Neutral current should be = Vector sum of currents in all three phases. So, you need phasor angless.

Those numbers may make sense on a "High Leg" delta system, maybe not but have to ask. eg:

--------------------
Ohm's law
Not just a good idea;
It's the LAW!

My experience with unexpected neutral currents was with a single phase system when the neutral was unexpectedly high.
That was a power factor issue.
One line to neutral load was at a very low power factor,the other at a much better power factor.
On single phase, it is easy to see that any power factor, or phase angle difference, will increase the current, not decrease it.
But shushilksk's post kicked my mind into gear.
It may not be safe to assume that the entire current difference is phase to neutral current.
I suspect that you have unbalanced line to line loads that are not affecting the neutral current.
And you may have unbalanced line to line power factors which will drive up the line to line unbalance but not affect the neutral current.
(Thanks for the mind jog, shushilksk)

--------------------
Ohm's law
Not just a good idea;
It's the LAW!

The OP's equation only works if the currents are 120 deg apart. If R is 0 deg, Y is -120, and B is 110 deg, the neutral current would be 17.15.
See attached spreadsheet.

• https://files.engineering.com/getfile.aspx?folder=13002f2a-9fd4-4d86-970f-1

"..RY – 400 V YB – 401 V BR – 402 V. R– 135 A Y – 188 A B – 167 A...
But the measured neutral current is only 18 Amps".
I have the following opinion, please advise.
1. Voltage is balance. Current is not. This big current difference can happen on a 3-ph Y system, with 1-ph unbalanced linear or non-linear load.
2. Note: A. For linear loads:
a) 3-ph balance loads, the Neutral current is Zero.
b) 3-ph unbalanced loads, Neutral current is NOT Zero. But the vector I1+I2+I3+I_N =0.
B. For non-linear (harmonic generating) loads:
a) 3-ph balance loads, the Neutral current is NOT Zero. The fundamental (frequency) current is Zero. The Neutral current = sum of harmonic currents.
b) 3-ph unbalanced loads, Neutral current is NOT Zero. The Neutral current = sum of harmonic currents + the fundamental (frequency) unbalance current.
3. The current reading R-135 A, Y-188 A, B–167 A, and N-18A, these are the [fundamental + the harmonics].
Note: Take the case say 3 non-linear balance loads, the fundamental current is Zero. The Neutral reads the harmonic currents, which is possible to be not very heavy. However, if the non-linear loads are unbalanced, the Neutral current is the [unbalanced fundamental frequency current + the Harmonic currents ].
Che Kuan Yau (Singapore)

Phase angles imbalance. Completely forgot it.

Thanks, sushil and jghrist. Will check the current waveforms and come back.

Muthu
www.edison.co.in

How about single phase load, A-B, single phase load B-C, single phase load C-A.
The neutral does not need to be present to connect single phase loads phase to phase.
Unbalanced phase to phase loads will change the phase angles, but will not cause a neutral current.
The neutral only carries the unbalanced current from line to neutral loads.
Please check and report on single phase,line to line loads.
Some three phase equipment may have internal devices such as heaters that cause unbalanced line to line loading WITHOUT CAUSING ANY NEUTRAL CURRENT.
With single phase, line to line loads disconnected, your neutral current should be as expected.
Unbalanced line to line loading must be eliminated and the neutral current measured and calculated on the remaining line to neutral unbalance.

--------------------
Ohm's law
Not just a good idea;
It's the LAW!

Or, my favorite (?). Gotten calls from the field that transformer relay and the "multi-function meter" were showing radically different transformer neutral currents. Short story is that the MFM was displaying RMS current, a big number, while the relay was displaying fundamental current (a much smaller number). Apples and oranges...

When one this sentence into the German to translate wanted, would one the fact exploit, that the word order and the punctuation already with the German conventions agree.

-- Douglas Hofstadter, Jan 1982

Quote (Short story is that the MFM was displaying RMS current, a big number, while the relay was displaying fundamental current (a much smaller number). Apples and oranges...)

In this case THD is 2.7% and difference in neutral current is >50%. There should be some other issue.

3 phase input RMS current waveform.


3 phase input THD current waveform


Do you see much of a phase angle difference here?

There are no 400 V (RY, YB or BR) single phase loads.

Only 3 phase air conditioners, UPS for computer systems, LED lights, fans.

Muthu
www.edison.co.in

UPS
3 ph, 10 KVA - 2 nos.
3 ph, 5 KVA - 2 nos.
1 ph, 5 KVA - 1 no

Muthu
www.edison.co.in

I have the following opinion for your consideration. Please advise.
1. Base on the I_rms readings:
I_Rrms = 136.3A, I_Yrms = 188.2A, I_Brms=168.9A
Note: Irms = I fundamental (with 0, -120, -240^o angles)+ harmonics (without angle).
2. Base on the THD% R = 3.2%, Y = 2.5%, B =2.6%
3. Base on above 1. and 2., the fundamental f0 current I_R0= 136.24A /angle 0^o, I_Y0= 187.25A /angle -120 ^o, I_B0= 168.84A / angle -240 ^o.
3.1 Note: Sum of 3 fundamental 120 deg apart currents with 1-phase loads on RN, YN, BN only = unbalance current = about 4.2A, . Excluding the Harmonic.
4. The actual current on the Neutral = unbalance current (4.2A) + the Harmonics.
4.1 Note: As the Harmonics are NOT very high, the Neutral current reads 18A is possible.
Che Kuan Yau (Singapore)

Quote:

There are no 400 V (RY, YB or BR) single phase loads.

Only 3 phase air conditioners, UPS for computer systems, LED lights, fans.

There are line to neutral 230V single phase loads though, right? Otherwise, there should be no neutral current.

Quote (Edison123)

Do you see much of a phase angle difference here?

Note that B peaks considerably after the crossing of R&Y. This would occur if the angles of R&Y were 0 and -120, and the angle of B was 100 deg.

Try moving the cursor on the meter to determine the zero crossing times of the three currents.

Looking at the loading type, we should be asking what is the frequency of the neutral current? There maybe more harmonic than you expect. In the worst case the neutral can be up to three times any phase current.
LED lighting, and UPS systems can be very dirty switching power supplies that generate loads of harmonics.
As David said above, the current read on different devices can be a big clue.

Caveat. Today's readings at low loads of 40 Amps (not the previous ones).

Also, there is a voltage regulation problem from utility side (430 V on low load to 370 V on high load).

Current phasor (low load)



Voltage phasor (low load



Will post high load phasors later.

Muthu
www.edison.co.in

Current phasor with full load




Voltage phasor with full load (75 to 80 V drop in voltage with full load. Utility has been informed about poor regulation)




3 phase current THD on full load (not much)




Measured neutral current 16 Amps with Fluke clamp-on.

Muthu
www.edison.co.in

What is the neutral current at low load?

--------------------
Ohm's law
Not just a good idea;
It's the LAW!

What do the angles phi_12, phi_23, phi_31 represent?

Neutral current at low load was 2 Amps

jghrist - The angles between the phasors A1, A2 and A3? How would you plug in these angles in your Excel sheet?

Muthu
www.edison.co.in

For Full Load

Note that angles are only given to zero decimals. If the 119 angles were 118.5, then N would be 18.0 A.

edison123.
I have great respect for you.
It worries me that we cannot find a solution.
As you know, uneven voltages may cause disproportionate current differences.
Motors are noted for this.
The amount of difference depends on the motor impedance, the voltage difference compared to the back EMF and to the source impedance.
Your readings are typical of either single phase line to line loads or unequal currents caused by enequal supply voltages.
A suggestion;
If possible measure the neutral current of each line to neutral load on each phase and correlate that with your neutral current.
Turn off individual motor loads and check for any change in neutral current and check the change in line currents.
Beware that some three phase equipment may have internal line to line single phase loads such as heaters and or fans.
Respectfully yours
Bill

--------------------
Ohm's law
Not just a good idea;
It's the LAW!

Thanks jghrist . Your calculation tracks what I measured at neutral. If I may ask, how did you arrive at 0, 119, 119 angles ?

waross - Input voltages are pretty much equal. It's regulation that is the issue. I had the utility guy measure the voltages at their transformer end, which is about 600 ft away, from low load to full load. Transformer output stayed constant at 430 V. The issue is the too small overhead line from the transformer to our school. They will address it by increasing the line cs or stringing a second line. LED's and fans are single phase loads and are spread evenly in three phases as you can see at full load. At inevitable partial loads (service factor), there are bound to be unbalanced currents. Also, as you said, all 3 phase ac's have their outdoor unit fans connected to the same phase, which would create some unbalance. I am addressing the ac fans issue by shifting single phase loads from that phase to the other two phases. At the end of the day, we will have to live with some current unbalance, which is not a big deal.

Muthu
www.edison.co.in

Quote:

Also, as you said, all 3 phase ac's have their outdoor unit fans connected to the same phase, which would create some unbalance. I am addressing the ac fans issue by shifting single phase loads from that phase to the other two phases.

My point; Phase to phase unbalance does not create neutral current. Hence the incorrect results from the incomplete formula.

--------------------
Ohm's law
Not just a good idea;
It's the LAW!

I arbitrarily chose 0° for the R (A1) phase angle. The difference between R & Y phase angles is 119° per the meter (Phi 12), so Y phase angle is 0 - 119 = -119°. The difference between B & R phase angles is 119° (Phi 31), so B phase angle is 0 + 119 = 119°.

Thanks jghrist. Got it. Would it work if another phase is taken as 0 deg? (Wish I could give more LPS).

Muthu
www.edison.co.in

As long as you are looking at the difference of currents it should be OK, but, using an arbitrary base for the angle reference, if the arbitrary angle assignment crosses the base line so that the PF goes from negative to positive on one phase, will the calculations still work?
I don't know.
I am asking not challenging.

--------------------
Ohm's law
Not just a good idea;
It's the LAW!

If you use another phase for the 0°, you will get a different answer, but only because the angles are rounded to zero decimals. Note that the sum of all of the phase angle differences has to equal exactly 360°, but 119 + 119 + 123 = 361.