Nonintrusive load monitoring (NILM) is the de facto technique for extracting device-level power consumption fingerprints at (almost) no cost from only aggregated mains readings. Specifically, there is no need to install an individual meter for each appliance. However, a robust NILM system should incorporate a precise appliance identification module that can effectively discriminate between various devices. In this context, this paper proposes a powerful method to extract accurate power fingerprints for electrical appliance identification. Rather than relying solely on time-domain (TD) analysis, this framework abstracts the phase encoding of the TD description of power signals using a two-dimensional (2D) representation. This allows mapping power trajectories to a novel 2D binary representation space, and then performing a histogramming process after converting binary codes to new decimal representations. This yields the final histogram of 2D phase encoding of power signals, namely, 2D-PEP. An empirical performance evaluation conducted with three realistic power consumption databases collected at distinct resolutions indicates that the proposed 2D-PEP descriptor achieves