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Stability boundary analysis for grid-following (GFL) and grid-forming (GFM) inverters

Stability boundary analysis for grid-following (GFL) and grid-forming (GFM) inverters
Stability boundary analysis for grid-following (GFL) and grid-forming (GFM) inverters
Studying the dynamics and stability of inverter-driven power systems has become a top priority for grid operators in view of the massive renewable energy deployment. The simplest and most widely used model for stability analysis for such networks is the single-inverter single-bus (SISB) equivalent model. Although quite insightful, SISB models with an L-filter for the inverter suffer from implementation difficulties due to algebraic loops. This paper develops a closed-form SISB model for grid-following (GFL) and grid-forming (GFM) inverters and derives symbolic formulation for the linearized system, which resolves algebraic loops and obtains fast results with uncompromised precision. This model is then used in an N-Dimensional Stability Boundary Tracking (ND-SBT) algorithm, which identifies the stability boundary for GFL and GFM inverters. This is the first method to infer the stability region for an arbitrary number of dimensions in a computationally efficient and software-agnostic manner while preserving accuracy. A detailed sensitivity analysis yields useful findings on the stability impact of individual parameters, while the results are validated using the IEEE 14-bus system.
Grid-following inverter (GFL), Grid-forming inverter (GFM), Renewables integration, grid strength, small-signal analysis, stability boundary
1949-3029
Luo, Xi
cfaf6d5c-15fa-4c03-bdca-9e3d80ea448a
Batzelis, Stratis
2a85086e-e403-443c-81a6-e3b4ee16ae5e
Singh, Abhinav Kumar
6df7029f-21e3-4a06-b5f7-da46f35fc8d3
Luo, Xi
cfaf6d5c-15fa-4c03-bdca-9e3d80ea448a
Batzelis, Stratis
2a85086e-e403-443c-81a6-e3b4ee16ae5e
Singh, Abhinav Kumar
6df7029f-21e3-4a06-b5f7-da46f35fc8d3

Luo, Xi, Batzelis, Stratis and Singh, Abhinav Kumar (2026) Stability boundary analysis for grid-following (GFL) and grid-forming (GFM) inverters. IEEE Transactions on Sustainable Energy. (doi:10.1109/TSTE.2026.3665371).

Record type: Article

Abstract

Studying the dynamics and stability of inverter-driven power systems has become a top priority for grid operators in view of the massive renewable energy deployment. The simplest and most widely used model for stability analysis for such networks is the single-inverter single-bus (SISB) equivalent model. Although quite insightful, SISB models with an L-filter for the inverter suffer from implementation difficulties due to algebraic loops. This paper develops a closed-form SISB model for grid-following (GFL) and grid-forming (GFM) inverters and derives symbolic formulation for the linearized system, which resolves algebraic loops and obtains fast results with uncompromised precision. This model is then used in an N-Dimensional Stability Boundary Tracking (ND-SBT) algorithm, which identifies the stability boundary for GFL and GFM inverters. This is the first method to infer the stability region for an arbitrary number of dimensions in a computationally efficient and software-agnostic manner while preserving accuracy. A detailed sensitivity analysis yields useful findings on the stability impact of individual parameters, while the results are validated using the IEEE 14-bus system.

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Accepted/In Press date: 9 February 2026
e-pub ahead of print date: 16 February 2026
Keywords: Grid-following inverter (GFL), Grid-forming inverter (GFM), Renewables integration, grid strength, small-signal analysis, stability boundary

Identifiers

Local EPrints ID: 510708
URI: http://eprints.soton.ac.uk/id/eprint/510708
ISSN: 1949-3029
PURE UUID: 15c2232b-c7ee-4ced-982e-99bd05c6b31f
ORCID for Xi Luo: ORCID iD orcid.org/0000-0001-6654-5087
ORCID for Stratis Batzelis: ORCID iD orcid.org/0000-0002-2967-3677
ORCID for Abhinav Kumar Singh: ORCID iD orcid.org/0000-0003-3376-6435

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Date deposited: 17 Apr 2026 16:38
Last modified: 18 Apr 2026 02:10

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Contributors

Author: Xi Luo ORCID iD
Author: Stratis Batzelis ORCID iD
Author: Abhinav Kumar Singh ORCID iD

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