Non-intrusive load monitoring systems (NILM) have attracted much attention due to their potential contribution to energy savings for individual households. The approach analyzes the load consumption of each device in terms of the total energy consumption of the house. The selection of essential load signatures for load identification expresses a crucial challenge with NILM techniques. Several studies that have been proposed in the literature claim that the Voltage and Current (V-I) trajectory has identified the most effective individual steady-state signature for appliance identification. In addition, multi-scale approaches utilized to derive the load signature have limitations. Therefore, this study is focused on one cycle of steady-state voltage and current used to generate a voltage-current trajectory. Next, the Fourier phase correction approach has been employed to eliminate the issue of current and voltage starting points. Afterward, the corrected starting point of the V-I trajectory of each electrical load appliance is then represented by the Triangle Area Representation (TAR) at various side lengths. Since the TAR signature contains an extremely highdimensional subspace, it is significant to perform Principal Component Analysis (PCA) to produce a low-dimensional space feature. Consequently, appliance identification has been improved based on the weighted K-nearest neighbor (W-KNN) multi-classification technique. In addition, the Plug Load Appliance Identification Dataset (PLAID) with three different versions is used to evaluate the performance of the proposed algorithm. As a result, our proposed algorithm with these datasets improves accuracy results compared to state-of-the-art approaches that relied on steady-state signatures for load identification.