Invisible Windows for Measurement of Harmonic Components

This work focuses on the measurement of harmonic signal components as they are usually performed for synchrophasors, harmonic phases or power quality measurements in electrical power systems. A class of windows is defined which, in combination with a periodic superposition of the signals, has no influence on the measurement of harmonic components. The combination of special windows and superposition shown here is invisible for harmonic signal components, but can significantly reduce the measurement errors caused by incorrect estimation of the fundamental frequency and inter-harmonic signal components.The commonly used rectangular window is a member of this class and is used as a reference for the evaluation. However, Bartlett, Hann and sine ramp base windows can also be designed as members of this class. All windows have a length of 2 timing intervals and are executed with 50% overlap. It is shown that an implementation of these windows is possible without significant additional effort.Leakage is caused by a difference between the fundamental frequency of the analyzed signal, which often varies over time, and the fundamental frequency assumed by the measurement system. The simulation results for a frequency offset of 100 mHz show time-variant measurement results of the measurand of fundamental wave when using a rectangular window. Other windows show a much better behavior and a higher stability. Of course, the phase error must still be compensated for separately.Interharmonic interference can cause the interference to spread over a wide range of measured harmonics. The rectangular window has a wide spread with limited attenuation. The best results with the lowest interference are obtained for the sine ramp base window.The sine ramp base window in combination with the superposition with a measurement interval of one line cycle seems to be the best choice for the measurement of harmonic components, whereby the reduced measurement interval reduces the risk of erroneous measurements due to transient behavior within the measurement period.