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wrote:

My OP snipped

This is probably a lot more than you wanted to know but the
trouble is that there's no simple answer.

The capacitor run problem has a lot in common with the often
discussed, capacitor only, 3 phase converter system.This copy of an
earlier post is a starting point

*****
A converter of this type is basically a capacitor/inductor phase
shift system which produces an open vee 3 phase system. This phase
shifter is a series resonant circuit and when it is set up to give the
60 deg phase shift it is working a long way below its natural resonant
frequency. 60 deg is of course the correct phase angle between the two
legs of an open vee system.

The motor(s) is the inductor in the system and unfortunately
the apparent inductance of the motor changes with rotor speed. For any
particular rotor speed greater than about 90% of synchronous speed
(the lower limit varies a bit with motor type) it is possible to
choose a capacitor combination which produces a pretty close
approximation balanced 3 phase at the motor terminals.

For near the full load rated speed of the motor, large run
capacitance is needed with most or all of it as a single capacitor
feeding the phantom phase from supply live. At light load the speed of
the rotor rises and if the capacitor value is chosen to achieve the
right phase angle the phantom phase voltage will be excessive. This
could be corrected by feeding the capacitor from a lower voltage
single phase source but this would mean feeding it from an auto
transformer across the supply.

It is much simpler (and of course everybody does this) to use
two capacitors arranged as a voltage divider to simultaneously achieve
the correct phase angle and phase voltage.

The effective capacitance of two capacitors connected in series
across the supply is the sum of the capacitances because the AC source
impedance of the supply is zero and this effectively parallels the two
capacitors.

Because the they also act as a voltage divider, this sum
capacitance is effectively fed from a source voltage of supply voltage
times C1/(C1+C2) where C1 is the top capacitor and C2 is connected
phantom phase to neutral.

*******

For a symmetrically wound capacitor run machine the same
arguments apply but with the additional difficulty that the ideal 90
deg phase shift is only reached when the capacitor fed leg is series
resonant. This is not too much of a problem at full load because the
loaded Q is so low, but can cause unacceptably high capacitor phase
voltages at light load.

The capacitor choice has to be a compromise but the best full
load choice results in roughly equal voltages on phase 1 and phase 2.
This exchanges some phase error for correct phase 2 flux density.

When optimised for full load, the rise in light load capacitor
phase voltage may be excessive; 10 to 20% above nominal is normally
acceptable. Any more than this has to be corrected by reducing the
capacitor value. Because best full load performance is the aim a
second "voltage dividing" capacitor is not fitted. This capacitor is
only appropriate in 3 phase converter systems which use an unloaded
pilot motor..

The situation gets more complicated with an unsymmetrical
machine. Roughly speaking you need to store a constant amount of
energy which, for a capacitor, is 1/2 x C x Vsquared. For the same
energy storage, most higher voltage AC rated capacitors are smaller
and cheaper than their lower voltage equivalents. Because of this some
machines have the capacitor phase wound with more turns of finer wire
as this allows them to use a smaller (and cheaper!) capacitor of
slighly higher voltage rating.

Without knowledge of the details of this winding, capacitor
choice is pretty close to guesswork. Some guidance can be obtained by
adjusting capacitor value for minimum phase 1 current (NOT including
the current drawn by the capacitor phase). The sensitivity of this
measurement can be improved by temporarily cancelling the phase 1
reactive current component by shunt capacitance directly across
phase 1

For slightly larger motor types, particularly those with lots
of stator teeth, some manufactures get even more cunning and fit the
stator with a deliberately unbalanced 3 phase winding - a low
resistance main winding and two windings with more turns of finer wire
occupying the two remaining phase positions. The old IBM golf ball
typewriters used motors of this type. Because it's a 3 phase winding
the phase change with load problem is eased because only 60 deg shift
is needed and the higher inductance of the two capacitor driven
windings permits the use of a smaller capacitor. These machines run
with roughly equal main and capacitor winding voltages at light load
dropping to about 80% capacitor winding voltage on heavy load.

If the motor has three leads the types are easily
differentiated by resistance measurement

True 3phase R R R

Symmetrical R R 2 x R

Asymmetric R n x R R + (n x R) "n" typically between 1.5 and 3

"3"phase R 2 x R 2 x R (typical - varies a bit with design)

Summing up - If it's a symmetrical or "3" phase machine
aim for equal volts. If it's unsymmetrical up to 50% higher on the
capacitor phase.

Jim

Many thanks, that's enough to make me glad that I already found an HVAC
service guy who looked up the right size capacitor for me; 45 mfd for a
36K BTU Lennox AC compressor. (The compressor, NOT the fan; the fan
capacitor was listed as 5 mfd.)

Nevertheless, your post made quite interesting reading, and I've filed
it away in case the problem comes up again during my remaining compus
mentus days.

Your response verifies once again the undisputible fact that rcm is
inhabited by worthy denizens of technology who are very knowledgeable in
many other venues, in addition to the chip making ones.

Jeff

--
Jeffry Wisnia

(W1BSV + Brass Rat '57 EE)

"Truth exists; only falsehood has to be invented."