Modified S transform and ELM algorithms and their applications in power quality analysis

Modified S transform (MST) and Extreme Learning Machine (ELM) algorithms are developed and are applied to power quality (PQ) analysis. Two adjustable parameters are introduced in MST to control the Gaussian window width, free from the limitation of time-frequency resolution in the standard S-transform (ST) with an uncontrollable window. Compared with ST, MST provides more convenient means for achieving desired time-frequency resolution for various PQ disturbances signals. In order to optimize the adjustable parameters, three optimization indexes are introduced to make the optimization process more adaptively. Based on the time-frequency matrix of MST, four disturbance features are enough to construct the feature vector, solving the problem of the statistical feature redundancy. Compared with the algorithms such as Back Propagation Neural Network (BPNN) and the Support Vector Machine (SVM), ELM has the advantages of simple structure, fast training speed and high precision, more suitable for engineering application. The simulation experiments show that the MST-ELM algorithms, could provide higher classification accuracy, better anti-noise property, less computational cost and independent of training set.