Identifying domestic appliances in the smart grid leads to a better power usage management and further helps in detecting appliance-level abnormalities. An efficient identification can be achieved only if a robust feature extraction scheme is developed with a high ability to discriminate between different appliances on the smart grid. Accordingly, we propose in this paper a novel method to extract electrical power signatures after transforming the power signal to 2D space, which has more encoding possibilities. Following, an improved local binary patterns (LBP) is proposed that relies on improving the discriminative ability of conventional LBP using a post-processing stage. A binarized eigenvalue map (BEVM) is extracted from the 2D power matrix and then used to post-process the generated LBP representation. Next, two histograms are constructed, namely up and down histograms, and are then concatenated to form the global histogram. A comprehensive performance evaluation is performed on two different datasets, namely the GREEND and WITHED, in which power data were collected at 1 Hz and 44000 Hz sampling rates, respectively. The obtained results revealed the superiority of the proposed LBP-BEVM based system in terms of the identification performance versus other 2D descriptors and existing identification frameworks.