Spatial-temporal evolution characteristics and critical factors identification of China's energy trilemma index

With the threats of energy consumption and climate change, energy trilemma has become a critical issue for sustainable energy development. Employing the VHSD-EM and coupling models to calculate the coupling coordination degree of the energy trilemma across 30 provinces in China from 2007 to 2022. Examining regional disparities and spatiotemporal evolution characteristics using Kernel Density Estimation (KDE), Dagum Gini coefficient, and spatial Markov chain analysis. Based on the TOE theoretical framework to explore pathways for improving the coupling coordination degree of the energy trilemma. The findings reveal four main aspects: (1) A steady improvement in the national coupling coordination level, indicating that China has made continuous progress in balancing energy trilemma; (2) Significant regional disparities exist—eastern provinces consistently exhibit higher coordination levels than central and western regions. Contributing to increasing intra- and inter-regional inequality; (3) The KDE and spatial Markov model results highlight a strong club convergence effect in the coupling coordination degree, with high-coupling regions exhibiting a "high-end path lock-in" pattern; (4) Regression analysis shows that digital economy, green finance, and urbanization significantly contributes to improving the coupling coordination degree. These results suggest that future policies should emphasize enhancing regional synergy, accelerating green infrastructure investment, and leveraging digital and financial innovations to foster long-term, balanced energy system transformation.