Mathematical methods for non-intrusive load monitoring

Abstract

The calculation of the Discrete Fourier Transform (DFT) of a discrete time signal is a fundamental problem in discrete-time signal processing. This thesis presents algorithms that use methods from number theory and algebra to exploit additional constraints about a signal to aid in the calculation of its DFT. First, an algorithm is presented that estimates the DFT of an unquantized signal given only a quantized version of that signal. Second, an algorithm to estimate the value of one subset of DFT coefficients from knowledge of another subset of DFT coefficients, for an appropriately constrained class of waveforms, is presented and analyzed. Thirdly, an algorithm to classify electrical loads on the basis of a subset of the DFT coefficients of load current is demonstrated. Finally, an embedded system that calculates DFT coefficients of measured current and makes this information available in convenient forms is considered.