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China's industrial sector generally relies on electricity as its main source of energy, and industrial production can be affected if there are problems with the electricity supply. In order to deal with the uncertain electricity supply and achieve the "dual carbon" target, the industrial sector needs to take effective measures to enhance carbon total factor productivity (CTFP). We use the biennial Luenberger productivity index (BLPI) to try to provide strategies for low-carbon industrial development in China. The results indicate that the overall CTFP of China's industrial sector showed an increasing trend from 2006 to 2019. Technology change was the main contributor to the change in CTFP, but fluctuations in efficiency change remained a challenge. Differences were observed between the light industry sector (LIS) and the heavy industry sector (HIS) in terms of changes in CTFP, with LIS showing more stable changes and HIS experiencing larger fluctuations. Most sub-sectors showed increased CTFP during the sample period. R&D investment and R&D personnel have a positive impact on CTFP, while energy structure is found to hinder CTFP. According to the research results of this study, we offer the corresponding policy implications. This study is the first to explore the balance between low-carbon goals and industrial production from the perspective of improving CTFP, providing a new viewpoint on the contributions of technological innovation to solving socio-economic issues. [ABSTRACT FROM AUTHOR]