Planning, fault diagnosis, and data compression using sparse signals to design electical systems

This dissertation presents an algorithm for fault detection and classification in transmission lines using the Haar-type wavelet mother transform. Voltage and current signals contain all the information of the power system, therefore when a fault occurs in the electrical power system, these signals present disturbances in their amplitude, phase changes, and presence of harmonics. Mathematically, all mother wavelets respond with an impulse when there is an abrupt change in the signals, which allows to detect when a fault has occurred (in time domain). Experimental results have shown that with frequencies above 100 kHz it is possible to detect a fault with 100% accuracy by taking only 4 samples of the signal and applying the Haar wavelet. The fault detection times vary between 0.31ms and 1.15ms and the fault classification times vary between 0.94s and 1.31s. Finally, the massive amount of data to be transported and stored generates a new problem in information compression. In this dissertation a high-performance algorithm is proposed to compress the data of electrical signals. First biorthogonal wavelet level six transform is applied, however after compression, the reconstructed signal will have a different amplitude and it will be shifted when compared to the original one. Then, normalization is used (for amplitude correction between the original signal and reconstructed one) by multiplying the reconstructed signal by the result of the division between the original signal maximum magnitude and the reconstructed signal maximum magnitude. Thirdly, the ripple in the reconstructed signal is eliminated by applying a moving average filter. Finally, the shifting is corrected by finding the difference between the maximum points in a cycle of the original signal and the reconstructed one. After the compression algorithm was performed the best rates are 99.803% for compression rate, RTE 99.9479%, NMSE 0.000434, and Cross-Correlation 0.999925.