Hi all,
How to mathematically explain the effect of harmonics on motors? It is said that harmonics will cause motor overheat, But since we have inductance (windings) whose reactance is 2(pi)(f)(L)...which means that more frequency, more reacance, less currant flowing, less losses, less overheat.

Any help?

Hello Riyad

One of the things to consider, is wht do the harmonics do?
The harmonics are all separate frequencies and each frequency sets up a rotating magnetic filed at that frequency. These rotating magnetic fields, all cause rotating torque fields at the harmonic frequencies, but the rotor can only operate at one frequenciy.
The result of the harmonic fields is that there are slip losses in the rotor.
i.e. if there is 10% 5th harmonic, then the motor will continue to operate at full speed, but there will be a torque field trying to make the rotor spin at 5 times full speed, so there will be slip losses due to this. If you consider the 5th harmonic field, the rotor is operating at 20% of it's speed and therefore has 80% slip at the fifith harmonic.

Best regards,