Abstract：As the penetration rate of renewable energy resources continues to increase, the traditional power system based on synchronous generators is evolving into a power system based on diversified power electronic equipment. The small disturbance stability analysis problem of multi-converter grid-connected system has attracted widespread attention. State-space model and impedance-based model are two main small disturbance stability analysis methods. Being as the white-box method, state-space model can be difficult to apply in practice because the differential equations describing the controllers of converters are not generally openly available due to commercial confidentiality. Impedance models have been popular in the field of power electronics for analysis of interactions between grid and converters. However, applying it directly to the stability analysis of multi-converter system will make the analysis process very complicated. Generally, the existing state-space and the impedance method still have room for improvement for the small disturbance stability analysis and sensitivity analysis of the oscillation mode of each converter. Firstly, this paper proposes a single-input single-output (SISO) dq impedance stability criterion for analyzing the small disturbance stability of the multi-converter grid-connected system. Secondly, based on the formula of the stability criterion proposed, an expression for calculating the closed-loop pole of the system is derived. Because this formula is only a scalar function, the accuracy can be guaranteed for the usage of vector fitting (VF) method. Furthermore, a method for analyzing the sensitivity of oscillation modes to the impedance/admittance of each converter is proposed. This method can effectively evaluate the influence of different converters on the oscillation modes and help identify the dominant converter that causes oscillations. Finally, the accuracy of the proposed method is verified by Matlab/Simulink simulation and hardware-in-the-loop experiment. The results are as follows: firstly, the proposed multi-converter system model can be used to represent the converter grid-connected system with any network structure and any number of grid-forming and grid-following converters. Based on the proposed method, it can be used to analyze the overall stability of the system as well as the influence of each converter on the system stability. Secondly, the proposed sensitivity analysis method can be used for evaluating which power converters are more sensitive to the close-loop poles and have a significant contribution to the harmonic instability. The following conclusions can be drawn from the above results: (1) A recursive stability evaluation method for analyzing the stability of the multi-converter grid-connected system based on SISO dq impedance ratio is achieved, and a complete stability evaluation procedure is provided. Compared with the stability analysis method based on generalized Nyquist criterion, the stability analysis problem of a MIMO system is transformed into the stability analysis of a series of SISO systems, and the stability analysis of the whole system can be realized only by the impedance ratio of d-axis and q-axis in the stability analysis process. Because the SISO impedance ratio is used for stability analysis, the solution of the eigenvalues of the high-order return rate matrix required by the traditional method can be avoided, and the complexity of Nyquist plot analysis required for MIMO system can be effectively reduced. (2) In the proposed impedance stability criterion, dq impedance is adopted to model the VCI while dq admittance is used to describe the CCI, so the complicated procedure for obtaining the RHP open loop poles can be avoided. (3) Based on the proposed stability criterion proposed, an expression for calculating the closed-loop pole of the system is derived. Since this paper adopts dq coordinate system for modeling and derivation, compared with the sequential impedance model, the transfer function matrix elements can be guaranteed to be rational fractions, so the closed-loop poles can be obtained by VF method. (4) The sensitivity formula of the system's closed-loop poles on the dq admittance/impedance of the converter in the system is derived in this paper. Combining with the residual of the closed-loop poles obtained by the VF method, it can be used to analyze the influence of each converter on the key modes in the system. Therefore, it is helpful to identify the source that causes oscillatory instability.
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