Technological innovations in the power industry can help reduce electricity consumption but may also have a negative result due to rebound effects. Estimation and refinement of electricity demand rebound effects are important for assessing the impact of technological innovations. For this purpose, this paper first constructs a Log Mean Divisia Index (LMDI) to measure the structural and technical effects. Secondly, a Data Envelopment Analysis (DEA)–Malmquist Productivity Index is used to calculate the change in the generalized rate of technological progress, narrow rate of technological progress, and technical use efficiency. Thirdly, the electric power demand rebound effect during the New Normal period is calculated to compare with the rebound effect of the overall energy. Finally, a vector auto-regressive (VAR) model and an impulse response function (IRF) are used to investigate the impact degree of electric power demand changes on other energy demand under the “electrical energy substitution” strategy. The empirical results indicate that the general technological progress rate of China’s electric power industry is increasing gradually in the New Normal period, and the variations in electric demand exhibit the characteristics of the backfire effect and partial rebound effect, respectively, in the context of generalized technological innovation and narrow technological innovation. Meanwhile, contrary to the changing trend of the overall energy demand intensity, electric power demand intensity increased continuously with the advancement of the “electrical energy substitution” strategy, which led to a continuous decline in other energy demands.