Non-intrusive load monitoring (NILM) is a large research topic dedicated to the detection and management of electrical loads, drawing international interest in the context of a growing global concern on sustainability in the energy sector. However, most current public datasets offer inadequate and non-unified sets of measured features, electrical devices and measurement methods, causing difficulties in method comparison and the application of research in new environments. In addition, previous studies faced challenges in classifying appliances with small and similar operational power or with large disparities in operational power. In this study, we utilized a combination of current-power characteristics in the time domain (e.g. RMS current (Irms), real power (P), power factor (pf), reactive power (Q), apparent power (S)) to monitor electrical appliances using their steady states. The combinative current-power characteristics were used to train machine learning models that can efficiently distinguish between appliances while addressing the posed challenges. Our dataset comprises 128 device combinations sampled at steady-state from 07 common electrical appliances in Vietnam, collected at a high sampling rate of 600 Hz, resulting in 73 million data points. By leveraging the current-power signatures in the time domain, we achieved a classification accuracy of approximately 99.1%, capable of differentiating between combinations containing devices with small and similar operational power and those with substantial disparities.