Testing an induction motor with a VFD, difference in voltage and mechanical power vs electric power
So when I compare Um.rms and Um.1h, with other words the RMS value of the output and the first harmonic of the output there is a difference difference between them. I think this is because, the other harmonics also have a big influence on the RMS value. I read in an technical article (I can't post the article url because reputation isn't high enough yet.) that the 5th and 7th harmonic could have an amplitude of 10% - 40% of the fundamental harmonic. So I think that this is the reason that there is such a big difference between the RMS value of the output and the first harmonic of the output. Is this true?



The 10-50% value in the WEG document refers to the harmonic content of the current to the inverter. The discussion of motor voltage harmonics starts on page 10, section 6. For modern design inverters, the pulse width modulation strategy makes the lower order harmonics lower. Because of the inductive nature of the motor, the higher order harmonic voltages have less effect on the motor current. It is true that the voltage harmonic content is causing the effect that you observed.



  When I compare Pe and Pm there is a big difference between them. The motor efficiency is around 50%. Is this because it is powered by a frequency regulator, because the harmonics in the current and voltage? Or those it have another reason. I have no clue why this is. (I can't post the plot because reputation isn't high enough.)



I believe that you are measuring the input power to the inverter, so the losses include both losses in the inverter and in the motor. If there are any fans cooling the inverter and motor, the power to drive them should also be included as losses. The motor is only operating at about half of the 1.5 kW output power. Since both the inverter and motor has some constant losses, not proportional to motor load, that will reduce the efficiency. Read section 6.2 in the WEG document. WEG shows the peak efficiency at 50 to 75 percent of rated load, but that is for larger motors. Also both the motor and inverter are presumably the WEG brand. Your equipment will likely have different results. There are additional losses due to harmonics, but the losses in the inverter and the normal motor losses are probably responsible for most of the losses.

Efficiency is difficult to measure accurately. You may have measurement error also.