# ADE7878 power factor and cos(phi) calculation

Document created by analog-archivist on Feb 23, 2016
Version 1Show Document

### Q

I’m developing a electric meter based on the ADE7878. The meter is calibrated
and working fine. However, I’m trying to show the power factor and the
cos(phi) for the different lines and the 3-phase.
To obtain the power factor I divide the instantaneous active power by the
instantaneous apparent power for every line. For the 3-phase value I add all
instantaneous active powers and then I divide it by the sum of all
instantaneous apparent powers. But for the cos(phi) I’m not very sure how I can
obtain it. Can I extract it for the angle measurements of every line? If not,
any ideas?

### A

When the voltages and currents do not have harmonics, the cos(phi) is equal to
the power factor. When there are harmonics, I believe you would like to compute
cos(phi) only on the fundamental. The ADE7878 provides the angle between the
fundamental components of the voltages and currents on each phase. One can
compute the cosine of these angles and obtain the cos(phi)/power factor on the
fundamental on each phase. This is useful when someone needs to compensate the
inductive reactive power to bring the power factor up as the capacitors that
are normally used are computed based on the fundamental power factor. See
section Time Interval between Phases, page 33, rev E ADE7878 data sheet.