You have a machine that requires 240 volt three phase power. It requires
connection to 3 phase lines and ground, but not neutral. You ask your
utility to supply 240 volt delta and they say no. The machine fails to
operate on 208 volts. What do you do? How many different solutions could
you think of to explore?
Get an appropriate star delta transformer, perhaps?
Move to a country where the distribution companies are actually helpful?
Connect the supply that you *do* have to the heater on a *large*
jacuzzi, ideally overlooking a large beautiful mountain range. The
jacuzzi to have a wine cooler and suitable quantities of a fine wine or
two. Chill the parts that benefit from chilling. Warm the parts that
don't. Life really is too short...
These days a lot of people are going to VFDs when they don't have the
flavor of power they need. They are getting cheaper than transformers
and a lot better than MG sets although the MG does a great job of
isolating line hits..
Even years ago we had solid state converters to get the 36KVA 400hz
they needed in computer rooms. It was part of the UPS system.
A Rockwell Allen Bradley VFD is the answer. The smaller one's that do
up to 10 hp cost less than a PC. The last one I used took about 160
variables programmed in using a little key pad. They can be connected
to a PC for even more fun.
Is this a residential application?
Obvious but not yet mentioned are autotransformers on each 208 volt
phase. Also, the utility will probably supply 480 volt delta and you
can use a 480240 volt transformer. Choice of solution would depend on
other 3 phase equipment that might require Y, delta at different
voltages and the magnitudes of these loads.
I'd put the phase converter at the bottom of the list no matter what
its initial cost advantage over a transformer.
But you know all of this so what's up?
Chuck

>You have a machine that requires 240 volt three phase power. It requires
>connection to 3 phase lines and ground, but not neutral. You ask your
>utility to supply 240 volt delta and they say no. The machine fails to
>operate on 208 volts. What do you do? How many different solutions could
>you think of to explore?

 Is this a residential application?
It's three phase. I didn't mention country. But in the USA, three phase
power to residential users is rare. But I'm not really asking about the
type of service, just how to get a picky 240 volt machine to work.
 Obvious but not yet mentioned are autotransformers on each 208 volt
 phase. Also, the utility will probably supply 480 volt delta and you
 can use a 480240 volt transformer. Choice of solution would depend on
 other 3 phase equipment that might require Y, delta at different
 voltages and the magnitudes of these loads.
They might supply 480Y/277, too.
At least one utility I found would provide 240Y/139 in certain locations.
I don't know how they accomplish that. Maybe they found some transformers
they can get the 138.564 volts out of, or approximate it some other way.
But I do know utilities prefer not to have delta secondary services these
days, presumably due to phase feedback situations and blowing lots of MV
fuses.
 I'd put the phase converter at the bottom of the list no matter what
 its initial cost advantage over a transformer.
I didn't think of that. But I don't think I would consider it, either.
 But you know all of this so what's up?
I'm just checking to see all the creative solutions. Personally, if I
were faced with this, I'd take the 208Y/120 and add the autotransformer
in boost configuration to get closer to that 240 volt need.
Although 208 volts might not work on some 240 volt machines, hopefully
just a few volts away would achieve that. Boosting each 120 volt leg
to 136 volts with a 120>16 volt transformer would give you 235.5589
volts linetoline. That might be enough. But if one really needs to
get closer, there are other configurations. The closest one I figured
out would get 239.7 Y / 138.4 volts. It would use a 240>24 volt
transformer with primary connected CA and secondary wired in series
from A, giving a "bent" leg. The primary would have 208 volts at a 30
degree phase angle relative to the NA leg, giving a boost of 20.8 volts
at the same angle. That would give 138.4 volts with a sum angle of 4.3
degrees for a LL voltage of 239.7. There are configurations for more
than 240 volts, as well.
Another option is a 208/120 to ScottT.
 
> You have a machine that requires 240 volt three phase power. It requires
> connection to 3 phase lines and ground, but not neutral. You ask your
> utility to supply 240 volt delta and they say no. The machine fails to
> operate on 208 volts. What do you do? How many different solutions could
> you think of to explore?

 Do your own homework.
I already did. I'm just checking to see if I missed any creative ideas and
to see what kind of diversity others as a group would have.
/
/
I actually have this issue Phil. I used a buck boost transformer. This is a
light and intermittent load. A bank of relays at the end of a long cable
run.

> >  > 
> > You have a machine that requires 240 volt three phase power. It
 requires
> > connection to 3 phase lines and ground, but not neutral. You ask your
> > utility to supply 240 volt delta and they say no. The machine fails to
> > operate on 208 volts. What do you do? How many different solutions
 could
> > you think of to explore?
> 
>  Do your own homework.
>
> I already did. I'm just checking to see if I missed any creative ideas
 and
> to see what kind of diversity others as a group would have.
>
> 
>
 /
>  Phil Howard KA9WGN (ka9wgn.ham.org) / Do not send to the address below
 
>  first name lower case at ipal.net / snippedforprivacy@ipal.net
 
>
 /


 I actually have this issue Phil. I used a buck boost transformer. This is a
 light and intermittent load. A bank of relays at the end of a long cable
 run.
I'm curious what the configuration is. I have a list of many different
configurations near to, and far from, 240 volts, than can be derived from
208Y/120.
Phil, why do you use terms like 235.5589 volts? No electrical
engineers do that. It is improper usage and unprofessional to imply
precision to 4 decimal places for common electrical circuits.
You have some unique and original ideas, but it almost seems that you
are off in a different electrical world somewhere, with your own
standards and conventions.

>Although 208 volts might not work on some 240 volt machines, hopefully
>just a few volts away would achieve that. Boosting each 120 volt leg
>to 136 volts with a 120>16 volt transformer would give you 235.5589
>volts linetoline. That might be enough. But if one really needs to
>get closer, there are other configurations.

 Phil, why do you use terms like 235.5589 volts? No electrical
 engineers do that. It is improper usage and unprofessional to imply
 precision to 4 decimal places for common electrical circuits.
The precision _IS_ there ... because the number is the result of an
arithmetic calculation using a high level of precision with a formula
I believe to be accurate. This is very different than if I were to
physically measure the voltage of a circuit with a voltmeter that has
4 digits of accuracy and precision. In the latter case you would see
me write "235.6" or whatever it happens to be.
It is an accuracy vs. precision issue. Accuracy is needed in order to
correctly reflect the mathematical formula used. In the event some other
formula results in a value somewhere near there, that would when rounded
in the practical manner yield the very same result, the accuracy value
is what will distinguish the different formulas. Precision is then how
the value is expressed to carry the accuracy (of the calculation).
Although in this case I do not know of another formula that could give
a result close enough to, when rounded, appear to be the same, I cannot
rule out some formula existing. In the past I have run into cases where
entirely different formulas ... formulas that are not mathematically the
same (e.g. one cannot be transformed into the other), give results that
are closer to each other than the practical precision normally used.
So ... as a standard practice, when numbers are produced as a result of
doing mathematical/arithmetic calculations, I use enough precision to
give a very high level of confidence in matching the correct formula.
Sometimes I express a precision as extreme as arithmetic being performed
can do. Sometimes I reduce it some for convenience, but leave enough to
be sure there is likely no ambiguity as to which formula is used.
Someone wishing to review my calculations can then match the numbers very
closely to be sure that not only am I using the correct formula, but am
also using valid trigonmetry implementations (e.g. code I did not write).
If I measure a voltage with a voltmeter, I will express it as precisely
as the device is capable of accurately measuring and precisely displaying.
If it has an accuracy of 1/10 of a volt in a 200 volt range (rather good)
I'll use that and might state the voltage as "119.1" or "121.0". But if
it only has an accuracy of 1 volt, I'll state it as "119" or "121".
So when you see me use a highly precise expression like "235.5589", it is
coming from a mathematical calculation done with at least 6 or 7 digits
of precision (probably more since I default to using the double type which
has 14 or so digots), using a formula I believe to be accurate.
If I ever manage to make a real physical measurement with such accuracy,
I'll be sure to let you know about that miracle device capable of doing
such a thing.
 You have some unique and original ideas, but it almost seems that you
 are off in a different electrical world somewhere, with your own
 standards and conventions.
Like doing mathematical formula based programming to automatically explore
lots of models?
Here is the output of one of my programs that explores a variety of ways
to configure different buckboost transformers, including 480/240/120 volt
transformers, and running transformers at much lower than design voltage
just as a means to get a desired ratio (e.g. 208 volts being fed to a
transformer designed step 480 volts down to 120 just because that is the
only common transformer to get a 4:1 ratio).
The first 2 mumeric colums give the resultant system (at calculation level
precision slightly reduced to fit the output format). The 4th and 5th give
the voltage being added to 120 volts, and the phase angle of that added
voltage vector. The 6th gives the buckboost transformer primary voltage,
and the 7th and 8th describe the buckboost transformer being used.
Notice the two "103.923048" volt results. They are really the same thing
in a geometric/vector sense, even if the configuration to arrive at them
are different. The precision of the expression reveals that.
Notice the rows with "228.630707" and "228.945408". Those are _different_
kinds of configurations that are _not_ the same as vector math goes. The
fact that the numbers are different reveals this. If these had been
rounded, that fact would be hidden. If you measured them with a typical
voltmeter, you wouldn't know as both might read "229".
There are other examples of close numbers in this list.
103.923048 Y / 60.000000 : 120.000 + 60.000 @ 180 (120.000 via 240 > 120)
103.923048 Y / 60.000000 : 120.000 + 103.923 @ 150 (207.846 via 240 > 120)
137.477271 Y / 79.372539 : 120.000 + 51.962 @ 150 (207.846 via 480 > 120)
152.420471 Y / 88.000000 : 120.000 + 32.000 @ 180 (120.000 via 120 > 32)
166.276878 Y / 96.000000 : 120.000 + 24.000 @ 180 (120.000 via 120 > 24)
168.000000 Y / 96.994845 : 120.000 + 27.713 @ 150 (207.846 via 240 > 32)
177.583783 Y / 102.528045 : 120.000 + 20.785 @ 150 (207.846 via 240 > 24)
180.000000 Y / 103.923048 : 120.000 + 60.000 @ 120 (120.000 via 240 > 120)
180.133284 Y / 104.000000 : 120.000 + 16.000 @ 180 (120.000 via 120 > 16)
181.865335 Y / 105.000000 : 120.000 + 15.000 @ 180 (120.000 via 120 > 15)
183.597386 Y / 106.000000 : 120.000 + 14.000 @ 180 (120.000 via 120 > 14)
185.329436 Y / 107.000000 : 120.000 + 13.000 @ 180 (120.000 via 120 > 13)
186.418883 Y / 107.628992 : 120.000 + 32.000 @ 120 (120.000 via 120 > 32)
187.061487 Y / 108.000000 : 120.000 + 12.000 @ 180 (120.000 via 120 > 12)
187.445992 Y / 108.221994 : 120.000 + 13.856 @ 150 (207.846 via 240 > 16)
190.494094 Y / 109.981817 : 120.000 + 24.000 @ 120 (120.000 via 120 > 24)
192.468179 Y / 111.121555 : 120.000 + 10.392 @ 150 (207.846 via 240 > 12)
193.989690 Y / 112.000000 : 120.000 + 8.000 @ 180 (120.000 via 240 > 16)
195.468668 Y / 112.853888 : 120.000 + 16.000 @ 120 (120.000 via 120 > 16)
196.150452 Y / 113.247517 : 120.000 + 15.000 @ 120 (120.000 via 120 > 15)
196.845117 Y / 113.648581 : 120.000 + 14.000 @ 120 (120.000 via 120 > 14)
197.453792 Y / 114.000000 : 120.000 + 6.000 @ 180 (120.000 via 240 > 12)
197.552525 Y / 114.057003 : 120.000 + 13.000 @ 120 (120.000 via 120 > 13)
198.272540 Y / 114.472704 : 120.000 + 12.000 @ 120 (120.000 via 120 > 12)
201.275930 Y / 116.206712 : 120.000 + 8.000 @ 120 (120.000 via 240 > 16)
202.849698 Y / 117.115328 : 120.000 + 6.000 @ 120 (120.000 via 240 > 12)
208.624064 Y / 120.449159 : 120.000 + 10.392 @ 90 (207.846 via 240 > 12)
209.227149 Y / 120.797351 : 120.000 + 13.856 @ 90 (207.846 via 240 > 16)
210.940750 Y / 121.786699 : 120.000 + 20.785 @ 90 (207.846 via 240 > 24)
213.232268 Y / 123.109707 : 120.000 + 6.000 @ 60 (120.000 via 240 > 12)
213.316666 Y / 123.158435 : 120.000 + 27.713 @ 90 (207.846 via 240 > 32)
215.109275 Y / 124.193398 : 120.000 + 8.000 @ 60 (120.000 via 240 > 16)
218.238402 Y / 126.000000 : 120.000 + 6.000 @ 0 (120.000 via 240 > 12)
218.979451 Y / 126.427845 : 120.000 + 12.000 @ 60 (120.000 via 120 > 12)
219.970453 Y / 127.000000 : 120.000 + 13.000 @ 60 (120.000 via 120 > 13)
220.970586 Y / 127.577427 : 120.000 + 14.000 @ 60 (120.000 via 120 > 14)
221.702503 Y / 128.000000 : 120.000 + 8.000 @ 0 (120.000 via 240 > 16)
221.979729 Y / 128.160056 : 120.000 + 15.000 @ 60 (120.000 via 120 > 15)
222.997758 Y / 128.747816 : 120.000 + 16.000 @ 60 (120.000 via 120 > 16)
223.615742 Y / 129.104609 : 120.000 + 10.392 @ 30 (207.846 via 240 > 12)
226.495033 Y / 130.766968 : 120.000 + 51.962 @ 90 (207.846 via 480 > 120)
228.630707 Y / 132.000000 : 120.000 + 12.000 @ 0 (120.000 via 120 > 12)
228.945408 Y / 132.181693 : 120.000 + 13.856 @ 30 (207.846 via 240 > 16)
230.362757 Y / 133.000000 : 120.000 + 13.000 @ 0 (120.000 via 120 > 13)
231.447618 Y / 133.626345 : 120.000 + 24.000 @ 60 (120.000 via 120 > 24)
232.094808 Y / 134.000000 : 120.000 + 14.000 @ 0 (120.000 via 120 > 14)
233.826859 Y / 135.000000 : 120.000 + 15.000 @ 0 (120.000 via 120 > 15)
235.558910 Y / 136.000000 : 120.000 + 16.000 @ 0 (120.000 via 120 > 16)
239.699812 Y / 138.390751 : 120.000 + 20.785 @ 30 (207.846 via 240 > 24)
240.399667 Y / 138.794813 : 120.000 + 32.000 @ 60 (120.000 via 120 > 32)
249.415316 Y / 144.000000 : 120.000 + 24.000 @ 0 (120.000 via 120 > 24)
250.567356 Y / 144.665131 : 120.000 + 27.713 @ 30 (207.846 via 240 > 32)
263.271723 Y / 152.000000 : 120.000 + 32.000 @ 0 (120.000 via 120 > 32)
274.954542 Y / 158.745079 : 120.000 + 60.000 @ 60 (120.000 via 240 > 120)
274.954542 Y / 158.745079 : 120.000 + 103.923 @ 90 (207.846 via 240 > 120)
289.309523 Y / 167.032931 : 120.000 + 51.962 @ 30 (207.846 via 480 > 120)
311.769145 Y / 180.000000 : 120.000 + 60.000 @ 0 (120.000 via 240 > 120)
374.699880 Y / 216.333077 : 120.000 + 103.923 @ 30 (207.846 via 240 > 120)
 219.970453 Y / 127.000000 : 120.000 + 13.000 @ 60 (120.000 via 120 > 13)
I didn't even notice this one before. But I checked. It is correct that
a vector of exact whole number length 120 at 0 degrees plus a vector of
exact whole number length 13 at 60 degrees (1/6 of the arc of a circle)
yields a sum vector that is an exact whole number length 127 (though at
an angle I am unable to find a rational relationship to PI for). While
it is possible to have triangles at any whole number lengths you pick, as
long as no side is equal to or greater than the sum of the other sides,
perhaps it is interesting when some can be formed with at least some
corners having a rational relation to PI (e.g. 1/6 of a full circle).
And I would not have noticed it had I rounded all the numbers to whole.
OK, so I like precision in calculations, like the square root of 3 is:
1.7320508075688772935274463415058723669428052538103806280558069794519330169088
But some people seem to prefer whole numbers. So for them I have:
13005325352767864879663023255649031427 / 7508628093319191445537920541850040962
`
These digital volt meters may have 4 digits of "precision" but nobody
says they have that degree of "accuracy". Most will give you an
inaccurate answer precise out to 4 decimal places unless you just got
them back from the calibration lab and you haven't done anything to
change the calibration (dropped it, had a static discharge while you
were using it, left in in a hot car or whatever)
Considering the utility only uses a +/ 10v "guideline" (they won't
give you your money back if it is worse) who cares about tenths of a
volt or less.
Just to be pendantic, just because the sqrt(3) can be known to a high degree
of precision, you're multiplying a number that has as many significant
digits as you could want, with a number that is stated to only have three
significant digits (120. with the decimal is three sig. digits, 120 without
the decimal is only two significant digits). Mathematical purists will tell
you that any multiplication or division can only be carried out to the same
number of significant digits as the least significant term. So...
120. * sqrt(3) = 236. (three significant digits in 120.)
120 * sqrt(3) = 240 (only two significant digits in 120)
And backing up a bit further, when you add you have to be even more careful
about precision.
120. + 16. = 136. (because 120. (with the decimal point) is three
significant digits.)
But ...
120 + 16 = 140 (because the '16' has to be shifted to at least the same
decade as the least significant digit of 120 and that means you round it off
to...
120 + 20 = 140
Most of us skimp on the rules a bit, but taking a number like 120 * sqrt(3)
and claiming the answer to seven significant digits is over the top.
daestrom
I told you I was going to be pendantic .... :)
 These digital volt meters may have 4 digits of "precision" but nobody
 says they have that degree of "accuracy". Most will give you an
 inaccurate answer precise out to 4 decimal places unless you just got
 them back from the calibration lab and you haven't done anything to
 change the calibration (dropped it, had a static discharge while you
 were using it, left in in a hot car or whatever)
Suppose you know that there is a 95% probability that the meter will be
off by plus or minus 1 volt. You get a reading of 121.3 volts. What is
the probability that the real voltage is 120.1 volts? Which of these is
a more correct sattement:
1. 95% probability the voltage is between 120.3 and 122.3
2. 95% probability the voltage is between 120 and 122
The interplay of accuracy and precision can be an interesting one. For more
information, see:
formatting link
is, if you have more than a 50% trust in the accuracy and precision of
Wikipedia :)

> > 
> >Although 208 volts might not work on some 240 volt machines, hopefully
> >just a few volts away would achieve that. Boosting each 120 volt leg
> >to 136 volts with a 120>16 volt transformer would give you 235.5589
> >volts linetoline. That might be enough. But if one really needs to
> >get closer, there are other configurations.
> 
>  Phil, why do you use terms like 235.5589 volts? No electrical
>  engineers do that. It is improper usage and unprofessional to imply
>  precision to 4 decimal places for common electrical circuits.
>
> The precision _IS_ there ... because the number is the result of an
> arithmetic calculation using a high level of precision with a formula
> I believe to be accurate. This is very different than if I were to
> physically measure the voltage of a circuit with a voltmeter that has
> 4 digits of accuracy and precision. In the latter case you would see
> me write "235.6" or whatever it happens to be.
>

 Just to be pendantic, just because the sqrt(3) can be known to a high degree
 of precision, you're multiplying a number that has as many significant
 digits as you could want, with a number that is stated to only have three
 significant digits (120. with the decimal is three sig. digits, 120 without
 the decimal is only two significant digits). Mathematical purists will tell
 you that any multiplication or division can only be carried out to the same
 number of significant digits as the least significant term. So...

 120. * sqrt(3) = 236. (three significant digits in 120.)
I get something closer to 207.84609690826527522329356098070468403313663 :)
If I use 1.732 I get 207.84
If I use 1.73 I get 207.6
If I use 1.7 I get 204
If I use 2 I get 240
I have no idea where the 236 came from. Did you mean to start with 208
and just copied the number I was using before?
 120 * sqrt(3) = 240 (only two significant digits in 120)
That's as bad as sqrt(3) = 2.
 And backing up a bit further, when you add you have to be even more careful
 about precision.

 120. + 16. = 136. (because 120. (with the decimal point) is three
 significant digits.)
In the three phase wye buckboost example, I consider the 136 to be
accurate and precise because the transformer can have an exact 15:2
winding ratio to derive 16 volts from 120 volts.
 But ...

 120 + 16 = 140 (because the '16' has to be shifted to at least the same
 decade as the least significant digit of 120 and that means you round it off
 to...
 120 + 20 = 140
You won't be able top tell the difference between using a 16 volt boost
transformer and a 24 volt boost transformer, if you express the result
as 140 volts.
 Most of us skimp on the rules a bit, but taking a number like 120 * sqrt(3)
 and claiming the answer to seven significant digits is over the top.
It depends on the context. If I am doing a calculation that _should_
come up with the same value as 120 volts times the square root of three,
but want to just express the result value to let someone else match it,
I will use more digits. Usually 6 is enough to not just identify the
system, but identify that the calculation did more than just get into
the right ball park.
 daestrom
 I told you I was going to be pendantic .... :)
I consider myself to be pedantic. My practice is that if there is a known
statistical error in the values I'm calculating with, I let those errors
work their way through in the appropriate way. I do NOT increase those
error artificially. So if I am working with 120 volts plus or minus 10
volts (at 95% confidence), then in three phase wye, the line to line value
is 207.846096908265275 volts plus or minus 17.3205080756887729 volts (at
95% confidence). THEN I round that result down to 208 volts plus or minus
17 volts, and let the confidence figure get a little fuzzy.
I would disagree with your "mathematical purist" (mentioned way above)
because I feel that is being quit UNpure to allow TWO sources of error
to operate in a formula when only one value (the measurement) has error
and the other (the mathematically defined square root of three) has no
error.
How much I round depends on the context. If I'm talking about a type of
electrical system, I'll say something like 208Y/120 or 220Y/127 as the
case may be. Accuracy is not important there as it is just identification,
not a measurement or calculation (which can be an identification of the
formula used).
Back when I was in junior high school, without the aid of any calculator
or computer, I pondered the meaning of the frequency 3.58 MHz as it related
to the TV broadcast standards (which at the time I "knew" to be 15,750 Hz
horizontal and 60 Hz vertical. But I found a book in the school library
that gave the value as 3.579545 MHz. Just that much information allowed
me to "reverse engineer" this number to determine it came from 5 MHz times
63 divided by 88, and really had "454545" repeated (3579545.45[45..] Hz),
and that the horizontal frequency was really 15734.265734[265734..] Hz,
and that the vertical frequency was really 59.940059[940059..] Hz. All
that semantic understanding came out of just getting 4 more digits of
precision. Over a decade later I found that the FCC broadcast rules
actully defined the value the same way, as 5 MHz times 63/88. It is still
identifiable as 3.58 MHz. But if I want to compare it to something else
semantically, I need a much more precise value. Would you recognize it
as the NTSC color subcarrier frequency if I called it 3.6 MHz? or 4 MHz?
Now along comes the new ATSC standard. Yes, I have very precise values
for it. What is _really_ scary about the exact DEFINED bits per second
rate it has is that the fractional part (in either MHz or Hz) in decimal
repeats only after 312 digits! But it is a lot easier to express it as
its exactly defined value in the form of 867996/44759 Mbps. Work out
that division on a calculation with thousands or more digits precision
adn you will get the repeat every 312 digits. Fortunately I only need
to express 11 digits to nail the value dead on.
How many digits of precision is needed from a calculation that _should_
give a result of exactly 1 do you need to see as a value just shy of 1
(e.g. 0.999....) to know that it _should_ be exactly one as opposed to
merely being _nearly_ 1? Does 0.999 do it? Does 0.999999 do it? How
about 0.999999999999999999999999999999999999999999999999? I would never
say 0.9 is 1. But as the number of 9's continues, the confidence that
the valus really should have been exactly 1 increases rapidly.
Do you do any computer programming? If so, do you just add up a long
list of floating point values in the order given, or do you sort them
so you accumulate the sum by adding the lowest values first?
How many digits do you want for the square root of three expressed as a
ratio of two integers with a precision in digits equal to or greater than
the SUM of the digits in the numerating AND denominator?
Anyone can just say:
17320508075688772935274463415058723669428052538103806280558069794519330169088
divided by:
10000000000000000000000000000000000000000000000000000000000000000000000000000
but that is only 77 digits of precision for 154 digits expressed.
But if I give you:
81637354237035839875406774706916734691676867556988461166524491402570869800626
divided by
47133348444681477624409145446409554706879415291771528507046516487702731598175
then you can be sure you have 154 digits of precision. Try it.
Remember 355/113 for the value of PI? I have way better fractions. You
won't _need_ them, of course. But I have them.
Many mid to high end multimeters are more accurate than that.
You are only talking about 1ppm or 0.1ppm. A lot of equipment exists with
that accuracy. I have calibration instruments in my lab that will do it.
However, that is several orders of magnitude better than any field
measurements that I make. Even if you did make measurements with that
accuracy on an electrical power system , it would be meaningless from a
practical standpoint. It would be difficult to measure the difference in
winding temperatures, for example, with a voltage variation of 0.0001%.
You are presenting a great mental excercize, but if you need to go that far
down to differentiate between the results of two formulas, then as a
practical matter in most power work, they are the same.
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