逆变器并网系统暂态同步稳定裕度评估及主导分岔识别方法

doi:10.19595/j.cnki.1000-6753.tces.251217

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Abstract With the rapid development of renewable energy, large-scale power electronic devices are increasingly integrated into power systems. Inverters, serving as key interfaces, rely on control strategies for grid synchronization. However, their inherently low inertia and strong nonlinearity differ significantly from those of traditional synchronous generators, leading to complex dynamic behavior under disturbances. Grid-connected inverter systems are prone to transient synchronous instability, threatening system safety. Existing stability assessment methods struggle to cope with the strong nonlinearity of inverters. Furthermore, the evolution of the basin of attraction induced by bifurcations complicates the evaluation of stability margins. Therefore, this paper proposes a quantitative method to characterize the basin of attraction across different dominant bifurcation modes. By analyzing the boundary conditions of transient synchronous instability, this approach achieves accurate stability assessment with minimal computation cost.
Firstly, the codimension-2 Bogdanov-Takens bifurcation and its induced generalized saddle-node, Hopf, and homoclinic bifurcations are analyzed. The parameter space is partitioned into four regions with distinct equilibrium characteristics and manifold structures, revealing that Hopf and homoclinic bifurcations are the primary mechanisms of transient synchronous instability. Secondly, the scaling laws for limit cycles in the Hopf-dominated region are derived from normal form theory. Simultaneously, a stability margin assessment method for the homoclinic-dominated region is proposed based on the tangent space of the saddle manifold. Finally, a method for identifying dominant bifurcation modes is developed. This method combines the derived indicators to identify the instability mechanism, thereby avoiding the computational burden of point-by-point time-domain simulations required to calculate the basin of attraction.
The correlation analysis between system parameters and stability margins indicates that as the PLL proportional coefficient increases, homoclinic bifurcation is more likely to become the dominant bifurcation mode. Conversely, as the integral coefficient increases, the system tends to exhibit oscillatory instability. Meanwhile, as the electrical distance and current reference values increase, oscillatory instability is more likely to dominate. In the Hopf-bifurcation-dominated region, the stability boundary is defined by an unstable limit cycle. Upon instability, the system's time-domain waveforms undergo a process of “stable-oscillatory divergence-constant amplitude oscillation”. The main reason is that when the system trajectory exceeds the limit cycle's range, although the limit cycle cannot pull it back to the stable equilibrium point, it is still attracted and circles around it for several turns. Such a phenomenon manifests as oscillatory divergence in time-domain waveforms. Consequently, after fault clearance, various electrical quantities continue to oscillate, exhibiting distinct oscillatory instability characteristics. In the homoclinic bifurcation-dominated region, the stability boundary is constituted by a homoclinic orbit. Both the phase angle and angular frequency diverge. Simultaneously, the three-phase voltage and current exhibit large amplitude oscillations after fault clearance, and the system transitions from a stable state to a non-periodic out-of-step state.
The following conclusions can be drawn. (1) The unstable limit cycle constitutes the basin of attraction boundary in the Hopf-dominated region. The proposed scaling law effectively quantifies its transient stability margin. (2) The homoclinic orbit forms the boundary in the homoclinic-dominated region. This paper approximates the geometric distance between the homoclinic orbit and the equilibrium point using the tangent space to the saddle's stable manifold, which serves as an indicator of the stability margin. (3) Based on the manifold distribution patterns, a dominant bifurcation mode identification method is proposed, operating by comparing the limit-cycle scaling law with the geometric distance between the equilibrium point and the homoclinic orbit.

Key words： Inverter transient synchronous stability Hopf bifurcation homoclinic bifurcation stability margin

Received: 10 July 2025

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TM464

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	Xu Yanhui
	Cheng Yundan

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Xu Yanhui,Cheng Yundan. Transient Synchronous Stability Margin Assessment and Dominant Bifurcation Identification Method for Grid Connected Inverter Systems[J]. Transactions of China Electrotechnical Society, 2026, 41(14): 4867-4887.

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https://dgjsxb.ces-transaction.com/EN/10.19595/j.cnki.1000-6753.tces.251217 OR https://dgjsxb.ces-transaction.com/EN/Y2026/V41/I14/4867

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