Synchronizing Stability Analysis and Region of Attraction Estimation of Grid-Feeding VSCs Using Sum-of-Squares Programming

Chen Zhang,Marta Molinas,Xu Cai,Zheng Li

doi:10.3389/fenrg.2020.00056

Abstract

Grid-synchronising Stability (GSS) is an emerging issue that exists in grid-feeding voltage-source converters (VSCs). Its occurrence is primarily related to the nonlinear dynamics of a type of vastly applied synchronization units - Phase-locked Loops (PLL). Dynamic characterisation and modelling for the GSS analysis can be achieved by using a simplified system model, which is a second-order and autonomous nonlinear equation; however, with the presence of an indefinite damping term. As revealed and demonstrated in this work, this indefinite damping effect can result in an inaccurate Region-of-Attraction (ROA) estimation of the traditional Equal Area Principle (EAP)-based method. To overcome this issue and achieve a valid ROA estimation, this paper adopts the sum-of-squares (SOS) programming technique, which is a numeric optimisation method with SOS relaxations. The development and implementation of the SOS program for ROA estimation are presented. Numerical case studies and time-domain verifications demonstrate that this method is valid for GSS analysis, and an almost precise estimation is achieved in the first quadrant. This evidence makes the SOS method a promising tool for GSS analysis because the GSS problem is most concerned with the stability within the first swing cycle, i.e., in the first quadrant.

Highlights

Voltage-source converters (VSCs) are becoming ubiquitous in electric power systems
Based on the procedure illustrated in Global Stability and Its SOS Program, and adding the non-negative condition of the Lyapunov function (LF), the following SOS problem for ROA estimation in a general sense can be obtained: Maximize β over s1, s2, c such that
It can be seen that in terms of the Grid-synchronizing Stability (GSS) analysis, where the focus is on the stability of the first swing cycle, the SOS-based method is rather accurate since its ROA estimation is similar to the exact one if compared in the first quadrant

Summary

INTRODUCTION

Voltage-source converters (VSCs) are becoming ubiquitous in electric power systems. According to their functionalities, they can be broadly classified as either grid-feeding and grid-forming. This analysis demonstrates that the EAP can result in misleading results if applied to the ROA estimation of the GSS, and the reason lies in the indefinite damping effect of the GSS model To overcome this issue and achieve an improved ROA estimation, the SOS programming technique (Prajna et al, 2002) will be adopted and presented . Based on the procedure illustrated in Global Stability and Its SOS Program, and adding the non-negative condition of the LF, the following SOS problem for ROA estimation in a general sense can be obtained: Maximize β over s1, s2, c such that. It can be seen that in terms of the GSS analysis, where the focus is on the stability of the first swing cycle, the SOS-based method is rather accurate since its ROA estimation is similar to the exact one if compared in the first quadrant. This time-domain study again demonstrates that the EAP-based ROA estimation is inaccurate and leads to a misleading stability result, as can be seen from Figure 7B, where point B is inside the estimated ROA while the time-domain result turns out to be unstable

CONCLUSIONS

DATA AVAILABILITY STATEMENT