Among various spectral analysis tools arisen in the last years, some were more prominent, such as Fourier transform, windowed Fourier transform and wavelet transform (WT). Nevertheless, all of them present implementation restrictions for an ideal extraction for low as well as high frequencies, of variant signals in time, as, for example, signals containing time-varying harmonics. In this sense, this study presents a review of concepts on the S-transform (ST), also known as Stockwell transform, applied in the analysis of some signals in the context of power quality (PQ). ST gathers, in a single function, positive qualities of both short time Fourier transform (STFT) and WT. This study presents a mathematical basis and some considerations regarding ST, referring to published papers, including a comparison between ST and STFT, as well as WT. It is worth emphasising that a final solution for the extraction of the low-and high-frequency information from time-varying signals is not yet available. ST is a satisfactory approach, but it still needs more detailed studies. This study presents a necessary set of steps for a better understanding of ST, reproduction of examples found in correspondent literature, as well as the ones regarding PQ.

This paper presents the impact caused by the Distributed Generators (DGs) on the Overcurrent Relays (ORs) performance for Distribution Systems (DSs) protection, as well as an analysis of the resulting disturbances associated to power quality. A real-time digital simulator was used to model the base test system and to perform the analysis. The base test system is composed by a DG, based on a solar farm, connected to a typical DS substation. The simulations consist of several fault scenarios, in order to show the OR misoperation. The voltage unbalances observed with the tests were used to improve the overcurrent function. Closed loop simulation was performed with a commercial relay to validate the proposed protection function.

This work proposes a method for the selection of the optimized window of analysis for the Generalized S-Transform (GST), through an adaptation in the Particle Swarm Optimization (PSO) algorithm. The new version of the algorithm, called Adaptive Individual Inertia Weight Based on Best, Worst and Individual (AIW-PSO), uses an inertia weight, where the performance of the best and the worst particle are employed in the adaptive process. The GST is applied to the signal by using AIW-PSO, whose objective function to be minimized is the concentration of energy that will provide the proposed window selection. To evaluate the efficacy of the proposed method, two synthetic signals were analysed by the GST, based on parameters r, m, p and k, and compared with the standard version and an optimized version of the S-Transform (ST) available in the literature. It was found that the GST, optimized via the AIW-PSO algorithm, provided a better response in the Time-Frequency Representation (TFR) when compared to the standard non-ideal ST window, as well as an additional gain in energy concentration relative to the optimized version approach.

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