The smart grid concept is being applied more and more frequently and this is due to the need to integrate all the components that are part of power systems today, starting from generation units, storage systems, communications and connected loads. Non-linear and non-stationary signals have been obtained in this type of systems, which have high penetration of non-conventional energy sources (NCSRE) and non-linear loads. The power quality criterion has had to be adapted to the new conditions of the electrical systems and this has led to the need to search for new analysis methodologies for the acquired signals. In this article we present a review on non-linear and non-stationary signal analysis methods in electrical systems with high NCSRE penetration. To this end we explore the application of the Hilbert-Huang Transform (HHT), Wavelet Transform (WT) and Wigner-Ville Distribution (WVD), exposing each of the advantages and disadvantages of these methods. To validate the methodology, we have selected some synthetic signals that adequately describe the typical behaviors in these systems.