## 5 Conclusions  
For the small-signal instability caused by the multi-VSCs connected to the grid, existing methods can only identify stability-weakest parameters without calculating the accurate parameter optimization values. To address this issue, this article proposes a parameter optimization to improve the stability of a multi-converter grid-tied system. The method can accurately identify the stability-weakest parameters and calculate the corresponding parameter optimization values. Specifically, the conclusions and contributions are summarized as follows:  
1. An improved stability evaluation function is constructed by considering the distance between the intersection point and \((-1,\,\mathrm{j0})\) when the Gerschgorin discs intersect with the real axis and Re\((L_{i(j)})\leq-1\). This method overcomes the misjudment of parameter sensitivity correction direction when the radius of the Gerschgorin disc changes due to the changes in VSC control parameters. 2. In the multi-converter grid-tied system, the contribution of control parameters in each VSC to the system stability varies. The proposed method can quantitatively analyze the influence of VSC control parameters on the stability of the multi-converter grid-tied system, and identify the parameters with large absolute sensitivity as the stability weak parameters. 3. Based on stability evaluation functions and parameter sensitivity analysis, an iterative calculations-based parameter optimization is developed. In the iterative calculations, one or multiple stability-weakest parameters can be rolling-optimized based on the quantitative results of the stability evaluation function. Theoretical analysis and simulation verify the correctness and feasibility of this approach. Conceptualization, B.C., Q.S. and P.J. ; methodology, B.C. and Q.S. ; software, Q.S. ; validation, B.C., Q.S. and X.Z. ; formal analysis, X.Z. ; investigation, X.Z. ; resources, B.C., Q.S. and P.J. ; data curation, B.C. and Q.S. ; writing--original draft preparation, Q.S. ; writing--review and editing, B.C. and X.Z. ; visualization, P.J. ; supervision, X.Z. ; project administration, B.C; funding acquisition, B.C. All authors have read and agreed to the published version of the manuscript. This study is supported by the Science and Technology Project of State Grid Jiangxi Electric Power Co., Ltd. (NO: 521820220006, Stability analysis and operation control technology for high proportion new energy integration into AC/DC power grids). Not applicable. Data Availability Statement: Data is contained within the article. Acknowledgments to [PERSON] and [PERSON] for their valuable contributions to the study reflected in this manuscript. Author [PERSON] was employed by the company Electric Power Research Institute of State Grid Jiangxi Electric Power Co., Ltd. The remaining authors declare that the research  
Figure 22: Real-time simulation-based results of system B before and after VSC parameter modification: (a) \(k_{\text{p2}}=6.600\times 10^{-3}\), \(k_{\text{p3}}=6.600\times 10^{-3}\); (b) \(k_{\text{ip2}}=8.800\times 10^{-4}\), \(k_{\text{ip3}}=8.800\times 10^{-4}\). * _[PERSON] et al. (2023)_ [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; et al. Real-World Subsynchronous Oscillation Events in Power Grids With High Penetrations of Inverter-Based Resources. _IEEE Trans. Power Syst._**2023**, _38_, 316-330. [CrossRef]
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* _[PERSON] et al. (2017)_ [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Modeling and Resonance Analysis of Multiparallel Inverters System Under Asynchronous Carriers Conditions. _IEEE Trans. Power Electron._**2017**, _32_, 3192-3205.