Watts is watts?

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Ohms outlaw

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Latrobe pa.
It has been said every where I read that 3 phase does not save any money on the electric bill over single phase with the exception of motors.

Here is my situation. My plant has 3 rows of HID low bay lights on one 230v 2 pole 30 a breaker.

Each row draws 8 amps at 230v.

watts law for single phase: v x a x pf = watt's so 230 x 24 x .9 = 4968 watts or 4.9 kw

Now if I split the load into 3 balanced circuits on 3 phase: Watt's law for 3 phase: volts pr phase x amps pr phase x pf x 1.732 = watts.

so... 230 x 8 x .9 x 1.732 = 2868.1 watts or 2.8 kw.

So if we are billed in kwh it looks to me that 3 phase saves money. So where is the flaw in my logic? What am I missing here? :dunce:

Thanks in advance for any help!
 
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GoldDigger

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The current used in the three phase power formula you list is the line current, not the line-to-line current. If you have the lights wired phase to neutral to a 230 volt wye, you simply multiply 3 x 230 x 8 x .9.
If you wire the lights line-to-line in a 230 volt delta, the line current will be 8 x 1.732.
Plug that into the three phase formula and you get .9 x 230 x 8 x 1.732 x 1.732. But 1.732 x 1.732 = 3.
QED.
It is easy to know it must be wrong, but it is harder to figure out just where the mistake is.
:)

Tapatalk!
 
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kwired

kwired

Electron manager
Location
NE Nebraska
Ohms outlaw said:
It has been said every where I read that 3 phase does not save any money on the electric bill over single phase with the exception of motors.

Here is my situation. My plant has 3 rows of HID low bay lights on one 230v 2 pole 30 a breaker.

Each row draws 8 amps at 230v.

watts law for single phase: v x a x pf = watt's so 230 x 24 x .9 = 4968 watts or 4.9 kw

Now if I split the load into 3 balanced circuits on 3 phase: Watt's law for 3 phase: volts pr phase x amps pr phase x pf x 1.732 = watts.

so... 230 x 8 x .9 x 1.732 = 2868.1 watts or 2.8 kw.

So if we are billed in kwh it looks to me that 3 phase saves money. So where is the flaw in my logic? What am I missing here? :dunce:

Thanks in advance for any help!
Click to expand...
Your formulas above:
v x a x pf = watt's

230 x 24 x .9 = 4968

230 x 8 x .9 x 1.732 = 2868.1

Why do you have a different "a" value in each case if the voltage is the same and presumably number of lights is the same?

Plus watts is watts like your thread title says. Your 1.732 factor is used when determining the proportions of current flowing in each phase.

I think I see what you tried to do, you probably have 24 amps when connected single phase, and in the second example you tried to relate that to 8 amps per phase if balanced across all three phases.

But you still have (230x24) 5520 VA. To find the current in each phase when connected (in balance) to a three phase system you would have 5520/230/1.732 = 13.85 amps per phase. Compared to 24 amps with same load connected to a single phase source.

Total VA and total watts is still the same in either situation. There will be less line losses in the three phase system, depending on conductor sizes and lengths, but likely low enough it is of no real significance either.
 
kwired

kwired

Electron manager
Location
NE Nebraska
hardworkingstiff said:
I thought the math I posted showed that. :?
Click to expand...
It probably did, OP's question is about why watts appears to be different for single phase as it is for three phase. His calculation results are not what he thinks they are. Total watts is same, watts on each conductor of the system is what changes, maybe that is the simple answer being sought.
 
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Ohms outlaw

Member
Location
Latrobe pa.
Here Is A Link To Where I Got My Formula. Maybe It Is Wrong Or I Did Not Use It Correctly.

http://nstar.apogee.net/foe/frwt.asp

now that I think about it I think this formula gives you the wattage total At any instant in time it is lower because some of the phases are near zero on the sine wave. but the total watts per phase per hour are the same as it would be with single phase. which is how the meter would record it I suppose.
 
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GoldDigger

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Ohms outlaw said:
Here Is A Link To Where I Got My Formula. Maybe It Is Wrong Or I Did Not Use It Correctly.

http://nstar.apogee.net/foe/frwt.asp

now that I think about it I think this formula gives you the wattage total At any instant in time it is lower because some of the phases are near zero on the sine wave. but the total watts per phase per hour are the same as it would be with single phase. which is how the meter would record it I suppose.
Click to expand...

I can see why you are confused by that site, as it is fundamentally flawed.
To try to clarify this, I will introduce two separate sets of symbols:
E = phase to phase voltage, while e = phase to neutral voltage ( assuming for the moment that there is a neutral). Similarly, I = phase-to-phase current while i = individual phase line current.
Now in the wye-delta you are envisioning V is 230 and v is 133. I is 8 and i is 13.9.
So P is equal to 230 x 8 x 3 ( there are three lines of lamps.)

But it is also equal to 230 x 13.9 x 1.732, which in turn is also equal to 133 x 14.9 x 3.

As long as you do not mix the upper case and lower case terms in the calculation the mysterious 1.732 does not appear directly.
It is only if you try to multiply V x i that you have to multiply by that factor. Although what you are really doing is multiplying by 3 and dividing by 1.732 to make up for using the "wrong" combination of voltage and current.
:).
And as for kwired's idea of watts per phase, that should really be calculated as v x i, giving 1840 watts per phase and the total power is just 3 times that.
To apply the same reasoning to single phase 120/240,
for a 2 amp 240 volt load we have the total power as V x I = 240 x 2 x 1 = 480 and also v x i x 2 = 120 x 2 x 2 = 480 ( since we are adding the power on the two lines.)
Watts just plain add. There are no vectors involved in that calculation!
As for the site you referenced, its only big problem is that it is mixing the line-to-line voltage with the line current ( since those are what is being directly measured) but is calling that current the phase current.
So to get the numbers right, instead of explaining it correctly it pulls the 1.732 out of a hat as a mysterious three phase correction factor.



Tapatalk!
 
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Ohms outlaw

Member
Location
Latrobe pa.
thanks everyone for the help. corporate wants us to save money on the electric bill looks like I'm going to recommend t8 fluorescent fixtures WIth
electronic ballasts.
 
Jraef

Jraef

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Ohms outlaw said:
It has been said every where I read that 3 phase does not save any money on the electric bill over single phase with the exception of motors. ...
Click to expand...

It has been said every where I read that 3 phase does not save any money on the electric bill over single phase.

Fixed it for ya...

The motor issue is a fallacy as well. Watts are watts.
 
Fulthrotl

Fulthrotl

~Autocorrect is My Worst Enema.~
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HB, CA (19 Hrs. 22 Min. from Winged Horses)
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Jraef said:
The motor issue is a fallacy as well. Watts are watts.
Click to expand...

+1 on that.

obviously, line loss plays a factor with the working voltage,
and there are inherent advantages of a three phase motor
over a single phase motor...... but.... 1 HP = 746 watts, and
it doesn't matter what color the horse is, or how high it lifts
it's feet when doing the work.
 
kwired

kwired

Electron manager
Location
NE Nebraska
Fulthrotl said:
+1 on that.

obviously, line loss plays a factor with the working voltage,
and there are inherent advantages of a three phase motor
over a single phase motor...... but.... 1 HP = 746 watts, and
it doesn't matter what color the horse is, or how high it lifts
it's feet when doing the work.
Click to expand...
Color of the horse would be like the difference between a Baldor motor and a US Motors motor. How high the horse lifts its feet would be like the power factor of the motor:)
 
Jraef

Jraef

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kwired said:
Color of the horse would be like the difference between a Baldor motor and a US Motors motor. How high the horse lifts its feet would be like the power factor of the motor:)
Click to expand...
And the horse doesn't lift his feet as much if he has had too much beer, unless of course the beer was mostly foam...
 
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