With the global energy crisis and environmental degradation getting more rigorous, an essential approach is required to attain introverted development through structural optimization, autonomous invention, and technological innovation system. It is an important way to include energy conservation, emission reductions, and the implementation of a low-carbon mode in the power industry, which is a highly polluting sector of the national economy. This article is based on the State Intellectual Property Office of China’s patent search and analysis database. We choose the number of green patents jointly submitted for innovative topics in the power industry from 2016 to 2020. The negative binomial regression is constructed from the standpoint of multidimensional closeness by employing Gephi visual analysis, Ucinet, and the Stata 15 regional model. Furthermore, we investigate the impact of geographical closeness, technological closeness, and institutional closeness, as well as their interaction, on the green innovation performance of inventive organizations in China’s power industry. According to the findings of the study, geographical and institutional closeness have an important influence in increasing the green innovation performance. The suggested model applies to the power sector, and technological closeness has an inverted U-shaped association with green innovation performance in the power business. Furthermore, the model output at inference time is just a collection of successive parameters that improve the interaction of the closeness of innovation subjects to the green innovation performance of the power industry, all of which are represented as complementary effects.