Calculated performance of a digital sampling wattmeter using systematic sampling

It is shown that if n voltage and current samples are taken uniformly over an exact number m of periods of a sinusoidal power system, the power measurement obtained by taking the mean value of their product multiplied by the sampling interval is exactly equal to the power; provided that 2m/n is not an integer, and that this is not dependent on the initial sampling phase angle or the load phase angle. This has enabled the construction of an accurate wattmeter with a wide frequency range, because the time needed for sampling A/D conversion, multiplication and summing can be much longer than if sampling were limited to a single cycle. In considering the application of such a wattmeter to nonsinusoidal waveforms, there is a large range of crossproducts of the current and voltage harmonics which gives rise to errors; of which the most significant are the products of the fundamental of one quantity with the (kn ± 1) th harmonic of the other, where k is an integer.