Digital twin (DT) is one of the most promising enabling technologies for realizing smart grids. Characterized by seamless and active---data-driven, real-time, and closed-loop---integration between digital and physical spaces, a DT is much more than a blueprint, simulation tool, or cyber-physical system (CPS). Numerous state-of-the-art technologies such as internet of things (IoT), 5G, big data, and artificial intelligence (AI) serve as a basis for DT. DT for power systems aims at situation awareness and virtual test to assist the decision-making on power grid operation and management under normal or urgent conditions. This paper, from both science paradigms and engineering practice, outlines the backgrounds, challenges, framework, tools, and possible directions of DT as a preliminary exploration. To our best knowledge, it is also the first exploration on DT in the context of power systems. Starting from the fundamental and most frequently used power flow (PF) analysis, some typical application scenarios are presented. Our work is expected to contribute some novel discoveries, as well as some high-dimensional analytics, to the engineering community. Besides, the connection of DT with big data analytics and AI may has deep impact on data science.