arXiv subjects

Liangxiao Luo

Publications and source records attributed to Liangxiao Luo.

4 recordsLinked to original sources

arXiv2026

Impacts of Heterogeneous Grid-Forming Devices on Power System Dynamics Quantified by DW Shells

The concept of grid-forming (GFM) converters has gained great attention in the past years. However, it remains challenging to analyze and quantify the impacts of heterogeneous GFM devices (e.g., GFM energy storage systems, GFM wind turbines, GFM HVDC stations) on power system dynamics, especially when taking into account the complex interaction between GFM converters and grid-following (GFL) converters. To this end, this paper focuses on the decentralized and scalable stability analysis of power systems containing both GFM and GFL converters, where we use Davis-Wielandt (DW) shells to characterize the dynamics of the converters and the power grid. In particular, we analytically derive how integrating heterogeneous GFM converters affects the DW shell of the power grid and therefore the system stability. Our approach does not require the detailed parameters or control schemes of the GFM converters; instead, we define the local passivity and imaginary-axis indices of GFM converters to compactly describe their characteristics. These two indices can be conveniently obtained by testing a GFM converter and greatly simplify the stability analysis and computation when handling large-scale power systems.

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arXiv2026

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

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 a decentralized and modular manner, and it is scalable for large-scale 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 single-converter and 54-converter wind power systems.

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arXiv2026

Quantifying Grid-Forming Behavior: Bridging Device-level Dynamics and System-Level Strength

Grid-forming (GFM) technology is widely regarded as a promising solution for future power systems dominated by power electronics. However, a universally accepted definition of GFM behavior and precise method for its quantification remain elusive. Moreover, the impact of GFM converter on system stability is not precisely quantified, creating a significant disconnect between device and system levels. To address these gaps from a small-signal perspective, at the device level, the paper introduces a novel metric, the Forming Index (FI) to quantify a converter's response to grid voltage fluctuations. Rather than enumerating various control architectures, the FI provides a metric for the converter's GFM ability by quantifying its sensitivity to grid variations. At the system level, a new quantitative measure of system strength that captures the multi-bus voltage stiffness is proposed, which quantifies the voltage and phase angle responses of multiple buses to current or power disturbances. The paper further extends and defines this concept to grid strength and bus strength to identify weak areas within the system. Finally, the device and system levels are bridged by formally proving that GFM converters enhance system strength. The proposed framework provides a unified benchmark for GFM converter design, optimal placement, and system stability assessment.

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arXiv2025

Geometric Decentralized Stability Certificate for Power Systems Based on Projecting DW Shells

The development of decentralized stability conditions has gained considerable attention due to the need to analyze multi-agent network systems, such as heterogeneous multi-converter power systems. A recent advance is the application of the small-phase theorem, which extends the passivity theory. However, it requires the transfer function matrix to be sectorial, which may not hold in some frequency range and will result in conservativeness. To address this issue, this paper proposes a geometric decentralized stability condition based on Davis-Wielandt (DW) shell and its projections. Our approach provides a geometric interpretation of the small-gain and small-phase theorems and enables decentralized stability analysis of power systems. It serves as a visualization method to understand the closed-loop interactions and assess the stability of large-scale network systems in a scalable and modular manner.

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