Abstract：As an effective and reliable distributed energy integration and consumption mode, converter-based microgrids can operate in grid-connected mode and islanded mode Due to the lack of stable voltage and frequency support, the islanded microgrid is prone to lose stability under fault disturbance. Besides, various converters with different control types interact with each other in the microgrid, making the system easier to lose stability. The interactions of GFL-VSC and GFM-VSC in the islanded microgrid system and their effects on system stability are rarely analyzed in the former studies. In addition, due to the negative damping characteristics of GFL-VSC, the analysis methods of the previous studies are quite conservative. A new Lyapunov analysis method based on quadratic form principle considering PLL frequency mutation effect is proposed in this paper, which provides a conservatively improved stability region estimation. Firstly, a conventional second order nonlinear mathematical model of GFL-VSC parallel GFM-VSC system considering the effect of reactive power loop is established. Simulation comparison shows that the conventional model has some transient errors. Secondly, a passive frequency mutation effect widely exists in GFL-VSCs is revealed, which is caused by the proportional controller of PLL. By deducing a unified frequency mutation formula for different types of large disturbances, a modified model considering frequency mutation effect is obtained, which greatly improves the transient-state error of the existing conventional model. Third, considering the influence of reactive power loop on the output voltage of GFM-VSC, a new parametric Lyapunov function based on quadratic form theory is proposed. By undetermined coefficient, the obtained dissipation interval is larger than that of conventional Lyapunov function. Therefore, a less conservative estimation of the transient stable domain of islanded microgrid system can be obtained. The less-conservatism of the proposed method is mathematical proved. Fourthly, considering the frequency mutation effect and combining with the obtained stable domain, the power angle stability range corresponding to different disturbance forms is derived, and the conclusion is drawn that the sensitivity of the system to different disturbance forms is different. Fifth, from the point of view of physical mechanism, the influence of dynamic interaction between GFL-VSC and GFM-VSC on the stability of the islanded microgrid system is explored, and corresponding to the terms in the state space equation. Sixth, based on the proposed Lyapunov's method, the size of transient stable domain of the islanded microgrid system is derived and compared to analyze the influence of different network parameters and controller parameters on the stability of the islanded microgrid system. Finally, the proposed method is verified by MATLAB/Simulink simulation and the RT-Lab based hardware-in-loop experiments. The following conclusions can be drawn from this paper: (1) The output frequency of the PLL will mutate due to the sudden change of voltage at the PCC when the converter is disturbed under large disturbance. Conventional modeling method ignore this phenomenon, which leads to transient model errors and potential misjudgment of stability. (2) Based on the different frequency mutation mechanism of different disturbances, the sensitivity of the islanded microgrid system to different forms of disturbances is different. The sensitivity order is voltage disturbance>current disturbance>inductance disturbance>phase disturbance. The higher the sensitivity, the more likely the system instability occurs. (3) The larger the voltage reference value, the stronger the system stability. The smaller the current reference value, droop coefficient and line inductance, the stronger the system stability will be. The influence of PLL's parameters on the stability is more complex and not a monotonous relationship. The larger the reactive load and reactive droop coefficient, the worse the system stability.
李锡林, 查晓明, 田震, 黄萌, 胡宇飞. 频率突变影响下基于Lyapunov法的孤岛微电网暂态稳定性分析[J]. 电工技术学报, 2023, 38(zk1): 18-31.
Li Xilin, Zha Xiaoming, Tian Zhen, Huang Meng, Hu Yufei. Lyapunov Based Transient Stability Analysis of Islanded Microgrid under the Influence of Frequency Abrupt Change. Transactions of China Electrotechnical Society, 2023, 38(zk1): 18-31.
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