Re: Balancing the Breaker Box

[daestrom]

[email protected] wrote:






The way a kWh meter works is the reverse of this. It develops a
torque proportional to VA*pf. Vary the power factor and the
torque developed in the disk varies. A drag magnet develops
counter-torque proportional to disk speed. The result is disk
*speed* is proportional to VA*pf.
-----------------
I have to disagree here, the instantaneous torque is proportional
to instantaneous va or power. Inertia averages this to get the
average power over each cycle (or longer). VA*pf implies that it
measures the product rms voltage and current and applies a bugger
(oops power) factor. The meter "sees" none of these because they
are not physically there. the equivalence is there in that the time
varying instantaneous values can be represented by their rms
frequency domain equivalents in steady state. Analysis of the meter
uses the rms approach as you have done (it avoids a nasty mess of
non-linear differential equations) but the meter doesn't.


But wouldn't you say that the torque developed is a function of the
phase angle between current and voltage? If the current lags 90
degrees from the applied voltage, then the magnetic fields of the
current coil and voltage coil are almost exactly in-phase (owing to
the high inductance in the potential coil). With the two magnetic
fields pulsing 'in-phase', there is no torque either forward or
reverse developed.
---------------
I have no problem with this. The meter doesn't measure phase angle.
Note that the induction disc motor is essentially a form of single
phase motor. The disc wont start but if already rotating there will
be a torque bias in that direction. A single phase motor depends on
this bias which is greatest near synchronous speed. However, in the
case of the induction disc there will be very little unbalance torque
-if any as the torque speed curve is essentially (and desirably)
constant torque in the operating region (just about standstill)
There will be a pulsating torque.

The simple fact that power flow in the opposite direction develops
torque in the opposite direction shows that phase-angle between
current and applied voltage is 'built-in' to the device.

Yes it is, in the same way it is built into a conventional
electromechanical (dynamometer) wattmeter. The torque at any instant
depends on the product of instantaneous voltage and instantaneous
current. On this basis, it simply averages the instantaneous torque.
If the voltage and current are 90 out of phase, the instantaneous
voltages and currents result in a double frequency power with 0 average

Mathematically we can say -for sinusoids:
p(t)=Vmcos(wt)*Imsin(wt+phi) =(VmIm/2){cos(phi) +a second harmonic
power term with 0 average]
The average over a period is (VmIm/2)*cos phi +0 =Vrms*Irms* cos(phi)

Physically the meter simply produces a torque which is proportional
to the instantaneous power and inertially averages it.
Specifically, it doesn't measure phase angles, rms voltages or find
pf -that is my point.
If the voltage and current coils have high R/X values then the meter
will be able to handle distorted waves with reasonable accuracy (and
without doing a fourier analysis). A digital KWH meter will simply
do the same v(t)*I (t) and averaging as a mechanical meter but with
a few bells and whistles can be made to measure KVAH (pf*H is
possible but meaningless) as well but such measurements aren't
required or necessary for determination of energy.

Yes, of course you're right that the inertia *averages* out the
torque, but it's not 'instantaneous va', it's 'instantaneous
power'. But 'average power' *is* rms-volt * rms-current *
power-factor in a sine-wave only system (i.e. no harmonic content)

instantaneous power = v(t)i(t) This happens to be the same as
instantaneous va but I should not have used that term. The concepts
of VA and VAR's are related to phasor analysis which is a
mathematical model which gives us the pertinent information without
the labor of solving a mess of differential equations. At your 120V
outlet- there is no actual 120V source as can be seen if you
examine the voltage with an oscilloscope.

Certainly, use of rms volts(magnitude)*rms current magnitude *power
factor will give the same average power. That's part of the reason we
use this model- it works.
Also, this "model" allows us a reasonable chance of solving
not-so-simple circuits. Think of what the situation would be in
solving load flows for large systems using differential equations!
Phasor analysis essentially replaces these differential equations by
algebraic equations.
Another convenient model is the use of symmetrical components for
fault studies.
Another is the use of forward/backward fields to model a single
phase machine as two opposing machines.
In these cases there are direct relationships between the model
quantities and the actual quantities present.

You know all this. The point of this long winded diatribe is that,
too often, people think that the model is the actual thing.

(you're too kind

I understand that the 'true' measure of power is instantaneous V *
instantaneous I and that that can simplify to simpler terms in certain
specific situations (such as DC or sine waveforms).

I guess I just can't 'wrap my head around' the meter responding to
instantaneous V*I when the magnetic field from the potential coil is
delayed nearly 90 degrees from V.

---
The voltage coil and current coils are not co-axial. If the voltage
coil is displaced from the current coil, then when the current is
maximum, the flux of this coil is maximum but that of the voltage coil
is 0. When the voltage coil produces maximum flux , the current coil
flux is 0. So , as seen from outside, there is a shift of flux .
Ideally, if the voltage coil is 90 degrees apart in space from the
current coil, you would get a "2 phase" motor with only a rotating field
. Since the displacement is not 90 degrees, you get a weaker rotating
field as well as a pulsating field. Another example is a shaded pole
motor as used in small fans.

Yes, yes, I'm familiar with two phase motors and the 'shift' of the
flux. But since the disk is not ferromagnetic, that alone doesn't
create a torque (i.e. it's not a reluctance motor). So we have to have
an eddy current induced in the disk (a 'rotor current') and to my mind
it's the interaction of that eddy current with the magnetic field that
produces a torque. Much like the current in the squirrel cage of a
conventional single-phase motor.

A disk that was composed of numerous 'pie slices' insulated from one
another would not work. Right?

I think you have part of it but a conventional single phase motor
without a starting winding will, at start, have 0 average torque but a
healthy pulsating torque. If you have a second winding which is
ideally 90 degrees electrically (physically 90 degrees for a two pole
machine) AND the flux due to the second winding is delayed 90 degrees in
time, then you have a situation where you have a true rotating field
with no pulsating torque- as in a 2 phase motor, 3 phase motor or a
single phase motor with a dominant capacitor on the second winding.
A single phase meter lies somewhere in between -think of the voltage
coil as a starting winding which is always in the circuit. It may not
be in physical quadrature (e.g the shaded pole doesn't shift flux by 90
degrees) The torque will have pulsations as well as a steady component
but the pulsations have a 0 average.
Should the disk R/X be low? Since the "start winding" is always in
service the physical position of this winding with respect to the other
winding provides the needed bias. It seems, on a first consideration,
that a R/X ratio near 1 in the disk may be desirable in that the torque
will be nearly constant and maximized near standstill- just as in the
case of a class D induction motor. --

R/X near 1 would certainly work, but an R/X near infinity might not
(i.e. there has to be some inductance). With the eddy currents exactly
in phase with one winding's flux, the currents would decay before the
other winding's flux increased very much. I see your point about R/X
near unity, after all as you said class D motors have some of the best
starting torques and that is how they achieve this.

The disk doesn't see the voltage and current directly but does respond
to the total of currents in the v and I windings interacting with the
currents in the disk. You can then consider a model with two stator
coils and two rotor coils and wade through a bloody "gawdoffal" mess of
math (task given to grad students) to come up with an expression for
torque dependent upon both the position of the coils and the currents in
them to find an instantaneous torque expression. Then you can consider
steady state (sinusoid) at some given speed ( in any motor the torque
has nothing to do with Ldi/dt but is affected by I*dL/dx* dx/dt or the
speed voltage) and come up with a model using rms voltages and currents
and the phase between them. The fact that this model typically agrees
with simpler approaches used in typical steady state handwaving analysis
of induction machines is comforting.
Krause "Analysis of Electric Machinery" deals with some of this (at near
graduate level) and an old book by White and Wilson "electromagnetic
energy conversion" is another- this is definitely a graduate level
text. Many other texts simply jump into the steady state models- a bit
more practical but losing some concepts.

Well without getting into 'gawdoffal' calculations, it just seems that
if the eddy currents in the disk lag behind the flux that produces them
(i.e. the disk has some inductance) then the torque pulses would seem to
lag behind the instantaneous power 'pulses' that occur at twice line
frequency.

So I wonder how close the disk is operating near 'synchronous speed'.
Where I think the synchronous speed in this case is function of
mechanical shift between current and voltage coils (i.e. the equivalent
'number of poles' arranged around the rotor). But also the phase shift
between current in the two coils (which of course depends on connected
load and R/X of potential coil). That is, the time shift between the
flux of one pole and the other.

If the maximum power to be registered is anywhere near a fraction of
this 'sync speed', then you effectively have a significant variation in
slip of the rotor. Of course some motors have a pretty flat torque
curve at the lower end of speed when starting and for a given applied
voltage/current, that's what we want here. So that torque produced is
*not* a function of %slip but only the measured power. Or variations in
%slip are tiny because the 'sync speed' is so much higher than expected
speed of the rotor.

(ouch, my head's starting to hurt ;-) )

--
The voltage coil may not have a low R/X ratio. However, you don't want
it producing flux in phase with the current -
High harmonic content is still a problem because you do want the torque
independent of winding impedance- variations which comes back to the
desirability of an R/X that is on the high side.

All of the references I've found on the matter seem to say that the
potential coil does have a low R/X so that magnetic flux is nearly 90
lagging from applied voltage. If it's something 'in between', wouldn't
that give you some calibration issues? For example, if R/X is 1 in the
voltage coil, then a connected load with a current lagging by 45 degrees
would be exactly in-phase with the voltage coil's current. No torque
produced but the customer is getting power (at 0.707 pf)

daestrom

 

[Guest]

Yes, yes, I'm familiar with two phase motors and the 'shift' of the flux.
But since the disk is not ferromagnetic, that alone doesn't create a
torque (i.e. it's not a reluctance motor). So we have to have an eddy
current induced in the disk (a 'rotor current') and to my mind it's the
interaction of that eddy current with the magnetic field that produces a
torque. Much like the current in the squirrel cage of a conventional
single-phase motor.

----------
I'm not even considering a ferromagnetic disk - and a good example of an
unbalanced two phase motor is an drag cup control motor. A beer can stuck on
a nail in a rotating field will run as a motor. All that is needed is a
conductor and a component of the stator field that "shifts". (A paper clip
will also rotate- done both)

A disk that was composed of numerous 'pie slices' insulated from one
another would not work. Right?

---
Not necessarily but I would expect poor performance. If the slices were
connected only at the center and periphery then it may actually work better
than an unsliced disk. Messy to analyze.

R/X near 1 would certainly work, but an R/X near infinity might not (i.e.
there has to be some inductance). With the eddy currents exactly in phase
with one winding's flux, the currents would decay before the other
winding's flux increased very much. I see your point about R/X near
unity, after all as you said class D motors have some of the best starting
torques and that is how they achieve this.

--
Using conventional steady state induction motor models, the slip at which
maximum torque occurs is determined by s =R/X The magnitude of this
maximum is independent of R/X. If R/X is infinite - infinite slip is the
result and the torque at any finite speed is 0.
However, consider a coil carrying a steady state sinusoidal current and
producing a flux in phase with the current. This flux induces a disk voltage
(d(flux)/dt which will lag the coil flux by 90 degrees. Now this voltage
will produce a disk current lagging the voltage by 90 degrees. This disk
current produces a flux in phase with the disk current -*Lagging the
original current by 90 degrees*-and the disk flux will produce a voltage
lagging by 90 degrees or 180 degrees out of phase with the original current.
In other words, when a current flows, it will see a back emf and power is
delivered to the disk and dissipated as I^2R loss in the disk. What you
have with this single coil is a transformer and the inductances that we
normally look at, which are the leakage inductances, do not enter into the
transformer action.
Any considerations of flux decay are transient conditions but since
transient conditions are really not of importance in a KWH meter, this is a
red herring.

Well without getting into 'gawdoffal' calculations, it just seems that if
the eddy currents in the disk lag behind the flux that produces them (i.e.
the disk has some inductance) then the torque pulses would seem to lag
behind the instantaneous power 'pulses' that occur at twice line
frequency.

-------------
So what? If you consider the flux due to each winding then you will have a
product depending on flux sub I and flux sub V with the same relative phase
angle as the original I and V and the same average over a cycle (even using
the same starting point for the average).

So I wonder how close the disk is operating near 'synchronous speed'.
Where I think the synchronous speed in this case is function of mechanical
shift between current and voltage coils (i.e. the equivalent 'number of
poles' arranged around the rotor). But also the phase shift between
current in the two coils (which of course depends on connected load and
R/X of potential coil). That is, the time shift between the flux of one
pole and the other.
If the maximum power to be registered is anywhere near a fraction of this
'sync speed', then you effectively have a significant variation in slip of
the rotor. Of course some motors have a pretty flat torque curve at the
lower end of speed when starting and for a given applied voltage/current,
that's what we want here. So that torque produced is *not* a function of
%slip but only the measured power. Or variations in %slip are tiny because
the 'sync speed' is so much higher than expected speed of the rotor.

(ouch, my head's starting to hurt ;-) )

OK- you've got it. Look at 2 phase drag cup control motors (and your Navy
experience may have introduced you to them) These operate near standstill
where ideally torque is independent of slip.

All of the references I've found on the matter seem to say that the
potential coil does have a low R/X so that magnetic flux is nearly 90
lagging from applied voltage. If it's something 'in between', wouldn't
that give you some calibration issues? For example, if R/X is 1 in the
voltage coil, then a connected load with a current lagging by 45 degrees
would be exactly in-phase with the voltage coil's current. No torque
produced but the customer is getting power (at 0.707 pf)

-----------
The R/X ratio is not simply that of the voltage coil itself. In fact a low
value is what one will expect. When one considers the effect of an R/X ratio
in a motor , the rotor R and the total X is considered. The disk has an
effect that is included. In fact the resistance and the leakage inductance
of the coil would ideally be 0- as in an ideal transformer. This also
means that the effect of the current winding and a hell of a lot of
geometrical considerations are important. I used the R/X ratio because, in
conventional steady state analysis, it can be shown that this is an
approximate maximum torque condition. Ideally the coil would have 0
resistance, 0 leakage inductance leaving only mutual inductance because
these do introduce a voltage drop in the winding which is a factor to be
considered. In this situation the R/X ratio is that of the disk itself.
When I said "you don't want it to have flux in phase with the current" I
should have said "you don't want it to have voltage coil flux in phase with
the current coil flux"

I have a feeling of going in circles because what is needed is an organized
step by step analysis which is hard to do without equations and diagrams.
Anyhow, you have presented intriguing questions .

Much of what I knew about these meters in particular has long faded so I am
looking at basic induction motor theory. I do recall that there are
corrective adjustments in the meter such as magnetic shunts, which can be
used in calibration. Obviously they work.

 

[Dave Foreman]

Krause "Analysis of Electric Machinery" deals with some of this (at near
graduate level) and an old book by White and Wilson "electromagnetic energy
conversion" is another- this is definitely a graduate level text. Many
other texts simply jump into the steady state models- a bit more practical
but losing some concepts.

Don
Do you have any more information on the second book by White and
Wilson? I used AddAll and found quite a few copies of the book by
Krause at very reasonable prices but did not find any thing on the
second book.
Thanks
Dave Foreman

 

[Guest]

Don
Do you have any more information on the second book by White and
Wilson? I used AddAll and found quite a few copies of the book by
Krause at very reasonable prices but did not find any thing on the
second book.
Thanks
Dave Foreman

Oops. Correction:

It is White & Woodson (of MIT), "Electromechanical Energy
Conversion"Wiley 1959, Lib. of Congress No. 59-5874
It is the original book that covers machines from a generalized basis and is
quite mathematical , by page 30 it has covered electromagnetic force
production basics and is starting on the Hamiltonian. The developments go
on to general basic models which can be used, depending on the restraints
applied, to represent any machine. Years ago, Westinghouse capitalized on
this to make a generalized lab machine set where, depending on connections
could be a DC machine, a 2 phase induction machine, a synchronous machine,
etc-- unfortunately is was atypical and somewhat inferior machine in any
configuration but did illustrate the theory.
Amazon lists one copy at $165 -it's not worth that! Krause,, while sticking
to more conventional machines is probably a better bet.

 

[Dave Foreman]

Oops. Correction:

It is White & Woodson (of MIT), "Electromechanical Energy
Conversion"Wiley 1959, Lib. of Congress No. 59-5874
It is the original book that covers machines from a generalized basis and is
quite mathematical , by page 30 it has covered electromagnetic force
production basics and is starting on the Hamiltonian. The developments go
on to general basic models which can be used, depending on the restraints
applied, to represent any machine. Years ago, Westinghouse capitalized on
this to make a generalized lab machine set where, depending on connections
could be a DC machine, a 2 phase induction machine, a synchronous machine,
etc-- unfortunately is was atypical and somewhat inferior machine in any
configuration but did illustrate the theory.
Amazon lists one copy at $165 -it's not worth that! Krause,, while sticking
to more conventional machines is probably a better bet.

Thanks Don
Dave Foreman

 

[daestrom]

----------
I'm not even considering a ferromagnetic disk - and a good example of an
unbalanced two phase motor is an drag cup control motor. A beer can
stuck on a nail in a rotating field will run as a motor. All that is
needed is a conductor and a component of the stator field that
"shifts". (A paper clip will also rotate- done both)

I was thinking of completely insulated, so there was no 'complete
circuit' in the rotor.

Thanks for the discussion, it helped refresh my mind how how these
buggers work. Of course the new digital ones are a whole different story.

daestrom

 

[Guest]

I was thinking of completely insulated, so there was no 'complete circuit'
in the rotor.

Thanks for the discussion, it helped refresh my mind how how these buggers
work. Of course the new digital ones are a whole different story.

daestrom

If no rotor currents cannot flow (or are restricted as in the situation you
mention- which is analogous to the concept of laminations to minimize eddy
current- then there will be little or no torque.

I have since run across a site which indicates that the flux from the
voltage coil is adjusted , apparently by a shading coil, so that it is , at
unity pf, 90 degrees out of phase with the current coil flux. Beyond this
the site really didn't get down to specifics other than considering the
meter as a type of 2 phase meter where torque at standstill (or at near
standstill) will be essentially directly proportional to current at a given
voltage. One could take a 2 phase control motor, add gears and come up with
a watthour meter. It is interesting that the "Ferranti effect" which is
related to induction machines, was known before Tesla came up with the
polyphase induction motor.

You have the term "bugger" correctly applied but in polite society it is
the "Bougerre Factor".

 

[Archimedes' Lever]

TROLLS AND CREEPS LIKE YOU SCARED USER ROYKEY FROM THIS MEDIUM WITH
YOUR NONSENSE AND FALSE ACCUSATIONS

KRW YOU HAVE BEEN SUBJECT TO SEVERAL CRIMNAL INVESTIGATIONS AND
PROBES YOU DECIETFUL FUCKTARD

YOU HAVE THE NERVE TO MENTION ROYKEY AGAIN AND AGAIN AS IF HE OWED YOU
SOMETHING

AS FAR AS I AND THE REST OF USENET IS CONCERNED THE LOST A GREAT ASSET
AND A HELPFUL FRIEND BECAUSE OF IDIOTIC RETARDS AS YOU AND THE REST OF
YOUR FAGGOTY TROLLOPING FRI3ENDS

IF RIGHTEOUSNESS MATTERS SO MUCH TO YOU
GO BACK TO SUCKLE ON YOUR MOMMY AND LEAVE TGHE GROUP WE ALL KNOW YOU
ARE DYING TO BLOW SOSMETHING UP CREEP

PERHAPS HE WILL EMERGE AND RETURN TO ASSIST THIS GROUP AGAIN



I AM PROTEUS

This "PROTEUS" retard is the WebTV idiot that has claimed for months to
be a computer program, and not a person at all. Then, the dope goes and
lets his emotions run away with him every time he posts.

Not only does this idiot need help, but merely asking him to seek it
isn't enough. He needs to be reported to someone that will actually
check him out and commit his aberrant ass to an institution.

I think that "Proteus IIV" is a danger to himself and others. He
should be placed into a mental institution or jail as is the current
practice.

Go away, ProTardeus, there is no help for your illness here.

 

[Guest]

I think that "Proteus IIV" is a danger to himself and others. He
should be placed into a mental institution or jail as is the current
practice.

Block him and then you'll only see his drivel if someone responds to him.