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| Generalized Small-Signal Linear Time-Periodic Model of Single/Three-Phase Grid Following Inverters Synchronization Method Based on Multiple Generalized Integrator-Frequency-Locked Loop |
| Feng Kaiwen1, Zheng Haoyang2, Qin Yuwen1, Yang Qiming3, Liu Jinjun1 |
1. School of Electrical Engineering Xi’an Jiaotong University Xi’an 710049 China;
2. Center for Power Electronics Systems Virginia Polytechnic Institute and State University Blacksburg 24061 USA;
3. Pudong Power Supply Company of State Grid Shanghai Electric Power Co. Ltd Shanghai 200122 China |
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Abstract The existing small-signal models of grid following inverters synchronization methods (GFI-SM) cannot meet the requirements of stability and frequency response analyses and lack generality. This paper proposes a general small-signal model for a multiple generalized integrator-frequency-locked loop (MGI-FLL).
First, the proposed MGI-FLL unified structure integrates single-phase and three-phase methods, various forms of generalized integrator (GI) branches, and different types of frequency estimation algorithms. Based on the unified structure, a time-domain model is derived to predict the system's dynamics under various disturbances and to analyze the stability of the method. Although the existing linear time-periodic (LTP) model can accurately analyze the method's stability, it cannot analyze its frequency response. Furthermore, the frequency-domain model is derived from the time-domain model to characterize the frequency response, thereby addressing the fixed input-disturbance frequency in the existing LTP model. According to the system's frequency response, the FLL gain and the steady-state harmonic-amplitude value significantly affect the strength of frequency coupling. The multiple-input multiple-output (MIMO) model of the three-phase method can be simplified to a two-input two-output (TITO) model by ignoring harmonic-frequency updates, which is equivalent to the existing dq-frame model. Further ignoring the fundamental frequency update, it can be simplified to a single-input single-output (SISO) model. That is, the traditional complex-coefficient transfer function model. The MIMO model of the single-phase method can be simplified to an SISO model by ignoring frequency updates, yielding the traditional transfer-function model. Finally, the correctness of the frequency-domain model is verified.
The following conclusions can be drawn from the simulation analysis. (1) Its generality and modularity characterize the proposed model. It encompasses both single-phase and three-phase methods, as well as methods for estimating harmonics, DC components, and unbalance components. These methods have been modeled in a unified manner. Moreover, the proposed model can include any number of parallel modules. (2) The proposed model follows the general approach of linearization for LTP models and assumes that the input signal contains arbitrary perturbation frequencies. Compared with existing LTP models, the proposed model maintains accuracy in stability analysis. It can predict the system's frequency response and avoid unnecessary input ports, significantly simplifying the model structure. (3) By deriving the HTF model of the MGI-FLL in the frequency domain, this paper takes into account the frequency coupling between input and output signals, as well as between the fundamental frequency updating path (FFUP) and the harmonic frequency updating path (HFUP). This refined model design improves signal extraction accuracy and the model's applicability. Frequency coupling, as an important aspect of model refinement, further enhances the model's adaptability to complex load conditions.
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Received: 29 March 2025
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2026, Vol. 41 
