Geometric Decentralized Stability Certificate of Power Electronics-Dominated Power Systems Covering Variable Operating Points

Jul 16, 2026

Power electronics integration is reshaping power-system dynamics while making stability assessment difficult due to strong grid–converter interactions and the curse of dimensionality. Stability depends on each converter’s operating point, defined by voltage magnitude as well as active and reactive power, creating a combinatorial set of conditions to be evaluated. This work introduces a geometric decentralized stability certificate for PE-dominated systems that covers heterogeneous converters and variable operating points. The certificate is decentralized, modular, and scalable, using Davis–Wielandt shell projections to visualize and guide worst-case search. An efficient algorithm computes stability margins and certified operating regions, validated on 1- and 54-converter wind systems.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages11

Reading Time28 min

Introduction

Operating-point dependence and computational challenge

Related decentralized stability certificates

Geometric Decentralized Stability Certificate of Power Electronics-Dominated Power Systems Covering Variable Operating Points Ruohan Leng, Linbin Huang, Liangxiao Luo, Huanhai Xin, Xiongfei Wang, and Florian Drfler arXiv :2607 . 10335v1 [ ee ss . SY] 11 Jul 2026 Abstract—The integration of power converters is profoundly changing the power system dynamics and poses significant challenges for stability analysis. The dynamic interactions between the power grid and the heterogeneous converters are highly complex and difficult to analyze due to the curse of dimensionality. Moreover, system stability varies with the operating points, which are determined by the voltage magnitude, active power, and reactive power of each converter. This further complicates the analysis as it is difficult to enumerate and examine all the possible operating points. To tackle these challenges, this paper proposes a geometric decentralized stability certificate for power electronics (PE)-dominated power systems, which can simultaneously handle heterogeneous power converters and their variable operating points. The certificate can be checked in adecentralized and modular manner, and it is scalable for largescale power systems. Our approach is developed based on the concept of Davis-Wielandt (DW) shell and its projections, which can effectively visualize the characteristics of high-dimensional complex matrices. We investigate how the projections of the DW shell vary with operating points and how this variation can guide the search for worst-case operating conditions. We further propose an efficient algorithm to compute the stability margin and construct the certified operating regions. The effectiveness of the proposed method is validated through case studies on singleconverter and 54-converter wind power systems. Index Terms—Decentralized stability analysis, DW shell, converters, power system dynamics, small-signal stability, x-z graph. I. INTRODUCTION Due to the developments of renewable energy generation, high-voltage DC transmission, and energy storage systems, modern power systems are evolving toward power electronics (PE)-dominated power systems where PE converters are widely used for energy conversion [1]–[3] . The stability analysis of PE-dominated power systems has long been considered an intricate task due to the complex dynamic interactions between the power grid and heterogeneous converters. Moreover, since power systems contain nonlinear dynamics, their smallsignal stability highly depends on the operating points [4], i.e., the active and reactive power of the converters. For instance, it has been shown that a converter often has a lower stability margin at its maximum active power output [5] . This work was supported by the National Natural Science Foundation of China under Grant U24B6008 . Ruohan Leng, Linbin Huang, Liangxiao Luo, and Huanhai Xin are with the College of Electrical Engineering, Zhejiang University, Hangzhou 310027, China. (e-mail: {lengruohan, hlinbin, luolx, [xinhh](xinhh}@zju.edu.cn)[}](xinhh}@zju.edu.cn)[@zju.edu.cn](xinhh}@zju.edu.cn)). Xiongfei Wang is with the Department of Electrical Engineering, Tsinghua University, Beijing, China. (e-mail: [xiongfei@tsinghua.edu.cn](xiongfei@tsinghua.edu.cn)). Florian Drfler is with the Department of Information Technology and Electrical Engineering at ETH Z¨urich, Switzerland. ([e-mail: dorfler@ethz.ch](e-mail: dorfler@ethz.ch)) . The operating points of a PE-dominated power system are difficult to enumerate due to the high-dimensional combinatorial nature of all converters’ active and reactive power outputs. Hence, it is computationally challenging to examine system stability over all possible operating points [6] . It remains an open question how to ensure that a PE-dominated power system remains stable under all possible operating points. Existing studies have investigated the impact of operating points on small-signal stability from several perspectives.

FAQs

What problem does the proposed geometric decentralized stability certificate address?

It addresses stability analysis for power-electronics-dominated power systems where stability depends on variable operating points and where heterogeneous converter interactions make exhaustive evaluation computationally difficult.

How does the method handle heterogeneous converters and variable operating points?

It constructs a decentralized, modular geometric certificate that simultaneously covers heterogeneous power converters and their operating points, avoiding the need to enumerate all possible conditions.

What mathematical idea is used to guide the search for worst-case operating conditions?

The approach is developed from the Davis–Wielandt (DW) shell and its projections, which visualize characteristics of high-dimensional complex matrices and reveal how they vary with operating points.

Jul 16, 2026

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