The prediction equation fails because the single-phase, line-to-line load connected B-C is not even connected to the neutral. It does not matter what phase angle the current is for this load. The only load contributing to the neutral current is connected A to N, so there is 100A on each A and N.
When is a neutral wire considered a conductor
- Thread starter james_mcquade
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Pierre C Belarge
Senior Member
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- Westchester County, New York
Nice to see you posting again... after essentially a four month hiatus
Hopefully things have improved for you on the homefront.
But not when calculating neutral current and the line amperage is in part three phase loads and/or line-to-line single phase loads. You have to subtract the current of these types of loads from the individual line amperages before you have the numbers to plug into the formula... and even then the formula is only approximate for it does not take into consideration the phase angle of the currents.
Pierre C Belarge
Senior Member
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- Westchester County, New York
Nice to see you posting again... after essentially a four month hiatus
Hopefully things have improved for you on the homefront.
Thanks, I appreciate the comment.
While we're partially on the subject of harmonics, is there any easy way to predict the harmonics of various types of loads?
winnie
Senior Member
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Agreed, that is how I set up the example.
The reason that the phase angles of the current are relevant is that if they are not 120 degrees apart, then even with equal magnitude current flow on all 3 lines, there will still be current on the neutral. The example that I posted was one selected to demonstrate this fact. By inspection the neutral current is not zero, and by inspection the current phase angles are not 120 degrees.
If you want a demonstration that uses only wye connected loads, consider the following: a resistor from phase A to neutral, an inductor from phase B to neutral, and a capacitor from phase C to neutral, each sized to cause 100A to flow at 120V. What is the neutral current? (As I was working it out, I realized that I'd have to spend too much time confirming standards for phase angle and such...the answer is either 73A or 273A)
-Jon
- Location
- Connecticut
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- Engineer
I agree with Smart$ that the phase angles aren't relevant because only one phase has current flowing to neutral. Obviously the current flowing on neutral will not be zero.
However, I also think it is also possible to have balanced current on all 3 phases with 120 degree phase angles between them, and still have neutral current (not considering harmonics.) For instance, consider connecting a 50A unity power factor load from A-C, a 100A unity power factor load from B-C, a 50A leading by 30 degree load from A-N, and a 50A lagging by 90 degree load from C-N. If my calculation is correct, you'll have 100 Amps on each phase, all at 120 degrees apart, and you'll have 100 Amps flowing in the neutral.
The phases have equal currents at 120 degrees apart, yet the neutral current is NOT zero.
winnie
Senior Member
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- Springfield, MA, USA
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- Electric motor research
Let me see if I can follow how you are generating this example.
You have a 100A unity power factor load connected B-C.
Then you add in a 50A unity power factor load from A to C. This puts 50A on terminal A, and something less than 150A on terminal C.
Then you add a 50A load from A to N, and you adjust its phase angle so that it is in phase with the A to C load, giving a net 100A at terminal A.
Finally you add a 50A load from C to N, and you adjust its phase angle so that it just balances out the A to C load as connected to terminal C. The net result is 100A at phase C.
If my understanding above is correct, then I believe that you will find that your phase angles are _not_ 120 degrees. The 100A flowing out of terminal A is in phase with the voltage from A to C, and the 100A flowing out of terminal C is in phase with the voltage from C to B giving a nice 120 degree phase difference. Unfortunately, the 100A flowing out of terminal B is in phase with the voltage from B to C, not in phase with the current from B to A as required for a balanced system.
A unity power factor load connected between terminals B and C draws current in phase with that voltage. If you look at the current flowing out of terminal C, it is in phase with Vcb, and if you look at the current flowing out of terminal B, it is in phase with Vbc.
If you know Ia, Ib, and Ic, both magnitude _and_ phase angle, then the current In is uniquely specified. For In to be zero, Ia, Ib, and Ic must have the same magnitude, and a 120 degree phase difference. (Or Ia, Ib and Ic must all equal zero in which case the phase angle is moot.)
-Jon
I'm well aware of the role phase angles play in neutral current... but your example, with one L-N and one L-L load does not depict what you are saying... whereas the one that you follow with does...
The answer for the given example is 73.21A@0?. If you were to change the inductor and capacitor phases, then 273.21A@-180?.
It took me a few minutes to follow what you are saying about Line-Neutral currents making this equation approx. But now I get it.
Any L-N loads will be 30 deg out of phase with any L-L loads (assuming resistive loads) because the L-N voltage is 30 deg out of phase with the L-L voltage. So when you have combinations of LL and LN loads on one phase, you can get up to a 30 deg phase shift on that current.
So we have 3 sources of error in this equation:
1. Mixes of LL and LN loads.
2. Non-unity power factor loads.
3. Harmonics.
I've always wondered why this equation seems to give currents that are lower than measured, even when harmonics are considered. Now I know.
LarryFine
Master Electrician Electric Contractor Richmond VA
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- Henrico County, VA
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Yes, welcome back, Kotter.Nice to see you posting again... after essentially a four month hiatus
Hopefully things have improved for you on the homefront.
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