Resolution enhancement in harmonic analysis by compressive sensing

Measurement in power systems and, particularly, in smart grids and smart microgrids is often concerned with harmonic analysis of voltage and current waveforms, which can be obtained by Fourier-based algorithms (e.g., phasor measurements, power quality analysis). Any such measurement algorithm is characterized by a fundamental time-frequency resolution tradeoff that relates the sampling frequency and the signal acquisition time. These well-known conditions determine basic limits of measuring equipment, for instance, when transient response times are considered. Phasor measurement reporting latency is also affected since, for any DFT-based algorithm, this time cannot be shorter than half the observation interval. This paper presents the application of an algorithm, based on the principles of compressive sensing (CS), that enhances frequency resolution by jointly processing multiple sets of DFT coefficients, computed from time-shifted acquisitions of the same waveform. By suitably merging such information, the CS algorithm can achieve an order-of-magnitude resolution improvement without significantly extending the total observation interval, since successive acquisitions can have a very large overlap. For harmonic analysis in power systems, this means accurate results can be obtained using shorter observation intervals, which allow to effectively track changes and reduce the effect of transients on measurements.