Timothy C. Green

Yifan Zhang, Yunjie Gu, Yue Zhu et al.

Grid-following inverters have been widely adopted as a grid interface for renewable energy, and ensuring their small-signal and large-signal stability is critical to modern power systems. Their large-signal, or transient, stability is a significant challenge to analyze because of the interaction of the phase-locked loop (PLL), which must maintain synchronism with various outer-loop controllers. Simple analysis in which outer-loop controllers are idealized is insufficient, and the interactions between the nonlinear dynamics of the PLL and the dynamics of the DC-link voltage control (DVC), as well as the AC terminal voltage control (TVC) when present, must be considered. An asymptotic analysis approach, termed the bandwidth separation method, is proposed. This method enables simplification and order reduction of the original differential equations when sufficient bandwidth separation exists. Through this method, the interaction between the DVC and PLL is explicitly characterized, revealing that such interaction degrades system stability and shrinks the stability region. The analysis also indicates that voltage instability, rather than PLL loss of synchronization alone, is often the root cause of transient instability. Optimal bandwidth configurations for the PLL and DVC are identified under various grid fault conditions: a larger PLL bandwidth improves resilience to phase-jump faults, while a larger DVC bandwidth enhances tolerance to power fluctuations. In addition, the influence of the TVC loop is analyzed, showing that a high TVC bandwidth can mitigate the destabilizing effects of PLL-DVC interaction and further improve transient stability. All analytical findings are validated through hardware-in-the-loop (HIL) experiments.

Yifan Zhang, Yaoxin Wang, Yunjie Gu et al.

Grid-following (GFL) inverters have very different large-signal stability characteristics to synchronous generators, and convenient concepts such as the equal-area criterion and global energy function do not apply in the same way. Existing studies mainly focus on the synchronization stability of an individual GFL inverter, while interactions between multiple inverters are less often addressed. This paper elucidates the interaction mechanisms between heterogeneous inverters, covering GFL, grid-forming (GFM), and grid-supporting (GSP) types, to determine the stability boundaries of systems with mixed inverter compositions. The generalized large-signal model for two-inverter systems is derived for various inverter combinations. This paper establishes that systems containing GFL inverters do not admit a global energy function, fundamentally limiting the applicability of traditional direct methods. To overcome this barrier, a manifold method is employed to accurately determine the region of attraction (ROA). To address the computational complexity of the manifold method, reduced-order models of inverter are used based on multiscale analysis. The large-signal stability margin is assessed by the shortest distance from a stable equilibrium point (SEP) to the boundary of the ROA, which is called the stability radius (SR). Using the proposed framework, the analysis reults of two-inverter system show that both GFM and GSP inverters significantly enhance the large-signal stability of a two-inverter system where the other inverter is GFL, with GFM providing slightly superior performance. This improvement is attributed to the voltage support effects and is maximized when the GFM or GSP inverter is located at the midpoint of the transmission line, where the voltage is lowest. All findings in this paper are validated through both EMT simulations and power hardware-in-the-loop (PHIL) experiments.