Key Takeaways & Executive Findings
- •• • Full-order small-signal state-space equations derived for GFL/GFM converters, capturing complete circuit and control dynamics; this eliminates the reduced-order approximations common in stability studies, enabling one-to-one correspondence between theoretical and simulation models, which is critical for mechanism research and parameter tuning. • • Modular white-box model implemented on CloudPSS with per-unit and single-machine multiplier equivalence; the model supports different voltage levels and rated capacities, allowing the same model to represent various devices (wind, PV, storage, SVG) by adjusting module combinations and parameters, thus reducing model development time and enhancing reusability. • • Validation against time-domain EMT simulations confirms accurate small/large disturbance responses; sensitivity analysis reveals that short-circuit ratio, reactance-resistance ratio, and double-loop PI parameters significantly affect stability margins, providing quantitative guidance for control parameter design and grid strength assessment. • • The model is integrated into a hybrid AC/DC grid standard test system, demonstrating high simulation efficiency; the open-source release on CloudPSS facilitates community-driven standardization of EMT models for renewable energy converters, addressing the lack of standardized white-box models in the industry.
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Abstract
The large-scale integration of power electronic converters in high-proportion renewable energy systems imposes stringent requirements on the accuracy and extensibility of grid-following (GFL) and grid-forming (GFM) converter models. This paper derives a theoretical model of GFL/GFM grid-connected converters that accounts for complete circuit and control dynamics, and constructs an open-source white-box converter model on the CloudPSS electromagnetic transient (EMT) simulation platform. The model adopts per-unit and structural design for electrical topology, control loops, and multiplier equivalence, enabling simulation of converters with various voltage levels and rated capacities. Theoretical calculations and simulation results demonstrate that the model exhibits accurate disturbance response, flexible parameter configuration, strong extensibility, and high simulation efficiency. The model provides a foundation for constructing a standardized EMT model library for renewable energy converters. The full-order small-signal state-space equations are provided, and the conversion between per-unit time and named time is derived. Case studies validate small/large disturbance responses, parameter sensitivity (short-circuit ratio, reactance-resistance ratio, PI parameters), and simulation efficiency in a hybrid AC/DC grid standard test system. The model and test cases are publicly available on the CloudPSS official website.
1. Introduction
Existing electromagnetic transient (EMT) simulation models for grid-connected converters suffer from three critical limitations: (1) disparate model architectures and parameters across simulation platforms, lacking modular theoretical models for mechanism research; (2) black-box models from manufacturers obscure signal processing and internal dynamics, hindering researcher modification and extension; (3) reduced-order state-space and transfer function models used for stability analysis omit non-dominant dynamics, causing discrepancies between theoretical and simulation results. These issues impede accurate transient analysis and standardized model development for high-proportion renewable energy systems.
This work addresses these bottlenecks by deriving a full-order small-signal state-space model that includes complete circuit and control dynamics for both grid-following (GFL) and grid-forming (GFM) converters. Based on this theoretical foundation, a modular, per-unit, white-box EMT model is constructed on the CloudPSS platform. The model features open interfaces, structural flexibility, and single-machine multiplier equivalence, enabling simulation of various converter-based devices (wind, PV, storage, SVG) under different voltage levels and capacities. The model's accuracy is validated through small/large disturbance tests, and its efficiency is demonstrated in a hybrid AC/DC grid standard case. The open-source release aims to support the construction of a standardized EMT model library for renewable energy integration.
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LAI Qiping, LI Tao, WANG Jili, SHEN Yi, LI Shuman, CAO Yuqi, SHEN Chen, LÜ Jinli (2026). Open-Source Electromagnetic Transient White-Box Model of Converters for Renewable Energy Grid-Connected System Analysis. Power Automation Equipment. https://doi.org/10.16081/j.epae.202606025
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Frequently Asked Questions
What specific numerical discrepancies between theoretical calculations and EMT simulations were observed, and how were they resolved?
The paper reports that the state-space theoretical calculations and time-domain EMT node analysis algorithm yield consistent results for small/large disturbance responses. The conversion between per-unit time and named time was derived to align the theoretical model with simulation software. No significant discrepancies were found after applying the conversion, validating the model's accuracy.
How does the model handle parameter sensitivity, particularly regarding short-circuit ratio (SCR) and reactance-resistance ratio (X/R), and what are the stability implications?
Sensitivity analysis reveals that SCR and X/R ratio significantly affect stability margins. For GFL converters, lower SCR (weak grid) leads to oscillations, while GFM converters exhibit better stability in weak grids but poorer stability in strong grids. The model allows quantitative assessment of these effects, enabling parameter tuning for stable operation across grid conditions.
What is the simulation efficiency gain compared to conventional detailed models, and what are the computational bottlenecks?
The paper states that the model achieves high simulation efficiency, though exact speedup factors are not provided in the extracted text. The modular and per-unit design reduces computational burden by avoiding redundant calculations. The model is integrated into a hybrid AC/DC grid standard case, demonstrating practical applicability. Bottlenecks may arise from the full-order state-space representation, but the white-box structure allows optimization.
How does the single-machine multiplier equivalence ensure accuracy when scaling to multiple converters, and what are the limitations?
The single-machine multiplier equivalence assumes identical converter dynamics and aggregated grid impedance. This is valid for converters with similar control parameters and operating points. Limitations include potential inaccuracies when converters have heterogeneous parameters or when interactions between converters are significant. The model's modularity allows extension to multi-machine scenarios by replicating modules.
What are the key challenges in adopting this white-box model for industrial standardization, and how does it compare to existing black-box models?
The white-box model provides open interfaces and transparent dynamics, enabling researchers to modify and extend it, unlike black-box models. Challenges include the need for user expertise in state-space modeling and parameter tuning. However, its per-unit and modular design facilitates standardization. Compared to black-box models, it offers greater flexibility and accuracy for mechanism research, though it may require more computational resources for full-order simulation.
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