Why it's difficult to measure active power under low power factor?

The short answer is that, at low displacement power factor, the active fundamental power measurement is highly sensitive to angle errors (usually introduced by current transducers). A couple of examples might make this clear. Fundamental power = fundamental volts x fundamental amps x cosine (angle between fund volts and amps). Suppose we have 230 volts and 10 amps, and we have a measurement error in the angle of +0.5 degrees.

If we have a resistive load, with perfect power factor, the correct fundamental power measurement is 230V x 10 amps x cosine (zero degrees) = 2300 watts, and measured fundamental power of 230 volts x 10 amps x cosine (0.5 degrees) = 2299.9 watts, for an error of 0.004%. If we have an almost perfectly inductive load, let's say with a fundamental angle of 88 degrees, then the correct fundamental power measurement is 230V x 10 amps x cosine (88 degrees) = 80.3 watts, and a measured fundamental power of 230V x 10 amps x cosine (88.5 degrees) = 60.2 watts, for an error of 25%.

As a general rule, the angle errors are contributed primarily by the current sensors, so it doesn't matter if you're using a digital measurement device or an analog meter -- the fundamental power is much harder to measure accurately when there is a poor fundamental power factor.

At very low phase angle levels, the angular error of the current probes used in the measurements can become a serious factor. I recently visited a site with hundreds and hundreds of gear drive motors powering conveyor belts. The power factor was close to 85 degrees lagging. Add in several degrees of angular error from the CTs and then consider using delta measurements versus wye measurements with the added 30 degrees offset and some less capable monitors may produce very strange data. Even with high quality meters, the user must judge carefully.

Matching panel meter data to revenue grade meters will always be a problem. Panel meters are seldom calibrated. They may do a decent job of providing voltage and current data with sinusoidal waveforms. Add in harmonic distortion along with questionable calibration and the displays may be very misleading. Finally, simple meter data will never match the measurement intervals used by the utility revenue meters.