Ubiquitous power Internet of Things (IoT) is a smart service system oriented to all aspects of the power system, and has the characteristics of universal interconnection, human-computer interaction, comprehensive state perception, efficient information processing, and other convenient and flexible applications. It has become a hot topic in the field of IoT. We summarize some existing research work on the IoT and edge computing framework. Because it is difficult to meet the requirements of ubiquitous power IoT for edge computing in terms of real time, security, reliability, and business function adaptation using the general edge computing framework software, we propose a trusted edge computing framework, named “EdgeKeeper,” adapting to the ubiquitous power IoT. Several key technologies such as security and trust, quality of service guarantee, application management, and cloud-edge collaboration are desired to meet the needs of the edge computing framework. Experiments comprehensively evaluate EdgeKeeper from the aspects of function, performance, and security. Comparison results show that EdgeKeeper is the most suitable edge computing framework for the electricity IoT. Finally, future directions for research are proposed.