In this paper, the clustering method is used to divide the 30 provinces of the country into high, medium and low electrification rates according to the electrification rate from 2000 to 2017. The heterogeneous panel technology is used to analyze the relationship of energy consumption structure, energy intensity, population density, urbanization rate and carbon intensity. According to Cross-sectional dependence(CD) test and cross-section Im-Pesaran-Shin (CIPS) test results, the data of each panel are not in the form of same order single integer, so α convergence analysis, β absolute convergence, and β conditional convergence analysis are required. The results show that the carbon intensity of the four panels shows an α convergence; the β absolute convergence shows there is a “catch-up effect”; β conditional convergence indicates that the carbon intensity approaches their respective steady state levels; there is a long-term equilibrium relationship of energy consumption structure, energy intensity, population density and carbon intensity in all panels, but the urbanization rate has a significant impact on carbon intensity only in areas with high electrification rates. Finally, based on the results of empirical research, policy recommendations for reducing the carbon intensity in different regions are proposed.