How do you calculate power factor if line voltage and line current are measured from motor terminal?

Answer 1

Power factor is the ratio of true versus apparent power. For example, a power factor of 1 means that one watt of measured power is one watt of real power, while a power factor of 0.5 means that one watt of measured power is two watts of real power.

To measure power factor, measure voltage, current, and the phase angle of current related to voltage. Phase angle is between 0 and 360 degrees, 360 degrees being one line cycle.

A power factor of 1 means that the phase angle is 0 degrees.

A power factor of 0.707, assuming that voltage and current are measured on the same scale, means that the phase angle is 45 degrees. It would be +45 degrees for a capacitive load and -45 degrees for an inductive load. You can use trigonometry, sines and cosines, to figure this out, or you can use the pythagorean theorem to figure this out - its just a right triangle where the angle is the phase angle.

By the way, a power factor of -1 means the load is actually a generator, and a power factor of 0 means the load is a pure capacitive or inductive load with a phase angle of +90 or -90 degrees.

Power factor is a concern because watt-meters measure apparent power. If the power factor is too low, it will seem that the energy used to lower than reality. The problem is, even in the worst case of + or - 90 degrees, energy is still required to move the current back and forth in the circuit, and that energy must come from the power supply. That's why we talk volts-amps (VA), volts-amps-reactive (VAR), and watts (W) in AC circuits, and none of them are the same thing.