Reconstruction of Harmonic and Transient Electrical Signals Through Compressed Sensing Technique

Harmonic, dynamic transient, and electromagnetic induction signals can propagate at very high speeds through the electrical network, causing insulation breakdown damage to system equipment or severely damaging sensitive electronic control devices, requiring costly maintenance repairs or replacement due to permanent loss. To prevent possible economically significant damage, it is crucial to have timely measurements of voltages and currents using a high-speed digital phosphor oscilloscope and mass storage in the sampling to obtain an accurate and timely diagnosis. The problem here is that when a very high sampling rate is used with a digital phosphor oscilloscope for the precise recording of the phenomenon, due to uncertainty at the trigger time, or by setting a wide recording aperture on the time scale, the process of extracting information for further signal processing becomes a problem of a lot of information that requires a lot of computing time and computational resources. Although there are different decimation methods for sampling rate, these are usually very slow and inefficient because they partly depend on an engineer analyst’s technical criteria and experience. This paper presents a new application of the compressed sensing method with a new improved and validated basis pursuit reconstruction algorithm for dynamic electrical signals of the harmonic and transient type, drastically reducing the number of samples and the processing time without losing accuracy in the results. The harmonic signal under study of 6.25k samples was reduced to a subsampling range between 100-3.7k samples with a minimum processing time of 0.1053s. The transient signal with 10k samples, was reduced to a range of 500-2.7k samples with a minimum processing time of 0.0861s. In both cases, the accuracy of the reconstructed signals is very high according to their validation using Parseval’s Theorem.