## 1 Introduction  
The promotion of new energy generation has become a global consensus to address the energy crisis and environmental pollution [1, 2]. An increasing number of power-electrolyzed sources and loads, such as wind power, photovoltaics (PV), and flexible load, are connected to power systems through voltage source converters (VSCs) [3, 4, 5]. However, the wide-frequency dynamic characteristics of VSCs can easily interact with the power grid, leading to small-signal instability in the system [6, 7, 8]. In a multi-converter grid-tied system especially, the interaction between the power grid and VSCs becomes more intense, leading to increased potential instability factors and further exacerbating the risk of system instability. Currently, the concepts and discussions on the small-signal stability issue of the multi-converter grid-tied system have been well established. Optimizing the control parameters of VSC is an effective method to improve system stability. Existing parameter optimization can be mainly divided into two categories: the direct method [9, 10, 11] and the sensitivity-based parameter optimization method [12, 13, 14, 15]. The direct method of parameter optimization is to substitute specific values into the impedance model of the VSC and observe the influence of control parameter changes on the system stability to identify the patterns of parameter variations. Based on this law,parameter optimization is carried out to achieve system stability [9; 10]. The patterns of parameter variations obtained by substituting specific numerical values may be not applied to parameter optimization for operating conditions with different parameter combinations. A universal parameter optimization method is proposed in [11] based on an analytical method used to uniformly analyze the influence of control parameters on the sequence impedance of grid-forming converters. However, the impact of parameter changes on the stability of a single-converter grid-tied system is analyzed but cannot guide the parameter optimization of a multi-converter grid-tied system. The direct method can only optimize parameters by qualitatively analyzing the impact of VSC control parameter changes on system stability, lacking theoretical support. The sensitivity-based parameter optimization method is to optimize parameters by quantitatively analyzing the influence of variables on system stability [12]. Then, the parameter optimization is carried out on this basis. The ports [13], subsystems [13], or state variables [14] that have the greatest impact on system stability can be identified by using participation factors. Then, only the parameters related to ports, subsystems, or state variables need to be analyzed, reducing the range of parameters that may be used for parameter optimization. A parameter optimization method is proposed based on parameter sensitivity analysis [15]. Through quantitative analysis of the influence of each VSC parameter on the system stability, the stability-weakest parameters are identified, that is, the parameter that had the greatest impact on the system stability. This method could minimally change the stability-weakest parameters to improve the system stability. However, this method still needed to be tried step by step for the optimization of stability-weakest parameters and could not provide specific parameter optimization values. In the current parameter optimization of the multi-converter grid-tied system, it is challenging to provide specific recommendations of control parameters for different units to improve the system stability. The current parameter optimization can only analyze the impact of parameter changes on system stability, and lacks specific quantitative parameter optimization goals. Specific parameter optimization values cannot be obtained directly. Naturally, the targeted theoretical guidance for enhancing system stability is insufficient.