Abstract In microgrid with high penetration of distributed generation, the generalized Nyquist criterion based on return rate matrix or return difference matrix is often used to analyse the grid-connection stability of virtual synchronous generator (VSG), but the calculation process is complicated. Besides, existing studies have not identified the root cause of the instability of VSG's integration into the strong grid, and the mechanism analysis of the influence of frequency coupling effect on the output impedance characteristics of VSG remains to be deepened. In terms of stability improvement, existing virtual impedance design methods do not take full advantage of the characteristics of VSG output impedance and its interaction with the grid impedance, and there is still room for further simplification. Therefore, this paper conducts a comprehensive and systematic research on the mechanism analysis of microgrid VSG grid-connection stability and the design method of virtual impedance. Firstly, on the basis of obtaining VSG output sequence impedance matrix, this paper analyses the grid-connection stability of VSG by establishing single input single output (SISO) equivalent model and combining with Nyquist criterion. Secondly, based on the established SISO equivalent sequence impedance model, the influence mechanism of frequency coupling effect on the output impedance characteristics of VSG and the root cause of the instability of VSG's integration into the strong grid are compared and analysed. Finally, based on the above mechanism analysis, this paper proposes a virtual impedance simplified design method to improve system stability, from the perspective of improving the amplitude margin of the system, this method directly uses the interaction relationship between SISO equivalent output impedance and grid impedance to realize the quantitative calculation of virtual impedance, which simplifies the design process of virtual impedance. The results are as follows: first, the stability analysis method based on SISO equivalent sequence impedance model can easily obtain accurate stability analysis results, the results show that the instability of the system is caused by the sub-synchronous oscillation near the fundamental frequency of 50 Hz. Second, the influence of frequency coupling effect on VSG positive sequence output impedance is mainly concentrated around the fundamental frequency 50 Hz. Considering the frequency coupling effect before and after, VSG positive sequence impedance changes from capacitive to inductive in the frequency band affected by frequency coupling effect. Lastly, near the critical frequency point where VSG's positive sequence output impedance shows negative resistance capacitance, the influence of grid inductance changes on its impedance characteristics can be ignored. Therefore, the virtual impedance design method based on SISO equivalent sequence impedance proposed in this paper can quickly and accurately obtain the critical threshold of virtual inductance. The following conclusions can be drawn from the above results: (1) The stability analysis method of VSG grid-connection system based on the SISO equivalent sequence impedance model can simplify the analysis process and lay a foundation for the subsequent quantitative design of virtual impedance. (2) Although the frequency coupling effect only affects the positive sequence impedance characteristics near the fundamental frequency 50 Hz, but this is the key to judging the stability of the VSG grid-connection. Through further analysis, the negative resistance capacitance of VSG positive sequence output impedance in a specific frequency band is the root cause of the instability of VSG's integration into the strong grid, the virtual impedance value can be quantitatively designed according to this point to improve the system stability margin. (3) On the basis of the above conclusions, this paper proposes a virtual impedance simplified design method based on the SISO equivalent sequence impedance model. From the perspective of improving the amplitude margin of the system, this method can be used to design virtual inductance directly by calculating or measuring VSG positive sequence output impedance. It avoids the repeated iteration and complex calculation required by traditional methods, and has good applicability to different grid impedance and control parameters.
Liu Xin,Guo Zhibo,Jia Jiaoxin等. Stability Analysis and Virtual Impedance Design of Virtual Synchronous Machine Based on Sequence Impedance[J]. Transactions of China Electrotechnical Society, 2023, 38(15): 4130-4146.
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