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Motor current imbalance.

Motor current imbalance.

Motor current imbalance.

(OP)
10hp 230V 3ph motor.

The three legs are:
241.8V
242.5V
243.0V

The currents are:
31.4A
31.4A
34.5A

Rural.
Open Delta.
Sole device on the two transformers.

Rolling the leads does not change the imbalance.
The imbalance stays with the leads.
Changing the motor does not change the imbalance.

What reasons can you offer for the 10% imbalance?
 

Keith Cress
kcress - http://www.flaminsystems.com

RE: Motor current imbalance.

Unbalance is defined as max deviation from average, divided by average (that is a very close approximation to the ratio of negative to positive sequence under assumption that there is no zero sequence... such as wye currents and phase-to-phase voltages... and under further assumption that all phase vectors are exactly 120 degrees apart).

Your voltage unbalance is 0.26%.
Your current unbalance is 3.2%.
Your ratio of current unbalance / voltage unbalance is 12

What do we expect the ratio to be?
We know the positive sequence equivalent circuit.
The constant-parameter negative sequence equivalent circuit looks similar to the positive sequence except we replace R2/s  with R2/(2-s).

Considering that |X1+X2| >> R2, the locked rotor impedance is approximately |X1+X2|.  Since |X1+X2| >> R2/(2-s) we can also say the negative sequence impedance is approximately |X1+X2| = locked rotor impedance.
The unbalance component of the current doesn't change with load.

At full load, based on the above model, we can expect the ratio of current unbalance to voltage unbalance to be on the order of the ratio locked rotor current to full load current:  5-7.  (At no-load we'd expect it to be higher by the ratio FLA/NLA.... since the negative sequence current won't change with load, but the fraction will).

Your ratio is 12 vs 6 predicted.   Not perfect, but we may not be dealing with imperfect measurements, AND the model is not quite perfect.  For one thing, we assumed constant parameters, but they change with frequency... as we increase frequency from locked rotor (rotor see line frequency) to negative sequence near full speed (rotor sees 2*line frequency), rotor sees a higher frequency.  Deep bar effect causes R2 to go up and X2 to go down.  Since the negative sequence is primarily inductive, the effect of X2 decreasing is the dominant effect and we expect a ratio somewhat higher than the locked rotor ratio of 6.

All in all, if you didn't tell us about a lead swap, a ratio of 12 doesn't seem unreasonable if the cause were simple supply system voltage unbalance.

You conducted a swap and the high current stayed on the same lead... does that mean same motor lead?  If you are positive of that, then forget about supply system unbalance, it would suggest an unbalance in the motor or the lead impedance between motor and connection point.  Is there a long run of cable between the connection point and the motor... there was a thread not too long ago that talked about possible unbalanced induced voltage in the long run of leads going down the hole based on positioning of the leads of a submersible
 

=====================================
(2B)+(2B)'  ?

RE: Motor current imbalance.

Here was the thread I was referring to:
thread237-267952: Earth Currents with Submersible Pumps
Now I see the subject was circulating currents induced in grounded components.  It seems like these effects might also contribute to possible phase voltage or current unbalance, but I'm not sure how much.

=====================================
(2B)+(2B)'  ?

RE: Motor current imbalance.

Can you confirm that unbalance stays with same lead means unbalance stays with same motor lead (rather than supply cable/"lead")?

If yes, can you describe distance between location of swap and the motor... and also describe the conductor configuration.

If no, can you provide locked rotor current or KVA code.
 

=====================================
(2B)+(2B)'  ?

RE: Motor current imbalance.

An open delta connection draws a neutral current. This causes a voltage drop in the neutral conductor. If the magnitude of the voltage drop is significant it may cause a phase shift. This will show up as unequal voltages, hence unequal currents.

Bill
--------------------
"Why not the best?"
Jimmy Carter

RE: Motor current imbalance.

I'd agree with Bill, you won't have 120° between the voltage phases, so despite good magnitude balance, you don't really have "balanced" voltages and therefore won't have balanced currents.

RE: Motor current imbalance.

There is a 120 degree angle assumption inherent in the approximate conversion between voltage unbalance (max deviation from average) and negative/positive sequence ratio.

However even if that assumption is not met, magnitude unbalance is still a rough indicator of voltage unbalance.  If you don't believe it, try to draw an triangle that has the same length for all 3 sides but doesn't have the same angles between all sides.... Obviously it can't be done.  

If you draw a closed triangle whose lengths match the three phase-to-phase voltage magnitudes reported above, and then calculate the angles between them by the law of cosines  (theta = arcos{<c^2-a^2-b^2>/<-2*a_b>}), then you get vertex angles theta as follows:
59.74
60.03
60.23

If you rearrange the equilateral triangle into a star configuration, then the angle between vectors is now given by 180 – theta (where theta was vertex angle of the equilateral triangle discussed above).  i.e. the angle between phase-to-phase voltage vectors would be:
120.26
119.97
119.77

I am still interested in clarification of what leads are referred to in "The imbalance stays with the leads".    The T-leads or the supply "leads" ?  

=====================================
(2B)+(2B)'  ?

RE: Motor current imbalance.

A little more interesting excercize is to use the angles computed aboe to compute the actual ratio of negative sequence to positive sequence (rather than the estimate we did originally using magnitudes).

Label the three phase to phase voltages as VA, VB, VC. (sorry about the notation, these are phase to phase voltages even though they carry only one letter).

Define the angle of V as angle 0.  If we draw a vector diagram starting with the equilateral triangle with VA on the horizontal pointing to the right, and VB, VC pointing CCW around the triangle, then we can rearrange into a star configuration and we see the phase to phase voltages as follows:
"VA" = 241.8    angle 0
"VB" = 242.5    angle 119.7678358
"VC" = 243    angle 239.7411481

Let q = exp(i*120 degrees)
Positive sequence voltage is
V1 = (Va + q^2*Vb + q*Vc)/3 = 242.43 - 0.69i

Negative sequence voltage is
V2 = (Va + q*Vb + q^2*Vc)/3 = -0.2827 + 0.4909i

|V1|/|V2| = 0.00233671
0.23% - just  a hair lower than we computed examining the magnitudes alone (0.26%).

I am always amazed at how closely the short-cut maximum-deviation from average works in computing ratio of negative to positive sequence.  In this case it works very well.  If you include the effects of voltage phase deviation, the computed true ratio negative to positive is a little bit lower than estimation based on using the magnitudes alone.
 

=====================================
(2B)+(2B)'  ?

RE: Motor current imbalance.

Out on a limb here but I have a feeling that due to the open delta source, two of the phases will see more source impedance than the one without the transformer winding in it and may be the cause of more current it one of the legs, especially when other two currents are identical. Does this make sense?

How large and where in the circuit is this open delta transformer?
 

Rafiq Bulsara
http://www.srengineersct.com

RE: Motor current imbalance.

I am assuming these voltage readings were taken under load.  But we know what they say about assumptions.... help me out Keith and let us know if readings were taken under load.

If readings are taken under load, then all of the effects of this unbalanced delta (be it impedance mismatch or ratio mismatch, or upstream neutral voltage drop, or whatever) are reflected in the voltage unbalance measurement.  For that matter, assuming the source of unbalance originates in the supply rather than the motor, the motor doesn't know the difference whether an open delta transformer causes 0.23% unbalance, or an unbalanced single-phase load on 3 phase system cause the 0.23% mismatch, or something else.  All it cares about is the voltage that it sees at its terminals under load.  At least that's the way I think about it.
 

=====================================
(2B)+(2B)'  ?

RE: Motor current imbalance.

Yes, pete, that was to be my follow up question as to where and under what conditions the voltages were taken.

Rafiq Bulsara
http://www.srengineersct.com

RE: Motor current imbalance.

Yes, good questions.

=====================================
(2B)+(2B)'  ?

RE: Motor current imbalance.

I have seen a distribution system that had so much neutral current (due to miles of two phase plus neutral loading) that our soft starts were often tripping out on "Phase angle error". All the motors in the mill ran hot.  

Bill
--------------------
"Why not the best?"
Jimmy Carter

RE: Motor current imbalance.

fwiw, a correction:
"VC" = 243    angle 239.7411481
should have been:
"VC" = 243    angle 240.03

This results in |V1|/|V2| = 0.00287
Still pretty close to the estimate based on magnitudes.
 

=====================================
(2B)+(2B)'  ?

RE: Motor current imbalance.

Attached is a spreadsheet that shows the vector diagram and calculations to compute the negative/positive sequence ratio 0.287% based on three measurements.  At first glance, you wouldn't think the angles can be determined from the magnitudes, but they can... based on the assumption that the three vectors sum to zero (like phase-to-phase voltages or like three-phase currents).
 

=====================================
(2B)+(2B)'  ?

RE: Motor current imbalance.

One correction to the figure:
Theta_a = arccos{(Qa^2-Qb^2-Qc^2)/(-2*Qa*Qb)}
should've been
Theta_a = arccos{(Qa^2-Qb^2-Qc^2)/(-2*Qb*Qc)}

=====================================
(2B)+(2B)'  ?

RE: Motor current imbalance.

(OP)
Thanks everyone for the lessons.  Pete... Whew!

Sorry for the delay I was out quoting a crazy job for the third  time. Then they wanted to "see me"  which hacks 3 hours out of my day for a 15 minute face to face...

The answers you've asked for and further info are:

1) All measurements taken with the motor fully loaded.

2) The voltages are measured while running.

3) The leads have been rolled until the lowest value on the high current leg is achieved.

4) The high current leg is always the same supply lead.

5) The two pole mounted POCO transformers solely running this pump are radically different sizes.

6) The POCO pole is about 10 feet away from the starter.

7) The motor is about 80 feet down some triplex 6AWG from the starter where the rolling took place.

Keith Cress
kcress - http://www.flaminsystems.com

RE: Motor current imbalance.

Thanks. Then I think my relevant answer is given in my first post (excluding last paragraph which discussed the other possibility for lead swap).

The voltage unbalance is not tremendously high (0.26%). But the motor is expected to react with a current unbalance that is higher by a factor of around 6 (negative sequence impedance ~locked rotor impedance is around 1/6).   You actually saw current unbalance a factor of 12 higher than voltage unbalance.  Possible reasons for that factor of 12 instead of 6:
1 - We do know that the negative sequence impedance is in fact expected to be a little bit lower than locked rotor impedance due to deep bar effect which decreases X2 further at negative sequence rotor frequencies (~2*LF) than at locked rotor frequencies (1*LF).  So expect  X- < 1/6...ratio > 6.
2 - Perhaps some small measurement errors.  We are dealing with small differences between large numbers... small errors have big effect.

The ratio of 12 doesn't seem unreasonable to me - a simple expected result of supply imbalance. There might be something else going on to explain the difference, but  I sort of doubt it.  

=====================================
(2B)+(2B)'  ?

RE: Motor current imbalance.

....the reason to doubt that anything else going on is because of the results of the lead-roll check

=====================================
(2B)+(2B)'  ?

RE: Motor current imbalance.

"I think my relevant answer is given in.."  should've been "I think the relevant portion of my answer is given in..".  I wasn't trying to suggest anyone else's answer was not relevant.  There was a lot of good info about open delta configuration... something I know nothing about.

Now I am still wondering about the difference between 6 and 12.  Some additional thoughts:
1:  The number 6 came from my assumption about ratio of LRC/FLA.  But for some motors that ratio could easily be 8, which may explain part of the difference.
2:  We have 0.26% voltage unbalance at ground level... so what is the voltage balance by the time the current flows thru 80' of 6AWG down to the motor.   Does the voltage unbalance tend to get bigger or smaller as the unequal currents travel along the cables (creating unequal voltage drops)?   My gut feel is that the voltage unbalance would tend to grow smaller  (the leg with the highest voltage with respect to some ficticious neutral tends to draw the most current... has a higher voltage drop... and get closer to the other phases), but I'm not positive about that. I'd be interested to hear if anyone else wants to weigh in on that question.

=====================================
(2B)+(2B)'  ?

RE: Motor current imbalance.

My two cents:

Quote:

4) The high current leg is always the same supply lead.
Tells me there is nothing wrong with the motor.

Quote:

5) The two pole mounted POCO transformers solely running this pump are radically different sizes.
are the probable culprits.

I will leave formulas to Pete.

Rafiq Bulsara
http://www.srengineersct.com

RE: Motor current imbalance.

Hi Rafiq.
If you look at the vector diagrams of an open delta connection you will see that the open delta forms a virtual transformer across the open side with the same characteristics as the two equal transformers.
But in the real world, you may have differing voltages due to the transformer regulation and different per unit loading on the transformers. This may cause phase angle errors. Neutral voltage drops will also cause phase angle errors.

Bill
--------------------
"Why not the best?"
Jimmy Carter

RE: Motor current imbalance.

Bill:
Yes, imho there is no "problem" just the field conditions and reality.

If overload is the concern, there are other means to address that.

Rafiq Bulsara
http://www.srengineersct.com

RE: Motor current imbalance.

I do understand that if the client believes he has a problem, there is a problem. In fact I am currently fighting one of those kind of "problems".

Rafiq Bulsara
http://www.srengineersct.com

RE: Motor current imbalance.

If the "issue" is that critical, there is another way to at least eliminate the "source" of the problem. Rent a 3 phase generator and run the motor/pump on that and see what happens.

 

Rafiq Bulsara
http://www.srengineersct.com

RE: Motor current imbalance.

So what do you guys think – if you could measure the voltage unbalance down the hole at the location where the cables enter the motor, would it be lower/higher/same as measured up above?

=====================================
(2B)+(2B)'  ?

RE: Motor current imbalance.

Keith – one more reference lists expected ratio of current unbalance to voltage unbalance as 6-10 times ... getting closer to the 12:

http://books.google.com/books?id=4-Kkj53fWTIC&pg=PA645&dq=unbalance+will+be+typically+6+to+10+times+the+voltage&hl=en&ei=-0yjTI-3F4KC8gaA4PXnCQ&sa=X&oi=book_result&ct=result&amp;resnum=1&ved=0CCUQ6AEwAA#v=onepage&q=unbalance%20will%20be%20typically%206%20to%2010%20times%20the%20voltage&amp;f=false

Quote (Handbook of Electric Motors by Kliman / Toliyat, page 645):


The currents at normal operating speed with unbalanced voltages will be greatly unbalanced in the order of approximately 6 to 10 times the voltage unbalance

=====================================
(2B)+(2B)'  ?

RE: Motor current imbalance.

(OP)
Rafiq;  I think you're right.  We just have to live with it. The customer isn't really in the loop.  Just the pump guy worried about the motor croaking "obviously early" yet after the motor warranty is up.  If a sub pump dies in less than 5 years you generally have very annoyed customers.

It's kind of a lame result promulgated by the pump makers.  The only real alternative is to stick on the next larger motor and run it lightly loaded.  But as a well guy you find yourself quoting against the next guy who doesn't use the larger motor that costs another half k dollars.

I'm glad I don't have to work in that arena.

BTW good luck with your "problem".


e-pete; I would expect down that little distance of grossly over-sized wire you'd see the same exact voltage.  That would be my guess.

Keith Cress
kcress - http://www.flaminsystems.com

RE: Motor current imbalance.

Thank you, Keith.

My "problem" is of a different kind, convincing another engineer that perfect coordination does not exist in real world, especially when using MCCBs! banghead       

Rafiq Bulsara
http://www.srengineersct.com

RE: Motor current imbalance.

6 AWG – approx 0.5 ohms/(1000 ft)
80 feet -> 0.04 ohms
The current difference among phases is 3A.
The associated difference in voltage drop is 3A*0.04 Ohms = 0.12 volts.

That sounds small, but the range of measured phase-to-phase voltages is only 0.6  (242.5 - 243.1).  The  0.12 volts difference in voltage drop is 20% of the 0.6 volt variation between highest and lowest phases.  At first glance I thought it might explain portion of the difference between 6 (or 8 or 10) and 12.

But voltage divider analysis shows that we do in fact expect the voltage unbalance to be lower at the motor terminals than at the supply.  We can show this by looking at voltage divider which applies to both positive and negative sequence circuits:
Vmotorterminal/Vsource  =  Zmotor / (Zmotor + Zcable).
Zcable is the same for positive and negative sequence assuming symmetrical layout of the three conductors.    Zmotor is much lower for negative sequence than for positive sequence (our factor of 6 lower).  So the ratio Zmotor / (Zmotor + Zcable) = Vmotorterminal/Vsource is lower for negative sequence than positive sequence.  Therefore the ratio of negative sequence to positive sequence voltage (i.e. the unbalance) is lower at the motor terminals than at the supply. So, it matches the intuition, the voltage unbalance would be lower at the motor terminals than at the supply... but it doesn't help to explain the difference between 6 and 12.

It was just a curiosity anyway - nothing to change the conclusion in this case.
 

=====================================
(2B)+(2B)'  ?

RE: Motor current imbalance.

Correction:
"but the range of measured phase-to-phase voltages is only 0.6  
should have been
"but the range of measured phase-to-phase voltages is only 1.2

=====================================
(2B)+(2B)'  ?

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