Conformable fractional-order grey prediction models have attracted considerable attention due to their versatile modeling techniques. However, existing models often suffer from limitations in adaptability. To address this, this study proposes a new extended conformable fractional-order grey prediction model, namely the ECFGM(1,1) model. By integrating an adaptive weighting coefficient into the conformable fractional-order accumulation process, the model can effectively prioritize new information, thereby enhancing its rationality and adaptability. Moreover, the adjusted process can be tailored to either emphasize new information or adhere to traditional accumulation methods, which improves its adaptability. To verify the effectiveness of the ECFGM(1,1) model, ECFGM(1,1) is applied to two examples from the literature. The model evaluation results show that the ECFGM(1,1) model has higher fitting accuracy and predictive accuracy than the GM(1,1), CFGM(1,1), and NIPGM(1,1) models. Using the constructed ECFGM(1,1) for predictive analysis of the per capita electricity consumption for daily life in China, the results show that this model can capture the laws of its changes over time. Finally, per capita electricity consumption for daily life in China from 2022 to 2026 is predicted. The results show that by 2026, such consumption is estimated to reach 1165.35 KW.h.