed with respect to the measured impedances in PSCAD/EMTDC, and their effects on the stability assessment were analyzed as well. It is proven that the accurate SISO model gives identical result as the MIMO (matrix-based) impedance model with respect to stability analysis. However, the reduced SISO model may lead to wrong results if the bandwidth of phase locked loop is large.

---
Source: https://tomesphere.com/paper/1704.04157