Traditional control parameter design methods of grid-connected converters (GCCs) are usually carried out under rated operation conditions. The stability margin is generally characterized by the magnitude margin (GM) and phase margin (PM). The bandwidth of the phase-locked loop (PLL) needs to be sacrificed for enough system stability margin, which ensures that the system can operate safely under non-rated working conditions. Therefore, traditional parameter design methods make it difficult to achieve a compromise between the stability and rapidity of GCC. Furthermore, the relationship between the stability margin and the output limit of the system is difficult to obtain, which relies on simulations or experiments. To address this issue, this paper proposes a control parameter design method based on the system stable operation domain, which com- prehensively considers the variable working conditions and different stability requirements.

Firstly, the complex vector open-loop transfer function G_s(s) is derived, which can analyze the stability of the system in a wide operating range or under different parameters. Secondly, varying the values of the PLL and current loop control parameters, the feasible domain of control parameters can be obtained by numerical analysis. PLL and current loop are coupled to each other due to the grid impedance. Therefore, the phase-locked loop parameter has a stable parameter boundary. Thirdly, based on the upper limit of the obtained PLL parameter, the three-dimensional diagram between the PLL parameter and the output current of the dq-axis is plotted, which shows the stable operation boundaries of GCC under different PLL parameters. Finally, taking the operation margin as the stability margin, the PLL parameter can be flexibly designed to realize the balance between the stability margin and the dynamic performance. Theoretical analysis results show that the control parameter design method based on the stable domain can ensure the safe and reliable operation of the system. Compared with traditional parameter design methods, determining the value of control parameter based on operation margin can improve the dynamic performance of PLL. At the same time, the corresponding relationship between different stability margin and the output current limit of the system can be obtained. Finally, the simulation and experiment results verify the correctness of the theoretical analysis and the effectiveness of the proposed design method.

The following conclusions can be drawn from the theoretical analyses: (1) The derived open-loop complex transfer function can be used to plot the control parameter feasible domain and the stable operation domain of GCC. The PLL control parameter satisfying the operation margin can be obtained quickly without repeated trial and error in the parameter design. (2) The analysis results show that the grid strength is positively correlated with the parameter feasible domain and the PLL cutoff frequency is negatively correlated with the stable operation domain. The cutoff frequency value of PLL is limited by the current loop parameter. The smaller the operating current in the parameter design, the wider the range of PLL cutoff frequency, and the better the dynamic performance of the PLL. (3) The control parameter design method based on the stable operation domain can directly quantify the influence of stability margin on the limit of the output current, which can be used for obtaining the stable boundaries under different stability margin. At the same time, the control parameters of PLL can be flexibly designed according to the actual needs of rapidity.