On Sat, 7 Jan 2006 17:21:30 -0600, "Robert Swinney"
wrote:

Don, now you are beginning to get the idea, my poor teaching technique not
withstanding. Take another look at your line below where you say, "but I
can see how one might regard them
as functionally in series, particuarly if neutral floats as it must
in an RPC." Yes, neutral *must* float in a RPC but it is still my
contention that the idler and load of a RPC are not truly connected in
parallel unless there is a solid connection between the 2 respective
neutral points. That satisfies the definiton of corresponding points being
connected, doesn't it?? Can we call your special definition of parallel
as applied to RPC's, maybe, huh, "quasi parallel"?

Bear with me for one more moment, please (courteously).

We have a 3-phase source and wish to connect n numbers of 3-phase loads
across it, in parallel. You'd have to agree there would be a "phase"
connected to each of the 3 input terminals (nodes ?) of the loads. In other
words, the connections looking into the loads would be in parallel, and
connected across the 3-phase source, would they not? OK, if you're with me
(I'm a poor teacher, I know), now disconnect the 3-phase source and look at
the loads, say, call one of them an idler and the rest of them loads. Now
the idler and load are not truly in parallel, by definition, because the
lead between star points (neutrals) is not there.

It has finally occurred to me that the neutral is what's causing the
confusion.

Nearly all three phase machines are three-terminal devices. There
may be a physical neutral in a Y-connected machine, but it's rarely
used. We agree that the neutrals would not be connected with
Y-connected idlers and loads. If they were delta-connected, there'd
be no neutrals to connect.

Consider a delta-connected idler and load(s). There are wires
connecting each terminal of the idler to corresponding terminals on
each load. The machines are connected in parallel. Each winding of
the idler is in parallel with a corresponding winding in the load(s).
There are only three nodes in this circuit. Now connect mains
to two of the three terminals. We haven't broken any connections,
so the idler and load(s) are still connected in parallel, each
winding in the idler is still in parallel with a corresponding winding
in the load(s). There are still only three nodes in the circuit,
with power fed to two of them. The power line is connected across
one winding and one phase. We might not know what the potentials
across the other two phases might be, but it's clear that the
voltages across corresponding phases of the two machines are the
same. They're in parallel.

Now consider Y-connected idler and load(s). The winding not tied to
mains on the idler is in series with the corresponding winding on the
load. There are still 3 nodes, the two that mains are connected
to and the one between the two third windings.

Are these machines still in parallel? I assert that they are.
The confusion comes from looking at those windings that are connected
in series and referring to neutral.

In a Y-connected machine, a winding is not a phase. A phase is from
terminal to terminal whether the windings within are delta or Y
connected.

Each phase in a Y connected machine has two series-connected windings
from one terminal to the other. Each winding is a member of two
adjacent phases, and each phase has two windings in series. If you
draw a circle around each *phase* (not winding) of a Y-connected
machine, from terminal to terminal, you see that the idler phases are
indeed connected in parallel with the load phases, whether or not
there are any power lines connected. Let's leave the power off for a
moment. You see not just one, but three loops of four windings in
series -- two idler windings and two load windings. But each phase
in the idler is still in parallel with it's corresponding phase in
the load.

Now connect real threephase power to the terminals. I think you've
agreed that in this situation the idler and load are still in
parallel. Phase currents are currents into a terminal, and are the
same as line currents when the system is driven with threephase
power. Each winding has two phase currents flowing thru it, so the
net current in any winding is the vector sum of these two currents.

Now remove the threephase feed and connect a single phase power line
to two terminals, or one phase, and try to figure out what's going on
in the other two phases with the terminal between those two phases (on
both idler and load) connected to nothing else. We see two
windings in series between neutral of idler and neutral of load. But
the same situation is true with the other windings! You can go from
neutral to neutral via three routes, each thru one winding in the
idler and a corresponding winding in the load. If you drew circles
around the *phases* (pairs of windings) before, you'll see that each
phase in the idler is still connected in parallel with a corresponding
phase in the load.


It's tempting to think of a phase as line to neutral thru just one
winding, because that looks easier to understand. But it's
incorrect unless the neutrals are actually connected because the
voltages from the third node to the other two nodes, the other two
phase voltages, do not depend only on the windings connected to the
third node. Similarly, the current thru the wire connecting the third
nodes does not depend solely on the voltage from third nodes to their
respective neutrals unless those neutrals are tied together or
otherwise held at some known potential from one neutral to the other.