构网型逆变器内部动态的扩展阻抗模态分析

doi:10.19595/j.cnki.1000-6753.tces.242266

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Abstract The dynamic characteristic of grid-forming inverter (GFM) is mainly affected by the control strategy, and the interaction with the power grid may cause instability such as oscillation. At the same time, the interactive coupling between different time-scale controllers in GFM makes the stability analysis more complicated. Modal analysis based on the state-space model (MASS) uses the participation factor (PF) to quantify the contribution of each state variable to a particular pattern. However, the number of electrical components in new power systems is increasing explosively, and the difficulty of state-space modeling of the whole system is increasing rapidly. In addition, state-space modeling requires detailed system structure topology and complete control parameters of each electrical component, and inverters usually only have impedance models that describe the characteristics of voltage and current ports, with gray box or black box characteristics.
In order to explore the interaction characteristics among all electrical components of the system, the dynamic model of the whole system is constructed by the closed-loop feedback formula of the whole system dynamic matrix. Based on this foundation, the modal analysis based on impedance model (MAI) can evaluate the contribution of each power device to oscillation modes at the device level. However, MAI treats inverters as single, holistic components, which limits its ability to identify dominant system dynamics at the control loop or state variable level. Decomposing different control loops into equivalent circuit components enables the stability analysis of internal inverter dynamics. However, the decomposition of synchronization control loops remains to be explored. This paper proposes an extended modal analysis based on impedance model (EMAI) method to address the current challenges faced by MAI.
First, a decomposition method for the GFM impedance model based on the matrix inversion lemma was proposed, dividing GFM dynamics into synchronous dynamics (SD), dominated by the power frequency synchronization loop (PFL), and electromagnetic dynamics (ED), governed by the voltage control loop (VCL). The detailed categorization of dynamics facilitates an in-depth exploration of the complex coupling mechanisms among controllers operating on different time scales. Subsequently, overall impedance participation factors and participation ratios (PR) were introduced to characterize different internal dynamics of GFM, enabling the evaluation of SD and ED contributions at the control loop level. These metrics help identify the dominant system dynamics and trace the root causes of system instability. Finally, an explicit parameter PF was introduced to precisely locate the critical control parameters of identified loops, serving as a metric for optimizing control parameters and enhancing system damping.
The analysis yields the following conclusion: as the frequency of oscillation modes decreases, the dominant dynamics within each GFM gradually shift from ED to SD. MAI can provide an overall assessment of GFM participation but fails to capture the dominant dynamics of individual GFMs. EMAI not only identifies interactions between various GFMs and the grid but also evaluates the contributions of ED and SD within GFM through overall impedance participation factors, thereby pinpointing the primary causes affecting system dynamics to specific control loops. Moreover, the results of EMAI and MASS in assessing the participation levels of different GFM dynamics are highly consistent, validating the effectiveness of the EMAI method. Furthermore, the explicit parameter PF provides effective recommendations for improving system damping and enhancing stability. EMAI offers nuanced insights into system stability analysis, enabling the rapid identification of the root causes of system instability.

Key words： Grid-forming inverter (GFM) extended impedance modal analysis impedance decomposition participation factor

Received: 17 December 2024

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TM614

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	Zheng Le
	Zheng Jiajie

Cite this article:

Zheng Le,Zheng Jiajie. Extended Impedance Modal Analysis of the Internal Dynamics in Grid-Forming Inverters[J]. Transactions of China Electrotechnical Society, 2025, 40(9): 2712-2723.

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https://dgjsxb.ces-transaction.com/EN/10.19595/j.cnki.1000-6753.tces.242266 OR https://dgjsxb.ces-transaction.com/EN/Y2025/V40/I9/2712

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