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This research focuses on restoring signals caused by power failures in transmission lines using the basis pursuit, matching pursuit, and orthogonal matching pursuit sensing techniques. The original signal corresponds to the instantaneous current and voltage values of the electrical power system. The heuristic known as brute force is used to find the quasi-optimal number of atoms k in the original signal. Next, we search for the minimum number of samples known as m; this value is necessary to reconstruct the original signal from sparse and random samples. Once the values of k and m have been identified, the signal restoration is performed by sampling sparse and random data at other bus bars of the power electrical system. Basis pursuit allows recovering the original signal from 70% of the random samples of the same signal. The higher the number of samples, the longer the restoration times, approximately 12 s for recovering the entire signal. Matching pursuit allows recovering the same percentage, but with the lowest restoration time. Finally, orthogonal matching pursuit recovers a slightly lower percentage with a higher number of samples with a significant increase in its recovery time. Therefore, for real-time electrical fault signal restoration applications, the best selection will be matching pursuit due to the fact that it presents the lowest machine time, but requires more samples compared with orthogonal matching pursuit. Basis pursuit and orthogonal matching pursuit require fewer sparse and random samples despite the fact that these require a longer processing time for signal recovery. These two techniques can be used to reduce the volume of data that is stored by phasor measurement systems.

Electrical Faults Signals Restoring Based on Compressed Sensing Techniques