Grid-following (GFL) renewable energy stations may experience phase-locked loop (PLL)-dominated small-disturbance synchronization instability in weak grids, while grid-forming (GFM) devices can improve the damping of this mode. However, most current studies directly approximate GFM as an ideal voltage source without providing rigorous proof. There is also a lack of in-depth analysis on how the parameters of GFM affect its enhancement effect on the small disturbance synchronization stability of GFL. To address this gap, this paper establishes an ordinary differential equation model of the GFL/GFM hybrid system and proposes a fourth-order polynomial approximate root method suitable for polynomials with two pairs of weakly damped conjugate complex roots. Based on this method, the approximated form of the PLL damping is given, and the effect of the inertia time constant, damping coefficient, and capacity of a virtual synchronous generator (VSG) on the PLL mode damping was analyzed analytically. Moreover, it was proven that VSG with a certain level of inertia can play a role close to the ideal voltage source in improving the small disturbance synchronization stability of GFL. Finally, an electromagnetic transient simulation model was established on MATLAB/Simulink, and these conclusions were verified.

Sub‐synchronous oscillation (SSO) of wind power system has long plagued grid operators and researchers. It is affected by different uncertain factors such as wind speed and its probability assessment is crucial for SSO prevention and emergency control. The black box characteristics of wind turbines impede the precise modelling and stability analysis. Meanwhile, researchers concentrated on the uncertainty of wind speed and ignored the impact of grid strength variation. This paper proposed a measurement‐based SSO probability assessment approach considering multiple uncertainties. First, a method is proposed to precisely estimate damping ratios of SSO mode based on measured impedance‐frequency curves. Then, probabilistic collocation method (PCM) theory is introduced to construct an approximate function between the damping ratio and multiple uncertain inputs. In SSOs induced by interaction between full power convert of Permanent Magnet Synchronous Generator and weak grid, both wind speed and grid impedance are set as uncertain inputs, while only wind speed is considered in SSOs induced by Doubly Fed Induction Generator. For common truncated distribution in power grid, the significant advantages of PCM over other analytical methods are pointed out. Finally, the efficiency and accuracy of proposed approaches, compared with Monte Carlo and other approaches, are validated by simulation.

Virtual synchronous generator (VSG) introduces small-disturbance synchronization stability issues similar to synchronous generators. However, most existing research either relies on numerical analysis or focuses on particular operation scenarios, whose conclusions may not be generally applicable. Analytical analysis is the way to address this issue. This paper presents an analytical analysis of small-disturbance synchronization stability in a 2-VSG system considering various operation scenarios. First, the simplified model of the 2-VSG system is built and linearized. Its eigenvalues are analytically approximated, and the accuracy is verified. Then, two sufficient conditions for system stability from the perspective of operation scenarios and control parameters are derived. Hopf bifurcation and transcritical bifurcation are found, and their mechanisms and bifurcation conditions are analyzed. Further, it is proven that the uniform distribution of damping and inertia assists in avoiding bifurcations and ensures system stability under various operation scenarios. The inverse distribution strategy can be applied to improve the damping ratio of low-frequency oscillations only in systems where all VSGs supply power relatively uniformly. Case studies are provided to validate these conclusions. In summary, this paper provides a new perspective on the synchronization stability of the 2-VSG system and an optimistic damping distribution approach to enhance stability.