I always wondered this.
Thanks
Joe Sweeney
Joe,
phase of a periodic phenomenon f(t), for a particular value of t) The fractional part t/P of the period P through which f has advanced relative to an arbitrary origin.
Note: The origin is usually taken at the last previous passage through zero from the negative to the positive direction.
One problem is the word
phase has at least 14 definitions. But I find the one above is the easiest to start from – if the recipient understands the mathematics.
The first thing to understand is we are discussing a “periodic phenomenon
f(t);” in our case, it is a sine wave. We will call it “sine wave
α” or just “α.” We will assume α has a regular period P. Note the amplitude of α is not relevant.
We will now pick our arbitrary origin, using the one suggested above; i.e., when
α last passed through zero from the negative to the positive direction.
Any sine wave that has the same period
P and passes through zero from the negative to the positive direction at the same time as
α is said to be “in phase” with α. All such sine waves are considered to be “single phase” since the “fractional part t/P of the period P through which t has advanced relative to an arbitrary origin” is the same for all of them.
Any other sine wave that has the same period
P but passes through zero from the negative to the positive direction at some other time than
α is another phase.
Using any two conductors of a properly installed 120/240 system as an arbitrary reference and assuming the system is stable; with the proper instruments, measuring any combination of the three conductors would establish there is a common period
P. Four (4) will be 120V and two (2) will be 240V. Since we can force the “passage through zero from the negative to the positive direction,” by simply reversing the instrument leads, of the six possible measurements, three will always be “in phase” with the original reference including itself. We will arbitrarily select them to be the “single phase” system. Two will be 120V and one will be 240V.
Using any two conductors of a properly installed 240
D system as an arbitrary reference and assuming the system is stable; with the proper instruments, measuring any combination of the conductors would establish there is a common period P. All six (6) be 240V. Since we can force the “passage through zero from the negative to the positive direction,” by simply reversing the instrument leads, of the six possible measurements, one will always have a negative to positive zero crossing displaced in time by 1/(3P) and one by 2/(3P) from the original reference. We will arbitrarily select those two along with the original reference to be the “three phase” system.
A similar analysis for 120Y-208 system would result in twelve (12) measured voltages. Six (6) would be 120V and six (6) would be 208V. Using the six measurements that had the same voltage as the original reference we would find similar 1/(3
P) and 2/(3
P) time displacements in two of them. If we only considered passing through zero and ignored amplitudes and the crossing direction, we would find this is actually a six-phase system. This is one of the reasons it’s so friggin’ hard to calculate a combination of L-L and L-N loads.

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