Abstract：As the power grid continues to evolve, the emerging power system exhibits “dual high” characteristics, characterized by a high penetration rate of renewable energy sources and a high proportion of power electronic devices. The new energy grid-connected equipment, featuring power electronics as the interface (referred to as a “converter”), has significantly altered the characteristics of power systems dominated by synchronous machines, and the issue of small disturbance stability has become a research focus. Currently, most small disturbance stability methods for multi-converter systems are based on the assumption that the system parameters are nominal. However, due to production processes, differences in operating environments, component aging, and measurement errors in transmission or distribution line parameters, deviations will occur between the component parameters and their nominal values in the actual system. With research on deterministic methods for the small disturbance stability of converter grid-connection systems, scholars have begun to focus on robust stability studies considering parameter uncertainties. The μ-analysis is a practical theory to analyze the robust stability of a multiparameter uncertain system, and the system’s robust stability margin can be quantified by the structured singular value (SSV). Utilizing linear fractional transformation and harmonic linearization modeling methods, a small-signal model is developed for the system comprising grid-following (GF) and grid-forming (GM) converters in the dq coordinate. This model can describe the parameter uncertainties of the grid-connected multi-inverter system, including converter filter parameters, dc link capacitance, and transmission or distribution line parameters. The multi-input multi-output MΔ structure model of the system and its corresponding transfer function matrix are derived, and an analysis method is proposed for evaluating the robust stability of the grid-connected multi-converter system. Compared to the state space method, the established dq model can avoid the dimensionality disaster problem caused by multi-converter grid-connected systems. The proposed method effectively reduces the computational burden and achieves a one-time analysis of the small disturbance robust stability. Furthermore, the curve of the structural singular obtained by the proposed method also has the following functions. (1) It can effectively evaluate the small disturbance robust stability of the overall system. (2) Based on the frequency corresponding to the peak of the SSV, the oscillation frequency of the system in the critical stable state can be predicted. (3) The reciprocal of the structural singular values can be used to quantify the small disturbance stability margin of the system. Two Matlab/Simulink simulation examples consisting of a GF and a GM converter, respectively, are analyzed. When the SSV peak reaches approximately 1, the system is in a critical stable state, and the frequency corresponds to the oscillation frequency of the system. Then, a Matlab/Simulink simulation comprising 10 converters, including GFL and GFM converters, is constructed. The proposed method can correctly evaluate the small disturbance stability of the multi-converter grid-connection system. Finally, a hardware-in-the-loop experiment involving 6 converters is implemented to verify the proposed method.
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