Stability Analysis of Power-Electronics-Dominated Grids Using Scaled Relative Graphs

TL;DR

The paper presents a novel SRG-based framework for stability certification of grid-connected converters in converter-dominated grids. By decoupling grid and converter dynamics and extending the SRG analysis to nonlinear CPLs, it enables frequency-wise, geometry-preserving stability assessments that remain invariant to dq-frame transformations. The approach yields a cSCR-based criterion for GFL stability, provides a nonlinear stability theorem for CPL-influenced grids, and validates the methodology on IEEE 14-bus and 57-bus systems, showing improved insight over traditional gain/phase or passivity tests. The work offers a scalable, modular tool for assessing and designing stable inverter-dominated grids with high renewable penetration and nonlinear loads.

Abstract

This paper presents a novel approach to stability analysis for grid-connected converters utilizing Scaled Relative Graphs (SRG). Our method effectively decouples grid and converter dynamics, thereby establishing a comprehensive and efficient framework for evaluating closed-loop stability. Our analysis accommodates both linear and non-linear loads, enhancing its practical applicability. Furthermore, we demonstrate that our stability assessment remains unaffected by angular variations resulting from dq-frame transformations, significantly increasing the method's robustness and versatility. The effectiveness of our approach is validated in several simulation case studies, which illustrate its broad applicability in modern power systems.

Figures (22)

• Figure 1: A converter connected to a grid composed of an infinite bus in parallel to constant impedance and constant power load.
• Figure 2: Closed-loop dynamics of a converter-grid system
• Figure 3: (a) 2D SRG projection of the GFL with $f_{\text{pll}}=30$ Hz in green, with $f_{\text{pll}}=70$ Hz in blue, for $\omega\in [10^{-3},10^3]$Hz, and all allowable SCR in orange. (b) Zoom on the 2D projection. (c) 3D SRG of GFL with $f_{\text{pll}}=30$ Hz, for $f \in [9,17]$Hz with cSCR in orange. (d) 3D SRG of GFL with $f_{\text{pll}}=70$ Hz, for $f \in [20,30]$Hz with cSCR in orange.
• Figure 4: Frequency of the GFL converter with SCR=$\{1.67,1.74,2\}$ for $f_{\text{pll}}=30$Hz.
• Figure 6: (a) 3D $\operatorname{SRG}(y_{l}(s))\forall \omega\in [10^{-2},10^4]$Hz in blue (b) the exact 2D $\operatorname{SRG}(y_{cp})$ in yellow and $\operatorname{SRG}(\widehat{y_{cp}})$ as the hatched red disk. (c) $\operatorname{SRG}(\widehat{y_{cp}})+\operatorname{SRG}(y_{l}(s))$ in orange.

Theorems & Definitions (16)

• Remark 1
• Remark 2: Availability of admittance models
• Theorem 1
• Definition 1
• Lemma 1
• proof
• Lemma 2
• proof
• Remark 3: Frequency-wise CPL model
• Example 1: SRG of linear load, CPL and their sum