Line Voltage vs phase voltage

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kunchesuryatej

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I have a 3 phase star connected motor (with three terminals a, b and c) . I wanted to calculate the power consumed by the motor when it running so I connected a data acquisition system to measure Vab (voltage across a and b terminals), Vbc, Vca. I also measured Ia (current through terminal a), Ib, Ic. Is there is means to compute the power given that I do not know the Van (voltage between terminal a and neutral). is it possible to convert the Vab, Vbc, Vca to Van, Vbn and Vcn.
 
kunchesuryatej said:
I have a 3 phase star connected motor (with three terminals a, b and c) . I wanted to calculate the power consumed by the motor when it running so I connected a data acquisition system to measure Vab (voltage across a and b terminals), Vbc, Vca. I also measured Ia (current through terminal a), Ib, Ic. Is there is means to compute the power given that I do not know the Van (voltage between terminal a and neutral). is it possible to convert the Vab, Vbc, Vca to Van, Vbn and Vcn.
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The motor is not using power through the neutral, so what's the point?
 
Then how can i calculate power consumed by the motor? If I knew Van the i can find the phase difference between Van and Ia then power consumed in line a is equal to Van*Ia*cos(phase difference).
 
Jraef said:
The motor is not using power through the neutral, so what's the point?
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Then how can i calculate power consumed by the motor? If I knew Van the i can find the phase difference between Van and Ia then power consumed in line a is equal to Van*Ia*cos(phase difference).
 
130315-1706 EDT

kunchesuryatej:

See "Basic Electrical Measurements". Stout, 1950, 447-449. Stout references that there is a theorem that N-1 wattmeters are required to measure the power in an N wire system.

Yours is a three wire delta. One wattmeter measures the current in leg X, and the voltage from X to Z. The second wattmeter measures the current in leg Y, and the voltage from Y to Z. The total power is the algebraic sum of the two power readings. Negative power readings are possible. I used X, Y, and Z so as to not imply any specific association with A, B, and C.

I did not find that Stout provided an explicit reference to find the source of the N-1 proof.

Fundamentally what you are doing is measuring the real power to phase X-Z, and separately Y-Z. So if you do not have wattmeters and want to work from current and voltage, then you need to somehow determine the associated phase angles.

.
 
gar said:
See "Basic Electrical Measurements". Stout, 1950, 447-449. Stout references that there is a theorem that N-1 wattmeters are required to measure the power in an N wire system.
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As long as the voltages are all referenced to one of the N wires.
 
kunchesuryatej said:
Then how can i calculate power consumed by the motor? If I knew Van the i can find the phase difference between Van and Ia then power consumed in line a is equal to Van*Ia*cos(phase difference).
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Just divide the phase voltages by sqrt(3) and then make the watt calculation. That will probably suffice for what you are doing.
 
mivey said:
As long as the voltages are all referenced to one of the N wires.
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And just to be complete about it, the assumption is made that the meters used actually do correctly compute the energy based on the current value and the voltage difference to the common conductor.

From our old friend Wikipedia (trust, but verify):

Electric energy meters that meet the requirement of N-1 elements for an N wire service are often said to be Blondel Compliant. This label identifies the meter as one that will measure correctly under all conditions when correctly installed. However, a meter doesn't have to be Blondel compliant in order to provide suitably accurate measurements and industry practice often includes the use of such non compliant meters.
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Among other things, a Blondel Compliant meter has to be able to run backwards!
 
mivey said:
I did not know that.
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It may not come up much with real life loads, but because the voltages are all referenced to one common wire which is not necessarily a neutral and you cannot assume that the loads are balanced, it is possible to come up with a current in one of the phase wires which is more than 90 degrees out of phase with the voltage from that wire to the common, even without back feeding. If the meter on that line cannot run backwards, the sum of the power readings on the N-1 meters will not be the true power.

PS: It is easier to visualize this if the number of phases is greater than three, but if you look at a wye, and choose the common voltage point to be one of the phases rather than the neutral, you will see that the current in the neutral can be anywhere on the map compared to the common-phase to neutral voltage. So sometimes the neutral power will be negative.
 
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GoldDigger said:
It may not come up much with real life loads, but because the voltages are all referenced to one common wire which is not necessarily a neutral and you cannot assume that the loads are balanced, it is possible to come up with a current in one of the phase wires which is more than 90 degrees out of phase with the voltage from that wire to the common, even without back feeding. If the meter on that line cannot run backwards, the sum of the power readings on the N-1 meters will not be the true power.

PS: It is easier to visualize this if the number of phases is greater than three.
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I'll have to think about that one.
 
GoldDigger said:
Take your time, and look at my final edit to that post.
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I'm thinking meters have a limited range of shift in which they are accurate. It sounds like you are talking about the stators in a multi-stator meter not the common moving element.

You could have a single two-wire meter on each phase but no one does that.

Still, I'll have to consider this later as I'm thunk out for the day.
 
130315-2041 EDT

GoldDigger:

I am not being critical, but I found it funny to describe a wattmeter as running backwards. I would probably use deflect, or indicate backwards (negative).

.
 
mivey said:
Still, I'll have to consider this later as I'm thunk out for the day.
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Enjoy the weekend and St. Padraigh's day.
If you come back to it, remember that a Blondel Compliant meter, by definition, measures from exactly one current and one voltage, involving exactly two of the N wires. In some cases one meter that connects to more than one phase can serve as more than one of the N-1 meters. But that is not what I am referring to.
 
GoldDigger said:
Enjoy the weekend and St. Padraigh's day.
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You too.

GoldDigger said:
If you come back to it, remember that a Blondel Compliant meter, by definition, measures from exactly one current and one voltage, involving exactly two of the N wires.
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Again, I'm thinking that is for each meter element (stator).

I'll have to go find my copy of Blondel's paper but here is what I grabbed from the EEI handbook:

Blondel?s Theorem?In a system of N conductors, N-l meter elements, properly connected, will measure the power or energy taken. The connection must be such that all voltage coils have a common tie to the conductor in which there is no current coil.
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mivey said:
You too.

Again, I'm thinking that is for each meter element (stator).
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Absolutely right, and I will happily let it go at that.
A single meter composed of N-1 stators does not have to be able to run backwards. But if you go back to Blondel's original theorem, which was stated in terms of discrete meters, each of those meters must be capable of running backwards.
And if you try to construct a metering system for some oddball situation using single stator meters or more than one Blondel Compliant multi-stator meter, then those physical meters must each be capable of running backwards.
With exactly one Blondel Compliant meter in the system, and no net energy backfeeding allowed, then it will always run forward (or stand still :)).
 
kunchesuryatej said:
I have a 3 phase star connected motor (with three terminals a, b and c) . I wanted to calculate the power consumed by the motor when it running so I connected a data acquisition system to measure Vab (voltage across a and b terminals), Vbc, Vca. I also measured Ia (current through terminal a), Ib, Ic. Is there is means to compute the power given that I do not know the Van (voltage between terminal a and neutral). is it possible to convert the Vab, Vbc, Vca to Van, Vbn and Vcn.
Click to expand...
You need to include power factor if you want to calculated the power consumed by the motor.
A typical 3-phase cage induction motor will take about 30% of rated current at no load. But obviously not 30% of rated power.
 
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