Abstract：In recent years, the large-scale integration of new energy sources, such as wind and solar power, into the power grid through power electronic devices has led to frequent system oscillations and instability. Due to the strong nonlinearity of power electronic devices, traditional linear analysis methods cannot accurately reveal the mechanisms of oscillatory instability. Although some scholars have proposed nonlinear system theories and signal analysis techniques, mostfocus on single converters and single parameters. Therefore, this paper uses nonlinear bifurcation theory to analyze the bifurcation characteristics of single-and double-parameter systems in heterogeneous grid-connected systems with coexisting grid-following and grid-forming control strategies, clarifying the mechanisms of oscillatory instability and determining parameter stability boundaries. First, a 22-order state-space model of the system is established by analyzing the main circuit structure and control strategies of the heterogeneous new energy grid-connected system. Then, the bifurcation characteristics of single and dual parameters under coordinated control of each link in the model are analyzed. Bifurcation diagrams and phase-plane trajectory diagrams are used to investigate the system's nonlinear dynamics. Furthermore, the parameter stability domain of the system is constructed from the bifurcation characteristics of each parameter, and changes in the characteristic roots near each bifurcation point are analyzed using the eigenvalue analysis method. Numerical calculations and simulation analyses reveal the following. (1) When the PI control parameters in the grid-forming converter are changed, a pair of conjugate complex roots changes from negative to positive real parts. The stable operating point becomes unstable, leading to a stable limit cycle and a supercritical Hopf bifurcation. As the parameters are adjusted, multiple pairs of conjugate complex roots cross the imaginary axis, and the limit cycle generates multiple tori along the periodic orbit, causing a Neimark-Sacker bifurcation. (2) When the PI control parameters in the grid-following converter are changed, a pair of conjugate complex roots also changes from negative to positive real parts and generates a stable limit cycle. A supercritical Hopf bifurcation is generated. As the parameters are adjusted, the system undergoes a loop saddle-node bifurcation and a period-doubling bifurcation, corresponding to the collision-disappearance and doubling of the limit cycle, respectively. (3) When the inductance parameter of the grid-side line changes, the unstable limit cycle disappears, and the stable operating point becomes unstable, leading to a subcritical Hopf bifurcation. As the parameters are changed, two unstable operating points approach each other, eventually collide, and disappear. A generalized saddle-node bifurcation occurs. (4) Dual-parameter bifurcation analysis of the proportional and integral coefficients in the PI controllers of grid-following and grid-forming converters reveals Hopf-Hopf bifurcation and general Hopf bifurcation. The system’s stability information and its dynamics’global picture can be obtained, helping to understand subsequent dynamic changes after system instability. Moreover, the weak nodes of the system can be identified from the bifurcation characteristics of each parameter, and the parameter stability domain can be constructed to prevent system oscillatory instability.
徐衍会, 董志伟, 成蕴丹. 异构新能源并网系统分岔特性与参数稳定域研究[J]. 电工技术学报, 2026, 41(4): 1248-1260.
Xu Yanhui, Dong Zhiwei, Cheng Yundan. Research on Bifurcation Characteristics and Parameter Stability Regions of the Grid-Connected System of Heterogeneous New Energy Sources. Transactions of China Electrotechnical Society, 2026, 41(4): 1248-1260.
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