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Graph-based signal processing (GSP) is an emerging field that has been used in many domains. Getting inspiration from the successful applications of GSP in signal filtering and image processing, in this paper, we demonstrate how GSP can serve as a feasible approach to non-intrusive appliance load monitoring (NALM). Specifically, NALM means disaggregating household's gross energy consumption down to single appliances through purely software solutions. Since NALM was proposed over 30 years ago, it has got a lot of attention. However, despite the fact that many solutions has been proposed, the majority of approaches can't work well without training and are prone to appliance variations requiring re-training on a regular basis. In this paper, we tackle this challenge by applying a GSP-based NALM approach that can perform well with no training. This algorithm uses GSP three times, which represents the datasets of active power measurements with 1 min resolution using graphs to perform adaptive thresholding, signal clustering and feature matching respectively. Simulation results using publicly available REDD dataset demonstrate the feasibility and potential of the GSP for NALM.

To understand the power line communication signal characteristics and overcome the shortcomings of traditional linear models and statistical parameters, which can't well describe non-stationary and nonlinear characteristics of power line communications signal, the fractal theory is introduced to understand the fractal characteristics of broadband power line communication signal (BB-PLC). This paper presents four methods for studying fractal, namely, rescaled range analysis, variance-time plot method, periodic diagram analysis and wavelet-based method. After verifying the obvious fractal characteristics, we perform fractal analysis using the measured signal at different frequencies and times, revealing self-similarity of the time series. Experimental results show that the power line communication signal has obvious fractal characteristics. All these results can provide reference for broadband power line channel modeling technology.