A Quantitative Analysis Framework for Investigating the Impact of Variable Interactions on the Dynamic Characteristics of Complex Nonlinear Systems

The proliferation of power electronics in renewable-integrated grids exacerbates the challenges of nonlinearity and multivariable coupling. While the modal series method (MSM) offers theoretical foundations, it fails to provide tools to systematically quantify dynamic interactions in these complex systems. This study proposes a unified nonlinear modal analysis framework integrating second-order analytical solutions with novel nonlinear indices. Validated across diverse systems (DC microgrids and grid-connected PV), the framework yields significant findings: (1) second-order solutions outperform linearization in capturing critical oscillation/damping distortions under realistic disturbances, essential for fault analysis; (2) nonlinear effects induce modal dominance inversion and generate governing composite modes; (3) key interaction mechanisms are quantified, revealing distinct voltage regulation pathways in DC microgrids and multi-path dynamics driving DC voltage fluctuations. This approach provides a systematic foundation for dynamic characteristic assessment and directly informs control design for power electronics-dominated grids.