Using Wavelet Packet Trees to Efficiently Estimate Clustered High Order Harmonics

This study deals with the capabilities of a 7 level Wavelet Packet tree (WPT) relative to fast estimation of joint harmonic contributions of components oscillating with frequencies higher than 2kHz. The analyzed signal from the tree’s root node spans across 7 periods such as to yield results unaffected by the edge effect. Clusters connecting nodes from the 7-th level and associated harmonics are deduced, along with flags to be used such as to obtain subtrees dedicated to each cluster for runtime savings. Tests on artificial signals with rich harmonic content and respectively with harmonics from a single cluster were made. The analysis of performance metrics revealed that 6 clusters can be used for the estimation of contributions of harmonic exceeding 2kHz, up to the limit of 4.25 kHz, while considering a threshold of at most 2.5% for the energy of individual odd harmonics to appear outside their associated cluster of nodes. An example of algorithm utilization for the output voltage of an auxiliary services converter used on a Romanian locomotive is provided.