Understanding demand-side energy behaviour is critical for making efficiency responses for energy demand management. We worked closely with energy experts and identified the key elements of the energy demand problem including temporal and spatial demand and shifts in spatiotemporal demand. To our knowledge, no previous research has investigated the shifts in spatiotemporal demand. To fill this research gap, we propose a unified visual analytics approach to support exploratory demand analysis; we developed E3, a highly interactive tool that support users in making and verifying hypotheses through human-client-server interactions. A novel potential flow based approach was formalized to model shifts in energy demand and integrated into a server-side engine. Experts then evaluated and affirmed the usefulness of this approach through case studies of real-world electricity data. In the future, we will improve the modelling algorithm, enhance visualisation, and expand the process to support more forms of energy data.