I copied the following paragraph of text from:
http://www.allaboutcircuits.com/vol_2/chpt_10/7.html

For the more mathematically inclined, this principle may be expressed symbolically. Suppose that A represents one waveform and B another, both at the same frequency, but shifted 120o from each other in terms of phase. Let's call the 3rd harmonic of each waveform A' and B', respectively. The phase shift between A' and B' is not 120o (that is the phase shift between A and B), but 3 times that, because the A' and B' waveforms alternate three times as fast as A and B. The shift between waveforms is only accurately expressed in terms of phase angle when the same angular velocity is assumed. When relating waveforms of different frequency, the most accurate way to represent phase shift is in terms of time; and the time-shift between A' and B' is equivalent to 120o at a frequency three times lower, or 360o at the frequency of A' and B'.

Kindly advise the following:

[Q1] In practice, do you think the waveforms of a 3-phase system (any 3-phase system, not restricted to power generation) might have different frequency? Please provide a practical example.

[Q2] If the waveforms in a 3-phase system have slightly different frequency, do you think the phase shift among between any two of them will be constant? If the phase shift is expressed in term of 'angle', will it be constant? If the phase shift is expressed in term of 'time', will it be constant?

Thank you very much

 

Phase shift is always expressed in angles. Time is not really important when the frequencies are all the same.

What is meant by the statement :

"When relating waveforms of different frequency, the most accurate way to represent phase shift is in terms of time"

is that with varying frequencies the phase angle is not constant, and therefore the phase angle can only be measured by looking at specific times. That is, at a given time T0, there may be a 120 degree phase shift between two waveforms, at time T15 there may only be a 37.4 degree phase shift between them, but at time T30, the angle may be the same (a 0 degree phase shift).


A 3-phase system would be useless (and dangerous) if the waveforms did not all have the same frequency:

In the case of a normal 3-phase delta system, 3 voltages are produced by 3 coils which are connected end-to-end, with the end of the 3rd coil being connected to the beginning of 1st coil. Symbolically, this closes the loop and creates a triangle (or delta) since the coils are not "bent." Before connecting the end of the last coil to the beginning of the first, a voltage measurement can be taken between the ends. You will find that there is no potential difference (0 volts) and therefore, connecting those ends together is safe. In a system where at least one voltage is a different frequency from the others, this will not always be the case (most of the time, there would be a potential difference greater than 0 volts), and so making that last end-to-end connection (closing the delta) would cause a short circuit.

With a 3-phase wye system, things would not be so dangerous, but there would still be problems. In a typical 208Y/120V system, any phase voltage (line-to-neutral) would be 120V and any line voltage (line-to-line) would be 208V (1.732 x the phase voltage). As the phase angle between two legs of this system changes (due to the different frequencies of the phase voltages), the line voltage would change anywhere from 2 times the phase voltage (240V in this example) down to 0 volts. This could cause damage to equipment connected to this system from under- or over-voltage. The phase voltages will change angles but not voltage levels. Being used for single-phase applications, only one phase (waveform) is used at a time (for a given device) and therefore, the angle is irrelevant and no damage will occur.