On Mon, 2011-03-14 at 00:04 -0400, Przemek Klosowski wrote:
> On Wed, Mar 9, 2011 at 12:35 AM, Kirk Wallace
> <kwall...@wallacecompany.com>wrote:
> 
> > Let me try to provide more details on my understanding of the phase
> > timing of DIY converters. Attached is a schematic of a common rotary
> > converter. The source is here:
> > http://www.metalwebnews.com/howto/ph-conv/ph-conv.html
> > http://www.metalwebnews.com/howto/ph-conv/fig1.html
> >
> > I used this to make my converter and is the only design I have some
> > understanding of. As the schematic shows L1 and L2 go straight to the
> > output and are unaffected. Since L1 and L2 are single phase, L1 is a
> > mirror of L2, therefore 180 degrees out of 360 apart.
> >
> >
> But, but, you are committing a tautology. If you reference L1 to L2 and vice
> versa, of course L1 is a mirror of L2. In your scheme there is no 'ground'
> or reference point, so you only have one phase coming in,

I agree if you combine any two sine waves of the same period, the result
is a single wave of the same period. I think what does change is the the
amplitude of the resulting wave as one changes the phase between the two
original waves. But I'll also agree that the ground or neutral is a red
herring because it isn't connected to any part of the motor circuit
(other than 120 VAC for a relay). 

So what we have at this point is a 240 Volt sine wave across the idler
motor connection at L1 and L2. If nothing else is connected, voltage and
current is alternating between L1 and L2. L3 looks like a center tap, so
V-L1L3 should be 120 Volts and 0 degrees in reference to V-L1L2, and
V-L2L3 is 120 Volts and 180 degrees in reference to V-L1L2, just as a
neutral would be. If the rotor had no mass, my guess is that it would
vibrate between 0 and 120 degrees. When the idler L1 and L2 is first
connected to the mains, a start capacitor is switched on between L1 and
L3, which for an instant, will look like a temporary short circuit of L1
and L3, as it charges, the field will rotate giving the rotor a kick in
one direction (?). The rotor mass should carry the rotor through
subsequent cycles and the start capacitor is disconnected. So now we
have the idler motor with 240 VAC across L1 and L2 with the rotor
spinning and nothing connected to L3. Now I'm thinking, what's going on
at L3? What comes to mind is that any motor is just as much a generator
as a motor, so there must be a very significant three phase signal
coming off of L1, L2 and L3 and because of the physical layout of the
stator windings, each generated leg is 120 degrees apart. Now I'm
beginning to think of the idler as a three phase generator that is being
back driven on one phase (L1L2), or as a motor that has two dead phases.
The only difference between a 240 Volt three phase motor and a 240 Volt
three phase generator is the current direction, so the idler has motor
like currents for 120 shaft degrees and generator currents for 240. Also
the rotor is decelerating or converting inertia into electrical energy
for 240 degrees and storing inertial energy for 120. I suppose the
capacitors between L1 and L3, and L2 and L3 are another means to store
energy to help the rotor get through the generator phase. Uugg, my brain
hurts but I think I'm getting a better understanding. I haven't even
begun to think about the math that follows. But, getting the correct
starting point helps the thought process. Thanks

>  and the motor
> generates the second (and third) phase L3, shifted with respect to L1/L2.
> One way to see it comes from the trigonometric identity  holding that sum of
> three sines shifted by 0, 120 and 240 degrees is zero:
> sin(x)+sin(x+2*%pi/3)+sin(x+4*%pi/3)=0
> 
> Let's say we take some arbitrary reference point, so that L1(t) is the
> voltage on the first leg. Assume L2(t)-L1(t) = V sin(2 pi f t). If the
> converter generates L3(t)=L1(t)-V sin(2 pi f t + 2/3 pi), then L1-L3 is V
> sin(2 pi f t + 2/3 pi), i.e. shifted by 120 degrees, and L3-L2 is -V sin(2
> pi f t + 2/3pi) - V sin(2 pi f t)  which reduces to V sin(x+4*%pi/3) i.e.
> the same AC shifted 240 degrees. Note that it doesn't matter what the
> reference point is, because its potential L1(t) drops out --- all that
> matters are voltage differences between the legs of the circuit, not the
> potentials of the legs themselves.



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