The Application of the Hilbert Transformer for Measuring of the Reactive Power

As is known, the reactive power of the signal can be determined by the phase shift of one of the signals to ${\pi}/2$ radians and the subsequent application of the active power measurement algorithm. The time delay units, integrators and differentiators are used in practice to perform phase shift. However, the application of these devices is limited by the requirement of sinusoidal input signals. This paper consider the method of phase shift of one of the signals to ${\pi}/2$ radian by using a digital Hilbert transformer. The application of this method allows to measure reactive power for polyharmonic input signals at the required frequency band. The effect of the order of the Hilbert transformer on the measurement error of reactive power is considered. A comparison of the digital implementation of the Hilbert transformer using the IIR-type digital filters and IIR-type digital filters is performed. The obtained analytical expression allows to estimate the error of measurement of reactive power due to the frequency deviation and phase response of the Hilbert transformer from the nominal value. Popular method of measuring of the active power based on the averaging of instantaneous power is considered. The analytical expressions relating the input signal frequency deviation and the measurement error of reactive power for the considered measurement methods are obtained. The validity of the obtained expressions is confirmed by simulation results of the mathematical modeling performed by the Simulink package software.