The rise of inverters integrated into power systems has raised enormous concerns about potential system instability. This paper aims to investigate the correlation between phase-angle and voltage dynamics and their impacts on the stability of power systems dominated by inverters, focusing on damping perspectives. To this end, we first develop a genetic model to unify the dynamics of synchronous generators and diverse inverter-interfaced devices. By exploring systems' damping characteristics, we find that angle-voltage coupling tends to undermine stability by redistributing the system's damping in a more dispersed manner, consequently rendering the system more vulnerable to inadequate or even negative damping. Our work also involves analyzing and quantifying the factors affecting coupling strength, including power flow, control parameters of devices, and the number of integrated inverters. Additionally, we design a cross-loop control strategy as a demonstration of the potential benefits of utilizing angle-voltage coupling to enhance stability. We validate these findings through simulations on a modified IEEE 39-bus system with heterogeneous inverter dynamics and other standard benchmarks with up to 500 buses. This comprehensive investigation yields insights into the complexities of angle-voltage coupling, which offers useful implications for the analysis and control of inverter-dominant power systems.

In Part I of this paper [1], we have proposed the new concept of generalized voltage damping (GVD) and derived the system-wise GVD (sGVD) index for the global assessment of voltage stability and system strength. In Part II of this paper, we extend this concept to develop a port-wise index for quantifying the voltage-damping characteristics locally. To this end, we decompose the sGVD index into individual ports (or buses), thereby forming the port-wise GVD (pGVD) index, which is computable using local measurements. By inheriting the interpretation of the system-wise index, we further prove that the average of pGVD indices across all buses is approximately identical to the sGVD index. Moreover, it exhibits favorable properties absent in existing indices based on the Maximum Lyapunov Exponents (MLE) of terminal voltages, empowering its application as an assessment metric for the supportive capability of specific devices/ports to short-term voltage stability. Experimental simulations carried on a heterogeneous IEEE 39-bus system confirm the theoretical results. The influence of voltage control strategies, control parameters, and integration locations are also analyzed, providing a new perspective to understanding the support of device dynamics to short-term voltage stability.

This two-part paper presents a generic methodology for assessing power systems' short-term voltage stability (STVS). This approach introduces the concept of generalized voltage damping (GVD), which allows us to quantify STVS from global and local perspectives. This concept leads to a modelfree approach to assess the voltage stability, the system strength, and the supportive capability of dynamic devices during transience. Part I of this paper focuses on deriving the system-wise generalized voltage damping (sGVD) index and its applications. The sGVD index is defined as the decay rate of voltage-related transient energy (VTE) dissipated on the (aggregate) buses of the power system, which can be obtained using the Maximum Lyapunov Exponent (MLE) technique. We show that the sGVD index approximately captures the actual voltage damping under certain conditions in single-machine and multi-machine systems. Additionally, we prove that a positive sGVD implies voltage stability. These unique properties enable a model-free approach to measuring STVS and system strength, even in the presence of heterogeneous bus dynamics. We verify the theoretical results by conducting simulations on the modified IEEE 39-bus systems, demonstrating the effectiveness and practicality of the proposed methodologies.