Michael said:
Not when you look at the delivered power to an ideal resistive load.
Not really- remembering that we consider the power delivered to be the
average power.
Polyphase power is almost always taught by plotting the voltage waveform
of each leg. All EEs are familiar with 3 phase power where one phase has
a voltage sinewave with a positive zero crossing at 0 degrees, a second
phase has the same voltage waveform with a positive zero crossing at 120
degrees, the third identical but at 240 degrees. IMO, this is a mistake
that leads to the "is-the-Edison-system-single-phase-or-2-phase" flamewars.
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If one has been through single phase AC analysis and phasor
relationships, this plotting is nice but not at all necessary.
polyphase voltage relationships- not power relationships are often shown
that way-and this is useful-. but then one gets into application of
phasors as previously learned in single phase analysis.
If, instead, we hook up N identical ideal resistors to the polyphase system
and plot the power delivered to each of them, we also get sinewaves, but
at twice the frequency, and shifted up so that the negative most excusion
is at 0. (it goes negative for reactive loads but let's ignore them)
So far what you say is also valid for single phase. Normally, however,
one goes from this presentation of the instantaneous power to a
mathematical formulation and from this to average power per cycle- which
is what is generally referred to as "power" and the relationship of this
average power to rms voltages and currents is shown. Power factor is
related to this as well. When we consider a 240V 60Hz source, the
voltage is then generally expressed as an rms voltage and the power
delivered to a resistive load as calculated from (Vrms^2)/R is the
average power- which is also what a wattmeter measures..
If we plot 3 phase power this way we still get 3 power waveforms shifted
at 0, 120, 240 degrees (when using the double frequency, or at 0, 60, 120
degrees if we use the original frequency scale). If we plot 90 degree 2
phase we still get two power waveforms at 90 degrees. However, the Edison
system produces 2 /identical/ power waveforms, completely different from
the other polyphase systems. There's only one power phase.
I see what you are getting at. It is not something fundamentally
different because the instantaneous power in this case is proportional
to the square of the instantaneous voltage so that the power waveform is
always positive, even when the voltage is negative. So when you have two
voltages 180 degrees out of phase (as you have in the Edison system-
measuring with respect to the neutral), the power waveforms will peak at
the same time for equal loads on each leg.
Now consider a two phase system with the voltages measured with respect
to a neutral which are x degrees apart, Now let x approach 180 degrees
and there will be a phase difference between the instantaneous power
waveforms that gets progressively smaller until it becomes 0 when the
voltages are exactly 180 degrees apart. There is no fundamental change
that takes place.
In terms of average power per phase and total power- no change exists.
Note also that if you look at the total power waveform rather than the
individual legs- then the waveform that you will get will be
indistiguishable from the single phase or the 2 phase case except for
magnitudes for the same phase voltages and resistive loads per phase. In
terms of average powers (using rms voltages) the average power will be
directly proportional to the number of phases for equal phase voltages
and loads.
This makes any any even number of phase system questionable. For example,
the "six phase" system mentioned by others. It's really three phase in
disguise. You could produce a /different/ six phase system with each of
the 6 power waveforms shifted by equal amounts, just like you can produce
90 degree two phase by shifting the power by 90 degrees. Like 90 degree 2
phase, it's not symmetrical (you can't plot the 6 voltage waveforms
symmetrically, just like with 90 degree 2 phase there's a neutral current
for a balanced load. For each of them you can connect the center tap of
the transformer secondaries as the neutral and bring out the 180 degree
voltage waveform/"the other leg", and you'd probably call it "12 phase"
(or "4 phase" for the 90 degree 2 phase system) and get the symmetrical
voltages. It's still only 6 power phases (2 for "4 phase"/90 degree 2
phase) I've heard the "4 phase" system called 4 or 5 wire 90 degree 2
phase, depending on whether the neutral is supplied to the load. For 4
wire the center tap can be omitted and we have 2 independent 2 wire
circuits.
It is true that 6 phase, 12 phase, etc are are derived from 3 phase
systems and provide no net power advantage over 3 phase. 6 phase has
some advantages in compact transmission lines because the interphase
voltage is the same as the voltage to neutral and this allows lower
clearances. 6 and 12 phase rectifier supplies offer better smoothing of
the DC. Other than these advantages -nothing.
Balanced 3 phase does have an advantage over balanced 2 phase (that is,
single phase, center tapped, as we both prefer to call it) in terms of
transmission, transformation, generation, and motors. This advantage has
nothing to do with power waveforms.
A n phase system is nothing more than n single phase systems that are
interconnected in Y or as a polygon (super delta). Certain advantages
accrue but these generally boil down to $ advantages.
What I've called the 3 wire version of 90 degree 2 phase. Two hots and the
neutral. The 5 wire variant needs no neutral current (the 4 wire variant
doesn't even have a neutral), but, of course, uses more copper.
OK 3 wire 90 degree 2 phase- which is not "balanced" in the sense of 0
neutral current- only the 180 degree version can be balanced- and that
balance is the reason that the Edison system is so useful.