From: scot@fc.hp.com (Scot Heath)
Subject: Re: 3 phase question
Date: Tue, 5 Jan 1993 16:41:56 GMT
Organization: Hewlett-Packard Fort Collins Site
X-Newsreader: TIN [version 1.1.8 PL6]


Can't stand it any longer, have to post.  Bear with me, if you like, for a
condensed description of single vrs 3 phase induction motors and finally a
rotating phase convertor.

clewis@ferret.ocunix.on.ca writes:

> Maybe I misunderstand how these converters worked.
> 
> I thought that you took a three phase motor, with leads A, B and C.
> 
> You connect the 220V to leads A and B.  Then kickstart the motor
> with a capacitor to lead C.
> 
> Then you connect your 3 phase equipment to leads A, B and C of the
> first motor.
>
> In such an arrangement, A and B will still be 180 degrees out of

Relative to what?  A and B are developed at the ends of a transformer winding
which is center tapped.  From the center tap to either A or B is 120v.  From 
A to B is 240v.  The only thing A and B are 180 deg. OOP with respect to is 
the center tap of the transformer.  This center tap might just as well not
exist for when useing A and B as a 240V source.  It is conveniently
connected to ground but that is immaterial.  If you were to look at a
voltage versus time diagram of A relative to B you would see a sign wave
with peak values of 339 volts.


> phase with each other.  And C will have a voltage induced upon
> it that's 90 degrees out of phase of both A and B.  There's no way
> that you can phase shift A and B because there's nothing in
> series with them, short of overpowering your hydro utility.

This, of course, makes no sense.  If we look at a 2 pole singel phase
induction motor, we can crudely model it as 2 windings (stator) opposite one 
another surrounding a ferromagnetic core (rotor) with current carying elements
imbedded in the core:

                     |           .          |
                     |        .     .       |
                     |      .         .     |
                     |     .   core    .    |
                     |     .  (rotor)  .    |
                     |      .         .     |
                     |        .     .       |
                     |           .          |
                     |                      |
                  winding                winding

                         END VIEW OF MOTOR

The windings are connected such that when a voltage is applied, a magnetic
field is produced in the same direction by both windings.  Since the
voltage applied is sinusoidal, the magnetic field (flux) is also sinusoidal.
As this time varying flux passes through the core, a voltage and hence
current is induced in the current carrying elements of the core.  This
current reacts with the flux to produce force.  Since the flux is
sinusoidal and symmetrical, no torque on the rotor is produced!  In fact,
the flux can be modeled by 2 equal magnitude non time varying fluxes
rotating in opposite directions 180 degrees OOP with each other.  Imagine
at time zero, one flux is pointing bottom to top and the other is pointing
top and to bottom in the diagram above.  The vector sum of these fluxes is zero.
Allow the fluxes to rotate, the one pointing top to bottom going CCW and
the other going CW.  After they have rotated 90 degrees, they both point
left to right and the vector sum of the fluxes is at a maximum magnitude in the
left to right direction.

To overcome the problem of no torque, a capactor is used to phase shift the
current in and flux produced by one winding.  This has the effect of shifting
one of the fluxes so they are no longer symmetrical.  This causes a torque
to be generated in the rotor.

As the rotor begins to turn and the capacitor is switched out of the
circuit, the force on the windings is no longer symmetrical because the
angular velocity (frequency) of the 2 rotating fluxes is no longer the same 
relative to the rotor.  One is higher than the other and in fact, when the
motor reaches operating speed (nearly 3600 rpm), the rotation velocity of
one of the fluxes is nearly the same as the rotor, the other is nearly
double.


Now picture a 3 phase motor.  It is the same diagram as above with 3x the
windings rotated 60 degrees:


                B winding                C winding
                         /              \
                        /        .       \
                       /      .     .     \ 
                            .         .  
                     |     .   core    .    |
         A  winding  |     .  (rotor)  .    |  A winding
                     |      .         .     |
                              .     .       
                       \         .        /
                        \                /
                         \              /
                C winding                 B winding

                         END VIEW OF MOTOR

The net flux that the rotor sees in this case is the sum of the fluxes from
each set of windings, each of which can be modeled by the 2 counter
rotating flux sources.  When the vector sum of these fluxes is determined,
it is one non time vaying flux rotating with an angular velocity (in rpm) of:

                       (frequency of power source in HZ) * 60
                       ______________________________________

                           number of pole pairs per phase

For the above pictured motor, the angular velocity of the flux if connected to 
60 hz would be 3600 rpm.

Since the net flux is non-time varying in magnitude, the torque on the
rotor is constant where as in a single phase motor, it is sinusoidal.  This
results in bigger torque for smaller physical size motors and the torque is
constant, so less vibration, chatter, etc. 


Finally, if a 3 phase motor is run with only 1 of it's winding pairs
powered by an external source, it will suffer the same fate as the single
phase motor.  Pulsating reduced torque and no self starting torque.  If the
motor is started by some means, the rotating flux in the motor will, along
with the applied voltage, generate some voltage in the 2 unconnected
winding pairs.

We know that the sum of the voltages around any closed loop is zero and
this is also true for the sum of the phasor voltages on the windings of the
motor.  If the motor is connected in a delta configuration the phasor sum of 
the voltage is:

                 phase A connection
                        /\
                       /  \
                      /    \
                     /______\
     phase B connection   phase C connection

   voltage A with respect to B + 
   voltage B with respect to C + 
   voltage C with respect to A = 0

If we have connected A and B to 240v single phase, the voltage on C must
satisfy the above equations.  Due to the symetrical physical construction of 
the motor, the voltages B to C and C to A are 120 degrees out of phase with 
each other and 120 degrees out of phase with the voltage A to B UNDER IDEAL
NO LOAD CONDITIONS.  Since to be useful, the motor must will be connected
to other loads and load current will flow, capactitors are normally added
to ballance the magnitude and phase shift of the voltages B to C and C to
A.

To summarize, let me say that the phase shift and voltage developed on the
windings B to C and C to A when a three phase motor is used as a phase
convertor is due to the physical construction of the motor and the
resulting rotating flux within, not just the applied voltage.

If you're really interested, I suggest reading:

1) Chapters 14 and 16 in the book "Basic Electrical Engineering" by 
   Fitzgerald, Higginbotham and Grabel

2) Chapter 5 in the book "Magnetoelectric Devices" by Slemon

The first is a good deal more basic than the second.  

Gee, this is kind of fun.  Reminds me of my days at GE!

-Scot