Measuring Active Power as the Difference between the Peak Value of Instantaneous Power and the Apparent Power

The traditional approach to calculate the active and reactive power in AC power systems requires the measurement of the phase shift between the voltage and current for the evaluation of the power factor. To do this, power analyzers can implement several methods. In principle, it is always necessary to identify specific points of waveforms (e.g., using a zero-crossing detection technique) and get their time shift. In a similar way, the frequency value must be evaluated in order to calculate the angular frequency. Unfortunately, this kind of common method exhibits some issues, such as the large sensitivity to noise. Moreover, inaccuracies in the evaluation of the power factor have a big impact on the final estimation of the electric power. This paper presents a simple but effective way to calculate the electric power, overcoming the need for a direct measurement of the phase shift and frequency. In particular, it is shown that the active power can be easily calculated as the difference between the peak value of the instantaneous power and apparent power. The reactive power and power factor are evaluated by exploiting the same quantities. The practical implementation of the proposed formulation in power analyzers guarantees several benefits without reducing accuracy.