As the most consuming devices in the video chain, it is necessary to master the power consumption of displays. However it necessitates to have a precise modeling of their power consumption. This paper proposes two approaches that outperform the state-of-the-art, to model the power consumption of emissive displays: first through the estimation of the display parameters from a theoretical RGBW model, then through two deep-based models agnostic of the display technology, that output either a global power value or a power map corresponding to an input image. All three modelings were made possible thanks to the release of DISPLAYPOWER2k, a large dataset of power consumption values for OLED displays.