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

Abstract

Grid-synchronizing Stability (GSS) is an emerging issue related to grid-feeding voltage-source converters (VSCs). Its occurrence is primarily related to the non-linear dynamics of a type of vastly applied synchronization unit-Phase-locked Loops (PLL). Dynamic characterization and modeling for the GSS analysis can be achieved using a simplified system model, which is a second-order and autonomous non-linear equation, but 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 optimization 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.

A Lyapunov approach based on gravitational search algorithm for transient stability assessment of AC/DC systems with wind power

“…Numerical problems will have an impact on the results, which may make the continuity condition of the piecewise Lyapunov function on the switching boundary of various control modes unsatisfied. In [14], the SOS method is also used in the analysis of grid‐synchronizing stability of systems with voltage source converters. However, the validation models of the SOS method are still relatively simple, and the dynamic characteristics of renewable generators have not been taken into account.…”

“…In the SOS technique, Positivstellensatz (P-Satz) theorem or S-Procedure theorem is often used to construct optimiza-tion problems with SOS constraints. And some LF level set approaches such as V-s iteration can be used to solve the ROA problem [12,14]. Although the method of estimating the ROA based on LF is proven to be effective, there is still the problem of conservative estimation.…”

Transient Stability Analysis and Enhancement of PLL-VSC Considering State-Dependent Damping

“…In this paper, the PLL-based VSC system is mainly studied. For the transient stability analysis, several methods including the time-domain simulation, phase portrait, equal area criterion (EAC), energy function, bifurcation analysis, etc have been developed recently [8]- [17]. Although the time-domain simulation always shows the dynamic process properly and it has been broadly used to verify the accuracy of system modeling [9] and the efficiency of transient stability enhancement strategies [10], it is timeconsuming and inconvenient.…”

“…However, this method is difficult to be understood from the physical perspective. In [17], the sumof-squares programming technique was used to improve the accuracy of the stability region by considering the indefinite damping effect, but it was still conservative.…”

Transient synchronization stability of photovoltaics integration by singular perturbation analysis

“…The rotor motion is represented by the second-order swing equation within the electromechanical timescale (Kundur, 1994). For the transient stability analysis of power-electronic-dominated power systems, several approaches have been developed, including the time-domain simulation (Zhao et al, 2021), energy function (Zhang et al, 2022), equalarea criterion (Xu et al, 2023), phase portrait (Wu and Wang, 2020), hyperplane method (Ma et al, 2023a), basin of attraction (Zhang et al, 2020), and bifurcation analysis (Ma et al, 2022a). Usually, the transient synchronization of the VSC grid-tied systems belongs to the electromagnetic timescale, including the DC voltage control timescale and AC current control timescale (Yuan et al, 2017;Ma et al, 2023b).…”