Open Access

ARTICLE

Unified Modeling and Multi-Frequency Response Analysis of Grid-Forming Wind Power Converters under Different Grid Conditions

Yihua Zhu¹, Tianyu Jiang^2,*, Guanming Zeng¹, Haoxiang Zong², Chao Luo¹, Chen Zhang²
1 Electric Power Research Institute, China Southern Power Grid, Guangzhou, China
2 School of Electrical Engineering, Shanghai Jiao Tong University, Shanghai, China
* Corresponding Author: Tianyu Jiang. Email:

Energy Engineering https://doi.org/10.32604/ee.2026.085885

Received 20 May 2026; Accepted 20 July 2026; Published online 12 August 2026

Abstract

Grid-forming (GFM) wind power converters exhibit different small-signal frequency-response characteristics under symmetric and asymmetric grid conditions. Existing dq-frame, sequence-domain, and harmonic-domain models are often developed under different assumptions, making it difficult to compare the required model dimensions and select dominant harmonic ports within a unified framework. To address this issue, this paper develops a linear time-periodic (LTP)/harmonic state-space (HSS)-based modeling and reduction method for a virtual synchronous generator (VSG)-controlled GFM converter and derives the corresponding harmonic transfer function (HTF)-based port admittance. The proposed framework integrates periodic steady-state (PSS) computation, HSS construction, HTF-based multi-frequency coupling analysis, and reduced port-model generation. Simulink validation confirms the calculated PSS trajectories and HSS modal results. The HTF projection maps show that the dominant responses are concentrated in the same-frequency and mirror-frequency channels, while higher-order even coupling remains weak and odd-order coupling is insignificant in the considered averaged model. Equivalent single-input single-output (SISO) impedance comparisons further show that the six-port model preserves the dominant port dynamics, whereas the ten-port model provides a more conservative reduced representation. These findings provide practical guidance for harmonic truncation, harmonic-port selection, and model-dimension reduction in LTP-based stability analysis of GFM converters.

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Keywords

Grid-forming converter; harmonic state space; harmonic transfer function; linear time-periodic system; multi-frequency coupling; impedance reduction

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