Application of Phase Shift for Reactive Power Measurement

The signals of voltage and input current of electrical networks nowadays are not sinusoidal. Currently, among the parameters of reactive power, the most interesting is the reactive power of the fundamental component of the spectrum. At the same time, to measure the parameters of the reactive power of the fundamental component, the approaches to measure sinusoidal current and voltage signals can be used. Most measurement methods of the sinusoidal signal reactive power are based on a phase shift of the voltage at an 90 degrees angle and the subsequent application of one of the well-known methods of the active power measurement. Among the known methods of the measurement of the reactive power of a sinusoidal signal can be distinguished: the time delay method, the integration method, the preliminary differentiation method, and the integration-differentiation method. The main cause of the errors in the considered measurement methods is the effect of the voltage and current harmonics and the input signal frequency deviation from the nominal value. In this paper, the analysis of the effect of these parameters on the measurement error of the reactive power of the fundamental spectral component for the above measurement methods was performed. The obtained analytical relationships allow estimating the reactive power measurement error when the input frequency deviates from the nominal value. The application of a discrete unit delay block for as a time delay block is considered. For the integration method the implementation based on a first-order digital integrator is considered. For the differentiation method, the implementation based on a first-order digital differentiator is considered. Simulation modeling was performed by Matlab and Simulink packages, which confirms the validity of the analytical expressions obtained. The comparison of the considered methods from the point of view of implementation complexity and error of reactive power measurement is made. It is shown that among the considered measurement methods the integration-differentiation method has the smallest error.